ENVIRONMENTAL POLICY ACROSS TERRESTRIAL SPACE
by
JOHN MATTHEW MOREHOUSE
A DISSERTATION
Presented to the Department of Economics
and the Division of Graduate Studies of the University of Oregon
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
June 2022
DISSERTATION APPROVAL PAGE 
Student: John Morehouse 
Title: Environmental Policy Across Terrestrial Space
This dissertation has been accepted and approved in partial fulfillment of the 
requirements for the Doctor of Philosophy degree in the Department of Economics by: 
Trudy Cameron Co-Chair
Mark Colas Co-Chair
Keaton Miller Core Member 
Edward Rubin Core Member 
Grant Jacobsen Institutional Representative 
and 
Krista Chronister Vice Provost for Graduate Studies
Original approval signatures are on file with the University of Oregon Division Graduate 
Studies.
Degree awarded June 2022
ii 
© 2022 John Matthew Morehouse
All rights reserved.
iii
DISSERTATION ABSTRACT
John Matthew Morehouse
Doctor of Philosophy
Department of Economics
June 2022
Title: Environmental Policy Across Terrestrial Space
This dissertation examines spatial heterogeneity that results from various
environmental policies. In Chapter 1, I provide a comprehensive overview of each
dissertation chapter.
Chapter 2 (with Ed Rubin) demonstrates that most coal-fueled power plants
are located on or near jurisdictional (county or state) borders. We find that coal-
fired power plants are disproportionately sited on downwind borders (within county
or state). Natural gas plants—much lower polluters—do not exhibit this behavior.
Motivated by the inferred strategic siting, we use an atmospheric dispersion
model developed by NOAA to estimate various aspects of the “pollution transport
problem.” We find that nearly 90% of coal-based particulate matter leaves its state
of origin within 48 hours of release.
Chapter 3 (with Mark Colas) examines the e↵ects of stringent land-use
regulations on national carbon emissions. We develop and estimate a general
equilibrium model of residential sorting and energy consumption. We find that
relaxing land-use restrictions in California leads to a 0.6% drop in national
carbon emissions. The mechanism behind this drop is straightforward. California
cities have a temperate climate, carbon-e cient power plants, and high land-
iv
use regulations. These land-use regulations inflate housing prices, thus keeping
households out of California cities. When households live outside of California, they
emit more carbon on average, and therefore national carbon emissions are higher
due to California’s land-use regulations.
In Chapter 4, I simulate the labor market e↵ects of a carbon tax across the
continental United States. To recover the welfare impacts of a carbon tax, I build
and estimate a spatial equilibrium model that features heterogeneous households.
I incorporate a rich level of heterogeneity into the model that allows me to answer:
(1) who is most a↵ected by a carbon tax, (2) how much the burden of a carbon
tax is borne on di↵erent households, and (3) where the households are that bear
the greatest burden from the tax. I find that workers without a college degree
in manufacturing bear a disproportionate share of the tax incidence. Chapter 5
concludes this dissertation.
This dissertation includes previously both previously published and
unpublished and co-authored material.
v
CURRICULUM VITAE
NAME OF AUTHOR: John Matthew Morehouse
GRADUATE AND UNDERGRADUATE SCHOOLS ATTENDED:
University of Oregon, Eugene, OR, USA
DEGREES AWARDED:
Doctor of Philosophy, Economics, 2022, University of Oregon
Master of Science, Economics, 2018, University of Oregon
Bachelor of Science, Economics, 2016, University of Oregon
AREAS OF SPECIAL INTEREST:
Environmental Economics
Labor Economics
Urban Economics
PROFESSIONAL EXPERIENCE:
Freelance Economist, Vivid Economics, 2020
Intern, Vivid Economics, 2020
Research Assistant to Dr. Edward Rubin, University of Oregon, 2020
Finance Associate, Summit Bank, 2017
GRANTS, AWARDS AND HONORS:
Thomas J. Sargent Dissertation Fellow, Federal Reserve Bank of San
Francisco, 2021
Kleinsorge Summer Research Award, University of Oregon, 2021
Best graduate student research paper award (Economics), University of
Oregon, 2020
General University Scholarship, University of Oregon, 2019
Kleinsorge Summer Research Award, University of Oregon, 2019
vi
Edward G. Daniel Scholarship, University of Oregon, 2018
Graduate Teaching Fellowship, University of Oregon, 2017-2022
PUBLICATIONS:
Colas, M., & Morehouse, J. (2022). The Environmental Cost of Land Use
Restrictions Quantitative Economics, 13(1): 179-223.
vii
ACKNOWLEDGEMENTS
I would like to express my gratitude to my committee chairs, Trudy
Cameron and Mark Colas, who provided endless support and guidance throughout
my graduate school career. I would also like to thank Keaton Miller, Edward
Rubin, and Grant Jacobsen for providing valuable feedback on various parts of
this dissertation. I would also like to thank my undergraduate mentors, Andrew
Schopieray and Ralph Mastromonaco, for their initial and continued belief in me.
Lastly, I am grateful for the boundless support from my family and friends. I am
particularly grateful to Annie and Olive.
viii
To my family
ix
TABLE OF CONTENTS
Chapter Page
I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . 1
II. DOWNWIND AND OUT: THE STRATEGIC
DISPERSION OF POWER PLANTS AND THEIR
POLLUTION . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2. Institutions: Siting of Plants . . . . . . . . . . . . . . . . . . 11
2.3. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4. Empirics . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.1. Power Plants’ Distances to Borders and Water . . . . . . . 15
2.4.2. Strategic Plant Siting: A Statistical Test . . . . . . . . . . 18
2.4.3. Strategic Plant Siting: Results . . . . . . . . . . . . . . 22
2.4.4. Pollution Mobility: Methods . . . . . . . . . . . . . . . 24
2.4.5. Pollution Mobility: Results . . . . . . . . . . . . . . . . 25
2.4.5.1. Transporting Pollution Away from Sources . . . . . 26
2.4.5.2. Decomposing the Sources of Local Pollution . . . . 27
2.5. Discussion and Conclusion . . . . . . . . . . . . . . . . . . . 29
2.6. Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.7. Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
III. THE ENVIRONMENTAL COST OF LAND USE
RESTRICTIONS . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3. Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . 54
3.3.1. Predicting Energy Usage Across Cities . . . . . . . . . . . 55
x
Chapter Page
3.3.2. Selection-Corrected Predicted Usage and Emissions . . . . . 60
3.3.3. Energy Usage and Climate . . . . . . . . . . . . . . . . 62
3.3.4. Policy and Emissions . . . . . . . . . . . . . . . . . . 63
3.4. Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4.1. Households . . . . . . . . . . . . . . . . . . . . . . . 66
3.4.2. Energy Production and Emissions . . . . . . . . . . . . . 70
3.4.3. Housing Supply . . . . . . . . . . . . . . . . . . . . . 74
3.4.4. Wages . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.5. Data Inference . . . . . . . . . . . . . . . . . . . . . . . . 78
3.5.1. Households . . . . . . . . . . . . . . . . . . . . . . . 78
3.5.2. Particulate Matter Concentration . . . . . . . . . . . . . 83
3.5.3. Parameter Estimates and Model Validation . . . . . . . . . 83
3.6. Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . . 87
3.6.1. Relaxation of Land Use Restrictions in California . . . . . . 89
3.6.2. Removing the Correlation Between Land Use
Restrictions and Emissions . . . . . . . . . . . . . . . . 94
3.7. Robustness and Extensions . . . . . . . . . . . . . . . . . . . 95
3.7.1. Sensitivity to Alternative Parameters . . . . . . . . . . . 95
3.7.2. Endogenous Electricity Pricing . . . . . . . . . . . . . . 97
3.7.3. Local Pollutants in Utility Function . . . . . . . . . . . . 99
3.7.4. Power Plant Substitution . . . . . . . . . . . . . . . . 100
3.8. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 101
IV. CARBON TAXES IN SPATIAL EQUILIBRIUM . . . . . . . . . . 103
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.2. Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.2.1. Households . . . . . . . . . . . . . . . . . . . . . . . 113
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Chapter Page
4.2.2. Firms & Housing Supply . . . . . . . . . . . . . . . . . 116
4.2.3. Energy Supply . . . . . . . . . . . . . . . . . . . . . 118
4.2.4. Emissions . . . . . . . . . . . . . . . . . . . . . . . 119
4.2.5. Equilibrium . . . . . . . . . . . . . . . . . . . . . . 120
4.3. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.3.1. Sources . . . . . . . . . . . . . . . . . . . . . . . . 121
4.4. Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.4.1. Labor Supply . . . . . . . . . . . . . . . . . . . . . . 123
4.4.2. Other Parameters . . . . . . . . . . . . . . . . . . . . 127
4.4.3. Parameter Estimates . . . . . . . . . . . . . . . . . . 128
4.5. Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . . 131
4.5.0.1. The Welfare E↵ects of Carbon Taxes . . . . . . . 132
4.5.1. The E↵ects of Coal-Fired Electricity . . . . . . . . . . . . 138
4.5.2. Equity and Emissions . . . . . . . . . . . . . . . . . . 142
4.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 147
V. DISSERTATION CONCLUSION . . . . . . . . . . . . . . . . . 150
APPENDICES
A. CHAPTER 2: APPENDIX . . . . . . . . . . . . . . . . . . . 152
A.0.1. Appendix: Methods . . . . . . . . . . . . . . . . . . . 152
A.0.1.1. Border-distance calculations . . . . . . . . . . . 152
A.0.1.2. Counterfactual grid . . . . . . . . . . . . . . . 152
A.0.1.3. Borders and water . . . . . . . . . . . . . . . 152
A.0.1.4. EGUs and water . . . . . . . . . . . . . . . . 153
A.0.1.5. HYSPLIT . . . . . . . . . . . . . . . . . . . 153
A.0.2. Appendix: Policy . . . . . . . . . . . . . . . . . . . . 153
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Chapter Page
A.0.2.1. The Clean Air Act and cross-border pollution . . . 153
A.0.3. Appendix: Figures . . . . . . . . . . . . . . . . . . . 154
A.0.4. Appendix: Tables . . . . . . . . . . . . . . . . . . . . 160
B. CHAPTER 3: APPENDIX . . . . . . . . . . . . . . . . . . . 163
B.0.1. Data and Theory Appendix . . . . . . . . . . . . . . . 163
B.0.1.1. Demographic Groups . . . . . . . . . . . . . . 163
B.0.1.2. Energy Prices . . . . . . . . . . . . . . . . . 164
B.0.1.3. NERC Regions . . . . . . . . . . . . . . . . . 164
B.0.1.4. Correction for Rented Homes and
Multi-Family Homes . . . . . . . . . . . . . . 165
B.0.1.5. Fuel Consumption and Population . . . . . . . . 166
B.0.1.6. Equilibrium Definition . . . . . . . . . . . . . . 167
B.0.1.7. Hedonic Rents . . . . . . . . . . . . . . . . . 168
B.0.1.8. Estimation: Production Parameters . . . . . . . 168
B.0.1.9. Calibration: Housing Supply . . . . . . . . . . . 170
B.0.1.10. InMAP and Derivation of the SR matrix . . . . . . 170
B.0.1.11. Derivation of Mean Utility Estimating Equation . . 172
B.0.2. Results Appendix: For Online Publication Only . . . . . . . 172
B.0.2.1. Comparisons of Specification of Control Function . . 173
B.0.2.2. Additional Summary Statistics: No
Selection Correction . . . . . . . . . . . . . . . 174
B.0.2.3. PM2.5: Additional Results . . . . . . . . . . . 178
B.0.2.4. Robustness of Main Parameter Estimates . . . . . 181
B.0.2.5. New Power Plant Development . . . . . . . . . . 183
B.0.2.6. Counterfactual results with model extensions . . . . 184
B.0.2.7. Birth-State Premium Parameters . . . . . . . . . 186
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Chapter Page
B.0.2.8. Demographic Group City Ranks . . . . . . . . . 186
B.0.2.9. Methane Emissions . . . . . . . . . . . . . . . 191
C. CHAPTER 4: APPENDIX . . . . . . . . . . . . . . . . . . . 197
C.0.1. Model Appendix . . . . . . . . . . . . . . . . . . . . 197
C.0.1.1. Firm FOC Derivation . . . . . . . . . . . . . . 197
C.0.1.2. Firm Parameters . . . . . . . . . . . . . . . . 198
C.0.1.3. Rent Parameters . . . . . . . . . . . . . . . . 200
C.0.2. Household Energy . . . . . . . . . . . . . . . . . . . . 201
C.0.2.1. Baseline Consumption . . . . . . . . . . . . . . 201
C.0.2.2. Energy Expenditure Shares . . . . . . . . . . . 201
C.0.2.3. HSV Transfers . . . . . . . . . . . . . . . . . 202
C.0.2.4. Model Fit: Energy Consumption . . . . . . . . . 203
C.0.3. Energy-Adjusted Income . . . . . . . . . . . . . . . . . 203
C.0.4. Estimation Summary . . . . . . . . . . . . . . . . . . 205
C.0.5. NERC Region Emissions Factors . . . . . . . . . . . . . 206
C.0.5.1. Heterogeneity in Incidence Across Space . . . . . . 207
C.0.5.2. Heterogeneity in Incidence Across Industries . . . . 213
C.0.5.3. Migration . . . . . . . . . . . . . . . . . . . 215
C.0.5.4. Voting and Tax Incidence . . . . . . . . . . . . 218
C.0.6. Computational Appendix . . . . . . . . . . . . . . . . 219
C.0.6.1. Nested Fixed Point Algorithm . . . . . . . . . . 219
C.0.6.2. Equilibrium Simulation . . . . . . . . . . . . . 220
C.0.7. Data Appendix . . . . . . . . . . . . . . . . . . . . . 221
C.0.7.1. Labor Supply & Demand . . . . . . . . . . . . 221
C.0.7.2. City-Sector Energy Use . . . . . . . . . . . . . 221
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Chapter Page
C.0.8. Additional Scatterplots . . . . . . . . . . . . . . . . . 222
C.0.9. Sector Energy Demand . . . . . . . . . . . . . . . . . 223
REFERENCES CITED . . . . . . . . . . . . . . . . . . . . . . . . 225
xv
LIST OF FIGURES
Figure Page
1. The distributions of EGUs’ distances to their nearest body
of water and EGUs’ generation capacities . . . . . . . . . . . . . . 33
2. Upwind and downwind areas for four coal-fired generators . . . . . . . 34
3. Empirical densities of the distributions of EGUs’ distances
to their nearest county or state border . . . . . . . . . . . . . . . 35
4. The share of county borders and state borders that coincide
with bodies of water . . . . . . . . . . . . . . . . . . . . . . . 36
5. Examples of the output of our calculations of county and
state borders that coincide with bodies of water . . . . . . . . . . . 37
6. Particle trajectory and dispersion in HYSPLIT for two plants . . . . . 38
7. The share of coal plants’ emissions that have left plants’
origin counties or origin states . . . . . . . . . . . . . . . . . . . 39
8. Source-based decomposition of location, coal-based pollution . . . . . . 40
9. The complexity of the Huntington-Ashland non-attainment
area (orange) . . . . . . . . . . . . . . . . . . . . . . . . . . 41
10. The origins, paths, and shares of all coal-plant-based NOx
emissions that eventually enter Shelby County, TN . . . . . . . . . . 42
11. Temperature and household energy use . . . . . . . . . . . . . . . 62
12. Predicted per-household CO2 emission and Wharton Lane
Use Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
13. Model fit results . . . . . . . . . . . . . . . . . . . . . . . . . 88
14. Histogram of CBSA level di↵erences in particulate matter concentration . 94
15. Percentage change in national emissions from relaxing land
use restrictions in California for various parameter values . . . . . . . 97
16. Model Fit Results . . . . . . . . . . . . . . . . . . . . . . . . 131
xvi
Figure Page
17. The distribution of compensating variation from a carbon
tax of $31. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
18. Share of electricity generated by coal nationally and across
NERC regions between 2004 and 2016 . . . . . . . . . . . . . . . 139
19. The distribution of compensating variation from a carbon
tax of $31 per ton in the absence of coal-fired electricity generation. . . . 140
20. Carbon emissions at the city-sector level plotted against
average wages . . . . . . . . . . . . . . . . . . . . . . . . . . 143
21. Simulated total emissions relative to lump-sum transfers
plotted against the progressivity parameter ( ) . . . . . . . . . . . . 146
A1. NARR prevailing wind directions . . . . . . . . . . . . . . . . . . 155
A2. A uniform grid within our nearest-border calculation . . . . . . . . . 156
A3. The relationship between (1) population density and (2) the
share of the county or state that is upwind or downwind of
the grid cell . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
A4. The relationship between (1) the share of the cell’s
population that is Hispanic or non-white and (2) the share
of the county or state that is upwind or downwind of the
grid cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
A5. The complexity of the Evansville, Indiana non-attainment area . . . . . 159
B1. Map of NERC region with regional conversion factors . . . . . . . . . 165
B2. Additional scatterplots: in which CO2 emissions plotted
against the Wharton Index . . . . . . . . . . . . . . . . . . . . 176
B3. Natural gas and electricity use are plotted against January
and August temperatures . . . . . . . . . . . . . . . . . . . . . 177
B4. The distribution of 2017 mean PM2.5 across CBSAs in our sample . . . 179
B5. The ratio of PM2.5 coming from electricity to total PM2.5 . . . . . . . 180
B6. Histogram of CBSA level di↵erences in particulate matter
concentration from electricity . . . . . . . . . . . . . . . . . . . 181
B7. Methane emissions regressed on Wharton Index . . . . . . . . . . . 192
B8. Methane emissions regressed on the Wharton Index . . . . . . . . . . 196
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Figure Page
C1. Baseline model fit for electricity, natural gas, and fuel-oil . . . . . . . 203
C2. NERC regional electricity emissions factors . . . . . . . . . . . . . 206
C3. Change in NERC region emissions factors from electricity in
the absence of coal-fired power plants . . . . . . . . . . . . . . . . 206
C4. Monetized regional tax incidence . . . . . . . . . . . . . . . . . . 207
C5. Non-Monetized tax incidence . . . . . . . . . . . . . . . . . . . 208
C6. Non-Monetized college-educated household tax incidence . . . . . . . 209
C7. Non-Monetized non-college-educated tax incidence . . . . . . . . . . 210
C8. Monetized tax incidence from a carbon tax . . . . . . . . . . . . . 213
C9. Non-Monetized industry tax incidence . . . . . . . . . . . . . . . 214
C10. Migration from a carbon tax . . . . . . . . . . . . . . . . . . . . 215
C11. College-educated worker migration resulting from a carbon tax . . . . . 216
C12. Non-college-educated worker migration resulting from a
carbon tax . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
C13. Tax incidence and voting . . . . . . . . . . . . . . . . . . . . . 218
C14. Compensating variation and voting . . . . . . . . . . . . . . . . . 218
C15. Total emissions per capita for each city-sector plotted,
against wages . . . . . . . . . . . . . . . . . . . . . . . . . . 222
C16. Total emissions per capita by city across industries plotted
against wages . . . . . . . . . . . . . . . . . . . . . . . . . . 223
xviii
LIST OF TABLES
Table Page
1. Testing strategic location: Comparing up- and down-wind
areas for coal and natural gas plants—before and after the
Clean Air Act (CAA) of 1963 . . . . . . . . . . . . . . . . . . . . 43
2. Predicted CBSA level CO2 emissions by fuel type . . . . . . . . . . . 60
3. Parameter Estimates. Standard errors in parentheses. . . . . . . . . . 84
4. Demographic group city ranks according to the shared,
unobservable component of amenities for households with
younger household heads. . . . . . . . . . . . . . . . . . . . . . 86
5. Counterfactual results . . . . . . . . . . . . . . . . . . . . . . . 89
6. Changes in the composition of population in response to
reduction in California land use restrictions. . . . . . . . . . . . . . 90
7. Changes in average income, rents, utility, and pollution
exposure by demographic group. . . . . . . . . . . . . . . . . . . 92
8. Model parameter estimates for household labor supply . . . . . . . . 129
9. Counterfactual results from a $31 per ton carbon tax . . . . . . . . . 135
10. Counterfactual results: a $31 per ton carbon tax in the
absence of coal . . . . . . . . . . . . . . . . . . . . . . . . . . 141
11. Change in sectoral employment in aggregate and by
education group for a $31 carbon tax with transfers . . . . . . . . . . 147
A1. Testing EGUs’ border distances relative to uniform US grid
border distance . . . . . . . . . . . . . . . . . . . . . . . . . . 160
A2. Robustness to omitting coastal counties: Upwind vs.
downwind areas for coal and natural gas plants . . . . . . . . . . . . 162
B1. Regression estimates of (B.1) . . . . . . . . . . . . . . . . . . . 164
B2. Regression estimates of fuel consumption on population . . . . . . . . 167
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Table Page
B3. Comparisons of various specifications of selection control
function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
B4. Predicted CBSA level CO2 emissions by fuel type . . . . . . . . . . . 175
B5. Parameter Estimates that vary by age . . . . . . . . . . . . . . . . 182
B6. Parameter estimates with alternative instrumental variables . . . . . . 183
B7. NERC regional mean carbon emissions from plants built
before 2000 and after 2000 . . . . . . . . . . . . . . . . . . . . . 184
B8. Counterfactual results with endogenous electricity pricing . . . . . . . 185
B9. Counterfactual results with pollution in the utility function . . . . . . . 186
B10.Parameter Estimates for 1990 Data . . . . . . . . . . . . . . . . . 187
B11.Parameter Estimates for 2000 Data . . . . . . . . . . . . . . . . . 188
B12.Parameter Estimates for 2010 Data . . . . . . . . . . . . . . . . . 189
B13.Parameter Estimates for 2017 data . . . . . . . . . . . . . . . . . 190
B14.Demographic group city ranks according to the shared
component of amenities . . . . . . . . . . . . . . . . . . . . . . 191
B15.Predicted CBSA-level methane emissions by fuel type . . . . . . . . . 193
B16.Counterfactual results for methane emissions . . . . . . . . . . . . . 194
B17.Predicted CBSA-level methane (CH4) emissions by fuel type . . . . . . 195
C2. Estimated energy-expenditure shares for college and non-
college workers, respectively . . . . . . . . . . . . . . . . . . . . 202
C3. Overview of calibration and estimation strategy for the
model’s parameters . . . . . . . . . . . . . . . . . . . . . . . . 205
C4. Monetized incidence across regions . . . . . . . . . . . . . . . . . 211
C5. No coal monetized tax incidence . . . . . . . . . . . . . . . . . . 211
C6. No-Coal Non-Monetized Tax Incidence . . . . . . . . . . . . . . . . 212
C7. Industry compensating variation . . . . . . . . . . . . . . . . . . 214
xx
CHAPTER I
INTRODUCTION
My dissertation seeks to provide insight into critical policy questions related
to the regulation of air quality and climate. I examine spatial heterogeneity in
response to (and as a result of) a set of environmentally related public policies. I
use various methods such as structural models, atmospheric dispersion modeling,
and reduced-form causal inference to answer these questions. This dissertation
contains previously published and unpublished co-authored material. Chapter 2
is joint work with Edward Rubin, and Chapter 3 is joint work with Mark Colas.
Chapter 2 demonstrates that most coal-fueled power plants are located on or
near jurisdictional (county or state) borders. Water is a crucial input for electricity
production, and many borders are water (i.e., rivers), so it is entirely possible
that this observed border siting results from minimizing input costs (and not
regulatory avoidance). We develop a simple statistical test that uses variation in
wind direction to distinguish strategic from non-strategic siting. We find that coal-
fueled electricity generators have been sited strategically to export their emissions
beyond the boundaries of their counties and states. Natural gas plants—much lower
polluters—do not exhibit this behavior.
Motivated by this apparent strategic siting, we use an atmospheric
dispersion model developed by NOAA to estimate various aspects of the “pollution
transport problem.” We find that nearly 90% of coal-based particulate matter
leaves its state of origin within 48 hours of release. We also document that up to
20% of coal-based particulates in some counties can be attributed to coal-based
electricity pollution in other counties. We then document the share of coal-based
particulate matter in a given county by whether or not the county meets the
1
Environmental Protection Agencies’ standards for local pollutants (under the Clean
Air Act). Counties that are “out of attainment” (i.e., do not meet the standard)
receive a substantial share of their total coal-based particulate matter emissions
from plants in attainment counties in neighboring states. Our results highlight the
importance of transport-focused regulation for local pollutants.
Chapter 3 shows that cities with restrictive land-use regulations tend to have
low-carbon emissions per capita. We develop and estimate a spatial equilibrium
model to understand the implications of these land-use regulations on national
carbon emissions. Our model features heterogeneous households that consume
energy and housing, and firms that employ college and non-college-educated labor
as imperfect substitutes. The model also features locations that vary in the carbon
e ciency of regional power plants, their amenities, and their marginal utility of
energy consumption. We estimated the model on publicly available data.
We find that the relaxation of excessive land-use restrictions in California
led to 0.6% lower overall national carbon emissions. The mechanism behind this
drop is intuitive. California cities have more temperate climates, carbon-e cient
power plants, and stringent land-use regulations. These land-use regulations inflate
housing prices, thus lowering the equilibrium population levels in California cities
(and raising the equilibrium population levels in states). When fewer people live in
California, carbon emissions are higher because household-level carbon emissions
are lower (on average) in California than in other states.
In Chapter 4, I simulate the labor market e↵ects of a carbon tax across the
continental United States. To recover the welfare impacts of a carbon tax, I build
and estimate a spatial equilibrium model that features heterogeneous households.
I incorporate a rich level of heterogeneity into the model that allows me to answer:
2
(1) who is most a↵ected by a carbon tax, (2) how much of the burden of a carbon
tax is borne by di↵erent households, and (3) where the households are that bear
the greatest burden from the tax.
I find that manufacturing workers without a college degree can be
expected to bear a disproportionate share of the tax incidence. Cities with mild
climates, carbon-e cient power plants, and services-oriented economies experience
modest population increases as households move in response to the carbon tax.
Additionally, I use the model to demonstrate that, relative to flat transfers,
progressive compensation leads to a decline in aggregate carbon emissions due to
a reallocation of workers into less carbon-intensive cities and sectors.
3
CHAPTER II
DOWNWIND AND OUT: THE STRATEGIC DISPERSION OF POWER
PLANTS AND THEIR POLLUTION
This chapter is co-authored with Edward Rubin. I had an essential role in
developing the initial idea that led to this project. I also wrote a significant amount
of code that generates the results in this paper. I wrote and edited many sections
of the paper. Furthermore, I wrote a successful application for external funding for
this project.
2.1 Introduction
Federalist systems o↵er potential e ciencies in many settings, but they
also may incentivize strategic responses from local governments—whose focus
tends to emphasize the provision of locally enjoyed goods (Oates, 1972, 1999).
As a consequence, local administrative units may seek to export the negative
externalities generated by locally beneficial economic activities. The extent to
which the local units can export their costs—and increase local net welfare—will
depend on the degree to which local actors can separate the externalities from the
productive activities themselves.
Consequently, federalist regulatory systems face two important challenges
when governing air quality. First, local governments face few incentives to
internalize the costs of pollution once it leaves their jurisdictions Monogan,
Konisky, and Woods (2017); Oates (1972); Revesz (1996); Tiebout (1956).
Second, air pollution can travel long distances (i.e., crossing city, county, and
state borders) (Oates, 2002; Sergi, Azevedo, Davis, & Muller, 2020; United
States Senate, Committee on Public Works, Sta↵ Report, 1963). In the U.S., the
spatially discontinuous patchwork of local and state authorities presents many
4
opportunities for local decision-makers to strategically site major polluters in
locations that reduce air-pollution exposure within the county/state. As a result,
local governments have incentives to site polluters where the jurisdiction can
simultaneously enjoy the benefits of production (e.g., increased jobs and wages)
while exporting the pollution costs. This hypothesized behavior is, in a sense, a
variation on NIMBY-ism: the property owner wants the activity on her property
but wishes to export the negative externalities.1
In two steps, we empirically substantiate the hypothesis that decision-
makers attempt to capture local benefits and export their negative externalities.
First, we identify strategic siting within a significant group of air polluters in
the United States—demonstrating that decision-makers sited coal-fired power
plants to reduce downwind pollution exposure within their own counties and
states. Establishing this result is necessary to demonstrate strategic exporting of
externalities, but it is not su cient—externalities must be su ciently exportable.
We document the extreme mobility of the pollution generated by these plants. We
first show that governments tend to site these major polluters near the downwind
border of administrative units, and then we quantify the extent to which these
polluters’ emissions are carried downwind from their source counties and states.
Together, these two tendencies support our hypothesis that local decision-makers
make siting choices that take advantage of polluters’ benefits while minimizing the
costs to their own constituencies.
1NIMBY is “Not In My BackYard,” as used by (Gates, 1980; Livezey, 1980; Mitchell & Carson,
1986)—and many individuals since.
5
We focus on coal-fired power plants, which historically have accounted for a
substantial share of air pollution in the U.S.2 Coal-fired electricity production o↵ers
a classic example of a negative externality: The plant’s operators and immediate
community enjoy positive economic benefits, while counties and states downwind of
the plant bear the costs of the plant’s pollution. The context of coal-fired electicity
generating units (EGUs) provides several advantages. First, natural-gas-fired power
plants—which produce much less pollution than their coal-fired counterparts—
provide a helpful ‘control group’ in our empirical framework. Second, while coal
and natural gas EGUs both use water as an input, neither type of EGU uses do
not use areas downwind or upwind as (non-strategic) inputs—a fact we exploit in
our empirical tests. Third, electricity generators are required to record important
emissions data—unlike many other major polluters. These emissions records are
advantageous when we model pollution transport for coal-fired power plants.
We first document that electricity generators tend to be sited near
administrative borders. Given that water both (a) forms many administrative
borders and (b) is a key input to electricity generation—thus a↵ecting EGU
siting—we develop a simple, non-parametric test that shows localities (states and
counties) sited coal plants to reduce within-unit, downwind exposure. Natural
gas EGUs do not exhibit this behavior. In other words, while water may explain
coal power plants’ proximity to borders, it does not explain their tendency to
be sited on downwind borders. Our natural gas placebo test corroborates this
finding. Finally, using a state-of-the-art particle-trajectory model, we illustrate
the extreme exportabilitiy of coal plants’ pollution: within six hours, 50% of coal
2E.g., in 2014, U.S. coal EGUs accounted for approximately 65.7% of SO2 emissions, 44.0% of
mercury emissions, 39.1% of arsenic emissions, and 10.6% of NOx emissions in the United States
U.S. Environmental Protection Agency (2018)—while contributing only 39% of total electricity
generation (EIA, 2021).
6
plants’ emissions leave their source states—and 99% depart their source counties.3
Together, these results illustrate critical challenges facing decentralized, federalist
approaches to administration and regulation. More broadly, we find significant
evidence that local decision-makers strategically respond to the spatial patchwork
of jurisdictions created by the federalist system in the U.S.
Our results parallel a growing literature documenting strategic pollution-
related responses in federalist systems. This nascent literature has so far identified
three main varieties of strategic responses by local decision-makers and polluters:
(1) strategic siting of polluting plants (Monogan et al., 2017), (2) strategic
production or abatement decisions (Zou, 2021), and (3) strategic monitoring
(Grainger, Schreiber, & Chang, 2018; Mu, Rubin, & Zou, 2021). Each of these
strategic responses implies di↵erent costs and requires di↵erent remedies. For
example, Zou (2021) provides evidence that scheduled intermittent monitoring leads
to significantly lower pollution levels on monitored days (relative to unmonitored
days). Consequently, air-quality levels near intermittent monitors are likely worse
than monitoring data would suggest. Grainger et al. (2018) find that the siting of
air-quality monitors is vulnerable to strategy—again, resulting in an underestimate
of local ambient air pollution. Mu et al. (2021) detect a set of monitors that appear
to shut down in anticipation of high-pollution events—also biasing air-quality
estimates downward. Broadly, this literature suggests that current regulatory and
3One might wonder whether this degree of exportability of emissions makes local strategic
siting irrelevant. A plant’s pollution tends to leave its county quickly, siting is still relevant within
the county. For local decision-makers and residents, there is a substantial di↵erence between (a)
a plant’s pollution passing through/over the major city within the county and (b) the plant’s
pollution immediately exiting the county. The same reasoning also applies at the state level.
7
political structures create opportunities for polluters and local decision-makers to
avoid fully internalizing pollution-based costs.4
Our paper most closely relates to Monogan et al. (2017). Like us, these
authors find significant evidence that industrial facilities with large emissions
systematically locate closer to states’ downwind borders relative to lower-emissions
industrial facilities. However, our analysis di↵ers from Monogan et al. (2017) in
four important ways. First, we define “strategic siting” (within a jurisdiction,
i.e., state or county) as choosing a plant location where the downwind area is
less than the upwind area (in the given jurisdiction)—based upon the location’s
prevailing wind.5 Comparing the area downwind to the area upwind—within the
same jurisdiction—implicitly controls for the size of the jurisdiction. In contrast,
Monogan et al. (2017) focus on polluters’ distance to the state’s “downwind
border.” Second, we study strategic siting at both the county and the state level,
while Monogan et al. (2017) focus only on state-level siting. We are unaware of
any existing analyses that detect within-county strategic siting. We believe both
levels warrant consideration. State and county governments each potentially face
incentives to mitigate pollution exposure—e.g., counties are often the most basic
unit of air-quality regulation, while state agencies coordinate county-level responses
to regulation. Beyond regulation, politicians at every level face political incentives
4Our paper also broadly relates to a large literature on the pollution-haven hypothesis (PHH),
which posits that polluters tend to locate in areas with less stringent environmental regulation.
Much of the PHH literature investigates this hypothesis at the international level—focusing on
how emissions-intensive production shifts towards countries with lax environmental regulation.
Cherniwchan, Copeland, and Taylor (2017); Cole (2004); Levinson (2008); Millimet and Roy
(2015) provide helpful overviews and discussions of the PHH literature. Our main hypothesis—
that local decision-makers site polluters to capture economic benefits while exporting pollution’s
costs—follows a similar line of reasoning as the PHH but focuses on within-unit spatial siting
decisions (enabling the export of pollution) rather than variation in regulatory stringency.
5As we explain below, we define downwind/upwind area using 30-year averages for prevailing
wind directions from NOAA (North American Regional Reanalysis, 2006).
8
to increase economic activity while maintaining some degree of environmental
quality (producing health and amenity values). Third, we focus exclusively
on electricity generators—and specifically compare coal EGUs to natural-gas
EGUs. As described above, coal EGUs account for a substantial share of local
and national air pollution (PM2.5, NOx, SO2, mercury, lead, ozone, and CO).6
Finally, we extend beyond both Monogan et al. (2017) and the current literature by
including additional descriptions of the geography of power plants and, importantly,
descriptions of the transport of coal EGUs’ emissions across the United States.
Methodologically, our empirical test of strategic siting overlaps with
a growing literature that uses wind direction for identification. For example,
Zivin, Liu, Song, Tang, and Zhang (2020) use the di↵erence between upwind and
downwind agricultural fires in China to identify the e↵ect of fire smoke on cognitive
test performance. Rangel and Vogl (2019) use a similar approach to estimate the
e↵ects of fire smoke on infant health at birth. Schlenker and Walker (2016) and
Anderson (2019) use upwind and downwind exposure to tra c-induced pollution
(from planes and automobiles, respectively) to measure the e↵ects of pollution on
local health. Our test uses the ratio of downwind area to upwind area within the
jurisdiction to identify strategic siting among major polluters.7
We are not the first to examine the challenges that pollution transport
creates—e.g., the Clean Air Act of 1963 was understood to limit federal power to
6Consequently, coal EGUs are regulated and monitored closely by both federal (especially
U.S. EPA) and local (state and county) authorities. In addition, coal EGUs are unique in their
tendency to build tall smokestacks: there are 15 smokestacks in U.S. of at least 1,000 feet and
nearly 300 smokestacks of at least 500 feet (CAMD, 2020; U.S. Government Accountability O ce,
2011).
7Many other papers use wind variation (rather than a comparison of upwind to downwind
areas) for causal identification, e.g., Barwick, Li, Rao, and Zahur (2018); Deryugina, Heutel,
Miller, Molitor, and Reif (2019); Freeman, Liang, Song, and Timmins (2019); Holland, Mansur,
Muller, and Yates (2019); Sullivan (2016).
9
cases where (1) “air pollution...originates in one state and adversely a↵ects persons
or property in another state” or (2) for “significant intrastate problems which
state and local agencies are unwilling or unable to deal with” (Edelman, 1966).
A host of “pollution transport” models have been developed to study the extent
to which pollution travels, as well as the health and policy problems posed by
pollution transit.8 Sergi et al. (2020) find that despite national reductions in PM2.5
from point sources since 2008, approximately 26% of counties have experienced
worsening health damages from pollution—noting that “around 30% of all U.S.
counties receive 90% of their health damages from emissions in other counties.”
Similarly, by decomposing pollution levels by each pollutant’s distance from its
source, Wang et al. (2020) find that “long-range” pollution is dominant in the
U.S.9 Nearly 60 years have passed since the CAA of 1963 recognized “the transport
problem” in air pollution, but substantial gaps remain in our understanding of the
origin and extent of the problem, or the damages that result.
More broadly, the evidence in this paper, in conjunction with the existing
literature, highlights important policy challenges facing federalist systems. Local
governments can export negative externalities ‘abroad’ when these externalities are
physically separable from local benefits. We provide evidence of this behavior in
an economically and historically important context: coal-fired power plants. First,
we show significant evidence that U.S. counties and states sited coal power plants
to reduce within-county and within-state downwind exposure. We then show that
these plants—their locations, in combination with prevailing wind patterns and coal
8Another class of pollution transport models—reduced-complexity air transport models—make
simplifying assumptions concerning meteorology and atmospheric chemistry equations in exchange
for large computational benefits, e.g., the InMAP model (Tessum, Hill, & Marshall, 2017).
9Wang et al. (2020) define “long range” as farther than 100 km from the source—reasoning
that this distance “likely represents regional background and long-range transport.”
10
plants’ tall smokestacks—export pollution quickly out of the source counties and
states. By documenting this strategic behavior and illustrating the incentives that
federalism’s decentralization creates, our results identify areas where policymakers
and regulators may reduce external costs and thereby increase net social benefits.
2.2 Institutions: Siting of Plants
Governments’ and firms’ decisions about where to site a new power
plant depend upon a host of variables—proximity to water,10 grid/transmission
availability,11 access to fuel12 (e.g., rail lines, pipelines, wind/solar capacity),
local regulatory oversight13 (i.e., friendliness to industry), and local community
characteristics as well14. In the rest of the paper, we will use “decision-makers”
to refer to the joint government-firm decision process for siting a plant. A large
literature considers how local environmental regulations and enforcement a↵ect the
locations of polluting firms across states and counties (see footnote 4). However,
location decisions on a finer scale—i.e., within state or county—have received far
less attention.
The logic of exporting negative externalities is simple. If a local decision-
maker reduces the area downwind of polluters within its administrative boundaries,
10Steam-driven turbines and water-cooled plants mechanically require water. We document the
distribution of plants’ proximities to water in Empirics and Figure 1.
11In the Texas electricity market, Woerman (2020) demonstrates that grid congestion can
induce market power—more than doubling firms’ markups.
12Preonas (2019) documents markups driven by market power in coal-by-rail delivery to coal
plants in the U.S.
13An abundant literature considers the e↵ect of local pollution regulations on polluter locational
choice—e.g., Becker and Henderson (2000); Gray (1997); Jeppesen and Folmer (2001); Jeppesen,
List, and Folmer (2002); Levinson (1996); List, Millimet, Fredriksson, and McHone (2003); Mani,
Pargal, and Huq (1997); McConnell and Schwab (1990); Millimet and List (2003); Shadbegian and
Wolverton (2010).
14Wolverton (2009) finds a significant negative association between plant sitings and income.
11
then fewer of its own residents bear the costs of pollution.15 As long as the
polluters remain within administrative borders, the locality captures many of the
plants’ benefits—tax revenue, employment, economic activity/growth. In addition,
by moving polluters farther downwind, the decision-maker may also complicate
pollution attribution and regulation—reducing local regulatory costs associated
with the emissions.16 Broadly, this story follows a similar logic to NIMBY behavior:
an actor (the local decision-maker) tries to enjoy the benefits associated with an
economic activity without bearing the activity’s costs. As we show, power plants
can easily export their pollution (their main external costs) using wind and tall
chimneys. Figure 2a shows an illustrative plant with limited downwind area (the
dark purple shaded area) in its home county.
2.3 Data
Overview We combine several publicly available datasets that originate from a
variety of federal agencies. The data fall into three broad categories: (1) electricity-
generator data (i.e., power plants), (2) meteorological data, and (3) geographic
data.
Electricity generators Our data on electricity generators (at both the
generator and plant levels) come from two sources: (i) the Emissions & Generation
Resource Integrated Database (Emissions & Generation Resource Integrated
Database, 2018) and (ii) the EPA’s EmPOWER Air Data Challenge,17 which
15E.g., health costs and diminished local amenities like visibility.
16For an example of diminished regulatory cost, consider the Clean Air Act’s National
Ambient Air Quality Standards (NAAQS). By reducing the area downwind of a polluter, there
is (mechanically) less space to site an air quality monitor.
17More details can be found at the EmPOWER website: https://www.epa.gov/airmarkets/empower-
air-data-challenge.
12
provides data through the EPA’s Clean Air Markets Division (CAMD, 2020).
Specifically, we use the eGRID data to obtain each EGU’s latitude, longitude,
year of construction, fuel category (e.g., coal, gas, hydro), generation capacity, and
operating status. These variables are available at the level of generator and plant.
We employ eGRID data from 2010, 2012, 2014, 2016, and 2018 (the intermediate
years are unavailable). The EmPOWER CAMD data supply each EGU’s daily
emissions of NOx and SO2 and the EGUs’ associated stacks’ heights—both of which
are inputs to the particle-trajectory model HYSPLIT. Both datasets include useful
data on EGU retirements and fuel conversions. Panel B of Figure 1 illustrates the
distribution of generators’ capacities across four broad fuel categories for units
operating in 2018.
Notably, the CAMD and eGRID datasets jointly allow us to construct the
historical distribution of power plants in the United States. Because we observe
both retirements and fuel conversions, the resulting dataset reflects the spatial
distribution and fuel types of power plants at their time of construction—the
information most relevant to our question of strategic siting.18
Meteorology Our meteorological data come from NOAA’s North American
Regional Reanalysis (NARR) daily reanalysis data (Mesinger et al., 2006; North
American Regional Reanalysis, 2006). We use the NARR meteorology data in two
applications. First, we utilize NARR’s long-term averages (1979–2000) for wind
speed and direction to determine prevailing, historical wind patterns in our analysis
of strategic plant sitings. Specifically, we use NARR’s first three pressure levels (the
18The repeated cross-sections of eGRID provide further confidence in constructing this historical
distribution. Further, the 2010 version of eGRID precedes the vast majority of coal EGU
conversions and retirements.
