ESSAYS ON INCOME INEQUALITY AND THE ENVIRONMENT
by
JOHN VOORHEIS
A DISSERTATION
Presented to the Department of Economics
and the Graduate School of the University of Oregon
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
June 2016
DISSERTATION APPROVAL PAGE
Student: John Voorheis
Title: Essays on Income Inequality and the Environment
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 Ann Cameron Chair
Peter Lambert Core Member
Caroline Weber Core Member
Ronald Mitchell Institutional Representative
and
Scott L. Pratt Dean of the Graduate School
Original approval signatures are on file with the University of Oregon Graduate School.
Degree awarded June 2016
ii
c© 2016 John Voorheis
iii
DISSERTATION ABSTRACT
John Voorheis
Doctor of Philosophy
Department of Economics
June 2016
Title: Essays on Income Inequality and the Environment
This dissertation considers two of the most pressing concerns of the current time,
income inequality and exposure to pollution, and provides evidence that these two
concerns may in fact be causally linked. In order to do this, I assemble novel datasets on
income inequality and pollution exposure, and propose an strategy for causally identifying
the effect of the former on the latter.
In the first substantive chapter, I develop a new dataset on income inequality
measured at the US state and metropolitan area level. I compare the trends in income
inequality measured using different income definitions. In general, pre-tax, pre-transfer
income inequality has increased in most states since 1980, but post-fiscal income inequality
has seen slow or no growth since about 2000. I conduct inference on how income
inequality has changed using a semi-parametric bootstrap method, and consider potential
correlates with state-level income inequality. I find that de-unionization is perhaps the
most important factor driving rising inequality.
In the second substantive chapter, I leverage satellite-derived remote sensing
data on ground-level concentrations for two important pollutants (NOx and PM2.5)
to measure the distribution of pollution exposure. I propose a dashboard approach
iv
to measuring environmental inequality and environmental justice, proposing and
applying several candidate measures to the satellite datasets. I find that environmental
inequality has largely decreased since 1998, as has average exposure. I consider potential
correlations between neighborhood demographics and the distribution of exposure, but
find inconclusive results.
In the third substantive chapter, I attempt to resolve this ambiguity by considering
whether rising income inequality within metropolitan areas (the subject of the first
chapter) might causally affect the distribution of exposure across people (the subject of
the second). Using a simulated instrumental variables identification strategy designed
to address potential endogeneity due to locational sorting, I find that income inequality
decreases the average level of exposure, but increases environmental inequality. I argue
this is consistent with the benefits of pollution reduction accruing to the most advantaged,
and provide evidence that this may work through the political system: inequality increases
the responsiveness of politicians to the environmental demands of the rich.
v
CURRICULUM VITAE
NAME OF AUTHOR: John Voorheis
GRADUATE AND UNDERGRADUATE SCHOOLS ATTENDED:
University of Oregon, Eugene, OR
Eastern Michigan University, Ypsilanti, MI
DEGREES AWARDED:
Doctor of Philosophy, Economics, 2016, University of Oregon
Master of Science, Economics, 2012, University of Oregon
Master of Arts, Economics, 2011, Eastern Michigan University
Bachelor of Science, Economics, 2009, Eastern Michigan University
AREAS OF SPECIAL INTEREST:
Income Inequality
Environmental Economics
Political Economy
Public Finance
GRANTS, AWARDS AND HONORS:
Young Scholar Grant, Washington Center For Equitable Growth, 2015
Edward G. Daniel Scholarship, University of Oregon, 2015
PhD Research Paper Award, University of Oregon, 2014
Kleinsorge Summer Research Fellowship, University of Oregon, 2013
Everett D. Monte Scholarship, University of Oregon, 2013
Dale Underwood Award, University of Oregon, 2012
Graduate Teaching Fellowship, University of Oregon, 2011-2016
PhD Research Paper Award, University of Oregon, 2014
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ACKNOWLEDGEMENTS
I am grateful for the advice and guidance I’ve received from from Trudy Ann
Cameron, Peter Lambert and Caroline Weber. Many helpful comments from Joe Wyer
made these papers much better. I have also benefitted from much useful feedback from
participants at the University of Oregon Micro Group, the 2015 Winter School on
Inequality and Social Welfare Theory, the 2015 AERE Annual Meeting, the 2015 Southern
Economics Association Annual Meeting and the 2016 Society for Benefit Cost Analysis
Annual Meeting. Any remaining errors are my own.
This research was made possible by a Major Research Instrumentation grant from
the National Science Foundation, Office of Cyber Infrastructure, “MRI-R2: Acquisition of
an Applied Computational Instrument for Scientific Synthesis (ACISS),” Grant #: OCI-
0960354, and was directly supported by a grant from the Washington Center for Equitable
Growth and by generous assistance from the Ray Mikesell Foundation at the University of
Oregon.
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To my father, James Voorheis.
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TABLE OF CONTENTS
Chapter Page
I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
II. STATE AND METROPOLITAN AREA INCOME INEQUALITY IN THE
UNITED STATES: TRENDS AND DETERMINANTS . . . . . . . . . . . . 4
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
From Market Income to Haig-Simons Income . . . . . . . . . . . . . . . . . 17
Inference on Changes in Income Inequality . . . . . . . . . . . . . . . . . . . 22
Potential Explanations for Changing State-level Income Inequality . . . . . 32
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
III. TRENDS IN ENVIRONMENTAL INEQUALITY IN THE UNITED STATES:
EVIDENCE FROM SATELLITE DATA . . . . . . . . . . . . . . . . . . . . 46
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Previous Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Data and Institutional Details . . . . . . . . . . . . . . . . . . . . . . . . . 52
Quantifying Environmental Inequality and Environmental Justice . . . . . . 54
Trends in Environmental Inequality and Environmental Justice . . . . . . . 62
Explaining the Distribution of Pollution Exposure . . . . . . . . . . . . . . 70
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
IV. ENVIRONMENTAL JUSTICE VIEWED FROM OUTER SPACE: HOW
DOES GROWING INCOME INEQUALITY AFFECT THE
DISTRIBUTION OF POLLUTION EXPOSURE? . . . . . . . . . . . . . . . 87
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Previous Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
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Chapter Page
Data and Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
V. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
APPENDICES
A. MEASURING STATE INCOME INEQUALITY BY COMBINING CPS AND
IRS DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
B. STATE AND MSA INCOME INEQUALITY IN THE AMERICAN
COMMUNITY SURVEY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
C. DECOMPOSITION ANALYSIS OF CHANGES IN ENVIRONMENTAL
INEQUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
D. ADDITIONAL TABLES AND FIGURES . . . . . . . . . . . . . . . . . . . . . 163
REFERENCES CITED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
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LIST OF FIGURES
Figure Page
1. State Income Inequality, 1977–2014: Crosswalking from Market Income to
Post-fiscal Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2. State Income Inequality, 1977–2014: Crosswalking from Market Income to
Post-fiscal Income, 4 largest States . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3. State-level Redistributiveness, 1977-2014 . . . . . . . . . . . . . . . . . . . . . . . 22
4. Difference in Gini Coefficient, 1986–1993 and 1994–2014 . . . . . . . . . . . . . . 26
5. Difference in top 1% Share, 1986–1993 and 1994–2014 . . . . . . . . . . . . . . . 27
6. Change in Lorenz Ordinates, 1994–2014, Pre-transfer and Post-transfer Income . 29
7. Change in Lorenz Ordinates, 1994–2014, Post-tax and Post-fiscal Income . . . . . 30
8. Determinants of Lorenz Ordinates, Selected Covariates . . . . . . . . . . . . . . . 43
9. Annual Average PM2.5 and NOx Exposure, 2005 . . . . . . . . . . . . . . . . . . 55
10. National Average NOx Exposure (in ppb), 2005-2011 . . . . . . . . . . . . . . . . 56
11. Kolm-Pollak Index, PM2.5 and NOx . . . . . . . . . . . . . . . . . . . . . . . . . 63
12. Atkinson Index, PM2.5 and NOx . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
13. Relative Lorenz Curves, NOx (2005-2011) and PM2.5 (1998-2014) . . . . . . . . . 65
14. Absolute Lorenz Curves, NOx (2005-2011) and PM2.5 (1998-2014) . . . . . . . . 65
15. Generalized Lorenz Curves, NOx, 2005-2011 . . . . . . . . . . . . . . . . . . . . . 66
16. National Black-White Exposure Gap, PM2.5, 1998-2014 and NOx, 2005-2011 . . 67
17. National Black-White Exposure Ratio, PM2.5, 1998-2014 and NOx, 2005-2011 . . 68
18. National Black-White Exposure Gap, by Percentile (PM2.5 and NOx) . . . . . . 69
19. Average Annual NOx Exposure by Census Tract, 2005–2011 . . . . . . . . . . . . 94
20. Initial MSA Income is Unrelated to Subsequent Changes in NOx Exposure . . . . 102
21. Actual Gini Coefficient as a function of Simulated Gini Instrument, for 265
MSAs, 2005–2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
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Figure Page
22. Reduced Form Visualizations Showing the Effect of Simulated Income Inequality
on Pollution Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
23. Illustration of how the estimated effect of Income Inequality on Absolute
Environmental Inequality changes as the assumed value of κ, capturing Absolute
Environmental Inequality aversion, increases . . . . . . . . . . . . . . . . . . . . . 113
24. Effect of Income Inequality on Relative Environmental Inequality, varying
Relative Environmental Inequality Aversion . . . . . . . . . . . . . . . . . . . . . 115
25. Effect of an increase in income inequality on NOx exposure. . . . . . . . . . . . . 117
26. Correlation Between League of Conservation Voter Scores and Ideology, US
senators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
27. Histogram of Adjusted LCV Scores by Party for US Senators, 1977-2014 . . . . . 123
28. State Gini Coefficients, 1997-2012: IRS Simulation vs. CPS Baseline . . . . . . . 137
29. State Top 1% Shares, 1997-2012: IRS Simulation vs. CPS Baseline . . . . . . . . 138
30. State Gini Coefficient, 1997-2012: IRS Simulation vs. Frank (2009) . . . . . . . . 139
31. State Top 1% Shares, 1997-2012: IRS Simulation vs. Frank (2009) . . . . . . . . 139
32. State Gini Coefficient, 1997-2012: IRS Simulation vs. GB2 Simulation . . . . . . 141
33. State Top 1% Shares, 1997-2012: IRS Simulation vs. GB2 Simulation . . . . . . . 142
34. Lorenz Curve Results, ACS (2005-2011) . . . . . . . . . . . . . . . . . . . . . . . 149
35. State-level Gini Coefficient, Pre-transfer Income . . . . . . . . . . . . . . . . . . . 163
36. State-level Gini Coefficient, Post-transfer Income . . . . . . . . . . . . . . . . . . 164
37. State-level Gini Coefficient, Post-tax Income . . . . . . . . . . . . . . . . . . . . . 165
38. State-level Gini Coefficient, Post-fiscal Income . . . . . . . . . . . . . . . . . . . . 166
39. National Black-White PM2.5 Exposure Ratio (by Percentile), 1998-2014 . . . . . 171
40. National Black-White NOx Exposure Ratio (by Percentile), 2005-2011 . . . . . . 172
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LIST OF TABLES
Table Page
1. Income Sources in the CPS by Year . . . . . . . . . . . . . . . . . . . . . . . . . 12
2. Crosswalking from Market to Disposable Income . . . . . . . . . . . . . . . . . . 19
3. Lorenz Dominance Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4. Determinants of State Income Inequality (Pre-transfer and Post-transfer) . . . . . 37
5. Determinants of State Income Inequality (Post-tax and Post-fiscal) . . . . . . . . 38
6. Determinants of State Top 1% Share (Pre-transfer and Post-transfer) . . . . . . . 39
7. Determinants of State Top 1% Share (Post-tax and Post-fiscal) . . . . . . . . . . 40
8. Determinants of State Top 1 % Share, Frank (2009) Data . . . . . . . . . . . . . 41
9. Quantile RIF Regression Results (NOx Exposure) . . . . . . . . . . . . . . . . . 76
10. Quantile RIF Regression Results (PM2.5 Exposure) . . . . . . . . . . . . . . . . 77
11. Relative Lorenz RIF Regression Results (NOx Exposure) . . . . . . . . . . . . . . 79
12. Relative Lorenz RIF Regression Results (PM25 Exposure) . . . . . . . . . . . . . 80
13. Generalized Lorenz RIF Regression Results (NOx Exposure) . . . . . . . . . . . . 81
14. Generalized Lorenz RIF Regression Results (PM25 Exposure) . . . . . . . . . . . 82
15. Absolute Lorenz RIF Regression Results (NOx Exposure) . . . . . . . . . . . . . 83
16. Absolute Lorenz RIF Regression Results (PM2.5 Exposure) . . . . . . . . . . . . 84
17. First Stage, key coefficient only . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
18. Effect of Income Inequality on Average NOx Exposure . . . . . . . . . . . . . . . 108
19. Effect of Income Inequality on Black-White Exposure Gap . . . . . . . . . . . . . 110
20. Effect of Income Inequality on Latino-White Exposure Gap . . . . . . . . . . . . 111
21. Effect of Income Inequality on Poor-Rich Exposure Gap . . . . . . . . . . . . . . 111
22. Effect of Income Inequality on Absolute Environmental Inequality . . . . . . . . . 112
23. Effect of Income Inequality on Relative Environmental Inequality . . . . . . . . 114
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Table Page
24. Effect of Income Inequality on Average Black Exposure . . . . . . . . . . . . . . 116
25. Effect of Income Inequality on Average White Exposure . . . . . . . . . . . . . . 116
26. Effect of State Inequality on Senators’ LCV Scores . . . . . . . . . . . . . . . . . 125
27. Effect of State Inequality on Senators’ LCV Scores, By Party . . . . . . . . . . . 126
28. Alabama Total AGI and Number of Returns, by Size of AGI, 2012 . . . . . . . . 143
29. Intermediate Calculations in the Pareto Interpolation Process . . . . . . . . . . . 144
30. Selecting the Pareto Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
31. NOx Quantile Detailed Decomposition, 2005 vs. 2011 . . . . . . . . . . . . . . . 153
32. PM2.5 Quantile Detailed Decomposition, 2005 vs. 2011 . . . . . . . . . . . . . . 154
33. NOx Relative Lorenz Curve Detailed Decomposition, 2005 vs. 2011 . . . . . . . . 155
34. PM2.5 Relative Lorenz Curve Detailed Decomposition, 2005 vs. 2011 . . . . . . . 156
35. NOx Quantile Detailed Decomposition, Diverse vs. Non-diverse tracts . . . . . . 157
36. PM2.5 Quantile Detailed Decomposition, Diverse vs. Non-diverse tracts . . . . . 158
37. NOx Generalized Lorenz Curve Detailed Decomposition, 2005 vs. 2011 . . . . . . 159
38. NOx Absolute Lorenz Curve Detailed Decomposition, 2005 vs. 2011 . . . . . . . 160
39. PM2.5 Generalized Lorenz Curve Detailed Decomposition, 2005 vs. 2011 . . . . . 161
40. PM2.5 Absolute Lorenz Curve Detailed Decomposition, 2005 vs. 2011 . . . . . . 162
41. Determinants of State Income Inequality (Pre-transfer and Post-transfer Gini),
All Covariates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
42. Determinants of State Income Inequality (Post-tax and Post-fiscal Gini), All
Covariates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
43. Effect of Income Inequality on Average Latino Exposure . . . . . . . . . . . . . . 173
44. Effect of Income Inequality on Average Poor Exposure . . . . . . . . . . . . . . . 174
45. Effect of Income Inequality on Average Rich Exposure . . . . . . . . . . . . . . . 174
xiv
CHAPTER I
INTRODUCTION
The dual challenges of rising income inequality and environmental degradation are
among the most pressing considerations facing policymakers in the contemporary United
States. In broad terms, my research examines the relationship between the distribution of
income and the distribution of exposure to air pollution. The three substantive chapters
provide new insights concerning income inequality, environmental inequality, and examines
the relationship between income ineuqality and the distribution of pollution exposure.
Chapter II addresses the measurement of spatially disaggregated income inequality
(within states and metropolitan areas). It offers a novel dataset on income inequality,
and new insights into the causes of rising income inequality. Chapter III considers the
broad question of how to measure environmental inequality in a normatively sensible way,
and applies these measurement tools to data on pollution exposure from satellite remote
sensing data. Chapter IV leverages the measurement work in each of the first substantive
two chapters to explore the causal effect of income inequality on environmental quality,
and explores potential political economy avenues by which these effects may occur.
Expanding on this brief summary, Chapter II considers the quantification of income
inequality measured at the US state and metropolitan area level, using income micro-
data from the Census Bureau. Measuring inequality using Census Bureau survey data
can be challenging, chiefly due to the fact that incomes are top-censored. To address this
challenge, I adapt a semi-parametric multiple imputation method proposed by Jenkins, et
al. (2009) to the new task of measuring sub-national income inequality. Further, I extend
this method to perform inference on changes in income inequality via semi-parametric
bootstrapping. Using this new semi-parametric bootstrap method, I find that income
1
inequality in most states and metropolitan areas has increased since the mid-1990’s, a
result which stands in contrast to some literature on inequality measured with survey
data. I then consider potential determinants of state income inequality. Consistent with
a long line of literature starting with Dinardo, Fortin and Lemieux (1996), among the
most (if not the most) important explanation for the rise in inequality since the 1970s
has been the decline in union density. In addition to these results, this paper produces a
dataset of state and MSA income inequality over time. This dataset is additionally used in
Chapter IV, as well as several projects by myself and other researchers that are currently
in progress.
Chapter III considers how to measure environmental inequality in an analogous
and normatively sensible fashion, and how environmental inequality has evolved within
the United States. I use two data sources of data on the distribution of exposure to air
pollution: satellite observations of NOx from NASA’s Aura satellite, and estimates of
ground level PM2.5 derived from several extant satellites. I find that average exposure
to these particular pollutants has decreased both nationally. Additionally, I find that the
distribution of pollution exposure has become more equal since the late 1990’s (using the
PM2.5 data) and since 2005 (using the NOx data). Using re-centered influence function
regressions, which identify how variations in individual census tract demographics affect
national inequality, I consider how census tract demographic characteristics are related to
environmental inequality. There is evidence that many of the dimensions of disadvantage
highlighted in the environmental justice literature (chiefly dimensions of race and class)
are correlated with environmental inequality.
Chapter IV builds on the results from the first two substantive chapters by exploring
the causal effect of income inequality on the distribution of pollution exposure. I leverage
the dataset developed in Chapter II on MSA level income inequality as well as the dataset
2
developed in Chapter III on the distribution of NOx exposure, and use a simulated
instrumental variables strategy to achieve causal identification. I find that metropolitan
area income inequality decreases average pollution exposure. There is also evidence that
income inequality increases pollution exposure inequality as well as the gap in exposure
between advantaged and disadvantaged groups. Together, these results imply that the
most advantaged members of society are disproportionately reaping the benefits of
pollution exposure reduction. I propose a political economy explanation for these results,
showing in particular that income inequality appears to increase the environmentalism
of US politicians, a result consistent with increasing responsiveness to the environmental
demands of the rich.
The final chapter of this dissertation concludes with a summary of this research
agenda as it currently stands, highlighting the contributions to existing literatures on
income inequality, environmental justice and political economy. This final chapter details
potential future extensions of the line of research outlined in this dissertation. The final
chapter also summarizes several research projects which are underway which run parallel
to the work in this dissertation.
3
CHAPTER II
STATE AND METROPOLITAN AREA INCOME INEQUALITY IN THE UNITED
STATES: TRENDS AND DETERMINANTS
Introduction
Rising income inequality has become one of the most pressing concerns of the
modern era. An extensive literature has attempted to explain why the distribution
of income in the United States has become more unequal. This literature has almost
exclusively relied on national-level data, however, both as a matter of convenience (official,
national income distribution statistics are often made available by national statistical
agencies) and as a matter of analytical preference (for many studies, countries are a
natural unit of observation). There has been less work done on the longer run trends in,
and determinants of, income inequality measured at sub-national geographic scales.
There are several reasons, to study income inequality at smaller geographic
resolution. Inequality can generally be thought of as being composed of between-subgroup
and within-subgroup inequality. In the United States, inequality between states has
actually been decreasing, implying that within-State income inequality has been the driver
of overall income inequality. This in turn suggests that in order to understand national
trends in income inequality it is necessary to first understand what has been happening at
the sub-national level. Additionally, a small but growing literature has begun to examine
whether rising income inequality affects other outcomes of interest. These effects may be
the results of individuals’ responses to rising inequality. Individuals are unlikely to be able
4
to accurately perceive the national level of income inequality, but are more likely to be
able to accurately perceive inequality in their own metropolitan area or state.1
This paper is innovative along two dimensions: first by offering a consistent time
series of inequality measures at the state and metropolitan area levels—using Metropolitan
Statistical Area (MSA) definitions—over a relatively long time period (as early as 1968
to the present), and second by applying recently developed tools for dealing with top-
coded Census Bureau data to sub-national geographic scales. Specifically, I apply the
Generalized Beta multiple imputation methodology proposed in Jenkins et al. (2011),
previously used only with national-level data, to the State and MSA level. I believe this
dataset to be more complete and better constructed than previous efforts.2 I leverage
the large set of information about income sources and household composition available
in Current Population survey data to construct income inequality measures using five
different definitions of income, which range from an Adjusted Gross income concept that
coincides with IRS tax return data to a broad post-fiscal household income definition that
considers the effect of taxes, transfers and in-kind social spending that most closely aligns
with the disposable income available for consumption. In addition to allowing the analysis
in this paper, these data has already proven to be useful in studies where researchers may
require measures of inequality at the State or MSA level.
Methodologically, I utilize a number of strategies to analyze how income inequality
has changed. I introduce a semi-parametric bootstrap technique for inference on inequality
measures, which complements the Generalized Beta II multiple imputation process used
to generate point estimates. I use this method throughout the analysis, first in pairwise
comparison of inequality measures, and then in a semi-parametric extension of the Barrett
1Gimpelson and Treisman (2015) provide some suggestive evidence for this disparity.
2One notable exception being the Frank (2009) state-level dataset, which utilizes IRS Statistics of
income data and Pareto interpolation from 1913 to 2005
5
et al. (2014) bootstrap test for Lorenz Dominance. I find that not only is there robust
evidence of an increase in inequality, this increase in inequality is not a purely the result of
increasing incomes at the top. Although the increase in income inequality is consistent
with an increase in the share of the top 1%, there are also substantial changes within
the bottom 99% of the distribution. Specifically, the top quartile of the distribution finds
itself relatively better off over the past decade, while the bottom 50-75% is unambiguously
relatively worse off. I examine several possible explanations for this increase in inequality
in subsequent regression analysis, and find that evidence for associations between income
inequality and both de-unionization and changes in top marginal tax rates, but less
evidence for associations between inequality and changes in technology or human capital
accumulation.
The paper proceeds as follows. Section 2 summarizes the related literature on local
area income inequality as well as the recent literature on strategies for dealing with
top-censored income microdata for the study of income distribution dynamics. Section
3 describes my strategy for constructing the state and MSA income inequality panel
datasets, and discusses the dynamics of the resulting income inequality measures. Sections
4 and 5 perform inference concerning the changes in income inequality over the last
decade, and use state-level data to analyze the determinants of these changes. Section
6 concludes with directions for future research, included suggested applications of the
inequality datasets.
Related Literature
There is substantive literature documenting a substantial increase in income
inequality in recent decades. It is almost too large to summarize here, though earlier
thorough reviews exist (see Acemoglu (2002) or Atkinson et al. (2011)). The literature
6
on income inequality in the United States can be categorized based on the underlying data
source, the income-receiving unit, and the definition of income. Studies based on IRS tax
return data (e.g. Piketty and Saez (2003)) use the tax unit as the unit of observation,
and the income concept is market income (pre-tax, pre-transfer). Studies based on
Census Bureau survey data (from the Current Population Survey, the decennial Census
and the American Community Survey) have tended to use the household as the unit of
observation, and pre-tax, post-transfer incomes as the income concept.3 I will use Census
Bureau survey data, so I highlight the most relevant literature using this data, as well as
the relatively small literature dealing with income inequality within states or metropolitan
areas.
Census Bureau Microdata
There are two main feature of Census Bureau data which must be addressed when
using these data to analyze income inequality: (1) these data do not measure capital
gains (either realized or unrealized) as part of income, and (2) incomes above a certain
threshold, which is different for each income source, are “topcoded” for privacy reasons.
The topcoding procedures have changed significantly over the history of the CPS, but the
basic process has been to replace the true reported income with a top-code value which
anonymizes the top income earners in the sample. Both topcoding and the exclusion
of capital gains should, other things equal, lead to lower estimates of income inequality
than a “true” inequality measure where there is no topcoding and the inequality measure
includes capital gains.
3Recently there has been some interest in more expansive income definitions (see, e.g. Armour et al.
(2014)). I use the standard pre-tax post-transfer income measure in this study, but using more expansive
income definitions might be a useful direction for further work.
7
The exclusion of capital gains can be justified on definition-of-income grounds, as
in Armour et al. (2014). Unrealized capital gains do not necessarily represent changes
in wealth available for consumption, and hence a reasonable definition of income might
exclude these gains. Topcoding presents a more pressing issue, however. One solution,
which is still occasionally used, is to simply eschew the use of income inequality measures
that are sensitive to the upper tail of the income distribution (e.g. the Gini coefficient
of top 1% share) and to use instead measures such as the 90-10 ratio.4 However, as
Burkhauser et al. (2009) note, there is still substantial topcoding in the public-use micro
data, even at the 90th percentile of the income distribution, so using the 90-10 ratio does
not necessarily eliminate the top-coding problem.
Two approaches have been proposed for correcting for top-coded income data. The
first involves collecting suitable cell means data for top incomes from the confidential CPS
data, and imputing these cell means in place of topcoded income amounts. The second
involves a multiple imputation approach wherein top-coded incomes are imputed as draws
from a suitable distribution. The cell means approach was actually used by the Census
Bureau in the public CPS data from 1996 to 20105, and Larrimore et al. (2008) extends
this cell means series back to 1976. The Larrimore series is at least as good as the internal
CPS data used by the Census Bureau for official analysis, but still probably understates
inequality, since top incomes are still censored. The multiple imputation approach directly
addresses the censoring by fitting a parametric model of the income distribution from the
raw, topcoded data, and then simulates distributions semi-parametrically by drawing
replacement values for topcoded incomes from the fitted model. Jenkins et al. (2011)
offers a detailed description of the suggested process. This approach is the one I adopt
4The 90-10 ratio is the ratio of income at the 90th percentile to income at the 10th percentile.
5From 2011 onwards, the CPS has a new top-coding process wherein top incomes are randomly
swapped within a cell, rather than replaced with the cell means.
8
in the analysis of local area income in this paper. More detail on my modifications of the
multiple imputation approach can be found in section 2.3.
Local Area Income Inequality
The above discussion of the current debates and developments in the inequality
literature has focused on national-level income inequality within the US. With notable
exceptions, very little of the economics literature on inequality has discussed inequality at
smaller geographic scales. Several early analyses of inequality at the state level do exist,
for instance Bishop et al. (1991). Several other papers have examined inequality at smaller
geographies as well. County-level analyses of trends in inequality have been conducted,
including Moller et al. (2009) and Peters (2013). No thorough MSA-level analysis of
income inequality has been done, at least to my knowledge.
Several papers have used state-level or local-level income inequality data as a way of
analyzing how inequality might affect certain outcomes. Frank (2009) constructs a state-
level panel of income inequality statistics to address a separate question (a time-series
analysis of the inequality-growth relationship). Frank’s data are derived from the public-
use version of the IRS data used by Piketty and Saez (2003), and extends from 1916-2005.
Several papers have used CPS or Census/ACS data for similarly separate ends, including
Mellor and Milyo (2002), who use CPS data to calculate MSA-level inequality in service
of analyzing the Wilkinson hypothesis of a link between inequality and health status.
A recent working paper, Daly and Wilson (2013), utilize county-level inequality data to
examine a similar relationship between inequality and health.
At least two recent papers have examined the determinants of inequality at the level
of individual MSAs. Florida and Mellander (2013) utilize both inequality measured using
the American Community Survey (ACS) well as ineuqality measured using wage data
9
from the Current Population Survey. Glaeser et al. (2009) also use inequality measures
calculated from ACS and Census data to examine the connection between home prices
and inequality. However, compared to these papers I make several contributions. First,
using the CPS, I construct an annual panel of inequality measures at the MSA (and state)
levels.6 Second, this study is unique among state or local area inequality studies in that it
directly addresses the top-coded nature of the CPS microdata via a multiple imputation
process along the lines of Jenkins et al. (2011).
Data
This paper seeks to add to this small but growing literature by examining income
inequality at the sub-national level using CPS data in a way that addresses the potential
pitfalls of the data (the right-censoring of incomes due to topcoding). To accomplish this,
I adapt the Generalized Beta II multiple imputation approach of Jenkins et al. (2011)
to a sub-national setting. Before carefully explaining the multiple imputation process, I
present some institutional information about Census Bureau survey data. The focus here
is on topcoding in the Current Population Survey, although there is also topcoding in the
decennial Census and American Community surveys.
Census Bureau Topcoding
The March Supplement to the Current Population Survey is an annual survey of
around 50,000 households which is designed to produce a nationally representative sample
of the US population. There has been some debate concerning the representativeness of
any given year’s CPS sample for individual states or localities. The decennial Census
and the ACS are designed to be representative for localities (e.g. the 1-year ACS public-
6In Appendix B, I construct a similar dataset using ACS data.
10
use files are intended to be representative for geographic areas with populations of at
least 100,000). I proceed under the assumption that the CPS is reasonably close to
representative, at least for sufficiently large MSAs and states.7
The CPS March Supplement includes a number of questions about income, which
have become more detailed in subsequent iterations of the survey. This disaggregated
individual income information is then aggregated up to form individual, family and
household income amounts for each relevant responding unit in the survey. From 1968
to 1975, the CPS included eight questions about personal income components. In 1976,
this was expanded to eleven items, and after 1988, the CPS included 24 separate questions
about income sources.8 The full list of income sources can be found in Table 1. Each of
these income sources is subject to topcoding. In order to satisfy their mandate to protect
individual privacy, the Census Bureau censors the raw reported amounts above a pre-
defined threshold for each income source. There are two levels of topcoding—a “hard”
topcode of the internal data, in which the raw survey results are replaced with a censored
amount, and a second topcode for the public-use data, in which the internal data amount
is replaced with a separate censored amount before the data are released for public-use.
The internal topcodes are usually, but not always, different from the public-use topcodes.
Until 1996, the Census Bureau simply replaced each topcoded income amount with
the topcoding threshold. From 1996 to 2010, however, the Census Bureau instituted a
more informative topcoding regime. They first divided the topcoded individuals into cells
(gender-by-race-by-employment status) and then calculated a mean of all the individuals
in each cell above the topcoding threshold (but below the hard-coded censoring point).
7Census Bureau documentation suggests that the CPS sample is probably representative for the largest
100 MSAs.
8The more recent surveys merely divide broad categories of income (e.g. government transfers) into
more disaggregated components. The various household income definitions I will use should be unaffected
by the granularity.
11
TABLE 1. Income Sources in the CPS by Year
1968-1976
Labor Sources: Wages, Self Employment, Farm Income
Non-labor sources: Social Security, Welfare, Government Programs,
Interest, Dividends and Rents
alimony, contributions, other
1976-1987
Labor Sources: Wages, Self Employment, Farm Income
Non-labor sources: Social Security, Supplemental Security, Welfare, Interest,
Dividends & Rental Income
Veterans & Workers Comp., Retirement, Other
1988-2012
Labor Sources: Wages, Self Employment, Farm Income
Non-labor sources: Social Security, Supplemental Security, Welfare, Interest,
Dividends, Rental Income, Alimony, Child Support,
Unemployment, Veterans Benefits, Workers Comp., Retirement,
Survivor Benefits, Disability Benefits, Educational Assistance,
Financial Assistance, Other
These cell means are then substituted for each respective topcoded income amount.
Compared to the previous regime, the cell means provide a better picture of the right
tail of the income distribution, although a substantial amount of information is still
suppressed. The Census Bureau change in topcoding policies after 1996 can lead to
discontinuities in any calculations of distributional statistics. However, Larrimore et al.
(2008) provide a series of cell means that is consistent with the official Census Bureau
series, and extends back to 1976.
