ESSAYS ON HEALTH AND DEVELOPMENT ECONOMICS
by
REBEKAH J. SELBY
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 2017
DISSERTATION APPROVAL PAGE
Student: Rebekah J. Selby
Title: Essays on Health and Development Economics
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:
Benjamin Hansen Chair
Alfredo Burlando Core Member
Van Kolpin Core Member
Ryan Light 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 2017
ii
c© 2017 Rebekah J. Selby
iii
DISSERTATION ABSTRACT
Rebekah J. Selby
Doctor of Philosophy
Department of Economics
June 2017
Title: Essays on Health and Development Economics
This dissertation explores the impact of policy and economic conditions on
the current economic crises of crime, substance abuse, and financial exclusion faced
domestically and abroad. Although these issues span the income distribution,
impoverished regions are disproportionately affected by the highest rates of risky behaviors
such as drug abuse and crime. The ability for public policy makers to affect large
populations of at-risk individuals can be difficult; oftentimes, these groups operate outside
of the public sphere and large-scale interventions can miss the mark.
In my first substantive chapter, I investigate the efficacy of state-wide insurance
reform aimed at reducing drug dependency by requiring insurance providers to cover
rehabilitation and detoxification. Utilizing state-level panel data in a generalized
differences-in-differences framework, I find that states which enact laws expanding
insurance coverage are successful at encouraging treatments for some types of conditions
but are limited in their ability to reach individuals struggling with opiate addiction and,
correspondingly, have little impact on deterring accidental overdose deaths.
In my second substantive chapter, I question the assumptions made in previous
empirical work regarding the relationship between economic conditions and crime.
Existing literature finds that property crime rates are positively correlated with the
unemployment rate. In this paper, I investigate whether this relationship is evolving over
iv
time and find that the relationship between property crime rates and unemployment has
diminished toward zero. Moreover, I find evidence that there is a non-zero relationship
between unemployment and violent crimes during certain periods in time.
In my last substantive chapter, we develop a theoretical model illustrating the
basic trade-offs in the functioning of financial institutions (Village and Savings Loan
Associations) designed to provide financial inclusion to under-served populations in
developing countries. We develop a theoretical model which suggests that these groups
lack a mechanism to ensure equilibrium in the supply and demand for funds. We test the
predictions of this model using experimental data from newly formed groups in Uganda
and find that groups operate with excess demand for loans but are often able to generate a
high return on savings.
This dissertation includes previously unpublished co-authored material.
v
CURRICULUM VITAE
NAME OF AUTHOR: Rebekah J. Selby
GRADUATE AND UNDERGRADUATE SCHOOLS ATTENDED:
University of Oregon, Eugene
Eastern Washington University, Cheney
DEGREES AWARDED:
Doctor of Philosophy, Economics, 2017, University of Oregon
Master of Science, Economics, 2012, University of Oregon
Bachelor of Arts, Economics, 2011, Eastern Washington University
AREAS OF SPECIAL INTEREST:
Health Economics
Development Economics
Labor Economic
Economics of Crime
GRANTS, AWARDS AND HONORS:
Kleinsorge Summer Research Fellowship, University of Oregon, 2016
Econometrics Scholarship, University of Oregon, 2012
Graduate Teaching Fellowship, University of Oregon, 2011-2017
Distinctive Scholar Award, University of Oregon, 2011
vi
ACKNOWLEDGEMENTS
I am grateful for the continuous support and advice I have received from Benjamin
Hansen, Alfredo Burlando, and Van Kolpin. I also appreciate the suggestions provided
by Glen Waddell and Michael Kuhn which have greatly improved the quality of my
work. I would also like to thank the individuals involved with University of Oregon
Microeconomics Group, the Western Economic Association International Annual
Conference, and the Northwest Development Workshop for the valuable feedback which
helped to shape the papers I present in this dissertation.
vii
For my daughter, Emma Grace Selby.
viii
TABLE OF CONTENTS
Chapter Page
I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
II. THE IMPACT OF SUBSTANCE ABUSE INSURANCE MANDATES . . . . . . 4
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Empirical Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Heterogeneity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
III. THE EVOLVING CYCLICALITY OF ECONOMIC CONDITIONS AND
CRIME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Empirical Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Age Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
IV. THE ECONOMICS OF SAVINGS GROUPS . . . . . . . . . . . . . . . . . . . . 77
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Background Information on Savings Groups . . . . . . . . . . . . . . . . . . 79
Some Stylized Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
A Model of Savings Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
ix
Chapter Page
V. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
A. LEDGER DATA CLEANING . . . . . . . . . . . . . . . . . . . . . . . 118
B. THEORETICAL EXTENSIONS . . . . . . . . . . . . . . . . . . . . . 120
C. MATHEMATICAL DERIVATIONS . . . . . . . . . . . . . . . . . . . 124
REFERENCES CITED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
x
LIST OF FIGURES
Figure Page
1. Drug Deaths by External Cause . . . . . . . . . . . . . . . . . . . . . . . . 9
2. Accidental Drug Death Rates by ICD Code . . . . . . . . . . . . . . . . . 9
3. Treatments per 100,000 Population . . . . . . . . . . . . . . . . . . . . . . 10
4. Treatment Admission Incidence Rates by Primary Drug Concern . . . . . 11
5. Property and Violent Crime Rates in the United States (1960-2010) . . . . 53
6. ECI Plot: Unemployment on Property Crime Rate (15 Year Window) . . . 57
7. ECI Plot: Unemployment on Violent Crime Rate (15 Year Window) . . . 58
8. ECI Plot: Unemployment on Property Crime Rate (10 Year Window) . . . 58
9. ECI Plot: Unemployment on Violent Crime Rate (10 Year Window) . . . 59
10. Annual Impact of Unemployment on Crime Rates . . . . . . . . . . . . . . 60
11. Annual Impact of Unemployment on Property Crimes By Age Group . . . 64
12. Annual Impact of Unemployment on Larceny By Age Group . . . . . . . . 65
13. Annual Impact of Unemployment on MV Theft By Age Group . . . . . . . 66
14. Annual Impact of Unemployment on Burglary By Age Group . . . . . . . 67
15. Annual Impact of Unemployment on Robbery By Age Group . . . . . . . 68
16. Annual Impact of Unemployment on Violent Crime by Age Group . . . . . 69
17. Annual Impact of Unemployment on Rape By Age Group . . . . . . . . . 70
18. Annual Impact of Unemployment on Assault By Age Group . . . . . . . . 71
19. Annual Impact of Unemployment on Murder By Age Group . . . . . . . . 72
20. Saving, Borrowing, and Cash-in-Box Over the Cycle . . . . . . . . . . . . 91
21. Individual Savings and Borrowing Choices . . . . . . . . . . . . . . . . . . 97
22. Two Examples of a Unique Equilibrium when k = 1. . . . . . . . . . . . . 101
23. Exogenous Shift in Aggregate Savings . . . . . . . . . . . . . . . . . . . . 104
xi
Figure Page
24. Shift in the Demand for Loans . . . . . . . . . . . . . . . . . . . . . . . . 106
25. Fraction of Groups with Low Balances by Meeting Quantile . . . . . . . . 109
26. Estimate of βq Over the Cycle . . . . . . . . . . . . . . . . . . . . . . . . . 111
xii
LIST OF TABLES
Table Page
1. State Substance Abuse Legislation . . . . . . . . . . . . . . . . . . . . . . 13
2. Summary Statistics for Substance Abuse Treatment, Overdose Rates, and
Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3. Substance Abuse Laws and Admissions into Treatment . . . . . . . . . . . 23
4. Substance Abuse Laws and Accidental Drug Overdose Deaths . . . . . . . 25
5. Impact of Laws on SAT by Primary Concern at Admission . . . . . . . . . 27
6. Impact of Laws on SAT by Source of Referral at Admission . . . . . . . . 28
7. Impact of Laws on SAT by Referral and Drug Concerns - Part A . . . . . 30
8. Impact of Laws on SAT by Referral and Drug Concerns - Part B . . . . . 31
9. Impact of Laws on SAT by Setting at Admission . . . . . . . . . . . . . . 32
10. Impact of Laws on Outpatient SAT by Drug Concern . . . . . . . . . . . . 33
11. Impact of Laws on Inpatient SAT by Drug Concern . . . . . . . . . . . . . 33
12. Robustness Checks: Scope of Law and Mental Health Laws . . . . . . . . 36
13. Robustness Checks: Placebo Tests . . . . . . . . . . . . . . . . . . . . . . 38
14. Event Study for Enactment of Laws on SAT and OD Rates . . . . . . . . 40
15. Summary Statistics: Unemployment and Crime . . . . . . . . . . . . . . . 52
16. Impact of Unemployment on Property Crime Rates . . . . . . . . . . . . . 55
17. Impact of Unemployment on Violent Crime Rates . . . . . . . . . . . . . . 56
18. Impact of Unemployment on Crime By Age Group . . . . . . . . . . . . . 62
19. Comparison of Different Types of Savings Groups . . . . . . . . . . . . . . 80
20. Summary Statistics from Audits of Ugandan Savings Groups and SAVIX . 87
21. Summary Statistics (By Share Value) . . . . . . . . . . . . . . . . . . . . . 89
22. Tabulation of Weekly Share Purchases of Individual Borrowers (44 groups) 90
23. Lending of Available Resources Over the Cycle . . . . . . . . . . . . . . . 113
xiii
Table Page
24. Description of Cashbook Cleaning Process. . . . . . . . . . . . . . . . . . . 118
xiv
CHAPTER I
INTRODUCTION
Public policy geared towards improving welfare of at-risk populations in both
developing and developed countries is both necessary and challenging. In the United
States, the opioid drug empidemic has claimed the lives of over 33,000 individuals in 2015
and the drug overdose death rate has been rising at an alarming rate over the last several
decades. Crime also continues to be an issue, particularly in impoverished regions in the
country. In developing countries, poorer rural regions often struggle to meet basic needs
and are particularly sensitive to environmental shocks such as droughts or floods.
Policy makers have long sought out large-scale policies or reforms to help improve
the outcomes for these vulnerable populations. However, because many of these
groups operate outside of the public sphere, large scale interventions may be limited in
effectiveness; thus, a rigorous analysis of the impact of interventions is warranted. In this
dissertation, I investigate the impact of state health care reform on drug abuse, revisit and
question the established relationship between unemployment and crime, and explore the
functioning of savings groups established by non-governmental organizations in Uganda.
One of the most pressing concerns in the United States has been the identification
of interventions that can successfully mitigate the continuous rise in opiate-related
fatalities. In Chapter II, I estimate the impact of state legislative insurance mandates
which increase coverage for rehabilitation and detoxification services for the treatment
of addictive disorders. Using text from state legislative acts, I exploit the variation in
timing of enactment of laws across states in a generalized differences-in-difference model
to identify the causal impact on admissions into treatment and accidental drug overdose
deaths. I find that laws encourage admission into substance abuse treatment, primarily
1
for alcohol and marijuana, but that they are less successful at attracting admissions into
programs to treat opiate addiction. Correspondingly, I find limited evidence that laws
have a significant impact on the accidental drug overdose rate.
In Chapter III, I provide an empirically rigorous exercise to challenge assumptions
regarding the time-stability of the impact of economic conditions on crime rates. Previous
literature has consistently identified a positive relationship between unemployment and
property crime and little to no impact on violent crime rates. The empirical work assumes
that parameters are consistent over time and thus exogenous to external factors. This
assumption, though convenient, is likely invalid because the individual’s choice to commit
crime is dependent on factors that affect the return to crime and the probability of
apprehension (Becker, 1968). In this paper, I explore whether the relationship between
unemployment and crime has changed over time and I find evidence that, for property
crimes, the parameter has diminished toward zero during recent years. I also find evidence
of non-zero impacts of economic conditions on violent crimes during some periods in time.
This highlights the need for further research on the topic and suggests that policy makers
should take caution in the assumption that economic downturns will drive up crime rates.
Chapter IV is coauthored with Alfredo Burlando (University of Oregon) and
Andrea Canidio (INSEAD). In this paper, we examine the pressing concern in developing
countries to increase financial inclusion for under-served communities. Non-governmental
organizations (NGOs) helped to guide the formation of local groups called Village Savings
and Loan Associates (or savings groups) which provide small-scale banking for vulnerable
populations. Savings groups operate in many ways as micro-credit unions where involved
members save funds in a group pot and funds are distributed out in the form of short-
term loans which are repaid with interest. In this paper, we develop a theoretical model
of the functioning within these groups and and a primary conclusion is that groups lack a
2
mechanism to ensure the supply and demand for funds are equal. We test the predictions
from this model using administrative data from newly formed Ugandan savings groups
and find that groups are typically rationing available funds yet are able to generate a high
return to savings. This is indicative that these groups are providing a valuable resource
to the communities but that there exist welfare-improving changes to policies on group
formation and operation.
Taken together, this dissertation highlights three important items. Firstly, policy
interventions, such as large scale insurance reform, may have measurable benefits
on reducing risky behavior but may miss the most at-risk groups by design. These
policies are a type of “one-size-fits-all” intervention, which may be inappropriate given
the socioeconomic and demographic heterogeneity between individuals in the target
population. Secondly, policy implications arising from literature connecting increased
crime rates to changes in unemployment may be off target as the relationship between
these measures is likely endogenous to other factors. Lastly, financial inclusion of poor
populations in developing countries is improved by the establishment of savings groups.
Groups are able to generate a high rate of return to savings and can obtain funds during
periods of need; however, there is evidence of sub-optimal group behavior. In all three
cases, there is reason to believe that problematic economic outcomes can be improved
through policy but that careful consideration of the limitations will help to make programs
more successful in the future.
3
CHAPTER II
THE IMPACT OF SUBSTANCE ABUSE INSURANCE MANDATES
Introduction
Drug-related mortality has been consistently increasing in the United States over the
last several decades. In 1999, there were fewer than five accidental overdose deaths per
100,000 population and, by 2015, this number surpassed thirteen per 100,000 population.
A major component to this rise has been increased usage of opioids (such as prescription
pain medication) and opiates (such as heroin) and in more recent years the availability of
highly potent pain management drugs like Fentanyl.
Many strategies exist to reduce this mortality rate. At the most basic, drug related
deaths can be reduced by preventing drug use and access, improving the health and safety
of drug users, or by treating addiction through rehabilitation, detoxification, and therapy.
Prevention policies, such as Prescription Drug Monitoring Programs, can reduce drug use
by increasing scarcity of drugs.1 However, these policies may have a limited effect for
individuals with severe dependency to substances (and thus on the margin for overdose)
as abrupt changes to use can be life-threatening. Facilities devoted to the treatment
of addiction, such as rehabilitation and detoxification, can provide a safe environment
for reducing drug use and provide addicts with a skill set for continued sobriety after
treatment concludes.
Since as early as 1975, states have been enacting laws which require insurance
providers to include or increase benefits for substance abuse treatment (SAT). These
laws are designed to expand coverage for addiction by decreasing the out-of-pocket cost
1Prescription Drug Monitoring Programs aim to reduce access to drugs by creating a centralized
information system of drug prescription histories to be used by medical professionals.
4
to individuals requiring treatment thus encouraging individuals enter into treatment.
SAT can be prohibitively expensive, with basic services starting at around $1,000, many
individuals without insurance coverage for treatment who develop an addiction would
opt out of treatment. These high costs increase the probability of continued drug use and
overdose death and other complications of heavy drug use.2
In this paper, I examine the effectiveness of state health mandates requiring SAT
benefits to be included in insurance policies. Using panel-data empirical methods, I
estimate the impact of these mandates on SAT admission rates into detoxification and
rehabilitation programs. I also estimate the effect of these policies on accidental drug
mortality rates. I further investigate the heterogeneous impacts of law implementation on
admission rates by primary drug concern, source of referral for treatment, and treatment
setting.
I find that states which enact legislation experience an increase in admissions
into SAT programs of 13 to 25 percent. The increase is driven surprisingly by alcohol,
amphetamines3 and marijuana treatments; I find no evidence of increases in admissions
for hallucinogens, opiates4 or sedatives and tranquilizers. Rates of admission do not vary
by referral source, suggesting that mandates are both providing benefits for the person
on margin of receiving treatment as well as individuals with an unrealized demand for
services.5 Moreover, admissions into both inpatient and outpatient settings, as well as
2Common conditions include aortic stiffening, arrhythmia, coronary heart disease, brain hemorrhages,
Hepatitis, HIV, and infection.
3Primarily methamphetamine (“meth”).
4“Opiates” in this paper are defined as opioids (such as prescription pain medication like OxyContin,
methadone, and other synthetics) or opiates, (such as opium, heroin, morphine, and other natural
opium derivatives). The remainder of the paper will aggregate opiates and opioids into the term opiates,
acknowledging heterogeneity within this count.
5This can include, but is not limited to, individuals who receive sentences for DUI/DWI, use
substances but do not currently have or recognize a dependency, and individuals who may develop an
addiction following long-term use of prescription medication due to a medical condition.
5
rehabilitation and detoxification, increase at a similar rate following the legislation. This
is indicative that the laws are not exclusively encouraging individuals to seek higher cost
services, such as inpatient therapy, but rather that individuals are seeking treatment based
on their needs.
Lastly, I examine the effect that laws increasing SAT benefits have on accidental
drug overdose death (OD) rates. I find limited evidence that drug-induced mortality
decreased in states which enacted mandates. This is consistent with the finding that
admissions into treatment for opiate addictions did not increase significantly following
the enactment of the mandates. However, when controlling for state insurance mandates
increasing coverage for treatment of mental illness (excluding addictive disorders), I find
that the accidental drug OD rate decreased by about 14 percent in states with either type
of law enacted. This suggests that treatment from practitioners, in general, can help to
reduce overdose deaths.
This paper contributes to the literature investigating the impact of policies on
accidental drug mortality. Papers examining prevention programs have largely focused
on Prescription Drug Monitoring Programs (PDMP). The effectiveness of these policies
are mixed. Paulozzi et al. (2011) find that PDMPs do not significantly decrease drug
overdose or consumption of opiates, whereas Reifler et al. (2012) shows that PDMPs
were associated with a significant decrease in accidental drug poisoning reported to
the Poison Control Center and an increase in substance abuse treatment admissions.
There is also a small literature investigating the impact of education and effectiveness
of rescue medication (primarily naloxone). In particular, Walley et al. (2013) finds that
a Massachussetts overdose education and nasal naloxone distribution program, which
educated opiate users of ways to identify overdose and how to administer the rescue
medicine, decreases opioid-driven death rates. Lastly, there are few economic papers
6
investigating the impact of SAT on drug mortality. Swensen (2015) finds that increases
in SAT facilities significantly decreases the drug overdose death rate by increasing access
to care. In my paper, I provide the complementary demand-side analysis investigating the
impact of a policy designed to encourage treatment uptake.
There is also a small literature which examines the impact of state insurance
legislation on substance abuse and other risky behavior. Lang (2013) investigates
the impact of mental health insurance laws on suicide rates and finds that suicides
significantly decline following enactment. Fernandez and Lang (2015) find that the
decrease in suicide rate corresponds to a decrease in available organs for donation.