13
levels nearest to the ground): 1000 hPa, 975 hPa, and 950 hPa.19 Second, we feed
the NARR data into HYSPLIT for the particle-trajectory model’s meteorology. In
both applications, we employ NARR’s highest spatial resolution with horizontal
and vertical spacing of approximately 32 km (at the lowest latitude) (North
American Regional Reanalysis, 2006).
Geography For state borders, county borders, coastlines, and bodies of water,
we rely upon the U.S. Census Bureau’s TIGER/Line shapefiles and cartographic
boundaries (US Census Bureau, 2016a, 2016b). The bodies of water are subdivided
into area files (i.e., polygons that enclose areas) and linear files (i.e., line-based
hydrology). Finally, we integrate data on counties’ non-attainment histories using
the U.S. EPA’s NAYRO file in its Green Book collection (U.S. Environmental
Protection Agency, 2017). In this paper, we focus exclusively on EGUs in the
contiguous U.S.—omitting Alaska, Hawaii, and U.S. territories.
2.4 Empirics
We now turn to our empirical analysis. Recall that the hypothesized
strategic negative-externality export requires (1) that decision-makers site large
polluters to reduce within-jurisdiction exposure and (2) that polluters’ emissions
are, in fact, su ciently exportable.
We begin in 2.4.1 by documenting the fact that state and county decision-
makers sited many EGUs very close to county and state borders. There are non-
strategic reasons EGUs might locate near borders—namely, many borders are
defined by water, a critical input for electricity production. Next, in 2.4.2, we
formulate a simple test for regulatory avoidance that implicitly accounts for non-
19Pressure levels (barometric pressure levels) represent the force exerted from the weight of the
air. Pressure levels decrease non-linearly with height.
14
strategic reasons for locating on an administrative border. In 2.4.3 we apply this
test for strategic siting and discuss its results.
Finally, in 2.4.4 and 2.4.5, using a particle-trajectory model (HYSPLIT),
we demonstrate that coal power plants’ emissions are indeed highly transportable.
Together, our results show that decision-makers have tended to site units of an
exportable externality strategically. These results jointly satisfy su ciency in
demonstrating our hypothesized behavior: local decision-makers attempt to capture
local benefits and export their negative externalities.
2.4.1 Power Plants’ Distances to Borders and Water.
Border distance We start by calculating each plant’s distance to the nearest
county and state border.20 Figure 3 illustrates the result of this calculation—the
distribution of EGUs’ distances to their nearest state and county borders. We
separate the distributions by the EGUs’ fuel categories, as EGUs’ fuel types drive
di↵erences in other inputs.21
Figure 3 demonstrates that many EGUs were sited very close to county
borders (Panel A) and state borders (Panel B). Further, this tendency is
particularly extreme in coal-fired and hydropower EGUs—though natural gas
plants also exhibit this trend. Of the 605 operating coal units in 2018 with
capacities of at least 25 MW, 30% are within 1 km of a county border, 57% are
within 5 km of a county border, and 77% are with 10 km of a county border. For
state borders, the corresponding percentages are 18% ( 1 km), 25% ( 5 km), and
20While plants are divided into generating units (e.g., boilers), latitude and longitude are
constant at the plant level in the eGRID dataset—i.e., all EGUs within a plant (ORIS code)
are specified as having the same location in eGRID. See appendix section A.0.1.1 for the details of
this calculation.
21E.g., coal units require access to coal—generally via rail or barge—while natural gas units
typically require access to the natural-gas pipeline.
15
29% ( 10 km). Only hydropower EGUs skew more toward administrative borders
than coal-fired EGUs. We formally test whether EGUs’ placements are independent
of borders using a Kolmogorov-Smirnov test. This test compares EGUs’ distances
to borders against a null distribution of distance-to-nearest-border for a uniform
grid covering the entire contiguous US. If EGU placements are independent of
borders, these distributions should be similar. All fuel types strongly reject this
independence except for solar/wind’s distance to county borders (see Table A1). As
Figure 3 and these statistics suggest, a substantial (and disproportionate) share of
U.S. coal-fired electricity generators sit near county and state borders.
Non-strategic explanations for EGUs’ proximity to borders One
explanation for coal EGUs’ proximity to county and state borders is the strategic
export of coal generation’s negative externalities. However, plants may site near
borders for other reasons. Most methods of electricity generation require water for
steam, cooling, locomotion, or transportation (solar and wind are exceptions). If
large bodies of water (rivers or lakes) form many state/county borders, then water
as an input could explain plants’ proximity to borders.22
We calculate the share of each county’s and state’s borders that intersect
bodies of water by spatially joining administrative borders (both state and county
borders) to the boundaries of bodies of water (using a 50-meter bu↵er to allow for
near misses).23
We find that approximately 46.1% of state borders and 27.4% of county
borders coincide with bodies of water. States di↵er greatly in the shares of their
22This explanation also requires that the interiors of counties (and states) do not contain other
large bodies of water. Otherwise, EGUs could just as easily locate in counties’ interiors rather
than on borders.
23Appendix section A.0.1.3 describes this operation in detail.
16
borders (county and state) formed by water. Figure 4 illustrates this heterogeneity,
and Figure 5 provides four examples of the county and state borders identified as
coinciding with water (in dark blue lines). As demonstrated by Figure 4, states in
the non-coastal, western U.S. make up the lower end of the distribution with very
few county or state borders coinciding with water—e.g., in Colorado, Wyoming,
and New Mexico, less than 1% of state borders coincide with water, and 2%–3%
of county borders coincide with water. Many coastal states (including the Gulf
Coast and Great Lakes) have relatively high shares of borders coinciding with
water. However, some interior states also have high water shares—e.g., 65% of
Kentucky’s state border and 41% of its county borders coincide with large bodies
of water. Thus, most states—and many counties—o↵er potential sites with water
and proximity to the border.
Panel A of Figure 1 confirms that EGUs locate near bodies of water (again,
except wind and solar): 99% of hydropower units and 62% of coal units are within
250 meters of a body of water.24 For natural-gas units, 48% are within 250 meters
of water. For wind and solar EGUs, only 30% of generators are within 250 meters
of a body of water. Given that hydro and coal units require large amounts of
water—and wind/solar units do not—these results validate the spatial calculations
in the rest of the paper and confirm that water is, indeed, a binding locational
constraint when siting plants. However, these results do not entirely explain
the phenomenon of siting coal plants near borders. Many bodies of water exist
24Measurement error in the latitude and longitude of generators and the Census water files
likely explains why hydropower does not hit 100%.
17
in the interiors of counties/states, yet coal EGUs tend instead to locate near
administrative borders.25
2.4.2 Strategic Plant Siting: A Statistical Test. We now develop
a simple, non-parametric test to detect whether plants have been strategically sited
near borders to reduce their home counties’ (or states’) exposure to the plant’s
pollution—rather than being placed near borders due to plant’s demand for water.
With this motivation in mind, it is clear that proximity to certain borders
is more advantageous than proximity to other borders. If a plant locates on the
downwind border of its county, then its emissions immediately will leave its county
(for example, the plants depicted in Figures 2a and 2b). If a plant locates near
the upwind border of its county, then its emissions will pass through a substantial
portion of its county (e.g., Figure 2d). Thus, all else equal, local decision-makers
wishing to reduce their county’s pollution exposure will prefer to reduce the area
within the county that is downwind of the plant.26
Now consider the possibility—our null hypothesis—that decision-makers do
not try to export their coal pollution. Under this null, decision-makers search for
a location that maximizes the plant’s profit, independent of the share of emissions
exported. Consequently, plants’ locations should be independent of the downwind
vs. upwind exposure of their emissions: this ratio is not an input to production,
nor is it an input to electricity production. In the absence of emissions exports, it
should be a 50-50 ‘coin-flip’ whether the area downwind of the plant is larger or
25For example: The interior Catawba County in North Carolina contains the Marshall Steam
Station, a 2.1-gigawatt coal plant located on Lake Norman.
26The same reasoning applies at the state level.
18
smaller than the area upwind (within the jurisdiction containing the EGU).27 In
other words, in the absence of strategic emissions exports, there is nothing special
about downwind water.
Therefore, a simple, non-parametric test for strategic emissions exports in
the siting of coal-fired power plants is to calculate the number of coal plants for
which the downwind area (in the county or state that contains the plant) is less
than the upwind area. We operationalize this test as an implementation of Fisher’s
Exact Test (Conover, 1971; Fisher, 1934, 1935; Imbens & Rubin, 2015). Under a
sharp (one-sided) null hypothesis of no strategic siting to reduce downwind area,
the test statistic ns (the number of plants for which downwind area is less than
upwind area) is distributed as a binomial distribution with size equal to the number
of plants in the sample (NT ) and probability p = 0.5. Under this null, the expected
share of plants with downwind area less than upwind area is 50%. Consequently
the p-value for the corresponding test statistic is
        XN ✓ ◆T N
p-Value n = P X   n ; n = N , p = 0.5 = T NTs s T 0.5 .
x
x=ns
Given that county and state decision-makers both potentially face incentives to
reduce pollution exposure within their administrative units, we implement our test
for strategic siting at both administrative levels.28
Our test o↵ers several attractive features. First, the identifying assumption
is that a decision-maker will only minimize a plant’s downwind area to avoid the
27Using a uniform grid covering the contiguous U.S.—e↵ectively a higher resolution version of
the raster depicted in Figure A1—we confirmed that the probability a point in this grid is more
upwind than downwind is, indeed, almost identical to 50 percent.
28It may be helpful to note that there is an upwind side and a downwind side for nearly every
border in the U.S. (at least for borders that run orthogonal to the wind). Our test simply asks
whether decision-makers disproportionately placed coal EGUs on the upwind side of the border
(reducing their downwind areas).
19
costs associated with the plant’s pollution. This assumption is plausible because
coal- and natural-gas-fired electricity generators do not use the areas upwind
or downwind—or their ratio—as inputs into their production or transport of
electricity. Put di↵erently, because EGUs do not use the ratio of downwind-to-
upwind area for production or transport, strategic pollution export is the only real
explanation for locating plants in a manner that reduces the county’s (or state’s)
exposure downwind. If a latent factor correlates with the ratio of the downwind-
to-upwind area at the state or county level, then our test will falsely conclude
strategic siting. However, very few social, political, or physical processes consider
the areas downwind or upwind of a point in space—let alone their ratio. Further
supporting this assumption: when we analyze a fine, uniform grid covering the
contiguous U.S., we find no evidence of a relationship between this ratio (or its
inputs) and population density or population demographics.29
Second, this test is simple, straightforward, and provides an exact p-value
that do not rely upon parametric or asymptotic assumptions (Imbens & Rubin,
2015).30 Third, natural-gas EGUs provide a convenient falsification test for our
approach. Natural-gas plants produce substantially less pollution than coal-fired
EGUs, so counties and states do not face the same incentives to reduce gas EGUs’
downwind pollution exposure. However, natural-gas plants face similar transmission
constraints to coal plants. Consequently, if a latent factor is biasing our test toward
29Figures A3 and A4 illustrate that there is no relationship between share of county (or state)
upwind (or downwind) and population density or population demographic composition. To falsify
our identifying assumption, population density (or population composition) would need to bunch
near downwind borders and avoid upwind borders. The figures contain no evidence that this
bunching occurs.
30One drawback of the test’s simplicity is that it does not incorporate other dimensions of
strategy, e.g., stack heights. This omission does not bias the test for our specific hypothesis. It
simply means we are testing for a specific strategy.
20
detecting “strategic siting,” we should detect strategic siting for coal EGUs and
natural-gas EGUs. In short, this simple procedure generates an intuitive test for
strategic siting with exact p-values, a plausible identifying assumption, and a
convenient falsification test.
In addition, our approach easily extends to test whether decision-makers
located plants jointly reduce county and state downwind areas. Under the null of
no strategic siting, the expected percentage of plants whose downwind area is less
than the upwind area at the county and state levels is 25%.31 More generally, this
non-parametric test provides simple and clear evidence of whether decision-makers
sited coal plants to reduce the downwind area in the plants’ home counties and
states.
To implement this test, we calculate the areas upwind and downwind of
each coal and natural-gas plant in our data within the plants’ counties and states.
For the wind component of upwind and downwind areas, we use NARR’s long-
term averages of wind direction. The area is defined by the county’s (or state’s)
intersection with right triangles emanating upwind or downwind of the plant.
Figure 2 provides four examples of this calculation—illustrating the direction of
the prevailing wind (the dark purple triangle in the compass), the downwind area
(shaded dark purple), and the upwind area (shaded light gray). The plants in
Figures 2a and 2b are located near borders in a manner that substantially reduced
the downwind area in the plant’s home county. The plants in Figures 2c and 2d
were sited in parts of their county in which the downwind area is larger than the
31The null of no strategic siting implies that decision-makers’ siting decisions are independent of
the area downwind (or upwind) at the state and county levels. Under this null, the probability a
plant is more downwind in the state is independent of the probability the plant is more downwind
in the county. Thus, the probability of being ‘downwind’ at both levels is 0.25 = 0.5⇥ 0.5.
21
upwind area. Using these downwind and upwind areas, we implement our test for
strategic siting.
2.4.3 Strategic Plant Siting: Results. Table 1 contains the results
of our test for strategically sited coal and natural-gas plants. Given that coal EGUs
produce substantial amounts of pollution, decision-makers have strong incentives
to strategically locate coal plants to reduce the amount of jurisdictional area
downwind of the plants. Natural-gas plants produce considerably lower emissions,
giving decision-makers much less incentive to site natural-gas plants strategically.
We separately test coal plants (column 1) and natural-gas plants (column 2).
Table 1 contains three panels that respectively test strategic siting (A) within
counties, (B) within states, and (C) within both counties and states. Each of the
three panels bears strong evidence of strategic siting of coal plants that reduced
the downwind areas within plants’ counties (Panel A), states (Panel B), and both
(jointly) counties and states (Panel C). There is no evidence that natural-gas plants
were strategically located to reduce their downwind areas at any level.
Panel A tests strategic siting at the county level. Among the 514 coal
plants, 56.81% sit where the area downwind of the plant (in its county) is less than
the area upwind. Under the null of no strategic siting, with 514 plants, one would
observe a distribution at least this extreme (in the right tail) approximately 0.12%
of the time (i.e., a p-value of 0.0012).32 For the the 1,254 natural-gas plants, the
corresponding share of strategically located plants at the county level is 49.44%
with p-value of 0.6641.33 At the county level, our test finds large and statistically
32We do not expect this number to be near 100%, as governments and firms face many
constraints when siting coal plants (e.g., water, rail, regulation, and local opposition to some
sites)—in addition to likely having heterogeneous preferences.
33Recall that under the null, the expected share of strategically located plants at the county or
state level is 50%.
22
significant evidence within the group most incentivized to strategically site (coal
plants) and no evidence within the group with few incentives to do so (natural gas
plants).
The results at the state level (Panel B) paint a very similar picture as the
county-level results. There is statistically significant evidence of strategic siting
among coal-fired power plants (53.89% strategic with a p-value of 0.0426) and no
evidence of strategic siting within natural-gas plants (45.77% with a p-value of
0.9987).34
In Panel C of Table 1, we test whether plants are strategically located
both within their counties and within their states. Under the null hypothesis of
no strategic siting at either level, the expected share of strategically sited plants is
25%. Across the 514 coal plants, 34.82% sit in locations consistent with strategic
siting at both county and state levels (p-value less than 0.0001). With an expected
value under the null of 25%, thr level of strategic siting in this case (34.82%) is
economically significant: an additional 50 coal plants (10%) sit in locations where
they can export their pollution. As before, natural-gas plants show no evidence of
strategic siting to reduce the area downwind of plants (25.04%; p-value of 0.4978).
Again, we find highly significant evidence that decision-makers sited coal plants
to reduce downwind exposure within the jurisdiction where the plant is located
(counties and states).35
34If anything, natural-gas plants appear to be sited in an anti-strategic manner at the state
level—i.e., where the downwind area typically exceeds the upwind area. One explanation for this
behavior is that natural-gas plants may share bodies of water with coal plants, but gas plants
are willing to ‘take’ the downwind side of the resource (the gas plants do not need the strategic
location). An alternative explanation is that, when converting coal units to natural gas, decision-
makers may prefer to replace less strategically located coal units with natural-gas units.
35These results are robust to dropping coastal counties; see Table A2.
23
Whether we consider counties, states, or both levels simultaneously, we
find substantial evidence that decision-makers sited coal plants to reduce the
areas downwind in plants’ counties and states. We apply the same test in the
case of strategic siting to natural-gas plants—a class of plants for which local
administrators should have few incentives to site strategically. We fail to detect
any significant evidence of strategic siting in this natural-gas-plant placebo test.
Therefore, we conclude that Table 1 provides strong and statistically significant
evidence that local decision-makers strategically placed coal-fired power plants to
reduce the area downwind of plants within plants’ counties and states.
This result of strategic siting is necessary for our hypothesis of local
strategic export of pollution from coal-fired power plants, but it is not su cient. In
the next section, we substantiate the second part of our hypothesis by documenting
the extent of coal pollution’s mobility.
2.4.4 Pollution Mobility: Methods. To estimate the extent to
which coal-fired EGUs’ emissions travel beyond the counties and states that
house the EGUs, we employ a state-of-the-art particle-trajectory model known as
HYSPLIT (HYbrid Single-Particle Lagrangian Integrated Trajectory) (R. Draxler,
Stunder, Rolph, Stein, & Taylor, 2020; R. R. Draxler & Hess, 1998). Developed by
NOAA’s Air Resources Laboratory, HYSPLIT is a heavily vetted and frequently
used tool for calculating the trajectory and dispersion of chemicals through the
atmosphere (Stein et al., 2015). Over its 30 years of development, researchers have
used HYSPLIT to model the transport and dispersion of emissions from coal-
fired EGUs (Henneman, Choirat, Ivey, Cummiskey, & Zigler, 2019; Henneman,
Choirat, & Zigler, 2019; Henneman, Mickley, & Zigler, 2019), facility-level pollution
(Grainger & Ruangmas, 2017; Hernandez-Cortes & Meng, 2020), smoke plumes
24
from forest fires (Stein, Rolph, Draxler, Stunder, & Ruminski, 2009), volcanic
ash (Stunder, He↵ter, & Draxler, 2007), mercury (Ryaboshapko et al., 2007), and
methane emissions from the Marcellus Shale play (Ren et al., 2019).
HYSPLIT requires pre-generated, gridded meteorological data, for which
we use the 32-km resolution NARR (North American Regional Reanalysis) data
from NOAA (North American Regional Reanalysis, 2006). We then model particle
trajectories for the NOx and SO2 emissions of every coal-fired EGU above 25 MW36
in the contiguous U.S. every day during January 2005 and July 2005. As described
in Data, unit-level emissions releases and stack heights come from CAMD (2020).37
Modeling emissions for January and July allows us to depict the di↵erences in
emissions and meteorology between winter and summer. We model particles’ paths
for 48 hours after their release.
We illustrate the output of HYSPLIT in Figure 6. The algorithm calculates
particle paths for hundreds of particles emanating from a specific EGU’s three-
dimensional location (longitude-latitude-height) at a given date-time of release.
2.4.5 Pollution Mobility: Results. From Figure 6 it is clear that
the two plants’ emissions leave their source counties within hours—and a large
amount of the plants’ emissions leave their source states within 24 hours of being
released. This quick departure from the source counties and states occurs in both
January and July. Figure 6 also highlights the fact that distance and direction for
pollution transport may vary significantly by season (even for a single plant).
36Our threshold of 25 MW is a common cuto↵ in regulation—e.g., the Acid Rain Program, the
Mercury and Air Toxics Standards (MATS), and the Cross State Air Pollution Rule (CSAPR)
each focused on EGUs of 25 megawatts or greater.
37One shortcoming of this HYSPLIT-driven approach is that it does not model chemical
reactions in the atmosphere (e.g., formation of PM2.5 or ozone).
25
2.4.5.1 Transporting Pollution Away from Sources. We now
formalize and generalize these insights concerning the export and transport of coal
emissions. For each coal plant, we calculate the share of that plant’s emissions that
travel beyond the plant’s county and state (for each hour after the initial release).
We separately calculate these plant-hour shares by administrative unit (county
vs. state), month (January vs. July), and pollutant (NOx vs. SO2). For instance,
in January 2005, 32.9% of NOx emissions from coal plant “3470” (depicted in
Figure 6c) left the plant’s county within one hour after the initial release. However,
none of these NOx emissions left the plant’s state (Texas) within one hour after
release. Four hours after release (still for plant 3470 in January 2005): 94.6%
of NOx emissions were outside the plant’s county, and 11.0% were outside the
plant’s state. As Figure 2d illustrates, plant 3470 is located upwind of much of
its county and even more of its state (Texas), so it is reasonable that it would take
time for its emissions to leave both jurisdictions. For plants that have been more
strategically located—e.g., plant 1378 in Figure 2b was ideally sited to reduce in-
county emissions—most of the emissions immediately leave the county: by one hour
after release, 69.5% of its emissions had already left the county.
Figure 7 displays our pollution-mobility results for all coal plants operating
in 2005. The four subplots separate the results by administrative level (top panel
(A): county ; bottom panel (B): state) and pollutant (left pane: SO2; right pane:
NOx). The x-axis shows the number of hours that have passed since the initial
emissions release; the y-axis gives the share of particles that have left the source’s
administrative unit. The thin lines in each figure depict individual coal plants’
monthly averages (black for January; light red for July). The heavy lines with dots
26
provide the average across all plants for each hour, weighted by each plant’s mass of
emissions.
The implications of Panel A of Figure 7 are clear. For most coal plants
in the U.S., nearly all of the plants’ pollution leaves these plants’ home counties
within six hours of the release. This fact holds in both seasons, but the departure is
even faster in winter months (since these months have, on average, stronger winds).
Panel B paints a similar picture for the timing of emissions’ departures from source
states: within 12 hours of release, 50%–85% of emissions leave the state of origin—
and for many plants, this number is closer to 90% (again, particularly in the
winter). Figure 7 demonstrates that pollution transport—a result of the geography
of plant sitings, stack heights, and local meteorology—-creates a substantial
wedge between the sources that export coal-based emissions and the downwind
counties/states that receive the emissions.
2.4.5.2 Decomposing the Sources of Local Pollution. For a
complementary perspective, we use HYSPLIT to decompose the sources of local,
coal-based pollution. We separate the total coal-EGU-generated pollution within a
county by the sources of the pollution. Specifically, we classify emissions sources by
(1) whether the sources are in the same county, (2) whether the sources are in the
same state, and (3) whether the sources’ counties are in attainment (compliance)
with national ambient air quality standards (NAAQS).38 In 2005, 485 counties were
out of attainment with the NAAQS (i.e., non-attainment) for at least one of the six
criteria pollutants.39
38Note that we first sum all coal-generated emissions that HYSPLIT locates within a county.
This sum ignores where the emissions originated—so long as HYSPLIT places the emissions in the
given county. We then decompose this sum by the emissions’ sources.
39Our HYSPLIT analysis focuses on 2005, so we only consider counties’ 2005 attainment status.
Counts of violations by standard: 8-hour O3 (1997), 422; PM2.5(1997), 208; PM10 (1987), 49; CO
27
Figure 8 illustrates the results of a source-based decomposition with
pollution sources separated into five groups: (1) the county’s own emissions, (2)
attainment counties within the same state, (3) non-attainment counties within the
same state, (4) attainment counties in a di↵erent state, and (5) non-attainment
counties in a di↵erent state. Panel A shows the results of the decomposition for
SO2 emissions; Panel B for NOx. In each panel, we repeat the exercise by ‘receptor’
county attainment status (attainment on left; non-attainment on right) and season.
Given our previous finding that nearly all emissions leave their origin county
within six hours, it is unsurprising that a tiny share of a county’s coal-EGU-based
emissions comes from the county’s own EGUs.40 However, it is rather remarkable
just how small the share of own-county emissions are relative to the contributions
of other sources: the own-county shares (in black in Figure 8) range from 1% to
8%. While still small, it is notable that the share of own-county emissions is much
larger for non-attainment counties than for attainment counties. This finding is
consistent with coal plants’ emissions (or existence) contributing to non-attainment
designations. However, the vast majority of coal-EGU-based emissions in non-
attainment counties appears to originate in other counties and states.
Across all counties, regardless of attainment state, the vast majority of
emissions originate in other states—i.e., 65% to 85% (the sum of the yellow and
orange segments in Figure 8). While this result may at first seem mechanical—
each county only has one own state and 49 other states—it requires substantial
transmission of other states’ emissions. Without sizable cross-boundary
(1971) 100; SO2(1971), 10; lead (1978), 2. A county can violate multiple standards (i.e., there
were 702 violations in 485 counties).
40This result is also driven by the fact that many counties do not have any coal EGUs of their
own.
28
transmission, counties and states would pollute themselves and not others. This
result reiterates the importance of long-distance transport of coal pollution.41
Coal pollution is indeed highly exportable—even at the scale of states (and
beyond). Along with our previous result of strategic downwind siting, this result
closes the loop on our hypothesis of strategic export of negative externalities.
2.5 Discussion and Conclusion
In this paper, we empirically investigate the hypothesis that decision-
makers have historically sited a major class of polluters—coal-fired power plants—
to strategically export their negative externalities (pollution) downwind. After
documenting coal EGUs’ tendency to locate near borders, we formally test whether
coal EGUs have been disproportionately sited nearer to the downwind borders of
the counties and states. Our test finds large and significant evidence that decision-
makers have located coal EGUs to reduce the area downwind of the plants within
the counties and states that contain these plants. Our placebo test—using natural
gas EGUs—does not exhibit this behavior.
Showing that local decision-makers have disproportionately located coal
EGUs downwind within counties and states is a necessary condition for our
strategic export hypothesis. For su ciency, we must also show that coal-based
pollution is exportable. Toward this goal, we use a particle-trajectory model
(HYSPLIT) that illustrates the extreme mobility of coal-based emissions. Our
results suggest that nearly all coal EGUs’ pollution leaves the source counties
41Also potentially of interest in Figure 8: the di↵erence between the emissions sources for
attainment and non-attainment counties (the left and right halves of the figure). In non-
attainment counties, the plurality (41%–50%) of coal-based emissions originates in non-attainment
counties in other states. For attainment counties, a larger share comes from attainment counties
in other states.
29
within six hours of the release. Within 12 hours of release, 50%–85% of emissions
leave the state of origin—and for many plants, it is closer to 90%.
Jointly, these two pieces of evidence demonstrate that many local decision-
makers historically located coal EGUs to enjoy their local benefits without facing
their costs.
While these results focus on historical siting decisions, they have important
implications for current environmental policy. In contemporary federalist
regulations—e.g., the Clean Air Act and the Cross-State Air Pollution Rule
(CSAPR)—dealing with cross-boundary pollution requires more coordination and
resources than pollution that remains in (and mainly a↵ects) its source county and
state.42 Strategically sited polluters emitting highly transportable pollution from
tall smokestacks43 create a complex and challenging regulatory situation.
The shapes of some non-attainment areas—areas deemed out of compliance
with the Clean Air Act air-quality standards—reflect this complexity. Some non-
attainment areas knit together whole counties with adjacent pieces of other counties
and “islands” surrounding major point sources (often coal plants). For example,
Figure 9 shows the Huntington-Ashland non-attainment area (which violated the
1997 PM2.5 standard) in light orange. The Huntington-Ashland non-attainment
area—a single non-attainment area—covers nine counties (5 whole counties; 4
partial counties) across three states (Kentucky, Ohio, and West Virginia). Six of
the counties form a contiguous area. The remaining three counties (two in OH; one
in WV) are islands—where each island circumscribes multiple coal plants (circled,
42To a degree, these challenges in federalist regulation of local pollutants mirror the
international community’s coordination failures for limiting greenhouse gases.
43In 2018, the average height of a smokestack attached to a coal-fired EGU in the U.S. was
approximately 500 feet, and the maximum height was 1,038 feet (calculated from CAMD (2020)
data).
30
red dots). This complex non-attainment area required substantial coordination
across counties and states, source-attribution modeling, and federal oversight.44
The Huntington-Ashland non-attainment area o↵ers a single example of the
complexities that can result from federalist environmental policy.
Figure 10 depicts a related challenge created by cross-boundary coal-based
emissions (here, NOx). In 2005, Shelby County (Tennessee) was designated as a
non-attainment due to its violation of the 8-hour Ozone standard of NAAQS.45
Panel A of Figure 10 shows all the coal-plant-generated NOx emissions that
eventually arrived in Shelby County during July 2005 (as estimated by HYSPLIT).
We draw emissions’ paths to Shelby County in grey; non-attainment counties (in
2005) are cross-hashed in red. We outline Shelby County in bright yellow. The
figure illustrates that Shelby County’s emissions originate throughout a broad
geographic swath, stretching from Texas to Kansas to Indiana to Georgia, including
attainment and non-attainment counties.46 Overall, Panel A emphasizes the fact
that large regions of the country a↵ect one locality’s air quality—a challenge for a
federalist system with many small units.
Panel B of Figure 10 zooms in on the region surrounding Shelby County,
Tennessee (the “zoomed” area is approximately 900 km east-west and 600 km
north-south). Counties’ fill color in Panel B matches their contribution (as a share)
to Shelby County’s coal-generated NOxin July 2005. Panel C provides both the
legend for the colors and the histogram for the distribution of counties’ shares of
44Figure A5 provides an example of another “complex” non-attainment area contained within a
single state (the non-attainment area containing Evansville, Indiana).
45NOx, which we consider in Figure 10, is a precursor of both Ozone and PM2.5.
46Notably, the emissions that eventually make their way to Shelby County come from a wide
range of directions—emphasizing the importance of the temporal variation in prevailing wind
directions embedded in HYSPLIT.
31
contribution to Shelby County’s NOx. Remarkably, although Shelby County had
an operating coal plant in 2005 (and was out of attainment), the coal plant in
Humphreys County, TN (a county which was in attainment in 2005) contributed
more to Shelby County’s NOx than did Shelby County’s own plant. Further, the
coal plant in Independence County, Arkansas (also an in-attainment county in
2005) contributed approximately the same amount of NOx emissions to Shelby
County as did Shelby County’s coal plant.47 As illustrated in Figure 10, the
vast majority of coal-based NOx emissions in Shelby County, Tennessee—a non-
attainment county—came from other states, and a majority of Shelby County’s
emissions originated from sources in attainment counties.
These two anecdotes highlight the challenges facing regulation and
coordination within federalist systems. The results in our empirical section confirm
that these cases and their challenges are not rare exceptions: Facing the spatial
patchwork of jurisdictions created by the federalist structure of the U.S., local
decision-makers have strategically sited polluters to export pollution. More broadly,
our results point to the potential for local governments’ actions to erode the
e ciency of federalist systems—and potentially suggest a more prominent role for
the federal government when externalities are exportable.
47Humphreys County, TN is home to the TVA’s Johnsonville Fossil Plant, a 1.5-gigawatt coal
power plant. Independence County, AR, houses Entergy Arkansas’s 1.7-gigawatt “Independence”
coal plant.
32
2.6 Figures
Panel A: Distance to nearest body of water Panel B: Generating-unit capacity
2018 operating/stand-by units, capacity ≥ 25 MW 2018 operating/stand-by units, capacity ≥ 25 MW
0.015 300
0.010 200
0.005 100
0.000 0
0.015 300
0.010 200
0.005 100
0.000 0
0.015 300
0.010 200
0.005 100
0.000 0
0.015 300
0.010 200
0.005 100
0.000 0
0 200 400 600 800 ≥ 1,000 0 100 200 300 400 ≥  500
Distance (m) Capacity (MW)
Figure 1. The distributions of EGUs’ distances to their nearest body of water (Panel A, left)
and EGUs’ generation capacities (Panel B, right) by fuel category (row and color).
33
Density
Count
Coal Gas Hydro. Solar/Wind
Coal Gas Hydro. Solar/Wind
(a) Plant 628 (b) Plant 1378
N N
W E W E
S S
(c) Plant 6113 (d) Plant 3470
N N
W E W E
S S
Figure 2. Upwind and downwind areas for four coal-fired generators. Dark, purple areas
denote the 90-degree downwind area from the plant’s location (the small, black diamond). Light
gray refers to upwind areas. The outlined shape depicts the plant’s county; the inset thumbnail
highlights the plant within its state. The purple arrow within the compass points in the direction
of the plant’s prevailing wind direction (North American Regional Reanalysis, 2006).
34
Panel A: Distance to nearest county border Panel B: Distance to nearest state border
2018 operating/stand-by units, capacity ≥ 25 MW 2018 operating/stand-by units, capacity ≥ 25 MW
0.6
0.06
0.4 0.04
0.2 0.02
0.0 0.00
0.6
0.06
0.4 0.04
0.2 0.02
0.0 0.00
0.6
0.06
0.4 0.04
0.2 0.02
0.0 0.00
0.6
0.06
0.4 0.04
0.2 0.02
0.0 0.00
0.6
0.06
0.4 0.04
0.2 0.02
0.0 0.00
0 5 10 15 20 ≥ 25 0 50 100 ≥ 150
Distance to nearest county border (km) Distance to nearest state border (km)
Figure 3. Empirical densities of the distributions of EGUs’ distances to their nearest county
(Panel A, left) or state (Panel B, right) border. The sample includes all operating and stand-by
EGUs with capacities  25 MW within the contiguous U.S. in 2018. The first five rows of colored
charts above separately produce the densities by fuel category. The final row reveals the density of
distance to the nearest border from a uniform grid of points covering the contiguous U.S.
35
Density
Density
Coal Gas Hydro. Solar/Wind Uniform US Grid
Coal Gas Hydro. Solar/Wind Uniform US Grid
100%
75%
50%
25%
0%
0%
25%
50%
75%
100%
Figure 4. The share of county borders (top) and state borders (bottom) that coincide with
bodies of water, by state. The states are sorted from smallest share of county-borders coinciding
with water (Colorado) to largest share (Maryland). Alaska and Hawaii are excluded. Figure 5
provides four example states (LA, OR, SC, and SD) from these calculations.
36
State border County border
Share water Share water
CO
WY
NM
KS
NV
IA
NE
OH
UT
MT
ND
SD
AZ
IN
IL
OK
MO
WV
OR
ID
TN
MN
VT
WI
MS
PA
TX
CA
NH
CT
AR
AL
MI
ME
NY
WA
GA
KY
NC
DC
VA
MA
FL
DE
SC
RI
LA
NJ
MD
(a) Louisiana (b) Oregon
(c) South Carolina (d) South Dakota
Figure 5. Examples of the output of our calculations of county and state borders that coincide
with bodies of water. Darker blue lines denote administrative borders (state and/or county)
that coincide with water; paler gray lines depict administrative borders that do not. Overall, our
algorithm for detecting where jurisdictional borders coincide with water appears to be successful.
37
(a) Plant 1378, January 2005 (b) Plant 1378, July 2005
(c) Plant 3470, January 2005 (d) Plant 3470, July 2005
Hours since release
0 12 24 36 48
Figure 6. Particle trajectory and dispersion in HYSPLIT for two plants (ORIS codes 1378
and 3470) during January 2005 and July 2005. For each day of the month, HYSPLIT models
420 particles starting at the latitude, longitude, and altitude of the plants’ chimneys. We track
particles for 48 hours after their initial release; particles’ colors denote the number of hours since
their emission. The plants correspond to Figures 2b and 2d.
38
Panel A: Percent of emissions outside of source′s county—by hours since emission
Weighted across plants by mass of SO2 emissions Weighted across plants by mass of NOx emissions
100% 100%
75% 75%
50% 50%
25% 25%
0% 0%
0 12 24 36 48 0 12 24 36 48
Hours since emission Hours since emission
Panel B: Percent of emissions outside of source′s state—by hours since emission
Weighted across plants by mass of SO2 emissions Weighted across plants by mass of NOx emissions
100% 100%
75% 75%
50% 50%
25% 25%
0% 0%
0 12 24 36 48 0 12 24 36 48
Hours since emission Hours since emission
Month of operation January July
Figure 7. The share of coal plants’ emissions that have left plants’ origin counties (top,
Panel A) or origin states (bottom, Panel B) by the number of hours that have passed since
the particles were released (as modeled by HYSPLIT). Each of the four subfigures contains two
months of emissions: January 2005 (black) and July 2005 (light, red). Thin lines depict individual
plants in a given month. Thick lines (decorated with hourly points) denote the monthly average
across plants (weighted by mass of emissions). The left column weights by SO2; the right column
by NOx. Di↵erences between the months capture seasonal di↵erences in meteorology and in the
distribution of generation. Sample: coal-fired generators   25 MW operating in Jan./July 2005.
39
Panel A: Sources of local coal-based particles, weighted by mass of SO2 emissions
Coal-fueled units in 2005 with capacity greater than 25 MW
Attainment counties Non-attainment counties
100%
75%
50%
25%
0%
January July January July
Panel B: Sources of local coal-based particles, weighted by mass of NOx emissions
Coal-fueled units in 2005 with capacity greater than 25 MW
Attainment counties Non-attainment counties
100%
75%
50%
25%
0%
January July January July
Location of emissions' source
Same county Other county in same state Other county in same stateSource county: In attainment Source county: Non-attainment
Other county in other state Other county in other state
Source county: In attainment Source county: Non-attainment
Figure 8. The Source-based decomposition of location, coal-based pollution. They described,
on average, where a county’s pollution come from based upon (1) the month (Jan. or July 2005),
(2) the county’s attainment status, and (3) the type of particle (SO2 or NOx). Particle trajectories
come from HYSPLIT. The five colors refer to five categories of pollution sources by the EGU
source’s location (described in the legend). Panel A focuses on SO2 emissions; Panel B on NOx.
Sample: coal-fired generators   25 MW operating in Jan./July 2005.
40
OH
KY WV
Non-attainment area Coal-fueled power plant County border State border
Figure 9. This map illustrates the complexity of the Huntington-Ashland non-attainment area
(orange), which covers nine counties (5 whole; 4 partial) across three states. Six of the counties
form a contiguous area. The remainder of the non-attainment area is comprised of “islands” that
cover six coal plants (red-circled dots) in three di↵erent counties (two in OH; one in WV). This
non-attainment area is for the 1997 PM2.5 standard. Figure A5 depicts another example of a
“complex” non-attainment area (Evansville, Indiana).
41
A.
NAAQS Status (2005)
B. Non-attainment In attainment
C.
20
15
10
Shelby Couny’s own coal-based NOx
5
0
0.0% 2.5% 5.0% 7.5% 10.0%
Pct. of coal-based NOx emissions
From source counties to Shelby Co., TN
Figure 10. This figure shows the origins, paths, and shares of all coal-plant-based NOx
emissions that eventually enter Shelby County, TN during July 2005 (modeled by HYSPLIT).
In 2005 Shelby County, TN was in violation of the 8-hour Ozone NAAQS (NOx is an Ozone
precursor). Subfigure A’s grey coal-based NOx trajectories reveal that the sources of coal-based
NOx emissions in Shelby County include many states (from TX to GA to IL) both in attainment
and non-attainment counties. Non-attainment (for any NAAQS) are hashed in red. B zooms in
on the region surrounding Shelby County (⇠900 km ⇥ 600 km). Counties are colored (filled) by
the share of coal-based NOx emissions that they contribute to Shelby County, TN. C provides the
legend for B’s colored shares and plots the distribution of these shares—the x axis is the share of
Shelby County’s coal-generated NOx emissions that each county contributes.
42
Count (N. counties)
2.7 Tables
Coal-fueled plants Natural-gas-fueled plants
(1) (2) (3) (4) (5) (6)
All Post-CAA Pre-CAA All Post-CAA Pre-CAA
Panel a: Siting strategically within county
Count 515 286 229 1,258 995 263
Count strategic 297 165 132 612 482 130
Percent strategic 57.67% 57.69% 57.64% 48.65% 48.44% 49.43%
Fisher’s exact test of Ho: In-county downwind area   upwind area
Under Ho: E[Percent strategic: County] = 50%
P -value 0.0003 0.0054 0.0122 0.8381 0.8448 0.5974
Panel b: Siting strategically within state
Count 515 286 229 1,258 995 263
Count strategic 279 152 127 575 466 109
Percent strategic 54.17% 53.15% 55.46% 45.71% 46.83% 41.44%
Fisher’s exact test of Ho: In-county downwind area   upwind area
Under Ho: E[Percent strategic: State] = 50%
P -value 0.0321 0.1574 0.0563 0.9989 0.9788 0.9978
Panel c: Siting strategically within both county and state
Count 515 286 229 1,258 995 263
Count strategic 182 98 84 310 249 61
Percent strategic 35.34% 34.27% 36.68% 24.64% 25.03% 23.19%
Fisher’s exact test of Ho: Downwind area   upwind area in county and state
Under Ho: E[Percent strategic: County ^ State] = 25%
P -value <0.0001 0.0003 0.0001 0.6258 0.5049 0.7710
Table 1. Testing strategic location: Comparing up- and down-wind areas for coal
and natural gas plants—before and after the Clean Air Act (CAA) of 1963. We define a
plant’s location as “strategic” if the downwind area within its home county (or state) is
less than its upwind area within its home county (or state). We calculate downwind and
upwind areas based upon 90-degree right triangles with a vertex at the plant pointing up-
or down-wind based upon the locally prevailing wind direction. Figure 2 illustrates this
calculation. The columns that reference Post-/Pre-CAA refer to whether the plant’s first
year of operation was after or before the Clean Air Act of 1963. Sources: Emissions &
Generation Resource Integrated Database (2018) and authors’ calculations.
43
CHAPTER III
THE ENVIRONMENTAL COST OF LAND USE RESTRICTIONS
This chapter is co-authored with Mark Colas. It is published as: “The
Environmental Cost of Land Use Restrictions.” Quantitative Economics, 2022.
13(1): 179-223. I had a crucial role in developing the project, the statistical
estimation, and writing the paper. Additionally, I formulated many of the
(ultimately successful) responses to reviewers that resulted in the paper being
accepted.
3.1 Introduction
Higher levels of carbon dioxide (CO2, hereafter “carbon”) are associated
with a multitude of global environmental issues. The amount of energy a household
uses, and therefore the amount of carbon emissions a household is responsible
for, depends partially on where the household lives.1 For example, Oklahoma
City has high summer temperatures and relies heavily on coal-fired power plants
while San Francisco has a moderate climate and uses electricity produced largely
by hydroelectric plants. Households in Oklahoma City therefore consume large
quantities of air conditioning using electricity generated by carbon-intensive power
plants. Conversely, households in San Francisco use less electricity generated
from more carbon-e cient power plants. As a result of these di↵erences in
electrical power plant technologies and climate, government policies that shape
the distribution of households across cities may have important implications for
national carbon emissions.