Starting with the 2011 March CPS, the Census Bureau has implemented a new
top-coding method, in which topcoded incomes are randomly swapped across individuals
within relatively narrow income bins. At the national level, this means that there should
be very little difference between the internal and public-use data when these are used
simply for the purpose of income inequality analysis. The internal CPS data is topcoded
at a higher threshold, so the bias due to topcoding is still present, albeit diminished
12
substantially. Additionally, the Census Bureau has additionally provided researchers with
“swap files” for the 1977–2010. I then use these “swap files” to perform the same rank-bin
swap process on the March CPS public-use data from 1977 to 2010. I will then use this
swap-file modified public-use CPS microdata from 1977 to 2010 and the CPS public-use
data from 2011 onwards to calculate measures of income inequality and perform inference
on trends.9
Generalized Beta II Imputation
Although the rank-proximity swap process reduces some of the problematic
topcoding in the public-use CPS, it does not affect the internal “hard” topcodes, which
are problematic for the study of income inequality.10 A large literature has emphasized
that the rise in income inequality since 1970 has been driven primarily by gains at the
very top of the income distribution. Inequality measured using censored top-income values
in the Census Bureau survey data is likely to miss changes at the very top of the income
distribution. The use of cell mean or rank-proximity swap replacement partially address
this censoring. One increasingly common method to address the remaining bias due to
topcoding and under-reporting, which I utilize in this study, is to implement a multiple
imputation approach. Jenkins et al. (2011) introduced this method for national level
income inequality, and I extend this approach to the state (and MSA) level.
The basic methodology for the multiple imputation process is as follows. First, a
parametric distribution is fitted to the observed size-adjusted household income data.
Then, partially synthetic income distributions are formed by taking draws from the fitted
9A previous version of this paper used the Larrimore et al. (2008) cell means series and the GB2
imputation method described in what follows. The current version of this current version uses the same
multiple imputation method, but with the swap-file-modified CPS microdata.
10Additionally, as noted by Diaz-Bazan (2015), there is reason to believe that incomes may be under-
reported at the top of the income distribution in the March CPS.
13
distribution and imputing these draws to the topcoded or potentially under-reported
individual incomes. Second, distributional statistics are calculated using the partially
synthetic data. This process is repeated n times, and the n point estimates are combined
according to the rules proposed by Reiter (2003). I use n = 200 for most of my analysis,
although preliminary results in small-scale simulations seem to imply that n = 100 or
even n = 20 is sufficiently large. In Jenkins et al. (2011), this process was conducted for
each year of the CPS to produce national-level inequality statistics. However, since I am
interested with sub-national-level inequality, there are slight modifications that must be
made to the Jenkins et al. (2011) methodology. In the following, I describe the specifics of
this modified process.
I merge the CPS swap-file with the public-use CPS microdata and then calculate
household incomes from the resulting dataset.11 I then flag all topcoded and potentially
under-reported individual income source amounts in the combined CPS sample from 1968-
2014.12 As shown in Appendix A, using a cutoff at the 97.5th percentile allows me to
reasonably approximate trends in top income shares and the Gini coefficient calculated
using IRS tax return data. I adjust for household size by using an equivalence scale
equal to the square root of the number of people in the household. Each individual in the
household is then associated with this size-adjusted household income amount.
I assume that the distribution of size adjusted household income is well
approximated by a Generalized Beta distribution of the second kind (GB2).13 The four
11The CPS counts business losses as income, so there are some households which report negative
total household incomes. I am utilizing some inequality measures (notably the Theil index) which are
only defined for positive incomes. After aggregating to the household level, I truncate all non-positive
household incomes to $0.01.
12All geographic identifiers are not available for all years. Some MSAs are identified starting in the 1968
March CPS, but states are not identified until 1977.
13See McDonald (1984), Majumder and Chakravarty (1990), Wilfling (1996) and McDonald and Ransom
(2008)
14
parameter GB2 distribution has a probability density function
f (y) =
ayap−1
bapβ (p, q)
(
1 +
(
y
b
)a)p+q
where β (·) is the Beta function, and a, b, p and q are positive parameters. Several well
known distributions used in the income inequality literature (including the Singh-Maddala
and Pareto distributions) are special cases of the GB2 distribution. In the model fitting
step of the imputation process, I estimate a GB2 distribution to fit the observed data via
maximum likelihood.14
I am interested in inequality at sub-national levels, so it would be natural to modify
the Jenkins et al. (2011) method to fit a distribution to local level incomes, and then
proceed with the imputation. However, in practice, there are often too few observations
at the local level. Hence I fit a single distribution for each year using observations from
the entire US in the swap-file-modified CPS microdata.15 I then perform the imputation
for each MSA or state separately based on the estimated parameters from this fitted GB2
distribution. This method maximizes the number of top incomes employed to fit the GB2
distribution, and hence should yield a more-accurate approximation of the true upper tail
of the distribution.
In the second step of the GB2 imputation process, I split the data for each year
by MSA or state, and construct partially synthetic datasets for each geographic unit in
each year. Non-topcoded households enter each partially synthetic dataset unchanged. For
households with topcoded (or potentially under-reported) incomes, I replace the topcoded
income with a draw from the fitted GB2 distribution. Specifically, each topcoded income
14I use the R package GB2 package (https://cran.r-project.org/web/packages/GB2/index.html)
to perform the maximum likelihood estimation.
15Following Jenkins et al. (2011), I use only the top 70% of incomes in the CPS sample in each year in
the estimation. This is intended to improve the fit at the right tail of the distribution.
15
yi is replaced by
y∗i = F
−1 (ui (F (yi) , 1))
where F (·) and F−1 (·) are the CDF and inverse CDF associated with the fitted GB2
distribution, and ui (a, b) is a draw from a uniform distribution with lower bound a and
upper bound b. I construct n = 200 such partially synthetic datasets for each MSA (or
state) in each year. The final step in the GB2 imputation process is to estimate income
inequality measures for each partially synthetic data set. I then follow the rules from
Reiter (2003) for combining estimates from partially synthetic datasets. For each income
inequality measure of interest, I produce a point estimate q∗ equal to the simple average of
the estimates qi over the n partially synthetic datasets: q
∗ = 1
n
n∑
i=1
qi.
16
I calculate several income inequality measures using this methodology.17 The two
most important are the Gini coefficient and the top 1% share. The Gini coefficient is
calculated as:
G =
1
µx2n2
n∑
i=1
n∑
i′=1
|xi − xi′ |
where xi is household i’s income. The top 1% income share is the income accruing to the
top 1% of the income distribution as a share of total income. If incomes are arrayed in
non-decreasing order i = 1, ..., n, and k is the closest integer to 99n
100
, then the top 1% share
is
Top1Share =
n∑
k
xi
n∑
i
xi
16The variance of this point estimate is given by V ∗ = 1n
(
1
n−1
∑n
i=1 (qi − q∗)2 +
n∑
i=1
vi
)
where vi is the
variance (calculated using asymptotic variance formulas) of the point estimate qi from the ith partially
synthetic dataset.
17In addition to the measures listed, I calculate the 90-10 ratio, Theil, Atkinson and Schutz indices,
various Generalized entropy indices (varying the α parameter from 0.5-2), the coefficient of variation, the
99-median and 95-median ratios, and the 80-20 ratio, as well as Kuznets ratios.
16
I also calculate a number of Lorenz ordinates for a variety of analyses. The pth ordinate of
the Lorenz curve is
L (p) =
1
µ
∫ F−1(p)
0
xf (x) dx
Note that the top 1% share can therefore also be expressed as a function of Lorenz
ordinates:
Top1Share = 1− L (0.99)
I calculate these measures for all 50 states (and the District of Columbia)
Unfortunately not all MSAs have enough observations in the CPS to perform reliable
income distribution analysis. Hence, I focus on MSAs which have at least fifty household
observations in each year of the CPS. The observations from MSAs with less than fifty
households are recoded as non-MSA households, so that they may still be used for the
fitting of the GB2 distribution. Additionally, since the evolution of income inequality is
of primary importance, households in MSAs which have large gaps in their time series are
likewise recoded as non-MSA households. After these modifications, 177 MSAs remain
in the dataset. The state-level and MSA-level inequality measures that I estimate here
are available in an online data appendix.18 I also perform similar exercises, generating
datasets of income inequality measures for all 50 states and 277 MSAs using microdata on
income from the American Community Survey, which are available in the same online data
appendix. The specifics of the ACS-based analysis can be found in Appendix B.
From Market Income to Haig-Simons Income
The GB2 imputation method addresses potential concerns about topcoding and
under-reporting of income at the top of the distribution. Using inequality measures
18Available at http://pages.uoregon.edu/jlv/state-and-msa-inequality.html
17
generated using this method, it is possible to examine how inequality has changed over
the last several decades. Before doing so, however, it is necessary to define carefully the
income concept to be used. The most conceptually attractive definition both i) treats
income receiving units equally (by adjusting for household size using an equivalence scale),
and ii) defines income as the change in net worth that can be used for consumption (where
this is usually referred to as “Haig-Simons income”). Measuring Haig-Simons income
requires information about changes in wealth due to capital gains, which are unavailable
in the Census Bureau surveys used in this study. Nonetheless, it is possible to use all of
the information available in the March CPS to construct an income definition that is as
close as possible to the Haig-Simons definition.
In the spirit of Armour et al. (2014), I will construct a “crosswalk” from the most
commonly used income concept in inequality studies using tax return data (e.g. Piketty
and Saez (2003)) to a broader measure of income that I will call “post-fiscal” income.
Table 2 summarizes each step along the crosswalk. The crosswalk consists of five income
definition, arranged in order of their “closeness” to Haig-Simons income, where each step
corresponds to an additional source of income or a change in income-receiving unit. The
first step is tax-unit Adjusted Gross Income (AGI), which includes all “market income”
received by a tax unit (the individuals included on a tax return). The second step, pre-
transfer income, changes the income receiving unit to the household, and adjusts for
household size by applying a square root equivalence scale.19 The third step, post-transfer
income, adds cash transfers from the government. The fourth step, post-tax income, is
post-transfer income after state and federal income taxes (including tax credits). The
final step, post-fiscal income, adds the cash value of in-kind aid to post-tax income. The
contrast between post-fiscal and pre-transfer income incorporates not just how market
19I divide each household’s income by the square root of the number of members in the household and
assign this size-adjusted household income to each individual in the household.
18
income has evolved, but also how state interventions to reduce income inequality have
evolved, in the form of changes to the tax and transfer system and, increasingly, the
provision of in-kind benefits to households in the bottom half of the income distribution.
TABLE 2. Crosswalking from Market to Disposable Income
Definition
AGI Income Tax unit adjusted gross income
Pre-transfer Income Pre-tax Household income (wages + investment)
Post-transfer Income Pre-transfer Income plus cash transfers
Post-tax Income Post-transfer income less taxes and tax credits
Post-fiscal income Post-tax income plus the monetary value of noncash benefits
Cash transfers include: TANF/AFDC, Social Security, Disability (SSDI or SSI),
unemployment benefits.
Non-cash benefits include SNAP (food stamps), the value of public housing and rental
subsidies, the value of home heating subsidies, the value of government provided school
lunch, the fungible value of Medicaid and Medicare benefits and the value of WIC benefits
To visualize how recent trends in inequality vary across states and across income
definitions, I present several graphs. First, I visualize the trends for all states and all
five income definitions simultaneously as a “spiderweb graph” in Figure 1 for the Gini
coefficient and the top 1% share. The central tendency across all 50 states for each
income definition is emphasizes to permit easy visualization of the average trend in
inequality across states. As expected, there are large differences in the level of income
inequality when using different income measures. Income inequality is highest for the AGI
definition of income, and lowest for post-fiscal income. The levels of measured income
inequality differ substantially depending on the income definition. Especially in the period
after about 2000, trends in income inequality vary by income definition as well. Income
inequality measured by the Gini coefficient using AGI income is on average increasing
19
(albeit at a slower rate after about 2000 than the run-up in inequality before 2000). There
is a noticeable decline in the post-fiscal Gini coefficient after 2000. This is also true of the
post-fiscal top 1% share, with particularly sharp drop occurring right after 2000. 20
FIGURE 1. State Income Inequality, 1977–2014: Crosswalking from Market Income to
Post-fiscal Income
0.2
0.4
0.6
0.8
19
80
19
90
20
00
20
10
year
St
at
e 
G
in
i
income
AGI
postfiscal
posttax
posttrans
pretrans
State Gini Coefficient, 1977−2014
0.1
0.2
0.3
19
80
19
90
20
00
20
10
year
St
at
e 
To
p 
1%
 S
ha
re income
AGI
postfiscal
posttax
posttrans
pretrans
State Top 1% Share, 1977−2014
Since the “spiderweb” graphs by design abstract from trends in any individual state,
it can be instructive to examine trends in a few states individually. Figure 2 illustrates
the Gini and top 1% share income inequality crosswalks from AGI market income to post-
fiscal income for the four largest states. For these large states, the pattern seen in the
central tendency across all states is even more readily apparent: measured using market
income, income inequality has increased almost monotonically since 1977, but measured
using a broader, post-fiscal definition, inequality has actually decreased since 2000.
20This may be due in part to the rising value of rental subsidies and Medicare/Medicaid given that both
health care costs and rents have been rising over this period.
20
Additionally, it is clear that the primary drivers of the difference between market and
post-fiscal income vary depending on the type of inequality measure used. If inequality is
measured by the top 1% share, household size is relatively unimportant, but the opposite
is true for inequality measured by the Gini.
FIGURE 2. State Income Inequality, 1977–2014: Crosswalking from Market Income to
Post-fiscal Income, 4 largest States
California Illinois
New York Pennsylvania
0.3
0.4
0.5
0.6
0.7
0.3
0.4
0.5
0.6
0.7
19
80
19
90
20
00
20
10
19
80
19
90
20
00
20
10
year
St
at
e 
G
in
i
income
AGI
postfiscal
posttax
posttrans
pretrans
State Gini Coefficient, 1976−2013
California Illinois
New York Pennsylvania
0.05
0.10
0.15
0.20
0.25
0.05
0.10
0.15
0.20
0.25
19
80
19
90
20
00
20
10
19
80
19
90
20
00
20
10
year
St
at
e 
G
in
i
income
AGI
postfiscal
posttax
posttrans
pretrans
State Gini Coefficient, 1976−2013
The difference in the level of income inequality when using pre-transfer versus post-
fiscal income is one way of quantifying the degree to which government intervention
is redistributive (Kakwani (1977). Examination of this Kakwani-style measure of
redistributiveness across states and over time can shed light on the degree to which
different states have adjusted policy in response to rising income inequality. Figure 3
summarizes the state-level trends in redistributiveness measured as the difference between
the Gini coefficient using pre-transfer income, and the Gini coefficient using post-fiscal
21
income. It appears to be the case that, on average, redistributiveness has increased since
2000, especially in the period of time corresponding to the Great Recession of 2007-2010.
FIGURE 3. State-level Redistributiveness, 1977-2014
0.0
0.1
0.2
0.3
1990 1995 2000 2005 2010
year
R
ed
ist
rib
u
tiv
e
n
e
ss
State−level Redistributiveness, 1986−2013
Inference on Changes in Income Inequality
Having generated a dataset measuring point estimates of state-level and MSA-level
income inequality as accurately as is possible with public-use data, the logical next step
is to analyze how inequality has been changing over time, and what might be driving
these changes. Towards that end, I pursue two lines of inquiry. First, I can perform
inference on scalar inequality measures and Lorenz ordinates. The scalar metrics and
different Lorenz ordinates are sensitive to changes in different parts of the distribution,
and hence comparing the results of these tests between these different inequality measures
can provide qualitative information on how inequality has been changing. A second line of
inquiry uses the bootstrap method of Barrett et al. (2014) to test directly the hypothesis
of Lorenz dominance. I can then make direct welfare statements based on this inference.
22
I will use bootstrap methods to make inferences based on the data. This is a partial
departure from much of the survey-based literature, which has relied on inference using
asymptotic variance formulas. There is reason to believe, however, that this type of
inference may lead to incorrect conclusions. Flaichaire and Davidson (2007) and Brzezinski
(2013) note that bootstrap procedures have lower nominal type I error probabilities than
inference using asymptotic variance formulas for the Theil coefficient and top income
shares respectively, and Mills and Zandvakili (1997) show that the same is true for the
Gini. Additionally, in simulation experiments, it appears that the hypothesis tests using
asymptotic variance formulas for Lorenz curves have extremely low power for the sort of
hypotheses I will be interested in testing, relative to bootstrap-based inference.
Mills and Zandvakili (1997) develop a simple bootstrap method for conducting
inference on the Gini coefficient. To extend this method to topcoded and potentially
under-reported data, I extend the semi-parametric bootstrap technique of Flaichaire
and Davidson (2007). For clarity, I first describe the simple Mills and Zandvakili (1997)
method, and then describe my extension of the semi-parametric bootstrap technique of
Flaichaire and Davidson (2007) for conducting inference on changes in inequality in the
presence of topcoded or potentially under-reported data. The main object of interest is the
difference between an inequality metric θ calculated using samples from two populations:
φ = θ2 − θ1.21 In the simple bootstrap method, one would bootstrap resample (sample
with replacement) from the samples of the two populations in the data, calculate the
inequality measures θ1, θ2 using the bootstrap samples, and calculate the difference φ
∗
j .
After performing this n times and collecting the bootstrap replicates Φ =
{
φ∗j
}n
j=1
,
inference can then be done by constructing confidence intervals
(
Φα/2,Φ1−α/2
)
, where
21I will be conducting inference where these two populations are a single state in two different years,
but this method could also be used to test a hypothesis of no difference in inequality between two different
states in a given year.
23
subscripts refer to percentiles of the distribution of bootrap replicates. Bootstrap p-values
can also be calculated, e.g. for the null hypothesis of no change, as
p∗ =
1
n
n∑
j=1
1
((
φ∗j − φ
)2 ≥ φ2)
where φ is the full sample (“true”) estimate of the difference in inequality.
To adapt this to our environment, I move to semi-parametric bootstrapping.22 For
each time period, I partition the data into topcoded and non-topcoded observations. The
non-topcoded observations are bootstrap resampled as in the simple case. The topcoded
observations are imputed as in the GB2 multiple imputation process used to generate
point estimates. That is, for each bootstrap replication, each topcoded observation yi is
replaced by a draw from the tail of the fitted GB2 distribution. In practice, for a fitted
distribution Fˆ (y), I take a uniform draw ui ∈
[
Fˆ (yi) , 1
)
, and then replace yi with
Fˆ−1 (ui). I then estimate θj from the full non-topcoded sample and the topcoded draws,
and θ∗j from the bootstrap sample of the non-topcoded observations and the topcoded
draws. From these I obtain φ∗j , φj as before. After repeating this process n times, I can
then calculate a point estimate of the difference in inequality as φˆ = 1
n
∑n
j=1 φj as in the
multiple imputation case. The bootstrap confidence interval is the same as before, and the
two sided p-value for a null of no change is
p∗ =
1
n
n∑
j=1
1
((
φ∗j − φˆ
)2
≥ φˆ2
)
22This semi-parametric method is similar to Flaichaire and Davidson (2007), differing in the parametric
distribution used (the Generalized Beta II distribution)
24
or, for a one-sided p-value for the null hypothesis of no change against the alternate that
the the change is negative,
p∗ =
1
n
n∑
j=1
1
((
φ∗j − φˆ
)
≤ φˆ
)
With this semi-parametric bootstrap method, I perform inference on the same scalar
inequality metrics for which I have produced point estimates in the previous section.
Performing inference in this case involves many more hypothesis tests than are feasible to
display individually, given that the focus is on with State-level and MSA-level inequality.
I summarize the results by the proportion of states or MSAs for which I can reject the
null hypothesis of no change in inequality, and show individual results for only the most
populous of states and MSAs.
To analyze trends in income inequality, I will perform tests of the null hypothesis
that inequality did not change over a specific period of time. Most but not all previous
studies utilizing Census microdata have shown little to no increase in inequality since
the mid-1990’s at the national level. Studies utilizing tax return data find that inequality
has increased dramatically, although in general at a slower rate than the 1980’s. Further,
these studies tend to find that the increase in inequality is driven by an increasing share of
income accruing to the richest 1%. In light of this, I will consider two questions: whether
income inequality increased from 1986 through 1993, and whether income inequality
has increased from 1994 onward.23 Due to a change in the way the Current Population
Survey was administered, estimates of income inequality from before 1994 are not easily
comparable with estimates after 1994, and hence dividing the sample at this discontinuity
has an intuitive appeal.
23For the pre-1993 test, I choose 1986 as the starting year, since this is earliest year in which the post-
fiscal income inequality series can be constructed.
25
Figures 4 and 5 summarizes inference using CPS microdata for two scalar inequality
measures—the Gini coefficient and the top 1%’s share of income, for the periods 1986–
1993 and 1994–2014 at the State level. These figures show the 95% confidence interval
around the change in the inequality measure in question for the eight most populous
states. These largest states all have positive point estimates for the change in inequality
by either measure in both time periods. For about half of all states, the change in the Gini
coefficient is not statistically different from zero in either time period. On the other hand,
the change in the top 1% share is statistically insignificant for almost all states from 1994
to 2014 and for most states from 1986 to 2014. There is some interesting heterogeneity
across the income definitions—notably the confidence intervals around the differences in
post-tax income inequality are substantially smaller than they are for the other income
concepts.
FIGURE 4. Difference in Gini Coefficient, 1986–1993 and 1994–2014
l
l
l
l
l
l
l
l
l
l
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l
l
l
l
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l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
l
New York
Pennsylvania
Ohio
Illinois
North Carolina
Florida
Texas
California
0.000 0.025 0.050
Income
l
l
l
l
Pre−transfer
Post−transfer
Post−tax
Post−fiscal
Change in Gini Coefficient, 1986−1993 (8 Most Populous States)
l
l
l
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l
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l
l
l
l
l
l
l
l
l
New York
Pennsylvania
Ohio
Illinois
North Carolina
Florida
Texas
California
−0.04 0.00 0.04 0.08
Income
l
l
l
l
Pre−transfer
Post−transfer
Post−tax
Post−fiscal
Change in Gini Coefficient, 1994−2014 (8 Most Populous States)
Given the properties of these two income inequality measures, these results suggest
that increases in income inequality between 1994 and 2014 might be driven by changes
26
FIGURE 5. Difference in top 1% Share, 1986–1993 and 1994–2014
l
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l
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l
l
l
l
l
l
l
l
l
l
l
l
New York
Pennsylvania
Ohio
Illinois
North Carolina
Florida
Texas
California
−0.025 0.000 0.025 0.050
Income
l
l
l
l
Pre−transfer
Post−transfer
Post−tax
Post−fiscal
Change in Top 1% Share, 1986−1993 (8 Most Populous States)
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l
New York
Pennsylvania
Ohio
Illinois
North Carolina
Florida
Texas
California
−0.05 0.00 0.05 0.10
Income
l
l
l
l
Pre−transfer
Post−transfer
Post−tax
Post−fiscal
Change in Top 1% Share, 1994−2014 (8 Most Populous States)
within the bottom 99% of the income distribution. Although there is less evidence for a
top incomes-driven change in income inequality, it is difficult to disentangle why there
is a failure to reject the null hypothesis of no change for the top 1% share. This may
be due to (a) inadequate coverage of top incomes in the CPS survey, or (b) because top
income shares did not increase. In an effort to further characterize the changes in income
distribution, I next consider inference concerning Lorenz curves, which allow fopr the
identification of the regions of the income distribution driving these changes in inequality.
Recall that the ordinates of a Lorenz curve
L (p) =
1
µ
∫ y=F−1(p)
0
xf (x) dx
can be interpreted as the cumulative share of income accruing to the bottom (p) 100% of
the income distribution. The change in specific Lorenz ordinates then describes the change
27
in income shares of the bottom p percent of the income distribution. Note that
dL (p)
dp
=
y
µ
where y = F−1 (p). Thus for two populations with income distributions subscripted as 1
and 2 for convenience,
d (L1 (p)− L2 (p))
dp
=
y1
µ1
− y2
µ2
Which is to say, the slope of the difference in Lorenz ordinates graphed in
(p, L1 (p)− L2 (p)) space describes the change in the pth percentile’s relative income.
This can be thought of as as how much the pth percentile is relatively better off. A slope
change can then be interpreted as delineating the portion of the income distribution
which is relatively better off under distribution 1 and which is relatively better off under
distribution 2.
Consider a case in which changes in income inequality are driven solely by increases
in the top 1%’s incomes while the bottom 99% stays the same. In this case, L1 (p) −
L2 (p) < 0,∀p ≤ 0.99 and d(L1(p)−L2(p))dp < 0,∀p ≤ 0.99. On the other hand, if
L1 (p) − L2 (p) < 0,∀p ≤ 0.99 but ∃p ≤ 0.99 s.t. d(L1(p)−L2(p))dp > 0 However if the former
holds but the latter does not, then this is evidence for both rising top incomes and changes
in inequality within the bottom 99%. If L1 (p) − L2 (p) has only one local minimum, this
further suggests that there is income polarization within the bottom 99%, with the top
of the bottom 99% seeing relative improvements, while the bottom of the bottom 99% is
relatively worse off.
Figures 6 and 7 inventory the evidence concerning changes in Lorenz curves at
the state level for the four income concepts of interest over the period 1994-2014. Each
figure visualizes the point estimate of the change in Lorenz ordinate, as well as 95%
28
FIGURE 6. Change in Lorenz Ordinates, 1994–2014, Pre-transfer and Post-transfer
Income
AK AL AR AZ CA CO CT DE
FL GA HI IA ID IL IN KS
KY LA MA MD ME MI MN MO
MS MT NC ND NE NH NJ NM
NV NY OH OK OR PA RI SC
SD TN TX UT VA VT WA WI
WV WY
−0.3
−0.2
−0.1
0.0
0.1
0.2
−0.3
−0.2
−0.1
0.0
0.1
0.2
−0.3
−0.2
−0.1
0.0
0.1
0.2
−0.3
−0.2
−0.1
0.0
0.1
0.2
−0.3
−0.2
−0.1
0.0
0.1
0.2
−0.3
−0.2
−0.1
0.0
0.1
0.2
−0.3
−0.2
−0.1
0.0
0.1
0.2
0.0
0
0.2
5
0.5
0
0.7
5
1.0
0
0.0
0
0.2
5
0.5
0
0.7
5
1.0
0
Percentile of Income
Ch
an
ge
 in
 L
or
en
z 
O
rd
in
at
es
Change in Lorenz Ordinates, 1994−2014, Pre−transfer Income
AK AL AR AZ CA CO CT DE
FL GA HI IA ID IL IN KS
KY LA MA MD ME MI MN MO
MS MT NC ND NE NH NJ NM
NV NY OH OK OR PA RI SC
SD TN TX UT VA VT WA WI
WV WY
−0.2
−0.1
0.0
0.1
0.2
−0.2
−0.1
0.0
0.1
0.2
−0.2
−0.1
0.0
0.1
0.2
−0.2
−0.1
0.0
0.1
0.2
−0.2
−0.1
0.0
0.1
0.2
−0.2
−0.1
0.0
0.1
0.2
−0.2
−0.1
0.0
0.1
0.2
0.0
0
0.2
5
0.5
0
0.7
5
1.0
0
0.0
0
0.2
5
0.5
0
0.7
5
1.0
0
Percentile of Income
Ch
an
ge
 in
 L
or
en
z 
O
rd
in
at
es
Change in Lorenz Ordinates, 1994−2014, Post−transfer Income
bootstrap confidence intervals (obtained via the semi-parametric bootstrap process
described above). For almost all states, the Lorenz curve for the income distribution in
2014 is lower than the Lorenz curve for 1994, although the changes at any specific ordinate
are not necessarily statistically different from zero.24 Further, the change in the Lorenz
curve ordinates is negative and decreasing with p until around the 80th percentile for
many states, at which point the change in the Lorenz curve ordinates begins to increase
(although it remains negative). In general, the Lorenz curves for the different income
definitions exhibit largely similar changes over the period 1994-2014. These patterns in
the change in Lorenz ordinates over the income distribution are consistent with both an
increase in top incomes, and increasing income inequality within the bottom 99%.
I have established that there have been statistically significant increases in income
inequality since the 1990’s, especially within the bottom 99% of the income distribution. I
24Oregon is the notable exception to this general trend.
29
FIGURE 7. Change in Lorenz Ordinates, 1994–2014, Post-tax and Post-fiscal Income
AK AL AR AZ CA CO CT DE
FL GA HI IA ID IL IN KS
KY LA MA MD ME MI MN MO
MS MT NC ND NE NH NJ NM
NV NY OH OK OR PA RI SC
SD TN TX UT VA VT WA WI
WV WY
−0.1
0.0
0.1
−0.1
0.0
0.1
−0.1
0.0
0.1
−0.1
0.0
0.1
−0.1
0.0
0.1
−0.1
0.0
0.1
−0.1
0.0
0.1
0.0
0
0.2
5
0.5
0
0.7
5
1.0
0
0.0
0
0.2
5
0.5
0
0.7
5
1.0
0
Percentile of Income
Ch
an
ge
 in
 L
or
en
z 
O
rd
in
at
es
Change in Lorenz Ordinates, 1994−2014, Post−tax Income
AK AL AR AZ CA CO CT DE
FL GA HI IA ID IL IN KS
KY LA MA MD ME MI MN MO
MS MT NC ND NE NH NJ NM
NV NY OH OK OR PA RI SC
SD TN TX UT VA VT WA WI
WV WY
−0.1
0.0
0.1
−0.1
0.0
0.1
−0.1
0.0
0.1
−0.1
0.0
0.1
−0.1
0.0
0.1
−0.1
0.0
0.1
−0.1
0.0
0.1
0.0
0
0.2
5
0.5
0
0.7
5
1.0
0
0.0
0
0.2
5
0.5
0
0.7
5
1.0
0
Percentile of Income
Ch
an
ge
 in
 L
or
en
z 
O
rd
in
at
es
Change in Lorenz Ordinates, 1994−2014, Post−tax Income
next examine Lorenz dominance, which gives normative content to the changes in Lorenz
curves shown previously. Distribution 1 is said to “Lorenz dominate” distribution 2 if
L1 (p) ≥ L2 (p)∀p ∈ (0, 1)
and
∃p ∈ (0, 1) s.t. L1 (p) > L2 (p)
I extend the bootstrap test for Lorenz dominance suggested by Barrett et al. (2014)
to accommodate topcoding by using the semi-parametric approach used previously. I
then perform this Lorenz dominance test for each state using the four household income
concepts.
I first review the Barrett et al. (2014) method, and then describe my extension.
Consider two distributions (numbered 1 and 2 for convenience) with associated Lorenz
30
curves L1, L2. Define φ (p) = L2 (p)− L1 (p), the functional I (φ) =
∫ 1
0
φ (p)1 (φ (p) > 0) dp
and Tn =
n1n2
n1+n2
. To test the null hypothesis H10
L2 (p) ≤ L1 (p) ∀p ∈ [0, 1] (2.1)
i.e. that distribution 2 does not Lorenz dominate distribution 1, I perform m bootstrap
replications, using the same semi-parametric scheme as above: I calculate φˆ∗i (p) from
a sample composed of bootstrap resampled observations for non-topcoded observations,
and GB2 draws for the topcoded observations, and φˆMi (p) from a sample composed of the
full non-topcoded sample and draws from the GB2 distribution imputed for the topcoded
observations. I then calculate φˆ (p) =
∑m
i=1 φˆ
M
i (p). Thus, φˆ
M
i (p) is just the GB2 multiple
imputation estimate of L2 (p) − L1 (p). Finally, I construct a one-sided bootstrap p-value
from the bootstrap replications
pˆ1 =
1
m
m∑
i=1
1
(
TnI
(
φˆ∗i (p)− φˆ (p)
)
> TnI
(
φˆ (p)
))
A test of the hypothesis in equation 2.2 can be conducted based on the rule “reject if pˆ <
α”. This is equivalent to a test of weak Lorenz dominance. It is straightforward to test the
opposite hypothesis H20 :
L2 (p) ≥ L1 (p) ∀p ∈ [0, 1] (2.2)
by reversing the order of the two distributions and constructing the bootstrap p-
value pˆ2. A test of strong Lorenz dominance can then be conducted by examining
both bootstrapped p-values. I conclude that distribution 1 strongly Lorenz dominates
distribution 2 if both pˆ1 < α and pˆ2 > α.
31
It is most straightforward to conduct a test for the Lorenz dominance of an early
distribution over a later distribution (e.g. when comparing 2014 to 1994, the 1994
distribution plays the role of distribution 2, and the distribution in 2014 takes the place
of distribution 1). Table 3 summarizes these results for the eight largest states and each
of the four income concepts. The table summarizes the two p-values which can be used
jointly to test for strong Lorenz dominance—if p1 < α and p2 > α the conclusion is that
the income distribution in 1994 Lorenz-dominates the distribution in 2014. I conclude that
this Lorenz dominance has occurred for many states, although the number of states where
this occurs diminishes with the level of redistributiveness encapsulated in the income
definition. Assuming α = 0.05, Lorenz dominance holds for 29 states using pre-transfer
income, and for 31 states using post-transfer income. However, Lorenz dominance holds
for only 23 states using post-tax income, and for only 20 states using post-fiscal income.