Dave and Mukerjee (2011) examines the impact of mental health insurance mandates
on uptake of rehabiliation and detoxification services and find evidence the laws have
a positive impact on treatment. Lastly, Klick and Stratmann (2006) find that states
which pass mental health laws that explicitly include substance abuse disorders see
increases in alcohol consumption. In contrast, I identify laws which affects substance abuse
insurance coverage directly, regardless of whether it has an impact on other mental health
conditions. In addition, I investigate the extent of the impact on admissions on accidental
overdose. Lastly, my heterogeneity analysis provides new insights on the mechanisms
behind the mandates.
This rest of this paper is structured as follows. First, I discuss the background
of substance abuse treatment and overdose in the United States, provide a detailed
explanation of laws in this analysis, and further discuss related literature on the impact
of insurance laws. I then describe the empirical models used in this paper and discuss
the data used in this paper. Following this, I report the results of this investigation and
conclude.
7
Background
Drug Use and Treatment in the United States
Accidental drug deaths make up the majority of drug-related mortality in the United
States.6 Intentional drug deaths (i.e. drug deaths from suicide or homicide) and deaths
where the intent is unknown make up the residual. Figure 1 illustrates the trends in
accidental, suicidal, and unknown intent drug death rates between 1999 and 2015. While
there has been little observable change in drug-related suicide over this period, there
has been large increases in the accidental drug death rate with 11,155 deaths occurring
in 1999 to well over 44,126 in 2015. This corresponds to less than four accidental drug
deaths per 100,000 population to more than thirteen per 100,000, respectively.7. This
three-fold increase is primarily driven by increases in narcotic deaths and deaths where
the drug is unspecified.8 On average there were 3.9 deaths per 100,000 population with
underling cause of death was due to an unspecified drug. Of these, these 2.4 deaths had
narcotics found during autopsy.9 The trends in death rates to non-narcotic other drugs10
experienced little change over this time period (see Figure 2).
6Drug-related mortality includes deaths where the cause of death was deemed to be “poisoning by and
exposure to noxious substances” (World Health Organization (1992)). For the purposes of this paper, I
exclude deaths due to alcohol, organic solvents, halogenated hydrocarbons, other gases and vapors, and
pesticides.
7Data accessed from CDC Wonder at http://wonder.cdc.gov on 05/19/2016. International
Classification of Diseases Codes 9th Revision (ICD-9) include E850-E858 for years 1990-1998, and ICD-
10 codes X40-X44 for years 1999-2014.
8ICD-10 codes for narcotics and unspecified other drugs is “X42” and “X44”, respectively.
9Multiple cause of death data includes up to twenty causes of death. The presences of narcotics is
coded as “T40” in these sections.
10These include nonopioid analgesics, antipyretics antirheumatics, antiepileptic, sedative-hypnotic,
antiparkinsonism, psychotropic drugs, and other drugs acting on the autonomic nervous system (ICD-10
codes “X40,” “X41”, “X43”).
8
FIGURE 1. Drug Deaths by External Cause
FIGURE 2. Accidental Drug Death Rates by ICD Code
9
Figures 3 and 4a-4h illustrate the change SAT admission rates (admissions per
100,000 population) for general admissions and by primary drug concern, respectively,
between 1990 and 2009. There is no clear upward trend in treatment admission rates, on
average, with yearly variation around the mean 650 admissions per 100,000 population.
Admissions reporting alcohol or cocaine as their primary concern have been declining
since 1992. For alcohol, treatments decreased from a high of over 350 to as low as 250
per 100,000 population. On the contrary, admissions reporting marijuana, opiates, or
sedatives and tranquilizers have been generally increasing over the period. The rise
in opiate and sedative admissions has been about two-fold and increase in marijuana
treatment admissions has been nearly three-fold.11 Treatment rates for hallucinogens and
other drugs12 did not increase or decrease systematically over the period.
FIGURE 3. Treatments per 100,000 Population
11Marijuana categorized as a Schedule I controlled substance and during this time period was illegal
under all state and federal law for recreational use. During this time, several states had passed legislation
to allow for medicinal marijuana use, but it remains illegal under federal law as of the date of this paper.
12Includes inhalants and over-the-counter medication.
10
FIGURE 4. Treatment Admission Incidence Rates by Primary Drug Concern
(a) Alcohol (b) Marijuana
(c) Opiates (d) Cocaine
(e) Amphetamines (f) Sedatives
(g) Hallucinogens (h) Other Drugs
11
SAT Insurance Mandates
Over the course of thirty years, states have enacted legislation requiring insurance
providers to increase coverage for treatment of substance abuse disorders. Table 1 includes
the enactment date and scope of law (discussed in the next subsection) for each state. By
2007, forty-two states had enacted a substance abuse insurance mandate and the majority
of laws were passed between 1990 and 2002. The laws were most often targeted at large
group health plans and often made exemptions for small group health plans.13 Typically,
mandates includes language which explicitly requires insurers to provide or offer coverage
for SAT, details the level of benefits that must be covered, discusses whether treatment for
other mental illness is subject to the law, and the effective implementation date of a law.
The following subsections discuss heterogeneity in substance abuse insurance
mandates as well as laws passed at the federal level.
Scope of Benefits Insurances laws can vary on the generosity and scope of mandated
benefits from state to state. For example, mandates may include explicit language
requiring that all new plans provide benefits if they had not done so before. Additionally,
the mandates may differ on the level of the benefits that must be provided when offered.
“Parity” laws are among the most generous, and require all new plans to include benefits
for SAT and that these benefits must be “no more restrictive” than for physical health.
“Minimum Mandated Benefit” (MMB) laws are slightly less generous; they require the
inclusion of SAT benefits in plans but allow lower coverage than benefits for physical
conditions. Lastly, “Mandated if Offered” (MIO) laws do not have explicit language
requiring benefits for treatment. However, plans including SAT benefits must meet some
minimum benefit level. While investigating the scope of benefits is not the primary focus
13The justification here is to avoid increasing premiums. Providers were also exempt if they could show
that the inclusion of benefits would increase premiums more than a minimum threshold.
12
TABLE 1. State Substance Abuse Legislation
of my paper, I investigate whether the results of the analysis are robust to breakdown by
type of law.
Health Legislation State legislatures often address substance abuse treatment
insurance coverage as a part of a comprehensive bill where addictive disorders are
categorized as a mental illness. However, several states enacted mental health laws which
explicitly excluded substance abuse disorders and other states which enacted SAT laws
without affecting other benefits. In addition, occasionally states amend an existing mental
health bill to include substance abuse disorders years after the original enactment date.
13
For the majority of this paper, I focus on laws which affect SAT benefits regardless
of whether it was packaged as part of a mental health law or passed alone. However,
there exists the possibility of spillovers from increasing mental health treatment onto
substance abuse treatment (such as referrals). Laws which increase benefits for mental
health treatment - excluding SAT - are also occasionally passed around the same time as
other laws which do increase SAT. To check for this potential endogeneity, I include other
mental health mandates in some specifications.
Federal Mandates Congress passed the Mental Health Parity and Addiction Equity
Act (MHPAEA) of 2008 which mandates that insurers provide benefits for SAT, as well
as other mental illness treatment, at parity with physical health in all plans which already
included benefits; however, this law did not require plans to offer or include benefits (a
MIO law). 14 In this paper, I focus on the impact of laws enacted at the state level before
the implementation of the MHPAEA.
Literature on Health Reform Policy
Previous literature has focused largely on the impact of legislation affecting coverage
for mental illness on treatments for mental disorders and suicide. A small set of papers
focus on substance abuse or substance abuse treatment, but do so through the lens of
mental health.
There has been mixed evidence in previous literature on the effectiveness of
insurance mandates in encouraging treatments for mental illness. Harris et al. (2006) used
quasi-experimental techniques to estimate the impact of mental health insurance reform
14Later, the Patient Protection and Affordable Care Act (ACA) in 2010 extended on the MHPAEA
by mandating all plans - including individual, HMO, and Medicaid/Medicare - to provide benefits in all
plans and that discrimination based on preexisting conditions could not be allowed. The ACA forced all
state laws to switch from MIO or MMB to full parity as well as provided insurance to over twenty million
previously uninsured individuals.
14
on mental health care utilization and found that mental health parity laws significantly
increase the probability of receiving treatment. Barry and Busch (2008b) find that mental
health parity laws are effective at increasing services for mental illness for people with
severe conditions and those who are of lower socioeconomic status. In their related paper,
Barry and Busch (2008a) find no evidence that these policies increased treatment rates for
children. Lastly, Bilaver and Jordan (2013) finds limited evidence for the effectiveness of
these laws on treatment for Autism Spectrum Disorder.
There have been several papers investigating the role of mental health insurance
laws on suicidal behavior. Suicide is strongly associated with severe mental illness and
increasing mental health insurance coverage can increase the likelihood of receiving
treatment before it manifests into suicidal behavior. Klick and Markowitz (2006) used
ordinary least squares and two-stage least square over a long panel of state suicide data
and found no evidence that a mental health parity law decreases the suicide rate. In
contrast, Lang (2013) and Fernandez and Lang (2015) find that parity laws are both
effective at reducing suicide rates but that there is a spillover onto availability of available
organs for donation.
To date, there is no paper which exclusively focuses on mandates pertaining to
substance abuse treatment. However, there are a few papers which examine differential
impacts of mental health insurance mandates which include or exclude substance abuse
disorders. Dave and Mukerjee (2011) create three categories for insurance mandates:
the first is a broad spectrum mental illness law which includes substance abuse and
has little to no exceptions, the second is a limited law which has limitations on certain
coverages, and the third being a weak law which allows exceptions for substance abuse.
In this study, they use a Poisson panel regression model and find that broad spectrum
parity laws are effective at increasing substance abuse admissions. Klick and Stratmann
15
(2006) categorize mental health insurance laws as explicitly including substance abuse,
not explicitly excluding substance abuse, and explicitly excluding substance abuse and
find that beer consumption increases if the law was a parity law that included alcohol
dependency benefits.
Empirical Methodology
Substance abuse insurance laws may affect demand for services by covering
previously uninsured individuals or by increasing the amount of services beneficiaries
undertake (extensive and intensive margin, respectively). However, if the laws increase
premiums15 then we may see fewer treatments following the laws. Further, treatment may
influence current and future drug use and alter the probability of dying due to accidental
overdose. However, there may be the reverse effect if individuals experience rational
addiction,16 or if SAT is increasing access to addictive substances.17
In order to identify the effect of insurance mandates on the SAT admission and
OD incidence rates, I exploit the timing of laws in different states. I define the vector of
indicator variables ~Lst for SAT insurance mandates laws, each taking on the value of one
in state s for all years on or after the effective year of the law and zero in previous years. I
then estimate the following log-linear model:
log(Yst) = β0 + βLst + ΓXst + δs + αt + Ωs ∗ t+ ust (2.1)
15The concern here is that as more at risk people are added to the insurance risk pool, insurance
premiums inflate. When this drives healthy people out of the risk pool, this is called a “death spiral”.
This is unlikely in these laws because of exemptions if it can be shown that premiums are likely to increase
substantially.
16That is, by reducing the cost of consuming drugs (i.e. the cost of treating addiction in the future)
individuals will increase their consumption in the present.
17Prescription methadone, in particular, is a highly abused substance and is made available through
treatment for opiate addiction.
16
where Yst is the incidence rate of SAT admissions or OD in state s at time t,
Xst includes the unemployment rate, Medicaid and Medicare expenditures per capita,
household income per capita, and demographic characteristics, δ and α are state and year
fixed effects, Ωs is a vector of state specific time trends (included in some specifications),
and st is an independent and identically distributed mean error term.
Interpretation of Estimates The null hypothesis is that β = 0, or that there is no
observable difference in SAT admission or OD rate in states following the enactment of a
law relative to having no law in place. Rejection of the null would imply that states which
switch from no law to having a law in place have a geometric average incidence rate which
is 100∗(eβ−1) percent different than the geometric average with no law enacted. For small
β, the estimated coefficient is similar in magnitude to this percent.
Identification There assumptions needed to identify causal effects in this model are
that states that enact laws have common trends in SAT and OD rates with states that
do not in absence of legislation and that state legislators are not endogenously enacting
mandates in response to generally worsening conditions in SAT or OD.
States certainly have heterogeneous trends in both measures due to differences
in other laws, preferences, and access to substances. However, the inclusion of state
fixed effects and state specific time trends help to correct for this issue. The matter of
endogenous enactment of laws is thus the primary concern and is reasonable considering
the motivations leading to propositions of SAT insurance reform. To check for this, I
perform an event-study which examines trends pre- and post-enactment. Trends prior
to enactment which show SAT rates decreasing or OD rates increases just prior to
the enactment date would create a concern that law makers are responding to these
conditions.
17
Data Description
SAT admission statistics come from the Treatment Episode Data Set for Admissions
(TEDS-A).18 The TEDS system collects administrative data on each admission into
facilities and is comprised of mainly providers that receive public funds (e.g. Federal Block
Grant) to provide substance abuse treatment. There are also some institutions that do not
receive these funds that submit their data as well. This data is available from 1992 to 2012
and the survey questions is consistent across the years.19 One primary data limitation
is the inability to distinguish between unique individuals rather than admissions. In
the same survey year, a single individual may be reported more than once if they were
admitted into a treatment program on more than one occasion. Thus, the calculated
incidence rate in this paper will be capturing service utilization rather than the percentage
of the population receiving treatment.
Data for drug-related overdose deaths comes from the Multiple Cause of Death
(MCD) files from the CDC’s National Center for Health Statistics. Spanning back to
1968, the MCD provides individual level data on the manner and place of death, the
decedent’s demographic and socioeconomic characteristics, and an array of information
about co-occurring conditions and toxicology results. I focus on deaths that are deemed
to be accidental and due to poisoning from drugs (excluding alcohol). For years 1990 to
1998, these are coded using the International Classification of Diseases, Version 9 (ICD-9)
as E850-E858. For years 1999 and forward, cause of death are coded as X40-X44 (ICD-10).
In order to construct incidence rates, I utilize state-level population data from the
Surveillance, Epidemiology, and End Results Program (SEER) funded by the National
18Obtained from Substance Abuse and Mental Health Services Administration (2014).
19While mostly balanced, there are some states in some years that are not included in TEDS-A (about
three percent of observations) due to reporting issues.
18
Cancer Institute. The SEER data set provides a modification of the Census Bureau’s
intercensal estimates and the county population estimates produced by the the Census
Bureau’s Population Estimates Program and also accounts for population changes
following Hurricane Katrina and Rita. State-level population is also decomposed by race
and single year ages. This data is also used to create state level demographic indicators,
such as percent of the population that is white, black, and in various age groups.
In addition to demographic characteristics, my analysis uses the Bureau of Labor
Statistics Local Area Unemployment Statistics estimate of the state level unemployment
rate, the Bureau of Economic Analysis estimate per capita income, and Medicaid and
Medicare health expenditures per capita (calculated using data from the Center for
Medicaid and Medicare Services and SEER population data).20 The unemployment rate
and income per capita are utilized to control for economic conditions that may influence
drug use. Medicaid and Medicare expenditures controls from contemporaneous welfare
systems that may affect health costs of individuals in these markets.
Summary Statistics
Table 2 reports summary statistics for the data used in this analysis between 1992
and 2008. There were on average 640 admissions per 100,000 population into substance
abuse treatment between 1992 and 2009. The top reported concerns at admission were
for alcohol, opiates21, cocaine, and marijuana. Approximately 62 percent of admissions
were into an outpatient program and 76 percent were into rehabilitation programs.
Over two-thirds of all admissions into treatment were from self-referrals and referrals
20This number does not reflect expenditures per enrollee. Rather it reflects the size of the health welfare
system in the state.
21“Opiates” include heroin, non-prescription methadone, and other opiates and synthetics.
19
from the courts and criminal justice system22 with 213.3 and 218.6 admissions per
100,000 population, respectively. Second to these are referrals from other health care
providers23 and community referrals24 (116.6 and 72.1 admissions per 100,000 population,
respectively). Lastly, there was an average of about 5.4 accidental ODs per 100,000
population.
Control variables include state unemployment rates, per capita real income,
real Medicaid and Medicare expenditures per capita, and state demographics. The
unemployment rate averaged about 5.4 percent and income per capita was about $36,880
in 2009 dollars. States had an average annual $1,730 and $2,140 per capita expenditures
on Medicaid and Medicare, respectively. About fifty-one percent of the population was
female, seventy percent white (non-Hispanic), thirteen percent black, fourteen percent
were between the ages of fifteen and twenty-four, fourteen percent between the ages of
twenty-five and thirty-four, thirty percent between the ages of thirty-five and fifty-four,
and thirty-percent older than age fifty-four.
Results
SAT Admissions
Table 3 reports the main results for the impact of substance abuse insurance
legislation on the SAT incidence rate. Columns (1) and (2) include estimates for univariate
and multivariate OLS with controls for socioeconomic and demographic conditions,
respectively. While insignificant, the coefficient on the dummy variable for the SAT
22Court referrals include DUI/DWI, deferred prosecution requirements, pretrial release, or before/after
judicial adjudication.
23Includes alcohol/drug abuse care providers, mental health providers, physical health providers,
hospital, and other licensed health care specialists.
24Includes schools, employers, and other community referrals such as shelters, unemployment assistance,
defense attorneys, and self-help groups like Alcoholics/Narcotics Anonymous.
20
TABLE 2. Summary Statistics for Substance Abuse Treatment, Overdose Rates, and
Controls
21
insurance mandate is positive for both specifications. Columns (3) includes the estimates
including state and year fixed effects. The exponentiated coefficient suggests that states
which enact SAT mandates have admission incidence rates 13 percent higher than in states
where there is no law in effect and is significant at the 95 percent level of confidence.
Column (4) includes the estimate when including state-specific time trends along with
fixed effects. The magnitude on the coefficient is higher than under the fixed effects
specification at 0.23 but is not statistically different than the fixed effects coefficient at
conventional significance levels. Due to the heterogeneity in SAT rates from state-to-state
in both average and trends, Columns (4) is the preferred specification.
The primary conclusion is that states which enact laws mandating insurance
coverage for SAT see substantial increases in treatment. This is indicative that the
affected population (employed and capable of maintaining health insurance coverage) has
an unmet demand for SAT in absence of legislation. However, this analysis does not reflect
the severity of conditions being treated or give any indication of whether individuals are
on the margin of receiving treatment. In a later section, I explore this by repeating this
analysis for admissions across drug concern, source of referral, and setting for admission.
Overdose Deaths
In this section, I report and detail the empirical findings on the impact of SAT
insurance mandates on overdose death incidence rates as shown in Table 4.