1For example, Glaeser and Kahn (2010) show that the median household in Memphis is
responsible for nearly twice the amount of carbon emissions as the median household in San
Francisco.
44
Local land use restrictions that limit urban population density are often
employed to improve the “greenness” of a city. However, these restrictions
potentially limit population growth in many of the most desirable cities (Glaeser,
Gyourko, & Saks, 2005). Additionally, Glaeser and Kahn (2010) document that
cities with lower average household carbon emissions also have tighter land use
restrictions, suggesting that these restrictions may discourage people from living in
lower carbon-emitting cities. The goal of this paper is to quantify the e↵ect of local
land use restrictions on national household carbon emissions.2
To this end, we specify and estimate a spatial equilibrium model wherein
power plant technologies and energy demand vary across cities. Heterogeneous and
imperfectly mobile households choose which city to live in and how much housing,
electricity, natural gas, and fuel oil to consume. Rents and wages are determined
in equilibrium by the location and consumption choices of these households.
Furthermore, cities vary in the tightness of local land use restrictions. All else
equal, tighter land use restrictions imply higher costs of living, which will reduce
the incentives for households to live in these cities.
Our model allows a household’s carbon emissions to vary across cities for
two main reasons. First, to reflect climate di↵erences, we allow the utility benefits
derived from the use of electricity, natural gas, and fuel oil to vary by city. Second,
due to spatial variation in the technologies employed in power plants, the carbon
intensity of electricity production varies across cities. Land use restrictions are
tighter in cities with more carbon-e cient power plants and lower energy demand.
Thus, households will be incentivized to live in “dirtier” cities.
2We take the relationship between land-use restrictions and carbon emissions as given and
examine the quantify the e↵ect of land use regulations on national carbon emissions. We leave it
to future work to determine why carbon-e cient cities generally have tighter land-use restrictions.
45
For our analysis, we combine data from three main sources. We use the US
Census and American Community Survey (ACS) for data on households’ city of
residence, income, and rents, as well as expenditures on electricity, natural gas, and
fuel oil for a large sample of households.3 We combine these household expenditure
data with state-level energy prices from the Energy Information Association (EIA)
to calculate implied household usage of each of these three energy types. Next, we
use data from the Emissions & Generation Resource Integrated Database (eGrid)
for power plant locations, output, and CO2 emissions.
Following Glaeser and Kahn (2010), we use these data to document how
the amount of carbon a household emits depends on the city in which they reside.
One issue is that di↵erences in emissions across cities may, to some extent, reflect
sorting of households with di↵erent propensities to use energy. Therefore, the
observed di↵erences in average emissions across cities may not reflect the direct
e↵ect of location on household emissions. In response to this issue, we employ the
semi-parametric selection correction approach introduced by G. B. Dahl (2002) to
estimate selection-corrected predicted energy usage and carbon emissions associated
with living in various US cities.
We document substantial variation in carbon emissions across cities.
For example, we estimate that if a household resides in Memphis, they would
produce three times the annual carbon emissions had they resided in Honolulu.
Additionally, we show that household carbon emissions are negatively correlated
3Throughout the paper we use the 70 largest Core Based Statistical Areas as our definition of
cities. The rest of the United States is aggregated up to the census division level.
46
with a standard measure of land use restrictions, the Wharton Land-Use
Regulation Index—greener cities tend to have tighter land use restrictions.4
Next, we combine these estimates of predicted energy usage with our
other data sources to estimate our spatial equilibrium model. We estimate the
parameters of household utility using the two-step estimator introduced by Berry,
Levinsohn, and Pakes (1995) with data on household locations from the Census
and ACS and our estimates of predicted energy usage.5 We use data from eGrid to
estimate the carbon emissions associated with electricity production across regions
and estimates from Saiz (2010) to calibrate the parameters of housing supply curves
as a function of land use restrictions.
California legislators recently voted down SB-50, a bill that would have
relaxed local land use restrictions in California cities.6 We use our estimated model
to simulate the e↵ects of such a policy. Specifically, we set land use restrictions in
California cities to the level faced by the median urban household in the United
States. Due to the moderate climate and carbon-e cient power plants, California
cities are associated with remarkably low carbon emissions. However, land use
restrictions are tight—the San Francisco CBSA is in the 86th percentile of the
Wharton Index while Los Angeles CBSA is the 78th.7
4The Wharton Land-Use Regulation Index was created from a survey sent to 6,896
municipalities across the US, with questions that range from how many regulatory boards one
must clear before construction to city-specific density and open space requirements.
5This approach has been utilized in a spatial setting by e.g. Diamond (2016), Piyapromdee
(2019), and Colas and Hutchinson (2021).
6SB-50 was referred to as the “More HOMES Act” (Housing, Opportunity, Mobility, Equity,
and Stability). The bill focused on the relaxation of density restrictions and reducing the number
of areas zoned for single-family homes, particularly in areas near public transit and in commercial
areas.
7Quigley and Raphael (2005) write, “California represents the most extreme example of
autarky in land-use regulations of any U.S. state.”
47
As a result of relaxing these restrictions, we find that the long-run
population in California cities increases. As demands for natural gas and electricity
are lower in California, national usage of natural gas and electricity drop by 0.3%
and 0.5%, respectively. Overall, this leads to a 0.6% decrease in national household
carbon emissions, associated with a decrease in the social cost of carbon of $310
million annually.8 This change is driven by a decrease in energy usage and an
increase in the proportion of total electricity consumption coming from cleaner
power plants in California. Furthermore, given that California cities have high
productivity levels, this leads to increases in average income for both unskilled and
skilled workers.
Next, we entirely remove the existing negative correlation between land
use restrictions and carbon emissions by setting the Wharton Index in all cities
to the level faced by the median urban household in the US. Households respond
by leaving the Midwest and South and moving to the West Coast and Northeast.
Demand for natural gas is higher and electricity demand is lower in the cold
Northeast. These population shifts therefore increase national gas usage and
decrease total electricity usage. Overall, these changes in the spatial distribution
of households and their energy consumption lead to a nearly 3.5% drop in national
carbon emissions, implying a drop in the social cost of carbon of $1.7 billion
annually.
The main goal of this paper is to better understand the relationship between
di↵erences in land use restrictions across cities and national household carbon
emissions. However, household energy consumption also contributes to local
pollution. Therefore, we also use the model to analyze the e↵ects of relaxing land
8For the social cost of carbon calculations, we use the estimate of the social cost of carbon in
the year 2020 from Nordhaus (2017) of $44.4 per metric ton of CO2 in 2020 dollars.
48
use regulations on exposure to local pollutants. We focus on particulate matter
of 2.5 micrometers or smaller (PM2.5), a common measure of local air quality and
that has been at the helm of US air quality regulation for the last two decades.9
Similar to household carbon emissions, emissions of PM2.5 vary across space due
to di↵erences in energy consumption and the spatial distribution of power plants.
However, unlike carbon emissions, emissions of local pollutants di↵erentially a↵ect
air quality across cities. We use the Intervention Model for Air Pollution (InMAP)
source-receptor matrix (Tessum et al., 2017) to map electricity production to
ambient air concentration of PM2.5 across locations in the United States.
We find that the air quality in most US cities improves as a result of
relaxing land-use restrictions in California. This result reflects that households use
less electricity in California and that power plants used in California, in addition
to being carbon-e cient, emit low levels of local pollutants.10 However, PM2.5
exposure for the average household increases slightly, as there is an increase in the
number of households in the relatively polluted Southern California.
Related Literature Our paper is related to two recent papers, Hsieh and
Moretti (2019) and Herkenho↵, Ohanian, and Prescott (2018), who find that
relaxation of land use restrictions in high-productivity cities would lead to large
9Exposure to fine-grained particulate matter is associated with various detrimental health and
economic outcomes such as (but not limited to): higher infant mortality (Chay & Greenstone,
2005), increased cognitive decline in seniors (Ailshire & Crimmins, 2014), and reduced property
values (Chay & Greenstone, 2003).
10These reductions in PM2.5 concentration in most cities can be thought of as a “co-benefit”
of the reduction in carbon emissions. See Aldy et al. (2020) for a discussion of co-benefits in air
quality regulation.
49
increases in GDP.11 Our model focuses on an entirely di↵erent set of outcomes and
incorporates energy demand, energy production, and emissions. Households in our
model are di↵erentiated in terms of education, family composition, age, race, and
the state in which they were born. As a consequence, our model allows for rich
substitution patterns across cities and allows us to analyze how changes in land use
restrictions a↵ect both the population and demographic composition across cities.
Our work builds on the descriptive findings in Glaeser and Kahn (2010)
(GK). GK measures predicted carbon emissions for households in di↵erent
cities across the country and documents a negative correlation between carbon
emissions and land use restrictions. Relative to GK, the primary contribution
of this paper is to build and utilize a structural model to quantify the e↵ects of
land use restrictions on national carbon emissions. National carbon emissions
are determined in equilibrium; household locational sorting, energy demand, and
housing supply/demand all determine the extent to which land use restrictions
a↵ect national carbon emissions. Estimating the e↵ects of a counterfactual change
in land use restrictions necessitates a structural equilibrium model.
This paper is also related to a large literature on how exposure to
environmental externalities varies by location (See Chay and Greenstone (2005);
Currie, Davis, Greenstone, and Walker (2015); Muehlenbachs, Spiller, and Timmins
(2015); or Fowlie, Rubin, and Walker (2019), for example). In our setting, exposure
to carbon emissions is independent of the household’s location—the e↵ects of
carbon emissions and thus climate change are felt globally, not just locally.
11Albouy and Stuart (2014) also find that relaxation land use restrictions would lead to a large
redistribution of households across cities, but are less concerned with the e↵ect of these changes
on national productivity.
50
However, the amount of carbon dioxide emitted by a household depends on where
the household is located.
Another related literature analyses the e↵ects of population density on
the local carbon emissions (See Fragkias, Lobo, Strumsky, and Seto (2013); or
Jones and Kammen (2014), for example). Other recent research uses simulation
methods to analyze the e↵ects of various land use restrictions and transportation
policies on within-city locational sorting and local carbon emissions (See Larson
and Yezer (2015) or Borck (2016), for example). Our work di↵ers from these two
themes in that we focus on the sorting of households across cities, rather than
the determinants of emissions within a city.12 This paper is also related to Fan,
Fisher-Vanden, and Klaiber (2018), who use a spatial equilibrium model to analyze
the e↵ects of climate change on household location choices and welfare. Finally,
in other complementary work, Mangum (2016) analyzes the e↵ects of housing and
land stock allocations on carbon emissions.13
3.2 Data
This paper utilizes individual data on household sorting and energy
expenditures from the Census and ACS, detailed data on power plants from eGrid,
and state level energy pricing data from the EIA. In what follows, we briefly
describe each of the main data sources and how they are used in our analysis.
Further details on the data can be found in Appendix B.0.1.
12Gaigné, Riou, and Thisse (2012) argue that analysis of the e↵ects of density-increasing policies
on carbon emissions must account for relocation of households and firms across cities.
13Compared to Mangum (2016), our paper focuses more on the households sorting across cities
and energy usage. Mangum’s focus on the housing construction process allows for a more nuanced
understanding of how di↵erent land use restrictions a↵ect the housing stock.
51
CBSA Level Data We utilize Core Based Statistical Areas (CBSAs) as our
definition of a geographic area. CBSAs correspond to distinct labor markets and
are the O ce of Management and Budget’s o cial definition of a metropolitan
area. To measure land use restrictions in each CBSAs we utilize a standard
metric developed by Gyourko, Saiz, and Summers (2008), the Wharton Land-
Use Regulation Index (WLURI). This index was created from a survey sent to
6896 municipalities across the US, with questions that range from how many
regulatory boards one must clear before construction to city-specific density and
open space requirements. A higher value of the Wharton-Index implies more
stringent restrictions and higher costs of developing land and is associated with
more inelastic housing supply curves (e.g. Saiz (2010), Albouy and Ehrlich (2018),
or Diamond (2016)).
Household Data We use household-level data from the US Integrated Public
Use Microdata Series (IPUMS); we utilize the 1990 Census, the 2000 Census,
5% five-year American Community Survey (ACS) from 2006 - 2010, and 5% five-
year American Community Survey (ACS) from 2013 - 2017 (Ruggles et al., 2010).
Since our model contains a rich-level of household heterogeneity, a large data-set is
imperative for our analysis. IPUMS provides information on yearly, household-level
expenditures data on natural gas, electricity, and fuel oil in addition to information
on demographics, location, and housing expenditures.14
Our model is concerned with emissions generated at home, therefore, we
focus on three primary energy types: natural gas, electricity, and fuel oil.15 We
14Renters and households living in multi-family homes may not pay for their own energy. We
describe how we correct for this in Appendix B.0.1.4.
15GK also impute emissions produced by cars. They find that di↵erential emissions from cars
are less important than di↵erences in emissions from electricity and natural gas in explaining total
52
combine data on expenditures on these three energy types with state level price
data from the US Energy Information Administration (EIA) to impute household
consumption of natural gas, electricity, and fuel oil.16
Power Plants and Emissions For each of the three energy types we
consider, we use linear conversion factors to map usage of each energy type to
carbon emissions. We assume 117 lbs of CO2 are emitted per thousand cubic
feet of natural gas consumed and 17 lbs of CO2 are emitted per gallon of fuel oil
consumed. Carbon emissions associated with electricity usage depend on where the
electricity is consumed—electricity used in areas that generate electricity via coal
plants will lead to more carbon emissions than in areas that rely more heavily on
renewable sources.
We therefore utilize power plant-level data from the Emissions & Generation
Resource Integrated Database (eGRID). These data provide information on the
location, primary fuel input, emissions rate, and total megawatt hours of electricity
generated for every power plant in the US. To assign households to power plants,
we use the nine North American Electric Reliability Council (NERC) regions.17
These regions can be thought of as closed electricity markets, as transmissions of
electricity within a region is common but electricity is rarely transferred across
regions (Glaeser & Kahn, 2010; Holland & Mansur, 2008).
di↵erences in emissions across cities. Furthermore, emissions from driving calculated in GK are
strongly correlated with total household emissions from other sources (⇢ = 0.56) and a decrease
in population density. If removing land use restrictions increases city density, this will also lead
to decreases in emissions from driving as well. Therefore, including emissions from driving in our
analysis would likely strengthen our main conclusions.
16https://www.eia.gov/state/seds/
17We omit the region for Alaska since no city in our model is in Alaska.
53
We calculate the emissions factor associated with each NERC region as the
weighted average CO2 emissions per megawatt hour of electricity of all plants in
the NERC region. The emissions factors range from roughly 800 to 1550 lbs of CO2
emitted per megawatt hour of electricity consumed.18 All CBSAs within a NERC
region have the same CO2 conversion factor.
For information on local pollutants, we employ data from the National
Emissions Inventory (NEI) and the EPA’s Air Quality System (AQS) data. The
NEI contains information about power plants such as stack height and emissions
velocity, and emissions of various local pollutants such as PM2.5. We use these data
as inputs to construct a “pollution-transfer” matrix, which maps electricity usage
in any given city to changes in ambient air quality in all other cities.19 The AQS
data provide hourly levels of total particulate matter by city. We average across
all hours in 2017 within each CBSA to obtain our measure of local average PM2.5
concentration.20
3.3 Descriptive Statistics
In this section, we calculate selection-corrected predicted household usage
of electricity, natural gas, and fuel oil usage across cities and the associated carbon
emissions. We focus on results calculated using data from 2017; earlier years are
primarily used for estimation of parameters in the structural model (described in
detail in Section 3.5).
18For the full distribution of emissions factors, see Section B.0.1.3.
19The pollution-transfer matrix and its construction are described in detail in Sections 3.4.2 and
B.0.1.10, respectively. The pollution-transfer matrix maps total energy production in each NERC
region to ambient air concentration in all cities in the model.
20To obtain census region average PM2.5 concentrations, we average over readings for all
counties that are not part of the CBSAs in the given region.
54
Our goal is to isolate the role of a household’s location on their energy
usage and therefore carbon emissions. This will allow us to understand how the
distribution of households – and therefore policies that a↵ect the distribution of
households – interact with national carbon emissions. We therefore construct a
measure of predicted energy usage per household in each CBSA, controlling for
di↵erences in household composition, demographics, and unobserved di↵erences in
propensity to consume energy. First, we calculate each household’s imputed energy
usage in natural gas, electricity, and fuel oil as their reported expenditure on each
of these energy types divided by the state-level price of each energy type. We then
employ the selection-correction method developed by G. B. Dahl (2002) to compute
the selection-corrected predicted usage of each energy type in each city.21
With the predicted per-household energy use in hand, we can calculate
predicted carbon emissions for each CBSA.22 We multiply the selection-corrected
predicted usage for each fuel type with the respective emissions factor. As discussed
in Section 3.2, we assume a constant emissions factor for fuel oil and natural gas.
The emissions factor for electricity use varies across NERC regions.23
3.3.1 Predicting Energy Usage Across Cities. Consider the
following equation for household i’s usage of energy type m conditional on living
in location j:
Em m m mij = ↵j +  j Xi + ui , (3.1)
21The results with no selection correction are included in Appendix B.0.2.2.
22We repeat this analysis with methane emissions in Appendix B.0.2.9.
23The emissions factor for each NERC region is displayed in Appendix B.0.1.3.
55
where Emij is household i’s usage of energy type m, conditional on living in
location j, ↵mj is a CBSA-specific intercept term, Xi is a vector of household i’s
observable characteristics,  mj is a vector of parameters which varies by location
j, and umi represents household i’s idiosyncratic propensity to use energy type
m, representing, for example, household i’s unobservable preferences for using air
conditioning.24
One di culty with estimating (3.1) is that households may sort across
locations based on their idiosyncratic propensity to use energy such that umi is not
mean-zero conditional on households’ chosen locations. For example, households
with a low tolerance for cold temperatures might avoid living in cities with cold
weather, and may also have a greater propensity to use heating and therefore
natural gas. This would induce a correlation between the unobserved propensity
to use natural gas and the probability of living in cold cities. Concretely, let
Vij = V̄ (Xi, Bi) + "ij represent household’s i’s return for living in city j,
where V̄ (·) is a component of utility which depends on household i’s observable
characteristics Xi and the birth state of the household head, Bi, and "ij represents
household i’s idiosyncratic preference for living in location j.25 A household
chooses to live in location j if it provides the highest return, that is if j =
argmaxj0 (Vij0). If E [umi "ij] 6= 0, then this will induce selection on unobservables:
⇥ ⇤
E umj |j = argmaxj0 (Vij0) 6= 0. This would occur, for example, if people who prefer
24This term could also vary by location j and be written as um. We have written it as a
ij
household level term rather than a household by location level term for expositional purposes.
25Importantly, the household head’s birth state is assumed to not di↵erently a↵ect the
households energy usage. As such, birth state serves as an exclusion restriction which helps to
identify selection on unobservables in the outcome equation. One concern with using birth state
as an exclusion restriction is that the climate in which an individual grew up might influence
their preferences for energy usage as an adult. In Appendix B.0.2.1, we consider alternative
specifications with controls for average temperature in the state where the household head was
born. The results are qualitatively similar.
56
to live in Houston also have stronger preferences for using air conditioning. We will
⇥ ⇤
refer to E umj |j = argmax (Vij0) as the “selection bias” term.
To deal with this selection issue, we employ a semi-parameteric selection
correction based on the method proposed by G. B. Dahl (2002) (henceforth
“Dahl”). Dahl shows that there exists a function that maps the household’s choice
probabilities to the selection bias term. Concretely, let PiJ give the vector of the
household’s choice probabilities for all cities in the set J . Then there exists a
⇥ ⇤
function Mmj (·), such that Mmj (P m 26iJ) = E uj |j = argmaxj0 (Vij0) . Therefore, the
selection bias can be controlled for if the econometrician controls for the function
Mmj (·) such that the estimating equation becomes
Emij = ↵
m
j +  
m
j Xi +M
m m
j (PiJ) + ûi . (3.2)
Dahl notes that full estimation of (3.2) is generally infeasible as Mmj (·)
is an unknown function of the choice probabilities for all J cities. Therefore,
we introduce two additional assumptions. First, following Dahl, we make an
“index su ciency assumption”: that the function Mmj (·) can be replaced with
an alternative function which only takes a subset of the choice probabilities as
arguments. Second, we assume that the amount of selection on unobservables is
⇥ ⇤
constant for all cities within the same state such that E umi |j = argmaxj0 (Vij0) =
h i
E umi |ĵ = argmaxj0 (Vij0) for any j, ĵ in the same state. For example, this
implies that, conditional on the vector of observables Xi, the expectation of the
idiosyncratic term umi is the same in Dallas as it is in Houston.
27
26This is subject to an invertibility condition: that these choice probabilities contain the same
information as di↵erences in subutility terms across cities.
27This second assumption is useful in generating predicted values of energy usage. As we
explain below, to separately identify ↵m0 from the intercept of the selection correction function,
57
Taken together, these two assumptions imply that the control function can
be written as a function of a subset of the state choice probabilities. Let Pst give
iŜ
the vector of the household’s choice probabilities for all states in the set Ŝ, where
Ŝ is a subset of the full set of states. We can then estimate the parameters of (3.1)
using the equation
   
Emij = ↵
m +  mX +Mm Pstj j i j + û
m, (3.3)
iŜ i
   
where Mmj P
st is a correction function which depends on Pst .
iŜ iŜ
In practice, we specify the function Mmj (·) as a function of the probabilities
of choosing the three largest states by population, the probability of choosing the
state containing city j, and the interactions between the probability of choosing the
state containing city j and the probabilities of choosing the three largest states.28
For estimates of the state choice probabilities, we use the same approach as Dahl.
Specifically, we divide households into cells which vary in their demographic
characteristics and their state of birth and calculate state choice probabilities as
the proportion of households within each cell that chooses a given state.
Finally, one complication arises because the intercept term ↵mj is
not separately identified from the intercept of the control function. We
overcome this identification issue by using the intuition of “identification at
infinity” (Chamberlain, 1986; Heckman, 1990): suppose the econometrician
observes households with demographics X̂ and birth state B̂ such that
⇣ ⌘
Prob j = argmaxj0 (Vij0) |X̂, B̂ = 1. Since households with these characteristics
we need to extrapolate the control function to households for which the probability of choosing
a given location is equal to one. As state choice probabilities are closer to one than city choice
probabilities, using state choice probabilities reduces the range over which we extrapolate the
control function.
28We show the sensitivity of our estimates to di↵erent choices of the correction function in
Appendix B.0.2.1.
58
choose location j with certainty, there is no selection on unobservables for these
h i
households: E umi |j = argmaxj0 (Vij0) , X̂, B̂ = 0. In terms of the selection
⇣ ⌘
st st
correction function, this implies that Mmj P̂iŜ = 0, where P̂iŜ is the vector of
choice probabilities where the probability of choosing the state containing city j is
equal to one and the probability of choosing all other states is equal to zero. We
⇣ ⌘
st
first estimate equation (3.3). Then, we use the restriction that Mmj P̂iŜ = 0 to
back out the intercept of the selection correction equation and thus ↵mj .
29
Finally, after estimating the parameters of the energy usage functions, we
calculate predicted usage of energy type m as
Êm = ↵̂m +  ̂mj j j X̄,
where ↵̂m and  ̂mj j denote parameter estimates and X̄ gives a vector of the mean
values of each demographic characteristic.
29As a simple example, consider the  case  where M
m is specified as a first-order polynomial
j
of choosing the state in question: Mm Pst = M + M st st
j iŜ 0 1
P ( ), where P ( ) is the probabilityis j is j
of choosing the state containing city j. Then the intercept of this correction function M0 can
simply be calculated as M0 =  M1. Note that the identification at infinity argument relies on the
econometrican observing households for whom the probability of choosing the state in question
is close to 1. If we allow selection to occur at the city level within each state, we would need to
observe households for whom the probability of choosing a given city is close to 1. This is a very
strong assumption in the case of many cities, given that we only observe data on an individuals
state of birth, not their city of birth.
59
CBSA Rank Emissions Gas Fuel Electricity Electricity Electricity
Emissions Emissions Use Conversion Emissions
(1000 lbs) (1000 lbs) (1000 lbs) (MwH) (1000 lbs/MwH) (1000 lbs)
Lowest
Honolulu, HI 1 14.24 0.00 0.00 9.36 1.52 14.24
Oxnard, CA 2 14.67 6.19 0.27 10.26 0.80 8.21
Riverside, CA 3 16.37 6.33 0.27 12.21 0.80 9.76
San Diego, CA 4 16.71 6.75 0.33 12.04 0.80 9.63
Los Angeles, CA 5 17.14 6.73 0.20 12.76 0.80 10.21
Sacramento, CA 6 17.96 7.72 0.47 12.23 0.80 9.78
Middle
Baton Rouge, LA 33 26.56 4.41 0.43 20.98 1.04 21.72
Birmingham, AL 34 26.86 5.79 0.21 20.15 1.04 20.86
Jacksonville, FL 35 26.90 0.62 0.06 25.92 1.01 26.22
New Orleans, LA 36 27.15 4.61 0.41 21.38 1.04 22.13
Pittsburgh, PA 37 27.41 12.02 2.43 11.73 1.11 12.97
Houston, TX 38 27.51 4.12 0.13 22.92 1.01 23.25
Highest
Tulsa, OK 65 40.21 12.47 0.28 21.60 1.27 27.46
Oklahoma City, OK 66 41.59 11.81 0.27 23.21 1.27 29.50
Indianapolis, IN 67 43.67 23.20 0.30 18.26 1.11 20.18
Memphis, TN 68 43.81 10.56 0.23 31.89 1.04 33.02
Omaha, NE 69 45.49 17.31 0.31 22.84 1.22 27.87
Milwaukee, WI 70 46.19 21.84 0.34 21.72 1.11 24.01
Table 2. Predicted CBSA level CO2 emissions by fuel type for the six lowest
emissions cities, the six median cities, and the six highest emissions cities in 2017.
The third column (“Emissions”) shows the sum of predicted CO2 emissions from
natural gas, fuel oil, and electricity for the CBSA. The next two columns show
emissions from gas and fuel oil respectively, which are equal to predicted usage
multiplied by the appropriate emissions factor. The last three columns show
predicted electricity usage, the electricity emissions factor, and predicted electricity
emissions, equal to predicted electricity usage multiplied by the emissions factor.
3.3.2 Selection-Corrected Predicted Usage and Emissions. The
predicted yearly household usage and emissions from the 2017 aggregated ACS
for selected cities are shown in Table 2. To calculate these predicted emissions,
we multiply selection-correction predicted usage by the appropriate emissions
factors. We show results for the six lowest emissions cities, the six highest emissions
cities, and the six median cities. The third column (“Emissions”) shows the
sum of predicted CO2 emissions from natural gas, fuel oil, and electricity for the
CBSA. Predicted household emissions vary considerably across cities. In Honolulu,
60
predicted emissions are slightly over 14 tons per year, whereas in Milwaukee they
are over 46 tons per year.
The next two columns show emissions from gas and fuel oil respectively,
which are equal to predicted usage multiplied by the appropriate emissions factor.
Natural gas emissions are generally the largest in colder regions.30 Emissions from
fuel oil are generally quite small in magnitude compared to emissions from the
other two energy types. The last three columns show predicted electricity usage,
the electricity emissions factor, and predicted electricity emissions, which is equal to
predicted electricity usage multiplied by the emissions factor.
Spatial variation in household carbon emissions comes from multiple sources.
For example, power plants utilized in Memphis emit less CO2 than Oklahoma City
(1.04 lbs per MWh in Memphis compared to 1.27 in Oklahoma City). However,
electricity usage in Memphis is so much higher than in Oklahoma City that
overall household emissions are higher in Memphis, despite greater consumption
of fuel oil and natural gas in Oklahoma City.31 Conversely, consider emissions
resulting from electricity in Houston compared to Tulsa. Households in Houston
use more electricity than those in Tulsa. However, power plants near Tulsa are less
carbon-e cient than those near Houston. Therefore, emissions from electricity use
are higher in Tulsa. This underscores an important feature of the data: spatial
variation in household electricity emissions is driven by both di↵erences in energy
usage and heterogeneity in power plants across regions.
30In Section 3.3.3, as in GK, we show that colder winter temperatures are highly predictive of
natural gas usage.
31Since consumption of natural gas and fuel oil have the same conversion factor nationally, a
higher level of emissions in one city necessarily means a higher level of consumption.
61
3.3.3 Energy Usage and Climate. To further understand the
di↵erences in energy usage across cities, we now examine the relationship between
energy usage and climate. Figure 11 shows the CBSA level relationship between
average August temperature and predicted electricity usage and between average
January temperature and predicted natural gas usage. Similar to Glaeser and
Kahn (2010), we find strong relationships between temperature and consumption
of di↵erent fuel sources. Electricity usage has a strong positive relationship with
August temperature. Similarly, as January temperature increases, natural gas use
decreases. Taken together, these results suggest that di↵erences in energy usage
across cities are largely driven by di↵erences in climate.
200
30
150
25
100 20
50 15
10
0
20 40 60 70 80 90
January Temperature August Temperature
Figure 11. Temperature and household energy use by CBSA. The left panel
displays predicted natural gas usage and average January temperature. The
right panel displays predicted electricity usage and average August temperature.
Temperature data was obtained from weather.com. Each point is a CBSA.
Temperature corresponds to the midpoint of the average minimum and maximum
daily temperature recorded in the month of interest. The size of each point reflects
the population of the CBSA. Electricity usage is measured in MWh and natural gas
usage is measured in 1000 ft3.
62
Selection-Corrected Natural Gas Use (1000ft3)
Selection-Corrected Electricity Use (MWh)
3.3.4 Policy and Emissions. Spatial variation in household carbon
emissions implies that any policy that a↵ects the spatial distribution of households
will also impact national carbon emissions. The primary policy we are interested
in is land use restrictions. Figure 12 shows a scatterplot between CBSA-level
predicted emissions and the Wharton Land-Use Regulation Index. The Wharton
Index is displayed on the horizontal axis; higher values of this index correspond
to tighter land use restrictions. The vertical axis displays predicted per-household
CO2 emissions, measured in pounds.32
40,000
30,000
Sacramento Fresno 
20,000 San Jose San Francisco
San Diego Los Angeles
Oxnard Riverside
-1 0 1 2
Wharton Index
Figure 12. Predicted per-household CO2 emission measured in pounds and
Wharton Lane Use Index. Each circle is a CBSA; California cities are highlighted.
The size of each circle reflects CBSA population.
32This statistic is the same as that displayed in the “Emissions” column of Table 2.
63
Selection-Corrected CO2 Emissions (lbs) 
Generally, tighter land use restrictions are associated with lower predicted
carbon emissions. In particular, California cities have very low predicted carbon
emissions due to a combination of temperate climate and clean power plants. Cities
in California also have very tight land use restrictions, as measured by the Wharton
Index.
To be clear, the goal of this paper is not to explain what generates this
relationship. Instead, our goal is to study the implication of this correlation, in
the sense that tight land use restrictions inflate housing prices and incentivize
individuals to live away from California and other cities with low carbon emissions.
We proceed by building a spatial equilibrium model to quantify the e↵ects of land
use restrictions on national carbon emissions.
3.4 Model
We employ a static spatial equilibrium featuring heterogeneous households,
with endogenous wages and rents, similar to those used in Diamond (2016),
Piyapromdee (2019), and Colas and Hutchinson (2021). We extend this class
of model by allowing locations to vary by carbon and local pollutant output of
regional power plants and the marginal benefits of energy usage. Therefore, our
model is able to map changes in the distribution of households across locations to
carbon and local pollutant emissions.
Household sorting is a static, discrete choice—households choose the city
which provides the highest utility in terms of wages, rents, amenities, and energy
prices. Households purchase three energy types—electricity, natural gas and
fuel oil—which they use to produce energy services (e.g. air conditioning, home
heating). The utility benefit of energy services varies by city. For example, the
benefit of air conditioning (and thus electricity) is high in Memphis while the
64
benefit of home heating (and thus natural gas) is high in Minneapolis. Each
location has an upward sloping housing supply curve whose elasticity depends on
local land use restrictions and the amount of land available for development. Cities
with tighter land use restrictions will have more inelastic housing supply curves and
higher rents, all else equal. Competitive firms combine skilled and unskilled workers
using a CES production function to produce a numéraire consumption good. Thus,
local wages and rents are endogenous to the distribution of households across cities.
Changes in land use restrictions across cities will change housing supply curves
across cities and impact the equilibrium distribution of households.33
As we show in Section B.0.1.1, emissions vary across household types. We
allow households in the model to vary in their education level, race, age group,
marital status, and whether or not the household has children. These households
types vary in their preferences over locations, energy services, and housing. Within
this demographic group, households also receive a premium for living in cities close
to their birth state. This allows for rich substitution patterns in response to policy
changes—a decrease in rents in San Francisco, for example, will lead to larger
inflows of households who are born in California. Finally, households receive an
idiosyncratic preference draw over each location, where the variance of the draw
depends on household demographics. Therefore, households are imperfectly mobile
across cities.
The amount of carbon emissions generated by a household varies for two
reasons in the model. First, the marginal benefit of each energy type varies by
city. Cities with a higher marginal benefit of energy usage will have higher levels
of energy usage, all else equal. Second, the production technology and carbon
33We define an equilibrium in this setting in Appendix B.0.1.6.
65
e ciency of power plants vary across NERC regions. Electricity used at a given
city must be produced by a power plant in the associated NERC region. Therefore,
electricity usage in cities located in NERC regions with more carbon-e cient power
plants will lead to lower emissions.
In addition to carbon emissions, household electricity usage also leads to
emissions of local pollutants and therefore deterioration in air quality – where
we explicitly focus on PM2.5 concentration as our measure of local air quality.
We construct a pollution-transfer matrix using a state-of-the-art source-receptor
matrix, the InMAP source-receptor matrix (ISRM) (Goodkind, Tessum, Coggins,
Hill, & Marshall, 2019).34 We use this pollution-transfer matrix to map household
electricity usage, and therefore PM2.5 emissions, in any given city to ambient
air quality in all cities in the model. In our baseline model, we do not directly
account for PM2.5 concentration in household utility. In Section 3.7.3 we show that
our results are very similar when we include PM2.5 concentration in the utility
function.35
3.4.1 Households. Let j index cities and i index households.36
Households are endowed with a demographic type d, which includes the household
34InMAP is a “reduced-complexity” air transport model. Other popular reduced complexity
models include COBRA (EPA, 2020) and APEEP (Muller & Mendelsohn, 2007). All of these
models make simplifiying assumptions around atmospheric chemistry equations to ease the
computational burden of estimating pollution transfer. More complex atmospheric dispersion
models such as HYSPLIT (Stein et al., 2015) and WRF-Chem generally perform better for
predicting pollution transfer over long-distances. However, the added complexity makes them far
more computationally expensive. InMAP performs similarly to many other reduced-complexity
models (Tessum et al., 2017) and is easy to implement, making it our preferred method for
modeling pollution transfer. See Hernandez-Cortes and Meng (2020) for a discussion of the
limitations of InMAP relative to HYSPLIT.
35Our model only endogenizes PM2.5 concentration arising from household electricity usage.
The changes in PM2.5 arising from household electricity usage are small relative to di↵erences in
total PM2.5 concentrations across cities.
36In Section 3.5, we introduce t subscripts to indicate which variables and parameters vary over
time. We omit these t subscripts for clarity as we present the model.
66
head’s education, marital status, race, whether or not they have children, and
age group.37 Locations vary by amenities, which we denote as  ij. To solve their
decision problem, the household chooses a location j that yields maximal utility
from consumption of the numeraire c, housing H, and energy services Êm (such as
heating or air-conditioning), and from amenities.
We parameterize the household’s utility function as:
X
u c H m mij = ↵d log c+ ↵d logH + ↵jd log Ê +  ij, (3.4)
m
where ↵c , ↵H md d , and ↵jd are parameters which scale the marginal benefit of
consumption, housing and energy services. We set ↵cd = 1 for each demographic
group d to normalize for scale. ↵mjd varies across cities to reflect di↵erences in the
marginal benefit of energy services across cities (perhaps due to di↵erences in
weather).38
We assume energy services are produced by the household using a fixed
proportions energy production function which maps energy types into energy
services. Let Em denote usage of energy type m, where m 2 {Elec,Gas, Fuel}.
The energy service production function takes the form:
Êm = f (xm) = amEm, (3.5)
where am is a parameter that maps units of energy into energy services.
37We divide households into two age groups based on the age of the household head.
Households with heads over 35 years old are defined as “older” households.
38In Section 3.3.3, we show that local temperature is highly predictive of energy usage. We
assume that these parameters are not a function of the local population or population density. In
Appendix B.0.1.5, we provide evidence that the population is not a significant predictor of energy
demand. Fragkias et al. (2013) come to a similar conclusion. Further, we assume that land use
restrictions do not directly a↵ect energy use. Some targeted land use restrictions, such as urban
growth boundaries or endangered species habitats, may have positive environmental e↵ects. See
Lawler et al. (2014), for example, for a discussion.
67
Substitution of 3.5 into 3.4 yields:
X
u = log c + ↵Hijt d logH + ↵
m
jd logE
m +  ij + C, (3.6)
P m
where C = m mm ↵jd log a is an additive constant that does not depend on the
household’s choices.
The households’ budget constraint is given by:
X
Ijd = c +RjH + P
m m
j E ,
m
where Ijd is the income level of a household of demographic d living in city j and
Em is usage of energy type m. Rj and Pmj represent the prices of housing and the
price of energy of type m in city j. We normalize the price of consumption of c to
one.
We decompose the amenity term,  ij, into five distinct components. In
particular, we let:
 ij =  
hp
d I (j 2 Bi) +  distd   (j, B ) +  dist2i d  2 (j, Bi) + ⇠jd +  d✏ij, (3.7)
where I (j 2 Bi) is an indicator for location j being in the head of household
i’s birth state,   (j, Bi) and  2 (j, Bi) are the distance and squared distance,
respectively, between the household head’s birth state and location j. ⇠jd is a
shared unobservable component of amenities and ✏ij is an idiosyncratic preference
shock with dispersion parameter  . Di↵erences in ✏ij across individuals and cities
reflect unobservable variation in attachment to a location that an individual might
have. We assume that ✏ij follows a Type 1 Extreme Value distribution.39 We make
39We do not allow for the possibility of endogenous amenities, as in Diamond (2016). We also
refrain from directly modeling the e↵ects of carbon emissions on household’s utility. Our model
only includes US households, and therefore cannot reliably capture the full social cost of carbon.
In Section 3.7.3, we consider an extension in which local pollutants enter the household utility
function.
68
an important assumption that unobserved amenities, ⇠jd, are taken as exogenous
and are not a function of land use restrictions, as is relatively standard.40
Solving the household’s maximization problem yields constant income shares
on housing and energy of all types. We write a household of demographic group d’s
optimal choice of housing, conditional on living in a city j as,
? ↵
H
d IH = jdjd ↵jdRj
P
where, to simplify notation, we define ↵jd ⌘ 1 + ↵H + ↵md m jd. Optimal usage of
energy type m is also a constant fraction of income:
↵mI
m? jd jdEjd = ↵ Pm
. (3.8)
jd j
We then solve for the indirect utility function associated with location j:
X
Vij = (↵
H m
jd) log Ijd   ↵d logRj   ↵jd logPmj +  ij, (3.9)
m
where we drop additive constants which have no a↵ect on household decisions.
The household’s problem can be thought of as a discrete choice over all the
locations, conditional on optimal housing and energy consumption. Given that
the idiosyncratic preference draws are distributed as Extreme-Value Type I, we can
write the probability that a household i chooses a location j as
   
exp V̄
P ij
/ d
Pij =     , (3.10)
j02J exp V̄ij0/ d
40See Hsieh and Moretti (2019), Piyapromdee (2019), or Colas and Hutchinson (2021), for
example. Diamond (2016) and Herkenho↵ et al. (2018) allow amenities to be endogenous to
household composition, but not land use restrictions directly. This assumption is supported
by the findings in Albouy and Ehrlich (2018), who find that land use restrictions increase
the cost of housing production without improving local quality of life. Clearly, some land use
restrictions, such as park systems, have a direct positive e↵ect on amenities. We can think of our
counterfactuals here as the relaxation restrictions that do not have a large direct e↵ect on local
amenities.
69
where V̄ij = Vij    d✏ij is the household’s indirect utility of choosing location j
minus the idiosyncratic preference draw. We write the total number of households
of demographic d who choose to live in location j as Njd.
3.4.2 Energy Production and Emissions.
Carbon Emissions We allow for three types of energy in our analysis: natural
gas, fuel oil, and electricity. We assume fuel oil and natural gas are purchased on
an international market and treat the supply for these types of energy as perfectly
elastic. We assume that the carbon byproduct of fuel oil and natural gas are
constant regardless of where energy is consumed. Total household emissions of
CO2 from natural gas and fuel oil in city j is the sum of usage of the energy type
multiplied by the appropriate conversion factor:
X
CO m =  ̂m N Em2j jd jd, m 2 {Gas, Fuel} ,
P d
where d N
m
jdEjd is the total amount of fuel of type m consumed by people living
in city j and  ̂m is the amount of CO2 emissions per unit of fuel of type m.
We assume electricity is generated across NERC regions in the United
States and then is transmitted to local labor markets within those regions. Within
each NERC region, perfectly competitive power plants produce electricity.41
In our baseline specification, we assume that the marginal cost of energy
production is constant.42 In Section 3.7.2, we consider a model extension with
41Electricity is a homogeneous good with a large number of with many producers. However,
when transmission constraints bind, generation companies may have local market power. See
Joskow and Tirole (2000) for a discussion.
42The short run supply of electricity is often modeled as a dispatch curve with constant
marginal or linear marginal cost curves. However, as we are considering a long-run equilibrium,
the supply curve is given by the long run marginal cost curve, allowing for the construction of new
reactors or the entry of new plants.
70
increasing marginal cost. The results are qualitatively similar in both cases.
We allow the conversion factor for electricity to vary by NERC region to reflect
geographic variation in the carbon intensity of power plants.43 For example, a
larger percentage of power in the Western NERC region (WECC) comes from
hydroelectric dams, whereas the Southern NERC region (SERC) relies more heavily
on coal power.