This is the strongest evidence yet that income inequality may not have risen as much if
taxes and transfers (including in-kind programs) are taken into account. This result is in
line with Armour et al. (2014).
Potential Explanations for Changing State-level Income Inequality
I have demonstrated that there have been significant changes in State and MSA-level
income inequality concentrated in the bottom 99% of the income distribution. Although
I do not find strong direct evidence of top-incomes-driven inequality changes, I cannot
rule these out. At any rate, such changes are not incompatible with the effects I observe
in the lower part of the distribution. To complete the examination of state-level income
inequality, I examine potential explanations for the rising income inequality observed since
32
TABLE 3. Lorenz Dominance Results
Pre-Transfer Post-Transfer
State p1 p2 p1 p2
California 0.006 1 0.002 0.130
Florida 0.136 0.090 0.048 1
Illinois 0.014 0.070 0.008 0.998
New York 0.098 0.076 0.016 1
North Carolina 0.002 0.052 0 1
Ohio 0.002 0.070 0.006 1
Pennsylvania 0.012 0.094 0.016 1
Texas 0.004 1 0.014 0.054
Lorenz Dominance: 29 States 31 States
Post-tax Post-Fiscal
State p1 p2 p1 p2
California 0.004 0.074 0.006 0.090
Florida 0.106 1 0.074 1
Illinois 0.002 0.998 0 0.996
New York 0.012 0.998 0 1
North Carolina 0.002 0.998 0.006 1
Ohio 0.012 1 0.016 1
Pennsylvania 0.002 1 0.002 1
Texas 0.020 0.056 0.036 0.048
Lorenz Dominance: 23 States 20 States
33
the 1990’s. Previous studies of inequality have suggested a number of factors that might
account for the increase in inequality observed in recent decades.
The evidence presented so far suggests that rising income inequality has been driven
both by rising top incomes and by changes within the bottom 99%. To examine each
of these factors, I will perform a “horse-race” type analysis, using fixed effects panel
regressions to compare the relative influence of five common explanations for rising income
inequality. These five candidate explanations are 1) unionization rates, 2) minimum
wages, 3) top marginal tax rates, 4) human capital attainment and 5) technological
advancement. The first two factors can be measured directly.25 To capture state variation
in top tax rates, I include both the overall marginal capital gains tax rate and the overall
marginal income tax rate in subsequent regressions. I capture human capital attainment
by the fraction of a state’s population with at least a bachelor’s degree, and technological
advancement by the number of patents granted per capita.
I first consider how these five potential factors are related to two scalar measures of
inequality (the Gini Coefficient and top 1% share) and then move to the use of ordinates
of the the Lorenz curve as dependent variables. As in Bishop et al. (1991), changes in
the slope of the size of the effect of a variable on the Lorenz share with respect to the
cumulative proportion p of the population can be interpreted as the marginal effect on the
income share (non-cumulative) of the pth percentile of the population.26
Other things equal, I expect that unionization rates and the real value of minimum
wages will affect primarily the bottom 99% of the distribution, while technological
advancement and top marginal tax rates will affect primarily top incomes. Educational
25I measure the minimum wage as the binding statutory minimum wage in a state, deflated by the CPI-
U price index.
26This is because the Lorenz curve is a sum of infinitesimal income shares, and therefore the effect on
cumulative income shares can be expressed as a sum of the effects on infinitesimal income shares
34
attainment may affect both parts of the distribution. Note that there is no ex ante reason
to expect that each of these factors might affect income inequality identically for each
income concept. In particular, note that the broader income definitions (e.g. post-fiscal
income) incorporate the effects of policies which may be designed in response to the
various factors’ effects on market income.
In the current setting, causal identification is difficult, especially given free labor
mobility between states. Neither unionization rates nor human capital attainment have
been subject to the types of exogenous discrete policy variation necessary for difference-in-
difference or regression discontinuity methods, and obviously exogenous instruments are
not readily available. To overcome potential simultaneity problems, the best available
course of action is to control for unobserved heterogeneity across states and over time
to the fullest extent possible via fixed effects, and to compare results across a number of
models and specifications. If most of the estimated effects lie in a relatively narrow band
this can be taken as suggestive evidence as to the true effect size.
The baseline horse-race model compares the influence of these 5 effects in a model
including State and year fixed effects:
Ineqit = αi + αt + β1Unionit + β2MinWageit+
β3Taxit + β4Educit + β5Patentsit + γXit + it
(2.3)
To modify the above to allow for more flexibility in absorbing time-varying heterogeneity, I
can allow for State-specific linear trends and/or quadratic trends, as in:
Ineqit = αi + αt + θ1,it+ β1Unionit + β2MinWageit+
β3Taxit + β4Educit + β5Patentsit + γXit + it
(2.4)
35
Ineqit = αi + αt + θ1,it+ θ2,it
2 + β1Unionit + β2MinWageit+
β3Taxit + β4Educit + β5Patentsit + γXit + it
(2.5)
In each model, Xit is a vector of other potential time-varying confounding factors which
might be related to inequality (including population density, government spending per
capita, demographic characteristics, changes in household size and composition, industry
composition, real state personal income per capita, the state unemployment rate and age
composition of the state).
Tables 4 and 5 report results from regressions estimated using the Gini coefficient
as the dependent variable, for each of the four difference income concepts. In line with
expectations, the unionization rate has a statistically significant and negative impact on
the Gini coefficient for three of the four income concepts, suggesting that unionization
reduces income inequality. The exception to this trend is post-fiscal income inequality,
with which neither unionization nor any of the other determinants of interest has any
statistically significant relationship. Top marginal tax rates also appear to have a
substantial impact on changes in income inequality, although interestingly top marginal
capital gains rates rather than income tax rates appear to drive this.27 The effects of the
other determinants have the expected signs for most income concepts. the level of the
minimum wage has reduces inequality while human capital attainment and technological
advancement increase inequality, although these estimated effects are not statistically
different from zero. The estimated effect of unionization appears to have a larger effect
on inequality using pre-transfer or post-transfer income concepts, which is consistent with
unionization primarily affecting wage income. Top marginal tax rates affect both pre-
tax and post-tax income inequality, which suggests that the effect of tax rates working
27This is interesting given that capital gains are not included in any of the income definitions. Changes
in capital gains tax rates may indirectly affect dividend income, however, which is included in the income
definitions.
36
through the elasticity of taxable income rather than the mechanical effect of redistributive
progressive taxes.
TABLE 4. Determinants of State Income Inequality (Pre-transfer and Post-transfer)
Dependent variable:
Pre-transfer Gini Post-transfer Gini
(1) (2) (3) (4) (5) (6)
Union Coverage −0.231∗∗∗ −0.323∗∗∗ −0.327∗∗∗ −0.183 −0.320∗∗ −0.338∗∗
(0.085) (0.108) (0.124) (0.121) (0.142) (0.163)
Minimum Wage −0.0001 −0.001 −0.002 0.0004 −0.001 −0.001
(0.002) (0.002) (0.002) (0.003) (0.002) (0.003)
Capital Gains Tax Rate −0.006∗∗∗ −0.007∗∗ −0.008∗ −0.008∗∗∗ −0.008∗∗ −0.009
(0.002) (0.003) (0.004) (0.002) (0.004) (0.006)
% College Educated 0.077 0.130 0.0001 0.163 0.183 0.062
(0.144) (0.169) (0.178) (0.188) (0.234) (0.247)
Patents per cap. 0.013 0.024 0.015 0.021 0.028 0.013
(0.011) (0.015) (0.023) (0.014) (0.020) (0.028)
Linear Trends? No Yes Yes No Yes Yes
Quad. Trends? No No Yes No No Yes
Observations 1,000 1,000 1,000 1,000 1,000 1,000
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
All models include State and Year fixed effects
Other variables included in regressions but omitted from this table: top marginal income
tax rate, real personal income per capita, the mean and standard deviation of years of
education, % employed in manufacturing, population density, R&D spending per capita, %
black, % Latino, median age, divorce rate, unemployment rate, % over 55, % under 25, %
non-citizens, % foreign born, government expenditures per capita
Tables 6 and 7 report analogous results using the top 1%’s share as a dependent
variable. When examining how the five factors of interest are related to state-level income
inequality when measured by the top 1%’s share of income, largely similar patterns of
estimated effects obtain in terms of signs, although not necessarily significance. Of the
37
TABLE 5. Determinants of State Income Inequality (Post-tax and Post-fiscal)
Dependent variable:
Post-tax Gini Post-fiscal Gini
(1) (2) (3) (4) (5) (6)
Union Coverage −0.160∗∗ −0.220∗∗ −0.195∗ −0.115 0.009 0.001
(0.080) (0.097) (0.113) (0.128) (0.145) (0.173)
Minimum Wage 0.001 0.00002 −0.001 −0.003 0.001 −0.0003
(0.002) (0.002) (0.002) (0.002) (0.003) (0.004)
Capital Gains Tax Rate −0.006∗∗∗ −0.006∗∗ −0.007∗ −0.005 −0.003 −0.005
(0.002) (0.003) (0.004) (0.003) (0.006) (0.007)
% College Educated 0.084 0.082 −0.014 −0.147 −0.056 −0.142
(0.130) (0.157) (0.168) (0.198) (0.271) (0.300)
Patents per cap. 0.012 0.021 0.016 0.004 0.040∗ 0.043
(0.010) (0.014) (0.020) (0.016) (0.023) (0.037)
Linear Trends? No Yes Yes No Yes Yes
Quad. Trends? No No Yes No No Yes
Observations 1,000 1,000 1,000 1,000 1,000 1,000
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
All models include State and Year fixed effects
For more details see Table 4
38
five potential factors outlined above, only the effect of tax rates has an individually
statistically significant effect on the top 1%’s share (although not for all specifications).
TABLE 6. Determinants of State Top 1% Share (Pre-transfer and Post-transfer)
Dependent variable:
Pre-transfer Top 1% Share Post-transfer Top 1% Share
(1) (2) (3) (4) (5) (6)
Union Coverage −0.106 −0.155 −0.206 −0.109 −0.180 −0.248∗
(0.080) (0.110) (0.134) (0.099) (0.123) (0.150)
Minimum Wage −0.001 −0.001 −0.001 −0.0002 −0.0002 0.0003
(0.002) (0.002) (0.003) (0.002) (0.003) (0.003)
Capital Gains Tax Rate −0.007∗∗∗ −0.006 −0.007 −0.009∗∗∗ −0.006 −0.008
(0.002) (0.005) (0.006) (0.002) (0.005) (0.006)
% College Educated −0.034 0.085 −0.011 −0.013 0.052 −0.031
(0.181) (0.230) (0.248) (0.201) (0.251) (0.270)
Patents per cap. 0.010 0.025 0.020 0.012 0.026 0.019
(0.013) (0.017) (0.030) (0.014) (0.018) (0.032)
Linear Trends? No No No No No No
Quad. Trends? No No No No No No
Observations 1,000 1,000 1,000 1,000 1,000 1,000
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
All models include State and Year fixed effects
For more details see Table 4
As noted, although the Generalized Beta II multiple imputation method used to
estimate income inequality attempts to address an important weakness in the current
population survey, the underlying microdata ultimately represent only a sample of top
incomes. As a robustness check for the analysis, I estimate regressions using state-level
estimates of the top 1% share from Frank (2009). Table 8 summarizes these results.
Notably, the estimated effects of all five major factors are qualitatively similar to the
39
TABLE 7. Determinants of State Top 1% Share (Post-tax and Post-fiscal)
Dependent variable:
Post-tax Top 1% Share Post-fiscal Top 1% Share
(1) (2) (3) (4) (5) (6)
Union Coverage −0.067 −0.096 −0.119 −0.144∗∗ −0.141∗∗ −0.153∗
(0.061) (0.082) (0.099) (0.068) (0.071) (0.083)
Minimum Wage 0.0003 0.0003 −0.0003 −0.001 −0.001 −0.001
(0.002) (0.002) (0.002) (0.002) (0.002) (0.002)
Capital Gains Tax Rate −0.005∗∗∗ −0.004 −0.006 −0.002 −0.001 −0.002
(0.002) (0.004) (0.004) (0.001) (0.001) (0.002)
% College Educated −0.041 0.035 −0.042 0.025 0.015 −0.012
(0.140) (0.175) (0.191) (0.125) (0.158) (0.167)
Patents per cap. 0.007 0.017 0.012 −0.001 0.007 −0.009
(0.010) (0.013) (0.022) (0.008) (0.010) (0.015)
Linear Trends? No Yes Yes No Yes Yes
Quad. Trends? No No Yes No No Yes
Observations 1,000 1,000 1,000 1,000 1,000 1,000
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
All models include State and Year fixed effects
For more details see Table 4
40
effects reported in Table 6. In addition, perhaps because the Frank (2009) data contains
the whole population of top incomes, estimated effects are actually more precise here.
In particular, note that at least for some specifications, rates of unionization have
a statistically significant effect on top income shares, as does, interestingly, the real
minimum wage. Top marginal tax rates exhibit a similarly sized effects as in Table 6,
although the estimates are less precise than those for the effects of unionization and
minimum wages.
TABLE 8. Determinants of State Top 1 % Share, Frank (2009) Data
Dependent variable:
(1) (2) (3)
Union Coverage −0.075 −0.172∗∗∗ −0.041
(0.064) (0.057) (0.071)
Minimum Wage −0.005 −0.009∗∗∗ −0.012∗∗∗
(0.003) (0.003) (0.004)
Capital Gains Tax Rate −0.002∗ −0.001 −0.001
(0.001) (0.001) (0.001)
% College Educated 0.085 −0.046 −0.031
(0.133) (0.102) (0.113)
Patents per cap. −0.005 0.005 0.020
(0.014) (0.014) (0.014)
Linear Trends? No Yes Yes
Quad. Trends? No No Yes
Observations 1,000 1,000 1,000
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
All models include State and Year fixed effects
For more details see Table 4
To further explore how these five factors might affect income inequality at different
points along the income distribution, I estimate regressions using the Lorenz ordinates as
dependent variables. Doing so allows me to examine of which factors might be closely
41
related to within-bottom-99% inequality, as opposed to those which are primarily
driving top incomes. Positive coefficients suggest a reduction in income inequality (a
positive coefficient implies an increase in the cumulative income going to incomes below
a given percentile) and negative coefficients imply an increase in income inequality. As
in the previous Lorenz curve inference, examining how estimated effects change across
the distribution has implications about the relevance of the factor in question for top
income inequality versus bottom 99% income inequality. Suppose that E (p;X) is the
“effect curve” for variable X, describing the estimated effect of X on the Lorenz curve at
percentile p. Then if E (p;X) < 0, ∀p or E (p;X) > 0∀p then variable X has an effect
primarily on top incomes. On the other hand, if there is a slope change in the effect curve,
this implies that variable X has an effect primarily on within-99% inequality.
Figure 8 shows the effect of unionization, capital gains tax rates and patents per
capita on Lorenz ordinates for the four income concepts. For each concept save post-fiscal
income, the effect of unionization has its greatest effect around the 80th percentile of the
income distribution, suggesting an effect on income inequality within the bottom 99%.
Top marginal tax rates, have increasing effects across the distribution (at least for pre-tax
inequality), suggesting an effect primarily on top income shares. Similarly, technological
advancement, proxied by patents granted per capita, has an increasing and negative effect
on Lorenz ordinates. This suggests that technology increases top incomes, although these
effects are not statistically significant. It is clear, however, that this is a borderline case:
95% confidence intervals contain only small areas greater than zero.
Of these five potential factors of interest, it can be argued that unionization is the
most important because it has the most robust statistical impact on income inequality.
However, this may be primarily affecting income inequality within the bottom 99% of
the income distribution. Top marginal tax rates are also important, and are probably
42
FIGURE 8. Determinants of Lorenz Ordinates, Selected Covariates
postfiscal posttax
posttrans pretrans
−0.2
0.0
0.2
0.4
−0.2
0.0
0.2
0.4
25 50 75 25 50 75
Lorenz Curve Ordinate
Es
tim
at
ed
 E
ffe
ct
Effect of Unionization on Lorenz Ordinates, by Income Concept
postfiscal posttax
posttrans pretrans
−0.005
0.000
0.005
0.010
0.015
−0.005
0.000
0.005
0.010
0.015
25 50 75 25 50 75
Lorenz Curve Ordinate
Es
tim
at
ed
 E
ffe
ct
Effect of Capital Gains Tax Rates on Lorenz Ordinates, by Income Concept
postfiscal posttax
posttrans pretrans
−0.06
−0.03
0.00
0.03
−0.06
−0.03
0.00
0.03
25 50 75 25 50 75
Lorenz Curve Ordinate
Es
tim
at
ed
 E
ffe
ct
Effect of Patents Per Capita on Lorenz Ordinates, by Income Concept
postfiscal posttax
posttrans pretrans
−0.004
0.000
0.004
0.008
−0.004
0.000
0.004
0.008
25 50 75 25 50 75
Lorenz Curve Ordinate
Es
tim
at
ed
 E
ffe
ct
Effect of Real Minimum Wage on Lorenz Ordinates, by Income Concept
43
responsible for changes in top incomes. Interestingly, variations in human capital
acquisition across states appear to have little to no effect on state-level changes in income
inequality.
Conclusion
This study has generated a new dataset consisting of inequality measures at the
State and MSA level using four different income concepts. The analysis of income
inequality measured using these different income concepts in this paper sheds new light on
the trends in income inequality within sub-national entities. This analysis also deepens our
understanding of which factors may be the driving forces behind rising income inequality.
Using semi-parametric multiple imputation and bootstrap methods, I show that income
inequality has increased substantially over the last two decades, and note that this change
has coincided with both rising top incomes as well as increasing inequality within the
bottom 99% of the distribution.
One important way forward in the study of state-level and MSA-level income
inequality is to attempt to bridge the gap between state-level income inequality datasets
such as Frank (2009) which use tax return data, and the survey based approach taken
here (using CPS microdata). Given matched survey and administrative data, it may be
possible to retain the benefits of both the survey based approach (more information about
household structure and non-taxable income sources) as well as the tax return data (the
full universe of top incomes), while potentially incorporating better administrative data
on program participation for in-kind transfers.28 Fully utilizing all available information
28Leveraging administrative records on transfer payments and participation in in-kind will require
linking these administrative records to Census survey records. This will require access and support of
official statistical agencies.
44
on incomes is important for deepening our understanding of the dynamics of income
inequality.
In addition to the analysis presented in this paper on potential determinants of
state-level inequality, there are a number of potential applications for this data. Several
papers have already made use of this data, including Voorheis (2016), which examines
the effect of income inequality on political polarization, Voorheis et al. (2015), which
examines the effect of income inequality on carbon emissions, as well as Chapter IV of
this dissertation, which uses the MSA-level income inequality dataset to examine the
connection between income inequality and environmental justice.
Income inequality is an important and much-discussed topic of obvious relevance to
both researchers and policymakers. This study has created a novel, and hopefully quite
useful dataset on state-level and MSA-level inequality that corrects for the censoring in
the underlying Census Bureau microdata. This dataset allows for inferences concerning
the trend in inequality since the 1990’s, about which there is some controversy in the
literature. I find that for most states and MSAs, there has been a statistically significant
increase in inequality (either in terms of Lorenz dominance or pairwise comparison of
inequality statistics.) This increase in inequality is driven by both top incomes (i.e. an
increase in the top 1% share) and by increasing disparities in income within the bottom
99%. This inequality increase seems to be driven by a decrease in workers’ bargaining
power (via union density). In contrast, human capital attainment and technological
advancement do not appear to explain the observed changes in income inequality within
the bottom 99%. Insofar as greater inequality is generally considered a poor outcome, one
policy implication is that laws strengthening the institutional position of unions may be an
effective tool for decreasing income inequality as a complement to the redistributive effects
of the tax and transfer system.
45
CHAPTER III
TRENDS IN ENVIRONMENTAL INEQUALITY IN THE UNITED STATES:
EVIDENCE FROM SATELLITE DATA
Introduction
Concerns about air quality and its negative health and ecological impacts are
widespread, both in developed countries and, increasingly, in developing countries. A wide
literature, spawned from the environmental justice movement, has documented differences
across sub-groups in average exposure to pollutants and toxic chemicals. However, little
is known what these differences imply about the overall inequality in the size distribution
of pollution exposure. This paper adds to the stock of knowledge about environmental
inequality by proposing a dashboard approach1, combining recently developed theoretical
tools for measuring environmental inequality with conventional environmental justice
measures. I also examine potential explanations for the variation in this environmental
inequality over time.
To examine trends in, and determinants of, environmental inequality, I utilize
two datasets of satellite-derived observations of ground-level pollution exposure. These
datasets provide fine-grained information about exposure to two important pollutants:
nitrogen oxides (NOx) and particulate matter smaller than 2.5 microns (PM2.5). These
two pollutants are relevant to human health. In addition to the direct health impact of
exposure to NOx and PM2.5, they are both highly correlated with other pollutants (e.g.
ozone) and as such can be taken as an index of overall air quality. These satellite-derived
datasets have been studied widely in other disciplines (e.g. in the atmospheric science
1I borrow the “dashboard” terminology from the multi-dimensional poverty literature, e.g. Alkire and
Foster (2011)
46
literature), however they have not yet found their way into the economics literature. These
data provide several advantages over conventional tropospheric air quality data derived
from ground-level air quality monitors or generated from air quality models using data on
emissions from point sources.
Using these two sources of data, I describe trends in environmental inequality
for the entire United States, as well as for states and major metropolitan areas within
the United States. I consider two different ways of considering the degree to which the
distribution of pollution exposure is “unequal.” The first follows from Sheriff and Maguire
(2014) and defines “environmental inequality” in terms of commonly used inequality
measures adapted from the income distribution literature. The second follows from the
environmental justice literature and quantifies “environmental justice” as the difference in
exposure between advantaged and disadvantaged subgroups. These two concepts can be
viewed as capturing “vertical equity” and “horizontal equity.”2
I examine how traditional environmental justice concerns relate to environmental
inequality (rather than simply average environmental quality) by examining how census-
tract-level demographic characteristics correlate with different measures of environmental
inequality. To accomplish this, I adopt a re-centered influence function (RIF) regression
approach. RIF regression is a general estimation strategy for examining how individual
characteristics affect a summary statistic of a distribution. RIF regressions have been used
mostly in the study of income or wage distributions (e.g. Dube (2013)) and I extend the
use of RIF regressions to the study of pollution exposure distributions.3
2To capture horizontal equity it would be best to compare exposure between groups conditional on
income levels. Doing so is difficult with the group demographic data available at the Census tract level,
however.
3In Appendix C, I further use an extension of Oaxaca-Blinder style decompositions to examine to what
degree observable demographics explain differences in exposure between advantaged and disadvantaged
census tracts across the exposure distribution, and to what degree demographic characteristics appear to
have contributed to changes in exposure across the distribution of exposure over time.
47
I obtain several key results. First, I confirm that the average level of pollution
exposure has decreased since 1998, a result consistent with other studies of trends in
environmental quality. Second, I examine how the measures of environmental inequality
and environmental justice comprising my “dashboard” have changed over time. I find that
most measures in the dashboard are declining over time, with heterogeneity across the two
pollutants of interest. In general, decreases in exposure inequality for NOx have occurred
through decreased exposure at the top of the distribution, while decreases in exposure
inequality for PM2.5 have come via changes at the bottom of the distribution.
By considering more than just average pollution exposure in examining the
correlation between demographic factors and pollution exposure (using RIF regressions),
I can expand upon the usual types of empirical results in the environmental justice
literature. I find that the African American proportion of the population of a census tract
is positively related to the level of pollution in very polluted tracts (increasing inequality),
but the relationship is negative at the median (reducing inequality), and insignificant for
less polluted tracts. However, the African American proportion of a census tract increases
national environmental inequality.
The rest of the paper proceeds as follows. First I briefly discuss the related literature
on environmental justice and inequality. I then describe the data to be used in the
analysis, and the process for assigning pollution exposure levels to each census tract.
I define the various measures of environmental inequality in the “dashboard”, and
investigate trends in exposure inequality, contrasting these to trends just average exposure.
Finally, I present results from re-centered influence function regressions, and conclude with
directions for future work.
48
Previous Literature
There is a large literature, scattered across disciplines, that has attempted to
quantify the degree to which environmental harms might be felt disproportionately by
disadvantaged communities. This literature has arisen at least in part as a response
to activists from the Environmental Justice movement. In fact, this literature takes its
name and often its terminology from these same political advocates, although in practice
most environmental justice scholarship is concerned with documenting environmental
disparities rather than making normative claims about alternative policies to address these
disparities.
One early study by an advocacy group that stimulated the subsequent environmental
justice literature is the so-called UCC study (Chavis and Lee (1987)), which noted
a correlation between the locations of toxic waste sites and local ethnic minority
populations. Subsequent analysis (e.g. Bryant and Mohai (1992)) of toxic waste sites has
confirmed that the African-American population share in a neighborhood is sometimes
an important correlate with the probability that a toxic waste site will be located in a
neighborhood. Other dimensions of disadvantage are also important correlates with toxic
waste siting. Despite this consensus, there remains some disagreement as to whether
this correlation implies racist siting policies by firms or local authorities. Several studies
(e.g. Been and Gupta (1997) and Wolverton (2009)) have persuasively shown that this
correlation may merely capture the subsequent hedonic general equilibrium effects—toxic
waste sites depress local property values, which leads to an inflow of poor, disadvantaged
individuals and an outflow of richer, advantaged individuals. This phenomenon is often
termed “coming to the nuisance.” Among others, Mohai et al. (2009) and Brulle and
Pellow (2006) ably summarize this vast literature.
49
The simple proximity of toxic waste sites to disadvantaged communities was
the primary early concern for the environmental justice literature, but this proximity
itself merely implies exposure without actually measuring it. Measuring the actual
disproportionate exposure to airborne and waterborne toxics and pollutants (and the
negative health impacts of these exposures) has also been a large concern. However, the
measurement of ambient pollution exposure is much more complicated than measuring
proximity to the point locations of fixed toxic waste sites. Studies of disparate pollution
exposure have utilized air pollution models derived from Toxic Release Inventory (TRI)
or National Air Toxic Assessment (NATA) data (e.g. Morello-Frosch and Jesdale (2006),
Zwickl and Moser (2015)) or data from the US Environmental Protection Agency’s (EPA)
network of air quality monitoring stations. At least one paper, by Clark et al. (2014)
has used satellite data on pollution exposure to document spatially disparate exposure
levels. This, and almost all other papers in this literature have considered only single cross
sections of data, and thus have not been able to consider how these disparate impacts
might be changing over time.
The literature has achieved consensus that in any given cross section at a point
in time, disadvantaged communities are exposed to disproportionately high levels of
environmental hazards. However, there is not yet a consensus on how best to summarize
or quantify the extent of these disparities for use either in policy analysis or for the
comparison of trends in the distribution of environmental hazards over time. This
confusion about measurement continues, despite the fact that, at least since Executive
order 12898, issued in 1994, US government agencies have been required to take
environmental justice concerns into account when enacting or changing regulations.
Several approaches to measuring environmental inequality (and environmental
injustice) have been advanced in the literature. The simplest possible measure of
50
environmental justice/injustice is of course just the difference in average exposure between
advantaged and disadvantaged populations—Clark et al. (2014) use this approach. To
address the possibility that there may be differential exposure across the distribution,
Boyce et al. (2016) have proposed comparing quantiles of the race-specific exposure
distributions. Another approach sporadically used by Zwickl et al. (2014), Zwickl and
Moser (2015) and Boyce and Voirnovytskyy (2010) among others has been to import
measurement tools from the income distribution literature to describe environmental
inequality. This approach has been extended and formalized by Maguire and Sheriff (2011)
and Sheriff and Maguire (2014), who adapt several commonly used income inequality
measures to produce normatively sensible conclusions. The important difference between
income and environmental hazards is that environmental hazards are “bads”. The
normative conclusions of unmodified income inequality measures calculated using pollution
exposure data may produce potentially unethical conclusions about policy—someone with
high income is highly advantaged, while someone with high pollution exposure is highly
disadvantaged.
In this paper, I advance the literature on environmental inequality and
environmental justice along several dimensions. First, I extend the use of satellite data
first used by Clark et al. (2014) to study environmental justice beyond a single cross-
section. This allows me to describe not just disparities in exposure across groups at a
point in time, but also how these disparities have been changing. Second, I propose a
dashboard approach to environmental justice analysis by cataloging and categorizing
different measures which quantify disparities in pollution exposure. I apply these measures
both to document how environmental inequality has been changing over time, and also to
reveal potential correlates of these changes in environmental inequality.
51
Data and Institutional Details
Any examination of the distribution of pollution exposure across space and across
sociodemographic groups requires measurements of ground-level pollutant concentrations
at a relatively fine spatial scale. Ideally, I would like to observe the actual exposure of
each individual as they go about their day. Such a dataset is infeasible without a universal
monitoring regime, a prospect that seems unlikely outside of a George Orwell novel. As
a next best alternative, I will estimate pollution concentrations at the level of US census
tracts.4 I can then estimate measures of inequality and environmental justice measures
using these concentrations, weighted by tract population. These measures of inequality can
be interpreted as the inequality across individuals in exposure.
There are two limitations that come with using tract-level average pollution
concentrations to estimate pollution exposure inequality or environmental justice
measures. First, weighting by tract population essentially assigns the tract-average
exposure to each individual residing in the census tract. This is equivalent to assuming
no tract-level inequality in pollution exposure. Second, using ground-level concentrations
as a measure of exposure ignores potential adaptation behavior on the part of individuals.
Adaptation behavior may further be related to sociodemographic characteristics such as
income, especially if adaptation requires purchasing expensive equipment. If likelihood
to engage in adaptation is positively related to, e.g. income, then tract-level average
concentrations will over-estimate the exposure of rich individuals, and hence underestimate
the gap in exposure between the rich and the poor. Thus each of these limitations
suggest that using tract-level average concentrations to calculate exposure inequality and
environmental justice measures will produce a lower bound estimate.
4Due to the limitation in spatial coverage of the satellite data, I am only able to calculate tract-level
concentrations for the contiguous United States.
52
This paper capitalizes on the use of two novel sources of data on pollution exposure
derived from remote sensing satellite observations. The first dataset, described in detail by
Lamsal et al. (2008), infers ground-level NOx concentrations using a chemical air transport
model and observations of the tropospheric vertical column densities of NOx. The second
dataset, described in detail by van Donkelaar et al. (2016), infers ground-level PM2.5
concentrations from aerosol optical depth observations from multiple satellite sources.5
Each of these datasets is available at relatively fine geographic resolution—the NOx
data are on a (0.1 × 0.1)-degree grid, while the PM2.5 data are on a (0.01 × 0.01)-degree
grid (this corresponds to 10 km and 1 km at the equator, respectively). Both datasets
provide observations for most of the globe, spanning approximately 70 degrees S through
70 degrees N. These datasets provide substantially more-comprehensive spatial coverage
than measurements of ground level exposure from unevenly distributed fixed monitors. By
way of comparison, note that there are about 500 NOx monitors in the EPA’s monitoring
network, while there are 100,000 uniformly distributed fixed geographic grid points within
the contiguous United States in the NOx satellite data.
To infer person-level exposure to NOx and PM2.5 respectively, it is necessary to link
information on the detailed spatial variation in remotely sensed ground-level pollutant
concentrations with information about where people are located. In the absence of any
more-fine-grained information about the spatial distribution of households, I assume
that each person in a census tract is exposed to, the average ground-level pollutant
concentration at the population-weighted centroid of her Census tract. For each satellite
data source in each year, I interpolate over the fixed grid to the centroid of each census
tract using inverse distance weighting. I use all gridpoints within a 10km radius from the
5These datasets are provided for public use by the Atmopsheric Composition Analysis Group at
Dalhousie University, and can be accessed at http://fizz.phys.dal.ca/~atmos/martin/
53
centroid of a census tract in calculating the IDW estimate of tract-level exposure.6 I using
this IDW interpolation, I obtain annual average concentrations for PM2.5 for each year
from 1998-2014, and for NOx from 2005-2011.
The spatial distribution of person-level exposure to PM2.5 and NOx can be
visualized using a choropleth map, as in Figure 9, which visualizes the data on exposure
to PM2.5 and NOx for 2005 for the contiguous United States. At this point in time, it is
clear that pollution exposure is concentrated in urban areas, although elevated ambient
exposure levels are also present in large parts of the rural eastern US. These higher
exposures may be in part due to this region’s relatively heavy reliance on coal-fired power
plants for electricity generation. Coal-fired power plants are a major source of emissions of
chemical precursors to NOx and PM2.5.
On average, pollution exposure has been declining over the sample periods for
the two satellite-derived pollution exposure datasets. Figure 10 shows the population-
weighted annual average exposure to PM2.5 and NOx exposure for the contiguous US. The
PM2.5 data span the period 1998–2014, while the NOx span 2005–2011. NOx and PM2.5
exposure have both also decreased markedly over these periods. Both datasets suggest
that decreases in exposure to pollution were most pronounced in the period before 2008.