Columns (1) through (4) reflect identical specifications as Table 3. Column (1)
reports a significant positive estimate on the dummy variable for SAT insurance mandate;
however, this is capturing a substantial amount of the overall upward trend in the OD rate
which would be controlled for using time fixed effects and state-specific trends. Column
(2) shows a small and insignificant decrease in accidental OD rate of about 7 percent
22
TABLE 3. Substance Abuse Laws and Admissions into Treatment
23
when controlling only for state economic conditions and demographics, suggesting that the
effects are not robust to the inclusion of additional controls. Columns (3) and (4) provide
fixed effects estimates and are both estimate the impact to be about a 11 percent decrease
(again insignificant at conventional levels).25
The results suggest that states which enact laws see increases in treatment but
that it is insufficient to significantly affect overdose. However, the consistently negative
estimate may be suggestive that there is an empirical specification issue that is adding
noise to the impact. In a later section, I include specifications in a robustness exercise
which include a possible omitted variable of laws which affect treatment for other mental
health conditions. These laws are often passed separately from SAT insurance mandates
but can encourage treatment through referrals by mental health providers and a general
increase in individuals concern for their health.
Heterogeneous Impacts on SAT
We should expect there to be be substantial heterogeneity in the treatment effect;
for instance, treatment for alcoholism can be substantially different than for opiates;
likewise treatment in an intensive inpatient setting is going to be substantially different
than treatment in an ambulatory outpatient therapy program. Depending on the needs of
the affected population, the enactment of SAT insurance mandates may affect admissions
heterogeneously.
I report the analysis of the impact of SAT insurance mandates on admissions by
drug reported as the primary concern, source of referral into treatment, and setting for
admission in Tables 5 to 9. Specifications in odd numbered columns are equivalent to
Column (3) of Table 3 and even numbers are analogous to Column (4).
25The p-value of Column (4) is 0.154.
24
TABLE 4. Substance Abuse Laws and Accidental Drug Overdose Deaths
25
By Primary Drug Concern
Admission rates for alcohol treatment are significantly higher in states which enact
SAT insurance mandates. States which enact laws see 16 to 20 percent more alcoholism
treatment admissions than no-law states. Likewise, admissions reporting marijuana
increased by 20 to 29 percent while amphetamines26 increased about 25 to 38 percent
after a law is enacted. The effect on admission rates for tranquilizers27 is not robust to
the inclusion of state time trends, though the estimated coefficient is similar in magnitude
(See Column (14)). Lastly, there was an increase in SAT for “other drugs,” which includes
over-the-counter-substances and inhalants, following the enactment of the law (when
accounting for state trends). Overall, the laws are primarily driving increases in commonly
treated substance abuse disorders, but not having a strong effect on addictions that are
the driving force behind the rise in drug related mortality.
In contrast, there is no evidence that state laws have a significant impact on rates
of admission reporting cocaine, opiates, or hallucinogens. The estimated coefficients are
both small and insignificant at conventional levels. The lack of impact on opiates SAT
admissions, in particular, is consistent with insignificant findings regarding the accidental
OD rate. Deaths due to alcohol poisoning are not included in the OD rate and there
are no recorded deaths where cannabis was the only contributing substance,28 so the
significant impact on treatments for abuse of these substances would not be expected to
have a direct spillover impact on drug related mortality.
26Primarily methamphetamine (meth), but also includes other amphetamines such as MDMA and
phenmetrazine as well as other stimulants such as methylphenidate.
27In this case, “tranquilizers” are actually an aggregate of benzodiazepines and non-benzodiazepine
tranquilizers as well as barbiturates and non-barbiturate sedatives and hypnotics.
28A very small number of ODs have poisoning due to cannabis derivatives as a multiple cause of death
(code T40.7).
26
TABLE 5. Impact of Laws on SAT by Primary Concern at Admission
27
By Referral Source
Treatment effects are likely to be heterogeneous by admission referral source. In
Table 6, I investigate the impact of implementation of SAT insurance mandates on
admissions into treatment programs by referral source. “Self” admissions reflect all
admissions that are made on behalf of the addict themselves. Admissions under the
category “Care” include all admissions coming from other SAT programs, mental health
practitioners, and all other medically licensed professionals. “Community” referrals include
all admissions from schools, employers, defense attorneys, welfare assistance, and self-
help groups like Alcoholics/Narcotics Anonymous. Treatment admissions from “Criminal
Justice” referrals include those from any judge, probation officer, prosecutor, or any other
person affiliated with the judicial system.
TABLE 6. Impact of Laws on SAT by Source of Referral at Admission
28
In this case, there is an observable difference across specifications including state-
specific time trends rather than fixed-effects alone for many referral sources. Excluding
these trends, there is only a significant increase in admissions coming from community
referrals of about 16 percent. When accounting for time trends, there is an increase in
admissions across all categories of referral sources ranging from 19 to 25 percent.
I further break down admissions by referral setting across primary substance
reported in Tables 7 and 8. Column specifications are analogous to Column (4) of Table
3. Self, substance abuse care, and criminal justice system referral admission rates were
significantly higher for alcohol, marijuana, amphetamines, and tranquilizers. Referral rates
from other community sources were significantly higher for marijuana conditions. There
is also evidence that treatments from schools reporting methamphetamine significantly
increased following passage of the law. Lastly, additional referrals for other drug
conditions were primarily from employers and the criminal justice system. As expected,
there is no evidence of significant increases for admissions into treatment for cocaine,
opiates, or hallucinogens from any of the source of referral.
The significant effects across self admissions, other SAT referrals, community
referrals, and court system referrals for alcohol, marijuana, and methamphetamine
treatments suggest that more than just the marginal person demanding treatment are
responding to these mandates. Individuals being referred to treatment from other SAT
programs suggest that individuals are receiving treatment on the intensive margin because
institutions recognize that individuals can now afford more treatment than previously.
Lastly, the responsiveness of treatment coming from court system reveals that the
insurance coverage is providing coverage for unexpected demand for services such as
DUI/DWI and other mandated treatment.
29
TABLE 7. Impact of Laws on SAT by Referral and Drug Concerns - Part A
By Admission Setting
Detoxification and rehabilitation services vary substantially on costs, location, and
types of services provided. For example, many inpatient rehabilitation services include
detoxification as well as therapy and provide health care assistance for individuals with
30
TABLE 8. Impact of Laws on SAT by Referral and Drug Concerns - Part B
medical complications arising from withdrawal. Increasing insurance may be substantial
enough to cover some levels of treatment but may not be sufficient to cover intensive and
costly sessions. In contrast, increased insurance may allow people who previously would
benefit from intensive therapy but settled for the cheaper less intensive options to switch.
31
Table 9 reports the estimates of this analysis investigating the heterogeneous impacts
by admission setting. I find that states which enact laws have significantly higher rates
of admission (between 19 and 32 percent) across all types of treatment when accounting
for state-specific time trends. When considering fixed-effects only, I find that states which
enact laws have about 19 percent more outpatient treatments than states which do not.
TABLE 9. Impact of Laws on SAT by Setting at Admission
I extend on this analysis in Tables 10 and 11 by investigating the impact for
inpatient and outpatient treatment across reported substances. The results are consistent
with previous analysis with the only observable impacts occurring for alcohol, marijuana,
and amphetamines. The impact for outpatient treatment for marijuana is significant at
the 95 percent level of confidence across both specifications and suggestions outpatient
treatment was higher by 17 to 25 percent in states with laws. Similarly, outpatient
treatment rates for amphetamines increased by 28 to 47 percent. For outpatient treatment
of alcohol and tranquilizers, the fixed effects specification suggests a weakly significant
coefficient of 0.14 and 0.22, respectively, but the significance disappears when controlling
for trends. There is no evidence of an impact on outpatient treatment for cocaine, opiates,
32
hallucinogens, or other drugs. Likewise, there is no indication of significant increases in
inpatient treatment across any of the substances.
TABLE 10. Impact of Laws on Outpatient SAT by Drug Concern
TABLE 11. Impact of Laws on Inpatient SAT by Drug Concern
33
Other Results
In this section, I explore the robustness of the results on SAT and OD rates to scope
of laws and inclusion of mental health mandates. The results from this analysis can be
found in Table 12. Columns (1a) and (2a) are identical to columns (3) and (4) of Table 3,
respectively. Columns (1b) and (2b) are the same as columns (3) and (4) of Table 4. In
Table 13, I also investigate sensitivity to enactment date as well definition of death rate.
Definition of SAT Laws
Substance abuse insurance mandates vary on two primary levels: whether the
language in the law requires benefits to be included in all plans and the level of benefits
that must be provided. In this section, I separate the laws into three categories.29 The
first, called “Parity” laws, are mandates which both require all plans to include or offer
benefits in their plans for SAT and that these benefits must be “no more restrictive” than
for physical health. The second category captures all other laws requiring benefits to be
included or offered, but that these laws require some minimum level of benefits that differs
from physical health (called “Minimum Mandated Benefits (MMB)”). The final category
“Mandated if Offered (MIO)” include all laws which mandate a certain level of benefits
but do not have requirements to include benefits in the plans. The results are included in
columns (3a), (3b), (4a), and (4b).
States which enact Parity or MIO laws experience significant increases in SAT
admission rates relative to having no law in effect (28 and 21 percent, respectively with
trends). There is no evidence that MMB laws signficantly increase SAT rates. For
accidental OD rates, there is no statistical evidence of an impact from substance abuse
insurance laws when accounting for state trends. With state and year fixed effects, states
29These definitions are adopted from Lang (2013).
34
which enact parity laws experience a decrease in accidental OD rates of about 25 percent
(significant at 95 percent confidence).
In addition to legislation affecting insurance benefits for the treatment of addiction,
many states enacted legislation which directly increased benefits for mental illness
treatment. In several cases, these mental health laws also increased benefits for SAT
by defining addictive disorders as a type of mental illness or had a subsection which
affected substance abuse conditions. Other states passed laws affecting mental illness
excluding. These laws could also indirectly affect demand for SAT by treating co-morbid
conditions which are correlated with substance abuse disorders. Additionally, mental
health practitioners may refer people into SAT more frequently as the utilization of mental
health services increases following the enactment of the mental health laws.
Columns (5a) and (6a) report the estimates of the impact of substance abuse
insurance mandates on SAT and (5b) and (6b) for OD rates when controlling for “mental
health only” (MH) laws. For SAT rates, I find that the inclusion of MH mandates do
not significantly alter the estimated impact from substance abuse insurance. Likewise,
there does not appear to be a significant impact on SAT rate from MH laws. The linear
combination of these impacts (including their interaction) suggests that states which enact
both laws see a 34 percent increase in SAT treatment admission rates (significant at the
99 percent level of confidence). However, this is not statistically different than having a
substance abuse insurance law alone.
When accounting for mental health only laws, the impact from SAT insurance
mandates on overdose death rates becomes significant at the 90 percent level of confidence.
Moreover, the independent impact from MH laws are similar in magnitude. The linear
combination of the coefficients and the interaction indicates that states which enact both
laws are no better off in terms of impact on OD rates than states which enact one or the
35
TABLE 12. Robustness Checks: Scope of Law and Mental Health Laws
36
other. This suggests that either type of mandate reduces accidental OD rates and that
the commonalities in both types of laws (namely increasing benefits for treatment by
professionals) may be the transmission method between legislation and reduced probability
of death.
Placebo Tests
To check whether the impact of laws was simply an artifact of time incorrect
specification of treatment, I perform an enactment date sensitivity analysis. Another
concern is that the enactment of the insurance mandate is correlated with overall
improvements to access to health care. To check for this, I regress the death rate due to
acute digestive disorders on the insurance laws. Table 13 reports the results from this
exercise.
To test sensitivity to enactment date, consider a “placebo” law enacted five years
prior to the actual enactment date. In the table, the dummy variable identifying this law
is labeled“Subs. Abuse Insurance Law Placebo.” I regress log SAT admission and OD
rates on this placebo law, controls, fixed effects, and state trends in Columns (1) and (2),
respectively. I find no evidence that either SAT or OD rates significantly change due to
this placebo law.
To test whether laws are representing overall improvements in health care, I regress
the log of the number of deaths due to digestive system conditions, primarily hernias and
appendicitis, on the enactment of the insurance law in Column (3). These conditions are
common, acute, and treatable by medical intervention; if access to health care is generally
increasing, we would anticipate that the number of deaths due to these conditions would
decrease. I do not find evidence that deaths due to these conditions significantly changed
following the enactment of the law.
37
TABLE 13. Robustness Checks: Placebo Tests
Event Study
The estimates presented so far represent the causal effect of insurance mandates on
outcomes, provided that the following holds: law makers are not responding to generally
worsening conditions in substance abuse morbidity and mortality by enacting legislation to
correct the issue. This potential source of endogeneity may cause positive bias in the effect
of laws on SAT and negative bias in the effect of laws on overdose deaths.
To investigate whether this occurring, I implement an event study which creates a
dummy variable for years before and after the passage of substance abuse laws. The year
that the law becomes effective is coded as year zero and I create dummies for each year
before and after this enactment year (Djst,−5 ≤ j ≤ 5). The dummy variable for j = −5 is
one if the year is less than or equal to five years before enactment and the dummy variable
for j = 5 is one if the year is more than or equal to five years after enactment. I regress
38
log SAT admission rates and log OD rates on these dummies, state and year fixed effects,
and a set of controls (omitted category is the enactment year where j = 0).
log(SAst) = β0 +
5∑
j=−5
(βjD
j
st) + ΓXst + δs + αt + ust
The coefficient βj captures the log difference in the incidence rate of admissions or
deaths j years after the enactment year relative to the year of enactment. In the case of
admission rates, if there is a general decrease in βj as time moves from j = −5 toward
j = 0, then there is concern that policy makers may be responding to generally worsening
conditions in substance abuse treatment by enacting the law. For accidental drug deaths,
if βj is increasing over this time, then law makers may be responding to heightened death
rates by enacting the policy. If βj is increasing (for SAT rates) or decreasing (for OD
rates) prior to enactment, then it is difficult to determine if the coefficient is just picking
up a trend in SAT and OD rather than the true causal effect.
This event study also permits us to examine the medium to long-run effect of these
laws. For j ≥ 1, the coefficient βj reports how persistent the effect from the law has been.
If the law is enacted and the effect continues, then these coefficients should be consistent
and statistically different than zero. However, if an effect is temporary, then we could
anticipate that the coefficients return toward zero.
Tables 14 report the estimates for the event studies for log admission and overdose
rates, respectively. On the left hand side of each table, I report the estimate for βj when
j ≤ −1 and on the right hand side I report the estimates for j ≥ 1. There is no evidence
that the log SAT rate prior to enactment is not statistically different than the year of
enactment. However, the years prior to enactment had OD rates that were significantly
higher than the year of enactment. Additionally, there was a downward trend prior to
39
enactment of the law. This suggests that the interpretation of the impact of insurance
mandates on OD rates should be taken with caution.
TABLE 14. Event Study for Enactment of Laws on SAT and OD Rates
This table also indicates that the effect on SAT admissions was persistent and
perhaps may have been slightly delayed, with the largest increases in admissions coming
two or more years after the law was passed. After five years, the SAT treatment effect is
no longer distinguishable from the year of enactment.
Conclusion
Over the last several decades, many states have been enacting health care reforms
to increase coverage for substance abuse in insurance plans. The intent of these laws
were to reduce dependency on addictive substances and increase overall social welfare.
In this paper, I examine the impact of these policies on measures of effectiveness, namely
substance abuse treatment (SAT) admissions and accidental overdose deaths (OD).
I find that the policies have a significant impact on SAT admission rates, but that
there is substantial heterogeneity across admission types by drug reported as primary
40
concern. In particular, laws increasing benefits for substance abuse treatment appear to
primarily increase admissions for alcohol, marijuana, and amphetamines. Admissions
for opiates, hallucinogens, and other drugs do not appear to change in response to
mandates. New admissions are being referred into treatment from other SAT programs
and the criminal justice system in addition to self-referrals, indicating an increase both
on the intensive margin for treatment as well as for individuals not actively considering
treatment. For marijuana treatment admissions, there are also additional treatments from
other community referrals such as self-help groups and welfare assistance. Lastly, I find
that there are significant increases to both inpatient and outpatient treatment.
I also investigate the impact of these laws on accidental OD rates. States which
enact laws do not appear to have significant decreases in OD rates which is consistent with
the findings for SAT where opiate and cocaine admissions did not appear to significantly
change in response to legislation. When controlling for other mental health laws, there is a
marginally significant decline in OD rates in states which enact a law. If this effect exists,
it would be indicative that professional treatment, in general, is a mechanism for deterring
overdose deaths.
I also find that the effect on treatment admissions took several years to reach highest
impact. This is expected as it may take time for individuals to understand their benefits,
allows old plans to expire and new plans to take place.
This paper adds to the existing literature on substance abuse, insurance markets,
and health care policies in three ways. First, I precisely define the treatment through
careful analysis of state legislation, identifying laws which directly address substance
abuse; past literature focused on mental health laws which may or may not include
substance abuse coverage. Secondly, I find that substance abuse insurance mandates are
effective at increasing treatment, but that this is primarily for alcohol, marijuana, and
41
amphetamines. Thirdly, I find evidence that laws are effective at increasing admissions
from other SAT programs, the criminal justice system, and community groups which is
indicative that the laws are increasing admissions for people who would not actively seek
treatment on their own.
Future literature on this topic could include an in depth investigation on states
which pass multiple substance abuse laws. Additionally, this paper indicates that mental
health laws significantly decreased OD rates and future papers would further explore
this result. Lastly, the these laws do not show a significant effect on opiate or cocaine
treatment rates. Next steps would be to seek to identify whether other health care policies
which affect other populations (such as Medicaid or Medicare) are effective at inducing
individuals into treatment programs for these drug concerns.
In this chapter, I explore the impact of a large-scale public policy on substance
abuse, a risky behavior that has become a wide spread health crisis in the United States.
Another major concern in the United States has been high amounts of criminal activity,
particularly during the early part of the 1990s. Many papers have drawn connections
between poor economic conditions and criminal behavior. In my next chapter, I revisit
this problem and question the assumptions made about the time-stability of this
relationship.
42
CHAPTER III
THE EVOLVING CYCLICALITY OF ECONOMIC CONDITIONS AND CRIME
Introduction
Crime in the United States has been a consistent concern for policy makers and
academics. In the early 1990s, crime reached a peak rate with nearly 5,500 property
crimes and 500 violent crimes being reported per 100,000 population. This rate has
declined steadily over time but continues to be high in some areas, particularly in urban
and poorer regions. Understanding the determinants of the crime trends has been of
continued interest to economists, and an influential literature on the specific effects of
macroeconomic conditions has emerged.
Academic literature investigating the effect of economic conditions on crime have
drawn the consistent conclusion that periods of high unemployment and low wages lead
to increases in the property crime rate (Raphael and Winter-Ebmer (2001), Gould et al.
(2002), Mocan and Rees (1999), Mocan and Bali (2010)). Each of these papers address
some variation of the following empirical model, estimated using panel data at the state or
county level.