Let  ̂mR represent the conversion factor of electricity to CO2 emissions in
NERC region R and let R (j) map cities to their corresponding NERC regions. We
write CO2 emission resulting from electricity usage in CBSA j as
X
CO m =  ̂m m2j R(j) NjdEjd, m 2 {Elec} .
d
For simplicity, we use the following notation for emissions factors:
8
<>> ̂m m 2 {Gas, Fuel}
 mj = > .:> ̂mR(j) m 2 {Elec}
Local CO2 emission of each energy type m can then be written as
X
CO m =  m N Em2j j jd jd.
d
We can then write national emissions from each energy type m as: COm2 =
P
CO mj 2j , and national emissions across all energy types is simply the sum of the
P
energy specific emissions levels, CO = m2 m CO2 .
Next we can examine how the distribution of households across cities a↵ects
the level of national carbon emissions.44 We rewrite national emissions in terms of
43Note that  ̂m for fuel oil and natural do not vary by location as conversion factors for these
types of fuel are independent of location.
44The main cost of carbon emissions are felt globally and not modeled directly here.
71
the covariance between the distribution of households and the e ciency of local
electricity usage multiplied by the local energy usage:
XX      ⇥ ⇤ 
CO = J · Cov N ,Em m2 jd jd j +NdE Em mjd j ,
m d
where Nd, the total number of households of group d, and J , the total number
⇥ ⇤
of cities, are both model primitives. The expectation E Em mjd j is taken over
cities j. National emissions are increasing in the covariance of population and the
product of energy usage and energy conversion factors. Therefore, policies that lead
households to live in cities that are associated with higher energy usage and less
carbon-e cient power plants will lead to increases in national carbon emissions.
As demonstrated in Section 3.3.4, the tightness of land use restrictions is
negatively correlated with local predicted CO2 emissions levels. Furthermore,
tighter land use restrictions increase local rents and, in equilibrium, lead to lower
population levels in these cities. In Section 3.6, we examine the quantitative
implications of this relationship between land use restrictions, energy demand, and
power plant technology on national carbon output.
Local Pollutants In addition to carbon emissions, the model features
local pollutants. We focus on Particulate Matter of 2.5 micrometers or smaller
(PM2.5) as our primary measure of local pollution. We focus on particulate matter
emissions from electricity only, as natural gas emits a negligible amount of PM2.5
(EPA, 2019).45 In the model, we distinguish between PM2.5 emissions (measured
in tons/year) and PM2.5 concentration (measured in micrograms per cubic meter
(measured in µ/m3).
45Furthermore, fuel-oil is used by households in relatively few states and will not have first
order consequences for overall PM2.5 concentration.
72
While PM2.5 is considered a local pollutant because it has negative
consequences for those directly exposed, emissions of PM2.5 from a given location
can impact air quality locally, regionally, and nationally. PM2.5 emissions are
highly transportable; Morehouse and Rubin (2021) estimate that roughly 90% of
particulate matter emissions from coal-power plants leave the state in which they
were emitted within 48 hours. Electricity demand in California, for example, will
lead to an increase in PM2.5 emitted from power plants in the associated WECC
NERC region. These additional emissions a↵ect air quality not only in California
but potentially all western states and—to a lesser extent—the rest of the United
States.
To map emissions of PM2.5 from a given NERC region to concentration of
PM2.5 for each city in the model, we employ a state-of-the-art “source-receptor”
(SR) matrix derived from a recent integrated assessment model, the Intervention
Model for Air Pollution (InMAP) (Goodkind et al., 2019). The entries of the SR
matrix provided by InMAP (henceforth ISRM) are “transfer coe cients” – which
give the marginal impact of particulate matter emissions (measured in tons/year)
in any given location on the ambient concentration (measured in µ/m3) in any
other location. ISRM accounts for power-plant stack height, the velocity at which
the particles were emitted, and local atmospheric conditions. We use ISRM to
construct a “pollution-transfer” matrix, where each entry gives the conversion
factor between electricity produced in NERC region R (measured in MWh) to
pollution in CBSA j (again, measured in µ/m3). With this matrix in hand, we
can estimate the extent to which changes in household energy demand lead to
changes in ambient air quality.46 Let P denote this pollution-transfer matrix, and
46For details on this procedure, see Appendix B.0.1.10.
73
let Eelec give the vector of household electricity produced in each NERC region.
The contribution of household electricity usage to PM2.5 concentration in each
CBSA is given by:
PMendog = Eelec ⇥ P. (3.11)
A given element of this vector, PM endogj , gives the concentration of PM2.5 in a city
that arises from (national) household energy usage.
In addition to emissions from household electricity usage, PM2.5 can
originate from many sources (EPA, 2019).47 To account for this, we assume that
PM2.5 concentration in a given city is the sum of PM2.5 concentration resulting
from household electricity usage and PM2.5 produced by other sources, which we
assume to be invariant to household location choices. Concretely, letting PMj
denote the overall level of PM2.5 in city j, we assume
PM = PM endogj j + PMj , (3.12)
where PM j is the fixed, city-level pollution.
3.4.3 Housing Supply. Each city has an upward sloping housing
supply curve. The elasticity of the housing supply curve is allowed to vary by
city as a function of the amount of available land and the strictness of land use
restrictions. Specifically, we follow Kline and Moretti (2014) and parameterize the
inverse housing supply curve in city j as:
k
Rj = zjH
j
j , (3.13)
47Furthermore, household energy consumption form a relatively small proportion of total PM2.5
emissions—for details see Appendix B.0.2.3.
74
where Hj is quantity of housing supplied, zj is a scale parameter, and kj
is a parameter equal to the inverse elasticity of the housing supply curve
⇣ ⌘
i.e., @ logRj@ logH = kj . Taking logs of (3.13), we obtainjt
log(Rj) = kj log(Hj) + log(zj). (3.14)
The term kj plays a crucial role in our analysis. Higher values of kj imply more
inelastic housing supply curves and higher rent levels. Therefore, cities with higher
values of kj will have lower equilibrium population levels, all else equal.
As shown by Saiz (2010), local land use restrictions, as measured by
the Wharton Land Use Index, and the fraction of land that is unavailable for
development due to geographic constraints are strong determinants of more
inelastic housing supply curves. We follow Saiz (2010) and parameterize kj as a
function of land use restrictions and geographic constraints:
k = ⌫ + ⌫  WRI + ⌫  GEOj 1 2 j 3 j
where  WRIj is the Wharton Land Use Index and  
GEO
j measures the amount of
land that is unavailable for development due to geographic restrictions.48 A higher
value of ⌫2 implies that cities with tighter land use restrictions will have a more
inelastic housing supply. As shown in Section 3.3.4, cities with higher values of
 WRIj generally have lower carbon emissions per household. In the model, this
disincentivizes households from living in cities with low carbon emissions.
48Another option would be to use a more dissagregated measure of land use restrictions.
This would allow us to decompose the e↵ects of various types of land use restriction on carbon
emissions.
75
Specifically, given that the idiosyncratic preferences draws are distributed
as Extreme-Value Type I, the partial equilibrium elasticity of location choice with
respect to rents is approximately equal to:49
@ logP Hij ⇡  ↵d .
@ logRj  d
We can solve for the partial equilibrium e↵ect of a household’s choice probability
with respect to land use restrictions as
@ logP Hij ⇡   ↵⌫ dWRI 2 log(Hjt)@ j  d
The partial equilibrium e↵ect of land use restrictions is proportional to the
expenditure share on housing and the importance of land use restrictions in
dictating the housing supply elasticity ⌫2, and inversely proportional to  d, the
dispersion in the idiosyncratic preference draw. Higher values of  d imply household
location choices are less responsive to changes in rents; thus, variation in land use
restrictions will have smaller e↵ects on household sorting.
3.4.4 Wages. Perfectly competitive firms in each city combine
skilled and unskilled labor in a CES production function to produce the numéraire
consumption good, where we define household heads with a college degree as skilled
and household heads with less than a college degree as unskilled.50 Therefore,
wages for skilled and unskilled workers in each city are determined endogenously
by the ratio of skilled to unskilled workers. Specifically, firms use a combination of
skilled (S) and unskilled labor (U), as inputs in the following production function:
H H
49Di↵erentiating P with respect to rents yields @ logPijij log =  
↵ ↵
d (1  P d
@ R   ij
) ⇡   for small
j d  d
values of Pij .
50Data on energy usage by firms are generally less readily available than data on household
energy usage. As such, we choose to focus on household emissions. Glaeser and Kahn (2010) argue
that commercial energy use and household energy use are likely to be highly correlated.
76
& 1 & 1
&
Yj = Aj[(1  ✓j)U & &j + ✓jS ] & 1j (3.15)
where Uj and Sj are defined as the total e ciency units of labor supplied
by unskilled and skilled workers in city j, respectively. Aj is the total factor
productivity in city j and ✓j is the relative factor intensity of skilled workers. The
elasticity of substitution between skilled and unskilled workers is given by &.51
Firms take wages as given and choose skilled and unskilled labor quantities
to maximize profits. We derive labor demand curves as a result of the firms skilled
and unskilled labor first order conditions for profit maximization:
✓ ◆ 1
Y &j   1W &js =Aj ✓jS
A jj
✓ ◆ 1 (3.16)
Y &   1
Wju =A
j
j (1  ✓j)U &
A j
,
j
where Wjs and Wju are the wage rates for skilled and unskilled labor, respectively.
Within education groups, demographic groups are perfectly substitutable in
production but vary in their productivity and therefore supply di↵erent amounts
of e ciency units of labor. Income levels for an individual household are given by
the number of e ciency units of labor supplied by the household multiplied by the
appropriate wage rate. Income for a household of demographic group d living in
city j is given by Ijd = Wju`d for unskilled workers and Ijd = Wjs`d for skilled
51One straightforward way to introduce capital into the model is the assume that
product✓ion is Cobb-Douglas in capita◆l and a CES labor supply such that Yjt =
  1 ⌘& 1 & 1
⌘ &AjtK [(1  ✓j)U & + ✓ & & 1jt j jS ] where ⌘ is a parameter. If capital supply is perfectlyj
elastic, this production function implies wage equations that are equivalent to those here. See
Colas (2019) for details.
77
workers, where `d represents the number of e ciency units supplied by agents of
demographic group d.
3.5 Data Inference
In this section we describe our estimation procedure. We focus most of
our exposition on the estimation of household location choice and energy use
parameters. Estimation of the housing supply and production are relatively
standard and details are therefore relegated to appendices B.0.1.8 and B.0.1.9.
The carbon emissions factors are calculated as in Section 3.2.52 We choose to use
the 70 largest CBSAs, as defined by population in 1980. These 70 locations make
up approximately 55% of the entire US population in 2017. We map individuals
that do not live in one of these 70 areas into their corresponding census division,
creating nine additional choices.
Note that by defining our locations as CBSAs, we are abstracting from
household location choices across municipalities or neighborhoods within CBSAs.
While neighborhoods or municipalities within a CBSA may di↵er in many
dimensions, they are unlikely to di↵er substantially in their associated carbon
emissions because climate and the set of power plants where electricity is produced
are relatively constant within a given CBSA.
3.5.1 Households. We estimate household preferences using the two-
step “BLP” procedure using repeat cross-sectional data from the 1990 Census, 2000
Census, 2010 aggregated ACS, and 2017 aggregated ACS (Berry, Levinsohn, &
52That is, we assume 117 lbs of CO2 emitted per thousand cubic feet of natural gas consumed
and 17 lbs of CO2 emitted per gallon of fuel oil consumed. We calculate the weighted average
CO2 emissions of all plants in a NERC region. We then assign each of the CBSAs to a NERC
region, thus assigning all individuals in our sample a carbon emissions factor for electricity.
78
Pakes, 2004).53 As we estimate household preferences using multiple cross sections
of data, we introduce t subscripts to indicate which variables and parameters vary
over time and which parameters are assumed to be constant over time. We rewrite
the household’s indirect utility function as
X
Vijt =(↵jd) log Ijdt   ↵Hd logR   ↵m m
hp
jt jd logPjt +  dt I (j 2 Bi)+
m (3.17)
 dist  (j, B ) +  dist2 2dt i dt   (j, Bi) + ⇠jdt +  d✏ijt.
Therefore, the set of parameters to be estimated are ↵Hd and ↵
m
jd, the parameters
governing the budget shares of consumption, housing and energy spending,
respectively;  hp distdt ,  dt and  
dist2
dt , the parameters governing the strength of home
premium and the disutility of living further away from one’s birth state; ⇠jdt, the
unobserved city-level amenities; and  d, the parameters that govern the variance of
idiosyncratic preference draws.
It will be useful to express indirect utility as the sum of the component
of utility that varies by household and the “mean utility” that is constant for
households of a given demographic group. Dividing (3.17) by  d, we can write
indirect utility as
V̂ = µ +  ̂hpI (j 2 B ) +  ̂dist  (j, B ) +  ̂dist2 2ijt jdt dt i dt i dt   (j, Bi) + ✏ijt, (3.18)
where
(↵ ) ↵H X ↵m
µjdt =
jd log I   djdt logR jd mjt   logPjt + ⇠̂jdt (3.19) d  d  m d
and where “hatted” parameters represent a given parameter divided by  d. Using
(3.19), we write the probability that an household i chooses a location j as
53This estimation procedure has been utilized extensively in the urban economics literature, for
example by Diamond (2016), Piyapromdee (2019), and Colas and Hutchinson (2021)
79
exp(µ hp⇣jdt +  ̂dt I (j 2 Bi) +  ̂
dist
dt   (j, Bi) +  ̂
dist2 2
dt   (j, BP = i
))
ijt P ⌘ . (3.20)
j02J exp µ
hp
j0dt +  ̂dt I (j0 2 B ) +  ̂dist 0 dist2 2 0i dt   (j , Bi) +  ̂dt   (j , Bi)
In the first step of estimation, we estimate the birth state premium
parameters and the mean utility via maximum likelihood. The log-likelihood
function is given by
XNd XJ
L( ̂hp,  ̂dist dist2dt dt ,  ̂dt , µjdt) = Iij log(Pijd), (3.21)
i=1 j=1
where Iij is an indicator equal to one if individual i lives in location j and zero
otherwise.54
In the second step of estimation, we decompose the mean utility terms,
↵m
µjdt. First, we define ↵̃mjd =
jd
↵ . Given the Cobb-Douglas utility function, thejd
expenditure share on fuel type m of demographic group d in city j is given by
EmPm
jd j
I = ↵̃
m
jd. We first choose the ↵̃
m
jd parameters to match the expenditure share
jd
on each fuel type by each demographic group in each city. Specifically, we calculate
the expenditure share on each type of fuel by city and demographic group using our
selection-corrected energy usage estimates from Section 3.3.1.55
As we show in Appendix B.0.1.11, we can rewrite mean utility as
µ =  wĨ +  rjdt d jdt d logRjt + ⇠̂jdt. (3.22)
P
log I   (↵̃m logPm 1+↵H ↵H
where Ĩ = jdt Pm jd jt
) ( )
,  w = d , and  r  ( d )jdt 1  ↵̃m d   d =   . We refer to Ĩjdt as
m jd d d
“energy-budget adjusted income”. This is a household’s log income after adjusting
54Computationally, we invert the choice probabilities using the contraction mapping in Berry
(1994) to obtain the unique mean utility associated with every guess of the parameter vector
[ ̂hp  ̂dist  ̂dist2].
d d d
55That is, we use the estimates of selection corrected-emissions from Section 3.3.2 and calculate
demographic specific energy usage as Em = ↵̃m+ ̂mX̄d, where X̄d gives the vector of demographicj j j
characteristics of households in group d.
80
for the fact that 1) the fraction of income that is spent on energy depends on local
energy prices, and 2) income is more valuable in locations with high marginal
utility of energy.
To limit the number of parameters to be estimated, we place additional
restrictions on ↵Hd and  d. As we show in Appendix B.0.1.1, conditional on
location, a household’s marital status, presence of children, and age of the
household head are the most important determinants of emissions. Conditional
on these characteristics, the education level and race of the household head play
only a minor role in determining emissions. As such, we allow the   Hd and ↵d
parameters to vary by household marital status and the presence of children.56
Therefore, we can write these parameters as ↵HMarr,Child and  Marr,Child and let
w (1+↵H ↵H  = Marr,Child
)
and  r
( Marr,Child)
Marr,Child   Marr,Child =   .Marr,Child  Marr,Child
Plugging in these parameter restriction and taking first di↵erences of (3.22)
over our four datasets yields our estimation equation:
 µ =  w rjdt Marr,Child Ĩjdt +  Marr,Child  logRjt + ⇠jdt. (3.23)
In general, we expect that changes in unobserved amenities,  ⇠jdt, will be
correlated with changes in rents,   logRjt, and adjusted incomes  Ĩjdt. For
example, consider an increase in unobservable amenities in city j: this will increase
utility directly and induce households into city j. Mechanically, this leads to an
56Many papers in the literature focus on di↵erences in mobility by education group, rather
than by marital status and the presence of children (e.g. Bound and Holzer (2000) or Diamond
(2016)). However, since education is not a strong predictor of household emissions, we found it
much more important to focus on marital status and the presence of children, which play a large
role in determining household emissions. We also considered specifications in which we allowed
these to vary by marital status, the presence of children, and age of the household head. These
results are included in Appendix B.0.2.4.
81
increase in housing demand, and as a result equilibrium rents rise, thus causing a
change in   logRjt. A similar argument can be made for adjusted income. As such,
we estimate (3.23) via two-step GMM, using instrumental variables to deal with
these endogeneity issues.57
First, we use the measure of labor-demand shifts introduced by Katz and
Murphy (1992) to generate variation in income across cities.58 The instrument
interacts historical industry concentration patterns at the city level with national
changes in hours worked across industry. Formally, letting ◆ index industries, and
letting e(d) denote the education group associated with demographic group d, the
Katz-Murphy index for city j from the previous period t0 to the period in question t
can be written as
X    
 Z = !1980jdt ◆je(d) Hours◆,e(d), j,t   Hours◆,e(d), j,t0 ,
◆
where !1980◆je(d) is the share of total hours worked in industry ◆ in city j by education
group e(d) in 1980 as a share of total hours worked in city j by education group
e(d) in 1980. Hours◆,e(d), j,t is the national hours worked in industry ◆, education
e(d), for all cities besides city j. Therefore, the term in parentheses gives the
change in national hours worked in industry ◆ between the current time period
and the previous time period. Cities with historical concentrations of growing
industries will generally experience increases in income while cities with declining
industries will experience decreases in income. The income changes generated by
57Estimates via two-stage least squares, continuously updating GMM and limited information
maximum likelihood are very similar.
58The instrument has been used as an instrument for cross city wage changes in Piyapromdee
(2019) and Notowidigdo (2013).
82
this instrument are assumed to be uncorrelated with  ⇠jdt, changes in city-level
unobservable amenities.59
To generate variation in rents, we also include the  WRIj , our measure of
land-use restrictions, and the interaction between the Katz-Muphy index and
 WRIj as instruments. In essence, cities with tighter housing supply restrictions
and therefore more inelastic housing supply curves will experience larger changes in
rents, especially in response to changes in population. As an example, if two cities
experience a positive labor-demand shock, captured by a positive value of the Katz-
Murphy index, the city with the more inelastic housing supply curve will experience
a larger rent increase. This variation in rents is assumed to be uncorrelated with
changes in unobservable amenities.60
3.5.2 Particulate Matter Concentration. Next, we estimate the
fixed level of PM2.5, PM j, in each city. Recall from (3.12) that total particulate
matter concentration in a city, PM j, is equal to the sum of particulate matter
that is endogenous to household location choices and PM j, the level of particulate
matter arising from other sources. We measure PM j using data on the overall level
of ambient particulate matter concentration for each CBSA from the EPA’s Air
Quality Systems data. With the total level and endogenous component in hand, the
exogenous component of particulate matter concentration can be calculated as
PM = PM   PM endogj j j .
3.5.3 Parameter Estimates and Model Validation.
59See Goldsmith-Pinkham, Sorkin, and Swift (2020) for a discussion of identification with
“Bartik”-style instruments.
60We consider alternative instruments and parameterizations in Appendix B.0.2.4.
83
Location Choice Parameters Table 3 shows our estimates of  wd and  
r
d, the
parameters which determine the location choice elasticities with respect to adjusted
income and rents. The first column provides estimates for single households, the
second for married households without children, and the third column provides
estimates for married households with children. We estimate that  w and  rd d are
largest in magnitude for single households, and lowest for married households
with children, implying that single households will be the most responsive in
their location decisions to changes in policy. This heterogeneity in location
choice elasticities has important implications for the e↵ects of relaxing land-use
restrictions in California. In particular, this implies that single households will be
the most likely to move to California in response to this policy change. However,
as we demonstrate in Appendix B.0.1.1, single households have the lowest average
carbon emissions of these three groups while married households with children have
the largest. Households who are the most mobile also have the smallest impact on
carbon output.
Married
Single No Children With Children
 w: Adjusted Income 15.09 11.72 7.33
(2.80) (2.19) (1.47)
 r: Rent -9.03 -6.90 -4.82
(2.40) (1.89) (1.29)
 : Idiosyncratic Component 0.17 0.21 0.40
(0.03) (0.04) (0.11)
↵H : Housing Parameter 1.49 1.44 1.92
(0.48) (0.48) (0.73)
Cragg-Donald Wald F Statistic 8.09 8.28 8.57
Table 3. Parameter Estimates. Standard errors in parentheses.
84
To the best of our knowledge, we are the first paper to estimate these
parameters by marital status and by the presence of children. Therefore, it is
di cult to directly compare our estimates to those in the literature. However, it is
reassuring that the magnitude of our location choice elasticities are similar to those
in Colas and Hutchinson (2021) and only slightly larger than those in Diamond
(2016), who estimate parameters which vary by education but not by marital status
or presence of children.61
The next rows of Table 3 translate these estimates to estimates of ↵Hd and
 d.62 We can use these parameters to calculate the budget share of housing for each
H
demographic group in each city as ↵d↵ . We find an average budget share of housingjd
across household groups of .49, which is consistent with what has been previously
estimated in the literature.63
Birth State Premium Appendix B.0.2.7 gives the estimates of  hpdt ,  
dist
dt and
 dist2dt , the parameters governing the strength of home premium and the disutility
of living further away from one’s birth state, for each year. For all years and
demographic groups, households receive a large utility premium for choosing a
location in their birth state. The utility value of a location is decreasing and convex
in distance from birth state for all demographic groups.
61One concern is that we might su↵er from a slight weak instruments problem as is relatively
common in this literature. We assess the robustness of our key results to these parameter
estimates in Section 3.7.1.
62This parameters cannot be directly compared with similar parameters in Colas and
Hutchinson (2021), Piyapromdee (2019), or Diamond (2016) as ↵H here does not equal the budget
H
share of housing. Here, the budget share of housing is given by ↵d↵ .jd
63For example, Suárez Serrato and Zidar (2016) estimate a budget share of housing of 0.3, using
data from the Consumer Expenditure Survey, Moretti (2011) estimates a budget share of housing
of .41 using Census data and Diamond (2016) calibrates an expenditure share of local goods of
0.62.
85
Panel (a): White College or more Less than College
Rank Single (no kids) Married (with kids) Single (no kids) Married (with kids)
1 Portland, OR Portland, OR San Diego, CA Seattle, WA
2 Miami, FL Miami, FL Miami, FL Portland, OR
3 Los Angeles, CA Seattle, WA Portland, OR Los Angeles, CA
4 San Diego, CA Los Angeles, CA Seattle, WA Honolulu, HI
5 Seattle, WA San Diego, CA Oxnard, CA San Diego, CA
66 Memphis, TN Memphis, TN Springfield, MA Memphis, TN
67 Youngstown, OH Worcester, MA Worcester, MA Springfield, MA
68 Syracuse, NY Springfield, MA Albany, NY Worcester, MA
69 Springfield, MA Syracuse, NY Rochester, NY Albany, NY
70 Worcester, MA Youngstown, OH Syracuse, NY Syracuse, NY
Panel (b): Non-white College or more Less than College
Rank Single (no kids) Married (with kids) Single (no kids) Married (with kids)
1 Honolulu, HI Los Angeles, CA Los Angeles, CA Los Angeles, CA
2 Los Angeles, CA Honolulu, HI Miami, FL Honolulu, HI
3 Miami, FL Seattle, WA San Francisco, CA Seattle, WA
4 Portland, OR Miami, FL San Diego, CA San Francisco, CA
5 San Diego, CA San Francisco, CA Seattle, WA Portland, OR
66 Rochester, NY Knoxville, TN Springfield, MA Springfield, MA
67 Scranton, PA Milwaukee, WI Syracuse, NY Albany, NY
68 Milwaukee, WI Syracuse, NY Albany, NY Syracuse, NY
69 Youngstown, OH Springfield, MA Milwaukee, WI Rochester, NY
70 Springfield, MA Youngstown, OH Rochester, NY Milwaukee, WI
Table 4. Demographic group city ranks according to the shared, unobservable
component of amenities for households with younger household heads.
Amenities Table 4 provides selected estimates of ⇠jdt, the shared unobservable
component of amenities, for the year 2017. Recall that this parameter is allowed to
vary by demographic group d and location j, meaning we estimate a separate value
of ⇠jdt for each of our 24 demographic groups in each of our 79 locations for each
year of our data. Table 4 displays the five cities with the highest and lowest values
of ⇠jdt for households in the younger age group that vary in their race, education
level, marital status, and the presence of children. The estimates for households
with older household heads are similar and are included in Appendix B.0.2.8.
Across demographic groups, Miami, Los Angeles, and Seattle consistently
rank among the highest amenity cities while upstate New York cities generally have
low amenities. There is also interesting heterogeneity across demographic groups—
86
Portland is especially popular among educated white households, while Honolulu is
more popular among minorities. Our estimates of ⇠jdt can be compared to estimates
of “Quality of Life” from the urban economics literature.64 Compared to Albouy
(2012), our estimates assign slightly higher amenities to higher population cities
relative to lower population cities. Consistent with Kahn (1995), we find that Los
Angeles and San Francisco have higher amenities than Chicago and Houston in
each year.
Model Fit Next, we assess how well our model fits the data. The results from
2017 are summarized in Figure 13. Panel (a) shows the log number of households in
each city in the data and the baseline simulation. Each circle represents a CBSA.
Given that we estimate a separate unobserved amenity value for each demographic
group and each city (⇠jdt), we can match these moments exactly. Next, we plot
the simulated and observed log average distance between an agent’s birth state
and chosen city for each CBSA. The results are displayed in panel (b) of Figure
13. Each circle represents a CBSA, and the size of the circle is proportional to its
population. The model fits this aspect of the data fairly well.
Panels (c) and (d) of Figure 13 show the predicted and actual average
usage of natural gas and electricity in each city. As we allow the benefit of energy
usage (↵mjdt) to vary by city and demographic group, we can match these moments
exactly.
3.6 Counterfactuals
In this section, we use the estimated model to simulate changes in land use
restrictions. The results of the counterfactuals are summarized in Table 5. The first
64E.g. Blomquist, Berger, and Hoehn (1988), Kahn (1995) Albouy (2012). See Lambiri, Biagi,
and Royuela (2007) for a review.
87
(a) Population by City (b) Average Distance
(c) Natural Gas (d) Electricity
Figure 13. Model fit results. Each circle represents a CBSA. Panel (a) shows the log number
of households in each city in the data and the baseline simulation. Panel (b) plots the simulated
and observed log average distance between an agent’s birth state and chosen city for each city.
The size of the circle is proportional to a city’s population. Panels (c) and (d) show the predicted
and actual average usage of natural gas and electricity in each city.
column shows the population distribution, fuel usage, emissions, and income in the
baseline specification, with all parameters set at their baseline levels. The following
columns present these statistics in each counterfactual.
88
(1) (2) (3)
Baseline Relax Cali Relax All
I. Percent Total Population
California Cities 9.1 11.0 7.2
Other West 13.6 13.1 17.8
Midwest 22.2 21.7 9.3
South 37.3 36.6 23.1
Northeast 17.9 17.6 42.6
II. Mean Usage
Gas (1000 cubic feet) 74.4 74.2 74.9
Electricity (MW h) 17.1 17.0 15.8
Fuel Oil (gallons) 60.4 59.5 138.6
III. Mean Emissions (lbs of CO2)
Gas 8711 8686 8772
Electricity 16331 16211 13242
Fuel Oil 1622 1598 3723
Total 26664 26495 25737
(%) 100 99.4 96.5
IV. Income (Relative to Baseline)
Skilled 100.0 100.5 113.0
Unskilled 100.0 100.0 100.4
All 100.0 100.2 104.8
Table 5. Counterfactual results when California land-use regulations are relaxed.
Each panel shows the simulated percent of the total population living in various
geographic areas, mean energy usage, mean emissions, and mean income in each
specification. See text for details on each simulation.
3.6.1 Relaxation of Land Use Restrictions in California.
California Senate Bill 50—which recently failed in the California legislature—would
have overridden tight land use restrictions in California cities. In this section,
we examine the e↵ects of California adopting such a policy and relaxing local
land use restrictions. As shown in Section 4.3, California cities are among the
most carbon e cient in the country. However, they also have very tight land use
89
restrictions—San Francisco and Los Angeles are in the 86th and 78th percentiles
in the strictness of land use restrictions, respectively. Intuitively, the relaxation of
land use restrictions in California will lead to increases in California’s population
and decreases in overall carbon emissions. However, the magnitude of the decrease
is an empirical and quantitative question.
Specifically, we simulate setting land use restrictions,  WRI , in California
cities to the level faced by the median urban household.65 We display the main
results in the second column of Tables 5. Setting land use restrictions in California
to the level of the median urban household leads to a 20.5% increase in the total
population in California cities, a 3.1% drop in the population of other locations in
the West, and 1% to 2% drops in the Midwest, South, and Northeast.
California Cities Other West Midwest South Northeast
I. Household Distribution
% Change Population 20.5 -3.1 -1.9 -2 -1.7
II. Composition
Change in Single Share 2.4 -0.5 -0.2 -0.2 -0.2
Change Share without Children 2.3 -0.4 -0.2 -0.1 -0.1
Change in College Share -0.4 0.0 -0.1 -0.1 -0.1
Change Minority Share 0.1 -0.4 -0.3 -0.4 -0.3
III. Prices
% Change Skilled Income -0.1 0.2 0.2 0.2 0.2
% Change Unskilled Income -1.0 0.2 0.0 0.0 0.0
% Change Average Rents -4.8 -1.2 -0.7 -0.7 -0.8
Table 6. Changes in the composition of population in response to reduction in
California land use restrictions.
Panels II and III of Table 5 show how these changes in the distribution of
households translate to average usage and emissions. The relaxation of land use
restrictions leads to decreases in usage of all three types of fuel, as households
65In a previous version of the paper, we simulated relaxing restrictions to the level of the
median city.
90
move to the temperate California climate. Specifically, natural gas usage drops
by 0.3%, electricity by 0.5%, and fuel oil usage drops by 1.5%. Panel III of Table
5 displays average emissions resulting from each type of fuel. Electricity emissions
drop by over 0.7% despite only a 0.5% decrease in usage. As power plants utilized
in California are relatively carbon-e cient, the drop in emissions from electricity
is larger than the drop in electricity usage. All together, this implies a drop in
national household carbon emissions of 0.6% or a $310 million dollar drop in the
social cost of carbon annually.66
In addition to low emissions, cities in California are very productive. Panel
IV of Table 5 shows the e↵ects on average income, relative to the average income in
the baseline. The average income of skilled workers increases by roughly 0.5% while
the average income of unskilled workers increases slightly. This leads to an increase
in income of 0.2% across all workers. Overall, the shift towards more productive
and lower-emitting cities increases the output to emissions ratio by 0.7%.
Regional E↵ects To better understand the regional impacts of the policy
change, Table 6 gives the change in population distribution and prices across
regions. Panel II shows the change in regional demographic composition. The
change in land use restrictions leads to increases in the share of unmarried
households and households without children in California. As these groups are
relatively lower usage groups, this composition e↵ect leads to slightly smaller
decreases in carbon emissions than the population change alone.
Panel III of Table 6 displays the change in average incomes and rents across
regions. Interestingly, within California cities, average income decreases slightly, as
66As mentioned in the introduction, we use the estimate of the social cost of carbon in 2020
from Nordhaus (2017).
91
the proportion of households in low-income Fresno increases while the proportion
in high-income San Jose decreases. Equilibrium rents in Californian cities drop
by roughly 5%, as a result of both the change the land-use regulations and the
resulting increase in population in California. Average rents decrease by roughly
1% in the other regions, reflecting drops in regional housing demand as households
move to Californian cities.
Percentage Change from Baseline
Income Rents Utility PM2.5 Exposure
I. Education
College Education 0.5 -0.7 0.9 0.3
Less Than College 0.0 -0.9 0.6 0.3
II. Family Size
Single 0.2 -0.8 0.7 0.4
Married w/o Children 0.2 -0.7 0.6 0.2
Married w/ Children 0.1 -1.0 0.3 0.1
III. Race
White 0.2 -0.8 0.6 0.2
Nonwhite 0.2 -0.9 0.8 0.4
Table 7. Changes in average income, rents, utility, and pollution exposure by
demographic group.
Distributional E↵ects In Table 7, we explore the distributional implications
of the relaxation of land use regulations in California. The four columns give
the percentage change in average income, rents, utility, and exposure to PM2.5
for di↵erent demographic groups. Utility is measured in log dollar equivalents.67
67Given that the idiosyncratic preference d⇣raws are dis tributed a⌘s Extreme-Value Type 1,P
household i’s expected utility is given by log 02 exp V̄ij0/ d plus a constant. To translatej J
this into log income equivalent, we first divide expected utility by ↵jd in each city j. Note thatP
log( 02 exp(V̄ 0/ j J ij d))
↵ gives expected utility measured in log income equivalent for a household whojd
92
Highly educated households benefit more than less educated households because
the income premium in cities is generally larger for educated workers (Baum-Snow
& Pavan, 2013). Further, single households experience larger utility gains than
married households, as single households are more mobile and therefore better
able to benefit from the drop in rents in Californian cities. Finally, all demographic
groups see a small increase in their average PM2.5 exposure as they increase their
concentration in large cities and in particular, the relatively polluted cities in
southern California.
Local Pollutants Figure 14 plots the changes in particulate matter
concentrations by CBSA when land-use restrictions in California are relaxed.
Specifically, the x-axis gives the change in PM2.5 concentration when we relax land-
use regulations in California compared to the baseline. The y-axis gives the number
of cities that fall into a given range of changes. The colors indicate the four Census
regions.
Similar to carbon emissions, there is a national reduction in PM2.5
concentration from relaxing land-use regulations in California. The mechanism
is quite similar to carbon emissions. Households are induced to live in California
where they use less electricity—due to California’s temperate climate—and the
power plants they use are less PM2.5-intensive. This leads to a reduction in PM2.5
in most CBSAs.
However, unlike CO2, the spatial distribution of PM2.5 emissions is
important as PM2.5 is a local, and not global pollutant. When households move
lives in city j—an increase in 0.01 in this object for example, provides a change in expected utility
equivalent to a 1% increase in income for household who lives in city j. We then take the average
across cities weighted by the household’s choice probabilities in the baseline counterfactual.
93
to California, this increases electricity demand in the WECC NERC region—
which overlaps closely with the Western Census region. This leads to an increase
in the level of PM2.5 emissions in WECC and therefore a slight increase in
PM2.5 concentrations in cities in the Western region. In all other regions, CBSAs
experience decreases in PM2.5. This is because energy demand falls in these regions
as households move away, and the o↵set in PM2.5 from local energy demand is
greater than the increase in PM2.5 from far away sources (namely, California). This
decreases both emissions of PM2.5 and concentration of PM2.5 in these regions.
Relax CA
15
10 Census Region
Midwest
Northeast
South
West
5
0
-0.010 -0.005 0.000 0.005
Change in PM2.5 Concentration from HH Electricity
Figure 14. Histogram of CBSA level di↵erences in particulate matter concentration
from electricity relative when land-use restrictions in California are relaxed relative
to the baseline.
3.6.2 Removing the Correlation Between Land Use Restrictions
and Emissions. The negative correlation between land use restrictions and city
94
Number of Cities
level emissions has important implications for national carbon emissions. To further
explore the implications of land use restrictions on carbon output, we simulate
setting land use restrictions to the level faced by the median urban household in
all cities.
The results are displayed in the third column of Table 5.68 The results in
panel I indicate that changing land use restriction in all cities leads to a dramatic
relocation from the South and Midwest to the West and Northeast. Specifically, the
population in the Northeast region increases from 18% of the total population to
43% while the population in the Midwest and the South decrease by roughly one
third to one half.
Panel II and III show usage and emissions from each energy type. Demand
for natural gas and fuel oil are high while demand for electricity is low in the cold
Northeast. As a result, natural gas usage increases by 0.7%, while electricity usage
decreases by 7.8%. As a result of this decrease in electricity usage and relocation
towards cities with more e cient power plants, emissions from electricity decrease
by 18.9%. Overall, this leads to a 3.5% decrease in national carbon output and over
an 8.5% increase in the national carbon e ciency of output. This implies a drop in
the social cost of carbon of $1.7 billion annually.
3.7 Robustness and Extensions
3.7.1 Sensitivity to Alternative Parameters. In this section, we
examine the robustness of our main results to alternative values of key parameters.
In particular, we recalculate the reduction in national carbon output resulting from
the relaxation of land use restrictions in California cities for a range of parameter
values. First, we examine the model’s sensitivity to the scale parameter of the
68In Appendix B.0.2.3, we show how the distribution of local pollutants change in this
counterfactual.
95
idiosyncratic preference draw,  d. Lower values of  d imply that household location
choice is more elastic with respect to wages and rents.69 Therefore, households will
be more likely to change their location decisions in response to changes in land use
restrictions.
The percentage reduction in carbon output relative to the baseline for a
range of values of  d for single and married households is shown in Panel (a) of
Figure 15. Recall in our baseline specification that we estimate  d = 0.17 for single
households,  d = 0.21 for married households without children, and  d = 0.40 for
married households with children and we found a decrease in carbon emissions of
0.6%. In the figure,  d for single households is displayed on the vertical axis and
the average of  d for married households is displayed on the horizontal axis. We
vary  d for married households such that the ratio of  d for married households
with children compared to married households without children is held constant
at the baseline level. Darker colors imply smaller changes in carbon emissions
while lighter colors imply larger changes. Figure 15 illustrates that the change in
carbon emissions is decreasing in  d for both single and married households. In
the extreme case when  d = 0.1 for both types of households, households are
very responsive to changes in rents. As a result, carbon emissions drop by 0.8%
when we relax land use restrictions in California. When  d = 0.8 for both types of
households, carbon emissions drop by roughly 0.3%.
Next, we examine the model’s sensitivity to the budget share of housing
parameter, ↵Hd . Recall that we estimated ↵
H
d = 1.49 for single households,
↵Hd = 1.44 for married households without children, and ↵
H
d = 1.92 for married
69For each counterfactual in which we change  d, we recalculate the amenity values ⇠jd such
as to keep the mean utility of each demographic group in each city equal to its baseline level.
Therefore, the distribution of households of each demographic group given the baseline levels of
land use restrictions will be equal to the baseline distribution with the original values of  d.
96
households with children. Higher values of ↵Hd imply households spend a larger
fraction of their income on housing and therefore will be more sensitive to housing
prices in their choice of where to live. The results are displayed in Panel (b) of
Figure 15. The vertical axis shows values of ↵Hd for single and the horizontal axis
shows ↵Hd for married households. We change ↵
H
d for married households such
that the ratio of the parameter for married households with children to married
households without children is held at the baseline level. Larger values of ↵Hd
of both types of households imply larger decreases in carbon emissions. When
↵Hd = 0.4 for both types of households, carbon emissions drop by 0.3% when
we relax land use restrictions in California. If we set ↵Hd = 3.2 for both types of
households, carbon emissions drop by roughly 0.8%.
Figure 15. Percentage change in national emissions from relaxing land use restrictions in
California for various parameter values. In panel (a), we display  d for single on the Y (vertical)
axis, and  d for married households on the X (horizontal) axis. Panel (b) shows the percent
reduction in carbon emissions as a function of ↵H for both types of households.
d
3.7.2 Endogenous Electricity Pricing. In our baseline
specification, we assume that electricity is produced at a constant marginal cost;
therefore, the supply curve of electricity is perfectly elastic. In this section, we
consider an extension in which the price of electricity is determined endogenously.
97
Specifically, we assume that electricity producers in each NERC region form
an upward sloping long-run electricity supply curve, reflecting di↵erences in costs or
productivity of potential electricity production opportunities within a region. For
low quantities, electricity can be produced at a low cost. As electricity production
increases, increasingly less productive resources must be utilized, which therefore
implies higher costs of production.
A number of papers examine the short run supply curves of electricity. The
short run electricity supply curve is often modeled as a “dispatch curve” with
constant or linear marginal costs, to reflect the unique way in which electricity is
allocated in the very short term.70 Essentially, electricity generators are ranked in
terms of their marginal cost of producing electricity. As demand increases, plants
are dispatched to produce power in increasing order of marginal cost. However,
this type of modeling approach is likely not a good representation of the long run
energy supply curve which we consider here. In the long run, energy producers may
respond to changes in energy demand by opening new reactors and new plants.
Therefore, we posit a more parsimonious long run electricity supply curve as:
CR = vRX

R
where XR is the total quantity of energy produced in region R,  is a parameter
equal to the inverse elasticity of the energy supply curve, and vR is a region specific
cost shifter.
Electricity is then transmitted to a specific local labor market at an additive
transmission cost,   .71j Given the assumption of perfectly competitive generation
companies, we can write the inverse energy supply curve to city j as
70For an example, see Ma, Sun, and Cheung (1999).
71This cost may directly reflect costs of transmissions or network congestion costs.
98
   
P elecj = bj +  log XR(j)
   
where bj =  j + log vR(j) .
To calibrate this model extension, we first calibrate the inverse elasticity
of the electricity supply curve as  = 11.27 , based on the estimates in C. Dahl and
Duggan (1996). We then choose the parameters bj to match state level electricity
prices.
The main counterfactual results with endogenous electricity pricing are
summarized in Appendix B.0.2.6, Table B8. Overall, the population distributions
across all counterfactuals are quite similar to the counterfactuals with perfectly
elastic electricity supply. Households spend a relatively small fraction of their
income on electricity and therefore changes in electricity prices have little impact
on their location choices. Natural gas and fuel oil emissions are also nearly identical
to the case with a perfectly elastic electricity supply. However, the reductions in
electricity usage and therefore overall carbon emissions are smaller in the case
of endogenous electricity prices. Overall this leads to a 0.4% reduction in carbon
emissions from the relaxation of land use restrictions in California.