After 2008, average exposure to both NOx and PM2.5 continued to decline, but at a slower
rate than the previous period.
Quantifying Environmental Inequality and Environmental Justice
Using two independent satellite-derived datasets, it is clear that average pollution
exposure has decreased markedly since the 1990s. There are a number of ways, however,
in which this reduction in average pollution exposure could have occurred. The uneven
6Because of the differing resolution of the gridded data, this translates to using the 4 nearest gridpoints
for the NOx data, and the 100 nearest gridpoints for the PM2.5 data.
54
FIGURE 9. Annual Average PM2.5 and NOx Exposure, 2005
55
FIGURE 10. National Average NOx Exposure (in ppb), 2005-2011
1.50
1.75
2.00
2.25
2.50
2006 2008 2010
year
Av
e
ra
ge
 N
O
x 
Ex
po
su
re
National Average NOx Exposure
10
12
14
16
18
2000 2005 2010
year
Av
e
ra
ge
 P
M
2.
5 
Ex
po
su
re
National Average PM2.5 Exposure
distribution of these pollution exposure reductions is of particular interest. Any effort to
explore how the changes in the distribution of pollution exposure that have accompanied
the average improvements in environmental quality requires some methods for quantifying
pollution exposure inequality, and normative tools to rank distributions according to some
social evaluation function.
Rather than seeking to identify a single measure which summarizes the distribution
of pollution exposure across and within different groups, and its relation to other
dimensions of disadvantage, I propose a “dashboard” consisting of several different
measures which together can be used for distributional policy evaluation. Considering the
whole dashboard provides a transparent view of how the distribution of pollution exposure
is evolving that is resistant to cherry-picking individual measures to provide ex-post
justification for preferred policy. This dashboard considers two ways of thinking about the
distribution of pollution exposure. The first, which I term “environmental inequality” can
be viewed as a vertical equity concept. Environmental inequality measures summarize the
56
size distribution of pollution exposure while preserving anonymity of the exposed — the
identities of the exposed individuals do not matter, only their exposure levels. The second
type, which I term “environmental justice”, can be viewed as a horizontal equity concept,
and summarizes the distribution of pollution exposure across demographic categories.
The measurement of environmental inequality can adapt some of the methods used
in the literature on the measurement of income inequality. However, it is not immediately
obvious that one can simply calculate income inequality measures using pollutant
concentration and obtain ethically sensible measures of environmental inequality. Pollution
exposure, unlike income, is a ”bad”, which means that “advantage” in pollution exposure
runs in the opposite direction from “advantage” in income. Thus the bottom 10% of the
pollution exposure distribution is actually the most advantaged segment of society along
an environmental dimension, whereas the bottom 10% of the income distribution is the
most disadvantaged segment of society along the income dimension.
One apparently straightforward way to transform the distribution of a “bad” into a
good, suggested by Sheriff and Maguire (2014) is to “reverse the sign”—use the negative
values of pollutant concentrations when calculating measures of environmental inequality.
This has the appeal of imposing the intuitively “correct” (or ethically sensible) ordering.
Individuals experiencing the largest absolute value of pollutant concentration are now
at the bottom of the distribution, and those who experience the lowest absolute value
of pollution exposure are at the top. The environmental inequality components of the
“dashboard” consist of three variants of the Lorenz curve, and two scalar environmental
inequality measures (the Atkinson index and the Kolm-Pollak index).
First, I consider the relative Lorenz curve
L (p) =
1
µ
∫ F−1(p)
−∞
xf (x) dx
57
Each ordinate L (p) can be estimated with discrete data by the Kovacevic and Blinder
(1997) estimator:
Lˆ (p) =
1
Nˆ µˆ
∑
wiyiI
(
yi ≤ F−1 (p)
)
where the wi are weights, Nˆ =
∑
wi, and µˆ is the weighted mean of the outcome.
Pollution concentrations are expressed as negative quantities, so the Lorenz curve will
lie above the line of perfect equality, contrary to the “usual” case of the income-based
Lorenz curve. For any two distributions 1 and 2, Lorenz dominance of distribution 2 over
distribution 1 requires
L2 (p) ≤ L1 (p) ∀p ∈ [0, 1]
For any two equal-mean distributions, relative Lorenz dominance has normative content: a
relative Lorenz dominating distribution would be preferred by every concave social welfare
function, as shown by Maguire and Sheriff (2011). Even for distributions with unequal
means, the relative Lorenz curve can still provides useful information about the fairness of
the distributions, although it no longer generates a unanimous ordering of distributions by
all concave social welfare functions.
Second, I consider the Generalized Lorenz curve, which is just the relative Lorenz
curve scaled by the mean of the outcome distribution (in this case, mean pollution
exposure):
GL (p) = µL (p) =
∫ F−1(p)
−∞
xf (x) dx
Generalized Lorenz ordinates can be estimated by a modification of the Kovacevic and
Binder (1997) estimator:
GˆL (p) = µˆLˆ (p) =
1
Nˆ
∑
wiyiI
(
yi ≤ F−1 (p)
)
58
The Generalized Lorenz dominance condition is the same for pollution the income
generalized Lorenz dominance criteria from Shorrocks (1983):
GL2 (p) ≥ GL1 (p)∀p ∈ [0, 1]
Generalized Lorenz dominance takes into account the outcome distribution as well as the
average level of the outcome. The normative content of generlized Lorenz dominance is
more general than the relative Lorenz case—any concave social welfare function will prefer
the Generalized Lorenz dominant distribution, regardless of the means of either of the
distributions.7
I also consider the absolute Lorenz curve proposed by Moyes (1987), which captures
the absolute cumulative gap in exposure between the overall average exposure µ, and the
average exposure of the bottom pth percent of the population. The absolute Lorenz curve
can be expressed as
AL (p) =
∫ F−1(p)
−∞
(x− µ) f (x) dx
However, note that the absolute Lorenz curve can be expressed in terms of either the
relative Lorenz or generalized Lorenz curves:
AL (p) = µ (L (p)− p)
or
AL (p) = GL (p)− µp
7The transformation of the pollution exposure data ensures that this result, proved by Shorrocks (1983)
for income, will hold for pollution exposure
59
Hence it is possible to modify the Kovacevic and Binder (1997) estimator for the absolute
Lorenz case:
AˆL (p) =
1
Nˆ
∑
wiyiI
(
yi ≤ F−1 (p)
)− µˆp
where µˆ is the mean exposure, weighted by tract population. Absolute Lorenz dominance
requires
AL2 (p) ≥ AL (p) , ∀p ∈ [0, 1]
Absolute and relative Lorenz curves are measuring the the two “unequal inequalities”
concepts of Kolm (1976). The absolute Lorenz curve captures an absolute environmental
inequality concept summarized by its translation invariance property: if every individual’s
pollution exposure increases by a constant amount, the Absolute Lorenz ordinates are
unchanged. In contrast, the relative Lorenz curve captures a relative inequality concept
captured by its scale invariance property: if every individual’s pollution exposure increased
by a constant proportion, the relative Lorenz ordinates would be unchanged.
None of these variants of the Lorenz curve guarantee a complete ordering of
distributions. If any pair of these Lorenz curves cross, then no normative conclusion is
possible. In income distribution studies, scalar indices (e.g. the Gini coefficient) are often
used to induce a complete ordering of distributions. However, it is not clear that many
of the most common inequality measures used in the income distribution literature are
directly applicable to a case where the distribution concerns a bad (or a transformation
of a bad, in this case). Sheriff and Maguire (2014) show that a transformation of
the Atkinson index induces a complete and sensible orderings of pollution exposure
distributions. The transformed Atkinson index is
IA =
(
1
N
∑(xi
x¯
)1+α) 11+α
− 1
60
where α is an inequality aversion parameter. I modify this formula so that I can weight by
tract populations wi
IˆA =
(
1
Nˆ
∑
wi
(xi
x¯
)1+α) 11+α
− 1
where Nˆ =
∑
wi, and x¯ is the weighted mean of the outcome distribution. The Atkinson
index has a normative interpretation. It is derived from a specific welfare function,
so it directly ranks income distributions (higher Atkinson indices are less preferred).
Additionally, the transformed Atkinson index has a cardinal interpretation. The Atkinson
index of environmental inequality can be interpreted as the percent increase in the average
pollution exposure necessary to maintain a constant level of welfare, if that higher average
pollution exposure level were to be distributed equally.
The Atkinson index, like the relative Lorenz curve, embeds a relative inequality
concept that corresponds to scale invariance: it aggregates ratios rather than gaps. Sheriff
and Maguire (2014) show that the Kolm-Pollak index is a suitable absolute inequality
measure. The Kolm-Pollak index, like the Absolute Lorenz curve, embeds an absolute
inequality concept corresponding to translation invariance. The Kolm-Pollak Index is
defined as
KI (x) = −1
κ
ln
1
N
N∑
i=1
e−κ(xi−µx), κ < 0 (3.1)
where κ can be interpreted as an environmental inequality aversion parameter for the
associated social welfare function.
In addition to these five vertical equity (environmental inequality) measures, I
include two measures of horizontal equity (environmental justice) in the “dashboard.”
These measures be capture by differences in exposure between demographic subgroups.
I follow the environmental justice literature and focus on differences in exposure by race
and ethnicity, specifically on the difference in exposure between non-Latino whites and
61
African-Americans. The first of these horizontal equity measures is a simple comparison
in averages, calculating the difference in average exposure between subgroups. The second
compares the distributions across subgroups by calculating the differences in exposure at
percentiles of the race-specific exposure distribution (i.e. comparing the 10th percentile of
the African-American exposure distribution to the 10th percentile of the white exposure
distribution.)
Trends in Environmental Inequality and Environmental Justice
Having defined this dashboard of measures to capture environmental inequality and
environmental justice, it is possible to examine how environmental inequality has changed
over time, utilizing the new satellite data on PM2.5 and NOx exposure that have not
been widely studied by environmental economists. This use of ambient air pollution as
an environmental disamenity in the study of environmental justice is in contrast to some
earlier literature focusing on proximity to toxic sites. Concerns about discriminatory siting
are less important when studying the distribution of pollution exposure.8
As with the calculation of average exposure levels, it is necessary to match ground-
level pollutant concentrations with census tract population data to calculate the various
environmental inequality and environmental justice measures. To fill in the gaps between
the 2000 Census and the American Community Survey, I linearly interpolate between
decennial censuses to estimate each census tracts’ population and racial demographics
from 2001-2004, and use weighted averages of overlapping ACS 5-year file estimates for
the period 2005-2014. I will calculate each of the components of the dashboard for the
contiguous US using the tract-level pollution exposure and population data
8Note however that there are steep gradients in exposure near freeways, as shown by Currie and Walker
(2011), which combined with the routing of freeways through minority or poor neighborhoods could be
seen as an analogue to discriminatory siting of toxic facilities.
62
Trends in the scalar environmental inequality measures are summarized in Figure
11 for the Kolm-Pollak index and 12 for the Atkinson Index. Absolute environmental
inequality has generally seen a downward trend for both types of pollutants over the
relevant sample, although decreases in the Kolm-Pollak index appear to have slowed in the
period after 2007 or so. Relative environmental inequality has a less clear overall trend,
on the other hand. NOx exposure is consistently more unequally distributed than PM2.5
according to the Atkinson index, but both pollutants exhibit seem to behave in a roughly
stationary way over time.
FIGURE 11. Kolm-Pollak Index, PM2.5 and NOx
2
3
4
2000 2005 2010
year
PM
2.
5 
Ko
lm
−P
o
lla
k 
In
de
x
National PM2.5 Exposure Inequality (Kolm−Pollak Index)
0.50
0.75
1.00
2006 2008 2010
year
Ko
lm
−P
o
lla
k 
In
de
x,
 N
O
x
Absolute NOx Exposure Inequality (Kolm−Pollak Index)
Examining the three variants of the Lorenz curve can shed some light on which parts
of the pollution exposure distribution may be driving the scalar inequality trends seen for
the Kolm-Pollak and Atkinson indexes. Select relative Lorenz curves are shown for the
period 2005-2011 for NOx and for PM2.5 from 1998-2014 in Figure 13. Relative Lorenz
curves provide unambiguous inference about environmental inequality, since the relative
Lorenz curves for, e.g. 2005 and 2011 cross at least once. Note that, unlike the relative
63
FIGURE 12. Atkinson Index, PM2.5 and NOx
0.0125
0.0150
0.0175
0.0200
2000 2005 2010
year
PM
2.
5 
At
ki
ns
on
 In
de
x
National PM2.5 Exposure Inequality (Atkinson Index)
0.09
0.10
0.11
0.12
2006 2008 2010
year
N
O
x 
At
kin
so
n 
In
de
x
Relative NOx Exposure Inequality (Atkinson Index)
Lorenz curves for NOx, the largest changes in the PM2.5 relative Lorenz curve seem to be
concentrated in the more advantaged (less exposed) part of the exposure distribution.
One the other hand, the point estimates of the the absolute and generalized Lorenz
curves are more unambiguous. Figure 14 visualizes the absolute Lorenz curves calculated
for NOx from 2005-2011, and for PM2.5 from 1998-2014. Absolute Lorenz curves for NOx
exposure are higher in 2011 than 2005 throughout the exposure distribution, and absolute
Lorenz curves for PM2.5 are similarly higher in 2014 versus 1998. Similar results hold
for generalized Lorenz curves, summarized in Figure 15 These results are suggestive of
absolute and generalized Lorenz dominance for both NOx and PM2.5.
The trends in the horizontal equity (environmental justice) components of the
dashboard show similar evidence of increasing equality over time. Figure 16 shows
the trends in the gap between the average exposure of African-Americans and whites
for PM2.5 and NOx. For both pollutants, this gap has shrunk considerably over the
duration of the sample, falling by a factor of almost two for PM2.5. Note that since the
64
FIGURE 13. Relative Lorenz Curves, NOx (2005-2011) and PM2.5 (1998-2014)
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
Cumulative Proportion of People
Cu
m
u
la
tiv
e
 P
ro
po
rti
on
 o
f E
xp
os
ur
e
Year
2005
2007
2009
2011
Lorenz Curves, 2005−2011, NOx
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
Cumulative Proportion of People
Cu
m
u
la
tiv
e
 P
ro
po
rti
on
 o
f E
xp
os
ur
e
Year
1998
2002
2006
2010
2014
Lorenz Curves, 1998−2014, PM2.5
FIGURE 14. Absolute Lorenz Curves, NOx (2005-2011) and PM2.5 (1998-2014)
−0.6
−0.4
−0.2
0.0
0.00 0.25 0.50 0.75 1.00
Cumulative Proportion of People
Cu
m
u
la
tiv
e
 E
xp
os
ur
e 
G
ap
Year
2005
2007
2009
2011
Absolute Lorenz Curves, 2005−2011, NOx
−2.0
−1.5
−1.0
−0.5
0.0
0.00 0.25 0.50 0.75 1.00
Cumulative Proportion of People
Cu
m
u
la
tiv
e
 E
xp
os
ur
e 
G
ap
Year
1998
2002
2006
2010
2014
Absolute Lorenz Curves, 1998−2014, PM2.5
65
FIGURE 15. Generalized Lorenz Curves, NOx, 2005-2011
−2.0
−1.5
−1.0
−0.5
0.0
0.00 0.25 0.50 0.75 1.00
Cumulative Proportion of People
Cu
m
u
la
tiv
e
 A
ve
ra
ge
 E
xp
os
ur
e
Year
2005
2007
2009
2011
Generalized Lorenz Curves, 2005−2011, NOx
−15
−10
−5
0
0.00 0.25 0.50 0.75 1.00
Cumulative Proportion of People
Cu
m
u
la
tiv
e
 A
ve
ra
ge
 E
xp
os
ur
e
Year
1998
2002
2006
2010
2014
Generalized Lorenz Curves, 1998−2014, PM2.5
two pollutants are measured in different units, the two black-white gaps are not directly
comparable. Black-white ratios are unit-free and hence directly comparable, however, and
are shown in Figure 17. Note also that the time periods of the two datasets differ, with no
NOx observations before 2005. In the overlapping period of time (2005-2011), the black-
white gap for NOx has a clear downward trend while the trend for PM2.5 is less clear.
There are, of course, a number of ways in which the gap in exposure between two
subgroups may have decreased, as is the case for both NOx and PM2.5 exposure from
the beginning to the end of the relevant time periods. In the case of NOx, the reduction
in the gap in exposure between blacks and whites has occurred because average black
exposure was declining faster than average white exposure. Average black exposure to
NOx declined from 2.89 ppb in 2005 to 1.71 in 2011 (a decline of 1.17 ppb) , while average
white exposure declined from 2.27 ppb in 2005 to 1.35 in 2011 (a decline of only 0.92
ppb). A similar trend is evident in the decline in the black-white gap in PM2.5 exposure.
Average black exposure declined from 20.73 µg/m3 in 1998 to 9.75 in 2014 (a decline of
10.97 µg/m3, while average white exposure to PM2.5 declined from 18.08 µg/m3 in 1998
66
FIGURE 16. National Black-White Exposure Gap, PM2.5, 1998-2014 and NOx, 2005-2011
0.5
1.0
1.5
2.0
2.5
2000 2005 2010
year
Av
e
ra
ge
 P
M
2.
5 
Bl
ac
k−
W
hi
te
 G
ap
National Average PM2.5 Black−White Gap
0.35
0.40
0.45
0.50
0.55
0.60
2006 2008 2010
year
Bl
ac
k−
W
hi
te
 N
O
x 
Ex
po
su
re
 G
ap
National Average Black−White NOx Exposure Gap
to 8.83 µg/m3 in 2012 (a decline of 9.25 µg/m3). Thus the decline in the black white gap
for both pollutants represents not just absolute but also relative improvements for the
disadvantaged group.
One way to examine how this trend of reduction in the average difference in exposure
across racial groups has played out across the exposure distribution is to examine how
the gap in exposure between blacks and whites has evolved at specific percentiles of the
exposure distribution. Figure 18 shows the black-white percentile gap curves for PM2.5
from 1998-2014 and NOx from 2005-2011 respectively. For PM2.5, a notable feature of
the percentile gap curves in each year is that the gap in exposure is actually larger at
the less exposed part of the exposure distribution. This may reflect in part the differing
rural/urban population distributions across the two groups. The percentile gap curve has
flattened over the period 1998-2014, largely due to the decline in the gap at low levels of
exposure. Environmental justice with respect to NOx appears to have evolved in roughly
the opposite manner, however. The black-white exposure gap is much larger at the highly
67
FIGURE 17. National Black-White Exposure Ratio, PM2.5, 1998-2014 and NOx, 2005-
2011
1.06
1.08
1.10
1.12
1.14
1.16
2000 2005 2010
year
Bl
ac
k−
W
hi
te
 P
M
2.
5 
Ex
po
su
re
 R
at
io
National Average Black−White PM2.5 Exposure Ratio
1.25
1.26
1.27
2006 2008 2010
year
Bl
ac
k−
W
hi
te
 N
O
x 
Ex
po
su
re
 R
at
io
National Average Black−White NOx Exposure Ratio
exposed end of the distribution, and the flattening of the percentile gap curve have largely
occurred through upper percentile gap reductions.
The evidence on whether the distribution of pollution exposure has become more
unequal is not consistent across the measures in the dashboard. One way of synthesizing
the evidence presented thus far is to examine the common features of the measures
which show relatively unambiguous evidence of decreasing inequality in contrast to those
measures for which such evidence is ambiguous. The Kolm-Pollak index, the absolute
Lorenz curve and the gap in average exposure between blacks and whites all point towards
declining exposure inequality, while the Atkinson index, relative Lorenz curve and black-
white exposure ratio all show somewhat ambiguous trends over time.9 Each of the former
group of measures aggregates, in one way or another, differences in absolute exposure,
while the latter group aggregates relative exposure. Thus, the trends in inequality in these
9The generalized Lorenz curve also shows declining inequality, although this is driven by declines in
overall average exposure.
68
FIGURE 18. National Black-White Exposure Gap, by Percentile (PM2.5 and NOx)
1998 1999 2000 2001 2002
2003 2004 2005 2006 2007
2008 2009 2010 2011 2012
2013 2014
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
0
1
2
3
4
5
0.25 0.50 0.75 0.25 0.50 0.75
percentile
Bl
ac
k/
W
hi
te
 P
M
2.
5 
Ex
po
su
re
 G
ap
Black/White PM2.5 Exposure Gap, by Percentile
2005 2006 2007
2008 2009 2010
2011
−1
0
1
2
3
4
−1
0
1
2
3
4
−1
0
1
2
3
4
0.00 0.25 0.50 0.75 1.00
percentile
Bl
ac
k/
W
hi
te
 E
xp
os
ur
e 
G
ap
Black/White NOx Exposure Gap, by Percentile
two groups of measures in the dashboard are consistent with more or less proportional
declines in pollution exposure across the pollution exposure distribution. This, in
turn, implies greater absolute improvements (declines in exposure) for disadvantaged
populations.
In general, the above patterns point toward the conclusion that average exposure to
NOx and PM2.5 has decreased, and so has the inequality in this exposure. These results
are less clear for the relative measure of environmental inequality than for measures
capturing absolute environmental inequality. The two pollutants have very different
cross-sectional distributions, and the two pollutants’ exposure distributions have evolved
in different ways. Nonetheless the most robust finding is that not only has exposure to
these two pollutants been decreasing over time, it is also likely becoming more equally
distributed.
69
Explaining the Distribution of Pollution Exposure
The trends in the distribution of pollution exposure at the national level point
to both a decrease in average pollution exposure and a decrease in pollution exposure
inequality. There are a number of potential reasons for this trend. In the context of the
environmental justice literature, it is perhaps most interesting to consider how these
changes may be related to the underlying demographics of the relevant geographic units
(here, census tracts). I will examine the relationship between tract-level demographics
and the distribution of pollution exposure by utilizing re-centered influence function (RIF)
regressions to describe the variation in a functional of the national pollution exposure
distribution as a function of tract-level demographics.10
Re-centered Influence Function Regressions
The RIF regression method is a way to estimate the effect that variation in
individual characteristics might affect a functional of the entire distribution. This
method has been used most extensively in the income distribution literature, where
the distributional functional is often the quantile function. In the quantile case, the
RIF regression can be interpreted as an unconditional quantile regression Firpo et al.
(2009). Essentially any functional of the distribution in question can be used in an RIF
regression. Essama-Nssah and Lambert (2012) catalog the RIFs for most commonly used
distributional functionals, including the Lorenz and Generalized Lorenz curve ordinates.11
I use RIF regressions to attempt to explain how census tract demographics may be
10Additionally, RIF regressions can be used to perform a decomposition analysis of the change in
exposure over time, and of the difference in exposure between diverse and non-diverse census tracts, as
in Appendix C.
11Essama-Nssah and Lambert (2012) also provide an expression for the standard Atkinson index, but
not for the transformed Atkinson index from Sheriff and Maguire (2014).
70
related to the observed trends in environmental inequality noted above. Recentered
influence function regressions have become an increasingly popular way of estimating
distributional effects, both in the conventional wage or income distribution setting (e.g.
Zhu (2016), Essama-Nssah and Lambert (2016), Dube (2013)) as well as in the study of
health inequality (e.g. Heckley et al. (2016), Gaskin et al. (2015)) but have not been used
in the study of environmental inequality.
To review, the influence function is an analytic device commonly used in robust
statistics. For a distribution of outcome variable y and a distributional functional ν, the
influence function IF (y, ν) describes how each individual’s observed y affects ν (F (y)).
Mathematically, the influence function is merely the directional derivative of the functional
from the observed distribution towards a distribution with all probability weight at
observed outcome y. The re-centered influence function merely adds the functional back
into the influence function: RIF (y, ν) = IF (y, ν) + ν (F (y)). Assuming that the
conditional expectation of the RIF is a linear function of some observable demographic
characteristics X, so that
E (RIF (y, ν)) = βX
then the parameters β can be estimated via OLS.
Estimating these RIF regressions can be seen as an extension of a common technique
used in the environmental justice literature. In this commonly used (e.g. by Morello-frosch
et al. (2002) and Clark et al. (2014)) technique, some measure of environmental hazard
(e.g. number of toxic sites or air pollutant concentrations) in a neighborhood or census
tract is regressed on neighborhood characteristics. Note that the RIF for the mean is
RIF (y, µ) = y
71
so that the usual linear regression E (y|X) = βX is a special case of the RIF regression.
Thus the RIF regression method I propose in fact nests the commonly used regressions in
the environmental justice literature, but allowing for functionals other than the mean as
outcomes.
I will consider four such functionals: the quantile function, and ordinates of each
of the three Lorenz curve variants: the relative, generalized and absolute Lorenz curves.
Following Essama-Nssah and Lambert (2012), the RIF for the pth quantile is
RIF (y,Q (p)) =

Qˆ (p) + p
f(Qˆ(p))
y > Qˆ (p)
Qˆ (p)− 1−p
f(Qˆ(p))
y < Qˆ (p)
where Qˆ is the empirical quantile point at p. The RIF for the pth Lorenz curve ordinate is
RIF (y, L (p)) =

y−(1−p)Qˆ(p)
µy
− Lˆ (p) y
µy
y < Qˆ (p)
pQˆ(p)
µy
− Lˆ (p) y
µy
y ≥ Qˆ (p)
where Lˆ (p) is the pth empirical Lorenz ordinate. Finally, the RIF for the pth Generalized
Lorenz ordinate is
RIF (y,GL (p)) =

y − (1− p) Qˆ (p) y < Qˆ (p)
pQˆ (p) y ≥ Qˆ (p)
Finally, absolute inequality in pollution exposure, and not just the relative inequality
captured by the relative Lorenz and Generalized Lorenz curves is of interest. A suitable
way of capturing this is the absolute Lorenz curve due to Moyes (1987). The Absolute
72
Lorenz curve is defined as
AL (p) = GL (p)− pµ
Because the recentered influence function is a linear operator, I can use the previous
expressions (plus the fact that RIF (µ (y)) = y) to define a recentered influence function
for the absolute Lorenz curve:
RIF (y, AL (p)) =

y − (1− p) Qˆ (p)− py y < Qˆ (p)
pQˆ (p)− py y ≥ Qˆ (p)
Or, more compactly, RIF (y, AL(p)) = RIF (y,GL (p))− py
Firpo et al. (2009) show that in the case of the quantile function, the estimated
coefficients of an RIF regression can be interpreted as “unconditional partial effects”,
namely the effect of a small location shift in the distribution of X on the functional
ν (F (y)). This logic directly extends to the Lorenz curve cases. The unconditional partial
effects estimated from an RIF regression allow for the examination of how demographic
characteristics of census tracts are related to the distributional statistics of interest, but
they do not directly speak to how demographics might be driving the observed trends in
environmental inequality above.12
RIF Results
I first report the results of RIF regressions estimated using pooled data from 2005
through 2011. I supplement the data on tract-level NOx and PM2.5 exposure with
tract-level demographic data from the ACS 5-year summary files. The ACS provides
12However, the RIF regression method can be used to perform a decomposition analysis that can
address this concern. This decomposition, performed in Appendix C allows for an examination of the
extent to which demographics have shaped the change in environmental inequality over time.
73
data on racial and ethnic composition, median income, poverty status, age distribution,
employment and educational status at the census tract level. However, these estimates
are only released as 5-year average summary files (2005-2009, etc). To back out yearly
estimates of the sociodemographic variables, I take a weighted average of all the five year
file estimates that contain a given year.13 So for instance, the estimate for 2005 is merely
the 2005-2009 5-year file estimate, but the estimate for 2007 is an average of the estimates
from the 2005-2009, 2006-2010, and 2007-2011 5 year files.14 The environmental justice
literature suggests that variables capturing various types of “disadvantage” will be of
interest. I will highlight in particular the proportion of the census tract that is African-
American, proportion Latino, and proportion under the poverty line, the proportion with
only a high school degree and the proportion with less than a high school degree.
My empirical strategy is to estimate a fixed-effects version of the RIF regression
outlined above:
RIFi,t = δi + δt + γ1Blacki,t + γ2Latino+ γ3Poverty + γ4HS +Xi,tβ + ei,t
where δi, δt are census tract and year fixed effects, and Xi,t is a vector of other
sociodemographic variables.15 I repeat this for four different distributional functionals
— quantiles, relative Lorenz ordinates, Absolute Lorenz ordinates and Generalized
Lorenz ordinates. For each functional, I will estimate separate regressions for each
p ∈ {0.05, 0.1, ..., 0.95}. Note that this linear and additively separable specification may
13The weights are linearly increasing in the difference between the middle year of the 5-year file and the
year I want an estimate for, placing more weight on files that contain more years that are “closer” to the
year in question.
14This approach is admittedly imperfect, and may induce measurement error. Other alternatives to
matching 5-year ACS files to annual data are similarly imperfect, which highlights the limits of the data
being used in this study.
15See Table 9 for a full list of covariates.
74
be subject to multicollinearity if the relevant degrees of disadvantage are correlated.16
However, note that among the independent variables, there are no pairwise correlations
above 0.85 in absolute value in the estimating sample.
Tables 9 and 10 summarize the results for RIF regressions estimated using quantiles
as the distributional statistic(s) of interest for NOx exposure and PM2.5 exposure
respectively. There is some evidence for a correlation between the minority population of
census tracts — blacker and more heavily Hispanic tracts are more likely to be exposed to
higher amounts of NOx and PM2.5. There is interesting heterogeneity; the proportion of a
tract’s population that is black has statistically significant and positive effects on exposure
mostly in less-exposed tracts, while the opposite is true for Hispanic populations. Median
tract income appears to be positively related to exposure at the more exposed end of the
exposure distribution, although this may be a function of the fact that high income tracts
are often found in central cities (with concomitant higher levels of exposure).
The unconditional quantile partial effect of a tract’s population proportion black is
actually negative at the top of the exposure distribution. This implies that tracts with
higher concentrations of African Americans are actually less exposed, at least at the highly
exposed end of the exposure distribution. The effect of educational attainment within
tracts is highly varied across the distribution; tracts with higher high school drop out
populations are more exposed at the bottom of the exposure distribution, while the high
school-only population is related to higher exposure near the top of the distribution.
Tables 11 and 12 summarizes the results of RIF regressions estimated using
the Lorenz curve ordinates as the distributional functionals of interest. Due to the
multiplication of raw NOx exposure by −1 in calculating the Lorenz curve ordinates,
the Lorenz curve will lie strictly above the line of perfect equality. This means that
positive coefficient estimates imply an increase in environmental inequality in conjunction
16One possible way to test for the appropriateness of the specification would be to more fully saturate
the model with interaction terms.
75
TABLE 9. Quantile RIF Regression Results (NOx Exposure)
Dependent variable:
NOx Quantiles
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
(1) (2) (3) (4) (5)
Black 0.124∗∗∗ 0.149∗∗∗ −0.065 −0.620∗∗∗ −2.141∗∗∗
(0.041) (0.046) (0.073) (0.153) (0.403)
Latino −0.064 −0.052 0.245∗∗ 0.029 −1.353∗∗
(0.052) (0.061) (0.106) (0.227) (0.573)
Poverty −0.121∗∗∗ −0.077 −0.245∗∗∗ 0.161 0.956∗∗
(0.043) (0.048) (0.079) (0.165) (0.388)
UR −0.447∗∗∗ −0.290∗∗∗ 0.192∗∗ 1.066∗∗∗ −1.299∗∗
(0.055) (0.056) (0.093) (0.190) (0.507)
HS Only −0.028 0.002 0.178∗ −0.419∗ 1.425∗∗∗
(0.052) (0.062) (0.104) (0.221) (0.495)
Less than HS 0.256∗∗∗ 0.351∗∗∗ 0.050 −1.176∗∗∗ 0.499
(0.061) (0.071) (0.118) (0.245) (0.553)
Log Med. Income −0.006 0.021 0.115∗∗∗ −0.058 0.403∗∗∗
(0.015) (0.018) (0.030) (0.061) (0.141)
Observations 470,569 470,569 470,569 470,569 470,569
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
All models include census tract and year fixed effects
Negative values can be interpreted as increasing inequality
Other variables included in regressions but omitted from this table: linguistic isolation,
median age, median home value, % between 20-24, % between 25-44, % between 45-64,
% between 5-19, % aged 65+, % asian/pacific islander, labor force participation rate,
% native, % other race, % more than bachelor’s, % unaffordable rent (30%+ of HH
income), tract Gini, % some college, % commuting by bike/walk, % commuting by car,
% commuting by transit, tract population, % unmarried parents, % veteran
76
TABLE 10. Quantile RIF Regression Results (PM2.5 Exposure)
Dependent variable:
Absolute Lorenz Ordinate
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
(1) (2) (3) (4) (5)
Black 0.403∗∗∗ 0.531∗∗∗ −0.002 −0.663∗∗∗ −0.286
(0.128) (0.131) (0.112) (0.176) (0.445)
Latino 0.265 −0.125 −0.042 0.522∗∗ 1.823∗∗∗
(0.239) (0.218) (0.169) (0.258) (0.603)
Poverty −0.203 0.392∗∗∗ 0.298∗∗ −0.056 −1.379∗∗∗
(0.151) (0.146) (0.120) (0.179) (0.444)
UR −0.064 0.054 −0.130 −1.614∗∗∗ −1.530∗∗∗
(0.188) (0.172) (0.139) (0.210) (0.529)
HS Only 0.159 −0.004 −0.131 0.001 0.227
(0.205) (0.203) (0.157) (0.241) (0.572)
Less than HS 0.263 0.297 0.288 0.430 0.014
(0.237) (0.226) (0.178) (0.274) (0.662)
Log Med. Income −0.159∗∗∗ −0.139∗∗ 0.044 0.484∗∗∗ 1.099∗∗∗
(0.059) (0.056) (0.044) (0.067) (0.165)
Observations 615,630 615,630 615,630 615,630 615,630
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Negative values can be interpreted as increasing inequality
All models include census tract and year fixed effects
For more details see Table 9
77
with an increase in the regressor in question, whereas negative coefficient would imply
greater equality in exposure. The most immediate result is that across the exposure
distribution, racial composition of census tracts has a large and significant effect on
inequality. Increases in the black proportion of a census tract are positively related to
the cumulative share of pollution exposure up through the 25th percentile, but negatively
related to cumulative exposure past the median. This implies that racial composition is
inequality-enhancing for more advantaged (less exposed) tracts, i.e. a more racially diverse
population is associated with greater disparities in exposure among less-exposed tracts.