Crime Ratest = β0 + β1Unemployment Ratest + εst
An assumption in this model is that the parameter β1 is exogenous to external factors.
However, there are reasons to suspect that this may not necessarily be the case. The
parameter β1 is understood to reflect the average person’s choice to commit crimes in
response to changes in unemployment.1 In his seminal paper, Becker (2000) predicts
that the choice to commit crime depends on the return to crime and the probability
1It may also capture changes in overall enforecement during periods of high unemployment.
43
of apprehension. In areas with high unemployment, the return to committing crime
may be higher due to lack of legal sector income. At the same time, in areas with
high unemployment the probability of apprehension may be higher due to more people
spending time at home watching their valuables.
The literature has found little evidence that economic conditions are associated with
violent crime. Indeed, the relationship is a priori ambiguous. Poor economic conditions
may affect crime rates by changing the number and type of interactions people make on
a daily basis. For example, increased unemployment may reduce a person’s exposure to
other individuals and therefore decrease their likelihood of committing a violent crime.
Moreover, job loss reduces the amount of money that can be spent drinking at bars or
attending sporting events where violent crimes are common (Madensen and Eck (2008);
Scott and Dedel (2006)). Additionally, if unemployment is more severe for men than
women, the relative wage gap between men and women decreases which corresponds to
heightened bargaining power of females in the relationship and reduced domestic violence
(Aizer (2010)). In contrast, increased joblessness heightens stress levels which can lead
to increased propensity toward criminal acts (Linn et al. (1985); Agnew (1992); Eitle
and Turner (2003)). Moreover, individuals are spending more time around family and
experiencing financial stress, thereby increasing the number of opportunities for domestic
violence to occur.
Over time, the probability of apprehension for property crimes has also increased
as protection methods to secure valuables, such as tracking devices and home theft
monitoring, has improved. This would lead to the typical person to be less likely to
commit theft in response to the economic stresses of unemployment. Moreover, when
44
economic conditions are poor, macroeconomic violent crime rates will depend on the traits
of the unemployed and thus may be time variant.2
In this paper, I relax the assumption that the relationship between crime rates
and economic conditions is constant across time. I utilize state panel data on arrests
for crime in an ordinary least squares estimation model. In the first exercise, I take
equal sized subsets of data over time and individual estimate the relationship between
unemployment and crime rates. I find that this relationship for property crimes has
diminished towards zero. Secondly, I allow for time heterogeneity in the parameter by
interacting unemployment with a series of yearly dummy variables. Again, I find that
for many property crimes the estimate appears to be falling throughout time and that
the impact appears to mostly disappear by the most recent decade. I also find that the
impact of unemployment on violent crimes is occasionally significant and non-zero for
some periods in the sample.
I also explore heterogeneity in the impact of unemployment on crime rates across
age groups. I find that those most affected by aggregate economic conditions are 25 to
44 years old. However, when allowing for parameters to vary over time, it becomes clear
that all age groups are sensitive to unemployment at some period in time and that the
relationship evolves over time.
This paper contributes to the small literature on the time-variance of the response of
crime to business cycles. Gould et al. (2002) suggest that unemployment plays a lesser role
in explaining crime over the last few decades and little to no part in the long-run change
in crime. Instead, they find that wages are a better determinant for long-run changes in
crime. Mocan and Bali (2010) examine whether there are asymmetric responses to crime
2For example, if the unemployed population is poorer on average, then unemployment may lead to
substantially higher stress than if the unemployed population is less poor. Likewise, if the unemployed
population is largely comprised of adult men, then we may expect fewer violent crimes on average.
45
across expansions and recessions by looking at how crime responds to unemployment
when the labor market is worsening and when it is improving (one-year differences). They
find that recovery times affect criminality significantly more compared to recessionary
periods and that unemployment is positively related to crime across both recessions and
expansions. Both of these papers, however, assume relationship between unemployment
and crime is constant over time.
The remainder of this paper is structured as follows. I begin by describing the
research design framework and describe the data used in this analysis. I then report my
findings across various specifications, discuss heterogeneous trends in parameters, and
conclude.
Empirical Methodology
I utilize a slightly modified version of the empirical model used by Mocan and Bali
(2010).3 The following estimating equation is the base specification.
Cst = β0 + β1tUst +XstΩ + δt + αs + Γst + ust (3.1)
Here, crime rates C in state s during year t are a function of the unemployment rate U , a
vector of covariates X, and subject to state and year fixed effects (α and δ, respectively)
as well as state-specific time trends in crime (Γ). The covariates included in X include
demographic structure of the region (percent white, black, and Hispanic), age distribution,
urbanization, alcohol consumption, and total inmates per capita. Each state also has a
distinct mean level of crime and a unique change in mean crime across time which may
be due to various factors such as law history, police budgets, and demographic trends.
3In this paper, their goal was to examine whether β1 differs across expansions and recessions. Equation
(1) is a generalized version of the empirical model they presented.
46
The inclusion of state and time fixed effects along with state-specific time trends and
covariates will control for these movements in crime and allow βˆ1t to capture the marginal
change in crime due to a percentage point increase in unemployment. The inclusion of the
t subscript on the parameter allows for time-variance in this generalized empirical model.
To begin, I assume that β1t = β1 for all t (i.e. that unemployment has a time-
invariant effect on crime) and examine how this effect changes over various subsamples
of the data. Next, I allow for a basic level of time-variance by allowing β1t to vary across
decades through the inclusion of dummy variable interactions.
Estimated Confidence Interval Plots
One way to examine whether there has been changes in the way that unemployment
affects crime is through the use of estimated confidence interval plots. To do this, I assume
that the parameter is time-invariant (β1t = β1 ∀t) and then estimate Equation (3.1) over a
selection of smaller, equally-sized subsamples of the data. I then take the set of parameter
and standard error estimates and plot them across time.
For the purpose of this paper, I focus on subsamples of ten to fifteen year lengths.
To illustrate, the selection of subsamples with a window size of fifteen years would have
years 1981 to 1996 in the first sample, 1982 to 1997 in the second, and so on. This totals
fifteen small subsamples spanning the entirety of the data set.
I then regress the following time-invariant version of Equation (3.1) for each
subsample i ∈ [1, . . . , n].
Cst = β0 + β1Ust +XstΩ + δt + αs + Γst + ust (3.2)
I obtain a vector of parameter estimates (βˆ11 , βˆ
2
1 , . . . , βˆ
n
1 , where n is the number of
subsamples) and associated standard errors and I plot 95 percent confidence intervals
47
across the time span. Evidence of a change in parameter can be seen through analysis
of the overlap of the confidence intervals and whether the confidence intervals include the
full-sample estimate or zero. However, this sort of analysis has inherent difficulties because
it relies heavily on the selected window size. For small windows, the model suffers from
low power due to sample size restriction. For larger subsamples, the estimates converge
toward the average estimate for the full sample.4 5 In order to compensate for these
possible limitations, I repeat this analysis using narrow (ten years) and wider (fifteen
years) selections.
Time-Varying Parameters
The estimated confidence interval methodology assumes that the parameter is time-
invariant but looks at small spans of time separately. Unfortunately, this loses the ability
to utilize the full power of the entire sample. An alternative is to use the full sample
and allow the parameter to be time-variant by interacting the unemployment rate with
a dummy variable for the year of interest. That is, I estimate
Cst = β0 + β1Ust +
2010∑
y=1982
(βyDyUst) +XstΩ + δt + αs + Γst + ust (3.3)
where Dy equals one if the year is equal to y and zero otherwise. The effect during the
first year (1981) is going to be captured by β1 and the deviance from this base year is βy
for y ≥ 1982. Thus, the effect of unemployment on crime for years after 1981 is the linear
combination
4This problem is a special case of the trade-off between variance (power) and bias resulting from
selecting data window sizes. The issue has been often noted in empirical literature.
5Ideally, the optimal window size would only include a single year, but this is not feasible given data
constraints.
48
β1 + βy
A significant estimate for any given βy indicates that there is sufficient evidence that
the parameter is different from that estimated in the 1981. A test of the null that the
linear combination β1 +βy is equal to zero determines if there is remains a significant effect
in year y.
I expand this analysis to look at the heterogeneous effects of unemployment
(currently decade level time variation) on crime across different age groups. That is, I
regress the crime rate of each age group j ∈ {15− 24, 25− 34, 35− 44,≥ 45} in state s
and year t on the same set of regressors found in Equation 3.3.6
By allowing dummy variables for each year, I can take advantage of the power of
the full sample and allow time-variance in the parameter without imposing any rigid
functional form on how it might be changing. If the parameter is changing in the same
way as the average, the results will be similar as the estimated confidence interval plots.
However, if there are certain years that demonstrate uniquely different trends, this
methodology would be preferable because estimated confidence intervals will smooth over
these outliers.
Data Description
Data Sources
I utilize crime data obtained through the Federal Bureau of Investigation’s Uniform
Crime Reporting System (UCR). The UCR Program collects data from 18,500 law
enforcement agencies throughout the country on the number of offenses and arrests
6That is, crime rate Cst = C
j
st.
49
made across a broad range of crime categories. State-level annualized data is publicly
available through the FBI website. More detailed data, including offenses by age, gender,
and ethnicity at the county level, has been made available through the Inter-University
Consortium for Political and Social Research’s (ICPSR) National Archive of Criminal
Justice Data (NACJD). Details on definitions of each of the crime variables as defined
by the UCR Program and list of imputations and modifications made to the data are
available upon request.
I utilize state unemployment rates as a proxy for aggregate economic conditions in
any given year. This data is obtained through the Bureau of Labor Statistics Local Area
Unemployment Statistics (LAUS) database.
I control for alcohol consumption, demographic decomposition, urbanization, and
prison inmate population.7 Data on alcohol consumption was obtained from LaVallee and
Yi (2011) who found estimates of statewide consumption of beer, wine, and spirits between
1977-2012. Prisoner population information was obtained through the National Prisoner
Statistics program, made available by the ICPSR. Demographic information was obtained
through the widely used Surveillance, Epidemiology, and End Results (SEER) database,
which creates annual estimates of population by age, gender, race, and ethnicity. Annual
data on the percent of population living in urban areas was obtained from the U.S. Census
Bureau Decennial Census Data.8
7These are comparable to the controls used in Mocan and Bali (2010).
8I create annualized urbanization data using a single exponential smoothing algorithm on the decennial
values.
50
Summary Statistics
In this paper, “crime rates” are defined as the number of arrests made per 100,000
population in the a given state. Property crimes include larceny,9 motor vehicle theft,
and burglary.10 Violent crimes include murder,11 forceful rape, aggravated assault,12 and
robbery.13 Because robbery is very similar to larceny, I examine it separately and exclude
it in my aggregate violent crime definition. Table 15 reports the summary statistics for
this study. On average, there were 4,170 reported arrests per 100,000 population for
property related crimes. Sixty-five percent of these property crimes are larcenies, twenty-
four percent are due to burglaries, and the remaining are due to motor vehicle theft.
Across the sample, there was an average of 379 violent crimes per 100,000 population (337
aggravated assaults, 35 rapes, and 7 homicides).
There has substantial changes in these rates across time. As shown in Figure 5, the
violent crime rate increases between 1970 and 1990, with only a modest decline following
the 1980 to 1981 recession. The violent crime rate declines steadily thereafter. Property
crime rates, on the other hand, have been more volatile. Between 1970 to 1980, property
crime tended to increase and peaked at around 5250 crimes per 100,000 population.
Between 1980-1985, property crimes declined but then increased again to a secondary peak
just over 5,000 crimes in 1990 after which they began a steady decline.
The unemployment rate is often considered a good proxy of economic conditions in
a year. Unemployment declines during expansions (usually with a small lag), and rises
9Theft of another person’s assets or property which involves carrying away of personal property
without permission of owner without intent to return property.
10Theft which involves physical entrance into a building illegally.
11Murder in this paper will include manslaughter charges as well.
12Assault with the intention of cause serious bodily injury.
13Larceny which includes force or intimidation.
51
TABLE 15. Summary Statistics: Unemployment and Crime
during recessions. The average unemployment rate across this time span was about 6.25
percent. The largest peaks in unemployment follow the 1980-1981 recessions and the 2007-
2007 Great Recession. Other covariates with crime were also included in this analysis.
First, I included the age, race, and ethnicity composition. Across this time period,
teens(15-19) and young adults (20-24) made up an average 14.5 percent of the population.
Property crimes, in particular, may very well be sensitive to the number of young people
in the population.14 About 72 percent of the population was white/non-hispanic origin, 13
percent black, and 4.7 percent indicated they were of either American Indian/Alaskan
14Freeman (1999) and Mocan and Bali (2010) both find age to be a significant controlling factor in
similar analysis.
52
FIGURE 5. Property and Violent Crime Rates in the United States (1960-2010)
53
Native or Asian/Pacific Islander decent. The large majority of the population was in
urbanized areas (77 percent). Other covariates included in the analysis were for alcohol
consumption and prison incarceration rates. The amount of alcohol consumed per capita15
is about 1.3 gallons of beer, 0.3 gallons of wine, and 0.7 gallons of hard alcohol every year.
The number of prison inmates comes from the National Prisoner Statistics survey. On
average each state had about 321 inmates per 100,000 population.
Results
Base Specification
Tables 16 and 17 report the time-invariant results of Equation (3.1). Odd numbered
columns include state and year fixed effects and even numbered columns add in state-
specific trends. Similar to the previous literature, I find a strong positive relationship
between unemployment and property crimes where a one percentage point increase in
unemployment translates to an additional 94.2 to 112.8 property crimes per 100,000
population. Decomposing the effect across types of property crimes, we find this large
number comes from mostly larcenies and burglaries (56.1 and 33.0 additional crimes per
100,000 population, respectively). Motor vehicle thefts see a small increase of about 12.0
additional arrests per 100,000 population, but this is not robust to the inclusion of state
trends. Among violent crimes, only robberies respond to changes in unemployment. For
a one percent increase in unemployment, there is an increase of 6.5 robberies per 100,000
population.
15For population aged 14 and older.
54
TABLE 16. Impact of Unemployment on Property Crime Rates
Estimated Confidence Intervals
Figures 6 and 7 show the estimated confidence interval (ECI) plots for a window size
of fifteen years. The red dashed line is the estimated average effect from Tables 16 and
17. For property crimes, there is a clear downward trend in the parameter estimate. For
samples excluding the years 2000 and onward, the parameter estimate was significantly
larger than the estimated parameter in the base model. For samples containing 1985 to
55
TABLE 17. Impact of Unemployment on Violent Crime Rates
2007, there was no significant difference between the estimated coefficient of the sub-
sample and the full sample. By the last 15 year window, however, the effect was not
different than zero and significantly different than the full sample estimate at a 90 percent
level of confidence. A similar exercise for violent crime rates show that the estimated
impact hovered around zero and was not different than the full sample estimate.
For the smaller ten-year window size (Figures 8 and 9), the decrease across time
for the property crime rates becomes much more pronounced. Furthermore, for windows
containing only data post-1996, there is sufficient evidence to reject the null that the
56
parameter is equal to the average one estimated by the full sample16. The estimates for
violent crime are not distinguishable from zero (or the estimated average) across the span
of sub-samples.
FIGURE 6. ECI Plot: Unemployment on Property Crime Rate (15 Year Window)
Time-Varying Parameters
From the previous analysis, I find evidence that the effect of unemployment on
property crime appears to be diminishing over time regardless of window size selection.
Moreover, hypothesis testing on the estimated parameters fails to reject zero for the
majority of the most recent data. By shortening the window size, the downward trend
becomes more apparent. This is suggestive that there is substantial yearly variation in the
impact of unemployment and crime which cannot be picked up using estimated confidence
16Again, these results are consistent when weighted by mean crime rates.
57
FIGURE 7. ECI Plot: Unemployment on Violent Crime Rate (15 Year Window)
FIGURE 8. ECI Plot: Unemployment on Property Crime Rate (10 Year Window)
58
FIGURE 9. ECI Plot: Unemployment on Violent Crime Rate (10 Year Window)
interval plots. In this section, I report the results of the estimation where I allow the
impact to vary annually by using dummy variable interactions with unemployment.
I plot the estimated effect of unemployment on crime between 1981-2010 in Tables
10a to 10i. The annual impact of unemployment on property crimes was significantly
different than zero for years prior to 1996, after which the estimated impact fluctuates
around zero. However, there is heterogeneity in the trends in parameter estimates for
the component crimes. The parameter for larceny crimes declined until about 2000,
rebounded temporarily during the next seven years. Arrest rates for motor vehicle thefts
were positively correlated with unemployment until 1995, but then shifted to a negative
correlation for the years after. The parameter on burglaries gradually diminished over the
course of the sample with insignificant estimates in the years following 1996.
Robbery crime rates appear to have been positively related to unemployment and
constant until 1996, after which the effect drastically declined and became insignificant.
59
FIGURE 10. Annual Impact of Unemployment on Crime Rates
(a) Property (b) Larceny (c) MV Theft
(d) Burglary (e) Robbery (f) Violent
(g) Rape (h) Assault (i) Murder
The effect for other violent crimes was positive briefly during the early 1990s and then
dropped below zero, though the effects are rarely significant. However, this trend can be
attributed primarily to the effect coming from aggravated assaults. The estimate for rapes
crimes appears to have a downward trend as well, with a significant negative impact by
2008. Lastly, the murder crime rate was unrelated to crime until the 1990s where the was
a brief period when unemployment was positively correlated with murder. By the 2000s,
murder was negatively correlated with unemployment.
60
Overall, there is evidence that the relationship between unemployment and crime is
not static. A dramatic change occurs in 1996 for many property crime rates. Moreover,
there is evidence that during some periods in time, unemployment has a non-zero
relationship with violent crime rates.
Age Decomposition
In this section, I investigate heterogeneity in time-varying parameters for different
age groups. More specifically, I estimate Equations 3.2 and 3.3 with crime rates for specific
age groups or census divisions as the dependent variables. The purpose of decomposing by
age group is two-fold. Firstly, it highlights whether age-specific crime rates are sensitive
to macroeconomic changes in unemployment. Secondly, allowing time-varying parameters
within age groups will indicate whether there are specific generations driving the results
seen in the aggregate.
For this analysis, I construct the following age-specific crime rates:
Ranst
Canst
P ast(100, 000s)
which is the number of arrests of persons from age group a for crime n in state
s during year t per 100,000 population of age group a in state s during year t. I then
estimate Equation 3.2 with the age-specific crime rates as the dependent variable. The
results from this analysis are included in Table 18.
Columns (1) through (9) include regression estimates for the impact of
macroeconomic unemployment on arrest rates of minors for property and violent
crimes. None of the estimated coefficients are large in size or statistically significant at
conventional levels. Columns (10) through (18) include the estimates for the impact of
unemployment on arrests for crimes committed by young adults (18 to 24 years old). A
61
TABLE 18. Impact of Unemployment on Crime By Age Group
62
one percent increase in the unemployment rate is associated with a higher level of burglary
of about 8.8 arrests per 100,000 18-24 years olds. The impact on arrest rates for other
crimes in this age group are insignificant at conventional levels.