3.7.3 Local Pollutants in Utility Function. In this section, we
consider an extension of our model in which local pollutants enter the utility
function. It is worth emphasizing that only local pollutants produced by household
electricity usage are endogenous in our model, while pollutants produced by
all other sources are held constant. A richer model would also include how the
distribution of households in space would lead to an increase in pollution from
changes in the spatial distribution of manufacturing firms, for example.
99
With this caveat in mind, let the households’ utility function be given by:
X
uij = ↵
c
d log c+ ↵
H
d logH + ↵
m m PM
jd log Ê + ↵ logPMj +  ij
m
PM
where PMj is the concentration of PM2.5 is city j. We set
↵
  =  .255 for alld
demographics groups based on the estimates from Bayer, Keohane, and Timmins
(2009).72 We recalculate the unobserved amenity parameters, ⇠jd, such as to keep
the mean utility of each demographic group in each city equal to its baseline level.
All other parameters are kept at their baseline levels. Mechanically, the inclusion
of PM2.5 in the utility function will lead to higher estimated values of ⇠jd, so the
population shares in the model match the data shares.
The results are displayed in Appendix B.0.2.6, Table B9. The results
are very similar to the baseline simulations. This is expected, given that PM2.5
emissions from power plants only constitute a small fraction of total PM2.5
emissions in a given city.73
3.7.4 Power Plant Substitution. One potential issue with our
counterfactuals is that new power plants built in order to accommodate increases
in demand for electricity may be cleaner or dirtier than the current stock of power
plants in that region. Therefore, the carbon emissions factors we use in our analysis
will change in response to increases in electricity demand. For example, our main
counterfactual of the relaxation of land use restrictions in California led to a
substantial increase in population and energy usage in California. As a result, new
power plants may be constructed in the corresponding WECC NERC region which
may be cleaner or dirtier than the current power plants in the region. If these new
72We use the instrumental variables results with no additional controls (Table 5, Column 3).
The results with other IV estimates are similar.
73We display the contribution of household electricity to total PM2.5 concentration across
various cities in Appendix B.0.2.3.
100
power plants are cleaner (dirtier) than the current stock of power plants, we will
underestimate (overestimate) the reduction in carbon emissions.
To investigate how endogenous changes in the composition of power plants
might a↵ect our results, we compare power plants built before and after 2000. We
find power plants built after 2000 emit considerably less CO2 per MWh than plants
built prior. Specifically, for the WECC NERC region, we find that power plants
built prior to 2000 emit 858 lbs of CO2 per MWh of electricity, whereas plants built
after 2000 emit only 597 lbs of CO per MWh.742 These results suggest that if new
power plants were built in response to increases in California’s population, these
new plants would be more carbon-e cient than the current stock of plants.
3.8 Conclusion
Household carbon emissions vary considerably across cities. Land use
restrictions, which are set by local governments, tend to be tighter in cities with
low carbon emissions and therefore encourage households to live in cities with less
moderate climates and higher greenhouse gas-emitting power plants.
We began by following Glaeser and Kahn (2010) and documented large
spatial variation in both the carbon e ciency of power plants and energy
consumption. Cities with more temperate climates (such as San Francisco) tend
to emit substantially less carbon than other cities. Furthermore, these cities also
tend to have very tight land use restrictions. To examine the e↵ects of land use
restrictions on national carbon emissions, we then estimated a model of household
sorting, energy demand, and locations that vary by power plant technology. We
found that the relaxation of land use restrictions in California leads to a decrease
in national carbon output of 0.6% and a decrease in the social cost of carbon of
74Section B.0.2.5 in the data appendix has further information on the full distribution of
emissions from power plants built before and after 2000.
101
$310 million annually. Our main conclusion is that the positive correlation between
tighter land use restrictions and the greenness of cities has large implications for
national carbon output.
Relaxing land use restrictions would likely impact the spatial distribution of
firms in addition to households. In our model, firms only use labor in production.
In reality, many firms use the same energy inputs as households – such as electricity
and natural gas. Additionally, firms also use land in production. Since local factor
prices (such as land) are first-order to firm location decisions (Suárez Serrato &
Zidar, 2016), relaxing land-use restrictions in California would lead to firms sorting
into California to take advantage of the lower land prices. Furthermore, when
energy is an input to production and more production shifts towards California—
where the electricity is carbon-e cient—carbon emissions would fall. Future
research could incorporate firm sorting and energy demand into our framework
to estimate the e↵ects of land use regulations on industrial carbon emissions.
Additional work could use our model to analyze the spatial implications of
the Clean Air Act. The model could also be used to analyze changes in carbon
emissions as a result of improved energy infrastructure and therefore easier
electricity transmissions across regions. Future research could extend the model to
analyze the e↵ects of improving insulation or policies that change the composition
of power plants – such as renewable energy subsidies.
102
CHAPTER IV
CARBON TAXES IN SPATIAL EQUILIBRIUM
4.1 Introduction
Carbon emissions create well-recognized negative externalities. The
Intergovernmental Panel on Climate Change (IPCC) inventories rising sea
levels, temperatures, and changes in the pattern, frequency, and intensity of
extreme weather events (storms, heat waves, and droughts) as a few of the likely
consequences of climate change. Among professional economists, carbon taxes
receive widespread support as a tool for reducing emissions due to the economic
e ciency o↵ered by the tax (Climate Leadership Council, 2021). Despite this
support from economists, global policy e↵orts to implement carbon prices have
been fairly limited.1 Sallee (2019) argues that the distributional concerns arising
from carbon pricing—and more specifically, the ability to precisely predict lump-
sum transfers for those who bear the greatest burden of the tax—account for
disparities between the policy preferences of economists and voters.
Several factors lead to heterogeneity across households in the burden of
carbon taxes. Carbon is a byproduct of energy production, so di↵erences in the
carbon intensities of power plants across regions will lead to spatial di↵erences in
the e↵ects of a carbon tax on electricity prices. These increases in electricity prices
(and other fuel prices)—and their di↵erences across space—create heterogeneous
initial impacts on households through two distinct channels: labor demand and
household energy expenditures. On the labor-demand side, a carbon tax will reduce
output from emissions-intensive industries and lead to a reallocation of input
demand away from energy and towards other inputs. Furthermore, industries
tend to cluster in particular cities; this clustering implies that a carbon tax
1As of 2020, some 40 countries had enacted some form of carbon pricing (World Bank, 2020).
103
will have di↵erential impacts on labor demand (and hence wages) across both
cities and sectors. On the energy expenditure side, household demand for energy
(derived from the demand for heating and cooling) varies across space, primarily
due to di↵erences in climate.2 Thus, a nationally uniform carbon price creates
heterogeneous impacts on households stemming from di↵erences across cities in
the energy price increases and the disutility delivered by these price increases
as a result of putting a price on carbon. The labor demand channel and the
household energy expenditure channel imply that the burden of a carbon tax
is a function of the joint spatial distributions of sectors (and their respective
production technologies), households, and the mix of fuels used regionally to
generate electricity. This paper contributes to the carbon-pricing policy debate by
estimating the spatial and sectoral distribution of incidence of a carbon tax across
education groups in the United States.
To measure the burden of a carbon tax, I develop and estimate a
quantitative spatial equilibrium model. At the core of the model is a discrete-
choice problem for households, where households must select both a sector and
a location. Wages are endogenous, and production is a city- and sector-specific
function of imperfectly substitutable labor and energy inputs. Locations vary
in terms of their amenities, their housing supply curves, the emissions intensity
of their electricity generation and power-plant technologies, and their input-use
intensities in producing goods and services. Output markets are assumed to be
perfectly competitive.
Within the model, the welfare e↵ects of a national carbon tax will vary
geographically and sectorally for four reasons. First, locations vary in terms of
2Lyubich (2022) demonstrates that location explains over half of the variation in household
carbon emissions—15-25% of the overall variation in carbon emissions.
104
the marginal benefit of energy consumption and the carbon content of the fuel mix
used by local power plants (Glaeser & Kahn, 2010). Cities with warmer climates,
such as Houston, tend to have a higher marginal benefit of electricity consumption
due to greater demand for air-conditioning, resulting in higher household energy
demand and thus greater carbon emissions. Second, within the U.S., the carbon
intensity of power plants varies significantly across regions; some areas, such as the
Midwest and South, are much more dependent on coal-fired electricity than other
areas, such as the West.3 Third, sectors vary in the amount of energy they use for
production processes and the degree to which labor and energy are technologically
substitutable. For example, the manufacturing sector is significantly more energy-
intensive than the services sector, so a carbon tax will have a considerably larger
e↵ect on manufacturing wages and employment than for services. Lastly, in the
context of the model, cities vary in their industrial employment composition.
Due to the di↵erences in the fuel mix used by regional power plants, a carbon
tax will di↵erentially impact energy prices across cities, which in turn will have
heterogeneous impacts on worker’s wages. In response to the energy price and wage
changes, workers can relocate across cities and sectors as the relative attractiveness
of each city-sector changes. This re-sorting of workers across space and sectors
results in equilibrium adjustments in rental markets that further a↵ect utility.
Therefore, accurate recovery of the overall tax incidence across di↵erent types of
households necessitates a general equilibrium analysis that permits households and
firms to respond in a variety of ways to the changes induced by the carbon tax.
I discipline the model’s structural parameters using a variety of publicly
available data. I use data from the American Community Survey (ACS) and
Census to estimate household preference parameters and household carbon
3Figure C2 in Section C.0.5 provides a map of US regional emissions rates from electricity.
105
emissions. More specifically, I estimate the model’s labor supply parameters using
a two-step procedure involving maximum likelihood and instrumental variables,
similar to the approach taken by Berry et al. (2004). I use a combination of
calibration and estimation to obtain production functions that are both city-specific
and sector-specific.
To monetize the incidence of a carbon tax, I calculate the average
compensating variation, which is the average dollar amount of additional income
that would be required for a household in each city-sector to maintain utility levels
in spite of the carbon tax. I find significant unequal distributional consequences
across cities and sectors from a uniform carbon tax. I find that a carbon tax of $31
per ton would result in a mean decrease of 926 vs. 1,417 utility-equivalent dollars
per year for college vs. non-college households, respectively – with significant
heterogeneity across cities and sectors. Furthermore, I find that this carbon tax
would reduce emissions by 19.8% and lead to a reallocation of workers away from
manufacturing (by 11.1%) and into less-carbon intensive jobs in the services sector.
Furthermore, to di↵erences in wages across cities, the compensating variation
measure (monetized incidence) masks important underlying heterogeneity in
the carbon tax burden. Thus, I separately examine compensating variation in
percentage terms rather than dollars— which I refer to simply as “incidence,” (as
opposed to monetized incidence or compensating variation). I find that cities on the
West Coast and New England experience lower incidence than cities elsewhere due
to their relatively carbon-e cient power plants and services-oriented economies.
The model predicts migration patterns across cities consistent with the
spatial variation in tax incidence. Generally, cities in the Western and New
England Census Divisions experience population increases, while cities in the
South and Midwest experience population decreases. For example, California
106
experiences an overall population increase of roughly 2%. Cities in California have
mild climates, source their electricity from carbon-e cient power plants, and have
services-oriented economies. Thus, a carbon tax induces migration to California, as
households benefit from California’s economy being relatively resilient to climate
policy. Despite being less mobile, non-college-educated households move at greater
rates in response to the carbon tax—underscoring the more-significant tax burden
that these households bear.
Motivated by the remarkable decline in the share of electricity generated
from coal over the last 15 years, I use the model to decompose the incidence of a
carbon tax into two distinct components: coal and non-coal.4 I re-calculate regional
emissions rates from electricity generation in the absence of coal and re-simulate
the $31 carbon tax in the context of this hypothetical alternative (and cleaner)
grid.5 I find that the compensating variation falls by nearly 40%, and this decline
exhibits regional heterogeneity. Coal-generated electricity is highly carbon-intensive
and thus is responsible for a larger share of the total incidence in coal-dependent
regions. This finding suggests that as the electricity grid decarbonizes, the payment
required to compensate households for a carbon tax will decline by a significant
amount.
I use my model to simulate a carbon tax with various compensation
schemes. Due to the regressive nature of flat carbon taxes, some proposed carbon-
pricing legislation includes progressive transfer payments.6 In simulations with
4The decline in coal’s share is well documented— for example, see Mendelevitch, Hauenstein,
and Holz (2019). I summarize the national and regional decline in the share of coal-generated
electricity in Figure 18.
5To be clear, this exercise is purely decompositional. Carbon pricing policies impact the rate of
adoption for carbon-e cient electricity generation since coal is carbon-intensive. For an example,
see Scott (2021a).
6For example, the recently introduced Stemming Warming and Augmenting Pay (SWAP)
act specifically calls for “...20% (of revenues) to establish a carbon trust fund for block grants to
107
carbon taxes and transfers, I focus on varying the progressivity of the payments
to households. The simulations reveal a novel relationship between the progressivity
of transfers and aggregate carbon emissions: aggregate emissions are lower with
progressive transfers than with lump-sum transfers. The mechanism behind this
relationship is straightforward. Wages exhibit spatial and sectoral correlation, so
progressive transfers are also correlated across space and sectors. In an equilibrium
with progressive transfers, lower-wage cities receive larger transfers and thus attract
more workers (relative to a policy with lump-sum transfers), all else equal. The
progressivity of the transfers will impact aggregate carbon emissions if wages are
correlated with carbon emissions (at the city-sector level) due to the reallocation of
workers into areas with higher transfers.
Indeed, there is a positive correlation between wages and emissions in the
data, and the model predicts a larger share of workers shifting away from jobs with
high wages in emissions-intensive sectors, thus causing aggregate emissions to fall.
My results suggest that using carbon tax revenue for income redistribution may
have the unappreciated additional benefit of reducing aggregate emissions—and
therefore, has the potential to enhance the e↵ectiveness of the policy in meeting
emissions targets.
Literature. I am not the first to recognize—or to model— the distributional
impacts of carbon taxation. For example, Rausch, Metcalf, and Reilly (2011)
(RMR) use a calibrated version of MIT’s US Regional Energy Policy model and
a sample of roughly 15,000 households to demonstrate considerable heterogeneity
o↵set higher energy costs for low-income households, climate adaptation, energy e ciency, carbon
sequestration, and research and development programs” (U.S. House of Representatives, 2019).
108
across demographic groups in the incidence of a carbon tax.78 Hafstead and
Williams (2018) use a two-sector general equilibrium model and conclude that
the unemployment e↵ects of a carbon tax will be negligible due to growth in clean
industries. Using a macroeconomic lifecycle model, Fried, Novan, and Peterman
(2021) (FNP) find that, in the welfare-maximizing allocation of carbon tax revenue,
two-thirds goes to a reduction in capital-income taxes and one third towards
increasing the progressivity of the income tax. My results are complementary to
those of FNP. While I abstract from dynamics, my model’s geographic and sectoral
heterogeneity allows me to capture the relationship between income redistribution
and aggregate emissions. In a recent working paper, Castellanos and Heutel (2019)
(CH) conclude that alternative assumptions about worker mobility potentially
play a significant role in the aggregate employment e↵ects from carbon pricing.
RMR and CH make di↵erent assumptions about labor mobility; in RMR, workers
are mobile across sectors but not locations. CH examines edge cases with perfect
mobility and perfect immobility. My work explicitly models (and then estimates)
the process by which households make city-sector choices—including moving
costs. Even if employment remains constant, my work accommodates the fact that
relocating to new jobs and locations is costly.
An extensive empirical literature has demonstrated that environmental
regulation has heterogeneous impacts across sectors. Recent work by Yamazaki
(2017) finds that more energy-intensive sectors saw larger relative losses in wages
7Other examples of research that examines the distributional consequences of carbon pricing
includes Goulder, Hafstead, Kim, and Long (2019), Williams III, Gordon, Burtraw, Carbone, and
Morgenstern (2015), and Beck, Rivers, Wigle, and Yonezawa (2015). To my knowledge, I am the
first to estimate the heterogeneous welfare e↵ects from a carbon tax specifically in a locational
discrete-choice setting.
8For details on the Regional Energy Policy model, see Yuan, Rausch, Caron, Paltsev, and
Reilly (2019).
109
from the carbon tax in British Columbia, Canada. In British Columbia, overall
unemployment decreased due to a shift in demand towards less energy-intensive
sectors due to the province’s revenue recycling decisions (i.e., transfers that
households received from the tax).9 In complementary work, Yip (2018) finds
that the British Columbia carbon tax was implemented mainly at the expense of
individuals without a college degree, as these workers are generally in more energy-
intensive sectors with fewer outside options.10 Other research has demonstrated
broader distributional e↵ects from environmental regulation. For example, Walker
(2013) examines the labor-market impacts of the 1990 amendments to the Clean
Air Act (CAA). These amendments involved command-and-control regulations
that established thresholds for the maximum allowable ambient concentrations of
pollutants. Using a triple-di↵erence approach, Walker finds significant reductions
in employment in manufacturing (and other energy-intensive sectors) due to these
regulations. Curtis (2014) examines the labor market impacts of the EPA’s NOx
budget trading program—which was a type of cap and trade program enacted in
2003—and reaches conclusions similar to Walker (2013). Specifically, sectors that
are more energy-intensive experience larger losses in unemployment.
Methodologically, the present paper is closely related to Diamond (2016),
Piyapromdee (2021), Colas and Hutchinson (2021), and Colas and Morehouse
(2022) (CM). These papers estimate general equilibrium models of location choice
in which wages and rents respond endogenously to agents’ location choices. The
model in CM is designed to measure changes in residential carbon emissions from
9The tax was supposed to be revenue-neutral. In practice, it did not turn out this way.
Yamazaki (2017) notes “tax credits have been exceeding tax revenues since its implementation.”
10Other recent empirical work has examined the e↵ects of carbon taxes implemented in di↵erent
countries, such as Martin, De Preux, and Wagner (2014). These authors find minimal adverse
unemployment impacts from the UK’s carbon tax.
110
the relaxation of stringent land-use regulations. The present paper departs from
the model in CM along three significant dimensions. First, I model energy as a
production input for firms. This allows for endogenous wage changes in response
to energy price changes that ensue from a carbon tax. Second, firms vary across
cities and sectors—with di↵erent factor intensities and productivities. The sectoral
composition of industries at a given location will impact the welfare of local
workers (for reasons described above) and thus will have first-order consequences
for household sorting. Lastly, households make a joint choice concerning both
their city and their sector. To assess the welfare e↵ects of a carbon tax, my
model combines empirical insights from a large literature on the distributional
consequences of carbon pricing and extends the modeling strategy used in Colas
and Morehouse (2022). I build a unified framework that simultaneously analyzes
the variation in labor-market responses to carbon taxes across both cities and
sectors.
Overall, my objective in this paper is to improve policy-makers’
understanding of the distributional consequences of carbon taxes. The empirical
structural model I develop allows me to obtain quantitative estimates of the
varying incidence levels across cities and sectors. The rest of this paper proceeds as
follows. Section 4.2 details the structural model, Section 4.3 provides an overview
of the data, Section 4.4 discusses the estimation procedure and how key parameters
are identified, Section 4.4.3 discusses the parameter estimates, section 4.5 examines
selected counterfactuals, and Section 4.6 concludes.
4.2 Model
This section describes a general equilibrium model where households make
a joint, discrete choice over location and sector. Conditional on location and
sector, households consume a numeraire good, housing, and energy services. These
111
di↵erent decisions, and the linkages between these related markets, are crucial for
determining the net welfare e↵ects of a carbon tax. Labor demand arises from
perfectly competitive firms that di↵er across locations and sectors. Housing demand
follows from the location choices of agents, and housing supply is increasing in the
price of housing.
More specifically, a household has an exogenously given education level and
birthplace. Locations vary in terms of the location-specific consumption goods
(amenities) they provide, wages, rents, the marginal utility of energy consumption,
and the carbon intensity of the local power plants. Sectors vary in input use
intensity and unobservable sectoral amenities (e.g., non-wage employment benefits).
Firms with nested CES technologies combine college-educated and non-college-
educated labor with electricity and gas to produce outputs within each sector at
each location. Each location functions as a small open economy, so wider national
and international markets always satisfy any excess demand.
To capture the labor-market e↵ects of a carbon tax, I introduce
heterogeneity across locations and sectors of production for the output good.
Across locations and sectors, firms vary by all input-use intensities (a set of
parameters). Variation in production parameters reflects di↵erences across locations
in available labor supply and variation in regional energy prices. Furthermore,
across sectors (but not locations), firms vary by their elasticities of substitution
across di↵erent types of energy inputs and the mix of energy and labor. Some
sectors, such as agriculture, can substitute relatively easily between labor and
energy. Other sectors, such as construction, cannot.
In my model, a uniform national carbon tax will have location- and sector-
specific welfare e↵ects for several reasons. First, locations vary in their marginal
utilities of energy consumption (e.g. they have di↵erent climates), and their power
112
plants have di↵erent carbon intensities. Consequently, the consumption of the
same amount of electricity will imply di↵erent levels of emissions across locations.
Second, a carbon tax will have varying e↵ects on wages. Consumption of energy
in production leads to emissions. The specific amount of energy used and carbon
emitted depends on the firm’s sector and location. After the carbon tax, wages will
change via two particular channels. First, as a direct result of the carbon tax, the
relative price of energy inputs will increase, so the firm will substitute other inputs
and reduce output. Second, there will be adjustments in equilibrium wages to the
extent carbon taxes have are di↵erential impacts on labor demand across locations
and sectors. Thus, workers in regions/sectors with higher carbon emissions will see
a relatively large decrease in wages and will sort towards sectors and locations with
lower carbon intensities.
4.2.1 Households. A household consists of one or more individuals.
If a household contains more than one working-aged individual, the “agent” refers
to the putative household head. Agents are endowed with an education level and
native birth state. They receive utility from the consumption of a numeraire good,
housing, energy services, and amenities. Each agent makes a one-time decision over
locations and employment sectors. Let j 2 J index cities, n 2 N index sectors,
and e 2 {l, c} index education groups (where l indicates that the household has
”less than a college degree” and c indicates that the agent has a ’college degree
or greater”). Agent i’s utility from living in city j and working in sector n is
characterized as:
X
ui(c, h, x
c
m|e, j, n) = ↵e log c+ ↵He log h+ ↵mejn log xm +  ijn, (4.1)
m
where c is consumption of the numeraire good, h is consumption of housing, xm is
consumption of fuel type m 2 {elec, gas, oil} and  ijn is amenities. I parameterize
113
amenities as
 ijn = f(j,Bi) + ⇠ejn +  e✏ijn, (4.2)
where the function f(j,Bi) is a function of the agent’s birth location, Bi, and
location j, ⇠ejn is an unobserved component of amenities that all workers share
within an education group-city-sector. The term ✏ijn is an idiosyncratic preference
shock drawn from a Type I Extreme Value distribution (EV1) with mean zero
and shape parameter  e. Variation in ⇠ejn captures di↵erences in amenities
across locations and sectors. Heterogeneity in ⇠ejn across cities (but within the
same sector) is driven by heterogeneity in location-specific market or non-market
consumption goods such as air quality, crime, schools, or the number of restaurants
in the city. Variation in ⇠ejn within the same city but across sectors is due to
variation in the availability of non-pecuniary benefits across sectors. I parameterize
f as:
           
f(j,Bi) =  dive I j 2 Bdiv +  disti e   j,Bsti +  dist2 2 j,Bste i , (4.3)
   
where I j 2 Bdiv is an indicator for j being in worker i’s birth division,  (j,Bsti )
is the Euclidean distance between location j and the agent’s birth state Bsti , and
 2(j,Bsti ) is the squared Euclidean distance between j and Bsti .11 As noted by
Bayer et al. (2009), individuals tend to have a preference for locations with greater
accessibility to their birth state, where I model accessibility simply as distance.
Agents face the following budget constraint
X
wejn = c+RjH + P
m
j xm, (4.4)
m
11This specification is slightly unusual in that I use an indicator for the individuals’ census
division of birth and not their state of birth. The model includes only 70 CBSAs (plus 9 census
divisions as outside options). Not every state is represented, but all census divisions are.
114
where wejn is the wage level for an agent of education level e in city j and sector n.
R mj and Pj represent the rental and energy prices (of each type m) in city j, which
are constant across sectors and demographic groups.
Maximizing the utility described by equation (4.1) subject to the budget
constraint represented by equation (4.4) yields constant shares of income devoted to
housing and fuel consumption:
? ↵
Hw
H = e ejnejn ↵ejnRj
↵mm? ejnwejnxejn = m 8m 2 {elec, gas, oil},↵ejnPj
where to simplify the notation in what follows, I define the parameter ↵ejn as:
X
↵ cejn = ↵e + ↵
H + ↵me ejn.
m
I then solve for the agent’s constrained utility maximization problem to yield
the corresponding indirect utility function associated with location j and sector n
X
vijn = (↵ejn) log(wejn)  ↵He logRj   ↵mejn logPmj + f(j,Bi) +  ̂ijn, (4.5)
m
where I again simplify the notation by defining:
X    
 ̂ijn =  ijn + ↵
m
ejn log ↵
m
ejn .
m
Given the EV1 assumption for the idiosyncratic preference shock (✏ijn) the
probability that agent i with education level e chooses option jn is given by the
familiar conditional logit form:
exp( v̄ijn )
P eijn = PP
 e
v̄ , (4.6)
exp( ij
0n0
  )
0 0 ej n
where v̄ijn = vijn    e✏ijn.
115
4.2.2 Firms & Housing Supply. Firms competing in perfectly
competitive factor markets combine both labor and energy inputs to produce a
sector-specific, tradeable good. I model each location as a small, open economy, so
firms treat their output price (denoted by Pn) as exogenous. Firms in city j and
sector n produce according to:12
Y ⌘ 1 ⌘jn = AjnKjnIjn ,
where Ijn is a conventional CES aggregator for energy and labor inputs which is
specific to that location and sector, jn:
⇣ ⌘ 1
⇢n ⇢n nI ⇢= ↵ E eljn jn jn + (1  ↵jn)L el eljn .
Furthermore, the CES aggregator is applied to two-component CES sub-
aggregators. Ejn aggregates the use of electricity (denoted by Ejn) and natural
gas (denoted by Gjn) by firms. Ljn aggregates the use of workers with a college-
degree-or-more education (denoted by Cjn) and workers having less than a college
degree (denoted by Ljn) by firms. Specifically, these sub-component aggregators are
parameterized as:
⇣ ⌘ 1
n n n
E ⇢e ⇢ ⇢e ejn = ⇣jnEjn + (1  ⇣jn)Gjn
    1
Ljn = ✓jnC⇢ljn + (1  ✓jn)L
⇢l ⇢
l
jn .
Electricity demand by firms generates emissions indirectly (at the regional
power plants), so these emissions are sensitive to both use and the carbon e ciency
of local power plants. Natural gas consumption leads to direct emissions but does
not vary by location in the model because I assume the carbon emissions rate of
natural gas is the same everywhere.
12The recent applied general equilibrium literature has utilized nested CES production functions
with various functional forms. See Brockway, Heun, Santos, and Barrett (2017) for a discussion.
116
Given that I assume factor markets are perfectly competitive, input prices
are equal to their marginal products. I assume the supply of capital is perfectly
elastic with rental rate r̄. The firm chooses its level of capital such that the price
of capital is equal to its marginal revenue product.13 Specifically, the first-order
condition for capital utilization yields:
 ! 1
P A ⌘I1 ⌘ 1 ⌘n jn
K = jnjn . (4.7)
r̄
Using equation (4.7), I can write the system of first-order conditions to derive the
inverse energy and labor demand curves:
n n n n
PE = A I1 ⇢ (⇢  ⇢ )el el e ⇢e 1jn jn jn Ejn ↵jn⇣nEjn
n n
G A I1 ⇢ E (⇢  ⇢
n) n
P = el el ejn jn jn jn ↵jn(1  ⇣ )G
⇢e 1
n jn
(4.8)
1 ⇢n (⇢nC A I L  ⇢l)W = el el (1  ↵ )(✓ )C⇢l 1jn jn jn jn jn jn jn
L A 1 ⇢
n (⇢n ⇢
W = el el l
)
jn jnIjn Ljn (1  ↵jn)(1  ✓jn)L
⇢l 1
jn ,
where
✓ ◆ ⌘
1 ⌘
A Ajn⌘jn = PnAjn (1  ⌘).
r̄
Rents. The housing supply curve is upward sloping with city-specific elasticities
and intercepts. Specifically, I parameterize the housing supply curve as:
 
Rj = K̄ H
j
j j . (4.9)
Di↵erences in K̄j across cities reflect di↵erences in local construction costs.
The amount of land available for production and the tightness of local land-use
restrictions drive variation in  j (Saiz, 2010). For example, consider a city with less
land available for development. All else equal, the marginal cost of developing land
that is relatively more scarce will be greater, which will lead to a higher value of  j.
13In Appendix C.0.1.1, I provide more details for the first-order condition derivations.
117
Taking logs of both sides of equation (4.9) yields:
log(Rj) = log(K̄j) +  j log(Hj). (4.10)
The log-log form in equation (4.10) highlights the constant elasticities of the
housing supply curves used in the model.
4.2.3 Energy Supply. There are three energy markets in the
model: electricity, natural gas, and oil. For each market, demand is endogenous
and downward sloping. I assume that natural gas and fuel oil are traded
on international markets, and their supply is perfectly elastic. Due to high
transmission costs, I assume electricity is traded within NERC regions but not
across them. Furthermore, I segment electricity supply into two separate markets:
residential and industrial. Electricity supply varies across the type of consumer
k due to di↵erences in transmission costs for households compared to firms.
Conditional on consumer type, electricity supply varies across local labor markets
j due to di↵erences in transmission costs within a NERC region R. I parameterize
the inverse supply curve for electricity as:
P eleckj = a
µ
kjQR(j), (4.11)
where k 2 {Residential, Industrial} indexes the consumer “type”, akj is the
consumer-city intercept, QR(j) is the electricity supply in NERC region R (where
R(j) maps cities to their corresponding NERC region), and µ is the inverse
electricity supply elasticity.
To be clear, the model developed in this paper says nothing about dynamics,
and any identified equilibrium is considered a “long-run” equilibrium. Typically in
the short run, electricity markets models use “constant-order dispatch curves.” In
118
the long run, however, electricity suppliers can respond to changes in demand by
opening new power plants or switching fuel types.14
4.2.4 Emissions. In the context of the model, carbon emissions arise
from the consumption of energy inputs by agents and firms. Agents consume
natural gas, fuel oil, and electricity, whereas firms consume natural gas and
electricity. I assume a constant carbon emissions factor of 117 lbs per thousand
cubic feet for natural gas and 17 lbs per gallon for fuel oil.15 Emissions from
electricity generation vary across NERC regions, denoted by  elecR . I assume
that total regional carbon emissions from electricity in a NERC region equals
the output-weighted average carbon-emission factors for individual electricity
generating units (EGUs). The emissions factor in NERC region R is therefore given
by:
X elec CO
 elec = g ⇥ 2,gR ,elecR elecg2R g
where elecg is the amount of electricity produced by a generator g, elecR is the
total amount of electricity produced in NERC region R and CO2,g is the total
(yearly) amount of carbon dioxide emitted by generator g. More generally, I write
the emissions factor for fuel-type m in city j as:
8
><> elec
m R(j)
if m 2 {elec}
 j =
:>> m if m 2 {gas, oil}
To obtain aggregate emissions, I multiply the energy consumption in city j and
sector n by the respective conversion factors for agents and firms and then sum
14Scott (2021b) shows that the EPA’s Mercury and Toxics Air standards induced many power
plants to convert their coal generators to natural gas.
15https://www.eia.gov/tools/faqs/faq.php?id=73t=11
119
these. Concretely, this is given by:
XX
Emis =  mj f̂jn,
j n
P P
where f̂jn = m e N
m
ejnxejn + Ejn + Gjn is the sum of agent fuel consumption
(Nejnxmejn) for each city-sector and firm fuel consumption.
4.2.5 Equilibrium. Equilibrium in the model is achieved when agents
and firms make optimal choices and all markets clear. Specifically, an equilibrium
requires:
(1) Utility Maximization. Each agent must be in a sector and at a location
that yields maximal utility, given their constraints. The equilibrium
population for each education group-city-sector, N?ejn, can thus be determined
P
by: N? 1 eejn = N ⇥ sejn, where sejn = N i Pijn are the shares computed from
the choice probabilities in equation (4.6).
The population distribution determines each city’s housing and energy
demand. Housing demand in city j is given by the sum of all individual
agents’ demands. I write total equilibrium housing and energy demand in
city j as
XX
D ? ⇥ ↵
H
H = N e
wejn
j ejn ↵
e2E n2N ejn
Rj
XX m (4.12)
D ? ↵ w⇥ ejn ejnxj = Nejn m 8m 2 {elec, gas, oil.}↵
e2E n2N ejn
Pj
Aggregate labor supply is given by the number of e ciency units of labor
supplied by each worker:16
LSejn = N eejn ⇥ ` . (4.13)
16Estimation of e ciency units of labor is relatively standard and thus the details can be found
in Section C.0.1.2
120
(2) Profit Maximization. Firms maximize profits. This implies that the first-
order conditions given by equation (4.8) must be satisfied.
(3) Market Clearing. All markets in the model need to clear. Namely, supply
and demand must be balanced in the labor market, in the housing market,
and in all energy markets.
4.3 Data
I combine data from multiple sources. I obtain individual-level data from the
ACS and Census. Data for energy prices and sectoral energy use data come from
the Energy Information Association (EIA). I employ data from the Environmental
Protection Agency (EPA) to calculate power-plant carbon emissions.
4.3.1 Sources.
Household Data. The time-aggregated 5-year ACS files (Ruggles et al., 2010)
have detailed individual-level information for more than 5 million individuals
in the US from 2012-2016. Crucially, the ACS has both the location where the
individual currently resides (down to the MSA level) and their current occupational
sector. Furthermore, the ACS provides information on the individual’s monthly
rent payments, pre-tax and after-tax wages, and energy expenditures for various
fuel types. In estimation, I use repeated cross-sections consisting of o cial 5%
samples of 1990, 2000, and 2010 decennial censuses. I stratify households into one
of two education levels: having a college degree (or more) or having less than a
college degree. In selecting my sample, I closely follow the strategies used by other
researchers and thus relegate the details of the process to Appendix C.0.7.
CBSA Data and Sectoral Data. My measure of a “city” (or location,
in the model) is a Core Based Statistical Area (CBSA). CBSAs correspond to
121
distinct (and relatively closed) labor markets and are the o cial definition of a
metropolitan area for the O ce of Management and Budget. For tractability,
I restrict the choice set to the 70 largest CBSAs by 1980 population, plus
nine additional “outside options”—one for each census division. I categorize
workers as participating in one of five sectors: services, construction, agriculture,
manufacturing, and an outside-option sector. These five sectors account for roughly
90% of total 2016 employment.17 My selection of cities and sectors results in a
choice set containing 395 elements, where each alternative is a city-sector pair.
Recall that I focus on household consumption of three energy types: electricity,
natural gas, and fuel oil. The ACS and Census datasets contain information on
household expenditures of each of these energy types. I combine household energy
expenditure data with state-level energy price data from the EIA to calculate
household energy consumption. The methods by which I construct wage, rent, and
household energy consumption series are detailed in in Appendices C.0.1.2, C.0.1.3,
and C.0.2 respectively.
Energy and Emissions Data. I use sector-level aggregated energy
consumption data from the EIA. The EIA’s Manufacturing Energy Consumption
Survey (MECS) provides information on aggregate manufacturing energy
consumption, while EIA’s Annual Energy Outlook provides aggregate energy
consumption data for construction, agriculture, and other sectors. I also collect
data on aggregate electricity and natural gas consumption for the services sector
from the EIA. For privacy (and security) reasons, none of my public-use data
contain information about sectoral energy demand at the city level. I impute
city-sector energy consumption as that city’s share of employment (for that
17I drop some sectors such as military and other public services from the sample. For more
details, see Appendix C.0.7.
122
sector) multiplied by total sectoral energy consumption. In other words, energy
consumption for a city-sector is proportional to the city’s level of employment for
that sector.18
Carbon emissions from electricity vary with the fuel used to generate that
electricity. I use plant-level data from the EPA’s Emissions Generation Resource
Integrated Database (eGRID). Local power plants often trade with each other to
meet demand, so I use nine North American Electric Reliability Council (NERC)
regions to calculate carbon emissions factors for electricity. While power plants
occasionally trade across the borders of these NERC regions, the NERC regions
are, for the most part, e↵ectively closed markets (see (Holland & Mansur, 2008)).
I calculate the emissions factor as the weighted average of CO2 emissions per
megawatt-hour of electricity across all plants in a given NERC region. A map of
these regions and their respective emissions factors is provided in section C.0.5.
4.4 Estimation
In taking my model to the data, I use a combination of calibration and
estimation techniques. I focus on the exposition of the labor supply parameters.
The labor demand and rent parameters are fairly standard, and are described in
Appendix sections C.0.1.2 and C.0.1.3, respectively. Appendix Table C3 provides a
full summary of the model’s estimation and calibration.
4.4.1 Labor Supply. To estimate the preference parameters
in the agent’s utility function, I use a two-step estimation procedure that
combines maximum likelihood and an instrumental variables approach. The
estimation procedure exploits repeated cross-sections of household microdata.
Specifically, I use repeated cross-sections of 5% samples of the U.S. Census for
18For more details, see Appendix C.0.7.2. This assumption implies that energy-labor ratios will
be constant across cities (but not necessarily across industries).
123
1990, 2000, and 2010 and the 2017 five-year American Community Survey. Let
t 2 {1990, 2000, 2010, 2017} denote the sample year. In what follows, I provide
details for each step of the estimation routine.
Step one: Maximum Likelihood. I normalize indirect utility by the scale
parameter of the idiosyncratic preference shock. More specifically, I divide equation
4.5 by  e to yield:
X
v = ⇥w log(w ) ⇥rijnt e ejnt e log(Rjt)  ⇥m mejnt logPjt +
m
           
⇥divet I j 2 Bdiv +⇥dist  j,Bst +⇥dist2 2 j,Bsti et i et i +
⇠ejnt + ✏ijnt,
where the new notation for the preference parameters (⇥) indicates the original
parameter multiplied by 1  . I write the shared (conditional on education group)e
component of utility associated with each city-sector as:
X notzo}b|se{rved
  = ⇥w log(w r m mejnt e ejnt) ⇥e log(Rjt)  ⇥ejnt logPjt + ⇠ejnt . (4.14)
| {z m }
observed
I will refer to the  ejnt values as the “mean utilities” associated with each
alternative. I emphasize the separability between the observable and unobservable
components to the mean utilities because this structure is crucial for matching the
model’s choice shares to the choice shares observed in the data. Given equation
(4.14), I can re-write the probability that agent i chooses city-sector jn as:
       
exp   +⇥divI j 2 Bdive jnt et   i +⇥
dist
  et   (j,B
st) +⇥dist2 2i et (j,Bst)Pi = P P i   .
exp  ej0n0t +⇥div 0 div distet I j 2 Bi +⇥et   (j0,Bst) +⇥dist2i et  2 (j0,Bsti )
j02J n02N
(4.15)
124
Then, using these choice probabilities, the log-likelihood function is given by:
XNe XX
L(⇥et) = Iijn log(Pi), (4.16)
i=1 n2N j2J
where Iijn is an indicator equal to one if agent i chooses to live in city j and work
in sector n and N e is the total number of workers of education group e. I jointly
estimate the mean utilities  ejnt and the parameter vector ⇥et with a nested fixed-
point algorithm, proposed in Berry (1994).19 For details of the implementation of
this algorithm, see appendix C.0.6.1.
Step two: Decomposition. In the second step, I decompose the mean
utilities to estimate the parameter vector (⇥we ,⇥
r
e). To limit the dimensionality of
the parameter space, I elect not to estimate the parameters ⇥mejnt. Instead, I follow
↵m
Colas and Morehouse (2022), and define ↵̃m ejntejnt = ↵ . Given the Cobb-Douglasejt
xm ⇥Pm
utility function, the expenditure share of fuel type m is given by ejnt jt = ↵̃mwm ejnt.
ejnt
I choose values for the ↵̃mejnt to match the estimated expenditure shares.
20 Next, I
rewrite the mean utility as:
 ejnt = ⇥
w
e log(w̃
EA r
ejnt) +⇥e log(Rjt) + ⇠ejnt, (4.17)
P    
m
where w̃EA
log(wejnt) 
= Pm
↵̃ejnt log(Pjt)
ejnt   m is net income adjusted for the1 m ↵̃ejnt
energy budget.21 Taking first di↵erences of equation (4.17) yields my estimating
equation:
   = ⇥w  log(w̃EA) +⇥rejn e ejn e  log(Rj) + ⇠ejn, (4.18)
19I implement this algorithm with the Nevo (2000) strategy to speed up the contraction
mapping proposed in Berry (1994). With a slight abuse of notation, the Nevo contraction is given
data
s
by exp( ⌧+1) = exp(  ) ⇥ jn⌧ model where ⌧ denotes iteration number and smodel( ⌧ ) are the
s (  ) jn
jn ⌧
predicted choice shares—which are a function of the mean utilities.
20For details on how I impute baseline energy use by city and demographic group, see Appendix
C.0.2.
21For details of this transformation, see Appendix C.0.3.
125
where  ⇠ejn is the change in the shared unobservable component of amenities.
Changes in unobservable amenities at the city or sector level (such as construction
of a new park) mechanically confound OLS estimates of ⇥we and ⇥
r
e. For example,
consider a city-wide school improvement program.22 Such a program will induce
migration towards this city (due to an increase in the value of choosing this
location). Equilibrium wages and rents adjust to the new population level
(governed by the equations described in Section 4.2), further a↵ecting utility. Thus,
even after taking first di↵erences, ⇥we cannot be consistently estimated via pooled
OLS due to the endogeneity caused by changes in unobserved amenities.
I use an instrumental variables strategy that exploits exogenous local labor
demand shocks. More specifically, I employ an instrument first introduced by
Katz and Murphy (1992). The instrument uses historical industry concentration
patterns at the city level and interacts them with changes in hours worked across
each industry.23 Specifically, I can write the Katz-Murphy (KM) index for city j
between any two sample periods as:
X
 Z = !1990ejnt ej◆ ⇥ ( Hourse, j,◆) ,
◆2n
where !1990ej◆ is the 1990 share of total hours worked by education group e in
industry ◆ in city j as a fraction of the total hours worked by education group e in
all industries in city j in 1990.  Hourse, j,◆ is the change in national hours worked
in all cities other than city j. I construct the di↵erences in national hours (omitting
city j),  Hourse, j,◆, as decadal di↵erences between each of my sample years.24
22Diamond (2016) considers the case where residential amenities are endogenous to individual
location choices.