The effect of median income is, as expected, negative throughout most of the
pollution exposure distribution — implying that higher income tracts exhibit lower
cumulative pollution shares. High poverty areas are strongly correlated with more
unequal pollution exposure — the effect of the proportion of the population poverty
implies an increase in environmental inequality across the whole pollution exposure
distribution. There is some evidence for a correlation between educational attainment and
environmental inequality — the effect of the proportion of the population with less than
a high school degree is negative and significant through most of the pollution exposure
distribution.
Tables 13 and 14 summarize the results of RIF regressions estimated using the
Generalized Lorenz ordinates as the distributional functionals of interest. The same
inference applies here as in the unconditional quantile partial effects case. Negative
coefficients imply movements towards more environmental inequality, positive coefficients
towards less inequality. The black and Hispanic proportions of population increase
inequality throughout the pollution exposure distribution. The Hispanic effect reaches
a maximum around the median of the distribution, while the black effect is largest for
the most polluted tracts. Poverty seems to have similar effects as in the Lorenz curve
78
TABLE 11. Relative Lorenz RIF Regression Results (NOx Exposure)
Dependent variable:
Relative Lorenz Ordinate
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
(1) (2) (3) (4) (5)
Black 0.120∗∗∗ 0.019 −0.021∗∗ −0.011∗∗ −0.005∗∗∗
(0.017) (0.016) (0.010) (0.005) (0.002)
Latino 0.015 −0.039 0.016 0.007 0.0003
(0.040) (0.031) (0.017) (0.007) (0.003)
Poverty 0.068∗∗∗ 0.078∗∗∗ 0.053∗∗∗ 0.019∗∗∗ 0.007∗∗∗
(0.021) (0.018) (0.011) (0.005) (0.002)
UR −0.096∗∗∗ −0.048∗∗ 0.058∗∗∗ 0.049∗∗∗ 0.022∗∗∗
(0.025) (0.022) (0.014) (0.006) (0.002)
HS Only 0.025 0.010 0.005 0.001 0.001
(0.029) (0.024) (0.015) (0.006) (0.002)
Less than HS −0.058∗ −0.083∗∗∗ −0.108∗∗∗ −0.049∗∗∗ −0.012∗∗∗
(0.034) (0.028) (0.017) (0.007) (0.003)
Log Med. Income −0.015∗ −0.021∗∗∗ −0.006 −0.0004 0.001
(0.009) (0.007) (0.004) (0.002) (0.001)
Observations 470,569 470,569 470,569 470,569 470,569
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Positive values can be interpreted as increasing inequality
All models include census tract and year fixed effects
For more details see Table 9
79
TABLE 12. Relative Lorenz RIF Regression Results (PM25 Exposure)
Dependent variable:
Relative Lorenz Ordinate
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
(1) (2) (3) (4) (5)
Black −0.004 −0.016∗∗ −0.026∗∗∗ −0.018∗∗∗ −0.006∗∗∗
(0.004) (0.006) (0.005) (0.003) (0.001)
Latino 0.011∗∗ 0.017∗∗ 0.012 0.003 −0.002
(0.005) (0.008) (0.008) (0.005) (0.003)
Poverty −0.017∗∗∗ −0.029∗∗∗ −0.015∗∗∗ −0.001 0.003
(0.004) (0.006) (0.005) (0.004) (0.002)
UR 0.010∗∗ −0.013∗ −0.026∗∗∗ −0.010∗∗ −0.001
(0.005) (0.008) (0.007) (0.004) (0.002)
HS Only 0.008 0.009 −0.001 −0.005 −0.005∗∗
(0.005) (0.008) (0.007) (0.005) (0.002)
Less than HS −0.008 −0.007 −0.004 −0.006 −0.001
(0.006) (0.009) (0.008) (0.005) (0.003)
Log Med. Income 0.008∗∗∗ 0.016∗∗∗ 0.016∗∗∗ 0.009∗∗∗ 0.002∗∗∗
(0.001) (0.002) (0.002) (0.001) (0.001)
Observations 615,630 615,630 615,630 615,630 615,630
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Positive values can be interpreted as increasing inequality
All models include census tract and year fixed effects
For more details see Table 9
80
RIF regressions, increasing exposure inequality near the middle-top of the pollution
distribution. Likewise, median income seems to decrease inequality throughout the
distribution, suggesting a significantly negative income-exposure relationship, which was
also visible in the relative Lorenz RIF results.
TABLE 13. Generalized Lorenz RIF Regression Results (NOx Exposure)
Dependent variable:
Generalized Lorenz Ordinate
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
(1) (2) (3) (4) (5)
Black −0.230∗∗∗ −0.052 0.014 −0.010 −0.022
(0.039) (0.049) (0.050) (0.046) (0.044)
Latino −0.042 0.044 −0.071 −0.064 −0.054
(0.093) (0.097) (0.094) (0.089) (0.086)
Poverty −0.161∗∗∗ −0.209∗∗∗ −0.195∗∗∗ −0.151∗∗∗ −0.137∗∗∗
(0.049) (0.056) (0.057) (0.053) (0.051)
UR 0.210∗∗∗ 0.148∗∗ −0.019 0.016 0.074
(0.058) (0.067) (0.067) (0.063) (0.061)
HS Only −0.061 −0.045 −0.051 −0.051 −0.054
(0.065) (0.074) (0.074) (0.070) (0.067)
Less than HS 0.187∗∗ 0.302∗∗∗ 0.421∗∗∗ 0.359∗∗∗ 0.308∗∗∗
(0.079) (0.088) (0.087) (0.082) (0.079)
Log Med. Income 0.029 0.040∗ 0.013 0.002 0.0003
(0.020) (0.022) (0.022) (0.021) (0.020)
Observations 470,569 470,569 470,569 470,569 470,569
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Negative values can be interpreted as increasing inequality
All models include census tract and ear fixed effects
For more details see Table 9
The effects of tract-level demographic characteristics on the final functional,
the Absolute Lorenz curve, are summarized in Tables 15 and 16. Once again, racial
composition is correlated with environmental inequality, although with heterogeneity
81
TABLE 14. Generalized Lorenz RIF Regression Results (PM25 Exposure)
Dependent variable:
Generalized Lorenz Ordinate
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
(1) (2) (3) (4) (5)
Black 0.046 0.163∗∗ 0.273∗∗∗ 0.192∗∗∗ 0.075
(0.044) (0.075) (0.082) (0.073) (0.065)
Latino −0.178∗∗∗ −0.310∗∗∗ −0.374∗∗∗ −0.370∗∗∗ −0.373∗∗∗
(0.061) (0.107) (0.129) (0.124) (0.114)
Poverty 0.204∗∗∗ 0.356∗∗∗ 0.257∗∗∗ 0.153∗ 0.127∗
(0.047) (0.078) (0.088) (0.083) (0.077)
UR −0.016 0.337∗∗∗ 0.622∗∗∗ 0.596∗∗∗ 0.578∗∗∗
(0.058) (0.093) (0.104) (0.098) (0.090)
HS Only −0.095∗ −0.122 −0.046 −0.023 −0.028
(0.057) (0.099) (0.117) (0.110) (0.100)
Less than HS 0.044 −0.006 −0.097 −0.127 −0.210∗
(0.066) (0.114) (0.132) (0.124) (0.113)
Log Med. Income −0.117∗∗∗ −0.248∗∗∗ −0.314∗∗∗ −0.293∗∗∗ −0.258∗∗∗
(0.017) (0.028) (0.033) (0.031) (0.029)
Observations 615,630 615,630 615,630 615,630 615,630
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Negative values can be interpreted as increasing inequality
All models include census tract and year fixed effects
For more details see Table 9
82
across pollutants. Tract African-American populations are associated with higher absolute
inequality at the more exposed end of the distribution for NOx, but are associated with
lower absolute inequality for PM2.5. Tract Hispanic population is associated with higher
absolute inequality for both pollutants, but this association is only statistically significant
for PM2.5. Interestingly, median tract income is actually associated with lower absolute
inequality for NOx, but with higher absolute exposure inequality across the distribution
for PM2.5.
TABLE 15. Absolute Lorenz RIF Regression Results (NOx Exposure)
Dependent variable:
Absolute Lorenz Ordinate
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
(1) (2) (3) (4) (5)
Black −0.227∗∗∗ −0.044 0.030 0.014 0.007
(0.036) (0.040) (0.029) (0.015) (0.006)
Latino −0.037 0.058 −0.044 −0.023 −0.005
(0.086) (0.077) (0.052) (0.025) (0.010)
Poverty −0.148∗∗∗ −0.177∗∗∗ −0.131∗∗∗ −0.056∗∗∗ −0.023∗∗∗
(0.045) (0.045) (0.033) (0.016) (0.006)
UR 0.198∗∗∗ 0.119∗∗ −0.077∗∗ −0.072∗∗∗ −0.031∗∗∗
(0.053) (0.053) (0.039) (0.020) (0.008)
HS Only −0.056 −0.032 −0.024 −0.011 −0.005
(0.060) (0.059) (0.043) (0.021) (0.008)
Less than HS 0.158∗∗ 0.228∗∗∗ 0.275∗∗∗ 0.139∗∗∗ 0.044∗∗∗
(0.073) (0.070) (0.050) (0.025) (0.010)
Log Med. Income 0.029 0.040∗∗ 0.012 0.001 −0.001
(0.019) (0.018) (0.013) (0.006) (0.002)
Observations 470,569 470,569 470,569 470,569 470,569
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Negative values can be interpreted as increasing inequality
All models include census tract and year fixed effects
For more details see Table 9
83
TABLE 16. Absolute Lorenz RIF Regression Results (PM2.5 Exposure)
Dependent variable:
Absolute Lorenz Ordinate
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
(1) (2) (3) (4) (5)
Black 0.045 0.160∗∗ 0.268∗∗∗ 0.185∗∗∗ 0.066∗∗∗
(0.041) (0.065) (0.058) (0.035) (0.017)
Latino −0.137∗∗ −0.206∗∗ −0.167∗ −0.060 0.0001
(0.056) (0.090) (0.088) (0.060) (0.033)
Poverty 0.188∗∗∗ 0.314∗∗∗ 0.174∗∗∗ 0.028 −0.023
(0.044) (0.067) (0.061) (0.040) (0.021)
UR −0.076 0.188∗∗ 0.323∗∗∗ 0.148∗∗∗ 0.040
(0.054) (0.081) (0.072) (0.048) (0.026)
HS Only −0.086 −0.100 −0.001 0.043 0.052∗
(0.053) (0.085) (0.082) (0.054) (0.027)
Less than HS 0.067 0.051 0.017 0.044 −0.004
(0.062) (0.097) (0.092) (0.060) (0.031)
Log Med. Income −0.093∗∗∗ −0.186∗∗∗ −0.190∗∗∗ −0.107∗∗∗ −0.035∗∗∗
(0.015) (0.024) (0.023) (0.015) (0.008)
Observations 615,630 615,630 615,630 615,630 615,630
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Negative values can be interpreted as increasing inequality
All models include census tract and year fixed effects
For more details see Table 9
84
These results together shine additional light on the interconnectedness of the
concepts of environmental justice and environmental inequality — it appears that racial
differences and poverty are important correlates of environmental inequality. However,
these results are at best only potentially interesting correlations, and cannot claim to
have uncovered the causes of environmental inequality. In particular, I cannot speak to
whether any correlation between the racial composition of census tracts and exposure
inequality necessarily represents environmental racism, although the generally more
robust correlations between income variables (median income and poverty) and exposure
inequality suggests that the level and distribution of income may be important for
explaining changes in the exposure distribution, a possibility I take up more formally in
Chapter IV of this dissertation.
Conclusion
This paper proposes a “dashboard” approach to the considerations of distributional
concerns in environmental policy analysis. Rather than choosing a single summary
statistic (e.g. the black-white exposure gap, or the Atkinson index) as a social evaluation
function when analyzing the (environmental) distributional effects of policy, looking at
several indicators can be a more fruitful approach that more fully illustrates how policy is
affecting the distribution of exposure to harmful pollutants.
I propose two ways of thinking about the degree to which the distribution of
pollution exposure is “unequal”: a horizontal equity concept, where the primary concern
is the inequality in exposure across subgroups, and a vertical equity concept, where the
primary concern is the degree of inequality across the whole population. I apply scalar
measures of each equity concept (e.g. the Atkinson index for vertical equity, and the
average black-white exposure gap for horizontal equity), in addition to measures that allow
85
for the examination of the whole distribution (black-white gaps by percentile for horizontal
equity, and Lorenz curves for vertical equity).
I apply this dashboard of measures of environmental inequality and environmental
justice to novel data on pollution exposure derived from remote sensing observations of
ground level NOx and PM2.5 concentrations. By matching these remote sensing data
with census data on the distribution of population, I am able to measure not just average
exposure, but also all of the environmental inequality and environmental justice measures,
on an annual basis over the period 1998-2014 (only 2005-2011 for NOx exposure). Average
exposure to both pollutants has decreased markedly over time, as have most measures of
environmental inequality and environmental justice.
I use a re-centered influence function regression estimation strategy to isolate
how individual tract-level demographic characteristics affect measures of environmental
inequality as a whole. I find that many characteristics that correlate with disadvantage —
such as poverty rates, education levels and racial minority populations — have statistically
significant associations with environmental inequality, although notably the patterns of
sign and significance often differ between pollutants, suggesting the interaction between
the distribution of people and the production and the fate-and-transport of pollution may
depend in part of the chemical properties of the pollutants in question.
This largely descriptive exercise has not, by design, involved the identification of
causal factors that might be related to the observed trends in environmental quality,
environmental inequality and environmental justice. The final substantive chapter of this
dissertation takes up this challenge by synthesize the first substantive chapter’s discussion
of trends in income inequality with this chapter’s discussion of environmental inequality,
and considers whether income inequality within metropolitan areas might have a causal
effect on changes in the distribution of pollution exposure.
86
CHAPTER IV
ENVIRONMENTAL JUSTICE VIEWED FROM OUTER SPACE: HOW DOES
GROWING INCOME INEQUALITY AFFECT THE DISTRIBUTION OF POLLUTION
EXPOSURE?
Introduction
Income inequality has increased substantially in the last several decades, both
within the United States as a whole (Piketty and Saez (2003)) and within individual US
states and metropolitan areas (Frank (2009), and Chapter II of this dissertation). This
fact has spawned a contentious debate, both within and outside of academia. Much of
this debate has concerned itself with the causes of this increase in income inequality.
Substantially less time and effort has been expended on considering the potential effects
of rising inequality. In this paper, I will examine how increases in income inequality might
affect the distribution of environmental disamenities, specifically, exposure to ground-level
nitrogen oxides (NOx). Exposure to NOx itself, and to the ozone and smog generated
when ground-level NOx interacts with sunlight and volatile organic compounds, is a major
health hazard, contributing as many as 10,000 excess deaths per year in the United States
(Caiazzo et al. (2013)). Concern about NOx has become particularly salient in light of the
recent Volkswagen emissions scandal, wherein software on several car models was designed
to circumvent emissions testing regimes in the US and Europe, resulting in thousands of
tons of excess NOx emissions.
Using data on ground-level NOx concentrations inferred from remote sensing
observations by NASA’s Aura satellite, I am able to measure pollution exposure at a fine
geographic resolution. I combine these data with information about income distributions
87
in US metropolitan statistical areas (MSAs) to examine the causal effect of changes in
within-MSA income inequality on the distribution of NOx exposure within MSAs. There is
likely to be some joint endogeneity between the income inequality and pollution exposure,
operating through migration between metropolitan areas. To identify a causal effect in
the presence of this endogeneity, I employ an instrumental variables approach, using a
version of the simulated instrument introduced by Boustan et al. (2013). I construct
an instrument for income inequality by simulating counterfactual MSA-level income
distributions which are independent of changes in the MSA-level distribution of pollution
exposure, thereby eliminating the potential endogeneity bias due to locational sorting.
Using this empirical strategy, I find that increases in metropolitan area income
inequality lead to decreases in the average level of NOx exposure within MSAs. However,
increases in income inequality are also associated with an increase in environmental
inequality. I conclude that the decrease in average exposure caused by income inequality
disproportionately benefits the most-advantaged, although the least-advantaged are
still better off in absolute terms. I then consider to what extent the political system
might serve as a potential mechanism for the effect of inequality on pollution exposure.
Specifically, I examine how income inequality is related to the pro-environmental voting
records of legislators, as measured by their League of Conservation Voters score. I find
that increases in income inequality within a US senator’s state lead to an increase in the
LCV scores of Democratic senators, but have no discernible effect on the LCV scores of
Republican senators.
The remainder of the paper proceeds as follows. I review the relevant literature
on environmental justice and income inequality. I then offer a conceptual model for
my analysis, and describe the data sources I use. Finally, I introduce my identification
strategy, and present estimation results. I discuss potential mechanisms, and examine
88
how the effect of income inequality on the distribution of environmental amenities may
work through the political system. I conclude with some ideas for potential extensions and
directions for future research.
Previous Literature
Environmental Justice
The earliest environmental justice literature was motivated by the identification of
differences in the levels of pollution exposure across discrete socio-economic categories.
There are many capable reviews of this literature, including a recent volume collected
by Banzhaf (2012) and surveys including Mohai et al. (2009) and Brulle and Pellow
(2006). The central claim in this literature is that minority and poorer households are
disproportionately more likely to be exposed to pollution, compared to white and richer
households. In practice, papers in this literature are often able to establish only that areas
near toxic emitting firms and areas with higher measured levels of pollution tend to be less
white, to be less educated and/or to have lower median income than less-polluted areas.
There are slightly fewer papers that deal explicitly with environmental inequality
rather than environmental injustice. By environmental inequality I am referring to a
measure capturing the entire distribution of the level of exposure to pollution within
an area.1 This contrasts with the concept of environmental injustice, which refers to
differences in subgroup means. This distinction is not entirely standard across the
broad environmental injustice literature (e.g. Downey (2007)). Maguire and Sheriff
(2011) and Sheriff and Maguire (2014) provide a direct adaptation, from the income
inequality literature, of tools to rank distributions of environmental amenities or
1For the purposes of this paper, Environmental Inequality will be captured by a scalar index, although
it is possible to measure environmental inequality using, e.g. Lorenz curves without sacrificing normative
content.
89
disamenities. They suggest that normatively based scalar indices should be used for
studying the environmental justice effects of a given policy. In a similar paper, although
in a different context, Harper et al. (2013), apply some of the tools from the literature on
the measurement of income inequality to the measurement of health outcomes, again in
the context of policy analysis.
Income Inequality and Environmental Quality
Scholars in environmental economics have long sought to model the simple
relationship between incomes and pollutant emissions. This relationship is often embedded
within considerations of the Environmental Kuznets Curve (EKC)—the idea being that
pollution levels first rise as countries develop (i.e. as average incomes increase), and
then, at some point, begin to decline, as demand for environmental amenities increases.
Although the EKC model concerns only average incomes, and not the full distribution of
income, the EKC model has spawned a few papers that examine how income inequality,
as distinct from just average incomes, might affect environmental quality. Berthe and
Elie (2015) summarize this small but growing literature, and attempt to synthesize
its findings by suggesting a theoretical structure which can explain all of the potential
pathways through which income inequality might affect environmental quality. This
literature has not yet reached any consensus on whether there is a relationship between
income inequality and environmental quality, let alone has it established the sign of this
relationship or whether this relationship is causal.
Boyce (1994) is perhaps the first to consider this relationship, followed by Scruggs
(1998), Ravallion et al. (2000) and others.2 Papers in this literature share a common
2A non-exhaustive list includes Torras and Boyce (1998), Heerink et al. (2001), Magnani (2000) and
Neumayer (2004). More-recent papers in this literature include Zwickl and Moser (2015) and Baek and
Gweisah (2013)
90
framework. Consider a propensity-to-emit function (PEF) which describes the amount
of emissions embedded in each household’s consumption activity at any given level of
household income, a function that I assume is non-decreasing over some range of income.3
To consider how income inequality might affect environmental quality, it is necessary
only to know the concavity of the PEF. If the function is concave, so that the marginal
propensity to emit is decreasing in income, then Pigou-Dalton transfers (mean-preserving
progressive transfers of income) may actually increase average emissions levels. Conversely,
if the PEF is convex, so that the marginal propensity to emit is increasing in income,
Pigou-Dalton income transfers will reduce average emissions levels. In other words,
increases in income inequality may account for environmental degradation if the PEF is
convex, while decreases in income inequality may account for environmental degradation if
the PEF is concave.
There is, however, no obvious reason to expect, a priori, that the propensity to
emit function need necessarily be either convex or concave. No consensus has emerged
from the resulting empirical literature, although patterns have sometimes been observed.
In cross-country regressions, generally suggest that rising income inequality increases
environmental degradation (e.g. Drabo (2011)). Basing the analysis simply on within-
country variation, however, has produced a wide array of estimates. There appear to be
rather different relationships for developing or middle income countries (e.g. China, in the
case of Golley and Meng (2012)) than for developed countries (e.g. Sweden, in the case of
Bra¨nnlund and Ghalwash (2008)). In particular, the weight of the evidence suggests that
the propensity to emit function may be convex for developing countries, but concave for
developed nations. This implies that developing countries may be able to reduce emissions
3In a recent working paper, Levinson and O’Brien (2015) introduce the related concept of an
environmental Engel curve
91
and enhance equity simultaneously, whereas developed countries face a trade-off between
equity and environmental quality.
There are two difficulties faced by earlier papers in this literature. First, the
observability of environmental quality is often incomplete, relying on irregularly spaced
ground monitors. Second, there is potential endogeneity between environmental quality
and the distribution of income. No paper in this literature has proposed a credible
strategy to recover estimates of the causal effect of income inequality on the environment
in the presence of this potential endogeneity. I address these issues by (1) utilizing satellite
data that provide information about air quality in unmonitored areas, and (2) using an
instrument for inequality that addresses endogeneity due to locational sorting.
Data and Empirical Strategy
My goal is to capture the impact of income inequality on some functional of the
pollution exposure distribution. As with many questions of distributional measurement,
the choice of the proper geographic scope is important. My analysis will be performed
at the level of metropolitan statistical areas (MSAs) in the United States. Metropolitan
areas are typically the geographic context in which the health effects of exposure to non-
uniformly mixing pollutants like NOx are most acute. The differences in these exposures
within an individual metropolitan area contribute to the environmental inequality I
measure. Metropolitan areas are also sufficiently large to allow for estimation of income
inequality measures using publicly available Census Bureau data at an annual frequency.
Thus MSAs are a natural choice as the geographic setting for this analysis.
To examine the relationship between income inequality and the distribution of
pollution exposure, I utilize two novel data sources. I use data on NOx concentration
levels from the Aura satellite to calculate both metropolitan-area average exposure levels
92
and environmental inequality, which I capture via two alternative measures (functionals
of the pollution exposure distribution). I supplement these pollution exposure data with
metropolitan area income inequality measures from Chapter II of this dissertaion, and
socio-demographic variables calculated from the American Community Survey (ACS) 1-
year files.
The Aura satellite was launched in 2004 with a mission to measure the atmospheric
composition both for the troposphere (i.e. at ground-level) and for the stratosphere (i.e.
the ozone layer). The Ozone Monitoring Instrument (OMI), carried by the Aura satellite,
provides comprehensive global observations of the tropospheric vertical column density
of NOx on a fixed grid. Vertical column densities do not correspond with ground-level
concentrations of NOx on a one-for-one basis. In general, it is necessary to infer the
ground-level concentrations via the use of ground-level observations from monitoring
stations and a chemical air-transport model. I use the SP GC v1.01 dataset provided by
the Air Composition Analysis Group (ACAG) at Dalhousie University, which is estimated
using the GEOS-CHEM chemical transport model.4 More information about these data
are available in Lamsal et al. (2008) and Lamsal et al. (2010).5 Figure 19 summarizes the
national distribution of NOx concentrations in the form of choropleth maps.
6
The ACAG data provide yearly average NOx concentrations on a 0.1×0.1-
degree grid for North America. To measure the person-level distribution of pollution
exposure, I geographically interpolate the ACAG data to the census-tract level by
4A previous version of this paper used an alternate approach to inferring ground-level concentrations
by comparing the distribution of ground-level observations from monitoring stations with the distribution
of vertical column densities.
5These data are available from the ACAG website at: http://fizz.phys.dal.ca/~atmos/martin/
6More detailed choropleths, including metropolitan area maps, are available in an online appendix
accessible at http://pages.uoregon.edu/jlv/jmp_appendix.html. An additional set of interactive maps
visualizing the distribution of NOx exposure in 2005 is available at http://pages.uoregon.edu/jlv/
interactive_NOX_maps.html
93
FIGURE 19. Average Annual NOx Exposure by Census Tract, 2005–2011
inverse distance weighting.7 These annual estimates of NOx concentrations at the
census-tract level are then used to calculate metropolitan area average exposure and the
necessary environmental inequality measures, which are functionals of the NOx exposure
distribution.
The final estimating sample includes observations for 265 MSAs, for the period from
2005 to 2011. Metropolitan area income inequality is measured by the well-known Gini
coefficient, estimated from income microdata provided in the 1-year American Community
Survey (ACS) files. I use the Gini coefficient estimates from chapter II of this disseration,
which address topcoding by adopting a multiple imputation approach, simulating
the censored right tail of the income distribution as following a Generalized Beta II
7Inverse distance weighting interpolates to unobserved locations xi by calculating the weighted average
of observed locations nearby (xj). The weights are calculated as wj =
1
d(xi,xj)
2 , where d (.) is the
Euclidean distance operator.
94
distribution. Income inequality estimates are calculated for all MSAs identified in the
public-use ACS microdata files (265 in total). I supplement my two main variables with
several demographic measures including median income, race, industry characteristics,
poverty, and transportation patterns.
Measuring Environmental Inequality
Most previous research focuses on the average level of pollution exposure within a
jurisdiction, generally calculated as the population-weighted mean of ground monitor
readings. I extend this by examining not just the average (i.e. first moment of the
distribution), but also functionals of the entire distribution of pollution exposure within
each MSA.8 I define two types of measures which summarize the pollution exposure
distribution. The first type I describe as measures of “environmental inequality.”
These measures summarize the marginal distribution of pollution exposure, across the
population, without considering individual attributes other than the level of exposure.
The second type I term measures of “environmental justice.” These summarize the joint
distribution of pollution exposure and other demographic characteristics, likewise across
the population.
Measures of environmental inequality thus summarize just the unconditional
distribution of pollution exposure, without considering subgroup differences. Sheriff and
Maguire (2014) describe how to adapt common measures of inequality to a case where
the distribution of interest is a “bad” (as for NOx exposure). If inequality measures are
interpreted purely as a description of the spread of a distribution, then this distinction
is largely irrelevant. However, normative interpretations of these inequality measures
8While I will not be using the higher moments (e.g. variance, skewness) of the distribution per se,
the measures I use can be thought of as capturing the same sort of information about the shape and
dispersion of exposure distributions.
95
are important for analyzing the tradeoff between equity and efficiency when making
environmental policy decisions, and these measures are not symmetric across the good/bad
distinction. I adopt the approach of Sheriff and Maguire (2014) and modify commonly
used inequality measures so that it is possible to rank distributions in an ethically sensible
fashion.
In contrast, measures of environmental justice are defined in terms of the differences
in average pollution exposure between subgroups, where the subgroups correspond
to conventional notions of advantage and disadvantage. I will consider differences in
exposures across racial lines: specifically, the difference in pollution exposures between
African-Americans and whites, as well as the difference in exposures between Latinos
and whites. I will consider differences in exposures across income levels as well, defined
as the difference in average pollution exposure between the top quintile of the income
distribution and the bottom quintile of the income distribution.
I will capture environmental inequality by two types of scalar inequality measures,
each of which induce a complete ordering of pollution exposure distributions.9 I will
divide these types of measures into two groups: relative inequality measures and absolute
inequality measures. The substantive difference in these measures lies in their invariance
properties. A relative inequality measure IR (x), for a vector x characterizing the empirical
pollution exposure distribution, satisfies the property of scale invariance:
∀x : IR (x) = IR (kx) , k > 0 (4.1)
9Environmental inequality can also be captured using a Lorenz curve (or variations thereof). However,
Lorenz curves induce only a partial ordering of pollution exposure distributions, since the Lorenz
dominance criteria requires that the curves do not cross.
96
In contrast, an absolute inequality measure, IR (x), satisfies the property of translation
invariance:
∀x : IA (x) = IA (x+ k) (4.2)
where k is any vector, in the domain of x, whose entries are all equal.
There has been some controversy over which of these two measures more accurately
captures moral intuitions about inequality in general. Following Kolm (1976), the key
distinction between the two types of measures lies in how the worst-off (most-exposed)
individuals are treated. Consider the two inequality-preserving transformations above.
A proportional increase in pollution exposure as in equation (4.1) will in fact result in
much larger changes for the most exposed individual. A equiproportional increase in
pollution of, e.g., 20% will by definition leave relative inequality unchanged, but will
increase absolute inequality. Likewise, an equal-sized increase in pollution will decrease
relative inequality, but leave absolute inequality unchanged.
Of the two measures, a strong case can be made that absolute inequality measures
may be more appropriate when considering the distribution of pollution exposures.
Absolute differences in exposure have negative health effects, while relative differences
in exposure may not necessarily correspond to substantive health disparities.. Thus,
the absolute measures will respect the spirit of the environmental justice movement’s
concept of equity (defined in terms of absolute differences in exposure), unlike the relative
measures.
I use the Atkinson index, as modified by Sheriff and Maguire (2014) to quantify
relative inequality:
AI (x) =
[
1
N
N∑
i=1
(
xi
µx
)1−α] 11−α
− 1, α ≤ 0 (4.3)
97
Here, α is an environmental inequality aversion parameter in the associated social welfare
function (SWF). As α → 0, the associated SWF becomes increasingly utilitarian, and as
α→ −∞ the implied SWF becomes increasingly Rawlsian.
Likewise, I use the (modified) Kolm-Pollak index to quantify absolute inequality:
KI (x) = −1
κ
ln
1
N
N∑
i=1
e−κ(xi−µx), κ < 0 (4.4)
where κ can be interpreted as an environmental inequality aversion parameter for the
associated social welfare function. Symmetrically with the α parameter in the previous
case, as κ → 0 the SWF becomes increasingly utilitarian, and as κ → −∞, it becomes
increasingly Rawlsian.
There are two reasons to believe that the estimates of these measures of
environmental justice and environmental inequality should be regarded as lower bound
estimates. First, by construction and due to data limitations, I assume that all census
tract residents have the same level of exposure, which is equivalent to assuming that
within-tract inequality is zero. Second, I use the actual ground level concentration of NOx
as a measure of exposure. However, individuals may be able to engage in averting behavior
to avoid exposure to a given ambient concentration level. If the ability to engage in
averting behavior is related to the degree of advantage then the estimates of environmental
justice and environmental inequality based on concentration levels will overestimate
exposure by advantaged groups and hence underestimate the gap in exposure between
advantaged and disadvantaged groups.
98
IV Approach
I assume, as a baseline, that the relationship between a functional of an MSAs
pollution exposure distribution ν and an MSA’s income inequality, measured by the Gini
coefficient, can be modeled as
ν (Pollution)i,t = β1Ginii,t + β2Xi,t + ui,t (4.5)
ui,t = αi + ei,t (4.6)
where αi is the MSA-specific fixed component of the error term, and ei,t is white noise.