The impact of unemployment on crime rates for adults aged 25 to 44 years can be
found in Columns (19) to (36). Higher unemployment is associated with higher arrest
rates for larceny and burglary for this group. For ages 25 to 34, arrests for larceny and
burglary increased by 13.9 and 4.3 per 100,000 population, respectively, for a one percent
increase in the unemployment rate. The estimated coefficients for 35-44 year olds were of
similar magnitude at 10.9 and 2.1, though the average arrest rate in this age group was
only about half of that for 25-34 year olds. Additionally, this age group experienced a
significant decrease in murder rates during periods of higher unemployment of about -0.26
fewer murder arrests per 100,000 population.
Lastly, the impact of unemployment on arrest rates for 45 and older ages are found
in columns (37) to (54). The murder arrest rate for 45-54 year olds significantly decreased
during periods of higher unemployment. Otherwise, there was no significant response to
high unemployment for this age group.
I then allow parameter estimates to vary across time for each age group a and crime
type n. I estimate Equation 3.3 and graph the linear combination of coefficients β1981 + βt
for t ∈ (1982, 2010) with a 95 percent confidence interval. These graphs can be found in
Figures 11 to 19.
Arrests for larceny crime increased during periods of high unemployment for age
groups 25 to 44 when the parameter was assumed to be constant. However, when allowing
the parameter to change over time, there are a few noticeable differences. For all age
groups, there was a significant increase in the parameter estimate in 1997 which eventually
diminished over the next decade. The increase was less noticeable for ages 25-34 which
63
FIGURE 11. Annual Impact of Unemployment on Property Crimes By Age Group
(a) Ages 0-17 (b) Ages 18-24
(c) Ages 25-34 (d) Ages 35-44
(e) Ages 45-54 (f) Ages 55+
64
FIGURE 12. Annual Impact of Unemployment on Larceny By Age Group
(a) Ages 0-17 (b) Ages 18-24
(c) Ages 25-34 (d) Ages 35-44
(e) Ages 45-54 (f) Ages 55+
65
FIGURE 13. Annual Impact of Unemployment on MV Theft By Age Group
(a) Ages 0-17 (b) Ages 18-24
(c) Ages 25-34 (d) Ages 35-44
(e) Ages 45-54 (f) Ages 55+
66
FIGURE 14. Annual Impact of Unemployment on Burglary By Age Group
(a) Ages 0-17 (b) Ages 18-24
(c) Ages 25-34 (d) Ages 35-44
(e) Ages 45-54 (f) Ages 55+
67
FIGURE 15. Annual Impact of Unemployment on Robbery By Age Group
(a) Ages 0-17 (b) Ages 18-24
(c) Ages 25-34 (d) Ages 35-44
(e) Ages 45-54 (f) Ages 55+
68
FIGURE 16. Annual Impact of Unemployment on Violent Crime by Age Group
(a) Ages 0-17 (b) Ages 18-24
(c) Ages 25-34 (d) Ages 35-44
(e) Ages 45-54 (f) Ages 55+
69
FIGURE 17. Annual Impact of Unemployment on Rape By Age Group
(a) Ages 0-17 (b) Ages 18-24
(c) Ages 25-34 (d) Ages 35-44
(e) Ages 45-54 (f) Ages 55+
70
FIGURE 18. Annual Impact of Unemployment on Assault By Age Group
(a) Ages 0-17 (b) Ages 18-24
(c) Ages 25-34 (d) Ages 35-44
(e) Ages 45-54 (f) Ages 55+
71
FIGURE 19. Annual Impact of Unemployment on Murder By Age Group
(a) Ages 0-17 (b) Ages 18-24
(c) Ages 25-34 (d) Ages 35-44
(e) Ages 45-54 (f) Ages 55+
72
had estimates hovering around the constant-parameter. By the late 2000s, the estimated
coefficient between unemployment and crime was not statistically different than zero for
any age group.
For motor vehicle theft arrests, there was little difference in trends in age group
parameters over time though there was substantial magnitude difference. During the
1980s and year 1990s, there is no evidence that any age group significantly responded to
unemployment by stealing cars. However, in the late 1990s, individuals aged 18-54 were
more likely to steal motor vehicles during periods of low unemployment. By the early
2000s, this trend had disappeared and during the Great Recession, each age group was
more likely to steal cars (a reversal of signs). By 2010, all trends had reverted to zero.
Burglary arrest rates for ages 18-44 were significantly and positively related with
unemployment within the constant parameter model. There is limited evidence that
this parameter has greatly changed over the time sample. However, when allowing the
parameter to be time varying, it becomes clear that during the late 1980s and 1990s that
higher unemployment was also associated with higher rates of burglary among minors.
Additionally, burglary arrests increased during the Great Recession for age groups 45-54.
There was no age group that experiences a significant increase in arrests for
robbery in the constant parameter model. However, for minors, there was a significant
positive relationship during the 1980s which diminished during the 1990s. For the oldest
population, there was the reverse relationship with a negative coefficient during the
1980s which increased over time. By the Great Recession, arrest rates for robberies
committed by individuals over the age 55 were significantly higher during periods of high
unemployment.
As with robberies, there was no age group which significantly responded to
unemployment by committing more rape crimes in the constant parameter model. While
73
the parameter hovers around zero a good portion of the sample, for years 2000 and onward
there appears to be a frequently significant positive relationship for minors and individuals
aged 18-34.
For each age group, the impact of unemployment on aggravated assault crime rates
was insignificant and around zero during the 1990s; however, there was a drop in the
parameter estimate to a negative value for ages 25 and older in the years following. The
standard errors on the estimate are noisy but the parameter follows a consistent trend
during these years.
Lastly, I find that the significant and negative estimate on the effect of
unemployment on murder crime rates for 35-54 year olds to actually be a remnant of
a strong negative relationship during the 1980s. By the 1990s there was no significant
relationship between unemployment and murder rates for any age groups.
Conclusion
Previous literature has often used long time series panel data to identify a
relationship between unemployment and crime. This process neglects potential changes
in the relationship of interest and effectively produces an average estimate. Consequently,
this can identify a significant effect even if it has faded over time. If the parameter has
indeed diminished, then the policy implications suggested by the time-invariant analysis
are no longer applicable.
In this paper, I show that the responsiveness to unemployment has indeed changed
over time. Repeating time-invariant regression procedures across small time samples
suggests that this relationship has weakened for property crimes. I also allow for the
parameter to vary over time using dummy variable methods and verify that the impact of
unemployment on property crimes has diminished. In 1997, there was a notable decrease
74
in the parameter estimate for the impact of unemployment on motor vehicle thefts and
robberies. For burglary and larceny, the parameter diminished gradually. I also find
evidence of non-zero impacts on violent crimes which has changed over the years. For
murder and aggravated assault, in particular, arrest rates decreased during recessionary
periods throughout the 2000s. The average effect is zero, which was the effect found in
previous literature.
I further investigate heterogeneity in the effect of unemployment on crime by
decomposing the effect by age group. Aggregate unemployment, as a measure for general
economic conditions, are likely to impact certain age groups differently as incentives
to commit crimes evolve throughout a person’s life. I find that unemployment is most
likely to affect crime rates for individuals aged 25 to 44. However, when the parameters
are allowed to vary, I find that some groups which do not have a significant response to
economic conditions in terms of crime, such as minors, experience periods in time where
the relationship is non-zero.
I also investigate the heterogeneous impact of unemployment on crime rates across
census regions. This potentially increases the precision of the estimated coefficient by
artificially creating regions that more closely resemble one another in terms of norms and
attitudes in regards to crime.17 I find that Southern states only experienced increases in
larceny during periods of high unemployment, where other regions experienced changes in
other property and violent crime rates. When allowing the parameters to vary over time,
there exists heterogeneous trend in the parameter across the region as well.
Taken together, the findings suggest that the relationship between unemployment
and crime rates is not as clear and predictable as previously thought. External factors
appear to be influencing this relationship and there is indication that during recent
17At the expense of loss of precision due to lower sample size.
75
years high unemployment is either not related or negatively related to property and
violent crimes. This has direct implications for predictions from policies which affects
unemployment, such as mass layoffs and prison releases. Moreover, it leads to the need
to identify the source or sources of endogeneity which are affecting the parameter estimate.
In doing so, the mechanism by which unemployment is affecting crime would likely become
clearer.
Future research on this topic would seek to identify the source of of variation in this
parameter. Papers addressing this topic should be cautious in examining the impact of
economic conditions on different age groups, as the incentive to commit crime during
recessionary periods greatly varies as a person ages.
In this chapter, I reopened the question of the impact of economic conditions
on crime. Like substance abuse, crime rates disproportionately affect poorer regions
in the United States. In developing countries, similar issues are at least as prevalent.
Additionally, these regions struggle with satisfying day-to-day needs which is exacerbated
by regional conflict, weather, and disease. Non-governmental agencies have been
establishing financial groups in these regions to help individuals save and borrow funds
to improve on these outcomes. In my next chapter, my coauthors and I develop a theory
and explore the functioning of one type of financial group which has become increasingly
popular and successful in developing countries around the world.
76
CHAPTER IV
THE ECONOMICS OF SAVINGS GROUPS
The theoretical model described in this chapter was developed by Andrea Canidio
and Alfredo Burlando. These coauthors also contributed substantially to this work by
developing and collecting experimental data from Ugandan savings groups and writing
large sections of the paper. I performed the bulk of the data cleaning, was responsible
for the development of empirical methods and analysis, wrote the sections on group
functioning, comparison to other financial institutions, creating tables and figures for
summary statistics and group behavior over time, and wrote the section on evidence for
group behavior including all regression analysis and graphic production. All coauthors,
myself included, collaboratively worked on the editing of this paper.
Introduction
Savings groups (SGs) are currently bringing financial inclusion to over 10 million
poor households worldwide,1 yet several important aspects of their functioning remain
unclear. SGs are composed of twenty to thirty members who meet weekly, save with
and borrow from the group over an operating cycle (usually lasting one year). At the
beginning of the cycle, the group agrees on a set of rules which include the interest rate
charged on disbursed loans. At the end of the cycle, the funds accumulated from savings
and loan repayments are redistributed to group participants in proportion to how much
each person saved, and the group may choose to start a new cycle.
1According to 2014 figures from the SEEP network, www.seepnetwork.org/filebin/docs/SG_Member_
Numbers_Worldwide.pdf. This number considers only members of SGs formed and trained by large
international NGOs, and does not include SGs formed by smaller organizations and independent agents, or
spontaneously replicated groups.
77
Despite sharing some similarities with ROSCAS, credit unions, and microfinance,
SGs have unique features distinguishing them from other group-based financial
institutions. Savings groups participants, for instance, can utilize the funds available
to smooth consumption, whereas ROSCA members are restricted to receiving a certain
amount of funds at a specific date. In addition, for many of their members SGs are the
only source of interest-bearing savings account and the only formal line of credit. Because
SGs are designed to operate without the support of a financial institution, they can reach
a population not reached by traditional microfinance interventions. Savings groups thus
serve as a savings and lending institution that operates in the space between ROSCAs and
microfinance, and require a separate understanding from either.
In this paper, we carefully describe the functioning of SGs, discuss the different
types of SGs currently existing, and argue that SGs differ from other types of financial
groups such as ROSCAs and credit unions. We then develop a theoretical model of an
SG, which we use to highlight its most salient feature: the lack of a mechanism to ensure
that the supply of funds equal its demand. Consequently lending may be rationed, in
the sense that not all members wishing to borrow at a given interest rate may be able
to do so. Importantly, when funds are scarce, there is no presumption that all members of
the groups are affected equally: some members of the group may be able to fully satisfy
their demand for loans while others are rationed out. If follows that groups may agree on
rules that generate scarcity for a significant part of the cycle, provided that the “median”
member is able to satisfy her demand for funds with these rules.
The possibility of scarcity gives rise to an externality problem, in that a member’s
borrowing and savings decisions affect other group participants. For example, an
additional unit of savings contributed to the group in periods in which funds are scarce
generates a positive externality, because this additional unit can be used to meet the
78
demand for loans of others. However, an additional unit saved in periods in which funds
are already abundant generates a negative externality, because this unit of savings is
not lent out and only decreases the return on savings for all members. Thus, shocks
affecting the borrowing and saving decisions of members can hurt or benefit the overall
group. Interestingly, shifting savings from later periods to earlier periods always generates
a positive externality on the other members of the group. This happens because early
savings can be lent out during the first part of the cycle, and these loans generate
resources that can be lent out again in subsequent periods.
In the last part of the paper, we use data from newly formed Ugandan savings
groups to show evidence of fund scarcity. Our analysis of the weekly activity records
indicates that loans are rationed for the first 80% of the cycle. Therefore our paper points
to the importance of encouraging early savings. Theoretically, saving early rather than
later has an unambiguous positive effect on the group; empirically, we find that the first
part of the cycle is when finds are more likely to be scarce.
The remainder of the paper is organized as follows. The next section provides some
background information on savings groups. Following this, we report some stylized facts
about savings groups from our sample of Ugandan groups. We then develop a model of SG
functioning and then provide evidence that savings groups operate under long periods of
scarcity. The last section concludes with a discussion of the policy relevance of our results.
Background Information on Savings Groups
History and Existing Literature
The first savings groups were created in the early 1990s in Niger by CARE
International and were called ”Village Savings and Loan Associations” (VSLAs). Shortly
after, several NGOs began promoting savings groups inspired by the VSLA model. The
79
most popular alternative models are Savings and Internal Lending Communities (SILC)
promoted by Catholic Relief Services and Oxfam’s Saving for Change (SfC) groups.
Despite the different names, all these savings groups operate under similar rules (see
Table 19 for a comparison of the various models). Therefore, while the description of the
functioning of savings groups in this paper most closely resembles VSLAs, we believe that
our empirical and theoretical results apply to the most common types of SGs.
TABLE 19. Comparison of Different Types of Savings Groups
80
Overtime, millions of members have joined these savings groups. Allen and Panetta
(2010) reports data from groups formed by CARE International, Catholic Relief Services,
and Oxfam, which together serve 1.86 million members. These groups are composed by a
majority of women (between 70 and 80%), and are fairly stable (the retention rate across
cycles is above 90%). Their members save between $12 and $27 on average (between 2.3
and 8.5 percent of national income per capita).
The development literature suggested that savings groups are an effective tool for
local development (see Ashe and Neilan, 2003). Randomized evaluations of savings groups
have shown that savings groups do indeed cause an increase in savings and borrowing,
and improve food security, livestock holding and overall consumption smoothing at
least in the short-run (Ksoll et al., 2015, Beaman et al., 2014, Gash and Odell, 2013,
Banerjee et al. (2015)). A more recent strand of the literature focuses on the mechanisms
internal to savings groups. Greaney et al. (2016) study the process of group formation,
and compare the performance of groups formed and trained for free by NGO officers
against the performance of groups formed by private trainers who charge fees. Cassidy and
Fafchamps (2015) study the allocation of capital within groups, and find evidence that,
due to the endogenous membership process, capital moves from those who demand savings
to those who demand credit. Burlando and Canidio (2015) randomly assign members to
groups with varying composition, and find that groups that are wealthier are better able
to generate loanable funds, which are then lent to their poorest members.
Functioning
Group Formation Groups are typically formed through a guided process led by a
trainer, or field officer. The trainer gathers a critical number of possible participants in a
community, and then proceeds to explain the basic functioning of a SG. The community
81
members who are interested in forming a SG undergo a training period, at the end of
which a membership list is drawn and group operation starts. A group can have anywhere
between 15 and 40 participants.
In many cases, trainers are employed by NGOs or by community-based organizations
that specialize in financial intermediation. It is quite common to find that experienced
savings groups members become trainers themselves, and start forming new groups in
nearby communities.
Rule and Leadership Selection Operations of the group are governed by a
constitution, which is typically adopted during the first meeting after the training period.
This document specifies a number of rules, such as the length of the savings cycle, the
interest rate charged on loans, the permissible savings amounts, the size and possible
uses of an insurance fund. In addition, groups often adopt an extensive set of policies and
procedures that govern how meetings are run, how collective decisions are taken or voted
on, attendance policies, and a set of fines and fees sanctioning violators of rules.
The group also selects a number of group officials or representatives, which may
include a chairperson and a treasurer.These officials ensure that accounts are kept
correctly and group meetings proceed in an orderly fashion and according to the rules.
Savings At the beginning of each weekly meeting, each member saves with the group
by purchasing shares. The share is a permissible and indivisible savings amount, and a
member can typically purchase between zero and five shares per meeting. As such, the
share value implicitly imposes an upper bound to the amount an individual can save
within the group. Savings deposits are recorded in a group ledger and in an individual
savings booklet. All cash deposits are pooled and kept in a metal safe box, which is
82
opened only when the group is in session. Members are not allowed to withdraw their
savings during the cycle.
Borrowing Funds that are accumulated in the safe box are made available to members
of the group as interest bearing loans. Individual loans are extended to group members
subject to three constraints: the group must agree on the stated purpose of the loan; loan
sizes are restricted to three times the amount saved by the borrower until that point; and
total loan disbursements should not exceed the amount available in the safe box. Within
these conditions, multiple borrowers can obtain loans of varying sizes at the same time.
Loans must be repaid within three months, and the interest on the principal compounds
monthly. Once the loan is paid back, the borrower is eligible to borrow again. Borrowing
starts three months after the beginning of the cycle. Three months before the end of the
cycle, loan disbursements ends and all outstanding loans are repaid.
Insurance In addition to loan intermediation, most savings groups provide insurance
as an additional financial service. Each member makes a required and fixed weekly
contribution to an insurance pool. Typically, this contribution is small relative to savings.2
Funds from the insurance pool are kept separate from the savings, and can be lent out to
members in case of an emergency, such as funerals or severe illness. Standard repayment
procedures are implemented, although no interest is collected on the emergency loan.
Accounting While individual members maintain their own passbooks, the group
assigns a record keeper who maintains a log of individual savings, group cash in (savings,
repayments, and fines), and loans serviced. The record keeper utilizes a savings ledger to
record the total amount saved by each member in any given meeting. Also included in this
2In the savings groups we study, the value of the weekly insurance contribution is between one fourth
of a share and one share.
83
ledger is a total savings balance amount. A cash-book is then updated with group-level
balances at the end of the meeting (including carryover balances from previous meetings).
All of these records are hand written and the record keeper is responsible for accurate
calculations and reporting. This technique, however, does allow for human error (see
Appendix A for a description of how we correct for these issues for the data used in this
paper).
Share Out A unique feature of savings groups is their ability to provide positive
returns on accumulated savings, which are realized at the end of the cycle in the process
generally known as share-out. During share-out, the content of the safe box is emptied
and divided among the members of the group in a way that is proportional to the amount
each person saved. Hence, each member receives back everything he or she saved with
the group, plus a fraction of the interest rate payments on loans. This fraction is equal to
the amount saved by this person relative to total savings. More formally, if during weekly
meeting t member i saves si,t, at share out she receives (1 + R)
∑
t si,t, where R is the
returns on savings,
R = r
∑
i
∑
t bi,t∑
i
∑
t si,t
,
r is the interest rate on loans and bi is the cumulative amount borrowed by participant i.