23For a discussion of shift-share instruments see Goldsmith-Pinkham et al. (2020).
24Given that I am estimating the model’s labor supply parameters using pooled first di↵erences,
I need to estimate mean utilities (and hence individual moving-cost parameters) for each of
my cross-sections. Each cross-section has a likelihood function constructed from millions of
observations and 395 alternatives. Even with cloud computing, it is not computationally feasible
126
Finally, to instrument for ⇥re, I follow Diamond (2016) and interact the
Katz-Murphy index with the elasticity of the housing supply curve. Note that I
construct my current instrument such that it generates exogenous labor demand
shocks at the city-sector level. Rents are assumed to vary only across cities (and
not sectors), so I use a slightly di↵erent version of the instrument in which I sum
over all industries and sectors within a city. Concretely, I write the “city-level” KM
P
index as:  Z̃ 1990ejt = n !ejn ⇥ ( Hourse, j,n). Di↵erences in the responsiveness of
housing prices to population changes generate the variation used to identify ⇥re. For
example, suppose we have two cities that experience identical labor demand shocks.
The city with the less-elastic housing supply curve will see rents bid up faster. This
variation in rents is assumed to be exogenous to changes in unobservable amenities.
After estimating the agent’s preference parameters and the mean utilities for each
sector-city alternative, I calculate the unobservable component of amenities as the
residuals from equation (4.17).
4.4.2 Other Parameters.
Electricity Supply The reduced-form equilibrium expression for residential
electricity prices is given by:
log(P elec) = a + µ⇥ log(xelec,Dkj kj j ),
m
where xelec,D
P P ↵ w
ejn ejn
j = e2E n2N Nejn⇥ ↵ Pm is electricity demand in city j. I calibrateej j
the electricity supply curve using  = 12.7 following C. Dahl and Duggan (1996).
to estimate the individual choice parameters on the entire sample. As a consequence, I make
various sample restrictions to limit the number of observations. I describe these in detail in
Section C.0.7.
127
Simplifying this expression yields an expression analogous to equation C.16:25
    !
µ XX ↵elec ⇥ wejn)
log(P eleckj ) = log N
ejn
ejn + akj for k = residential,
1 + µ ↵
e n ejn
(4.19)
I choose the akj values to match the data. When k = industrial, I set akj =
P
log(P eleckj )   µ ⇥ log(Ej), where Ej = n Ejn is firm energy consumption in city
j (aggregated across sectors).
Firms and Rents As does Card (2009), I calibrate the elasticity of
substitution between college and non-college workers to 2.5. I set my baseline
calibration of energy-labor substitution elasticities to those in Koesler and
Schymura (2012).26 Inter-fuel-substitution elasticities come from Serletis, Timilsina,
and Vasetsky (2010).
I solve for input use intensities and total factor productivity (TFP) using
relatively standard algebra and thus relegate the details to Appendix C.0.1.2. I
calibrate housing supply elasticities to those estimated in Saiz (2010). The reduced-
form rental supply can be found in Appendix C.0.1.3.
4.4.3 Parameter Estimates. Table 8 displays the preference
parameters estimates.
25I abuse notation here slightly. Technically, the intercept term in equation 4.19 is aj1+ .
26Fried (2018) calibrates a similar parameter, the elasticity of substitution between energy and
non-energy inputs, to be close to zero. This requires energy and non-energy inputs to be used in
approximately fixed proportions.
128
No College College
Year ⇥div ⇥dist ⇥dist2 ⇥div ⇥distlt lt lt ct ct ⇥
dist2
ct
1990 1.696 -3.4318 0.741 1.418 -2.649 0.628
(0.004) (0.002) (0.001) (0.063) (0.033) (0.016)
2000 1.677 -3.438 0.806 1.412 -2.618 0.644
(0.011) (0.005) (0.003) (0.036) (0.010) (0.004)
2010 1.702 -3.226 0.711 1.474 -2.523 0.601
(0.003) (0.003) (0.002) (0.011) (0.006) (0.003)
2017 1.698 -3.218 0.696 1.489 -2.609 0.644
(0.004) (0.005) (0.004) (0.012) (0.006) (0.003)
Income and Rents No College College
⇥w 3.558⇤⇤⇤ 7.0362⇤⇤⇤e
(0.591) (0.815)
⇥re -2.160
⇤⇤⇤ -3.731⇤⇤⇤
(0.372) (0.348)
Cragg-Donald F-Stat: 14.63
Table 8. Parameter estimates for household labor supply. Standard errors are in
parentheses. Maximum likelihood standard errors are estimated with numerical
derivatives. Stars indicate statistical significance: ⇤p<0.05; ⇤⇤p<0.01; ⇤⇤⇤p<0.001.
All of the parameter estimates have signs that are consistent with the extant
literature. For each education group and year, ⇥divet > 0 and thus agents receive
a utility premium for locating within their birth division. Furthermore, all agents
receive disutility for locating farther away from their birth state (⇥distet ¡ 0).
However, the marginal disutility of an additional mile on utility declines with
distance (⇥dist2et ). The birth-division premium and marginal disutility per mile are
also larger in absolute magnitude for college than non-college-educated agents.
These estimates suggest that household heads with a college degree are more
mobile than those without a college degree.
To my knowledge, none of the existing literature uses the exact functional
form I have chosen for individual moving costs. However, Diamond (2016)
129
estimates a birth-division indicator (⇥divet ) for college-educated and non-college-
educated workers while Colas and Hutchinson (2021) estimate the distance and
distance squared parameter (⇥distet and ⇥
dist2
et ). My estimates for ⇥
dist2
et are very
stable across years for both education groups, with the premium being roughly 20%
higher for agents without a college degree. My parameter estimates for ⇥distet and
⇥dist2et are in a range similar to what is estimated in Colas and Morehouse (2022)
(CM). However, CM estimate the parameters for di↵erent demographic groups, so a
direct comparison is inappropriate.
It is even more di cult to compare my estimates of ⇥we and ⇥
r
e to the
literature, given that I am the first to estimate these parameters for city-sector
pairs. My estimates are slightly smaller in magnitude than those of Colas and
Hutchinson (2021) and in a similar range to those of Diamond (2016). As do both
of these other papers, I find ⇥wc > ⇥
w
l , which indicates that workers with at least a
college degree are more responsive to changes in wages. I also find that |⇥rl | > |⇥rc |,
which is di↵erent from Colas and Hutchinson (2021) but consistent with some
specifications of Diamond (2016).
Model Fit. I use the fully estimated model to simulate the baseline equilibrium.27
In Figure 16, I compare the model’s predicted city-sector choice shares by education
group to the data:
27Details of how I solve for the equilibrium of the model can be found in Section C.0.6.2.
130
College No College
12.5
10.0
7.5
5.0
2.5
2.5 5.0 7.5 10.0 12.5 2.5 5.0 7.5 10.0 12.5
Log Data Counts
Figure 16. Model Fit Results by education group. For college and non-college-
educated workers, these two graphs plot the model’s predicted log city-sector shares
on the vertical against the corresponding log city-sector shares in the data. The
black dashed line is the 45-degree line.
Appendix C.0.2.4 provides analogous scatterplots for household energy
consumption. The model appears to fit the data well.
4.5 Counterfactuals
Recently, there has been an increasing legislative e↵ort in the US to pass
a carbon tax. In late July of 2019, three carbon tax bills were introduced to
Congress: the Climate Action Rebate Act of 2019 (CAR act), the Stemming
Warming and Augmenting Pay Act (SWAP Act), and the Raise Wages, Cut
Carbon Act of 2019 (RWCC Act). Fundamentally, all three bills are examples
of Pigouvian taxes; however, their implementations vary. One of the primary
di↵erences between the bills is the use of government revenue. For example, the
CAR act proposes distributing 70% of the tax revenue to low-income and middle-
income households in the form of lump-sum payments. In contrast, the SWAP and
131
Log Model Counts
RWCC acts propose using revenues to reduce payroll taxes.28 Motivated by these
recent examples of proposed legislation, I use my model to assess carbon pricing in
conjunction with various transfer schemes.
A carbon tax will a↵ect the price of energy di↵erently for each fuel type.
Recall that I assumed the supply curves for fuel oil and natural gas are perfectly
elastic, and the emissions rate for each of these fuel types is constant across
locations and given by  m. With the introduction of a carbon tax, the price of
natural gas and fuel oil in city j is given by:
P̃mj = P
m
j + ⌧ 
m.
For electricity, I construct city-level supply curves as in Equation (4.11).
With the carbon tax, the supply curve is given by:
P eleckj (⌧,  
µ elec
R(j)) = akjQR(j) + (⌧ ⇥  R(j)),
where I write the electricity supply curve, P eleckj (⌧,  R(j)), as a function of the tax
level ⌧ , and the emissions rates  R(j).
4.5.0.1 The Welfare E↵ects of Carbon Taxes. In this section,
I simulate a carbon tax of $31 dollars per ton—the Social Cost of Carbon (SCC)
as estimated by Nordhaus (2017). I calculate the compensating variation (CV) for
agent i as:
CVi = E
w
[V (⌧ > 0)]  E[V (⌧ = 0)]⇥ ejn , (4.20)
⇥we
where V (⌧) = vijn(⌧, j?, n?) is the indirect utility, given tax level ⌧ , evaluated at
equilibrium choices j? and n? and the expectation E is taken over the idiosyncratic
28For more details of these bills, see https://taxfoundation.org/carbon-tax-bills-introduced-
congress/.
132
preference shocks. Note that because vijn is measured in log-utility units, E[V (⌧ >
0)]   E[V (⌧ = 0)] is approximately equivalent to percentage change in utility.
Multiplying by wejn⇥w converts this to a dollar amount. Agent i’s expected utility ise
given by:
XX
E[V (⌧)] = ̄ + log( exp(⇥we log(w rej0n0) ⇥e log(Rj0) 
j02J n02N
X
⇥m mej0n0 logPj0 + ⇠ej0n0 + f(j,Bi; ✓̂e)))
m
where  ̄ is Euler’s constant and f(j,Bi; ✓̂e) is the distance function (equation 4.3)
evaluated at the estimated parameter vector ✓̂e. The distribution of CV across
cities and sectors is displayed in Figure 17.
Figure 17. The distribution of compensating variation from a carbon tax of $31.
Figure 17 demonstrates considerable household-level heterogeneity in the
burden of a carbon tax. The model predicts that carbon prices are regressive; the
mean tax burden for college-educated agents is $926 while the mean tax burden
133
for non-college-educated agents is $1, 417.29 The tax regressivity is consistent
with a large literature that observes that lower-income households spend larger
portions of their income on energy, and work in more energy-intensive sectors.
Indeed, this is reflected in my estimates of ↵̃mejn (the budget share of energy type
m).30 Additionally, the model predicts a significant decline in manufacturing
employment. Manufacturing, which is relatively carbon-intensive, experiences an
11.1% decrease in employment with a 12.7% reduction in college workers and a
10.4% reduction in non-college workers. The services sector—which is relatively
green—experiences an increase in employment. There is a 2.01% increase in
aggregate services employment, with a 1.78% increase for college workers and a
2.34% increase for non-college workers.
Figures C4 and C9 in Appendix C.0.5.2 disaggregate Figure 17 by industry
and Census Region. Manufacturing has a substantially higher tax burden than
other sectors for both college-educated and non-college-educated workers. Cities
and sectors in the Midwest and West have marginally higher average compensating
variations associated with the tax, comapred to other regions. Table 9 summarizes
the consequences of the carbon tax.
29I did not impose the tax regressivity on the model’s structure in any way.
30Summary statistics for these estimates can be found in Table C2.
134
⌧ = $31/ton:
Mean CV ($) Mean/st.dev CV %  Man. Emp %  Ser. Emp
Total  1, 221  3.14  11.1 2.01
College  926  3.55  12.7 1.78
Non-College  1, 417  4.16  10.4 2.34
Table 9. Counterfactual results from a carbon tax of $31 per ton. Mean CV is
calculated using equation (4.20). Percent changes in emissions and employment are
relative to baseline levels.
Non-Monetized Incidence. While my primary welfare metric is
compensating variation, I also examine tax incidence defined as the percent change
in wages needed to compensate households for the carbon tax.31 Compensating
variation may mask substantial underlying heterogeneity in the tax burden due
to di↵erences in wages across cities. For example, San Francisco may experience a
small-degree tax burden as a percent of wages. San Francisco has a services-based
economy with a mild climate and carbon-e cient power plants. However, San
Francisco has high average wages. Thus, the average household in San Francisco
may require a large dollar transfer in response to the carbon tax. Conversely,
Detroit may experience a large loss in utility due to its manufacturing-oriented
economy, harsher climate, and relatively dirtier power plants. Detroit also has
relatively low wages, which lowers the dollar amount needed to compensate
households in Detroit for the carbon tax, all else equal. Despite the potentially
larger loss in utility in Detroit, the compensating variation in San Francisco could
be higher due to di↵erences in wages across the two cities.
31Compensating variation is in levels; the non-monetized incidence is a percent change. I
calculate percent change in utility as CV ⇥ 1 , or just (E[V (⌧ > 0)]  E[V (⌧ = 0)])⇥ 1
w ⇥w
.
ejn e
135
Indeed, I find compensating variation is larger (in magnitude) in cities that
exhibit high wages, such as those on the West Coast and New England. In Figure
C5, I replicate figure C4, except I compare non-monetized tax incidence rather than
changes in compensating variation. I aggregate these changes to the state level
and map them in Figures C6 and C7. These figures reveal that households in the
Midwest and South generally experience larger percent decreases in utility from the
carbon tax, despite having similar, if not lower, compensating variations.
Migration. Next, I examine how the spatial distribution of households shifts
with the carbon tax. More specifically, I calculate the percent change in aggregate
population and by education group for each city, aggregated across all sectors. I
display the results in Appendix C.0.5.3 at the state level, both in the aggregate and
disaggregated by education level.
In general, the model predicts that cities with milder climates and power
plants that are less emissions-intensive will experience population increases. For
example, the carbon tax induces an inflow of households to Seattle, Washington,
increasing the city’s population by 1.5%. Washington is part of the WECC NERC
region (see Figure C2) and has relatively carbon-e cient power plants, so electricity
prices do not increase as much in Seattle as in other cities. Additionally, Seattle’s
economy is more services-oriented than many other cities. On the other hand,
cities such as Cincinnati experience population decreases. Relative to Seattle,
Cincinnati’s climate requires more household energy, and the electricity generation
in Cincinnati is less carbon-e cient than in Seattle. Additionally, Cincinnati has
a smaller share of workers in relatively carbon-e cient services-based jobs than
Seattle. Overall, the model predicts that the carbon tax will reduce Cincinnati’s
population by 2.29%.
136
Despite them being less mobile than college-educated households, the model
predicts larger changes in shares of non-college-educated households in most cities.
In Figures C12 and C11, I show that the average city experiences a 0.1% decrease
in its share of non-college-educated households, and only a .03 % decrease in its
share of college-educated households. College-educated workers are more responsive
to changes in prices (as estimated in section 4.4), so the relatively larger migration
flows of non-college-educated workers demonstrate the greater tax burden borne by
these households.
Tax Incidence and Elections. Next, I examine how changes in utility from
the carbon tax correlate with political preferences. I focus my analysis on the share
of cities voting for Donald Trump during the 2016 presidential election. Donald
Trump’s voting base was less educated and concentrated in less-populated areas
(Doherty, Kiley, & Johnson, 2018)—features that are correlated with higher tax
incidence in my analysis.32
I combine my tax-incidence estimates with publicly available, county-
level presidential election voting data from the MIT Election Data and Science
Lab (MIT, 2018). For each CBSA in my sample, I compute the average (across
counties within the CBSA) share of the vote going to Donald Trump in the 2016
primary presidential election, weighted by total votes in each county. In Figure
C13, I plot the tax incidence (again, defined as the percent change in wages
needed to compensate households for the carbon tax) against Trump’s vote shares.
Additionally, I plot compensating variation against the share of households voting
for Trump in Figure C14.
32Donald Trump has been consistently skeptical of climate change and policy. On December
6th, 2013, in a tweet that was subsequently deleted alongside his account, Donald Trump stated
“Ice storm rolls from Texas to Tennessee - I’m in Los Angeles and it’s freezing. Global warming is
a total, and very expensive, hoax!”
137
As expected, counties with a larger share of Trump votes experience
larger decreases in utility, on average.33 The counties with a higher percentage
of Trump voters (and thus larger tax incidence) are arguably those least likely
to vote in favor of a carbon tax. Further complicating the political feasibility of
the tax is that areas with a lower share of Trump voters would require a higher
(in magnitude) compensating variation, on average. This di↵erence between tax
incidence and monetized tax incidence (compensating variation) is again driven
by di↵erences in wages across cities; cities such as San Francisco have a low share
of Trump voters, relatively low tax incidence, but relatively high compensating
variation due to the high baseline wages in San Francisco. Overall, these results
highlight a particular challenge concerning the political feasibility carbon-pricing
legislation.
4.5.1 The E↵ects of Coal-Fired Electricity. In large part
due to significant decreases in natural gas prices with the advent of fracking
technologies, the share of electricity generated by coal in the United States
has dropped precipitously since the mid-2000s. In the early 2000s, coal-fired
generation accounted for over 70% of power nationally. By 2015, coal’s share had
diminished to under 40% of generation.34 Coal emits a considerable amount of
carbon compared to natural gas, so the declining share of coal will have first-order
consequences for the welfare e↵ects of pricing carbon. As coal’s share of electricity
generation continues to decline, the revenue needed to compensate households for
33Note that I did not target political preferences in the estimation, so this result strengthens the
validity of the model’s parameter estimates.
34The decline in the share of electricity generated by coal is for many reasons in addition to
the decline of natural gas prices. See Arias, Reinbold, and Restrepo-Echavarria (2017) for a brief
discussion.
138
carbon pricing will also fall. I illustrate the decline in coal nationally and across
NERC regions in Figure 18.
1.0
0.6 0.8
0.6
0.4
0.4
0.2
0.2
0.0 0.0
2004 2006 2008 2010 2012 2014 2016 2004 2006 2008 2010 2012 2014 2016
Contiguous United States FRCC NPCC SERC TREMRO RFC SPP WECC
Figure 18. Share of electricity generated by coal nationally and across NERC
regions between 2004 and 2016. Shares are computed using annual plant-level
generation data from eGRID.
No Coal. Motivated by the remarkable decline in the share of the electricity
generated by coal, I use the model to decompose the tax incidence into two
components: coal and non-coal. More specifically, I estimate the proportion of
the total compensating variation that is attributable to the e↵ect of a carbon tax
on coal-fired electricity generation. I recalculate emissions factors for each region
in the absence of coal. Without coal, there are considerably lower emissions rates
across the US. A map of the changes in emissions factors from dropping coal is in
Section C.0.5. With the new, absent-of-coal emissions factors in hand, I resimulate
the $31 per ton carbon tax for a “no-coal” economy. I display the distribution of
CV, split by education level, in Figure 19.
139
Generation Share Coal
Generation Share Coal
Figure 19. The distribution of compensating variation from a carbon tax of $31 per
ton in the absence of coal-fired electricity generation.
Without coal, the mean college and non-college agents experience a $352
and $543 dollar decline in their tax incidence. Percentage-wise, the change is
marginally larger for non-college workers as they are generally located in more
energy-intensive cities and work in more sectors.
Furthermore, the distribution of incidence without coal-fired electricity has
a smaller variance. The distributions of tax incidence have less dispersion due to
the geographic distribution of coal; many coal plants are in the Midwest and South.
In Appendix C.0.5.2 figure C6 I show that for non-college-educated workers, the
change in tax incidence is greatest in the midwest. In contrast, for college-educated
workers, the change in incidence is remarkably stable across regions. I display the
main results for the “no-coal” scenario in Table 10 below.
140
⌧ = $31/ton:
No Coal Mean CV ($) Mean/st.dev CV %  Man. Emp %  Ser. Emp
Total  757  3.11  8.15 1.51
College  594  3.33  9.56 1.31
Non-College  874  4.06  7.51 1.68
Table 10. Counterfactual results: a $31 per ton carbon tax in the absence of coal.
Mean CV is calculated using equation (4.20). Percent changes in emissions and
employment are relative to baseline levels.
To be clear, this is purely a decompositional and bounding exercise
with respect to the tax incidence. It suggests what could be the distribution of
tax incidence without coal. A carbon price will impact the rate at which coal-
fired power plants are shut down. In reality, the supply curves of electricity are
determined by a “constant dispatch order.” The plant uses the generating unit
with the fuel type that has the lowest marginal cost, up to a fuel-specific capacity
constraint. The plant then switches on the next lowest (fuel-specific) marginal cost
generators upon hitting each fuel-specific constraint. Given that coal has a low
marginal operating cost, removing coal would be likely to impact significantly the
slope of the supply curve, further changing the impact of a carbon tax on electricity
prices and tax incidence. I leave it to future work to recover the incidence of carbon
pricing with dynamic coal shares and a micro-founded electricity supply curve.
This counterfactual is highly policy-relevant as coal’s decline continues. My
decomposition demonstrates that a significant proportion of the total compensating
variation (roughly 40%) from carbon pricing is attributable to losses in coal-
fired electricity. These simulations suggest policymakers may need to compensate
141
households significantly less to remain indi↵erent between a carbon tax and no tax
in a low-coal future.
4.5.2 Equity and Emissions. Next, I examine the relationship
between progressive transfers and aggregate emissions. I provide a motivating
example from the data and then extend the baseline model to include government
payments.
Wages and Emissions. Variation in household carbon emissions across cities
and sectors is well documented. This variation is driven largely by (1) di↵erences
in climate across cities, (2) di↵erences in emissions intensities from regional power
plants,(3) di↵erences in preferences for energy consumption, and (4) di↵erences
in income levels across households. Cities also host di↵erent sets of industries
which vary in their energy use, and hence their emissions intensities. Thus, any
policy that a↵ects the spatial and sectoral population distribution will also impact
aggregate emissions.
If lower-wage city-sectors have, on average, higher emissions, then
progressive redistribution may increase aggregate emissions. This relationship
arises because the more carbon-intensive city-sector combinations will receive larger
transfers (all else equal), which will induce a larger share of workers to move to
these cities and/or into these sectors, raising aggregate emissions. However, the
e↵ect of the transfers on aggregate emissions also depends on substitution patterns
across cities and sectors. For example, even if the correlation between wages and
emissions is positive, progressive transfers may induce a large share of workers
into a low-wage yet emissions-intensive city-sector. Thus, the e↵ect of progressive
142
transfers on aggregate emissions depends on both the correlation between wages
and emissions and substitution patterns across city sectors.35
In Figure 20, I plot city-sector emissions per capita—defined as the sum, per
capita, of firm and household emissions per capita—against city-sector wages.
12
11
10
10.0 10.5 11.0 11.5 12.0
Log(Average Wage)
Figure 20. Carbon emissions at the city-sector level plotted against average wages.
On the vertical axis, total emissions per capita are calculated as aggregated firm
and household emissions divided by the respective city-sector employment count.
On the horizontal axis, wages are estimated by city-sector-education group in
Equation (C.3), then averaged by city-sector, weighted by the count of workers in
that education group.
As Figure 20 indicates, the average household that lives and works in
a lower-wage city-sector also tends to emit less carbon. In Appendix C.0.8, I
35There are two exceptions to this: when there are only two alternatives (cities and or
sectors), or when wages and emissions are perfectly correlated. In the first case, there is only
one alternative for workers to switch into (the alternative with higher transfers), and given the
negative correlation between wages and emissions, this alternative will be lower. In the second
case, lower-wage alternative have strictly lower emissions. Thus any substitution to a lower wage
alternative would reduce aggregate emissions.
143
Log(Total Emissions per capita)
(in lbs)
disaggregate Figure 20 by education group to reveal that the positive relationship
between emissions and wages holds for college-educated and non-college-educated
workers considered separately.36
The positive cross-city correlation between emissions and wages has
important implications for redistributing the revenue from a carbon tax. Often,
policymakers and academics propose progressive transfers as a way to alleviate
distributional concerns with pricing carbon.37 However, whether or not these
transfers increase or decrease aggregate emissions depends on both the correlation
between wages and emissions and substitutions across the agent’s choice sets.
Carbon Taxes with Transfer Payments. I extend the model so that
the agent receives a transfer equal to T (w). The agent’s post-transfer wage
is then w̃ejn = wejn + T (w). One of the primary goals of this paper is to
capture the relationship between the progressivity of government transfers and
aggregate carbon emissions. Thus, for the transfer function, I use the parsimonious
specification employed by Heathcote, Storesletten, and Violante (2017) (henceforth
HSV), which is given by:
T (w) =  w1  ejn
where   > 0 is the overall level of the reimbursement and     1 indexes the
progressivity of the transfers.38 Note that when   = 1, transfers are proportional
to wages, and when     1, transfers are decreasing in wages. A higher value of  
implies higher-wage agents will receive smaller transfers. In counterfactuals with
transfers, I append the definition of the model’s equilibrium to include a balanced-
36Additionally, I disaggregate by education group and industry. For some industries, the
relationship between emissions and wages is positive.
37See Carattini, Carvalho, and Fankhauser (2017) for an example.
38If   < 0 and   < 1 then this is the familiar HSV tax function.
144
budget condition for the government. The balanced budget assumption implies that
  is endogenously determined in equilibrium; more details are included in Appendix
C.0.2.3.
I use the model to estimate numerically the general equilibrium elasticity of
aggregate emissions with respect to the relative progressivity of transfers. I define
this elasticity as:
@Emis  
✏Emis,  = . (4.21)
@  Emis
Note that the level of transfers an agent receives may change the agent’s
city-sector choice, which impacts the agent’s emissions and thus aggregate
emissions. Equation (4.21) is thus an implicit function, e↵ectively, of all the model’s
underlying parameters. If labor supply—especially non-college labor supply—
is highly mobile and responsive to changes in wages, then an increase in   will
cause a larger change in emissions as more workers migrate or switch sectors.
Firm production parameters (and hence labor demand), energy, and rental supply
all determine the full extent of the price changes and hence aggregate emissions
change. I estimate equation (4.21) numerically by simulating the model under
  2 {1, 1.2, 1.4, 1.6}. I display the result from this exercise graphically in Figure
21 below.
145
0.000%
-0.020%
-0.040%
-0.060%
1.0 1.2 1.4 1.6
Progressivity Parameter ( )
Figure 21. Simulated total emissions relative to lump-sum transfers plotted against
the progressivity parameter ( ). Simulated emissions are calculated in equilibrium
as the sum of total emissions from agents and firms across all cities and sectors.
Figure 21 illustrates that, in the US, equity-of-transfers and aggregate
carbon emissions are inversely related. More specifically, I estimate ✏Emis,  =
 0.00104. Put di↵erently, this indicates that a 1% increase in the progressivity of
the transfer system would result in approximately a  0.001% decrease in aggregate
emissions. In Table 11, I show the change in sectoral composition under a carbon
tax with lump-sum transfers (  = 1) and a carbon tax with progressive transfers
(  = 1.2).
146
Simulated Emissions Change (Relative to = 1)
  = 1 %  Man. Emp %  Ser. Emp %  Con. Emp %  Ag. Emp
Total  11.8 2.42 1.57  2.78
College  13.7 1.99 0.07  3.51
Non-College  10.9 2.80 1.7  2.62
  = 1.2
Total  11.9 2.49 1.36  1.86
College  13.8 2.03 0.05  2.78
Non-College  11.1 2.91 1.5  1.65
Table 11. Change in sectoral employment in the aggregate and by education group
for a $31 carbon tax with transfers. The change is relative to the same $31 carbon
tax, but with no transfers.
As shown in Section 4.3, cities and sectors with lower wages also tend to
have lower carbon emissions. Thus, more-progressive transfers induce a larger
share of agents to move into greener cities and sectors, lowering aggregate
emissions.39 When   = 1.2, I find that manufacturing employment declines by
11.9% (compared to 11.8% with lump-sum transfers) and services employment
increases by 2.49% (compared to 2.42% with lump-sum transfers). The model also
predicts modest increases in construction employment (1.57%) and decreases in
agricultural employment (2.78%). These results suggest that carbon tax policies
with progressive transfers have the added benefit of modestly reducing aggregate
emissions due to the compositional changes in the workforce induced by these
transfers.
4.6 Conclusions
I explore the distributional e↵ects of a uniform national carbon tax. To
accomplish this, I estimate a model of worker sorting across cities and sectors, in
39If the relationship between wages and emissions were negative, then there would be an equity-
emissions trade-o↵.
147
which imperfectly mobile agents that vary by education level consume three goods:
numeraire good, energy, and housing. The model incorporates the incidence of a
carbon tax, including endogenous wages, rents, and electricity prices. To take the
model to the data, I utilized a combination of estimation and calibration methods.
There are three main takeaways from a set of counterfactual exercises.
First, the incidence of a carbon tax exhibits substantial spatial and sectoral
heterogeneity—workers in the carbon-intensive manufacturing experience a much
greater tax burden than workers in the less carbon-intensive services sector.
Overall, I find that a carbon tax has a mean compensating variation of $926 for
college-educated workers and $1,417 for non-college-educated workers.
Second, the share of this incidence attributable to coal varies across space.
Coal use accounts for a larger share of the total burden in some coal-dependent
regions, such as the Midwest, particularly for non-college-educated workers. Other
regions, like New England, have a small share of the burden attributable to coal
dependence. These findings imply that policymakers will need to adjust expected
compensation with via recycling of carbon tax revenues as the grid decarbonizes
at potentially di↵erent rates across space. Finally, I document a new relationship
between equity and emissions: aggregate emissions fall as compensation becomes
more equitable. Lower-wage city-sectors are less carbon-intensive, so progressive
transfers induce a larger share of workers to move into these cities and sectors.
This relationship suggests that progressive transfers may have the added benefit
of helping achieve emissions targets.
Despite the detailed heterogeneity included in the model, I have made
several simplifying assumptions in my analysis. I make two strong assumptions
about capital in the production function. First, I assume the elasticity of
substitution between capital and other inputs is one (e.g., the production function
148
is Cobb-Douglas in capital and other inputs). Second, I assume capital is traded on
international markets, and there are no di↵erences in local prices. Complementarity
between capital and energy may have important implications for the distribution
of carbon tax incidence. Third, I assume perfectly competitive input and output
markets. Heterogeneity in market power across cities and sectors could bias my
estimates of the tax incidence. In addition, I use natural gas and electricity as
primary fuel inputs for firms; while this may be reasonable for many sectors, it
certainly underestimates the e↵ects of carbon pricing on agriculture since a large
share of agricultural carbon emissions are from livestock. Future work could extend
the model by generalizing the production function to incorporate these features.
My results speak to the importance of considering place-based incidence
when designing federal policy. Much of the literature has identified negligible
employment e↵ects, but I note that even if, on net, the number of jobs is the
same or increases, reallocation is costly. My model provides insights concerning
the mechanisms via which spatial-sectoral heterogeneity would be created by the
tax, and my empirical results substantiate the possibility of costly re-allocations of
labor. Understanding heterogeneity in the incidence of a carbon tax is paramount
for policymakers looking to reduce the current political headwinds faced by
proposals for carbon pricing. As Sallee (2019) notes, “...the failure to create a
Pareto improvement is due to a prediction problem; lump-sum transfers can only
undo the distribution of burdens if they can be targeted precisely.” Due to the
rich level of heterogeneity in the model, and hence in the simulation results, the
analyses this paper may help design policymakers design compensating schemes
that can be more precisely targeted.
149
CHAPTER V
DISSERTATION CONCLUSION
In this dissertation, I have demonstrated the importance of accounting for
spatial heterogeneity in environmental policy and related outcomes.
In Chapter 2, we focused on the geography of the US power sector. We first
documented that many power plants are located near jurisdictional (county and
state) borders. This behavior may indicate strategic siting (intended to export
pollutant emissions to neighboring jurisdictions). However, many county and state
borders are composed of water (rivers and lakes), a key input for many types of
electricity generation. We developed a statistical test to distinguish strategic sites
from non-strategic sites. We then used our test and found strong circumstantial
evidence that coal-fired power plants have been sited downwind within their own
counties and states to export a greater share of their emissions. Motivated by
these findings, we employed a state-of-the-science atmospheric dispersion model,
HYSPLIT, to document the pervasiveness of the “pollution-transport problem.”
We provided new statistics on the speed and scale of particulate matter transport
from coal-fired power plants.
In Chapter 3, we examined how a locally set policy (land-use regulations)
can impact aggregate carbon emissions. To facilitate our analysis, we developed and
estimated a quantitative spatial equilibrium model. We used the model to reduce
existing stringent land-use regulations in California to a reasonable level. Relaxing
these land-use regulations mechanically lowers rents, and, in the model, households
respond by migrating to California. Since California has a temperate climate and
carbon-e cient power plants, households emit less carbon in California than they
do elsewhere. Thus, aggregate carbon emissions fall when households move into
California (due to lower land-use restrictions).
150
In Chapter 4, I studied the distributional e↵ects of a national uniform
carbon tax in the United States. The incidence of a carbon price on a given
household will depend not only on location but also on the employment sector for
that household since di↵erent sectors use di↵erent amounts of carbon-intensive
inputs. Thus, a carbon tax may lower wages (or even cause a loss of employment)
for workers in carbon-intensive sectors. In addition, if a household lives in an area
with an extreme climate and carbon-intensive power plants, the carbon tax will
significantly impact their energy bill. To understand how a carbon tax would
impact di↵erent households, I built and estimated a quantitative spatial equilibrium
model. I found that non-college-educated workers in manufacturing bear a
significant share of the tax incidence. The model also predicts that states with
services-oriented economies, such as California, will experience modest population
increases in response to a carbon tax. I simulated a carbon tax with progressive
transfers given the tax’s regressivity. As the progressivity of the transfers increases,
aggregate carbon emissions will fall as households sort into greener cities and
sectors.
The results from my dissertation underscore the importance of spatial
variation in public policy. As demonstrated in Chapter 2, even local pollutants
such as PM2.5 can travel long distances very quickly. Our results suggest that the
geographic level of regulation is a first-order concern for air-quality management.
Furthermore, hypothetical policies such as carbon taxes will have unequal impacts
on the population, even if implemented uniformly.
151
APPENDIX A
CHAPTER 2: APPENDIX
A.0.1 Appendix: Methods.
A.0.1.1 Border-distance calculations. We first project the plant’s
location and the Census shapefiles into the plant’s zone of the Universal Transverse
Mercator (UTM) coordinate system. Then we calculate the distance to the plant’s
nearest county and state border. We use R’s sf package for these calculations
(Pebesma, 2018).
A.0.1.2 Counterfactual grid. If the county and state borders do
not impact or correlate with EGUs’ locations, then EGU’s distances to borders
should mirror the overall national distribution of distances to borders.To build
this comparison distribution, we cover the contiguous U.S. with a uniform,
hexagonal grid of points as illustrated in Appendix Figure A2. The number of
grid points is approximately equal to the area covered in square kilometers. We
then calculate each point’s distances to the nearest county border and the nearest
state border.1 This process produced a nationally representative distribution (for
the contiguous U.S.) of distances to state and county borders using a uniform grid
of approximately 7.91 million points.2 This distribution represents the expected
distribution of EGUs’ distances to borders if they were sited in a manner that
ignores borders and features that correlate with borders.
The last row of Figure 3 depicts the distribution of distance-to-nearest-
border for the uniform grid covering the U.S. This grid’s distribution demonstrates
that it is not the case that all points in the United States are near borders. Only
8% of the U.S. (area-wise) sits with 1 kilometer of a county border (36% within
5 km; 62% within 10 km). For state borders, only 1.1% of the U.S. sits within 1
kilometer (6% within 5 km; 11% within 10 km). These numbers stand in stark
contrast to the distributions of EGUs.
A.0.1.3 Borders and water. We calculate the share of each county’s
and state’s borders that coincide with bodies of water in four steps. First, we
convert each administrative unit’s linear boundaries into a series of points with
1Specifically, we work in the counties’ UTM zones and subset the grid points to the points
within the county under consideration—a point’s nearest border is always the border of the unit
that contains that point. Again, we employ R’s sf package for these calculations (Pebesma, 2018).
2For comparison, the area of the contiguous U.S. is approximately 8.08 million km2.
152
50-meter spacing. Second, we calculate the distance to the nearest body of water
for each of these boundary points (if the boundary point is within a body of
water, then the distance is zero). These bodies of water cover all rivers, lakes,
and coastlines including in the U.S. Census’s TIGER/Lines shapefiles discussed
in Data. Third, we designate a boundary point as including water if the nearest
body of water is less than 50 meters. This step allows for near misses in the Census
geography files without including too many false positives. Finally, we smooth this
includes water indicator variable using a moving-window average of all boundary
points within a 2.5 kilometer radius of the given boundary point. This final step
allows neighboring boundary points to vote on whether the boundary indeed
coincides with water—e.g., a single, spurious includes water will be overwhelmed
by non-water neighbors. The final product is a series of points with 50-meter
spacing covering all county and state borders in the contiguous U.S.—with each
point measuring whether the boundary substantively coincides with water.
A.0.1.4 EGUs and water. To calculate the distance to the nearest
body of water, we include all bodies of water contained in the U.S. Census’s areas
of water, linear water, and coastline shapefiles, (US Census Bureau, 2016b). After
merging these calculated distances with eGRID’s EGU characteristics, we build the
distribution of distance-to-water for each fuel category.
A.0.1.5 HYSPLIT. The R packages splitr, hyspdisp, and dispersR
were extremely helpful in developing our computational approach—as was GNU
Parallel (Tange, 2011).
A.0.2 Appendix: Policy.
A.0.2.1 The Clean Air Act and cross-border pollution. The
Clean Air Act (CAA)—often called the “crown-jewel” of environmental regulation
in the U.S. (Browning, 2020; Feldman, 2010))—recognizes that cross-border air
pollution is a challenge on a scale larger than neighboring counties. The original
texts of the 1963 CAA limited federal involvement mainly to (a) resolving trans-
boundary pollution issues—when invited by a governor—and (b) funding/guiding
research related to air pollution (Edelman, 1966; United States Congress (90th),
1968; United States Senate, Committee on Public Works, Sta↵ Report, 1963).
Known as the “good neighbor” provision, section 110 of the CAA explicitly
prohibits “any source or other type of emissions activity within the State from
emitting any air pollutant in amounts which will (I) contribute significantly to
153
non-attainment in, or interfere with maintenance by, any other State with respect
to any such national primary or secondary ambient air quality standard” (U.S.
Environmental Protection Agency, 2013a).3 Further emphasizing the importance
of cross-border pollution transport, in 2011 the U.S. EPA enacted the Cross-State
Air Pollution Rule (CSAPR). The CSAPR covers 27 states4 in the eastern U.S.—
especially targeting power-plant emissions of SO2 and NOx and their formation of
fine-particulate matter (PM2.5) and Ozone (O3) (U.S. Environmental Protection
Agency, 2020). The CSAPR links emissions-source states to recipient states—
emphasizing non-attainment areas—and creates a budget-and-trading program for
emissions within the covered states (U.S. Environmental Protection Agency, 2020).
Despite this substantial infrastructure addressing cross-border pollution, disputes
regarding trans-border pollution continue—e.g., in 2018 Delaware announced its
intent to sue the EPA over emissions from power plants based in Pennsylvania
and West Virginia, and in 2019 New York, Connecticut, Delaware, New Jersey,
Maryland, Massachusetts, and NYC sued the EPA regarding upwind ozone
precursor emissions (Groom, 2019; Sanders, 2018; Volcovici, 2018).
One of the complexities of monitoring and regulating air pollution from
coal-fired EGUs is the degree to which emissions can travel long distances from
the initial source, polluting distant destinations. In 2018, the average height of a
smokestacks attached to a coal-fired EGU in the U.S. was approximately 500 feet,
and the maximum was approximately 1,038 feet (calculated from CAMD (2020)
data). While tall smokestacks aid in dispersing high concentrations of harmful
chemicals, they also substantially increase the transport of emissions to other
counties and states (U.S. Government Accountability O ce, 2011).
A.0.3 Appendix: Figures.
3The CAA also allows states to petition the EPA for reviews of upwind sources (U.S.
Environmental Protection Agency, 2013b).
4Texas, Oklahoma, Kansas, and Nebraska comprise the western edge of the CSAPR states.
154
Figure A1. NARR (North American Regional Reanalysis, 2006) prevailing wind directions
across the US.
155
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156
A. B.
Correlation: 0.012 Correlation: 0.0098
5.0 5.0
0.0 0.0
-5.0 -5.0
-10.0 -10.0
0% 25% 50% 75% 100% 0% 25% 50% 75% 100%
Share of county upwind Share of county downwind
Count 500,000 1,000,000 Count 500,000 1,000,000
C. D.
Correlation: -0.0062 Correlation: 0.0028
5.0 5.0
0.0 0.0
-5.0 -5.0
-10.0 -10.0
0% 25% 50% 75% 100% 0% 25% 50% 75% 100%
Share of state upwind Share of state downwind
Count 500,000 1,000,000 Count 500,000 1,000,000
Figure A3. Using a uniform grid that covers the entire contiguous U.S., these figures show the
relationship between (1) population density (here, transformed via base-10 log) and (2) the share
of the county or state that is upwind or downwind of the grid cell. Due to the large number of
grid cells, we use a heat map rather than the typical scatter plot. Note: Because we define upwind
and downwind using a 90-degree angle, very few points in the U.S. are upwind or downwind of
more than 75% of their states or counties.
157
Log10(Population density) Log10(Population density)
Log10(Population density) Log10(Population density)
A. B.
Correlation: 0.0066 Correlation: 0.020
100% 100%
75% 75%
50% 50%
25% 25%
0% 0%
0% 25% 50% 75% 100% 0% 25% 50% 75% 100%
Share of county upwind Share of county downwind
Count Count
500,000 1,000,000 500,000 1,000,000
C. D.
Correlation: -0.024 Correlation: 0.038
100% 100%
75% 75%
50% 50%
25% 25%
0% 0%
0% 25% 50% 75% 100% 0% 25% 50% 75% 100%
Share of state upwind Share of state downwind
Count Count
500,000 1,000,000 500,000 1,000,000
Figure A4. Using a uniform grid that covers the entire contiguous U.S., these figures show
the relationship between (1) the share of the cell’s population that is Hispanic or non-white and
(2) the share of the county or state that is upwind or downwind of the grid cell. Due to the large
number of grid cells, we use a heat map rather than the typical scatter plot. Note: Because we
define upwind and downwind using a 90-degree angle, very few points in the U.S. are upwind or
downwind of more than 75% of their states or counties.