To recover the effect of income inequality on the pollution exposure distribution, I can
estimate a model in first-difference form:10
∆ν (Pollution)i,t = β1∆Ginii,t + β2∆Xi,t + ∆ui,t (4.7)
Alternatively, I could estimate equation (4.5) directly using a fixed-effects specification.
This baseline model does not absorb time-varying unobserved heterogeneity. I address this
heterogeneity by allowing for MSA-specific linear trends:
ν (Pollution)i,t = β1Ginii,t + β2Xi,t + αit+ ui,t (4.8)
which can be estimated either in a first-difference or fixed-effects specification. Even
after allowing for time-varying heterogeneity, however, none of these estimates of β1 are
sufficient on their own to establish a causal effect.
When attempting to investigate the relationship between inequality in the
distribution of income and inequality in the distribution of pollution exposure, there
10This is the preferred OLS specification in Boustan et al. (2013).
99
are two significant challenges to identifying a causal effect. First, there may be long-
run reverse causality, as implied by the literature on the intergenerational transmission
of inequality (for example Currie (2011)). Increases in environmental inequality might
lead to increases in future income inequality, although only on intergenerational time
scales. Second, on shorter time scales, there may be endogenous locational sorting between
metropolitan areas, where sorting differs systematically across the income distribution.
For example, if rich households disproportionately migrate out of metropolitan
areas with high average levels of pollution exposure, or high inequality in pollution
exposures, then there is the potential for reverse causality. At the other end of the
income distribution, poorer households may disproportionately migrate into metropolitan
areas with higher levels of pollution (or alternatively with less equitable distributions of
pollution exposure) which may change the income distribution in these areas.11 These
two potential migration flows have conflicting effects on the income distribution—if
rich households migrate out, this will decrease the Gini coefficient of income inequality,
however if poor households migrate in, this will increase the Gini coefficient of income
inequality.12 If both types of flows occur, the effect on the Gini coefficient is ambiguous.
To address these concerns about endogeneity, I adopt a simulated instrumental
variables strategy. Specifically, I construct an instrument for income inequality that
definitionally rules out any between-MSA sorting by “freezing” the MSA-level income
distribution in an initial year and simulating the evolution of counter-factual income
distributions. These counter-factual income distributions are constructed by allowing
11These are related to the concept of “coming to the nuisance”, wherein environmental disamenities
depress local rents, which in turn attracts lower income households.
12To see this, consider the following toy example. Suppose there are 4 people in a city, with incomes of
10,25,50 and 150. The Gini coefficient in the city is 0.473. If the richest person leaves, the Gini coefficient
drops to 0.314. If, on the other hand, a new poor person (with income 10) moves in, the Gini coefficient
increases to 0.52
100
each decile of each MSAs income distribution to follow the growth trends observed for
the corresponding deciles of the national income distribution. Using this instrument makes
it possible to identify the causal effect of income inequality on the distribution of NOx
exposure by cutting off any potential variation due to between-MSA sorting.
This instrument is very similar to the instrument used in Boustan et al. (2013).
This type of identification strategy has also been used in other settings, as in Enamorado
et al. (2014), who examine the causal effect of income inequality on crime in Mexican
municipalities. This class of simulated instruments are examples of “Bartik-style”
instruments, which have been used in a wide variety of settings. As Baum-Snow and
Ferreira (2015) note, the ability of this strategy to identify the causal effect of income
inequality hinges on the assumption that the initial level of income inequality within
metropolitan areas is independent of changes in the distribution of pollution exposure,
except through its effect on the actual trends in MSA-level income inequality. One test
of this identifying assumption would then be to examine the correlation between initial
income inequality and subsequent changes in the distribution of NOx exposure. Figure
20 visualizes the relationship between initial income inequality and changes in average
exposure. The slope of the line of best fit through this scatterplot is not statistically
different from zero, which can be taken as evidence that the identifying assumptions
hold. Essentially identical results hold for all the other functionals of the NOx exposure
distribution used as outcome variables.
To construct the instrument, I use the same microdata on incomes from the ACS
1-year files that I used to calculate the measures of MSA-level income inequality (using
the Generalized Beta II multiple imputation method described in Chapter II of this
101
FIGURE 20. Initial MSA Income is Unrelated to Subsequent Changes in NOx Exposure
−1.0
−0.5
0.0
0.5
0.35 0.40 0.45 0.50
Initial Gini Coefficient
Ch
an
ge
 in
 A
ve
ra
ge
 N
O
x 
Ex
po
su
re
Initial Inequality vs. Changes in Exposure
dissertation).13 For each MSA identified in the ACS microdata, I calculate the mean
income of each decile of the MSA income distribution in the first year of the sample
(2005). I also calculate the means of each decile of the national distribution for each
year, and calculate the growth rates for each of these decile means from 2006 to 2011. I
leave each MSA’s information out of calculations of national decile average income levels
and trends when constructing that MSA’s simulated counterfactual income distribution.
This eliminates the possibility that large MSAs, e.g. New York, may be disproportionately
driving national level income trends.14
I then use these national decile-mean growth rates to construct synthetic income
distributions for each MSA in each year in the period 2006-2011. I assign each MSA decile
13The income concept used here is pre-tax, post-transfer household income, adjusted for household size
by applying an equivalence scale equal to the square root of household size.
14Previous versions of this paper used the same national decile income levels and trends for each MSA.
There is no qualitative difference in results when using the instruments, although the “leave-one-out”
estimates are more precise.
102
in 2005 to its matching national decile in 2005. I calculate the instrument by assuming
that every MSA decile grew at the same rate as the corresponding national decile mean for
each year in 2006-2011. In other words, I “freeze” the individual MSA income distribution
in 2005, and then simulate future counterfactual distributions based only on nationwide
trends. Once I have these sets of simulated decile means, I calculate a Gini coefficient
using the simulated decile means for each year between 2006 and 2011.
With these simulated Gini coefficients as my instrumental variable, I can estimate
the relationship between income inequality and environmental inequality using two-stage
least squares methods. The baseline model can be estimated in first-differences as
First stage: ∆Ginii,t = α + γ1∆SynthGinii,t + δ∆Xi,t + vi,t (4.9)
Second stage: ∆EnvIneqi,t = α + β∆Ĝinii,t + Γ∆Xi,t + i,t (4.10)
To account for potential time-varying heterogeneity, as mentioned above, I additionally
estimate models that include MSA-specific trends αi:
First stage: ∆Ginii,t = αi + γ1∆SynthGinii,t + δ∆Xi,t + vi,t (4.11)
Second stage: ∆EnvIneqi,t = αi + β∆Ĝinii,t + Γ∆Xi,t + i,t (4.12)
where in either case Xi,t is a vector of exogenous sociodemographic covariates that
enter into both the first and second stages. These controls include median income, race,
industry characteristics (proportion of employment in manufacturing), poverty, and
transportation patterns (such as the percent of the population that commutes by car,
and the average commute time). Like fixed-effects models, these first difference models
will absorb any permanent features (terrain, climate, etc) which will affect between-MSA
103
variation in environmental inequality. The remaining variation in pollution exposure can
be attributed to socio-demographic factors and economic activity.
Figure 21 and Table 17 summarize the first-stage results of the model. As Figure
21 shows, my simulated instrument for MSA-level income inequality is highly correlated
with actual MSA-level income inequality. The first column of Table 17 reports first-stage
results for a model without MSA-specific linear trends, while the second column reports
first-stage results for a model with MSA-specific linear trends. The estimated coefficient
associated with the instrument is positive and close to unity, and the F-statistics for
the two first-stage specifications are 70.5 and 55.34 respectively. These F-statistics are
well above the rule-of-thumb value of 10, which indicates that a weak first stage is not a
problem. Together with the construction of the instrument, this can be taken as evidence
that I obtain unbiased causal estimates of β. Additionally, Figure 22 summarizes the
reduced form effect of the simulated instrument on the outcomes of interest (average NOx
exposure, the black-white gap, and the Kolm-Pollak and Atkinson indexes).
FIGURE 21. Actual Gini Coefficient as a function of Simulated Gini Instrument, for 265
MSAs, 2005–2011
0.3
0.4
0.5
0.30 0.35 0.40 0.45 0.50
Simulated Gini Coefficient
Ac
tu
al
 G
in
i C
oe
ffi
cie
nt
First Stage (Simulated vs. Actual Gini)
−0.02
0.00
0.02
0.04
−0.004 0.000 0.004 0.008
Change in Simulated Gini Coefficient
Ch
an
ge
 in
 A
ct
ua
l G
in
i C
oe
ffi
cie
nt
First Stage
104
TABLE 17. First Stage, key coefficient only
Dependent variable:
MSA-Level Gini
(1) (2)
Simulated Gini 1.302∗∗∗ 1.600∗∗∗
(0.175) (0.263)
MSA-specific Linear Trend? No Yes
F-stat 70.5 55.342
Observations 1,578 1,578
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Standard Errors allow for MSA clustering
Other control variables not shown: homeownership rates, % linguistic isolated, mean
commute time, mean # of bedrooms in housing stock, mean household size, % latino, %
black, % in school, % native, % asian % other race, % with a high school education , %
with some college, % with a bachelor’s degree, % with postgraduate education, % female,
unemployment rate, % non-English speakers, Average Duncan Socioeconomic Index, %
who commute by car, median age, median home value, % employed in 16 broad NAICS
categories
105
FIGURE 22. Reduced Form Visualizations Showing the Effect of Simulated Income
Inequality on Pollution Exposure
−0.4
−0.2
0.0
0.2
−0.004 0.000 0.004 0.008
Change in Simulated Gini Coefficient
Ch
an
ge
 in
 M
ea
n 
NO
x 
Ex
po
su
re
Reduced Form Effect on Average NOx
−0.05
0.00
0.05
−0.004 0.000 0.004 0.008
Change in Simulated Gini Coefficient
Ch
an
ge
 in
 B
la
ck
−W
hi
te
 E
xp
os
ur
e 
G
ap
Reduced Form Effect on Black−White Exposure Gap
−0.002
0.000
0.002
0.004
0.000 0.004 0.008
Change in Simulated Gini Coefficient
Ch
an
ge
 in
 E
nv
iro
nm
en
ta
l A
tk
in
so
n 
In
de
x
Reduced Form Effect on Atkinson Index
−0.010
−0.005
0.000
0.005
0.000 0.004 0.008
Change in Simulated Gini Coefficient
Ch
an
ge
 in
 K
o
lm
−P
o
lla
k 
In
de
x
Reduced Form Effect on Kolm−Pollak Index
106
Results
I will consider three main sets of results. The previous literature has largely
discussed the effect of income inequality on environmental degradation in terms of average
exposure or emissions. Thus, to ensure comparability with previous results, I begin
by examining the effect of MSA-level income inequality on average exposure to NOx.
Second, I consider whether increases in MSA-level income inequality affect measures
of environmental injustice (which I define as the disparity in average exposure across
subgroups). Third, I consider whether increases in income inequality affect measures of
environmental inequality, which I define in terms of a functional of the distribution of
pollution exposure. Examination of these last two relationships constitutes one of the
main innovations in this research.
Table 18 reports the estimates of the key coefficient measuring the effect of income
inequality on the average level of pollution exposure within a metropolitan area.15 The top
panel in the table shows results from an IV model using the simulated Gini coefficient
described above as an instrument for actual income inequality. For comparison, the
bottom panel shows results from a naive OLS regression of average NOx exposure on
the MSA-level Gini coefficient, ignoring potential endogeneity. The first column reports
results for a model with no other covariates. The second column includes the full set of
time-varying controls (see Table 17 for a full list). Finally, the third column reports results
from a model with all time-varying controls and MSA-specific linear trends (equivalent to
an MSA fixed effect in first differences). All models allow for MSA-level clustering in the
standard errors.
15For this and other specifications, coefficient estimates for additional control variables are not
presented. Full tables of all parameter estimates are available in supplemental material.
107
TABLE 18. Effect of Income Inequality on Average NOx Exposure
(1) (2) (3)
IV Results: Gini −3.772∗∗∗ −5.698∗∗∗ −6.405∗∗∗
(1.346) (1.681) (2.111)
OLS Results: Gini −0.330 −0.503 −0.507
(0.359) (0.364) (0.426)
Observations 1,578 1,578 1,578
First Stage F 86.22 70.5 55.34
Control Variables? No Yes Yes
MSA-specific Trend? No No Yes
Notes: See Table 17 for further details
For specifications with and without MSA-specific linear trends the sign of the
effect of income inequality on pollution exposure is negative, implying that rising
income inequality decreases average exposure.16 These estimated effects are statistically
significantly different from zero, and quantitatively important. To put this in perspective,
the average cumulative change in NOx exposure across metropolitan areas from 2005-
2011 is −0.582. According to the results in the third column of Table 18, a one Gini-
point increase (i.e. a 0.01 increase in the Gini coefficient) in income inequality reduces
average NOx exposure by about 0.064 parts per billion, which is approximately 11% of the
average cumulative change in NOx concentration in our sample (from 2005 to 2011). A
one-standard-deviation change in inequality (approximately 0.035) would decrease NOx
16There is a relatively large difference in the estimated coefficients between a model with no control
variables and a model with the full set of control variables. This difference appears to be driven by
population density and total population.
108
concentrations by 0.22 ppb, which can account for approximately 38.5% of the average
cumulative change in exposure over the study period.
These results are consistent with some, but not all, of the literature on the
environmental effects of income inequality. Ravallion et al. (2000) and Scruggs (1998),
among others, find that greater income inequality decreases the average level of emissions
or pollutant concentrations. However, a recent study by Zwickl and Moser (2015), which
utilizes variation within regions of the United States over time as I do here, finds that
income inequality, when measured by the Gini coefficient, increases average pollution
exposure. My results, when they differ from the previous literature, however, have two
distinct advantages that tend to make them more arguably credible. First, unique in
this literature, my results directly address potential time-varying endogeneity due to
household locational sorting. Second, my data on pollution exposure, derived from satellite
observations, uniformly covers areas which are not directly observed by EPA monitoring
stations. Measuring pollution exposure from outer space thus allows for more-accurate
measurement of the distribution of exposure.
Income inequality’s effect on the pollution exposure distribution is unlikely to be
fully summarized by changes in the first moment of the exposure distribution, however.
To move beyond the mean, I first examine how increasing income inequality within
metropolitan areas affects measures of “environmental injustice,” which capture the
differences in average exposure across sub-groups which are traditionally assumed to
experience different degrees of advantage or disadvantage. Table 19 presents results from
models using within-MSA differences in average exposure between African-Americans
and whites as a dependent variable. The structure of Table 19 mimics Table 18, with
increasing sets of controls from left to right (no controls in the first column, control
variables in the second, and control variables and MSA-specific trends in the third).
109
Regardless of whether the models include MSA-specific trends, greater income inequality
increases the difference in exposure between blacks and whites. This pattern is also
broadly apparent when examining the effect of increasing income inequality on the Latino-
white exposure differences in Table 20 and the rich-poor exposure gap in Table 21. The
effects of increasing income inequality on black-white differences are larger in terms of
effect size, and are statistically different from zero in almost all models, while the effect of
inequality on the rich-poor exposure gap, and the Latino-white exposure gap are at best
marginally significant.
TABLE 19. Effect of Income Inequality on Black-White Exposure Gap
(1) (2) (3)
IV Results: Gini 1.000∗∗∗ 1.091∗∗∗ 1.024∗∗
(0.320) (0.382) (0.455)
OLS Results: Gini 0.096 0.064 0.067
(0.069) (0.075) (0.089)
Observations 1,578 1,578 1,578
First Stage F 86.22 70.5 55.34
Control Variables? No Yes Yes
MSA-specific Trend? No No Yes
Notes: See Table 17 for further details
As an alternative way of moving beyond the mean, I also consider whether
rising income inequality affects the distribution of NOx exposure as summarized by
measures of environmental inequality. Table 22 reports the results of models using
my preferred measure of absolute environmental inequality, the Kolm-Pollak index. I
110
TABLE 20. Effect of Income Inequality on Latino-White Exposure Gap
(1) (2) (3)
IV Results: Gini 0.595∗∗∗ 0.549∗∗ 0.684∗∗
(0.217) (0.228) (0.285)
OLS Results: Gini 0.030 0.014 0.006
(0.054) (0.058) (0.069)
Observations 1,578 1,578 1,578
First Stage F 86.22 70.5 55.34
Control Variables? No Yes Yes
MSA-specific Trend? No No Yes
Notes: See Table 17 for further details
TABLE 21. Effect of Income Inequality on Poor-Rich Exposure Gap
(1) (2) (3)
IV Results: Gini 0.478∗∗∗ 0.462∗∗ 0.488∗∗
(0.183) (0.194) (0.239)
OLS Results: Gini 0.048 0.027 0.033
(0.038) (0.041) (0.052)
Observations 1,578 1,578 1,578
First Stage F 86.22 70.5 55.34
Control Variables? No Yes Yes
MSA-specific Trend? No No Yes
Notes: See Table 17 for further details
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select an environmental inequality aversion parameter κ = 0.5, which corresponds to
relatively utilitarian social preferences. The Kolm-Pollak index is sensitive to the absolute
differences in exposure between highly exposed and minimally exposed individuals, and
is ethically similar to the environmental justice measures used previously in this paper.
It is perhaps unsurprising that, consistent with the environmental justice results above, I
find that greater income inequality increases absolute environmental inequality across all
models.
TABLE 22. Effect of Income Inequality on Absolute Environmental Inequality
(1) (2) (3)
IV Results: Gini 0.283∗∗∗ 0.203∗∗ 0.150∗
(0.098) (0.092) (0.090)
OLS Results: Gini 0.013 0.002 0.003
(0.012) (0.012) (0.013)
Observations 1,578 1,578 1,578
First Stage F 86.22 70.5 55.34
Control Variables? No Yes Yes
MSA-specific Trend? No No Yes
Notes: See Table 17 for further details
The choice of an absolute environmental inequality aversion parameter, κ, that
corresponds to relatively utilitarian preferences is conservative in that it produces the
smallest estimated effect size. To illustrate the influence of this parameter choice on the
results, I allow for more Rawlsian preferences by allowing the absolute environmental
inequality aversion parameter to vary from κ = 0.5 to κ = 5. The size of the effect
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of income inequality on the Kolm-Pollak index of absolute environmental inequality is
monotonically increasing in κ over this range of κ.17 These results are summarized in
Figure 23. Intuitively, as social preferences become more Rawlsian (as κ → ∞), these
preferences are more sensitive to the the fate of the most exposed individual.
FIGURE 23. Illustration of how the estimated effect of Income Inequality on Absolute
Environmental Inequality changes as the assumed value of κ, capturing Absolute
Environmental Inequality aversion, increases
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Table 23 reports results from models which use, alternatively, the Atkinson index of
relative environmental inequality as a dependent variable. I find that increasing income
inequality universally increases relative environmental inequality. This is unsurprising
given the previous results on the effect of income inequality on the Kolm-Pollak index.
Recall that absolute environmental inequality indexes are translation-invariant and relative
inequality indexes are scale-invariant. Hence, if increasing income inequality reduces
average exposure in a manner that increases the differences between highly and minimally
exposed individuals, then the ratio between the highly and minimally exposed individuals
17This pattern continues for larger values of κ, although around κ = 30 the effect seems to level off.
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will also increase (so the Atkinson index would be expected to increase). These results use
a relative inequality aversion parameter of α = 0.5, which again corresponds to relatively
utilitarian social preferences. Paralleling the previous analysis, selecting larger values of α
(more Rawlsian preferences) results in larger effect sizes, as shown in Figure 24.
TABLE 23. Effect of Income Inequality on Relative Environmental Inequality
(1) (2) (3)
IV Results: Gini 0.101∗∗∗ 0.106∗∗∗ 0.100∗∗∗
(0.020) (0.023) (0.027)
OLS Results: Gini 0.008∗∗ 0.007∗ 0.006
(0.004) (0.004) (0.005)
Observations 1,578 1,578 1,578
First Stage F 86.22 70.5 55.34
Control Variables? No Yes Yes
MSA-specific Trend? No No Yes
Notes: See Table 17 for further details
Income inequality has a complex effect on environmental quality: it decreases the
average level of NOx exposure within metropolitan areas, but it also causes this exposure
to be more unequally distributed, measured either in terms of environmental justice
(across race/class lines) or in terms of an environmental inequality index. This implies
that the benefits of pollution reduction induced by greater income inequality accrue
disproportionately to the most-advantaged. This does not necessarily mean, however, that
income inequality makes the most-disadvantaged worse off in an absolute sense. Table 24
shows results of models using the within-MSA average exposure among African-Americans
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FIGURE 24. Effect of Income Inequality on Relative Environmental Inequality, varying
Relative Environmental Inequality Aversion
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as a dependent variable. Increased income inequality decreases pollution exposure among
African-Americans, across different specifications and for different sub-samples. Similarly,
Table 25 summarizes results for models using average white exposure as a dependent
variable. Rising income inequality decreases white exposure, and the estimated effect is
larger than is the effect on average black exposure.
Figure 25 illustrates how a five Gini-point increase in income inequality (roughly
the size of the observed change in the aggregate national Gini coefficient between 1990
and 2010) would affect a hypothetical distribution of NOx exposure.
18 I take as given
the estimated effect sizes in the second columns of Tables 24 and 25 as the race-specific
marginal effects of income inequality on pollution exposure. I assume for simplicity that
African-Americans and whites each experience a decrease in pollution exposure equal to
the race-specific marginal effect multiplied by a five Gini-point change in inequality. The
overall result is depicted by the distributional changes between the top and bottom panels
18The hypothetical pollution distributions are generated by simulating distributions from a Generalized
Beta distribution fitted to the aggregate national data in 2005 for whites and blacks separately.
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TABLE 24. Effect of Income Inequality on Average Black Exposure
(1) (2) (3)
IV Results: Gini −3.311∗∗ −4.951∗∗∗ −5.680∗∗∗
(1.436) (1.759) (2.190)
OLS Results: Gini −0.243 −0.427 −0.423
(0.384) (0.387) (0.452)
Observations 1,578 1,578 1,578
First Stage F 86.22 70.5 55.34
Control Variables? No Yes Yes
MSA-specific Trend? No No Yes
Notes: See Table 17 for further details
TABLE 25. Effect of Income Inequality on Average White Exposure
(1) (2) (3)
IV Results: Gini −4.311∗∗∗ −6.041∗∗∗ −6.704∗∗∗
(1.328) (1.671) (2.109)
OLS Results: Gini −0.339 −0.491 −0.490
(0.355) (0.360) (0.422)
Observations 1,578 1,578 1,578
First Stage F 86.22 70.5 55.34
Control Variables? No Yes Yes
MSA-specific Trend? No No Yes
Notes: See Table 17 for further details
116
of Figure 25. An increase in income inequality decreases the average exposure of both
groups in absolute terms, but increases the difference in average exposures across the two
groups.
FIGURE 25. Effect of an increase in income inequality on NOx exposure.
baseline
counterfactual
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       on distributions of NOx exposures for blacks and whites
This illustrates the predicted effect of a 5 Gini-point increase in inequality (approximately
the size of the increase from 1990 to 2010 nationally) on the distribution of NOx exposure
among blacks and whites. I observe (1) average exposure decreases for both groups
and (2) the gap between the two groups increases in the counterfactual higher income
inequality scenario. Baseline scenario is the smoothed national distribution of NOx
exposure in 2005, counterfactual assumes that the baseline distributions are “shifted” by
the marginal effect (column 2 in tables 24 and 25) for a 5 Gini-point change in inequality.
Mechanisms
Across a variety of model specifications, and using a number of different
measurement tools for summarizing the NOx exposure distribution in each of 265 different
MSAs, I have shown that increasing income inequality tends to reduce the average
level of pollution exposure, but also increases exposure inequality and the differences in
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exposure between advantaged and disadvantaged subgroups. My findings are inferred
from reduced-form models, so they cannot directly address the underlying mechanisms
by which these results might occur (i.e the pathways through which changes in the income
distribution might affect the pollution exposure distribution). I can, nonetheless, appeal
to some other studies to suggest potential mechanisms for the effects I observe. There are
several potential pathways from income inequality to environmental quality, including
(1) differential demands for clean air across the income distribution, (2) residential or
industrial sorting within MSAs, and (3) the political process working through legislator
ideology or legislator voting behavior.
As noted, the Environmental Kuznets curve literature provides some insight as to
how increasing income inequality might affect the level of pollution exposure. One can
think of this in two ways. First, suppose that the NOx emission intensity of a household’s
consumption bundle can be summarized by a “propensity to emit” function. Over the
range of incomes in the United States, this function is assumed to be non-decreasing
in income. If the PEF is concave in income, so that the marginal propensity to emit is
decreasing with income, then an immediate conclusion is that regressive income transfers
should decrease emissions. The marginal decrease in emissions by a poor household at
one end of the regressive transfer is larger in absolute terms than the marginal increase
in emissions by the rich household at the other end of the transfer. Although there is
not much direct evidence on the concavity of the PEF, Levinson and O’Brien (2015)
use US expenditure data to show that the closely related Environmental Engel curve—
the pollution embedded in consumption along a household’s income expansion path—is
concave in household income.
A second potential pathway from increased income inequality to decreased average
pollution exposure (and also increased environmental inequality) might occur through
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residential sorting within MSAs.19 If increases in income inequality are associated with
differential rates of migration towards relatively more polluted areas by disadvantaged
groups, perhaps due to property market dynamics, this might increase my measures of
environmental inequality, despite decreasing pollution exposure on average. Matlack and
Vigdor (2008) show, for example, that increases in income inequality within metropolitan
areas lead to higher rents and home prices at the bottom of the home price distribution.
This effect may induce poorer and more-disadvantaged households to “come to the
nuisance” in search of cheaper housing (see also Banzhaf (2012)).
A final mechanism for the relationship between income inequality and environmental
quality might work through the political system. This mechanism, however, is specific to
the institutional arrangement of US politics, and may not generalize to other countries.
Within the US political system, the party of the left (the Democrats) is generally
considered to also be the party of the environment. In other research, Voorheis et al.
(2015) investigate the effect of within-state income inequality on the average ideological
position of political parties within state legislatures. Perhaps the most striking result in
Voorheis et al. (2015) is that increasing income inequality moves state Democratic parties
further to the left.
Another small but growing literature in political science has suggested that income
inequality may be connected to what is termed “unequal democracy”. As an exemplar,
Bartels (2009) shows that US Senators are more responsive to the political opinions of
rich constituents than poor constituents. This suggests a potential mechanism for the
relationship between income inequality and pollution exposure observed in the present
study. This political mechanism can be summarized as a two-stage process. First, if
19my identification strategy addresses potential reverse causality from pollution exposure to income
inequality due to between-MSA sorting. Within-MSA residential sorting poses no such endogeneity
problems, since the Gini coefficient satisfies the property of anonymity. Within-MSA locational sorting
will not affect the Gini coefficient for that MSA.
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income inequality increases the responsiveness of legislators to rich constituents, and
demand for clean air is increasing in income, then this may induce legislators to support
more environmentally friendly legislation. Second, increased likelihood of enacting or
enforcing environmental regulation, would be expected to decrease average pollution
exposure.
Inequality and LCV Scores
I can directly examine the first stage of the proposed political mechanism in the
last section by modeling how increasing income inequality affects the environmental
voting record of elected legislators. However, this makes it necessary to change the
geographic scale of analysis to account for the specifics of the US political system. Most
environmental regulation occurs at the Federal level, making members of the US House
and Senate the obvious legislators to analyze. For reasons of data availability, I will
further restrict my attention to just the US Senate.20
To measure the environmental voting record of US senators, I will use the League
of Conservation Voters’ National Environmental Scorecard.21 The LCV has published
the scorecard annually since 1970. The scorecard gives each federal legislator (senator
or member of the House of Representatives) a score between 0 and 100, based on their
votes on a list of bills selected by the LCV as being important for the environment and
natural resources. A score of 100 represents a voting record in a given year where a
legislator voted in agreement with the LCV on all bills, while a score of 0 represents a
voting record where a legislator always voted against the LCV’s policy position. The LCV
20Income inequality data for US House districts is available only in the decennial Censuses or in the
ACS 5-year files, while Chapter II of this dissertation produces State-level inequality measures annually for
the period 1977-2014.
21The nominal, unadjusted LCV scorecard data can be accessed via the LCV website, at: http:
//scorecard.lcv.org/
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gives a separate score in each year a senator serves, so there can be non-trivial within-
senator variation that can be exploited.22 Since there are different sets of bills that are
voted on in each year, I follow the method proposed by Groseclose et al. (1999) for scaling
nominal LCV scores to ensure comparability over time. These scores are correlated with
the ideology of legislators. The most commonly used data on the ideology of senators are
the DW-NOMINATE 23 scores, which place legislators on a scale from -1 (most left-wing)
to 1 (most right-wing). Figure 26 summarizes the correlations between LCV scores and
DW-NOMINATE scores.
As expected, there is party polarization along the environmentalism dimension. To
see this further, Figure 27 plots the histogram of LCV scores by party for each Senator
serving between 1977-2014. Although the Republican party is substantially more unified
on environmental issues than is the Democratic party, as can been seen by the pronounced
peak in Republican LCV scores near zero, there is still substantial heterogeneity within
both parties.
I will analyze the effect of state-level income inequality on these adjusted LCV scores
for all senators who served during the period 1977-2014. State-level income inequality
data is available over the same time period from Chapter II of this dissertation. Unlike
the MSA-level data used above, these state-level inequality measures are calculated using
the Current Population Survey, and address Census Bureau censoring and potential under-
reporting by modeling the right tail of the income distribution as following a Generalized
Beta II distribution. I supplement these two variables of interest (State-level income
inequality and LCV scores) with state-level demographic and economic information from
22This within-legislator variation is in contrast to ideal-point estimates of legislator ideology which
assume that legislators do not change positions over time.
23Dynamically-Weighted Nominal Three-step Estimation
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FIGURE 26. Correlation Between League of Conservation Voter Scores and Ideology, US
senators
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Nominal League of Conservation Voter (LCV) scores represent the the percentage of
votes cast on environmental legislation by a senator that agree with the LCV position.
The adjusted LCV Scores shown here rescale each year’s Nominal scores to make them
comparable over time, and hence can be less than 0 or greater than 100. DW-NOMINATE
scores represent the “ideal point” of a senator on a latent ideology scale ranging from -1
(most liberal) to 1 (most conservative)
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FIGURE 27. Histogram of Adjusted LCV Scores by Party for US Senators, 1977-2014
D R
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the Current Population Survey and the Bureau of Economic Analysis’ national income
accounts.
I assume that each senator is potentially responsive to changes in income inequality
within the state that he or she represents. As with the previous analysis of the effect
of MSA-level inequality on environmental quality, and similar to Voorheis et al. (2015),
there is potential endogeneity between income inequality and the outcome of interest (in
this case, the environmental voting record of senators). In addition to the possibility of
locational sorting by a senator’s constituents, the examination of the effect of inequality
is potentially complicated by an additional source of endogeneity bias stemming from the
distributional consequences of environmental policy. To address these potential sources of
endogeneity bias, I implement an instrumental variables identification strategy similar to
that used in the earlier sections of this paper.
As before, I require an instrument for state-level income inequality that is
uncorrelated with changes in a senator’s voting record, but is correlated with the actual
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state-level income inequality experienced by that senator. I propose a version of the
simulated inequality instrument used in the previous analysis. In the state-level setting,
I construct the instrument by freezing each state’s income distribution in 1976 (the first
year in which the state-level income inequality data are available), and simulating future
counterfactual state income distributions based on nationwide trends in decile income
growth. This is instrument is constructed identically to the instrument used in Voorheis
et al. (2015), with the sole difference being an earlier starting year.
I estimate the effect of income inequality on a senator’s LCV score using a two-stage
least squares model in first differences:
First Stage: ∆Ginii,t = δi + γ∆SynthGinii,t + θ∆Xi,t + νi,t (4.13)
Second Stage: ∆Scorei,t = αi + β∆Ĝinii,t + Γ∆Xi,t + i,t (4.14)
where i now indexes senators, t indexes time in years, αi and δi are senator-specific linear
trends, and Xi,t is a vector of time varying controls, including the proportion of the
population that is black or Hispanic, the median age, median household income, poverty
rates and educational attainment in the state each senator represents.
Table 26 summarizes the basic results from this estimation. The first two columns
report the full-sample effect of income inequality on senators’ LCV scores with and
without senator-specific linear trends, respectively. The final columns report the effects
(again with and then without senator-specific linear trends) for just the sub-sample of
senators serving after 2004. This latter subsample corresponds to the time period in the
previous MSA-level results describing the effect of income inequality on the distribution
of NOx exposure. Across all specifications and all subsets of the data considered,
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however, I find that rising income inequality seems to have a positive effect on a senator’s
environmental voting record. Using results with the senator-specific trends, a one-Gini-
point increase in income inequality would increase a senator’s adjusted LCV score by 1.6
points (i.e. this greater degree of income inequality would increase the proportion of times
a senator agrees with the LCV by 1.6 percentage points).