Comparison to Other Financial Institutions
It should be readily apparent that savings groups share many features with financial
institutions common in developing and developed countries alike.
SACCOs Savings groups are most similar to credit unions (commonly known as
Savings and Credit Cooperative Societies or SACCOS in sub-Saharan Africa), in that
84
they facilitate formal lending among the membership. However, savings groups are
significantly less flexible than credit unions. Savings groups operate on short-term cycles,
which prevents a sizable accumulation of capital; members are not allowed to withdraw
savings during the cycle; interest rates are fixed and predetermined for all loans during the
cycle; and the membership is quite small. Given these limitations, it is perhaps surprising
that participation in SACCOS in Sub-Saharan Africa has been much more limited than
participation in savings groups. For instance, in Uganda SACCOS participation is 3% of
the population while membership in informal savings groups is 61% (FinScope (2010)).
Reasons for differences in popularity require further research, although we speculate that
the active participation of all members of a SG to its management is responsible for the
popularity of SGs relative to SACCOS (where decisions are delegated to professional
managers).
ROSCAs Other than credit unions, savings groups are often compared (and confused)
with ROSCAs and self help groups. Like ROSCAs, savings groups pool savings from the
membership on a weekly or monthly basis, and make those savings available to the group.
A key difference with ROSCAs is the availability of a storage technology (a metal safe)
and an accounting technology (book-keeping). Thus savings groups are much more flexible
in the accumulation and use of their funds over time: group members are not required to
save the same amount every period, multiple borrowers can borrow at the same time, and
loan sizes can vary.
Self-Help Groups Self-help groups developed in India independently from Savings
Groups. Similarly to savings groups, they collect savings from its members and distribute
loans. However, they do not follow the rules of functioning of SG. In particular, they do
85
not liquidate at the end of a cycle. Rather, the group distributes profits or dividends over
time, and membership is allowed to vary.3
Some Stylized Facts
We now turn to the empirical analysis of the functioning of 110 newly-formed
Ugandan savings groups.4 This analyses is conducted using three primary sources of data.
First, we collect audit records at shareout on all groups. These records contain: group-level
characteristics; the cumulative amounts saved, borrowed, and repaid by each member; if
the borrower was in arrears; and whether the member dropped out of the group during
the evaluation period. This data set is the most comprehensive (includes information
on all 110 groups). We then acquired savings ledgers recording the amount deposited by
each member during each meeting and cash-books recording weekly cash inflows, outflows
and balances from the same groups. These data sources turned out to be difficult to use
(see Appendix 24 for more details), and we ended up with complete savings ledgers for 43
groups and complete cash books for 22 groups.5
We start by describing the end-of-cycle group savings and borrowing using the audit
records for all 110 groups and how these figures compare to the Savix dataset (which is a
repository of data from savings groups from all over the world). We then explore how the
3For more details see Allen and Panetta (2010), Ashe (2009), Vanmeenen (2010). Note that the
distinction between self-help groups and savings groups described here is gaining popularity but is
not universally adopted. For example, Greaney et al. (2016) study SILCs (which, according to our
classification are savings groups) but call these groups “self-help groups”. Blattman et al. (2015) also
follow the same terminology when referring to VSLAs.
4These groups were formed in 2013 and were geographically dispersed throughout Uganda. See
Burlando and Canidio (2015) for detailed information on these groups and on the data collection protocol.
5Groups also maintain loan ledgers, which keep record of all lending transactions and repayment
histories. While we found that savings and cash ledgers are very standardized and were easily imported
in an electronic database, loan ledgers were impossible to work with–we found that each group had their
own recording standard for loans, and the records are often hopelessly confusing. For this reason, we have
no individual level information on loans.
86
share price affects individual savings using the ledger data for the 43 groups. Lastly, we
describe the evolution of funds over the course of a cycle using the cash-book data.
Savings Group savings and borrowing behavior is reported in Table 20.6 Average
cumulative savings is about $976 per group ($37 per member). The typical group and
member savings for all CARE International savings groups (again from SEEP data) are
also reported in this Table. It is clear that the audited groups saved only slightly less on
average than other groups in Uganda.
TABLE 20. Summary Statistics from Audits of Ugandan Savings Groups and SAVIX
The amount of savings a member can accumulate is regulated by the share price.
In our study groups, share values are quite low. All groups chose share values of 500,
1,000 or 2,000 UGX (approximately 19, 38 and 75 US cents in 2013 at the time). The
implied ceiling of weekly savings is 93 cents, 1.88 dollars, and 3.75 dollars respectively.
These small differences could amount to large differences in overall savings: Over a period
6All estimates are reported in USD$ using the conversion of 1 USD: 2,660 UGX.
87
corresponding to the median length of the cycle (47 meetings), a person who saves the
maximum allowed would have been able to accumulate US$133 less in a group with a
share value of 500 UGX than in a group with a share value of 2,000 UGX ($44 versus
$176).
Table 21 reports group statistics at shareout by share price. It is clear that outcomes
vary significantly with this price. Average savings at the end of the cycle was USD$28
(64% of the maximal limit) among 500 UGX groups, USD$38 (39% of the limit) among
1,000 UGX groups, and USD$62 (43% of the limit) among the 2,000 UGX groups.
We study in greater detail the constraints imposed by the share price by looking at
person-meeting records from the 43 savings ledgers. In Table 22, we report the frequency
that a particular number of shares was purchased in groups with a particular share price.
The table reveals some interesting patterns. First, savings transactions often do not
happen: members choose to save nothing 24% of the time in groups with “expensive”
shares (2,000 UGX share value). The proportion is only slightly lower for groups with
500 UGX share value (21%), suggesting that the main difficulty facing participants is
coming up with any savings for the meeting (or coming to the meeting itself), rather than
meeting the minimum savings threshold. Secondly, the upper limit on savings imposes a
real constraint on savings. This can be seen by the proportion of transactions that involve
the purchase of 5 shares. In our sample, 48% of transactions in 500 UGX groups, 30% in
1,000 UGX groups, and to 23.5% for 2,000 UGX groups fall into this category. Finally, the
table indicates that the distribution of savings is bimodal throughout. In 500 UGX groups,
most transactions are either zero or 5 shares; at the other extreme, in 2,000 UGX groups
transactions are either at zero or one share, or 5 shares.
Borrowing Table 20 also includes information on group borrowing. On average
members took out about 2.6 loans totaling approximately USD$56 over the course of the
88
TABLE 21. Summary Statistics from Audits of Ugandan Savings Groups (By Share
Value)
cycle (an average of $1,480 per group). Clearly this is substantially more than savings
per member and is the result of frequent repayment of these interest-bearing loans. By
the end of the cycle, individuals saw an average rate of return on savings of about 12.83%
and a ratio of cumulative loans to cumulative savings of about 1.5.7 Finally, we note that
7Among a subsample of 780 study participants, the single most common use (44% of loans and 39% of
share out) is the payment of school fees. In addition, 35% of loans and 40% of share out amounts are used
for some type of productive investment, including starting a new business, purchasing of farm inputs such
89
TABLE 22. Tabulation of Weekly Share Purchases of Individual Borrowers (44 groups)
Share purchase Freq. Percent Freq. Percent Freq. Percent
none 3,294 21.51 8,422 23.94 1,275 24.23
1 share 374 2.44 4,474 12.72 1,422 27.02
2 shares 2,188 14.28 6,119 17.39 417 7.92
3 shares 529 3.45 2,823 8.02 286 5.44
4 shares 1,610 10.51 1,717 4.88 153 2.91
5 shares 7,315 47.76 10,488 29.81 1,237 23.51
Other amount 7 0.05 1,143 3.25 472 8.97
Total 15,317 100 35,186 100 5,262 100
Share price =500 Share price=1,000 Share price=2,000
defaults on loans are rare: only 3% of members were reported not having paid the whole
loan by shareout.
As with savings, borrowing behavior and savings returns depend on the share price
chosen by groups. As seen in Table 21, lower share prices tended to have slightly smaller
but more frequent loans per member, lower total group borrowing. However, we see that
the smallest share price (500 UGX) experienced the highest loans-to-savings ratio and
return on savings which is suggestive that these groups are lending a larger portion of
their available funds throughout the cycle.
Balances Over Time We finally provide a dynamic view of group operations by
making use of the cashbook data. Figure 20 plots the evolution of cash balances, per-
period savings and loans disbursed in a sample of 22 Ugandan savings groups. Saving
contributions remain quite stable over the duration of the cycle, whereas loans grow over
time and peak towards the end of the cycle. On average, balances remain close to zero for
as livestock and land, or other business investment. Loans are somewhat more likely than share out to
be used for emergencies, such as a health incident or unemployment (22% versus 16%.). Conversely, and
quite predictably, households are almost twice as likely to consume their share out (29%) than their loans
(16%). See Burlando and Canidio (2015) for further details.
90
FIGURE 20. Saving, borrowing, and cash-in-box over the cycle.Data from 22 savings
groups with complete records of all financial transactions. Length of the cycle normalized to twenty
quantiles (x axis). Left axis is the scale for flow variables (savings and loans per meeting); right axis is
scale for stock variables (carryover balance), which we refer as ”cash in the box”.
almost half of the cycle, suggesting that groups are unable to generate sufficient funds to
meet the demand for loans of their members. We formally test for the presence of funds
scarcity using these data in a later section.
A Model of Savings Groups
In this section we present a theoretical model of SG. Our goal is to discuss how
SG rules determine the individual incentive to save and borrow, and to show that funds
may be in excess or fall short of the demand for loans. We abstract away from other
91
potential sources of inefficiencies such as moral hazard, adverse selection, behavioral
biases, voluntary or involuntary defaults (which, as we previously discussed, are a rare
occurrence in our data).
Consider a group composed of n individuals. The timing of the game is the
following:
– In period 0, the group meets and agrees on the interest rate that will be charged
on loans r and on the maximum savings per period s. As previously discussed, the
maximum savings per period is implicitly determined by the share value chosen by
the group. Here, we abstract away from the fact that savings are allowed only in
multiples of the share values. As a consequence the only role of the share value is
determining s.
– In periods 1 to k > 1 each member i:
∗ first receives wi,t, which is a per-period wage (i.e. non-investment income
generated outside of the group),
∗ then saves si,t with the group,
∗ then borrows bi,t from the group,
∗ then invest yi,t in an outside project,
∗ then earns fi,t(yi,t) from the funds invested outside of the group, where fi,t() is
continuous and strictly concave.8
∗ repays (1 + r)bi,t to the group, saves ai,t ≥ 0 outside of the group, and consumes
the rest.
8The assumption of concavity allows us to show the existence of the equilibrium of the game. The
reason is that, if fi,t() is locally convex, then optimal savings and borrowing may be a non-convex
correspondence, which prevents us from invoking standard fixed point theorems,
92
Given this sequence of events, a single period of our model is better interpreted as 3
months, which is the duration of each loan.
– In period k + 1, the money collected by the group is redistributed to members in
proportion to the amount saved by each.
Both fi,t(yi,t) and wi,t are deterministic. Finally, by assuming that the return on the
outside project fi,t(yi,t) is independent on the group composition, we are effectively
ignoring other relevant channels through which the group may impact the return on
investment, such as learning from peers, changes in the social network structure, and
aspirations.
Independently on the rules agreed upon in period 1, no member is allowed to borrow
more than 3 times the total amount saved with the group up until that period, and
therefore
bi,t ≤ 3
t∑
x=1
si,x for t ∈ {1, .., k}, (4.1)
which we call the leverage constraint. In addition, the agent can save with the group up to
s, so that:
si,t ≤ min{wi,t + ai,t−1, s}, (4.2)
where we assume ai,0 = 0, so that the resources available for saving are wi,1 in period 1,
wi,1 + ai,1 in period 2, and so on.
9 Note that the timing described above implies
yi,t ≤ bi,t + wi,t − si,2 + a1,t−1 for t ∈ {1, .., k}. (4.3)
In other words, the resources available for investment are equal to own funds (either
earned during that period wi,t or carried from the previous period a1,t−1) minus the
9We implicitly assume that the resources saved outside of the group do not generate any return.
93
savings with the group, plus borrowing with the group. Finally, consumption at the end
of each period is:
ci,t = fi,t(yi,t)− yi,t − rbi,t + wi,t + ai,t−1 − ai,t − si,t ≥ 0, (4.4)
which is the agent’s budget constraint.
Individual Maximization Problem At the beginning of each period of operation
of the group, a member i decides how much to save and borrow with the group by
maximizing her utility, taking as given the assets accumulated outside of the group ai,t,
and the savings previously accumulated with the group
∑t−1
x=1 si,x. This problem can be
expressed in recursive form:
Vi,t
(
ai,t,
t−1∑
x=1
si,x
)
= max
bi,t,si,t,yi,t,ai,t
{
ui(ci,t) + βiVi,t+1
(
ai,t+1,
t∑
x=1
si,x
)}
s.t.

bi,t ≤ C˜i,t aggregate resource constraint
equations 4.1 to 4.4
with the utility at share out:
Vi,k+1
(
ai,k,
k∑
x=1
si,x
)
=
(
k−1∑
x=1
si,x + si,k
)
(1 +R) + ai,k.
where βi ∈ (0, 1) is agent i discount factor, and ui(.) is agent i utility from consumption,
strictly increasing and strictly concave. Note that in the above specification implies that
the agent’s utility function is linear in the money received at share out.10
10All results derived are robust to a utility function that is curved in money, provided that the
curvature is not too strong.
94
The term C˜i,t is the cash available to member i of the group at the beginning of each
period, defined as
C˜i,t = St +
t−1∑
x=1
(Sx −Bx) + (1 + r)
t−1∑
x=1
Bx −
∑
j 6=i
bj,t (4.5)
where Bx =
∑
i bi,x and Sx =
∑
i si,x are aggregate borrowing and savings in period
x. In other words, the cash available for borrowing to agent i in period t is given by the
sum of all excess savings (aggregate savings minus aggregate borrowings) plus the loans
repayments collected by the groups from period 1 to t, minus period-t loans given to all
other members. The term R is the implicit return on savings, defined as
R =
r ·∑kt=1Bt∑k
t=1 St
We conclude the description of the model by introducing our main assumption:
Assumption 1. The return on savings at the end of the cycle R and the funds available
to each member of the group in each period C˜i,t are taken as given by the group members
but are determined in equilibrium.
In other words, the group members fail to anticipate that by increasing the amount
saved (or borrowed) they will affect the return on savings and the availability of funds
for the entire group. As a consequence, we can treat the return on savings and the funds
available to the group in each period as equilibrium quantities.11
11Given that the group is large, the incentives to influence the return on savings by setting a specific
si or bi are likely to be negligible. Note also that all our results are robust to assuming that the aggregate
resource constraint is bi,t ≤ αisi,t+C˜i,t, and C˜i,t = St+
∑t−1
x=1 (Sx −Bx)+(1+r)
∑t−1
x=1Bx−
∑
j 6=i bj,t+(1−
α)si,t, where αi is the amount of an agent’s own savings that this agent expects to be able to borrow back
from the group. The parameter αi should depend on the rationing mechanism employed by the group
(discussed in a later section on rationing).
95
Individual Saving and Borrowing Decision
Call si,t(r, R, C˜i,t) the optimal savings and bi,t(r, R, C˜i,t) optimal borrowings of agent
i in period t.
Lemma 1. si,t(r, R, C˜i,t) and bi,t(r, R, C˜i,t) are upper hemicontinuous in r, R and C˜i,t.
In addition, si,t(r, R, C˜i,t) is weakly increasing in R. If the aggregate resource constraint
is binding, si,t(r, R, C˜i,t) and bi,t(r, R, C˜i,t) are weakly increasing in C˜i,t. If the aggregate
resource constraint is not binding, si,t(r, R, C˜i,t) and bi,t(r, R, C˜i,t) are independent on C˜i,t.
We complement the above lemma with a remark that follows from inspecting the
individual maximization problem:
Remark 1. The cost of borrowing is decreasing in R. Conditional on being a borrower,
bi,t(r, R, C˜i,t) is weakly increasing in R. However for R sufficiently large, the agent may set
bi,t(r, R, C˜i,t) = 0 and only save.
Because of the leverage constraint (Equation 4.1), a member who wishes to borrow
must first save. Hence, as the return on these savings increases, the cost of borrowing
decreases. This reduction on the cost of borrowing weakly increases the amount saved
(by Lemma 1) and the amount that can be borrowed (by Equation 4.1). This is achieved
by reducing the fraction of a project that is self financed, and increasing the scale of the
investment. However, if R increases sufficiently, then the agent may switch from being
a net borrower to being a net saver. This possible “jump” from borrower to saver is
the reason why the amount borrowed and saved may be discontinuous in R. In case of
discontinuity, si,t(r, R, C˜i,t) and bi,t(r, R, C˜i,t) are nonetheless upper hemicontinuous: if
two borrowing (savings) levels solve the utility maximization problem, then any convex
combination of the two also solves the utility maximization problem. In other words, the
savings and borrowing correspondences have no “holes”.
96
Figure 21 illustrates a possible si,t(r, R, C˜i,t) and a possible bi,t(r, R, C˜i,t) for the same
agent in two situation: one in which the aggregate resource constraint is never binding
(left panel), the other when it sometimes is (right panel). For low and high R, the two
panels are identical because borrowing is either too low or zero, so that the upper bound
C˜i,t is not reached. For intermediate R’s instead, the two panels are different. Relative to
the left panel, in the right panel borrowing is constrained by C˜i,t and, as a consequence,
savings is also depressed.
We conclude by pointing out two additional results. First, note that the scarcity of
funds may not impact all group members equally. It may be the case that the aggregate
resource constraint is binding, but some members can fully meet their demand for loans
while the burden of rationing falls disproportionately on others. We say that a member
FIGURE 21. Individual savings and borrowing choices: In Panel (a), the aggregate resource
constraint is never binding. In Panel (b), the aggregate resource constraint may be binding. In both
cases, demand bi and supply si are initially increasing with the return on savings R, although savings si,t
is capped at s¯. Below R1 and R
′
1 savings and borrowings are positive. Above R1 and R
′
1 the borrower
switches to savings only. In addition, in Panel (b), the amount that can be borrowed has an upper bound
C˜i. The constraint shifts the savings curve downward whenever it is binding, and savings and borrowing
choices are now lower than when in the left panel. While the savings decision at high levels of savings
is not affected by the constraint, whenever the constraint is binding the borrower may switch to zero
borrowings at lower values of R. Hence R1 ≥ R′1.