158
Share Hispanic or Non-White Share Hispanic or Non-White
Share Hispanic or Non-White Share Hispanic or Non-White
IN
KY
Non-attainment area Coal-fueled power plant County border State border
Figure A5. This map illustrates the complexity of the Evansville, Indiana non-attainment
area (orange), which covers six counties (3 whole; 3 partial) within Indiana (along its borders with
Kentucky to the south and Illinois to the west). Six of the counties form a contiguous area. The
remainder of the non-attainment area is formed by islands in three counties that cover nearby
coal plants (circled, red dots). As with Figure 9, the non-attainment area is for the 1997 PM2.5
standard.
159
Table A1. Testing EGUs’ border distances relative to uniform US grid border
distance
County borders State borders
Fuel category K-S test stat. p-value K-S test stat. p-value
Coal 0.248 < 1⇥ 10 6 0.194 < 1⇥ 10 6
Gas 0.143 < 1⇥ 10 6 0.107 < 1⇥ 10 6
Hydro. 0.477 < 1⇥ 10 6 0.178 < 1⇥ 10 6
Solar/Wind 0.037 0.106 0.096 < 1⇥ 10 6
Testing EGUs’ border distances relative to uniform US grid border distance. The
columns labeled K-S test stat. contain Kolmogorov-Smirnov test statistics testing EGUs’
distances to borders against the distribution of distance-to-border built by our uniform
national grid. We conduct the tests by EGU fuel category (rows) and administrative level
(county and state). The p-values correspond to the adjacent Kolmogorov-Smirnov test
statistic.
A.0.4 Appendix: Tables. To test whether the distribution of
EGUs’ distances to nearest borders is consistent with random sampling from the
national grid we employ a simple, non-parametric, Kolmogorov-Smirnov test. The
Kolmogorov-Smirnov test is designed to test whether the empirical distribution of
a sample statistically di↵ers from a known distribution, which is exactly our goal
of this exercise: does the spatial distribution of the EGUs di↵er from a uniform-
national distribution of points?5 We focus on five major fuel categories: coal, gas,
hydropower, and other renewables (wind and solar). For each fuel category, we test
whether its EGUs’ distances to county (or state) borders statistically di↵er from
the distribution of grid points’ distances to borders (the grid described above).6
The results are displayed in A1.
The K-S test resoundingly rejects that null hypothesis that the EGUs’
distributions mirror the uniform grid’s distribution for each combination of
administrative level (county or state) and fuel category (coal, gas, hydro, or
solar/wind) with one exception. As one may guess from Figure 3, the one exception
is the distance from solar and wind generators to the nearest county border.
5Alternatively, the two-sample Smirnov test (sometimes called the two-sample Kolmogorov-
Smirnov test) tests whether the underlying distributions of two samples statistically di↵er.
6We use R’s base function ks.test().
160
This distribution fails to reject the null with a p-value of approximately 0.106
(and a K-S test statistic of 0.037). Except for the solar and wind generators’
distances to county borders, we observe overwhelming evidence that EGUs are
disproportionately sited near county and state borders—particularly for coal and
hydropower units. This observation emphasizes the complexity of monitoring and
regulating emissions from EGUs.
161
Table A2. Robustness to omitting coastal counties: Upwind vs. downwind areas for
coal and natural gas plants
(1) (2)
Coal-fueled plants Natural-gas-fueled plants
Panel a: Siting strategically within county
Count 475 915
Count strategic 263 461
Percent strategic 55.37% 50.38%
Fisher’s exact test of Ho: In-county downwind area  upwind area
Under Ho: E[Percent strategic: County] = 50%
P -value 0.0108 0.4214
Panel b: Siting strategically within state
Count 475 915
Count strategic 251 437
Percent strategic 52.84% 47.76%
Fisher’s exact test of Ho: In-state downwind area  upwind area
Under Ho: E[Percent strategic: State] = 50%
P -value 0.1164 0.9175
Panel c: Siting strategically within both county and state
Count 475 915
Count strategic 157 230
Percent strategic 33.05% 25.14%
Fisher’s exact test of Ho: Downwind area  upwind area in county and state
Under Ho: E[Percent strategic: County ^ State] = 25%
P -value 0.0001 0.4746
Robustness to omitting coastal counties: Upwind vs. downwind areas for coal and
natural gas plants. By omitting counties on the coast, this table shows the results of
Table 1 are not driven by siting in coastal areas. As before, we define a plant’s location as
“strategic” if the downwind area within its home county (or state) is less than its upwind
area within its home county (or state). We calculate downwind and upwind areas based
upon 90-degree right triangles with a vertex at the plant pointing up- or down-wind
based upon the locally prevailing wind direction. Figure 2 illustrates this calculation.
Sources: Emissions & Generation Resource Integrated Database (2018) and authors’
calculations.
162
APPENDIX B
CHAPTER 3: APPENDIX
B.0.1 Data and Theory Appendix.
B.0.1.1 Demographic Groups. We drop households living in group
quarters and for which the household head is over age 65. A demographic group
in our model is defined by the household head’s level of education, marital status,
age, minority status, and whether there are children in the household. We split
education by those that have a college degree. Marital status is defined as either
being married or single. Minority status is characterized by whether the individual
is white or not. Lastly, very few single individuals in our sample have children.
Therefore, we do not di↵erentiate between single households with and without
children. In total, this gives us 24 distinct demographic groups.
To better understand which demographic characteristics play the most
important roles in determining household-level emissions, we run the following
regression of household level emissions on the demographics of a household using
data from the 2017 aggregated ACS:
Emissionsij =  Xi +  j + "i (B.1)
where Xi is the vector of demographic variables, and  j is a CBSA level fixed e↵ect.
163
Household Emissions (pounds)
White -183.4***
(24.23)
College Plus 423.3***
(18.27)
Old 3,487***
(24.92)
Married 2,286***
(23.30)
Has Children 3,378***
(22.06)
Constant 19,347***
(33.21)
Observations 2,709,529
R-squared 0.126
CBSA FE YES
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
Table B1. Regression estimates of (B.1)
Being married, having children, and having an older household head are
associated with large values of emissions, while the other demographic variables
only play a small role in dictating a household’s carbon emissions.
B.0.1.2 Energy Prices. We obtain data on average residential
electricity, natural gas, and fuel oil prices by state for 1990, 2000, 2010, and 2017
from the Energy Information Association. For each energy type and year, we
assign the average residential price to all CBSAs within a state. Furthermore, for
electricity prices, we use the prices given from “full-service providers.” Fuel oil
prices are reported at a weekly level. We average across weeks to obtain yearly
average fuel oil prices. Additionally, as fuel oil is used primarily in the northeast,
many states do not report average prices. For states that do not have fuel oil prices
in the EIA’s dataset, we assign the yearly average across all states that do have
prices.
B.0.1.3 NERC Regions. We calculate the emissions factor for each
region as a weighted average of the average CO2 emissions rate in each NERC
164
region. We weight the average by each plant’s total yearly MWh generation as
a fraction of the total MWh generation in the region. Figure B1 is a map of the
NERC regions for the contiguous United States with the conversion factors.
Carbon Emissions from Electricity Across NERC Regions
MRO NPCC CO2
MWh
RFC 507
WECC 800
1012
SPP 1015SERC
1035
1105
1220
TRE
1271
FRCC
Figure B1. Map of NERC region with regional conversion factors. In the model,
there is an additional NERC region for Hawaii (HICC) with an emissions factor of
1522.10.
B.0.1.4 Correction for Rented Homes and Multi-Family
Homes. One concern is that rented homes and multi-family homes are less likely
to pay for energy themselves and the proportion of renters and multi-family homes
varies across cities. As the ACS and Census contain information only on energy
costs, not energy usage, this may lead us to understate under usage in cities with
high amounts of renters of residents in multi-family homes. Similar to Glaeser
and Kahn (2010), we correct for this using data from the 2015 Residential Energy
165
Consumption Survey (RECS), which contains data on energy usage for a sample of
over 5,0000 households.
We use these data to estimate the following regression which compares the
energy usage of renters, and those who live in multi-family housing, to owners of
single-family housing:
log(Em) =  mi MFMultiFamilyi +  
m
RentRenti + controls+ e
m
i (B.2)
where controls include controls for household size, number of children, age of
household head, whether the household head is white, and division dummies. We
then use the coe cients  mMF and  
m
Rent to impute energy usage for households who
are renters and who live in multi-family housing. For example, if we estimate that
owners of single-family housing in San Francisco use 8 MWh of electricity and
estimate  mMF = .1, we would impute that owners of multi-family housing use
8 ⇥ 1.1 = 8.8 MWh of electricity. Finally, we estimate the fraction of renters of
single-family housing, and multi-family housing, owners of single-family housing,
and owners of multi-family housing, using data from the ACS and Census, and
calculate the predicted usage as the weighted average of the estimated predicted
usage of owners of single-family housing, and the imputed usage of the other three
groups.
B.0.1.5 Fuel Consumption and Population. We assume that the
marginal benefit of fuel consumption is exogenous to the population of a given city.
As a simple test of the relationship between population and energy consumption,
we estimate:
log(Êm + 1) = ↵m + ↵mj 1 log(Populationj) + "j (B.3)
where m 2 {Elec,Gas, Fuel} and Êmj is the predicted per-household, selection-
corrected energy consumption of type m in city j. Given the selection-correction
usages predict zero fuel consumption in certain CBSAs, we use log(Êmj + 1). The
results presented here are not sensitive to this choice. Table B2 provides estimates
for the parameters in equation (B.3).
166
Dependent variable:
Electricity Gas Fuel
Consumption Consumption Consumption
(MwH) (1000 ft3) (gal)
log(Population)  0.012  0.413 0.049
(0.136) (0.310) (0.036)
Constant 4.276⇤⇤ 8.428⇤⇤ 2.232⇤⇤⇤
(1.809) (4.088) (0.484)
Observations 70 70 70
Note: ⇤p<0.1; ⇤⇤p<0.05; ⇤⇤⇤p<0.01
Table B2. Regression estimates of fuel consumption on population. Heteroskedastic
robust standard errors are in parentheses. As the selection-correction usages predict
zero fuel consumption in certain CBSAs, we use log(Êmj + 1). Each observation is a
CBSA.
The coe cients on all of the regressions for the energy consumption
variables are statistically insignificant. This suggests population increases do not
lead to significant changes in the average benefits of energy usage.
B.0.1.6 Equilibrium Definition. In this environment, an
equilibrium is characterized by household and firm optimization, and market
clearing in the housing and labor markets.1
More specifically, as we have shown in Section 3.4.1, given prices, household
i’s optimal choice maximizes utility.
Household optimization defines housing demand, energy demand, and labor
supply. Housing demand in a city j is given by the sum of housing demand across
all agents living in that city. We can write this as
X
D ↵
H
H = N d
Ijd
j jd , (B.4)R
d j
↵jd
where, as before, Njd is the total number of workers of demographic d who choose
to live in city j, and where we allow D and S superscripts to denote demand and
supply quantities, respectively. Similarly, energy demand is the sum of energy
1In Section 3.7.2 we consider the case when energy prices are determined in equilibrium. In
this case, an equilibrium is also defined by market clearing in the energy markets.
167
demand of all individuals living in a city:
X ↵m
mD jd
Ijd
Xj = Njd . (B.5)Pm
d j
↵jd
Labor supply is the sum of e ciency units of labor supplied by all agents of
a given skill level in city j. For more-skilled (college-educated) workers:
X
SSj = Njd`d0
d02dS
and for less-skilled (non-college-educated) workers:
X
USj = Njd`d0
d02dU
where dS and dU are the sets of demographic groups with a college degree and
without a college degree, respectively.
Labor demand for skilled and unskilled workers are implicitly defined by
(C.3), the first-order conditions of the production firms.
Housing supply is given by (3.14).
Finally, an equilibrium is defined by the two market clearing conditions:
1. Housing Market Clearing: HS = HDj j , for all cities, j.
2. Labor Market Clearing: SSj = S
D
j for skilled workers and U
S D
j = Uj for
unskilled workers in all cities.
B.0.1.7 Hedonic Rents. A major concern about producing a
measure of housing costs across CBSA’s is that they should reflect the user cost
of housing. To accommodate this, we use data only on renters as home prices
reflect both the current cost and expected future costs. Secondly, it is di cult to
compare housing units across CBSA’s. Thus, we estimate hedonic regressions of log
gross rent on a set of housing characteristics and CBSA fixed e↵ects. Specifically,
we control for the number of units in the structure containing the household, the
number of bedrooms, the total number of rooms, and household members per
room. To generate the rent index, we utilize the predicted values from the hedonic
regressions, holding constant the set of housing characteristics and CBSA fixed
e↵ects.
B.0.1.8 Estimation: Production Parameters . Let x 2 {s, u}
index worker education/skill levels. Income for workers of demographic d living in
168
location j is Ijd = Wjx`d, where `d is the number of e ciency units supplied by
workers from demographic group d.
We specify e ciency units as the demographic-specific probability of being
employed multiplied by the productivity conditional on being employed. We
therefore write
`d = E ˆ̀d d
where Ed is the national employment-to-population ratio of workers in demographic
group d.
We parameterize ˆ̀d as
log(ˆ̀d) =  
1
xWhite (d) +  
2
xOver35 (d)
where White (d) is an indicator variable indicating workers of demographic group
d are white and Over35 (d) indicates workers of demographic d are over age 35.
Therefore ˆ̀d of nonwhite workers below age 35 is normalized to one.
Conditional on working, the log-income of workers of demographic group d
and skill level x living in city j is given by
log (Ijd) = log (Wjx) +  
1
xWhite (d) +  
2
xOver35 (d) .
We therefore estimate the city-level wage rates and parameters of the
e ciency unit of labor using the following individual-level income regression
conditional on working:
log Iijd =  
x
j +  ̂
1
xWhite (d) +  ̂
2
xOver35 (d) + "ij
where Iijd is the income level of individual i,  xj is a city- by-skill-level fixed e↵ect
which is an estimate of log (Wjx), and "ij is an individual-level error term.
The remaining unknown parameters of the production function are the
elasticity of substitution, &, the vector of city level total factor productivities, Aj,
and the vector of factor intensities, ✓j. We calibrate the elasticity of substitution,
& = 2.
Note that the lo✓g-wage◆-ratio in cit✓y j is◆given b✓y ◆
W 1 S ✓
log js =   log j + log j .
Wju & Uj 1  ✓j
As wage levels, labor quantities, and the elasticity of substitution, &, are already
known, the factor intensities ✓j can be solved by using the above equation.
The final set of parameters are the total factor productivities, Aj. These are
chosen so that wage levels are equal to those in the data.
169
B.0.1.9 Calibration: Housing Supply. We know that total demand
for housing in city j is given by:
X ↵H
H = N d
Ijd
j jd , (B.6)
R ↵
d j jd
where Njd is the total number of workers of demographic d living in city j.
Plugging this equation for housing demand into the housing supply curve and
rearranging yields the following reduced-form relationship:
k X H
log(R ) = j
↵ I
log( N d jdj jd ) + ⇣j. (B.7)
1 + kj ↵d jd
where ⇣j =
log zj
1 k .j
Saiz (2010) estimates the role of physical and regulatory constraints in
determining the role of local housing supply elasticities by using labor demand
shocks and instruments for housing demand. As in this paper, we set  WRIj equal
to the log of the Wharton Regulation Index plus 3, and use Saiz’s measure of the
unavailable land share (due to geography) for  GEOj . We calibrate ⌫1, ⌫2 and ⌫3
based on the estimates in Saiz (2010).2 We then choose the values of ⇣j to match
the rent levels observed in the data.
B.0.1.10 InMAP and Derivation of the SR matrix. In this
section, we provide a broad overview of InMAP and our process for deriving our
pollution-transfer matrix that maps electricity generation in a given NERC region
to ambient concentration in a given CBSA.
InMAP and ISRM The Intervention Model for Air Pollution (InMAP,
Tessum et al. (2017)), is a reduced-complexity air transport model that allows
users to estimate how changes in emissions impact concentration nationally.
InMAP takes into account atmospheric chemistry, local meteorological conditions
(i.e. wind), and variables regarding the point of emission (such as stack height
and velocity at which the particle was emitted). To estimate particulate-matter
concentration, InMAP uses data on emissions of primary PM2.5 and secondary
pollutants that react with gasses in the air and form PM2.5. The secondary
2Specifically, we use the estimates from Column (4) of Table III in Saiz (2010), as these are the
closest to our specification. Given that the estimate of the coe cient on the interaction between
housing supply constraints is quite similar across specifications in Saiz (2010), we do not suspect
that our results will be sensitive to the specific estimates we choose.
170
pollutants used by InMAP are Volatile Organic Compounds (VOC), Nitrogen
Oxides (NOx), Ammonia, (NH3), and Sulfur Oxides (SOx). InMAP estimates
concentrations for grid cells that vary in size by area population; for urban areas,
the grid cells are small, and for rural areas, they are large—expedient for making
the model more computationally tractable.
In Goodkind et al. (2019) InMAP is run over 150,000 times to obtain
average transfer coe cients for each grid cell—resulting in the InMAP SR matrix
(ISRM). Furthermore, ISRM has 3 “height” layers for each of the grid cell; 0
to 57m, 57-379m, and >379m. The Python code provided by Goodkind et al.
(2019) uses information about a plant’s stack height, and the velocity at which the
particle, is emitted to estimate into which of these three height layers the plant’s
plume of the emissions will fall, at any given time and distance
Derivation of the “transfer matrix” Let  PM2.5R,j be the factor that converts
electricity produced in region R into concentrations of PM2.5 in city j. We
calculate  PM2.5R,j as an emissions-weighted average of conversion factors for each
individual power plant in region R. Let s index an individual source (power
plant) and S(R) be the set of all sources within NERC region R. Let  PM2.5s,j
be the conversion factor between electricity production at source s and PM2.5
concentration in city j, given by:
 PM
PM
2 5 2.5,s,j.
s,j = xelecs
where PM2.5,s,j is the ambient air pollution in city j originating form source s (in
NERC region R) and xelecs is the total electricity produced by source s. Then we
compute  PM2.5R,j as the emissions-weighted average of these source-level conversion
factors: P
elec PM2.5
PM2 s2S(R)
xs  s,j
  .5s,j = P elec
s2S(R) xs
Plugging  PM2.5 into  PM2.5s,j s,j yields: P
PM
PM 2.5,s,j  2 5
s2S(R)
.
s,j = P xelec
P s2S(R) s
where s2S(R) PM2.5,s,j is the average ambient PM2.5 concentration in city j,
originating from region R and xelecs is total electricity production in region R.
3
3In practice, we calculate PM2.5,s,j as population-weighted averages within a CBSA.
171
P
s2S(R) PM2.5,s,j is estimated via ISRM by setting pollutant emissions in all
regions R0 =6 R to zero, and computing the resulting ambient concentration in
all cities for emissions from just region R. We note that ISRM has coe cients only
for the contiguous United States; thus for Hawaii, we set all transfer coe cients
to zero. In the model, this means that the level of particulate matter in Honolulu
is fixed and no particulate matter from Honolulu is transferred to the rest of the
United States.
B.0.1.11 Derivation of Mean Utility Estimating Equation.
Mean utility i s given byP  
1 + ↵Hd +
m H X m
µ = m
↵jd ↵ ↵log I   djdt jdt logR jdjt   logPmjt + ⇠̂jdt. d  d  m d
↵m
Recall that we have defined ↵̃m jPdjd = H m . Therefore, it is fairly1+↵ + ↵
d m jd
straightforward to show that
X P 0    m H
m0↵ = m
0 ↵̃jPd
1 + ↵d
jd   m01 0 ↵̃
m0 m jd
and therefore that    
↵̃m 1 + ↵H
↵mjd =
jd P d
  0
.
1 m0 ↵̃
m
jd
Plugging these identit✓ies into the mean utility◆expression yieldsP
m
H ↵̃m Pjd(1+↵
H
d )1 + ↵d + 1  ↵̃m H
m jd
µ = log I   ↵djdt jdt logRjt 
     d  d
1 + ↵H X ↵̃m
P d jd logPm0 jt + ⇠̂  m jdt
.
1 m0 ↵̃jd  m d
where can rearrange this to yield
    P    
1 + ↵H log I   ↵̃m m Hd jdt Pm jd
logPjt ↵
µ = djdt   m   logRjt + ⇠jdt. d 1 m ↵̃jd  d
P
log I   (↵̃mjdt logPm 1+↵H ↵HDefining Ĩ = Pm jd jt
) w ( d ) r ( d )
jdt 1  ↵̃m ,  d =   and  d =d   , we arrivem jd d
at (3.22):
µjdt =  
w r
d Ĩjdt +  d logRjt + ⇠jdt.
B.0.2 Results Appendix: For Online Publication Only. Table
B3 compares various specifications of the selection control function in estimating
(3.3), which we use to generate selection-corrected predicted emissions. For each
172
specification, we estimate the predicted emissions in each CBSA. Then we calculate
the population-weighted mean, standard deviation, and correlation with the
Wharton Regulation Index across CBSAs.
Standard Correlation w/
Mean Deviation Land Use Restrictions
I. No Selection Correction
a. Raw Means 24946 5729 -0.18
b. OLS 23711 5526 -0.21
II. Selection Correction
a. Choice Location and 3 Biggest States
i. Linear Choice, Linear States, Choice ⇥State Interactions 25518 5740 -0.28
ii. Linear Choice, Quadrartic States, Choice ⇥State Interactions 26815 6622 -0.22
iii. Linear Choice, Linear States, No Interactions 23934 5652 -0.28
iv. Linear Choice, Quadrartic States, No Interactions 24107 5488 -0.28
v. Quadrartic Choice, Linear States, Choice ⇥State Interactions 33185 12114 -0.21
vi. Quadrartic Choice, Quadrartic States, Choice ⇥State Interactions 32300 11747 -0.24
vii. Quadrartic Choice, Linear States, No Interactions 32581 11328 -0.27
viii. Quadrartic Choice, Quadrartic States, No Interactions 31199 10508 -0.23
b. Choice Location and 5 Biggest States
i. Linear Choice, Linear States, Choice ⇥State Interactions 27635 6801 -0.17
ii. Linear Choice, Quadrartic States, Choice ⇥State Interactions 27339 7073 -0.19
iii. Linear Choice, Linear States, No Interactions 23940 5654 -0.28
iv. Linear Choice, Quadrartic States, No Interactions 24203 5483 -0.26
v. Quadrartic Choice, Linear States, Choice ⇥State Interactions 32277 11283 -0.17
vi. Quadrartic Choice, Quadrartic States, Choice ⇥State Interactions 30837 11252 -0.20
vii. Quadrartic Choice, Linear States, No Interactions 32679 11563 -0.28
viii. Quadrartic Choice, Quadrartic States, No Interactions 31150 10662 -0.23
c. Choice Location and Birth States
i. Linear Choice, Linear Birth State 25327 6147 -0.32
ii. Linear Choice, Quadrartic Birth State 25467 6202 -0.32
iii. Quadratic Choice, Linear Birth State 30878 9608 -0.22
iv. Quadratic Choice, Quadrartic Birth State 30416 9308 -0.23
d. Controls for Climate in Birth State
i. Linear Choice, Linear States, Choice ⇥State Interactions 23418 5667 -0.12
ii. Linear Choice, Quadrartic States, Choice ⇥State Interactions 25281 6524 -0.19
iii. Linear Choice, Linear States, No Interactions 20369 6609 -0.15
iv. Linear Choice, Quadrartic States, No Interactions 22764 6262 -0.25
Table B3. Comparisons of various specifications of selection control function.
B.0.2.1 Comparisons of Specification of Control Function.
Panel I gives the predicted emissions without any selection correction. Row I.a
gives simply the mean emissions without including any demographic controls and
I.b estimates (3.3) without any selection correction but including demographics
controls.
173
Panel II includes the results with di↵erent specification of the control
function M (·). Subpanel II.a present estimates in which M (·) is a function of
the probability of choosing the state in question, and the probabilities of choosing
the three largest states. Row II.a.i consitute our preferred specification, where
the selection control function consists of the probability of choosing the state in
question entering linearly, the probabilities of choosing the three largest states
entering linearly, and the interactions between (a) the probability of choosing the
state in question and (b) each of the three largest-state choice probabilities.
The following rows of the table give alternative specifications in which state-
choice probabilities enter as a quadratic, in which the probability of choosing the
state in question also enters as a quadratic, and the interaction terms are omitted.
Subpanel II.b considers an analogous specification except where we include the
probabilities of choosing the 5 largest states. Finally, Subpanel II.c considers
a control function written as a function of choosing the state in question and
choosing the individual’s birth state.
Subpanel II.d compare estimates when we also include controls for the
average yearly temperature in the state of birth. These specifications are otherwise
identical to those in II.a.i through II.a.iv, in which we include controls for the three
largest states by population, and the probably of choosing the state in question.
In general, the estimates are relatively similar across specifications.
The exception is when the choice probability for the state in question enters
as quadratic. In these cases, the standard deviation of the predicted emissions
increases. As mentioned before, estimating the intercept of the energy usage
equation relies on extrapolating the control function to Pis(j) = 1. For smaller
states, the probability of choosing the state in question is farther from one, so this
extrapolation becomes more sensitive to the choice of the control function.
B.0.2.2 Additional Summary Statistics: No Selection
Correction. In this section, we replicate our Table 2 and our main descriptive
scatterplots without demographic controls and without the selection correction.
Table B4 gives estimates of energy usage and emissions by CBSA, where
estimates of energy use are given simply by the unconditional mean for households
living in the CBSA. There are no controls for demographics, and no selection-
correction is implemented.
174
CBSA Rank Emissions Gas Fuel Electricity Electricity Electricity
Emissions Emissions Use Conversion Emissions
(1000 lbs) (1000 lbs) (1000 lbs) (MwH) (1000 lbs/MwH) (1000 lbs)
Lowest
Honolulu, HI 1 12.83 0.47 0.07 8.08 1.52 12.29
Oxnard, CA 2 12.85 5.80 0.17 8.61 0.80 6.89
Riverside, CA 3 13.64 5.59 0.17 9.85 0.80 7.88
Los Angeles, CA 4 14.41 6.06 0.09 10.32 0.80 8.26
San Diego, CA 5 14.87 6.42 0.23 10.27 0.80 8.22
Sacramento, CA 6 15.84 7.28 0.40 10.20 0.80 8.16
Middle
Atlanta, GA 33 25.24 6.46 0.17 17.97 1.04 18.61
Pittsburgh, PA 34 25.77 11.43 1.35 11.74 1.11 12.98
Akron, OH 35 25.85 12.05 0.58 11.95 1.11 13.21
Birmingham, AL 36 26.10 5.42 0.17 19.81 1.04 20.51
Virginia Beach, VA 37 26.19 6.12 0.71 18.70 1.04 19.36
Houston, TX 38 26.37 4.62 0.08 21.35 1.01 21.67
Highest
Oklahoma City, OK 65 32.29 8.26 0.20 18.76 1.27 23.84
Detroit, MI 66 32.48 18.72 0.36 12.12 1.11 13.40
Philadelphia, PA 67 33.32 11.39 3.12 17.02 1.11 18.81
Memphis, TN 68 34.45 8.37 0.19 25.01 1.04 25.89
Milwaukee, WI 69 35.22 16.71 0.52 16.28 1.11 17.99
Omaha, NE 70 35.98 15.79 0.28 16.31 1.22 19.91
Table B4. Predicted CBSA level CO2 emissions by fuel type for the six lowest-
emissions cities, the six median cities, and the six highest-emissions cities in 2017.
The third column (“Emissions”) shows the unconditional mean CO2 emissions
from natural gas, fuel oil and electricity for the CBSA. The next two columns
show emissions from gas and fuel oil respectively, which are equal to predicted
usage multiplied by the appropriate emissions factor. The last three columns show
predicted electricity usage, the electricity emissions factor, and predicted electricity
emissions, equal to predicted electricity usage multiplied by the emissions factor.
The next figures are replicates of Figures 11 and 12—without selection-
corrected energy usage. Figure B2 plots household carbon emissions against
the Wharton Index. In the scatterplot on the left, we predict household energy
use with a simple OLS regression that controls for demographic groups. In the
scatterplot on the right, we predict household energy use with CBSA-level means.
Overall, the pattern is qualitatively similar regardless of the specification; California
cities have low household carbon emissions and relatively stringent land-use
restrictions.
Figure B3 plots household natural gas usage against January temperature
and electricity usage against August temperature. In the two scatterplots in
the top row, we predict household energy use with a simple OLS regression that
controls for demographic groups. In the scatterplots on the bottom row, we predict
household energy use with CBSA-level means.
175
HH Energy Usage: HH Energy Usage:
OLS w/ Demographic Controls Raw Data
35,000 35,000
30,000
30,000
25,000
25,000
20,000
Sacramento Fresno 20,000 San Jose
San Jose Fresno San Francisco Sacramento
15,000 San Francisco
San Diego Los Angeles 15,000 San Diego Los Angeles
Oxnard Riverside Oxnard Riverside
-1 0 1 2 -1 0 1 2
Wharton Index Wharton Index
Figure B2. Additional scatterplots: in which CO2 emissions plotted against the
Wharton Index. An observation is a CBSA; a larger circle represents a larger
population. California cities are in green.
176
CO2 Emissions (lbs) 
CO2 Emissions (lbs) 
HH Energy Usage: HH Energy Usage:
OLS w/ Demographic Controls OLS w/ Demographic Controls
150
20
100
15
50
10
0
20 40 60 70 80 90
January Temperature August Temperature
HH Energy Usage: HH Energy Usage:
Raw Data Raw Data
25
150
20
100
15
50
10
0
20 40 60 70 80 90
January Temperature August Temperature
Figure B3. Additional scatterplots in which natural gas and electricity use are
plotted against January and August temperatures, respectively. January and
August temperature refers to the midpoint between average daily highs and lows
for the given month. An observation is a CBSA; a larger circle represents a larger
population.
177
Natural Gas Use (1000ft3) Natural Gas Use (1000ft3)
Electricity Use (MWh) Electricity Use (MWh)
B.0.2.3 PM2.5: Additional Results . This section provides
additional summary information about PM2.5. Figure B4 plots the distribution of
total PM2.5 concentrations across cities and Figure B5 the estimated contribution
of household electricity to total PM2.5.
From Figure B4, there are a few key takeaways. First, the histogram
demonstrates considerable variation across CBSAs in terms of total PM2.5. Second,
California cities are relatively dispersed throughout the distribution—some are
relatively clean, while others have high concentrations of PM2.5.
Next, Figure B5 with the city-level ratios of household electricity
contribution to total PM2.5 illustrates two things. Overall, household electricity
contributes fairly little to overall PM2.5. Second, the amount by which household
electricity use contributes to total PM2.5 varies across cities; Portland gets nearly
zero percent of its particulate matter emissions from electricity, while Dallas gets
roughly 6.5%.
178
9
6
CA
Other
3
0
5.0 7.5 10.0 12.5
Total PM2.5 Concentration
Figure B4. The distribution of 2017 mean PM2.5 across CBSAs in our sample.
179
Number of Cities
Honolulu, HI
Portland, OR
Phoenix, AZ
San Diego, CA
Riverside, CA
Fresno, CA
Oxnard, CA
San Francisco, CA
Los Angeles, CA
Sacramento, CA
Seattle, WA
Tucson, AZ
San Jose, CA
Salt Lake City, UT
Miami, FL
Worcester, MA
Detroit, MI
Milwaukee, WI
Springfield, MA
Hartford, CT
Boston, MA
Minneapolis, MN
Denver, CO
New Haven, CT
Albany, NY
Kansas City, MO
Grand Rapids, MI
Bridgeport, CT
Birmingham, AL
Orlando, FL
Providence, RI
Akron, OH
Chicago, IL
Knoxville, TN
Buffalo, NY
Atlanta, GA
Tulsa, OK
Omaha, NE
Oklahoma City, OK
Toledo, OH
Cleveland, OH
Youngstown, OH
Scranton, PA
Allentown, PA
Syracuse, NY
Baton Rouge, LA
Tampa, FL
Jacksonville, FL
Nashville, TN
Rochester, NY
Philadelphia, PA
New York, NY
Charlotte, NC
Memphis, TN
Pittsburgh, PA
Indianapolis, IN
Washington, DC
St. Louis, MO
Richmond, VA
San Antonio, TX
Columbus, OH
Virginia Beach, VA
New Orleans, LA
Baltimore, MD
Dayton, OH
Austin, TX
Cincinnati, OH
Houston, TX
Louisville, KY
Dallas, TX
0.00 0.01 0.02 0.03 0.04 0.05
Ratio of PM2.5 from HH electricity to total PM2.5 concentration
Figure B5. This figure plots the ratio of PM2.5 coming from electricity to total
PM2.5 as measured by the EPA.
Next, Figure B6 plots a histogram of PM2.5 changes from the baseline when
we set land-use restrictions to the level faced by the median urban household in all
cities.
180
CBSA
Relax All
20
Census Region
Midwest
Northeast
South
West
10
0
-0.3 -0.2 -0.1 0.0 0.1 0.2
Change in PM2.5 Concentration from HH Electricity
Figure B6. Histogram of CBSA level di↵erences in particulate matter concentration
from electricity relative to the case where land-use restrictions in all cities.
B.0.2.4 Robustness of Main Parameter Estimates. Table
B5 gives estimates that vary by the age of the household head. The first three
columns give estimates for which the head of the households is under 35 years
old for (1) single households, (2) married households without children, and (3)
married households with children. The next three columns present estimates for
which the head of the households is over 35 years old for (4) single households, (5)
married households without children, (6) and married households with children.
The estimates of  w and  r are slightly larger in magnitude for households with
older household heads, conditional on marital status and the presence of children.
181
Number of Cities
Head under 35 years experience Head over 35 years experience
Married Married
Single No Children With Children Single No Children With Children
 w: Adjusted Income 13.37 9.96 7.35 16.81 13.45 7.37
(3.48) (2.62) (2.16) (4.45) (3.58) (2.01)
 r: Rent -7.27 -5.02 -5.13 -10.77 -8.76 -4.56
(2.99) (2.27) (1.92) (3.79) (3.09) (1.74)
 : Idiosyncratic Component 0.16 0.20 0.45 0.17 0.21 0.36
(0.04) (0.05) (0.20) (0.06) (0.07) (0.12)
↵H : Housing Parameter 1.19 1.02 2.30 1.79 1.87 1.62
(0.56) (0.51) (1.37) (0.83) (0.90) (0.79)
Cragg-Donald Wald F Statistic 3.92 4.04 4.27 4.16 4.24 4.29
Table B5. Parameter estimates that vary by age. Standard errors in parentheses.
Table B6 gives estimates using alternative instrumental variables. The
first panel presents our baseline estimates. Panel II uses estimates for a model
that employs the measure of land use availability from Saiz (2010) in place or the
Wharton Land Use Index. Panel III presents estimates when we use both measures
as instruments.
182
I. Baseline Estimates
Married
Single No Children With Children
 w: Adjusted Income 15.09 11.72 7.33
(2.80) (2.19) (1.47)
 r: Rent -9.03 -6.90 -4.82
(2.40) (1.89) (1.29)
 : Idiosyncratic Component 0.17 0.21 0.40
(0.03) (0.04) (0.11)
↵H : Housing Parameter 1.49 1.44 1.92
(0.48) (0.48) (0.73)
Cragg-Donald Wald F Statistic 8.09 8.28 8.57
II. Available Land Instrument
Married
Single No Children With Children
 w: Adjusted Income 19.39 18.36 16.14
(4.66) (4.52) (4.07)
 r: Rent -9.99 -9.06 -9.22
(3.00) (2.88) (2.62)
 : Idiosyncratic Component 0.11 0.11 0.14
(0.03) (0.03) (0.04)
↵H : Housing Parameter 1.06 0.98 1.33
(0.28) (0.26) (0.36)
Cragg-Donald Wald F Statistic 5.41 5.14 5.05
III. Both Instruments
Married
Single No Children With Children
 w: Adjusted Income 15.42 12.40 9.08
(2.36) (1.90) (1.46)
 r: Rent -8.43 -6.46 -5.61
(1.73) (1.39) (1.09)
 : Idiosyncratic Component 0.14 0.17 0.29
(0.02) (0.03) (0.06)
↵H : Housing Parameter 1.20 1.09 1.61
(0.26) (0.24) (0.38)
Cragg-Donald Wald F Statistic 7.91 8.10 8.21
Table B6. Parameter estimates with alternative instrumental variables. Standard
errors in parentheses.
B.0.2.5 New Power Plant Development. Table B7 gives the
full distribution of emissions and percent of plants that use renewables, split on
whether they were constructed before or after 2000.
183
Mean Emissions Percent Renewables
NERC Pre-2000’s Post-2000’s Pre-2000’s Post 2000’s
ASCC 935.55 842.37 37.38 15.50
FRCC 935.66 857.27 3.65 2.90
HICC 1649.43 461.88 9.22 70.62
MRO 1566.42 188.09 9.49 80.18
NPCC 410.31 747.15 24.42 14.71
RFC 1176.69 850.51 2.18 14.75
SERC 1055.78 941.07 6.16 5.25
SPP 1741.86 521.45 5.93 46.90
TRE 1135.47 620.07 1.18 29.53
WECC 858.24 597.01 40.48 36.47
Table B7. NERC regional mean carbon emissions from plants built before 2000 and
after 2000. Emissions rates are measured in lbs/MWh.
B.0.2.6 Counterfactual results with model extensions.
Endogenous Electricity Pricing Table B8 displays the counterfactual results
when electricity pricing is endogenous.
184
Baseline Relax Cali Relax All
I. Percent Total Population
California Cities 9.1 10.9 7.3
Other West 13.6 13.1 17.1
Midwest 22.2 21.8 10.0
South 37.3 36.6 25.3
Northeast 17.9 17.6 40.3
II. Mean Usage
Gas (1000 cubic feet) 74.4 74.2 75.1
Electricity (MW h) 17.1 17.0 15.5
Fuel Oil (gallons) 60.4 59.5 133.0
III. Mean Emissions (lbs of CO2)
Gas 8711 8688 8792
Electricity 16331 16267 14030
Fuel Oil 1622 1599 3572
Total 26664 26553 26394
(%) 100.00 99.6 99.0
IV. Average Log Income
Skilled 100.0 100.5 112.3
Unskilled 100.0 100.0 100.1
All 100.0 100.2 104.4
Table B8. Counterfactual results with endogenous electricity pricing. Each panel
shows the simulated total energy usage, total emissions, average log income, and
fraction of total population living in various geographic areas in each specification.
See text for details on each simulation.
E↵ects of Local Pollutants on Utility Table B9 presents counterfactual
results in the case where PM2.5 enters directly into the utility function. As noted
in the text, the results are very similar to the baseline specification, given that
changes in household electricity are the only component of the model that changes
PM2.5—and electricity contributes little to overall PM2.5.
185
Baseline Relax Cali Relax All
I. Percent Total Population
California Cities 9.1 11.0 7.2
Other West 13.6 13.1 17.8
Midwest 22.2 21.7 9.3
South 37.3 36.6 23.1
Northeast 17.9 17.6 42.6
II. Mean Usage
Gas (1000 cubic feet) 74.4 74.2 74.9
Electricity (MW h) 17.1 17.0 15.8
Fuel Oil (gallons) 60.4 59.5 138.6
III. Mean Emissions (lbs of CO2)
Gas 8711 8686 8771
Electricity 16331 16211 13246
Fuel Oil 1622 1598 3722
Total 26664 26495 25738
(%) 100.0 99.4 96.5
IV. Average Log Income
Skilled 100.0 100.5 113.0
Unskilled 100.0 100.0 100.4
All 100.0 100.2 104.8
Table B9. Counterfactual results with pollution in the utility function. Each panel
shows the simulated total energy usage, total emissions, average log income, and
fraction of total population living in various geographic areas in each specification.
See Section 3.7.3 for details.
B.0.2.7 Birth-State Premium Parameters. Tables B10 through
B13 display parameters governing the birth-state premium for each of the years
we use in estimation. In all years, households receive a large utility premium for
choosing a location in their home state and the amenity value of a location is
estimated to be decreasing and convex in distance from the household head’s birth
state.
B.0.2.8 Demographic Group City Ranks. Table B14 provides
selected estimated of ⇠jdt, the shared unobservable component of amenities, for the
year 2017 for households with heads over the age of 35.
186
Unskilled
Nonwhite
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 3.14 2.77 2.77 2.94 2.52 2.85
(0.08) (0.6) (0.14) (0.07) (0.27) (0.1)
Distance -1.78 -1.22 -1.71 -1.78 -1.75 -1.71
(0.07) (0.31) (0.09) (0.07) (0.21) (0.08)
Distance Squared 0.3 0.21 0.29 0.2 0.21 0.19
(0.01) (0.03) (0.01) (0.01) (0.03) (0.01)
White
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 3.15 3.03 2.94 3.15 3.08 3.13
(0.02) (0.06) (0.02) (0.01) (0.02) (0.01)
Distance -1.03 -1.41 -2.05 -1.06 -1.03 -1.38
(0.02) (0.06) (0.02) (0.01) (0.02) (0.01)
Distance Squared 0.21 0.31 0.54 0.17 0.09 0.25
(0.00) (0.01) (0.01) (0.00) (0.00) (0.00)
Skilled
Nonwhite
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 2.3 2.17 2.43 2.38 2.16 2.37
(0.47) (1.99) (1.1) (0.4) (1.21) (0.46)
Distance -1.19 -1.04 -1.11 -1.48 -1.09 -1.12
(0.27) (0.93) (0.63) (0.24) (0.56) (0.25)
Distance Squared 0.16 0.12 0.14 0.2 0.11 0.09
(0.03) (0.08) (0.06) (0.02) (0.05) (0.02)
White
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 2.02 2.04 2.1 2.13 1.92 2.11
(0.05) (0.1) (0.06) (0.04) (0.05) (0.02)
Distance -2.17 -2.16 -2.35 -1.96 -2.05 -2.11
(0.04) (0.08) (0.06) (0.03) (0.04) (0.02)
Distance Squared 0.62 0.6 0.64 0.52 0.5 0.54
(0.01) (0.02) (0.02) (0.01) (0.01) (0.00)
Table B10. Parameter Estimates for 1990 Data. Standard errors multiplied by 1000
in parentheses.