TABLE 26. Effect of State Inequality on Senators’ LCV Scores
Adjusted LCV Score
1977–2014 2005–2014
(1) (2) (3) (4)
Gini 163.324∗∗∗ 160.154∗∗ 281.250∗ 278.416
(60.356) (64.949) (158.769) (193.750)
Control Variables? Yes Yes Yes Yes
Senator-specific Trend? No Yes No Yes
N 3,356 3,356 742 742
Notes: ∗∗∗Significant at the 1 percent level.
∗∗Significant at the 5 percent level.
∗Significant at the 10 percent level.
See Table 1 for other variables not shown here
Politics within the US Senate has become increasingly one-dimensional over the
period of the estimating sample—over 80% of roll votes can be correctly classified based
only on a senator’s DW-NOMINATE score, which captures conservative-liberal differences
(see McCarty et al. (1997)). As politics has become more polarized, it is likely that
the effect of income inequality on senators’ environmental voting records might also
be polarized along party lines. Table 27 summarizes the effect of income inequality on
the environmental voting records of senators, stratified by political party.24 The first
two columns report results for the subsample of Democratic senators (with and without
24There were 5 senators without formal party affiliation who were elected during this period. I exclude
these senators from the party-stratification analysis.
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senator-specific trends), while the final two columns report results for Republican senators.
The effect of income inequality on the environmental voting record of Democratic senators
is statistically significant, positive, and larger than the full sample results. On the other
hand, the effect on the environmental voting record of Republican senators is negative,
substantially smaller in absolute value, and very imprecisely estimated.
TABLE 27. Effect of State Inequality on Senators’ LCV Scores, By Party
Adjusted LCV Score
Democrats, 1977–2014 Republicans, 1977–2014
(1) (2) (3) (4)
Gini 499.237∗∗∗ 495.279∗∗∗ −105.548∗ −102.157
(138.356) (149.892) (56.372) (62.321)
Control Variables? Yes Yes Yes Yes
Senator-specific Trend? No Yes No Yes
N 1,708 1,708 1,597 1,597
Notes: ∗∗∗Significant at the 1 percent level.
∗∗Significant at the 5 percent level.
∗Significant at the 10 percent level.
See Table 1 for other variables not shown here
These results imply that increasing income inequality improves the environmental
voting record of Democratic senators, but has no discernible effect on Republican senators.
If demand for environmental quality is increasing in income, this is consistent with the
concept of “unequal democracy”, wherein the positions of elected officials are more closely
aligned with the preferences of the rich than the poor or middle class. In this case, an
increase in income inequality, and hence an increase in the local bargaining power of
the affluent, moves Democratic senators towards the typical position of the affluent in
terms of more environmentally friendly legislation. The differential effect of inequality on
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Democratic and Republican senators is likely the result of differing underlying levels of
environmentalism, or a different income-environmentalism gradient among party elites.
This suggests that the political system may be a plausible pathway through which
increases in income inequality affect the distribution of environmental amenities. Note
that the previous result that effects of income inequality on the distribution of NOx
exposure were stronger for the subsample when Democrats controlled federal institutions
is consistent with the Democratic-party-specific political mechanism implied in these state-
level results. To reiterate, however, these results are context-specific, and may not describe
how changes in income inequality affect environmental policy at other levels of government
(e.g. the restrictiveness of state regulations or local land use ordinances).
Conclusion
Viewing environmental justice from outer space—using satellite remote-sensing
data to infer the distribution of ground-level exposure to harmful pollutants like NOx—
provides a viable way forward for the measurement and analysis of environmental justice
and inequality. Leveraging these remotely sensed data to study environmental justice and
environmental inequality is one important contribution of this study. The near-universal
coverage and fine geographic resolution of the satellite data used in this study are far
superior to the incomplete coverage (and the endogenous placement) of ground-monitor
data so often used in previous studies.
I have shown that there is consistent and robust evidence that rising income
inequality decreases the level of average NOx exposure within metropolitan areas.
Increasing income inequality also appears to increase the differences in exposure between
advantaged and disadvantaged groups, and increases measures of environmental inequality.
This pattern implies that the benefits of pollution reduction tend to disproportionately
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accrue to the most advantaged. However, income inequality still decreases the absolute
level of exposure among the most disadvantaged—either in terms of class, race or degree
of exposure. These results hold for a variety of specifications, and for various normative
assumptions underlying the empirical measurement of environmental inequality (such as
the assumed degree of environmental inequality aversion in the social welfare function).
I offer some evidence that the effect of increasing income inequality on the
distribution of environmental amenities may work through the political system. Using a
state-level simulated instrument strategy similar to that employed elsewhere in this paper
for MSAs, I use state-level data to identify the causal effect of income inequality on the
environmental voting record of US senators. I find that income inequality increases the
LCV scores of senators, and that this effect appears to be concentrated among Democratic
senators.
NOx exposure is a major public health concern in the United States and Europe,
contributing to thousands of premature deaths. The fact documented here—that rising
income inequality appears to mitigate this exposure to a measurable extent—suggests
that there may be unanticipated local effects of inequality that have not previously been
recognized. These reductions in exposure are not equally shared, because greater income
inequality increases the difference in exposure between advantaged and disadvantaged
groups. These results add nuance to the discussion of the effects of increasing inequality
in the United States. One particularly important implication of this research is that
the effect of inequality on the distribution of pollution exposure may lead to a further
propagation of inequality into the future, due to the widening gap in exposure between
children born to rich and poor parents.
There is considerable further work to be done on this topic. In particular, I have
shown an effect only for one pollutant. Using satellite data and/or monitoring data to
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examine the relationship for other important pollutants, including particulate matter and
ozone, may be instructive. It will also be relevant to examine the relationship between
inequality and pollution exposure for other countries and regions, including the EU, India
and China. Further investigating the possible mechanisms behind the observed reduced-
form relationship between income inequality and the environment is another important
direction for research.
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CHAPTER V
CONCLUSION
In the three substantive chapters of this dissertation, I have shown how rising income
inequality may be an important driver of improvements in environmental quality and,
more sinisterly, inequality in the distribution of environmental disamenities. These results
are highly relevant in the current policy environment, in which rising income inequality
and the environmental challenges of climate change and the health impacts of air pollution
are salient topics. These chapters add to several important literatures across sub-fields
within economics, and introduce new data, modelling tools and extend identification and
inference strategies in ways that will benefit future researchers.
Chapter II adds to the stock of knowledge about one of the most pressing concerns
of the current time: the growth in income inequality. The new datasets of income
inequality measures at the state and metropolitan area level represent an extension of
the literature on using survey data to measure income inequality, specifically by extending
the method of using the Generalized Beta II distribution to address topcoding and under-
reporting first proposed by Burkhauser et al. (2011). Using this data, I also contribute to
understanding the determinants of rising inequality, identifying declining unionization and
reductions in top marginal tax rates as the most important among potential explanations.
I find less compelling evidence for explanations relying on changes in human capital or
skill-biased technological change. This bolsters claims by, among others, DiNardo et al.
(1996) and Piketty et al. (2014) that the recent rise in inequality may be the result of
policy, such as changes in tax rates and legislation designed to reduce the bargaining
power of unions.
Chapter III provides two main contributions to the literature on environmental
inequality and environmental justice. First, I leverage satellite-derived remote sensing
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data to measure the distribution of exposure to two important pollutants. Although the
use of satellite data to measure pollution exposure is common in other fields, it has not yet
become common in the environmental economics literature (this chapter, and Chapter IV
represent the first use of these data in economics to my knowledge). Due to the fact that
satellite data provide substantially better spatial coverage than data derived from ground
monitoring stations, and provide a better picture of actual exposure than conventional
air quality models, since the satellite data captures ground-level concentrations deriving
from all sources, whereas most air quality models only capture exposure to pollution
from stationary emissions sources. In addition to bringing this potentially quite valuable
data source into the economics literature, I also contribute to the literature on measuring
environmental inequality. I propose a dashboard approach to measuring environmental
inequality, combining the vertical equity approach of Sheriff and Maguire (2014) with
the horizontal equity approach of the environmental justice literature (e.g. Mohai et al.
(2009)). Using the satellite data to calculate the various environmental inequality
measures that compose this “dashboard” for the entire United States annually over the
period 1998-2014.
Chapter IV combines the datasets introduced in the Chapters II and III to examine
whether rising income inequality within metropolitan areas might be related to changes
in the distribution of pollution exposure. Identifying the causal effect of inequality on
an outcome such as pollution requires care, as locational sorting may bias naive OLS
estimates which do not account for reverse causality. I extend an approach to causal
inference on the effects of income inequality first proposed in Boustan et al. (2013), in
which I simulate an instrument for MSA-level income inequality using national level trends
in income growth at deciles of the income distribution. This approach is an important
tool in the small but growing literature on the causal effects of rising income inequality
on other outcomes of interest. Using the new datasets produced in the previous chapters
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with the causal identification approach presents a way forward for the literature on the
environmental effects of income inequality, which, since Boyce (1994) has been plagued by
insufficient or incomplete data and a lack of clean identification. I also examine a potential
political economy explanation for the environmental effects of inequality. This adds to the
political economy literature on the connection between income inequality and the political
process (e.g. McCarty et al. (1997), Bartels (2009)), and connects this political economy
literature to the literature of environmental inequality and the environmental effects of
income inequality.
The results presented in this dissertation represent the core of a broader research
agenda examining interrelations among income inequality, the environment and the
political process. One important project running parallel to this is dissertation is Voorheis
et al. (2015), an examination of the effect of income inequality on political polarization in
US State legislatures. Using the data from Chapter II and a similar identification strategy
to that used in chapter IV, we find that income inequality increases political polarization
by inducing the replacement of moderate Democratic legislators with more conservative
Republican legislators. We provide suggestive evidence that campaign contributions may
serve as a potential mechanism for this effect, by allowing the effect of income inequality
on polarization to vary systematically in state-years in which pre-Citizens United caps on
independent campaign expenditures were in effect. I further examine the effect of income
inequality on the environment in Voorheis (2016), which presents evidence that income
inequality might lead to a reduction in carbon emissions, a result consistent with Chapter
IV.
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APPENDIX A
MEASURING STATE INCOME INEQUALITY BY COMBINING CPS AND IRS DATA
Introduction
We have income information from two sources: public use microdata from the
Current Population Survey, and data on number of tax returns and adjusted gross income
for income bands. The first substantive chapter of this dissertation uses the former to
estimates measures of state-level income inequality, while Frank (2009) and uses the
latter. Each data source has drawbacks. The CPS data may incorrectly capture top
incomes for two reasons: (1) top earners may systematically under-report (or differentially
non-respond), and (2) the Census Bureau censors incomes above a certain threshold
(“topcoding”). Both of these will bias estimates of income inequality downwards. The IRS
data, on the other hand, contains no information on the income of non-filers. Estimates
of inequality from IRS data will likely overstate the level of inequality, especially when
inequality is captured by top income shares.
One obvious way to improve on estimates of inequality using each of the above data
sources individually is to combine information on top incomes from tax return data with
information on the rest of the income distribution using survey data. Atkinson (2007) and
Alvaredo (2011) suggest an approach for the Gini coefficient based on the approximation
that for top income share S, the Gini coefficient is approximately G∗ (1− S) +S, where G∗
is the Gini coefficient estimated for the non-top incomes. Diaz-Bazan (2015) shows that
is possible to estimate the population Gini coefficient by combining estimates of the Gini
coefficient computed using conditional distributions estimated from survey and tax data.
We propose an alternative, but similar, approach to this problem which improves
on the previous methods for combining survey and tax data in two dimensions. This
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approach relies on simulating top incomes rather than relying on an approximation based
on asymptotic behavior. This means that in practice this method can be used to estimate
any income inequality measure, not just the Gini coefficient. Additionally, as in Flaichaire
and Davidson (2007), it is possible to perform inference via semi-parametric bootstrapping
and calculate point estimates of inequality measures simultaneously.
I proceed as follows: I describe the data in detail and the steps necessary to make
income information in the CPS comparable to income information in the IRS data. I
describe the proposed method for combining information from the two series, as well as an
approach to selecting the optimal cutoff percentile. I then present estimates of inequality
using this method for US states, and compare these estimates to estimates calculated
using an approach using only information from CPS data.
Methodology
In order to combine the information from the two data sources, I need to first
accomplish three tasks. First, I need to ensure that the income concepts in the two data
sources are identical to ensure comparability. Second, I must identify the point at which
top incomes may be censored or underreported in the survey data. Finally, I need to
translate information on top incomes from the tax return data back to the survey data
in order to estimate income inequality.
Microdata from the March Current Population survey provides information on
income from a variety of sources for each member of a household. These sources include
earnings (wages, small business income, farm income), unearned income (rent, interest,
dividends) as well as taxable and non-taxable transfer income (unemployment insurance,
social security and AFDC/TANF). The summary data available from the IRS reports
“Adjusted Gross Income” (broad income), which is the sum of all taxable gross income
less a set of pre-defined allowances.
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In order to incorporate information from both sources, it is necessary to transform
the CPS income data to conform with the IRS AGI definition. I do this in two steps. I
first form “tax units” from the CPS households as follows. I first identify all dependents
in each year’s sample (all children under 18 and all students currently in school under the
age of 25). I then assign these children to the head of household (or to their parent if their
parent is not the head). I then define all non-dependents in a household as either married,
single of head of household filers depending on their marital status and whether they have
children. Finally, I define all dependents with total personal income above a threshold
($3000) as dependent taxpayers. For each of the tax units I form, I simulate AGI using
NBER’s TAXSIM, using the income information in the CPS. Since there is no information
on essentially all “above-the-line” deductions in the CPS, this may overestimate AGI.
Next, I determine the point past which I believe CPS income data is either censored
(topcoded) or under-reported; this will determine the cutpoint at which I will use IRS
information. Heuristically, I search for a point at which the CPS distribution and the IRS
distribution “match up”. For each percentile p ∈ {0.9, 0.901, 0.902, ...., 0.999}, I calculate
the threshold income at this percentile in the CPS AGI distribution, and estimate the
percentile pP at which the CPS threshold income falls in the IRS AGI distribution using
Pareto interpolation. I choose as the cutpoint past which I will use IRS information only
by minimizing |p− pP |.
Finally, I combine the information from the survey and tax return data to estimate
measures of inequality by simulating incomes above the optimally chosen percentile p.
For each state and year, I estimate the Pareto parameter α using IRS data, again via
Pareto interpolation. I then simulate n partially synthetic income distributions. For
each replication, I combine all the CPS tax units below the cutoff p, and replace all
tax units above p with random draws from a Pareto distribution with shape parameter
α and location parameter equal to the threshold income at p. I calculate income
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inequality measures ν (Fi) for each partially synthetic distribution. The resulting estimate
of inequality, considering information from both the survey and tax return data is
1
n
∑n
i=1 ν (Fi)
Data and Results
I will compare estimates of two measures of income inequality (the Gini coefficient
and the top 1%’s share of income) using the IRS Pareto imputation against two baselines.
I first compare inequality measures estimated via the IRS Pareto imputation with
estimates calculated using just the CPS data with no corrections for topcoding, and
second with the estimates from Frank (2009), which use just the IRS data. The readily
available IRS SOI summary data used in the Pareto imputation spans 1997-2012, a
relatively short period. Data for years before 1997 was published in the SOI bulletin,
although it is not made freely available in machine readable form by the IRS.
Figure 28 shows the estimates of the Gini coefficient estimated with the IRS
Pareto simulation method (in blue) and with just CPS microdata (with no correction for
topcoding, in red). For all states, the Gini coefficient estimated via the Pareto simulation
process is higher than the Gini estimated using just CPS data. There is a wide degree
of heterogeneity in the degree to which the Pareto simulation estimates diverge from the
CPS-only estimates, however. Unsurprisingly, states which are relatively richer on average
(e.g. Connecticut, New York) exhibit the widest differential between the two estimates,
while states which are poorer on average (e.g. Mississippi) exhibit only small differences.
For many (though not all) states, the trends in the Gini coefficient are largely similar for
the two measures.
Figure 29 shows the estimates of inequality measured by the top 1%’s share of
income, again comparing estimates using the Pareto simulation to estimates using only
CPS data. As with the Gini coefficient, using the Pareto simulation method substantially
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FIGURE 28. State Gini Coefficients, 1997-2012: IRS Simulation vs. CPS Baseline
Alabama Alaska Arizona Arkansas California
Colorado Connecticut Delaware Florida Georgia
Hawaii Idaho Illinois Indiana Iowa
Kansas Kentucky Louisiana Maine Maryland
Massachusetts Michigan Minnesota Mississippi Missouri
Montana Nebraska Nevada New Hampshire New Jersey
New Mexico New York North Carolina North Dakota Ohio
Oklahoma Oregon Pennsylvania Rhode Island South Carolina
South Dakota Tennessee Texas Utah Vermont
Virginia Washington West Virginia Wisconsin Wyoming
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increases estimates of the top 1% share relative to the CPS-only baseline. Unlike the Gini
coefficient case, however, the Pareto simulation estimates deviate from the CPS baseline
not just in the level of inequality, but also in trends over time for many states. This is
especially true in the last few years of the sample, where most states exhibit increasing top
1% shares from 2009-2012 using the Pareto simulation method, while top 1% shares are
flat or falling in the CPS baseline.
Figures 30 and 31 compare IRS simulation method estimates of the Gini coefficient
and top 1% share, respectively with estimates from Frank (2009), which are estimated
using only IRS data.1 The Pareto simulation estimates of the top 1% share are much
closer to the Frank estimates than they are to the CPS baseline. The largest deviations
occur between 2004-2008 for most states, where the Frank estimates of the top 1%
1This dataset has been updated through 2013, and is available at http://www.shsu.edu/eco_mwf/
inequality.html
137
FIGURE 29. State Top 1% Shares, 1997-2012: IRS Simulation vs. CPS Baseline
Alabama Alaska Arizona Arkansas California
Colorado Connecticut Delaware Florida Georgia
Hawaii Idaho Illinois Indiana Iowa
Kansas Kentucky Louisiana Maine Maryland
Massachusetts Michigan Minnesota Mississippi Missouri
Montana Nebraska Nevada New Hampshire New Jersey
New Mexico New York North Carolina North Dakota Ohio
Oklahoma Oregon Pennsylvania Rhode Island South Carolina
South Dakota Tennessee Texas Utah Vermont
Virginia Washington West Virginia Wisconsin Wyoming
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share are much higher than the IRS simulation results. The Frank estimates of the Gini
coefficient deviate much more considerably from the Pareto simulation results, however,
both in level and trends. Overall, as expected, the IRS simulation method seems to
produce estimates that are a compromise between the IRS and CPS estimates. It is
notable that the IRS simulation method can roughly match the level and trends from the
updated State inequality dataset from Frank (2009).
The IRS simulation method is only feasible for circumstances where the income
definitions in survey data can be aligned to the IRS definition, and where summary data
on tax returns and aggregate AGI by income group is available. In cases where the desired
income concept is not tax unit AGI, such as equivalized household income, or a broad
income concept that includes in-kind transfers, it is not clear how to integrate information
on the tail of the AGI distribution into an estimate of inequality in another distribution.
Nonetheless, concerns about under-reporting and censoring in the survey data are still
138
FIGURE 30. State Gini Coefficient, 1997-2012: IRS Simulation vs. Frank (2009)
Alabama Alaska Arizona Arkansas California
Colorado Connecticut Delaware Florida Georgia
Hawaii Idaho Illinois Indiana Iowa
Kansas Kentucky Louisiana Maine Maryland
Massachusetts Michigan Minnesota Mississippi Missouri
Montana Nebraska Nevada New HampshireNew Jersey
New Mexico New York North CarolinaNorth Dakota Ohio
Oklahoma Oregon Pennsylvania Rhode IslandSouth Carolina
South Dakota Tennessee Texas Utah Vermont
Virginia Washington West Virginia Wisconsin Wyoming
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FIGURE 31. State Top 1% Shares, 1997-2012: IRS Simulation vs. Frank (2009)
Alabama Alaska Arizona Arkansas California
Colorado Connecticut Delaware Florida Georgia
Hawaii Idaho Illinois Indiana Iowa
Kansas Kentucky Louisiana Maine Maryland
Massachusetts Michigan Minnesota Mississippi Missouri
Montana Nebraska Nevada New HampshireNew Jersey
New Mexico New York North CarolinaNorth Dakota Ohio
Oklahoma Oregon Pennsylvania Rhode IslandSouth Carolina
South Dakota Tennessee Texas Utah Vermont
Virginia Washington West Virginia Wisconsin Wyoming
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139
salient in these cases. One way to address these concerns is to use a semi-parametric
method similar to the Pareto simulation method described above using only survey data.
I will use a specific version of this survey data-only approach to estimate state inequality
and compare it to the Pareto simulation results produced above to judge the quality of the
survey-data only approach.
One specific way to address potentially downward biased top incomes in the survey
data is to use a multiple imputation approach. In this approach, a Generalized Beta
II distribution is fitted to the national income distribution from the CPS microdata
in each year. A cutoff is selected, past which incomes are believed to be censored or
underreported. To maintain comparability with the Pareto simulation estimates above, I
will use the cutoffs identified above using the ”lining up” method. The two data sources
line up, on average, at about the 97.5th percentile. This, and the fact that it is only
possible to use the “lining up method” for AGI income, supports the use of the 97.5th
percentile as a cutoff for non-AGI income definitions (as in Chapter II of this dissertation).
Then, as in the Pareto simulation method above, N partially synthetic datasets are
formed; each partially synthetic dataset is formed by concatenating all incomes below the
cutoff with n1 draws from the fitted GB2 distribution, where n1 is the number of incomes
above the cutoff. Inequality measures ν (Fi) are calculated from each partially synthetic
dataset, and the resulting estimate of inequality is again νˆ = 1
N
∑N
i=1 ν (Fi).
Figure 32 compares the Pareto simulation estimates of the Gini coefficient with
estimates produced using the GB2 approach using only CPS data. Remarkably, the GB2
simulation method produces estimates that very closely matches the level and trends
in inequality estimated using the Pareto simulation approach, but it does so using only
information available in the CPS. The one notable exception appears to be Wyoming,
for which the GB2 method spectacularly fails. This is likely due to the combination of
low population and extreme inequality in the right tail of the income distribution that is
140
unique to Wyoming.2 Figure 33 compares Pareto simulation estimates of the top 1% share
to the GB2 simulation estimates. Here the GB2 estimates are not quite as impressively
matched. For many states, the GB2 estimates are relatively close to the Pareto simulation
estimates, although not nearly as close as the Gini estimates are. Nonetheless, the
GB2 estimates are a substantially improvement on the baseline CPS estimates with no
correction for topcoding or underreporting.
FIGURE 32. State Gini Coefficient, 1997-2012: IRS Simulation vs. GB2 Simulation
Alabama Alaska Arizona Arkansas California
Colorado Connecticut Delaware Florida Georgia
Hawaii Idaho Illinois Indiana Iowa
Kansas Kentucky Louisiana Maine Maryland
Massachusetts Michigan Minnesota Mississippi Missouri
Montana Nebraska Nevada New Hampshire New Jersey
New Mexico New York North Carolina North Dakota Ohio
Oklahoma Oregon Pennsylvania Rhode Island South Carolina
South Dakota Tennessee Texas Utah Vermont
Virginia Washington West Virginia Wisconsin Wyoming
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Pareto Interpolation
In order to estimate the Pareto parameter α using IRS summary data, I use Pareto
interpolation. I describe the process using a single state (Alabama) in a single year (2012)
2In 2012, the average income of the top 1% in Wyoming was $4,844,205, the highest in the nation,
despite the fact that Wyoming has the smallest population of any state.
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FIGURE 33. State Top 1% Shares, 1997-2012: IRS Simulation vs. GB2 Simulation
Alabama Alaska Arizona Arkansas California
Colorado Connecticut Delaware Florida Georgia
Hawaii Idaho Illinois Indiana Iowa
Kansas Kentucky Louisiana Maine Maryland
Massachusetts Michigan Minnesota Mississippi Missouri
Montana Nebraska Nevada New Hampshire New Jersey
New Mexico New York North Carolina North Dakota Ohio
Oklahoma Oregon Pennsylvania Rhode Island South Carolina
South Dakota Tennessee Texas Utah Vermont
Virginia Washington West Virginia Wisconsin Wyoming
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IRS Pareto
by way of example. This process and notation is adapted from Sommeiller and Price
(2014). Table 28 shows the information available in Historical Table 2 in the Statistics
of Income Bulletin for Alabama.
Pareto Interpolation allows us to calculate the threshold incomes at a given
percentile p, and to estimate the Pareto shape parameter α past this threshold. To do
the interpolation, I need to proceed in steps. First, define si as the lower bound of each
income bin i. Next, define N∗ and Y ∗ as the cumulative sums of Returns and AGI, from
highest bin to lowest:
N∗i =
i∑
j=9
Nj
Y ∗i =
i∑
j=9
Yj
142
TABLE 28. Alabama Total AGI and Number of Returns, by Size of AGI, 2012
Income Bins Number of Returns AGI
1 under 10,000 340, 890 −116, 087, 000
10,000 under 25,000 575, 210 9, 742, 551, 000
25,000 under 50,000 491, 320 17, 622, 052, 000
50,000 under 75,000 254, 210 15, 629, 937, 000
75,000 under 100,000 159, 820 13, 821, 966, 000
100,000 under 200,000 182, 240 24, 071, 292, 000
200,000 under 500,000 37, 950 10, 701, 664, 000
500,000 under 1,000,000 6, 280 4, 271, 645, 000
1,000,000 or more 2, 970 8, 525, 047, 000
Define yi =
Y ∗i
N∗i
. Then I can define bi =
yi
si
, and hence the Pareto shape parameter is
αi =
bi
bi−1 . Let pi =
N∗i
Ni
and ki = si
(
p
1
αi
i
)
. I can finally derive an expression for the
threshold income value at percentile p
TI (p) =
ki
(1− p) 1αi
Or, equivalently, if I know a threshold income, the equivalent percentile is
p = 1−
(
TI (p)
ki
)−αi
This process yields estimates of TI (p) , p, αi using information from each income bin. The
final step in the interpolation process is to select which income bin’s estimates are to be
used. To do this, I select the income bin for which |p− pi| is minimized (in other words,
the bin whose cumulative percentage of incomes are higher is closest to percentile p).
I illustrate how this Pareto interpolation method can be used to improve estimates
of inequality. Let’s suppose that I know that incomes above the 99th percentile are
143
understated in the CPS data. For Alabama in 2012, the 99th percentile of AGI in the
CPS data is $215527.10. To improve these estimates, I would like to replace incomes above
this threshold with draws from the Pareto distribution implied by the IRS data. To do
this, I first calculate the percentile at which the CPS cutoff income falls in the IRS AGI
distribution pPi , and then select the income bin for which
∣∣pPi − pi∣∣ is minimized. The
Pareto parameter αi for the selected bin can then be used to simulate top incomes.
Table 29 summarizes the intermediate calculations of yi, bi, αi, pi, ki, and Table 30
summarizes the calculation of cutoff percentiles pPi and the choice of income bin, and the
Pareto parameter selected.
TABLE 29. Intermediate Calculations in the Pareto Interpolation Process
Income Bin yi bi αi pi ki
1 under 10,000 50, 841.380 5, 084, 137.000 1.000 1 0.010
10,000 under 25,000 61, 044.540 6.104 1.196 0.834 8, 589.864
25,000 under 50,000 83, 401.870 3.336 1.428 0.553 16, 518.010
50,000 under 75,000 119, 697.200 2.394 1.717 0.314 25, 459.060
75,000 under 100,000 157, 713.600 2.103 1.907 0.190 31, 373.360
100,000 under 200,000 207, 329.400 2.073 1.932 0.112 32, 177.260
200,000 under 500,000 497, 846.500 2.489 1.671 0.023 20, 944.210
500,000 under 1,000,000 1, 383, 426.000 2.767 1.566 0.005 15, 885.180
1,000,000 or more 2, 870, 386.000 2.870 1.535 0.001 14, 123.570
144
TABLE 30. Selecting the Pareto Parameter
Income Bin pPi
∣∣pPi − pi∣∣ αi
1 under 10,000 1.000 1.000 1.000
10,000 under 25,000 0.979 0.813 1.196
25,000 under 50,000 0.974 0.528 1.428
50,000 under 75,000 0.974 0.288 1.717
75,000 under 100,000 0.975 0.164 1.907
100,000 under 200,000 0.975 0.086 1.932
200,000 under 500,000 0.980 0.003 1.671
500,000 under 1,000,000 0.983 0.012 1.566
1,000,000 or more 0.985 0.014 1.535
145
Conclusion
Previous estimates of income inequality within US states have relied on data from
either the Current Population Survey or IRS tax returns. How ver, each data source has
conceptual shortcomings. I have described an approach to incorporate information from
both sources in a way that addresses the shortcomings while preserving the advantages.
This method produces estimates of income inequality which are generally much larger
than the naive results estimated from CPS data, while generally somewhat smaller than
estimates using just IRS data.
Additionally, I show that I can closely match the level and trends in the Gini
coefficient estimated using information from both the IRS and the CPS using a semi-
parametric method that uses only CPS data. This suggests that CPS-based estimates
of income inequality using income definitions other than tax unit Adjusted Gross Income
should be regarded as with significantly less skepticism than that which they are often
greeted.
146
APPENDIX B
STATE AND MSA INCOME INEQUALITY IN THE AMERICAN COMMUNITY
SURVEY
As noted earlier, the issues presented by topcoding are most severe in the Current
Population Survey. However, topcoding is not limited to the CPS. The decennial Census
and the American Community Survey1 both topcode incomes, although at a much higher
threshold than in the CPS. The Census/ACS also has much less disaggregated income
information, collecting data on only eight income sources. Each income source has a
state-specific topcode in the public use data equal to the 99.5th percentile of that income
source’s distribution in a given state. Additionally, there is a hard topcode of $999,999
in the internal Census data. For the 1990 and 2000 decennial Censuses, and for the
ACS from 2005-2011, the public use data imputes topcoded incomes with state-specific
cell means calculated in a similar manner to the CPS cell-means, although the cells are
state-based rather than demographic-based. Applying the GB2 multiple imputation
methodology to Census and ACS data is then relatively straightforward. It should be
noted, however, that there are slight differences in sample design between the CPS and
Census/ACS that must be addressed to make the two series comparable.2 I calculate the
same scalar inequality metrics and Lorenz ordinates for the Census and ACS microdata as
those produced from the CPS microdata.
Figure 34 visualizes the point estimates and bootstrap confidence intervals for the
change in Lorenz curve ordinates from 2005–2011 using ACS. I see that for almost all
1The ACS can be thought of as a successor to the decennial Census, since it replaces the “long form”
survey after 2000. The ACS is smaller, providing 1% samples of the US each year, compared to the 5%
sample available in the public use long form Census data.
2The chief difference here is that the ACS/Census and CPS have different coverage of individuals in
group quarters. Following I dropped observations from the ACS and Census coded as living in institutions,
old age homes or prisons.
147
states, the size of the change in Lorenz ordinates reaches a local minimum around the
middle of the income distribution (generally between the 50th and 75th percentiles). This
is very strong evidence against a pure “top incomes” story. It appears that not just the
top 1%, but much of the top half of the distribution, is relatively better off. This also
implies that the changes in inequality since 2005 are characterized not just by income
gains among the top 1%, but by the fact that the bottom half of the distribution is
relatively worse off than it was a decade ago. This important fact would be missed by
analyses that focus solely on the share of income going to the top 1% of the distribution.
148
FIGURE 34. Lorenz Curve Results, ACS (2005-2011)
149
APPENDIX C
DECOMPOSITION ANALYSIS OF CHANGES IN ENVIRONMENTAL INEQUALITY
RIF regressions can be used to decompose the changes between two different
distributions. Suppose that I want to analyze the difference in some functional ν between
two distributions A and B. Firpo et al. (2011) show that the overall change in the
functional νB − νA can be decomposed as
νB − νA =
K∑
k=1
XB,k
(
βˆB,k − βˆA,k
)
+
K∑
k=1
βˆA,k
(
XB,k −XA,k
)
where X i,k is the mean of the kth demographic covariate in distribution i ∈ {A,B}, and
the βˆi,k are the parameter estimates from an RIF regression using distribution i data.
Borrowing terminology from Oaxaca-Blinder wage decompositions, the first term in the
decomposition is the “structure effect,” where some part of the change is due to a change
in parameters, and the second is the “composition effect,” where some part is due to a
change in variables.