(a)
R
Sa
vin
gs
, b
or
ro
wi
ng
si(R,C)
si(R,C)
bi(R,C)
bi(R,C)
s_
Ci~
R1
(b)
R
Sa
vin
gs
, b
or
ro
wi
ng
si(R,C)
si(R,C)
bi(R,C)
bi(R,C)
s_
Ci~
R1'
97
is rationed out in period t if her demand for loans is strictly increasing in C˜i,t. Second,
given the generality of the individual maximization problem, we do not link individual
characteristics of each group member to a precise borrowing and savings behavior. In
what follows, we characterize each member of the group directly by her si,t(r, R, C˜i,t) and
bi,t(r, R, C˜i,t), under the restriction that these functions satisfy Lemma 1 and Remark 1.
Rationing Mechanism
Before solving for the equilibrium of the model, we need to discuss how C˜i,s is
determined. We assume that in each period, after the savings decisions are made, each
member of the group announces her demand for loans, and the group determines each
C˜i,t according to a rationing mechanism. We also assume that the rationing mechanism
adopted by the group is:
– Resource monotonic: for given r, s and R, increasing the funds available to the
group weakly increases the amount borrowed by each member,
– Pareto efficient: the allocation of funds induced by the mechanism is never Pareto
dominated by another feasible allocation,
– Strategy-proof: no member has an incentive to misreport her demand for funds.
A large literature has investigated allocation mechanisms in the context of single
peaked preferences. One mechanism often highlighted is the so-called uniform rule. This
rule amounts to imposing an upper bound on the level of borrowing achievable by each
member. If any member borrows less than the upper bound announced (because her
peak is below the upper bound), the remaining resources are distributed among the
other members using again the same mechanism. Kıbrıs (2003) considers an allocation
problem with single peaked preferences and free disposal (i.e. not all resources need to
98
be allocated), and shows that the uniform rule is the only strategy-proof mechanism that
satisfies efficiency, no-envy, and is resource monotonic.12 In our context, preferences are
single peaked over bi,t (and the results in Kıbrıs, 2003, apply) because the return on the
outside investment fi,t(yi,t) is strictly concave for all i and t.
13
Note, however, that the uniform rule has very appealing properties for given savings
contributions. It is unclear whether the uniform rule maintains its properties once we take
into consideration that savings depend on the rationing rule. More theoretical work is
needed to characterize the set of optimal rationing mechanisms in savings groups. For
this reason, in what follows we simply assume that the rationing mechanism is resource
monotonic, efficient and strategy-proof for given savings contribution. Hence, for the most
part we will abstract away from the specific rationing mechanism employed by the group.
An exception will be discussed in a later section, where we solve for the period-0 choice of
r and s, because the “median” member of the group will depend on the rationing rule in
use.
Equilibrium
Despite being taken as given by the group’s members, R and C˜i,t are determined in
equilibrium. In particular, the equilibrium R ≡ R? solves:
R?
k∑
t=1
St(R
?) = r
k∑
t=1
Bt(R
?) (4.6)
12A rationing rule satisfies no-envy if for every announcement profile, the allocation implemented by the
mechanism is such that no group member wants to swap what she received with what some other group
member received. For a review of this literature and the formal definition of these properties, see Thomson
(2014).
13A second widely studied mechanism is serial dictatorship, in which members take turns in choosing
their optimal borrowing amount until no funds are left. In Appendix B we argue that this rationing rule
may be resource monotonic, Pareto efficient and strategy-proof in situations in which the uniform rule fails
to satisfy these properties.
99
where St(R) and Bt(R) are the aggregate demand and supply of funds in period t.
Note that, whereas the individual demand and supply of funds depend both on R
and on C˜i,t, the expressions for the aggregate demand and supply for funds only depend
on R (we omit the dependency on r). The reason is that, in the individual maximization
problem, C˜i,t matters only if the aggregate resource constraint is binding. Furthermore,
because the rationing mechanism is Pareto optimal, the aggregate resource constraint is
either binding for everybody or not binding for anybody. Therefore, in the aggregate we
can simply distinguish between R for which the aggregate resource constraint is binding
and R for which the aggregate resource constraint is not binding during a given period.
Whenever the aggregate resource constraint is not binding, aggregate borrowing depends
on aggregate savings only through the equilibrium R?. Instead, in periods in which the
aggregate resource constraint is binding, aggregate borrowing depends on aggregate
savings directly. In particular, when the resource constraint is binding in a given period,
bi,t = C˜i,t ∀i, and by Equation 4.5:
Bt(R) = r
t−1∑
x=1
Bx(R) +
t∑
x=1
Sx(R). (4.7)
Hence, in periods in which funds are scarce, aggregate savings and aggregate borrowings
are perfectly correlated. This observation will play a central role in the next section, where
we empirically address the issue of funds scarcity.
Figure 22 provides an illustration of the equilibrium, for the case in which the
aggregate borrowing and savings are continuous functions and the group is active in only
one period (i.e., k = 1). The left graph presents the case where the resource constraint in
binding, and the right graph the case where it is not binding. In each case, the top panel
provides a description of the behavior of the supply curve S(R) and demand curve B(R)
100
FIGURE 22. Two examples of a unique equilibrium when k = 1. In both cases
the equilibrium R? is determined in the bottom panel by the intersection of RS(B) and
rB(R).
(a) No rationing in equilibrium. The
equilibrium occurs at point A. As shown by
points B and C S(R∗) > B(R∗). It follows that
R∗ < r.
 
 
Funds
RS(R)
rB(R)
R
Rationing
B(R)
S(R)
rR*
A
B
C
R
~
R
(b) Rationing in equilibrium. For R < R˜,
funds are rationed and supply of funds is
equal to demand: S(R) = B(R). Because the
equilibrium (point A) occurs on the rationing
area, S(R∗) = B(R∗) and R∗ = r.
 
 
Funds
RS(R)
r(B(R)
R
Rationing
B(R)
S(R)
RR*=r
A
B
R~
with respect to the realized rate R. The bottom panel describes the behavior of the two
curves RS(R) and rB(R).
Distinguishing between periods in which the aggregate resource constraint is
binding or not will be relevant when performing our comparative statics analyses. For
example, assume that a member of the group drops out and is replaced by another
person with a higher propensity to save in every period and at every R.14 If the resource
constraint is never binding, we can solve for the new equilibrium simply by shifting
14If the rules of the group are chosen by majority voting, then changing the composition of the group
does not affect the rules adopted by the group as long as the median member of the group does not
change. Hence, we can analyze changes in the demand and supply of funds due to a change in the group’s
composition keeping the rules adopted by the group constant.
101
upward
∑n
t=1 St(R
?). If instead the aggregate resource constraint is binding in some
periods, then aggregate borrowing in these periods will also respond to an increase in
overall funds available to the group.
We now provide an important result of our framework: that an equilibrium R∗
always exists. We also derive a sufficient condition for an unique equilibrium, which we
will use in comparative statics.
Proposition 1. An equilibrium R? always exists. If βi is sufficiently small for all i, then
the equilibrium is unique. Assuming that at the unique R? both
∑
t St(R) and
∑
tBt(R)
are functions, then the LHS of equation 4.6 crosses the RHS of equation 4.6 from below.
Note that βi determines the sensitivity of the borrowing decision to the return on
savings. If this sensitivity is low the cost of borrowing is determined mostly by r and
not by R. Hence, as βi decreases, the elasticity of aggregate borrowing with respect to
R decreases, and multiple equilibria disappear. In what follows, we always assume that R?
is unique for all r and s.
Comparative Statics
Using proposition 1 and assuming that the equilibrium is unique, we next analyze
the effect of changes in the demand or the supply of funds in these groups.
Increase in Aggregate Savings Suppose that the aggregate savings increases in all
periods. This could be the case if a member of the group who only saves drops out of the
group and is replaced by another agent who also only saves but has a larger propensity to
save at every r, R and C˜i,t. Clearly, if the resource constraint is never binding, then, for
given R, the increase in aggregate savings has no effect on aggregate borrowing. Hence,
102
the behavioral responses of the group members is driven by the fact that, by proposition 1,
when
∑
t St(R) shifts upward R
? decreases.
Corollary 1. Suppose that the aggregate resource constraint is never binding.
Furthermore, suppose that there is a change in the behavior of one of the group members,
leading to an upward shift in St(R) (for some t). As a consequence, R
? decreases and
everybody else in the group is worse off.
If instead the aggregate resource constraints is always binding, adding resources
to the group has also a direct effect on the borrowing levels that are possible within the
group.
Corollary 2. Suppose that the aggregate resource constraint is always binding.
Furthermore, suppose that there is a change in the behavior of one of the group members,
leading to an upward shift in St(R) by the same factor in every period t. Each member’s
borrowing (weakly) increases and everybody else in the group is (weakly) better off.
The above corollary considers only shifts in aggregate savings by the same factor in
every period. We discuss later the fact that the time-profile of savings has an impact on
the availability of funds for the group members. In particular, we will argue that shifting
savings from later periods to earlier periods is always welfare improving to the group;
while the opposite is welfare decreasing (see Remark 2). Hence, the above corollary is true
also when early savings increases more than later savings (in percentage terms), but may
not hold if later savings increase less than early savings.
The two corollaries illustrate one of the main results of the model: that exogenously
increasing the funds available to the group (for example, by replacing one of the members
of the group) will impose an externality on other participants. The key determinant of
the sign of this externality is whether the group is resource constrained. Quite intuitively,
103
FIGURE 23. Exogenous shift in aggregate savings: In both cases, the initial
equilibrium is determined by point A. Increasing savings to S ′(R) shifts the borrowing
curve to B′(R) (dotted line) for values of R < R˜ (i.e. when there is rationing).
(a) Initially non-binding resource
constraint. R∗ drops to R
′∗. Savings increase
from C to C’, and loans increase from B to B’.
 
 
Funds
RS(R)
rB(R)
R
B(R)
S(R)
rR*
A
B
C
R
~
R
RS'(R)
rB'(R)
A'
C'
B'
~
R'
S'(R)
R'*
(b) Initially binding resource constraint.
The new equilibrium remains rationed, R is
unchanged and loans increase to B’.
 
 
Funds
RS(R)
rB(R)
R
B(R)
S(R)
RR*=r
A
B
R~
RS'(R)
rB'(R)
A'
~
R'
B'
S'(R)
B'(R)
when the resources within the group are scarce, adding more resources is beneficial to the
others. More interestingly, when the group is not resources constrained, adding resources
to the group hurts the group by decreasing the return on savings. These effects are
demonstrated graphically in figure 23, which show the effect of a shift in the aggregate
savings function assuming that k = 1, and that both S(R) and B(R) are continuous
functions. The figure shows that loanable funds increase without affecting returns if
borrowing remains rationed, but returns fall when funds are not rationed.
When the resource constraint is binding only in some periods, the overall welfare
effect of adding resources to the group is ambiguous. All members are made worse off by
the addition of extra funds because they decrease R?. However, net borrowers who are
rationed out benefit from the availability of extra funds.
104
Increase in Aggregate Borrowing We can similarly analyze what happen when
the group composition changes in a way that shifts Bt(R) up in every period, leaving
unchanged the aggregate supply of funds St(R). This would be the case if, for example,
a net saver is replaced with a net borrower who saves the same amount in every period,
but uses these savings to actually borrow funds from the group.
If the aggregate resource constraint is never binding, by proposition 1, the effect of
an increase in aggregate borrowing is an increase in R?, leading to the following corollaries
(which we illustrate in Figure 24 for the case k = 1).
Corollary 3. If the aggregate resource constraint is never binding, then an increase in∑
tBt(R) leads to an increase in R
?, higher individual savings and borrowing. Everybody
in the group is better off.
If instead the aggregate resource constraint is always binding, then the impact of an
increase in aggregate borrowings depends on how the funds are rationed among borrowers.
For example, if the new demand for funds goes completely unmet, then the existing
member of the group are indifferent to the increase in the demand for funds. If instead
the addition of a borrower decreases the amount of funds available to the other borrowers,
then the existing borrowers are made worse off by the increase in the demand for funds.
Corollary 4. If the resource constraint is always binding, an increase in the demand for
loans has no effect on R?, but may make rationing worse for some group members. As a
consequence, everybody in the group is weakly worse off.
Similarly, if the resource constraint is binding in some periods but not the others,
the welfare effect of increasing the demand for funds is ambiguous. On the one hand, R?
increases and everybody benefits. On the other hand, net borrowers may be hurt by the
fact that rationing is now worse.
105
FIGURE 24. Shift in the demand for loans: In both cases, the initial equilibrium is
determined by point A. Increasing demand for loans shifts the borrowing curve to B′(R)
(dotted line) for values of R > R˜ (i.e. when there is no scarcity).
(a) Initially non-binding resource
constraint. The new equilibrium is the
intersection point A’. R∗ increases to R
′∗.
Realized savings increase from C to C’, and
realized loans increase from B to B’.
 
 
Funds
RS(R)
rB(R)
R
B(R)
S(R)
rR*
A
B
C
R~R
B'(R)
rB'(R)
C'
B'
A'
R'*
~
R
(b) Initially binding resource constraint.
The group remains rationed. R, realized savings
and realized loans are unchanged.
 
 
Funds
RS(R)
rB(R)
R
B(R)
S(R)
R*=r
A
B
R
~
R
B'(R)
~
R'
rB'(R)
Overall, increasing aggregate borrowing and increasing savings have opposite effects
on the group. When the aggregate resource constraint is binding, increasing savings makes
the group better off while increasing borrowing makes the group (weakly) worse off. When
the aggregate resource constraint is not binding, increasing savings makes the group worse
off, while increasing borrowing makes the group better off.
Supply of Funds Over Time There is an additional dimension that is relevant in
determining the efficiency of the group: the timing of saving. Suppose that cumulative
aggregate savings are constant, but the group can substitute one or more members, so
that the timing of savings changes. In particular, assume that the reallocation leads to
106
saving earlier. It is quite immediate to see that if the aggregate resource constraint is
never binding, this reallocation of savings has no impact on the return on savings and
no impact on the group members’ welfare.
Instead, suppose that the aggregate resource constraints is binding in a given period
t < k − 1, and savings are reallocated from period t+ 1 to period t. If the period-t demand
for loans is rationed, then this reallocation increases the loans given out in period t. In
addition, all these loans will be repaid at the end of period t. So, for every dollar that is
reallocated from period t + 1 to period t, 1 + r dollars become available in period t + 1.
Hence, if the resource constraint is binding also in period t + 1, this reallocation eases
rationing in period t+ 1 as well.
Remark 2. Suppose the resource constraint is binding in period t¡k-1. Suppose that St(R)
increases and St+1(R) decreases by the same amount. It follows that R
? increases, and all
agents increase their level of borrowing and savings. All agents are better off. If instead
the resource constraint in period t is not binding, reallocating funds from one period to the
other has no impact on R? and no impact on the group members’ welfare.
Hence, contrary to changing the level of savings, changing the timing of savings has a
unambiguous welfare effect.
Period 0: Setting the Rules
So far, we have treated the price of a loan r and the maximum savings s¯ as given.
In reality, these values are chosen by the group at the beginning of the cycle, possibly
through voting. Might an optimal selection of these values eliminate the mismatch of
demand and supply?
In short, the answer is “no”. In Appendix B we argue that the payoff at share out
is far in the future relative to the moment in which the choice of r and s are made, and
107
hence plays a small role in deciding over r and s. If we consider the limit case in which
this payoff is completely disregarded by the the group members, then we can analyze
the group’s choice over r and s as a voting game and a Condorcet winner exists. The
important observation is that, in general, when funds are scarce, some members may still
be able to satisfy their demand for loans. Hence, the groups will choose rules that induce
scarcity of funds, provided that the “median” member of the group is able to satisfy its
demand for funds at these rules.
Evidence
The main takeaway from the theoretical model is that, in any given period, the
demand for loans may not match its supply, and therefore groups are either operating
under rationing or generating low return on savings. Whether and to what degree groups
operate under scarcity or excess funds is thus an important issue, which we explore in this
section.
Here, we use information from the cashbooks of 22 savings groups. For each
meeting, the records include loan repayments, deposits and collected fines as inflows, loan
disbursement as outflows, and a running balance of the cash remaining in the box (See
appendix A for further discussion of the data). We begin by studying the amount of funds
available in savings groups at the end of each meeting. Figure 25 shows the proportion
of meetings in any meeting quantile that ended with a low balance. 20 to 35 percent
of groups had less than 15,000 UGX ($5.60) available at the end of the day during the
first half of the cycle. This proportion drops to less than 10 percent during the rest of the
cycle. The graph is suggestive that groups may be operating under scarcity. However, it is
possible that groups largely satisfy loan demand even if occasionally the box is empty. It
108
FIGURE 25. Fraction of Groups with Low Balances by Meeting Quantile
is also possible that groups that have cash on hand may still be rationing loans if potential
borrowers need loan amounts that surpass the group balance.
An alternative strategy is to use the variation of inflows and outflows within the
group in a regression setting. As we argue in the theoretical section, if groups are indeed
resource constrained at any given meeting, the relationship between cash brought in
(savings, repayments, and fines) and the amount lent out is close to one-to-one (see
equation 4.7). That is, every dollar put in the box at the beginning of the meeting is
lent out in the same meeting. This number can easily surpass one in magnitude if there
are residual resources from previous meetings that are lent out. Groups are not resource
constrained, on the other hand, if the amount of loans disbursed does not depend on the
cash put into the box that day.
109
In order to identify whether groups are resource constrained across a lending
cycle, we regress loans made at a particular meeting t in group g on the cash added
to the box controlling for the cost of borrowing (captured by a group fixed effect). To
allow for the relationship to change across time, we interact this cash-in measure with a
series of dummy variables for the quantile of the meeting.15 Equation (4.8) is our base
specification:
Lgt = β0 + β1CashIngt +
Q∑
q=2
(βqCashIngt ∗Dqt ) +
Q∑
q=1
Dqt + αg + ugt, (4.8)
where Lgt are loans disbursed in group g during meeting t, CashIngt are savings, fines,
and loan repayments collected during that meeting, Dq is a dummy variable that takes on
a value of one if the meeting falls in quantile q and zero otherwise, α captures group fixed
effects (which controls for groups’ characteristics and group’s rules, including the cost of
borrowing), and ugt is an error term.
By including dummy variables in this way, we can interpret β1 to be the fraction of
cash brought in that was distributed out in loans during the first five percent of meetings,
and β1 + βq for (q = 2, ..., Q) is the fraction of cash inflows that is lent out in each
subsequent quantile. Periods where β1 + βq = 1 correspond to periods where all cash
inflows are lent out, which suggests that loans are being rationed and limited by the
availability of funds. Periods where lending is not constrained should be characterized
by saving and borrowing being uncorrelated: β1 + βq = 0.
Figure 26 reports the parameter estimates (β1 + βq) across twenty meeting quantiles.
Initially, the group does not lend out all the cash brought in, possibly because each
15Meeting quantiles were used because groups varied in the total number of meetings held. Twenty
quantiles were chosen, so the first quantile corresponds to the first 5% , the second quantile corresponds to
the second 5%, and so on.