187
Unskilled
Nonwhite
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 3.11 2.62 2.69 2.89 2.66 2.73
(0.06) (0.52) (0.13) (0.04) (0.14) (0.07)
Distance -1.59 -1.3 -1.55 -1.75 -1.34 -1.71
(0.05) (0.29) (0.09) (0.03) (0.11) (0.05)
Distance Squared 0.27 0.23 0.26 0.27 0.16 0.24
(0.01) (0.03) (0.01) (0.00) (0.01) (0.01)
White
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 3 3.03 3.16 2.8 2.67 2.9
(0.02) (0.08) (0.03) (0.01) (0.01) (0.01)
Distance -1.34 -1.37 -1.05 -1.84 -2.07 -1.92
(0.02) (0.08) (0.03) (0.01) (0.02) (0.01)
Distance Squared 0.29 0.32 0.19 0.45 0.49 0.47
(0.00) (0.02) (0.01) (0.00) (0.00) (0.00)
Skilled
Nonwhite
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 2.22 2.02 2.33 2.37 2.15 2.33
(0.25) (1.27) (0.81) (0.18) (0.54) (0.28)
Distance -1.13 -1.12 -1.19 -1.37 -1.06 -1.02
(0.14) (0.65) (0.45) (0.11) (0.27) (0.15)
Distance Squared 0.17 0.15 0.18 0.2 0.12 0.09
(0.01) (0.06) (0.04) (0.01) (0.02) (0.01)
White
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 2.08 2.15 2.2 2.21 2.01 2.13
(0.04) (0.1) (0.07) (0.03) (0.03) (0.02)
Distance -2.04 -2.01 -2.3 -1.73 -1.96 -2
(0.03) (0.08) (0.07) (0.02) (0.03) (0.02)
Distance Squared 0.59 0.55 0.63 0.46 0.51 0.53
(0.01) (0.02) (0.01) (0.00) (0.01) (0.00)
Table B11. Parameter Estimates for 2000 Data. Standard errors multiplied by 1000
in parentheses.
188
Unskilled
Nonwhite
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 3.09 2.57 2.57 2.87 2.76 2.85
(0.07) (0.75) (0.2) (0.03) (0.11) (0.09)
Distance -1.61 -1.19 -1.49 -1.65 -1.3 -1.27
(0.06) (0.41) (0.13) (0.03) (0.09) (0.06)
Distance Squared 0.28 0.22 0.25 0.25 0.16 0.15
(0.01) (0.04) (0.01) (0.00) (0.01) (0.01)
White
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 2.83 2.85 2.72 2.77 2.63 2.74
(0.02) (0.1) (0.04) (0.01) (0.01) (0.01)
Distance -1.79 -1.36 -2.12 -1.8 -2.17 -2.02
(0.02) (0.09) (0.04) (0.01) (0.01) (0.01)
Distance Squared 0.41 0.31 0.5 0.45 0.57 0.49
(0.01) (0.02) (0.01) (0.00) (0.00) (0.00)
Skilled
Nonwhite
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 2.31 1.99 2.16 2.44 2.18 2.21
(0.19) (0.95) (0.58) (0.12) (0.31) (0.2)
Distance -1.03 -1.06 -1.51 -1.25 -1.13 -1.1
(0.11) (0.48) (0.35) (0.07) (0.17) (0.1)
Distance Squared 0.15 0.15 0.24 0.18 0.13 0.11
(0.01) (0.05) (0.03) (0.01) (0.02) (0.01)
White
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 2.15 2.19 2.37 2.2 2.02 2.09
(0.04) (0.08) (0.06) (0.02) (0.02) (0.01)
Distance -2.04 -2.03 -2.02 -1.8 -1.89 -2.16
(0.03) (0.07) (0.06) (0.01) (0.02) (0.01)
Distance Squared 0.57 0.55 0.51 0.48 0.49 0.6
(0.01) (0.02) (0.02) (0.00) (0.00) (0.00)
Table B12. Parameter Estimates for 2010 Data. Standard errors multiplied by 1000
in parentheses.
189
Less than College
Nonwhite
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 3.14 2.34 2.68 2.98 2.75 2.94
(0.07) (0.68) (0.25) (0.03) (0.11) (0.09)
Distance -1.58 -1.22 -1.31 -1.62 -1.54 -1.17
(0.06) (0.33) (0.16) (0.03) (0.09) (0.06)
Distance Squared 0.27 0.22 0.21 0.24 0.22 0.12
(0.01) (0.03) (0.02) (0.00) (0.01) (0.01)
White
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 2.89 2.84 2.84 2.7 2.66 2.82
(0.02) (0.11) (0.04) (0.01) (0.01) (0.01)
Distance -1.8 -1.42 -1.6 -2.04 -2.16 -1.87
(0.03) (0.11) (0.04) (0.01) (0.01) (0.01)
Distance Squared 0.43 0.34 0.34 0.52 0.56 0.43
(0.01) (0.04) (0.01) (0.00) (0.00) (0.00)
College or More
Nonwhite
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 2.35 2.01 2.38 2.53 2.04 2.26
(0.15) (0.74) (0.54) (0.09) (0.24) (0.16)
Distance -0.91 -0.91 -1.09 -1.25 -1.38 -1.05
(0.08) (0.36) (0.32) (0.06) (0.13) (0.08)
Distance Squared 0.14 0.13 0.15 0.18 0.19 0.11
(0.01) (0.04) (0.03) (0.01) (0.01) (0.01)
White
Young Old
Single Married Married Single Married Married
w/o Children w/ Children w/o Children w/ Children
Birthstate Premium 2.21 2.23 2.37 2.3 2.02 2.13
(0.03) (0.07) (0.05) (0.02) (0.02) (0.01)
Distance -1.99 -1.92 -2.3 -1.8 -1.94 -2.2
(0.02) (0.06) (0.06) (0.01) (0.02) (0.01)
Distance Squared 0.58 0.52 0.62 0.5 0.51 0.61
(0.01) (0.02) (0.02) (0.00) (0.00) (0.00)
Table B13. Parameter Estimates for 2017 data. Standard errors multiplied by 1000
in parentheses.
190
Panel (a): White College or more Less than College
Rank Single (no kids) Married (with kids) Single (no kids) Married (with kids)
1 Miami, FL Portland, OR San Diego, CA Seattle, WA
2 Portland, OR Miami, FL Miami, FL Portland, OR
3 Los Angeles, CA Seattle, WA Portland, OR Los Angeles, CA
4 San Diego, CA Los Angeles, CA Seattle, WA Honolulu, HI
5 Orlando, FL San Diego, CA Oxnard, CA San Diego, CA
66 Youngstown, OH Memphis, TN Springfield, MA Memphis, TN
67 Bridgeport, CT Worcester, MA Worcester, MA Springfield, MA
68 Memphis, TN Springfield, MA Albany, NY Worcester, MA
69 Worcester, MA Syracuse, NY Rochester, NY Albany, NY
70 Syracuse, NY Youngstown, OH Syracuse, NY Syracuse, NY
Panel (b): Non-white College or more Less than College
Rank Single (no kids) Married (with kids) Single (no kids) Married (with kids)
1 Los Angeles, CA Los Angeles, CA Los Angeles, CA Los Angeles, CA
2 San Francisco, CA Honolulu, HI Miami, FL Honolulu, HI
3 Miami, FL Miami, FL San Francisco, CA Seattle, WA
4 Honolulu, HI San Francisco, CA San Diego, CA San Francisco, CA
5 San Diego, CA San Diego, CA Seattle, WA Portland, OR
66 Albany, NY Knoxville, TN Springfield, MA Springfield, MA
67 Memphis, TN Syracuse, NY Syracuse, NY Albany, NY
68 Syracuse, NY Springfield, MA Albany, NY Syracuse, NY
69 Rochester, NY Scranton, PA Milwaukee, WI Rochester, NY
70 Milwaukee, WI Youngstown, OH Rochester, NY Milwaukee, WI
Table B14. Demographic group city ranks according to the shared component of
amenities. Ranks are by unobservable component of amenities for households with
older household heads.
B.0.2.9 Methane Emissions. As an alternative to carbon-dioxide
emissions, we also explore the relationship between the stringency of land use
regulation and methane emissions. Methane is a global issue; while it is odorless
and thus not considered a local pollutant, it is classified as a greenhouse gas.
According to the Bernstein et al. (2008), pound for pound, methane has 25 times
the global warming potential over a 100 year period compared to carbon dioxide.
The relationship between the Wharton Index and methane emissions is quite
similar to that of carbon dioxide emissions. Cities with more stringent land use
restrictions tend to have lower methane emissions.
191
4.0
3.0
2.0
Fresno 
Sacramento San Francisco
San Jose Los Angeles
San Diego Riverside
1.0 Oxnard
-1 0 1 2
Wharton Index
Figure B7. Methane emissions regressed on Wharton Index. Each observation is a
CBSA. Size of each observation reflects population of CBSA. CBSAs in green are
CA cities.
Methane emissions come from two sources: natural gas and electricity
generation. Combustion of natural gas does not produce methane; however, natural
gas is composed of 70% methane. Furthermore, natural gas leakages are estimated
to be 1.4% according to the EPA. To impute the amount of methane emitted from
natural gas ise, we use a conversion factor of 0.7*0.014 = 0.0098. As with carbon
dioxide, methane emissions from electricity vary by NERC region. We compute
the weighted emissions rate for methane in the same manner as we did for carbon
dioxide emissions. Table B15 provides an array of city-level energy consumption,
ranked on methane emissions.
192
Selection-Corrected CH4 Emissions (lbs) 
CBSA Rank Emissions Gas Electricity Electricity Electricity
Emissions Use Conversion Emissions
(1000 lbs) (1000 lbs) (MwH) (1000 lbs per MwH) (1000 lbs)
Lowest
Hartford, CT 1 1.06 0.29 13.48 0.06 0.77
New Haven, CT 2 1.11 0.29 14.32 0.06 0.82
Worcester, MA 3 1.15 0.39 13.33 0.06 0.76
Oxnard, CA 4 1.25 0.56 10.26 0.07 0.69
Bridgeport, CT 5 1.28 0.42 15.06 0.06 0.86
Springfield, MA 6 1.30 0.56 12.83 0.06 0.73
Middle
New Orleans, LA 33 2.00 0.41 21.38 0.07 1.59
Jacksonville, FL 34 2.01 0.06 25.92 0.08 1.96
Birmingham, AL 35 2.02 0.52 20.15 0.07 1.50
Atlanta, GA 36 2.03 0.36 22.45 0.07 1.67
Austin, TX 37 2.04 0.34 22.00 0.08 1.70
Salt Lake City, UT 38 2.09 1.26 12.36 0.07 0.83
Highest
Memphis, TN 65 3.32 0.95 31.89 0.07 2.37
Tulsa, OK 66 3.44 1.12 21.60 0.11 2.32
Oklahoma City, OK 67 3.56 1.06 23.21 0.11 2.50
Indianapolis, IN 68 3.68 2.08 18.26 0.09 1.60
Milwaukee, WI 69 3.86 1.96 21.72 0.09 1.90
Omaha, NE 70 4.10 1.55 22.84 0.11 2.55
Table B15. Predicted CBSA-level methane emissions by fuel type for the six
lowest-emissions cities, the six median cities, and the six highest-emissions cities.
The third column (“Emissions”) shows the sum of selection-corrected methane
emissions from natural gas, fuel oil, and electricity for the CBSA. The next two
columns show emissions from gas and fuel oil respectively, which are equal to
predicted usage multiplied by the appropriate emissions factor. The last three
columns show predicted electricity usage, the electricity emissions factor, and
predicted electricity emissions, equal to predicted electricity usage multiplied by
the emissions factor. Use is measured in 1000 pounds per megawatt hour.
Our main counterfactual was to relax land use restrictions in California
cities to the national median. To do this, we simulated how demand for energy
services changed as a result of the changes in rental prices from the relaxation of
land-use restrictions. To estimate average CBSA-level emissions, we multiplied
the respective usages by the local emissions factors for each source of carbon
dioxide. We can use the same simulation to examine the changes in methane
emissions by using the relevant conversion factors for methane emissions. Table
B16 demonstrates how methane emissions change as a result of our simulation.
193
Baseline Relax Cali Relax All
II. Emissions (lbs of Methane)
Gas 0.78 0.78 0.79
Electricity 1.33 1.32 1.16
Fuel Oil 0.00 0.00 0.00
Total 2.11 2.10 1.95
Table B16. Counterfactual results for methane emissions. Each column shows the
amount of methane emitted from each energy source under various counterfactual
scenarios.
Similar to the summary statistics for carbon emissions, we include a table
without the selection correction—and additional scatterplots using OLS with
demographic controls and the raw data.
194
CBSA Rank Emissions Gas Fuel Electricity Electricity Electricity
Emissions Emissions Use Conversion Emissions
(1000 lbs) (1000 lbs) (1000 lbs) (MwH) (1000 lbs/MwH) (1000 lbs)
Lowest
Honolulu, HI 1 12.83 0.47 0.07 8.08 1.52 12.29
Oxnard, CA 2 12.85 5.80 0.17 8.61 0.80 6.89
Riverside, CA 3 13.64 5.59 0.17 9.85 0.80 7.88
Los Angeles, CA 4 14.41 6.06 0.09 10.32 0.80 8.26
San Diego, CA 5 14.87 6.42 0.23 10.27 0.80 8.22
Sacramento, CA 6 15.84 7.28 0.40 10.20 0.80 8.16
Middle
Atlanta, GA 33 25.24 6.46 0.17 17.97 1.04 18.61
Pittsburgh, PA 34 25.77 11.43 1.35 11.74 1.11 12.98
Akron, OH 35 25.85 12.05 0.58 11.95 1.11 13.21
Birmingham, AL 36 26.10 5.42 0.17 19.81 1.04 20.51
Virginia Beach, VA 37 26.19 6.12 0.71 18.70 1.04 19.36
Houston, TX 38 26.37 4.62 0.08 21.35 1.01 21.67
Highest
Oklahoma City, OK 65 32.29 8.26 0.20 18.76 1.27 23.84
Detroit, MI 66 32.48 18.72 0.36 12.12 1.11 13.40
Philadelphia, PA 67 33.32 11.39 3.12 17.02 1.11 18.81
Memphis, TN 68 34.45 8.37 0.19 25.01 1.04 25.89
Milwaukee, WI 69 35.22 16.71 0.52 16.28 1.11 17.99
Omaha, NE 70 35.98 15.79 0.28 16.31 1.22 19.91
Table B17. Predicted CBSA-level methane (CH4) emissions by fuel type for the six
lowest-emissions cities, the six median cities, and the six highest-emissions cities in
2017. The third column (“Emissions”) shows the unconditional mean methane
emissions from natural gas and electricity for the CBSA. The next two columns
show emissions from gas and fuel oil respectively, which are equal to predicted
usage multiplied by the appropriate emissions factor. The last three columns show
predicted electricity usage, the electricity emissions factor, and predicted electricity
emissions, equal to predicted electricity usage multiplied by the emissions factor.
195
HH Energy Usage: HH Energy Usage:
OLS w/ Demographic Controls Raw Data
3.00
3.00
2.50
2.50
2.00
2.00
San Jose Fresno 
1.50 Sacramento San Francisco 1.50 Fresno San Jose Sacramento
San Diego Los Angeles San Diego San Francisco Los Angeles
1.00 Oxnard Riverside 1.00 Oxnard Riverside
-1 0 1 2 -1 0 1 2
Wharton Index Wharton Index
Figure B8. Methane emissions regressed on the Wharton Index. Each observation
is a CBSA. The size of each observation reflects the population of CBSA. CBSAs in
green are in California.
196
CO2 Emissions (lbs) 
CH4 Emissions (lbs) 
APPENDIX C
CHAPTER 4: APPENDIX
C.0.1 Model Appendix.
C.0.1.1 Firm FOC Derivation. This section derives the first-order
conditions for the firms. Recall that firms in city j and sector n produce according
to
Yjn = A K
⌘ I1 ⌘jn jn jn ,
where Ijn is the CES aggregator between energy and labor inputs. Specifically,
⇣ ⌘ 1
n n n
I ⇢ ⇢ ⇢jn = ↵ el el eljnEjn + (1  ↵jn)Ljn ,
where
⇣ ⌘ 1
⇢n nE ⇢
n
e
jn = ⇣jnEjn + (1  ⇣
⇢e e
jn)Gjn
  ⇢   1L ljn = ✓jnCjn + (1  ✓ )L
⇢l ⇢
jn ljn .
Note that I assume factor markets are perfectly competitive so input prices
are equal to their marginal revenue products. The firm’s profit function is given by:
⇡jn = PnA
⌘ 1 ⌘ C L G
jnKjnIjn  WjnCjn  WjnLjn   PjnGjn   PEjnEjn. (C.1)
Di↵erentiating equation C.1 with respect to each of the firm’s inputs yields
the following expressions for energy prices (denoted by PEjn and P
G
jn) and pre-tax
wages (WCjn and W
L
jn): ✓ ◆
E Yjn I1 ⇢
n n
P = eljn I jn ↵jn(1  ⌘)⇣ E
⇢e 1
jn jn
✓ jn◆
f YP = jn
1 ⇢n ⇢nI el e 1jn I jn ↵jn(1  ⌘)(1  ⇣jn)Gjn✓ jn◆
Yjn 1 ⇢nWC = I el(1  ↵ )(1  ⌘)(✓ )C⇢l 1jn I jn jn jn jn✓ jn◆
L YW = jn I1 ⇢
n
el
jn I jn (1  ↵jn)(1  ⌘)(1  ✓
⇢l 1
jn)Ljn .
jn
I assume that capital supply is perfectly elastic and has rental rate r̄. The firm
chooses its level of capital such that the price is equal to the marginal product.
Specifically, this is given by
 ! 1
P A 1 ⌘ 1 ⌘n jn⌘I
K = jnjn . (C.2)
r̄
197
Plugging equation C.2 into the FOCs and rearranging yields the desired
FOCs as in equation 4.8.
C.0.1.2 Firm Parameters. In this section, I outline my estimation
and calibration of the production function parameters. I break the following
discussion into two sections: labor and energy.
Labor Parameters. I need city-sector wages, labor elasticity of substitution ( l),
and factor intensities (✓jn’s). Let e 2 {C,L} index worker education levels. A
worker of demographic d’s income in location j and sector n is given by
I eejn = Wejn` (C.3)
where `e is the number of e ciency units of labor supplied by a worker of education
level e. I parameterize `e as the probability that a worker of education level e in
city j and sector n is unemployed (denoted by ⇡ejn) multiplied by the e ciency
units. That is
`e = ⇡ ˆ̀eejn , (C.4)
where I parameterize ˆ̀e as
ˆ̀ e ee    = white 1i over35
2
i . (C.5)
Conditional on working, the workers’ pre-tax income is given by substituting
equation C.4 into equation C.3 and taking logs:
log(Iejn) = log(Wejn) +  
e
1 log(whitei) +  
e
2 log(over35i). (C.6)
I thus estimate city-sector-education wages using equation C.6. Specifically, I
estimate:
log(Iejn) = ⌫ejn +  
e
1 log(whitei) +  
e
2 log(over35i) + "ijn, (C.7)
where ⌫ejn is a city-sector fixed e↵ect (which estimates log(Wejn) ). I estimate
equation C.7 using individual data from the ACS. To account for variation in
unemployment across city-sectors, I then weight the estimated wages by the
employment rate in the city-sector. This is calculated directly from the ACS data.
The remaining labor parameters to be calibrated are the labor elasticity of
substitution  l and the labor input use intensities, ✓jn. Note that the log wage ratio
is given by
198
 !
C ✓ ◆ ✓ ◆I 1 C
log jn =   log jn ✓L + log
jn . (C.8)
Ijn |{ z}l L 1  ✓| {z jn } | {z jn| {z } }
Calibrated
Estimated Data Unknown
Note that the only unknowns in equation C.8 are the ✓jn values. By rearranging, I
can solve for these as:
B
✓ = jnjn (C.9)
1 + Bjn
where
 !
C ✓ ◆I C  l
B jn jnjn = L .Ijnl Ljn
Energy Parameters. Similar to the above, the log ratio of energy prices is given
by  ! ✓ ◆ ✓ ◆
PE
log jnG =  
1 E ⇣
log jn + log jn  . (C.10)Pjn |{ ze| {z } }
G 1 ⇣
| {z jn } | {z jn }
calibrated
data data unknown
As with the labor parameters, I solve for the factor intensities using equation C.10.
Specifically,
Z
⇣jn =
jn , (C.11)
1 + Zjn
where
 !
PE
✓ ◆ e
Z = jn
Ejn
jn .
P f Gjn jn
After recovering the ⇣n and ✓jn, I can recover the final set of input intensities: the
↵jn. The ratio of the price of electricity to college educated labor is given by:
 !  !  !
⇢n n nE ✓ ◆ ✓ ◆P E e 1 E⇢el  ⇢e
log jn = log jn + log jn
⇣ ↵
C ⇢ n + log
jn + log jn .
W C l 1 L⇢  ⇢el ljn ✓ 1  ↵jn jn jn| {z } | {z } | {zjn } | {z } | {z }
data data data solved above nknown
(C.12)
199
Thus I solve for these as:
Q
↵ = jnjn , (C.13)
1 +Qjn
where
 ! !  
E ⇢  1 ✓ ◆ L⇢
n  !⇢
P C l ✓ el
l
Q = jn jn jn jnjn
WC E⇢
n n
e 1 ⇣ E⇢  ⇢
n . (C.14)
jn el ejn jn jn
The final set of parameters are the Ajn values. I pick these to match the data (i.e.
I invert the first-order conditions, now that I have all variables except for the total
factor productivities).
C.0.1.3 Rent Parameters. Hedonic Rents. I construct a rental
index for each city in my sample to make comparisons in prices across CBSA’S
more sensible. I regress individual gross log rent on a set of CBSA fixed e↵ects and
housing characteristics. I include the number of bedrooms, the number of rooms,
household members per room, and the total number of units in the structure
containing the household. Specifically, the equation I estimate to explain rental
rates for household i is given by:
✓ ◆
members
log(R ii) =  CBSA(i) +  2Roomsi +  3Unitsi +  4Bedroomsi +  5 + "i.roomsi
(C.15)
I then take the averages of these characteristics across all CBSA’s and hold
them constant, and use the predicted value for each CBSA (generated from the
fixed e↵ects) as the hedonic housing rental index.
Rent Parameters. After obtaining the rental index, I can calculate the remaining
parameters of the housing supply curve. The reduced-form relationship for the
housing supply curve is given by  
XX    
!
 j ↵
H
e ⇥ wejn)log(Rj) = log Nejn + ⌘j (C.16)
1 +  j ↵e n ejn
I first calculate Rj using equation C.15. I then calibrate  j using the values in Saiz
(2010).1 For the two CBSAs in my model in which are not included among Saiz’s
elasticities (Honolulu & Sacramento), I compute  j =  0 +  1WRIj where WRIj is
1Specifically, I use the estimates reported in Table VI.
200
the Wharton Regulation Index for city j 2 {Sac,Hono}. I take parameter estimates
for  0 and  1 from column VI, Table III of Saiz (2010). I then choose the ⌘j value
to match the data (following the standard approach in the literature).
C.0.2 Household Energy.
C.0.2.1 Baseline Consumption. I follow Glaeser and Kahn
(2010) very closely in constructing household emissions across CBSAs. I estimate
household level regressions using CBSA fixed e↵ects to impute the predicted energy
use by CBSA. Specifically, I estimate:
xmi =  CBSA(i) +  1 log(Incomei) +  2HHsizei +  2Ageheadi + "i. (C.17)
where xmi is household i’s consumption of fuel type m 2 {gas, elec, oil},  CBSA(i)
is a fixed e↵ect for the household’s CBSA, Incomei is the household’s income
obtained from equation C.8 and the other variables are the same controls used in
Glaeser and Kahn (2010). I adjust the estimated coe cients by the composition of
a city’s single unit/multi-unit and home ownership/rental composition to address
the concern that rented homes and multi-family homes are less likely to pay
separately for energy. The ACS has flags for whether the household owns or rents
their household, and if they live in single or multi-family housing. I reweight the
estimated coe cients by the fraction of each of the four groups in every CBSA.
C.0.2.2 Energy Expenditure Shares. This section contains
m m
summary statistics for the model’s energy expenditure shares: ↵̃m = P ⇥xW . The
estimates can be found in Table C2.
201
Expenditure Share on: College Non-College
Electricity
Mean (SD) 0.025 (0.013) 0.046 (0.018)
Range [0.005, 0.084] [0.014, 0.133]
Natural Gas
Mean (SD) 0.03 (0.03) 0.04 (0.05)
Range [0.00, 0.39] [0.00, 0.36]
Fuel-Oil
Mean (SD) 0.001 (0.003) 0.003 (0.005)
Range [0.000, 0.021] [0.000, 0.025]
Table C2. Estimated energy-expenditure shares for college-educated and non-
college-educated workers, respectively. Summary statistics are taken over the
choice set (N=395). Estimates of energy use of type m come from equation C.17.
Estimates of wages come from equation C.7. State-level electricity prices come from
EIA data.
C.0.2.3 HSV Transfers. Let post-transfer income be determined by:
w̃ij = wij +  w
1  
ij ,
where   > 0 is the overall level of the reimbursement and   > 1 indexes the
progressivity of the transfers. Note that the government’s total revenue from a
P P
carbon tax of size ⌧ is given by T = ⌧ n j  j f̂jn where again f̂jn is total energy
use in city-sector jn. Denote the household’s transfer as g = w1  i ij . In equilibrium,P
the sum of government transfers, G = i gi must be equal to total carbon tax
revenue. I can solve for   that satisfies the government budget constraint,  ?, by
equating total payments to total revenues:
XX XXX
 ? N? 1   m mejnwejn = ⌧  j f̂jn
e j n j m
P P P
⌧ m m
? P nP j m
 j f̂jn
  = .
N? 1  e j ejnwejn
Note that the allocation of workers across cities, Nj, and energy
consumption, f̂jn, are functions of   in equilibrium. Computationally, I guess a
value of  g and the shares, calculate the implied  ? and check whether  ? =  g.
202
If the condition does not hold, I update my guess as a convex combination of my
original guess and  ?.
C.0.2.4 Model Fit: Energy Consumption. Figure C1
demonstrates model’s baseline fit for the three di↵erent fuel types for households:
electricity, natural gas, and fuel oil.
40 300
200
100
30 0
0 100 200 300
Data Oil Use
(Gallons)
600
20
400
200
0
20 30 40 0 200 400 600
Data Electricity Use Data NatGas Use
(MWh) (Lbs)
Figure C1. Baseline model fit for electricity, natural gas, and fuel-oil. The x-axis in
each graph gives city-sector fuel consumption (predicted from equation C.17), and
the y-axis has the baseline equilibrium energy consumption in the model.
C.0.3 Energy-Adjusted Income. In thisPsect ion, I derive t he
EA log(wejnt)  ↵̃
m
m ejnt log(Pjt)“energy-adjusted budget income,” wejnt = P  m , used1 m ↵̃ejnt
in estimating equation 4.18, following Colas and Morehouse (2022). Recall that the
mean utilit y is given by:P !
1 + ↵H + ↵m h X m
  = e m ej
↵e ↵
ejnt log(wejnt)  log(Rjt)  ej logPmjt + ⇠ejnt, e  e  m e
P P 0m m
m ↵ 0 ↵̃ (1+↵
h)
Note that ↵̃ ejnt
0
ejnt = ↵ implies that
m m
m0 ↵̃ejt = P
ejt e and thus ↵m =
1  0 ↵m0 ejtejnt m ejt
↵̃m (1+↵h)
Pejt e 0 . I can plug these into the equation for mean utility to get:
1  0 ↵e˜ mm jt
203
Model Electricity Use
(MWh)
Model NatGas Use Model Oil Use
(Lbs) (Gallons)
0 1
m
h ↵̃ (1+↵
h)
1 + ↵ + Pejt eB e 01  ↵˜ m@ m0 ejt C
↵h
 ejnt = A log(w eejnt)  log(Rjt) 
 e  e
(1 + ↵h) X ↵̃mP e ej0 logPmjt + ⇠    m ejnt
.
1 1 m0 ↵˜ejt  m e
Rearranging yields:
 ejnt = ⇥
w
et log(w
EA ) +⇥r log(Rj) + ✏ejn,
P  
ejnt  et
log(wejnt)  ↵̃m log(Pjt) h h
where wEA = Pm ejnt ,⇥w = 1+↵e , ⇥rejnt   m e   e =
↵e
1 ↵̃ e  
. I use the
e
m ejnt
notation wEA to denote “energy-adjusted” wages. Given estimates for ⇥we and ⇥
r
e, I
can then solve for ↵he and  e.
204
Parameter Name Notation Source
Labor Supply
Moving Costs ⇥div,⇥dist,⇥dist2e e e MLE (equation 4.16)
Marginal Utility of Income/Rents ⇥we ,⇥
r
e IV (equation 4.18)
Variance of pref. shock  e Algebra
Housing Parameter ↵He Algebra
Utility of Energy param. ↵mejn Algebra
Wage Index Wejn OLS (equation C.7)
Firm Parameters
Energy-Lab EoS  nel (Koesler & Schymura, 2012)
Gas- Elec EoS  ne (Serletis et al., 2010)
College-No College EoS  l (Card, 2009)
Factor Intensities ↵jn,✓jn, ⇣jn Relative demand curves
TFP Ajn Firm FOCs
Energy and Rent Parameters
Intercepts  j, amj Algebra
Energy Supply Elasticity  (C. Dahl & Duggan, 1996)
Rent Supply Elasticity  j (Saiz, 2010)
Carbon Emissions Factor  m Data
Rent Index Rj OLS (equation C.15)
Table C3. Overview of calibration and estimation strategy for the model’s
parameters. For shorthand, I abbreviate elasticity of substitution as EoS and total
factor productivity as TFP.
C.0.4 Estimation Summary.
205
Carbon Emissions from Electricity Across NERC Regions
MRO NPCC
RFC
WECC
SPP SERC
TRE
FRCC
CO2 506 1012 1035 1220
MWh 799 1015 1104 1271
Figure C2. NERC regional electricity emissions factors. Emissions factors are
calculated as output-weighted averages of individual plant’s emissions rates.
Change in Carbon Emissions from Dropping Coal Across NERC Regions
MRO NPCC
RFC
WECC
SPP SERC
TRE
FRCC
CO2 -1045 -717 -468 -262
MWh -742 -573 -443 -29
Figure C3. For each NERC region, emissions factors from electricity in the absence
of coal-fired power plants. Emissions factors are calculated as output-weighted
averages of individual plants’ emissions rates, for all plants in a region excluding
coal.
C.0.5 NERC Region Emissions Factors.
206
Figure C4. Monetized regional tax incidence. For each Census Region, the
distribution of mean compensating variation across cities and sectors from a $31
per ton carbon tax. CV is measured in dollars.
C.0.5.1 Heterogeneity in Incidence Across Space.
207
Figure C5. Non-Monetized tax incidence. For each Census Region, distribution of
tax incidence (non-monetized) in utility across cities and sectors from a $31 per ton
carbon tax.
208
College-Educated Household Tax Incidence
-1.30% -1.20% -1.10%
Figure C6. Non-Monetized college-educated regional tax incidence as a percent of
baseline wages. Tax incidence (non-monetized) across states from a $31 per ton
carbon tax for college educated households.
209
Non-College-Educated Household Tax Incidence
-4.00% -3.80% -3.60% -3.40%
Figure C7. Non-Monetized non-college-educated regional tax incidence as a percent
of baseline wages. Tax incidence (non-monetized) across states from a $31 per ton
carbon tax for non-college educated households.
210
⌧ = $31/ton:
No Transfers Midwest Northeast South West
Overall  1, 290 1, 195 1, 255 1, 291
(309) (315) (321) (355)
College 971 967 962 178
(181) (218) (178) (257)
Non-College  1, 471 1, 404 1, 455 1, 508
(203) (235) (230) (257)
Table C4. Monetized incidence across regions. By Census Region, compensating
variation across cities and sectors from a $31 per ton carbon tax. Standard
deviations are in parentheses.
Table C5. No coal monetized tax incidence. By Census Region, the change in
compensating variation from “dropping” coal from a $31 per ton carbon tax.
211
Table C6. No-coal non-monetized tax incidence. By Census Region, the percent
change in tax incidence (non-monetized) from “dropping” coal from a $31 per ton
carbon tax.
212
C.0.5.2 Heterogeneity in Incidence Across Industries. In this
section, I decompose the monetized (compensating variation) and non-monetized
incidence from a $31 per ton carbon tax.
Figure C8. Monetized tax incidence from a carbon tax. By industry, the
distribution of mean compensating variation across cities by industries from a
$31 per ton carbon tax. CV is measured in dollars.
213
Figure C9. Non-Monetized industry tax incidence. By industry, the distribution of
tax incidence (non-monetized) across cities from a $31 per ton carbon tax.
⌧ = $31/ton:
No Transfers Manufacturing Services Construction Agriculture
Overall  1, 446 1, 156 1, 491 1, 012
(263) (271) (304) (217)
College 1, 170 949 916 708
(224) (187) (151) (171)
Non-College  1, 565 1, 360 1, 598 1, 094
(174) (168) (180) (142)
Table C7. Industry compensating variation. By industry, mean compensating
variation across cities from a $31 per ton carbon tax. Standard deviations are in
parentheses.
214
C.0.5.3 Migration. In this section, I map out changes in population
across cities from a $31 per ton carbon tax. I aggregate the changes in population
level across CBSAs to the state level. My sample only includes 34 states, I use
changes in population at the Census-Division level for states with missing data,
excluding the population changes from the included CBSAs within the respective
census division.
Percent Change in Population
-2.00% -1.00% 0.00% 1.00%
Figure C10. Migration from a carbon tax. Population changes are computed using
the equilibrium arising from the model using a $31 per ton carbon tax.
215
Percent Change in College-Educated Population
-0.80% -0.40% 0.00% 0.40%
Figure C11. College-educated worker migration resulting from a carbon tax.
Population changes are computed using the equilibrium arising from the model
using a $31 per ton carbon tax.
216
Percent Change in Non-College-Educated Population
-3.00% -2.00% -1.00% 0.00% 1.00% 2.00%
Figure C12. Non-College migration from a carbon tax. Population changes are
computed using the equilibrium arising from the model using a $31 per ton carbon
tax.
217
C.0.5.4 Voting and Tax Incidence. This section provides plots
that explore the relationship between predicted carbon tax incidence and the share
of each given CBSA that voted for Trump in the 2016 Presidential election.
-1.0% -3.2%
-1.1%
-3.5%
-1.2%
-3.8%
-1.3%
-1.4%
-4.0%
-1.5%
0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6
Share Voting for Trump Share Voting for Trump
Figure C13. Tax Incidence and voting. An observation is a CBSA; the size of each
observation reflects the total number of voters in the 2016 presidential election in
the CBSA. Tax incidence is measured as the relative change in utility (measured in
percent of income) from a $31 per ton carbon tax, calculated using equation 4.20.
-$1,200
-$800
-$1,400
-$1,000
-$1,200 -$1,600
-$1,400
-$1,800
-$1,600
0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6
Share Voting for Trump Share Voting for Trump
Figure C14. Compensating variation and voting. An observation is a CBSA; the
size of each observation reflects the total number of voters in the 2016 presidential
election in the CBSA. Compensating variation is measured as the average dollar
amount required to make a household indi↵erent to a $31 per ton carbon tax,
calculated using equation 4.20.
218
Compensating Variation: College-Educated Tax Incidence: College-Educated
Compensating Variation: Non-College-Educated Tax Incidence: Non-College-Educated
C.0.6 Computational Appendix.
C.0.6.1 Nested Fixed Point Algorithm. In this section, I outline
the nested-fixed-point algorithm I use to obtain the preference parameters:
XNd XX
⇥⇤ = Ii(j, n) log(Pi),
i=1 n2N j2J
where Pi is defined in equation 4.15. In what follows, let t denote iteration number
(not time). I proceed in the following manner:
Outer-Loop
(1) Start with an arbitrary guess for the parameter vector, ⇥⇤,0
Inner-Loop
(2) Guess an arbitrary level of mean utilities for each city-sector pair and
education level,  0ejn
(3) Given the guess of the parameter vector and mean utility, compute the
model’s predicted share of agents in each sector-city pair. This is given
by
XNd
S0model = Pi,ejn
i
(4) Use the Nevo (Nevo, 2000) improvement of the contraction mapping
from Berry (1994):
 !
1 0 S⇥ dataexp(  ejnejn) = exp( ejn) 0 , (C.18)Smodelejn
where Sdata is the share of agents of education level e that choose cityejn
j and sector n in the data.
(5) Check for convergence of equation C.18. Specifically, I check whether
   
sup   1ejn    0  ejn < ✏.
If the equation hasn’t converged, update the new guess of   to  1 and go
back to step (3). Repeat 3-5 until   has converged. This ends the inner-
loop.
219
(6) After obtaining the unique   for the guess of ⇥⇤,0ejn , I can compute the
value of the likelihood function. Check to see if the log-likelihood function
is maximized. If not, go back to step (1). To update the guess of ⇥⇤, I use
the Nelder-Mead algorithm (Nelder & Mead, 1965).
C.0.6.2 Equilibrium Simulation. In this section, I outline how I
solve for the counterfactual equilibrium.
(1) Guess a vector of wages, rents, residential electricity prices, industrial
electricity demand, and industrial natural gas demand.
(2) Given these guesses, calculated labor supply in each city using the implied
choice shares multiplied by the total population of college-educated and non-
college-educated workers.
(3) Calculate the value of the labor aggregator, the energy aggregator, and finally,
the input aggregator using the implied populations from step 2 and the
guesses of industrial energy consumption.
(4) Calculate total housing demand using equation. C.16.
(5) Check whether the new vectors of wages, rents, and residential energy prices
and industrial energy consumption from steps 3 and 4 are within ✏ of the
guess made in step 1. If not, return to step 1, using updated guesses that
are convex combinations of the old guess and new prices that come from
the firm’s FOC and rent equations. To update the guess of industrial gas
demand, I check whether the price from the firm’s FOC matches the prices
in the data. Otherwise, I update the new guess of industrial gas to be larger
than the old. If so, I update the new guess to be smaller. For electricity, I
use the same process but compare the firm’s FOC prices to city-level supply
prices (according to the supply curve) and update accordingly.
220
C.0.7 Data Appendix.
C.0.7.1 Labor Supply & Demand. Cleaning. My sample consists
of all non-military, non-institutionalized, employed, (16-64) individuals. I drop all
observations with missing or negative incomes. Additionally, I drop all workers not
in the 5 sectors described in the model section. A household is defined by the ACS
identifying variable SERIAL, which assigns all individuals in a household the same
number. The decision-maker in the model is the “household head” (given by the
IPUMS indicator variable RELATE ).
Geography. I construct the labor quantities supplied and demanded from the
5-year aggregated ACS 2012-2016 data. My geographic unit of observation is a
“Core-Based Statistical Area” (CBSA). I follow closely the strategy used in other
literature, in constructing the sample, to make my analysis more comparable
to other papers. Specifically, I choose the 70 largest CBSAs, as defined by the
population in 1980. I then map other individuals, who do not live in one of these
70 CBSAs into their corresponding broader census division, creating an additional
nine alternatives. Thus the model consists of 79 unique, geographic alternatives.
All wage estimates and alternative counts are weighted by the exogenous sampling
weights provided by the ACS.
Industry. To construct the model’s industries, I use the “INDNAICS” variable
from the ACS. While the ACS has NAICS codes at the 6-digit (least aggregated),
I constrain the model to contain 5 sectors: agriculture, manufacturing, services,
construction, and an outside option sector.
C.0.7.2 City-Sector Energy Use. In this section, I detail how
I assign energy consumption by city-sector to firms in the baseline case. I
observe energy consumption by sector at the national level from the EIA data.
Additionally, the EIA has utility-level electricity and natural gas use by aggregated
industrial, commercial, and residential sectors. I construct a sector n’s consumption
of electricity (natural gas) as proportional to the city-sectors’ share of aggregate
employment. Note that for sectoral employment, Ln, I use BLS data. For the
numerator, Ljn, I use counts from my sample. Given that En is aggregated across
all US cities, my strategy using the fraction of workers in my sample across the
whole US adjusts firm energy consumption to match my subset of households.
221
Specifically, electricity and gas consumption bu firms is given by:
L
E jnjn = ⇤ En
Ln
L
G = jnjn ⇤Gn.
Ln
C.0.8 Additional Scatterplots. In this section, I disaggregate
Figure 20 by education group in Figure C15 and then by both education group
and sector in Figure C16.
Firm + College Household Emissions Firm + Non-College Household Emissions
City-Sector Level City-Sector Level
12 12
11 11
10 10
9 9
10.0 10.5 11.0 11.5 12.0 10.00 10.25 10.50 10.75 11.00
Log(College Wage) Log(Non-College Wage)
Figure C15. Total emissions per capita for each city-sector, plotted against
wages. Wages are constructed as city level averages estimated from equation C.7.
Emissions are the sum of firm emissions per capita and household emissions for a
given education group.
222
Log(Total Emissions per capita)
(in lbs)
Log(Total Emissions per capita)
(in lbs)
Firm + College Household Emissions Firm + Non-College Household Emissions
City-Sector Level City-Sector Level
12 12
11 11
10 10
9 9
10.0 10.5 11.0 11.5 12.0 10.00 10.25 10.50 10.75 11.00
Log(College Wage) Log(Non-College Wage)
agriculture construction manufacturing services
Figure C16. Total emissions per capita by city across industries plotted against
wages. Wages are constructed as city-level averages estimated from equation C.7.
Emissions are the sum of firm emissions per capita and household emissions for a
given education group.
C.0.9 Sector Energy Demand. The EIA classifies the Industrial
and Commercial sector in the following manner:
– Industrial sector: An energy-consuming sector that consists
of all facilities and equipment used for producing, processing, or
assembling goods. The industrial sector encompasses the following
types of activity manufacturing (NAICS codes 31-33); agriculture,
forestry, fishing and hunting (NAICS code 11); mining, including
oil and gas extraction (NAICS code 21); and construction (NAICS
code 23). Overall energy use in this sector is largely for process
heat and cooling and powering machinery, with lesser amounts
used for facility heating, air conditioning, and lighting. Fossil fuels
are also used as raw material inputs to manufactured products.
Note: This sector includes generators that produce electricity
223
Log(Total Emissions per capita)
(in lbs)
Log(Total Emissions per capita)
(in lbs)
and/or useful thermal output primarily to support the above-
mentioned industrial activities. Various EIA programs di↵er in
sectoral coverage.
– Commercial Sector: An energy-consuming sector that consists of
service-providing facilities and equipment of businesses; Federal,
State, and local governments; and other private and public
organizations, such as religious, social, or fraternal groups. The
commercial sector includes institutional living quarters. It also
includes sewage treatment facilities. Common uses of energy
associated with this sector include space heating, water heating, air
conditioning, lighting, refrigeration, cooking, and running a wide
variety of other equipment. Note: This sector includes generators
that produce electricity and/or useful thermal output primarily
to support the activities of the above-mentioned commercial
establishments.
224
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