In the aggregate, these two effects can be viewed as the unexplained and explained
variation in the change in the distributional functional of interest. Additionally, each
element of the aggregate composition effect can be examined individually (this is often
termed a “detailed decomposition”). The structure effect captures all of the variation
in environmental inequality that is not due to changes in observable demographic
characteristics. The estimated structure effect in a decomposition of the change in
environmental inequality in 2005 vs. 2011 can then be thought of as an upper bound on
the environmental policy that applies to all census tracts.
I decompose the difference in each of the distributional functionals of interest
between 2005 and 2011, providing a detailed decomposition of the composition effect,
150
which describes how changes in each sociodemographic variable contribute to the overall
change in the functional.1 The aggregate structural effect then captures all variation that
is not explained by sociodemographic and economic factors. One unexplained factor that
I cannot separately identify is the aggregate influence of environmental policies (chiefly,
the continuing regulations associated with the Clean Air Act). The structure effect can
be interpreted as a rough upper bound of the aggregate effect of environmental policy on
environmental inequality.
Tables 31 and 32 summarize the results of a Oaxaca-Blinder style decomposition
using the quantile points as distributional functionals for NOx exposure and PM2.5
exposure respectively. The aggregate composition effect is positive and statistically
significant at conventional levels for the entire pollution exposure distribution, while the
aggregate structure effect is negative throughout the distribution (and larger at each
quantile). Aggregate sociodemographic changes appear to be responsible for a net increase
in exposure at any given quantile, but this effect is swamped by the effect of policy (the
structure effect).
Tables 33 and 34 decompose the changes in Lorenz ordinates for the two pollutants.2
It is possible to glean information about the contribution of changes in demographics from
the detailed decomposition terms. I can see that race and ethnicity correlate positively
with measured inequality according to the Lorenz curve, with proportionally larger effects
on the cumulative share of pollution exposure for the most polluted tracts. The black
share of a tract’s population contributes positive changes in Lorenz curves across the
exposure distribution for both PM2.5 and NOx. The opposite is true for the Hispanic
share of the population, suggesting that the proportion African-American contributes
1The detailed decomposition of the structure effect, as noted by Firpo et al. (2011) has no clear
interpretation in most cases.
2Tables 37, 38, 39 and 40 repeat the exercise for generalized and absolute Lorenz curves.
151
to rising environmental inequality, while the proportion Hispanic contributes to falling
environmental inequality.
As noted in chapters III and IV of this dissertation, the environmental justice
literature highlights the degree to which black and Latino populations are exposed to
excess pollution exposure relative to non-Hispanic whites. I can perform decomposition
exercises to further illuminate this disparity, and its connection to environmental
inequality. Following Fowlie et al. (2012), I divide census tracts into “diverse” tracts
(where the proportion of African-Americans and Latinos exceeds 30%) and non-diverse
tracts. I have observations of annual average PM2.5 and NOx exposure (and demographic
characteristics) for all tracts for each year from 2005-2011. This means I can use a panel
data extension of the RIF-based decomposition above.
Following Firpo et al. (2011), I allow each census tract to have a tract-specific fixed
effect θi, and assume that the return to the fixed effect is 1 for the non-diverse tracts (now
distribution A in my notation), and σ for the diverse tracts (now distribution B). The
change in any functional ν can be decomposed as
νB − νA =
K∑
k=1
XB,k
(
βˆB,k − βˆA,k
)
+ θB (σ − 1) +
K∑
k=1
βˆA,k
(
XB,k −XA,k
)
+
(
θB − θA
)
Where there are two new terms: θB (σ − 1) is the structure effect of the fixed effect, and(
θB − θA
)
is the composition effect of the fixed effects.
Tables 35 and 36 summarize decompositions of the difference in quantile points
between diverse and non-diverse census tracts for NOx and PM2.5 respectively. I find that
the first evidence of education effects — for heavily polluted tracts, the composition effect
of the less than high school educated proportion is negative and statistically significant.
Poverty and the unemployment rate both contribute positively to the diverse vs. non-
diverse gap for highly exposed tracts, but negatively for lightly-exposed tracts.
152
TABLE 31. NOx Quantile Detailed Decomposition, 2005 vs. 2011
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
aggregate composition 0.575*** 0.854*** 1.958*** 2.578*** 4.908***
(0.030) (0.038) (0.055) (0.071) (0.170)
aggregate structure -0.672*** -0.992*** -1.085*** -2.059*** -3.503***
(0.046) (0.048) (0.066) (0.102) (0.191)
black 0.000*** 0.001*** 0.000 -0.005*** -0.008***
(0.000) (0.000) (0.000) (0.001) (0.001)
highschool -0.008*** -0.017*** -0.036*** -0.046*** -0.034***
(0.001) (0.001) (0.002) (0.003) (0.005)
incometoneeds50to99 -0.003*** -0.005*** -0.009*** -0.021*** -0.042***
(0.000) (0.001) (0.001) (0.001) (0.003)
latino -0.021*** -0.023*** -0.041*** -0.017*** 0.002
(0.001) (0.001) (0.003) (0.003) (0.009)
lessthanhs -0.001*** 0.000* 0.001 -0.003*** 0.007***
(0.000) (0.000) (0.000) (0.001) (0.002)
medianinc 0.011*** 0.021*** 0.039*** 0.032*** -0.037***
(0.001) (0.001) (0.002) (0.002) (0.005)
unemployment 0.006*** 0.027*** 0.062*** 0.071*** 0.087***
(0.001) (0.001) (0.002) (0.003) (0.008)
Estimates show the contribution to the change in quantile points from 2005-2011.
Bootstrapped standard errors shown in parentheses.
Other sociodemographic variables omitted.
153
TABLE 32. PM2.5 Quantile Detailed Decomposition, 2005 vs. 2011
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
aggregate composition 3.043*** 1.664*** 1.779*** 2.420*** 4.940***
(0.280) (0.140) (0.169) (0.113) (0.235)
aggregate structure -2.910*** -2.863*** -3.983*** -3.463*** -2.650***
(0.391) (0.165) (0.161) (0.152) (0.167)
black -0.010*** -0.010*** -0.017*** -0.004*** 0.004***
(0.002) (0.002) (0.003) (0.001) (0.001)
highschool -0.057*** -0.039*** -0.062*** -0.029*** 0.009
(0.008) (0.004) (0.006) (0.004) (0.008)
incometoneeds50to99 -0.021*** -0.021*** -0.036*** -0.024*** -0.020***
(0.004) (0.002) (0.004) (0.002) (0.004)
latino -0.129*** -0.179*** -0.131*** -0.022*** 0.082***
(0.013) (0.008) (0.009) (0.005) (0.012)
lessthanhs -0.032*** -0.026*** -0.013*** -0.006*** -0.017***
(0.005) (0.004) (0.002) (0.001) (0.003)
medianinc 0.085*** 0.040*** 0.036*** -0.007*** -0.065***
(0.007) (0.003) (0.004) (0.002) (0.006)
unemployment 0.060*** 0.097*** 0.189*** 0.131*** 0.209***
(0.009) (0.005) (0.009) (0.006) (0.011)
Estimates show the contribution to the change in quantile points from 2005-2011.
Bootstrapped standard errors shown in parentheses.
Other sociodemographic variables omitted.
154
TABLE 33. NOx Relative Lorenz Curve Detailed Decomposition, 2005 vs. 2011
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
aggregate composition 0.001 -0.006∗ 0.038∗∗∗ 0.107∗∗∗ 0.197∗∗∗
(0.002) (0.003) (0.007) (0.009) (0.008)
aggregate structure -0.006∗∗∗ -0.023∗∗∗ -0.031∗∗∗ -0.023∗∗ -0.036∗∗∗
(0.001) (0.003) (0.006) (0.010) (0.008)
black 0.000 0.000∗∗∗ 0.000∗∗∗ 0.000∗ 0.000∗∗∗
(0.000) (0.000) (0.000) (0.000) (0.000)
highschool 0.000 0.000 -0.002∗∗∗ -0.004∗∗∗ -0.004∗∗∗
(0.000) (0.000) (0.000) (0.000) (0.000)
incometoneeds50to99 0.000∗∗∗ 0.000∗∗∗ 0.000∗∗∗ 0.001∗∗∗ 0.000
(0.000) (0.000) (0.000) (0.000) (0.000)
latino 0.000∗∗∗ -0.001∗∗∗ -0.005∗∗∗ -0.005∗∗∗ -0.002∗∗∗
(0.000) (0.000) (0.000) (0.001) (0.000)
lessthanhs 0.000∗∗∗ 0.000∗∗∗ 0.000∗ 0.000∗∗∗ 0.000∗∗∗
(0.000) (0.000) (0.000) (0.000) (0.000)
medianinc 0.000∗∗∗ 0.001∗∗∗ 0.005∗∗∗ 0.009∗∗∗ 0.008∗∗∗
(0.000) (0.000) (0.000) (0.001) (0.000)
unemployment -0.001∗∗∗ 0.000∗∗∗ 0.003∗∗∗ 0.008∗∗∗ 0.011∗∗∗
(0.000) (0.000) (0.000) (0.000) (0.000)
Estimates show the contribution to the change in RLC points from 2005-2011.
Bootstrapped standard errors shown in parentheses.
Other sociodemographic variables omitted.
155
TABLE 34. PM2.5 Relative Lorenz Curve Detailed Decomposition, 2005 vs. 2011
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
aggregate composition 0.019∗∗∗ 0.038∗∗∗ 0.014∗∗∗ -0.010∗∗∗ 0.003
(0.002) (0.004) (0.005) (0.003) (0.002)
aggregate structure 0.004∗∗ -0.008∗∗ -0.020∗∗∗ -0.024∗∗∗ -0.014∗∗∗
(0.002) (0.004) (0.004) (0.003) (0.002)
black 0.000∗∗ 0.000∗∗∗ 0.000∗∗∗ 0.000∗∗∗ 0.000∗∗∗
(0.000) (0.000) (0.000) (0.000) (0.000)
highschool 0.000∗ -0.001∗∗∗ -0.001∗∗∗ -0.001∗∗∗ -0.001∗∗∗
(0.000) (0.000) (0.000) (0.000) (0.000)
incometoneeds50to99 0.000 0.000∗∗ 0.000∗∗∗ 0.000∗∗∗ 0.000∗∗∗
(0.000) (0.000) (0.000) (0.000) (0.000)
latino -0.001∗∗∗ -0.004∗∗∗ -0.005∗∗∗ -0.004∗∗∗ -0.003∗∗∗
(0.000) (0.000) (0.000) (0.000) (0.000)
lessthanhs 0.000∗∗∗ -0.001∗∗∗ -0.001∗∗∗ 0.000∗∗∗ 0.000∗∗∗
(0.000) (0.000) (0.000) (0.000) (0.000)
medianinc 0.001∗∗∗ 0.002∗∗∗ 0.002∗∗∗ 0.002∗∗∗ 0.001∗∗∗
(0.000) (0.000) (0.000) (0.000) (0.000)
unemployment 0.000∗∗ 0.000 0.000∗ 0.000∗∗ 0.001∗∗∗
(0.000) (0.000) (0.000) (0.000) (0.000)
EEstimates show the contribution to the change in RLC points from 2005-2011.
Bootstrapped standard errors shown in parentheses.
Other sociodemographic variables omitted.
156
TABLE 35. NOx Quantile Detailed Decomposition, Diverse vs. Non-diverse tracts
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
aggregate composition -0.117*** -0.174*** 0.000 0.528*** 1.193***
(0.024) (0.025) (0.033) (0.064) (0.136)
aggregate structure 0.167 -0.096 0.597 -2.655*** -6.035***
(0.265) (0.279) (0.427) (0.949) (1.599)
black -0.192*** -0.201*** -0.025 0.454*** 0.928***
(0.019) (0.019) (0.026) (0.052) (0.097)
highschool -0.001*** 0.000 0.000 -0.001 0.001
(0.000) (0.001) (0.001) (0.001) (0.003)
incometoneeds5099 0.010** 0.005 0.007 0.046*** -0.037*
(0.004) (0.004) (0.007) (0.009) (0.020)
latino 0.056*** 0.009 -0.008 0.033 0.336***
(0.018) (0.019) (0.025) (0.050) (0.103)
lessthanhs -0.060*** -0.085*** -0.077*** 0.028 0.210***
(0.010) (0.010) (0.014) (0.024) (0.049)
medianinc -0.007* 0.012*** 0.013* -0.112*** -0.276***
(0.004) (0.004) (0.007) (0.013) (0.032)
unemployment 0.047*** 0.026*** 0.014*** -0.035*** -0.028**
(0.003) (0.004) (0.005) (0.008) (0.014)
Estimates show the contribution to the change in quantile points between
Diverse vs. Non-diverse tracts.
Bootstrapped standard errors shown in parentheses.
Other sociodemographic variables omitted.
157
TABLE 36. PM2.5 Quantile Detailed Decomposition, Diverse vs. Non-diverse tracts
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
aggregate composition -0.486*** -0.106 0.190*** 1.491*** 2.042***
(0.088) (0.117) (0.064) (0.170) (0.225)
aggregate structure 2.869** 4.826*** -1.206 -5.141*** -3.520
(1.284) (1.007) (0.840) (1.769) (2.648)
black -0.168*** -0.201** -0.135*** 0.572*** 1.291***
(0.052) (0.089) (0.050) (0.126) (0.165)
highschool -0.005** -0.002 -0.002 0.004 0.000
(0.002) (0.003) (0.001) (0.004) (0.005)
incometoneeds5099 -0.030* -0.031* 0.003 0.042 0.151***
(0.018) (0.019) (0.011) (0.027) (0.031)
latino -0.274*** 0.257*** 0.315*** 0.647*** 0.233
(0.086) (0.084) (0.042) (0.115) (0.153)
lessthanhs -0.042 -0.320*** -0.254*** -0.416*** -0.074
(0.042) (0.048) (0.024) (0.065) (0.082)
medianinc -0.026 -0.093*** -0.094*** -0.150*** 0.148***
(0.021) (0.022) (0.014) (0.032) (0.043)
unemployment 0.008 0.127*** 0.092*** 0.184*** 0.053**
(0.014) (0.014) (0.008) (0.023) (0.026)
Estimates show the contribution to the change in quantile points between
Diverse vs. Non-diverse tracts.
Bootstrapped standard errors shown in parentheses.
Other sociodemographic variables omitted.
158
TABLE 37. NOx Generalized Lorenz Curve Detailed Decomposition, 2005 vs. 2011
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
aggregate composition 0.045*** 0.140*** 0.490*** 1.071*** 1.644***
(0.002) (0.006) (0.014) (0.025) (0.033)
aggregate structure -0.050*** -0.178*** -0.438*** -0.813*** -1.201***
(0.003) (0.008) (0.020) (0.033) (0.042)
black 0.000** 0.000*** 0.000*** 0.000*** -0.002***
(0.000) (0.000) (0.000) (0.000) (0.000)
highschool -0.001*** -0.002*** -0.009*** -0.019*** -0.026***
(0.000) (0.000) (0.000) (0.001) (0.001)
incometoneeds50to99 0.000*** -0.001*** -0.003*** -0.006*** -0.010***
(0.000) (0.000) (0.000) (0.000) (0.001)
latino -0.001*** -0.004*** -0.013*** -0.020*** -0.022***
(0.000) (0.000) (0.001) (0.001) (0.002)
lessthanhs 0.000*** 0.000*** 0.000 0.000 0.000
(0.000) (0.000) (0.000) (0.000) (0.000)
medianinc 0.001*** 0.003*** 0.011*** 0.021*** 0.023***
(0.000) (0.000) (0.001) (0.001) (0.001)
unemployment 0.000 0.002*** 0.014*** 0.031*** 0.044***
(0.000) (0.000) (0.001) (0.001) (0.001)
Estimates show the contribution to the change in GLC points from 2005-2011.
Bootstrapped standard errors shown in parentheses.
Other sociodemographic variables omitted.
159
TABLE 38. NOx Absolute Lorenz Curve Detailed Decomposition, 2005 vs. 2011
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
aggregate composition -0.143*** -0.330*** -0.450*** -0.339*** -0.048***
(0.003) (0.008) (0.014) (0.015) (0.011)
aggregate structure 0.105*** 0.210*** 0.338*** 0.350*** 0.195***
(0.005) (0.012) (0.022) (0.026) (0.024)
black 0.000*** 0.000*** 0.001*** 0.000*** -0.001***
(0.000) (0.000) (0.000) (0.000) (0.000)
highschool 0.002*** 0.004*** 0.005*** 0.001* -0.002***
(0.000) (0.000) (0.001) (0.001) (0.001)
incometoneeds50to99 0.001*** 0.003*** 0.005*** 0.005*** 0.003***
(0.000) (0.000) (0.000) (0.000) (0.000)
latino 0.002*** 0.003*** 0.000 0.000 0.003**
(0.000) (0.000) (0.001) (0.001) (0.001)
lessthanhs 0.000*** 0.000*** 0.000** -0.001*** -0.001***
(0.000) (0.000) (0.000) (0.000) (0.000)
medianinc -0.001*** -0.001*** 0.004*** 0.010*** 0.010***
(0.000) (0.000) (0.000) (0.001) (0.001)
unemployment -0.004*** -0.007*** -0.005*** 0.003*** 0.010***
(0.000) (0.000) (0.001) (0.001) (0.001)
Estimates show the contribution to the change in ALC points from 2005-2011.
Bootstrapped standard errors shown in parentheses.
Other sociodemographic variables omitted.
160
TABLE 39. PM2.5 Generalized Lorenz Curve Detailed Decomposition, 2005 vs. 2011
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
aggregate composition 0.340*** 0.857*** 1.237*** 1.736*** 2.363***
(0.031) (0.062) (0.093) (0.101) (0.115)
aggregate structure -0.117*** -0.621*** -1.506*** -2.411*** -2.867***
(0.022) (0.059) (0.094) (0.108) (0.109)
black -0.001*** -0.003*** -0.006*** -0.009*** -0.009***
(0.000) (0.000) (0.001) (0.001) (0.001)
highschool -0.003*** -0.012*** -0.025*** -0.033*** -0.037***
(0.001) (0.002) (0.002) (0.003) (0.004)
incometoneeds50to99 -0.001*** -0.005*** -0.013*** -0.019*** -0.023***
(0.000) (0.001) (0.001) (0.002) (0.002)
latino -0.014*** -0.052*** -0.091*** -0.107*** -0.104***
(0.001) (0.003) (0.005) (0.005) (0.006)
lessthanhs -0.002*** -0.008*** -0.013*** -0.014*** -0.016***
(0.000) (0.001) (0.002) (0.002) (0.002)
medianinc 0.008*** 0.020*** 0.029*** 0.032*** 0.028***
(0.001) (0.001) (0.002) (0.002) (0.003)
unemployment 0.005*** 0.022*** 0.059*** 0.097*** 0.127***
(0.001) (0.002) (0.003) (0.004) (0.005)
Estimates show the contribution to the change in GLC points from 2005-2011.
Bootstrapped standard errors shown in parentheses.
Other sociodemographic variables omitted.
161
TABLE 40. PM2.5 Absolute Lorenz Curve Detailed Decomposition, 2005 vs. 2011
p=0.1 p=0.25 p=0.5 p=0.75 p=0.9
aggregate composition 0.068*** 0.178*** -0.123*** -0.304*** -0.085***
(0.024) (0.042) (0.042) (0.029) (0.016)
aggregate structure 0.196*** 0.162*** 0.060 -0.062** -0.048**
(0.019) (0.038) (0.045) (0.027) (0.019)
black 0.000*** 0.000*** -0.002*** -0.002*** -0.001***
(0.000) (0.000) (0.000) (0.000) (0.000)
highschool 0.000 -0.004*** -0.008*** -0.008*** -0.007***
(0.001) (0.001) (0.001) (0.001) (0.001)
incometoneeds50to99 0.001*** 0.001 0.000 -0.001** -0.001***
(0.000) (0.001) (0.001) (0.000) (0.000)
latino -0.004*** -0.029*** -0.046*** -0.039*** -0.023***
(0.001) (0.002) (0.002) (0.002) (0.001)
lessthanhs -0.001*** -0.004*** -0.004*** -0.001*** -0.001***
(0.000) (0.001) (0.001) (0.000) (0.000)
medianinc 0.006*** 0.015*** 0.018*** 0.016*** 0.009***
(0.000) (0.001) (0.001) (0.001) (0.001)
unemployment -0.009*** -0.013*** -0.011*** -0.008*** 0.002**
(0.001) (0.001) (0.002) (0.001) (0.001)
Estimates show the contribution to the change in ALC points from 2005-2011.
Bootstrapped standard errors shown in parentheses.
Other sociodemographic variables omitted.
162
APPENDIX D
ADDITIONAL TABLES AND FIGURES
Chapter II Miscellaneous Tables and Figures
FIGURE 35. State-level Gini Coefficient, Pre-transfer Income
1986 1994
2000 2012
25
30
35
40
45
50
25
30
35
40
45
50
−120 −100 −80 −120 −100 −80
long
la
t
Gini
0.40
0.45
0.50
0.55
0.60
0.65
State Pre−tax, Pre−transfer Income Inequality, 1986−2012
163
FIGURE 36. State-level Gini Coefficient, Post-transfer Income
1986 1994
2000 2012
25
30
35
40
45
50
25
30
35
40
45
50
−120 −100 −80 −120 −100 −80
long
la
t
Gini
0.4
0.5
0.6
State Pre−tax, Post−transfer Income Inequality, 1986−2012
164
FIGURE 37. State-level Gini Coefficient, Post-tax Income
1986 1994
2000 2012
25
30
35
40
45
50
25
30
35
40
45
50
−120 −100 −80 −120 −100 −80
long
la
t
Gini
0.30
0.35
0.40
0.45
0.50
State Post−Tax Income Inequality, 1986−2012
165
FIGURE 38. State-level Gini Coefficient, Post-fiscal Income
1986 1994
2000 2012
25
30
35
40
45
50
25
30
35
40
45
50
−120 −100 −80 −120 −100 −80
long
la
t
Gini
0.25
0.30
0.35
0.40
State Post−fiscal Income Inequality, 1986−2012
166
TABLE 41. Determinants of State Income Inequality (Pre-transfer and Post-transfer
Gini), All Covariates
Dependent variable:
(1) (2) (3) (4) (5) (6)
union cov −0.231∗∗∗ −0.323∗∗∗ −0.327∗∗∗ −0.183 −0.320∗∗ −0.338∗∗
(0.085) (0.108) (0.124) (0.121) (0.142) (0.163)
state minwage −0.0001 −0.001 −0.002 0.0004 −0.001 −0.001
(0.002) (0.002) (0.002) (0.003) (0.002) (0.003)
Total rate capgains −0.006∗∗∗ −0.007∗∗ −0.008∗ −0.008∗∗∗ −0.008∗∗ −0.009
(0.002) (0.003) (0.004) (0.002) (0.004) (0.006)
Total rate wages 0.003 0.004 0.004 0.006∗ 0.005 0.004
(0.003) (0.004) (0.005) (0.004) (0.005) (0.006)
UR 0.004∗∗∗ 0.003∗∗ 0.002 0.004∗∗ 0.004∗ 0.002
(0.001) (0.001) (0.002) (0.002) (0.002) (0.003)
Real PersIncPC 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000∗
(0.00000) (0.00000) (0.00000) (0.00000) (0.00000) (0.00000)
college prop 0.077 0.130 0.0001 0.163 0.183 0.062
(0.144) (0.169) (0.178) (0.188) (0.234) (0.247)
std educ 0.009 0.012 0.011 0.017 0.022 0.016
(0.017) (0.023) (0.021) (0.022) (0.030) (0.025)
mean educ −0.021 −0.032 −0.013 −0.005 −0.007 0.002
(0.022) (0.026) (0.030) (0.028) (0.036) (0.039)
manufacturing −0.035 0.044 −0.073 0.022 0.090 −0.063
(0.070) (0.111) (0.132) (0.090) (0.144) (0.170)
popdens −0.0001 −0.0002 −0.001 −0.0001 0.00004 −0.001
(0.0001) (0.0005) (0.001) (0.0001) (0.0005) (0.001)
RD percap −0.042∗∗ −0.125∗∗∗ −0.048 −0.034 −0.159∗∗∗ −0.055
(0.018) (0.039) (0.062) (0.023) (0.047) (0.070)
total patents PC 0.013 0.024 0.015 0.021 0.028 0.013
(0.011) (0.015) (0.023) (0.014) (0.020) (0.028)
GovtPC −7.169 −15.692∗∗ −9.810 −4.184 −13.262 −9.147
(4.772) (7.443) (8.851) (6.066) (9.290) (10.275)
black 0.108∗∗ 0.121∗∗ 0.097 0.099 0.105 0.115
(0.054) (0.061) (0.073) (0.069) (0.083) (0.095)
167
latino 0.087 0.085 0.099 0.198∗∗∗ 0.149 0.160
(0.064) (0.091) (0.099) (0.076) (0.119) (0.129)
age 0.001 0.0001 −0.001 0.002 0.001 −0.001
(0.001) (0.002) (0.001) (0.002) (0.002) (0.002)
married 0.158 0.098 −0.036 0.328∗∗∗ 0.240∗ 0.082
(0.102) (0.115) (0.121) (0.126) (0.144) (0.147)
divorced 0.181 0.057 −0.115 0.159 0.023 −0.156
(0.166) (0.172) (0.152) (0.218) (0.228) (0.197)
over55 0.038 0.098 0.040 −0.100 0.024 −0.017
(0.085) (0.099) (0.116) (0.116) (0.130) (0.149)
under25 0.120 −0.017 −0.177 0.162 0.019 −0.171
(0.135) (0.147) (0.127) (0.175) (0.184) (0.143)
noncitizen 0.260∗ −0.003 −0.064 0.255 0.069 −0.037
(0.140) (0.205) (0.243) (0.155) (0.258) (0.285)
nativeborn 0.143 −0.011 −0.006 0.226 0.088 0.076
(0.127) (0.155) (0.178) (0.155) (0.193) (0.221)
Linear Trends? No Yes Yes No Yes Yes
Quad. Trends? No No Yes No No Yes
Observations 1,000 1,000 1,000 1,000 1,000 1,000
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
All models include State and Year fixed effects
TABLE 42. Determinants of State Income Inequality (Post-tax and Post-fiscal Gini), All
Covariates
Dependent variable:
(1) (2) (3) (4) (5) (6)
union cov −0.160∗∗ −0.220∗∗ −0.195∗ −0.115 0.009 0.001
(0.080) (0.097) (0.113) (0.128) (0.145) (0.173)
state minwage 0.001 0.00002 −0.001 −0.003 0.001 −0.0003
(0.002) (0.002) (0.002) (0.002) (0.003) (0.004)
Total rate capgains −0.006∗∗∗ −0.006∗∗ −0.007∗ −0.005 −0.003 −0.005
(0.002) (0.003) (0.004) (0.003) (0.006) (0.007)
Total rate wages 0.004∗ 0.004 0.004 0.004 0.004 0.005
(0.002) (0.004) (0.005) (0.004) (0.007) (0.009)
UR 0.003∗∗∗ 0.003∗∗ 0.003 0.001 0.001 −0.0004
168
(0.001) (0.001) (0.002) (0.002) (0.002) (0.003)
Real PersIncPC 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
(0.00000) (0.00000) (0.00000) (0.00000) (0.00000) (0.00000)
college prop 0.084 0.082 −0.014 −0.147 −0.056 −0.142
(0.130) (0.157) (0.168) (0.198) (0.271) (0.300)
std educ 0.006 0.011 0.009 −0.018 −0.027 −0.027
(0.015) (0.020) (0.018) (0.022) (0.027) (0.031)
mean educ −0.015 −0.016 −0.003 0.031 0.015 0.026
(0.020) (0.025) (0.028) (0.029) (0.038) (0.044)
manufacturing 0.006 0.044 −0.054 0.192∗ 0.106 −0.006
(0.062) (0.099) (0.117) (0.098) (0.164) (0.182)
popdens −0.0001 0.00001 −0.0004 −0.0003∗∗ 0.0001 0.00002
(0.0001) (0.0003) (0.0004) (0.0001) (0.001) (0.001)
RD percap −0.025∗ −0.116∗∗∗ −0.031 −0.054∗ 0.052 −0.051
(0.015) (0.032) (0.054) (0.033) (0.075) (0.115)
total patents PC 0.012 0.021 0.016 0.004 0.040∗ 0.043
(0.010) (0.014) (0.020) (0.016) (0.023) (0.037)
GovtPC −3.729 −11.331∗ −6.775 4.831 −1.080 0.248
(4.034) (6.566) (7.622) (8.164) (9.778) (13.843)
black 0.110∗∗ 0.118∗∗ 0.098 0.124 0.135 0.085
(0.049) (0.057) (0.067) (0.139) (0.149) (0.173)
latino 0.102∗∗ 0.111 0.115 0.066 0.298∗ 0.326∗
(0.052) (0.085) (0.091) (0.111) (0.160) (0.172)
age 0.001 0.0003 −0.001 0.003 0.002 0.001
(0.001) (0.001) (0.001) (0.002) (0.002) (0.003)
married 0.184∗∗ 0.129 0.021 −0.063 −0.053 −0.185
(0.083) (0.097) (0.101) (0.201) (0.213) (0.247)
divorced 0.162 0.067 −0.081 −0.009 −0.075 −0.217
(0.148) (0.156) (0.137) (0.199) (0.215) (0.229)
over55 −0.059 0.020 −0.007 −0.218∗ −0.176 −0.270
(0.079) (0.088) (0.107) (0.121) (0.148) (0.178)
under25 0.110 0.001 −0.137 −0.112 −0.181 −0.330
(0.121) (0.130) (0.109) (0.217) (0.242) (0.281)
noncitizen 0.191∗ 0.001 −0.027 0.115 −0.815∗∗ −0.787∗
169
(0.103) (0.179) (0.210) (0.182) (0.354) (0.414)
nativeborn 0.124 0.028 0.053 0.032 −0.247 −0.187
(0.109) (0.134) (0.149) (0.146) (0.203) (0.247)
Linear Trends? No Yes Yes No Yes Yes
Quad. Trends? No No Yes No No Yes
Observations 1,000 1,000 1,000 1,000 1,000 1,000
170
Chapter III Miscellaneous Tables and Figures
FIGURE 39. National Black-White PM2.5 Exposure Ratio (by Percentile), 1998-2014
1998 1999 2000 2001 2002
2003 2004 2005 2006 2007
2008 2009 2010 2011 2012
2013 2014
1.0
1.2
1.4
1.0
1.2
1.4
1.0
1.2
1.4
1.0
1.2
1.4
0.25 0.50 0.75 0.25 0.50 0.75
percentile
Bl
ac
k/
W
hi
te
 P
M
2.
5 
Ex
po
su
re
 R
at
io
Black/White PM2.5 Exposure Ratio, by Percentile
171
FIGURE 40. National Black-White NOx Exposure Ratio (by Percentile), 2005-2011
2005 2006 2007
2008 2009 2010
2011
1.0
1.5
2.0
2.5
3.0
1.0
1.5
2.0
2.5
3.0
1.0
1.5
2.0
2.5
3.0
0.00 0.25 0.50 0.75 1.00
percentile
Bl
ac
k/
W
hi
te
 E
xp
os
ur
e 
Ra
tio
Black/White NOx Exposure Ratio, by Percentile
172
Chapter IV Miscellaneous Tables and Figures
TABLE 43. Effect of Income Inequality on Average Latino Exposure
(1) (2) (3)
IV Results: Gini −3.717∗∗∗ −5.493∗∗∗ −6.020∗∗∗
(1.388) (1.702) (2.114)
OLS Results: Gini −0.309 −0.477 −0.484
(0.373) (0.377) (0.445)
Observations 1,578 1,578 1,578
First Stage F 86.22 70.5 55.34
Control Variables? No Yes Yes
MSA-specific Trend? No No Yes
Notes: See Table 17 for further details
173
TABLE 44. Effect of Income Inequality on Average Poor Exposure
(1) (2) (3)
IV Results: Gini −3.696∗∗∗ −5.460∗∗∗ −6.117∗∗∗
(1.374) (1.701) (2.131)
OLS Results: Gini −0.287 −0.465 −0.461
(0.368) (0.373) (0.437)
Observations 1,578 1,578 1,578
First Stage F 86.22 70.5 55.34
Control Variables? No Yes Yes
MSA-specific Trend? No No Yes
Notes: See Table 17 for further details
TABLE 45. Effect of Income Inequality on Average Rich Exposure
(1) (2) (3)
IV Results: Gini −4.174∗∗∗ −5.922∗∗∗ −6.605∗∗∗
(1.341) (1.683) (2.121)
OLS Results: Gini −0.335 −0.491 −0.494
(0.359) (0.366) (0.428)
Observations 1,578 1,578 1,578
First Stage F 86.22 70.5 55.34
Control Variables? No Yes Yes
MSA-specific Trend? No No Yes
Notes: See Table 17 for further details
174
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