110
FIGURE 26. Estimate of βq Over the Cycle
member needs to save with the group before being able to borrow. By the second quantile
of meeting (10%) they appear to be lending at a nearly one-to-one rate with cash coming
in, and that rate remains high for the first half of the cycle. Occasionally this estimate
exceeds one, suggesting that residual balances may be compiling early in the cycle. Twice
during the cycle, groups appear to loan only a fraction of the cash brought in during those
meetings (at 30 and 50 percent of meetings). This may indicate a desire to accumulate
funds for future lending of large loans. By three quarters of the meetings completed,
groups are beginning to lend less (many stop lending all together) and cash brought in
no longer affects lending decisions. Lending is shut down at the end of the cycle to allow
repayment, and loans and cash in become uncorrelated.
Regression estimates for this figure can be found in Table 23. The first column
of this table reports the OLS estimate for the average fraction of cash brought in that
is distributed as loans across the cycle (controlling for group level difference in lending
behavior). Because at the end of the cycle groups end lending altogether, this estimate is
111
averaging over a series of zeros and we can anticipate that it may be biased downward. To
accomodate for changes across the cycle, we interact the flow of cash in during a meeting
with a dummy variable for the percentage of meetings that has passed.
Column (2) presents these results and are the basis for Figure 26. The first five
percent of meetings are held as the base, so the parameter estimate for “Meeting Cash
In” is the fraction of cash during the first five percent of meetings that was lent out. The
following estimates report the difference in lending behavior from those first meetings. We
find that during the first half of meetings, the fraction of cash brought in that is lent out
increases compared to the first five percent of meetings. One exception to this is at the
30% meeting quantile where there appears to be a pause in the relationship.
This fluctuation between resource constraints and brief moments where groups have
excess cash may be indicative of periods of savings, potentially for large loan amounts in
subsequent meetings. As shown in Figure 1, loans do grow more frequent during the latter
part of the cycle, so this sort of time rationing is plausible.
Robustness One potential concern that arises from this specification is that there may
be an omitted variable influencing contemporaneous cash brought in during a meeting
(savings, repayments and fines) and loans disbursed during that meeting. In particular,
repayments on past loans are going to depend on the stock of outstanding loans in a
particular period. Because each member can have only one outstanding loan at the time,
groups with a larger stock of outstanding loans may have a higher cash-in and a lower
demand for loans. Column (3) of Table 23 includes an interaction term for outstanding
balance with the meeting quantile but the results do not appear to be sensitive to his
change (the magnitudes and linear combinations are robust).
Seasonality may also affect how groups decide to loan out cash. This is a concern
if the majority of the groups have meetings in roughly the same time of the year, and
112
TABLE 23. Lending of Available Resources Over the Cycle
113
if groups face increased demand for loans at similar times (perhaps tied to agricultural
planting and harvesting needs). In this setting, groups started the cycle at different
periods of time. Moreover, to account for potential seasonality, we include dummy
variables for month of meeting and report the estimated in Column (4). In general, the
results from estimating Equation (4.8) do not change drastically with this adjustment.
Conclusion
In this paper we provided a theoretical framework for the analysis of supply and
demand for loans within savings groups. The main result from the theory is that there
is no mechanism to ensure that demand and supply of funds are in equilibrium, and
that consequently groups either face excess supply of funds or rationing of loans. In this
context, shocks to individual demand or supply curves create a spillover effect: they affect
the availability of funds to rationed borrowers, or the return of savings.
**** We use the model to perform some comparative statics analyses. Most notably,
we find that shifting savings from late to early in the cycle is always Pareto improving,
because it eases scarcity in periods when the demand for loans exceeds the supply for
loans without reducing the return on savings. Furthermore our empirical analysis shows
that groups face binding resource constraints in the first part of the operating cycle.
Hence, overall, the paper points at the importance of encouraging early savings.
From a policy perspective, encouraging early savings may be achieved by adjusting
the rules of operation of savings groups. For example, decreasing the number of shares
that can be purchased (starting from a relatively large number) could successfully shift
savings from later periods to early periods. Alternatively, early savings could earn a higher
return than later savings. For example, shares could be sold at a discount during the
initial period of operation of the group, under the condition that each share receives the
114
same payout at share-out. Finally, programs that temporarily fund savings groups early in
a cycle through a microfinance loan may also encourage early lending without necessarily
hurting savings returns.
115
CHAPTER V
CONCLUSION
This dissertation examines three major economic issues facing developed and
developing countries today: substance abuse, criminality, and financial inclusion. I present
two papers which explore the impact of a novel policy and question the assumptions
made about determinants of risky behavior in the United States. I also include one paper
focusing on policies designed to improve welfare of individuals in developing nations.
Chapter II contributes to our understanding of the impact of state-wide health
insurance reform on substance abuse and overdose. Legislators began passing laws
requiring insurers to cover rehabilitation and detoxification treatments in insurance plans
as a way to mitigate the growing concern over substance abuse in the United States. I
show that these laws have a measurable impact on the uptake of services but that they are
limited in the ability to reach groups struggling with certain types of addiction, notably
addiction to opiates. Moreover, I illustrate that coverage of substance abuse treatment
is not necessarily having a significant impact on the overdose death rate. This has
several major implications. First, in absence of legislation expanding insurance to risky
populations, populations most at risk for overdose are less affected by the law. Secondly,
did have large amounts of uptake suggesting affected populations have unmet demand for
services.
In Chapter III, provides several factors to our understanding of the determinants
of criminality. Previous literature has found a consistent positive relationship between
unemployment and property crime rates and no relationship with violent crime rates.
Appealing to the seminal paper by Becker (2000), I provide reason to suspect time-
variation in these relationships and explore whether this has occurred using estimated
116
confidence intervals and dummy variable techniques. The results suggest that crime rates
are no longer positively correlated with unemployment in recent years. Additionally, there
is evidence that some measures of violent crime are negatively related to unemployment
rate during the last decade. This upends our current understanding of this determinant of
crime and creates a need for further investigation on the subject.
In my last substantive chapter, I present a coauthored investigation where we
contribute novel theory on the functioning of savings groups, an increasingly popular type
of informal financial institution. A main conclusion from this theory is that groups are
likely to operate under scarcity of funds or have surplus of savings that are not distributed
as loans. Using administrative data from a set of newly formed Ugandan savings groups,
we text these predictions and find that groups are typically rationing available funds,
which indicates that there are welfare improving changes to group formation and operation
that can be made. However, we also find that despite rationing, savings groups are able to
generate high returns to savings.
The results from the papers included in this dissertation fit within a general research
agenda focusing on policies design to improve the welfare of at risk populations domestic
and abroad. Risky behaviors such as drug abuse, suicide, and crime are continuing
problems world-wide and continued investigation on the impact and determinants of these
issues is necessary.
117
APPENDIX A
LEDGER DATA CLEANING
The paper made use of meeting-level data from handwritten registries of a number
of Ugandan savings groups (see Table 24). Of the 110 groups that were part of the study,
70 groups submitted photographs of their cashbooks for their first cycle. Many of these
pictures had missing pages, poor focus, or were otherwise difficult (if not impossible) to
digitize. We found that 29 groups had substantial portions of their cashbooks missing
or were in formats that were illegible. Of the remaining 41 groups, 22 were thoroughly
cleaned and reconciled.
TABLE 24. Description of Cashbook Cleaning Process.
In order to determine whether there was an error in any particular record, we
reconstructed the cash-in-the-box balance from meeting to meeting (cash-in minus cash-
out plus balance from previous period). We then looked at the difference between the
118
reported balance with our calculated balance and found that 59.2% of the observations
required an edit. The primary reason for these edits were omissions and typos due to the
digitization of the picture data which was easily corrected for by looking at the photos
and inputting the correct amounts. Occasionally, there was a miscalculation or written
error by the record keeper for the group which could be correctly interpolated from correct
data. Even through our careful cleaning, 44.1% of observations retained some level of
discrepancy (but we minimized this amount as much as possible). On average the size of
this discrepancy was about 972 UGX, but the range of this amount was quite substantial.1
1A lot of these discrepancies occurred on observations in the middle of the cycle which were corrected
for by audits throughout and there was fewer discrepancies during the latter parts of the cycle.
119
APPENDIX B
THEORETICAL EXTENSIONS
More on Rationing
It is interesting to note that, if we allow some convexities in the outside investment,
the uniform rule may fail to be either efficient or resource monotonic. For example,
suppose that all investment opportunities are discrete, in the sense that they require a
fixed investment level to deliver a given return. It follows that an agent’s utility may have
local maxima, which emerge whenever extra funds allocated to the agent are not sufficient
to start a new investment opportunity, but need nonetheless to be repaid with interest.
When resources are scarce, an agent may borrow little and settle for a local maximum. As
aggregate resources increase, some agents may discretely increase the amount borrowed
with the group, potentially decreasing the resources available to other members of the
group.
Motivated by this observation, we consider here a second widely-studied rationing
rule: serial dictatorship, in which all agents are ordered and each of them can, in turn,
choose how much to receive from the available funds. Serial dictatorship is appealing
because it is efficient, strategy proof and satisfies resources monotonicity whenever two
conditions are met:
– when indifferent between multiple borrowing levels, members demand the lowest
level.
– consider the list of dictators, 1, 2, ...k, where dictator 1 chooses before all other
dictators (and so on). If the kth dictator borrows a positive amount, then all k − 1
120
dictators fully meet their demand for loans. i.e. they would not borrow more even if
more resources were available.
To understand better the last point, suppose that an earlier dictator leaves funds to the
following dictator, who then uses these funds. The above condition rules out situations
in which an earlier dictator can only invest in projects requiring an upfront investment
larger than the available funds (and therefore leaves funds on the table), while the later
dictator can invest in projects that require an upfront investment lower than the available
funds. This condition is always satisfied if the return on investment is continuous, smooth
and concave. It is also satisfied if all investment opportunities faced by all agents have the
same minimum investment level (but may deliver different returns).
Hence, the uniform rule has very appealing properties if all fi() are smooth and
concave, but it fails to be resource monotonic in other cases. Serial dictatorship has less
appealing properties (in particular, it does not satisfy the no-envy condition), but remains
efficient, strategy proof and resource monotonic also for some fi() that are not convex.
Rules Setting
In period 0, the choice of r and s is determined by two basic trade-offs. For given R?
and given available funds, a higher r or a lower s will make everybody in the group weakly
worse off. However, a higher r or a lower s may actually increase R?, benefiting everybody
in the group. Furthermore, r and s have an additional effect on the availability of funds
and on whether some borrowers will be rationed out. Crucially, each group member will
solve these trade offs differently depending on their demand for funds and on the rationing
mechanism.
For this reason a voting game over the rules r, s¯ may not have a Condorcet winner.
A group member may have a preferred r and s in case she is a borrower and a preferred
121
r and s in case she is a pure saver (i.e. no borrowing). If a borrower, an agent is facing a
trade off between availability of funds (which is increasing in r), and cost of borrowing. In
general, an agent prefers the smallest r such that her demand for loans is fully met to any
larger r (but may, in fact, prefer an even smaller one). If a pure saver, the agent prefers
the r and s that maximize R?. Hence, an agent’s utility may be first decreasing and then
increasing with r if the agent switches between being a borrower to being a saver.
When preferences are not single peaked, the collective decision over r and s depends
on the details of the voting game being played, such as who can propose options for
voting, how many voting rounds are allowed, how long can voting last, whether options
that have previously been outvoted can be re-proposed, and so on. Because the voting
procedure is not part of the model, each group is likely to have adopted a different voting
game. Despite these difficulties, we can show that, under some strong assumptions, the
voting game has a Condorcet winner. We assume here a uniform rule for allocating scarce
funds.
Proposition 2. Suppose that βi = 0 for all i, so that, in period 0, each group
member maximizes u1(ci,1). Call r
?
i the preferred r of agent i (if it exists). There exists
a Condorcet winner of the game, which is the median r?i (which we call r
?
m) and the s
maximizing the availability of funds for this r.
It is reasonable to assume that, in period 0, all members of the group discount
heavily the payoff at share out relatively to the instantaneous payoffs earned while the
group is operating, because the share-out date is sufficiently far in the future while the
date at which each agent may borrow from the group is much closer. The proposition
considers the limit case βi = 0 for all i, in which the utility at share out is completely
ignored and the only determinant of the choice over r and s is the ability to borrow
cheaply in period 1. Hence, for every r, everybody agrees that s should maximize the
122
availability of funds.1 When choosing over r, conditioned on the agent being a borrower,
preferences are single peaked, because a higher r reduces rationing but makes borrowing
more expensive. In case an agent does not expect to borrow, she will be indifferent over r
and s. A Condorcet winner exists if agents break their indifference in favor of the option
closer to their peak.
Finally, some agents are never borrowers and therefore do not have a peak r. The
Condorcet winner is the median peak if these agents abstain. However, other Condorcet
winners may exists, depending on the number of agents who never borrow and on how
these agents break their indifference. For example, of only one agent in the group is always
a saver, there are two other Condorcet winners. Assuming that the agent who is always
a saver always votes for the largest r, then the peak just above the median peak is a
Condorcet winner. Similarly, assuming that the agent who is always a saver always votes
for the smallest r, then the peak just below the median peak is a Condorcet winner.
Despite being based on fairly strong assumptions, the above proposition is relevant
because it shows that the outcome of the voting game will, in general, not reflect the
”preferences” or ”welfare” of the group, but rather the preferences of the median member
of the group. In particular, note that if r?i > r
?
m for at least one i, then the interest rate
chosen by the group will generate rationing, because some of the group’s member will not
be able to borrow as much as they want at the chosen r?m.
1Note the amount of cash available for borrowing may not be monotonic in s. For example, if the
person saving the most is actually a net borrower, constraining this person in the amount she can save
may generate more resources to the remaining members of the group.
123
APPENDIX C
MATHEMATICAL DERIVATIONS
Proof of Lemma 1
Proof. Because the objective function of the utility maximization problem is quasiconcave, and
all constraints are continuous and convex valued, by the theorem of the maximum si,t(r,R, C˜i,t)
and bi,t(r,R, C˜i,t) are upper hemicontinuous, closed and convex for all r, R and C˜i,t. In addition,
note that si,t and R are complements in the objective function. Therefore by Topkins’s theorem
si,t(r,R, C˜i,t) is weakly increasing in R (if si,t(r,R, C˜i,t) is a correspondence, then lower and
upper bound of this correspondence are weakly increasing in R).
Finally, bi,t(r,R, C˜i,t) is weakly increasing in C˜i,t because increasing C˜,ti relaxes the
aggregate resource constraint and allows for higher borrowing. At the same time, because
of Equation 4.1, an agent may save to borrow. When the resource constraint is binding,
bi,t(r,R, C˜i,t) = Ci,t. Hence, as Ci,t increases, the amount that can be borrowed increases, and
with it the amount that may need to be saved in order to reach a given level of borrowing.
Proof or Proposition 1
Proof. Note that the aggregate demand for savings and aggregate demand for loans inherit the
properties of the individual demand for savings and loans derived in Lemma 1 and remark 1.
Note also that each St(R) is bounded above by
∑
i mini{wi, s}. It follows that each Bt(R) is also
bounded above. Hence, for R sufficiently large:
R
∑
t
St(R) > r
∑
t
Bt(R)
At R = 0 members are indifferent between saving inside or outside of the group. Whenever
savings inside of the group are positive, also borrowings can be positive and r
∑
tBt(R) ≥ 0.
124
Hence, it must be the case that
R
∑
t
St(R)|R=0 = 0 ≤ r
∑
t
Bt(R)|R=0
Together with the fact that all functions are upper hemicontinuous and compact valued, these
results imply that an equilibrium exists.
Finally, as βi decreases, each Bt(R) becomes progressively flat, because the borrower’s
behavior becomes independent on R (and depends exclusively on r). At the same time, by
Lemma 1 St(R) is always (weakly) increasing. Therefore, as βi decreases for all i, r
∑
tBt(R)
becomes flat, while R
∑
t St(R) is strictly increasing and diverges to infinity. It follows that the
equilibrium must be unique. It also follows that at the unique equilibrium R
∑
t St(R) must cross
r
∑
tBt(R) from below.
Proof of Corollary 2
Proof. If all aggregate resource constraints are binding, then at R = R?:
R
k∑
t
St(R) = r
k∑
t
St(R)
k−t∑
s
(1 + r)s
Which implies that increasing all St(R) by the same factor does not change R
?. At the
same time, higher St(R) relax the aggregate resource constraint. Net savers and borrowers
who are not rationed out are indifferent, while borrowers who are rationed out increase their
borrowing and are better off.
Proof of Proposition 2
Proof. We start by making few preliminary observations. First, the availability of funds within
the group is increasing in r. An increase in r causes three responses. Those who did not borrow
at all do not change their behavior. Some of the borrowers will decrease the amount borrowed,
but continue borrowing. Finally, some of the borrowers will switch from being borrowers to
125
being savers. It follows that increasing r always (weakly) increases the availability of funds to
those who remain borrowers. Second, because the individual demands and supplies of funds are
are upper hemicontinuous in r (by the theorem of the maximum), also the funds available for
borrowing are upper hemicontinuous in r. Third, for r sufficiently large, nobody will want to
borrow and, quite trivially, the demand for loans of the entire group is satisfied.
For every agent i, call r?i this agent’s preferred r, which is computed solving for the trade
off between borrowing cheaply and being able to access funds. Note that this r?i may not exist
for all group members, but will exist for some member as long as f ′i,1(0) > 0 for some i. The
reason is that, by the uniform rule, as long as the group has some funds to distribute (i.e. as long
as there is one saver in the group), then everybody who demands funds will receive some. On
the other hand, if the agent expects to be a saver for every r, then r?i does not exist because this
agent is indifferent among all r.
If r′ > r?i , r
′′ > r?i , r
′ > r′′, and assuming that the agent is a borrower at r′′, the agent
prefers r′′ to r′, because conditionally on being able to meet his demand for loans, this agent
strictly prefers lower r. Similarly, if r′ < r?i , r
′′ < r?i , r
′ > r′′, and assuming that the agent
can borrow a positive amount at r′, this agent prefers r′ to r′′, because this agent will be able
to access more funds (remember that, by the uniform rule, more funds for the group imply more
funds available for each member of the group). Furthermore, this agent always prefers an r at
which she is a borrower to an r at which she is a saver, and is indifferent between all r for which
she is a net saver.
Hence, preferences are single peaked over r (and a Condorcet winner exists) as long as we
impose the following tie breaking rule: in case of indifference, an agent will vote for the option
that is closer to her peak. Note, however, that agents who are always savers do not have a peak
r. Depending on how these agents break their indifference, we may have different Condorcet
winner. Here we assume here that, if indifferent among all options, these agents do not vote, so
that the Condorcet winner is the median peak r. To conclude, note that every borrower prefers
126
the s that generates more funds to any other s, because it allows to maintain the same level of
rationing but at lower r’s.
127
REFERENCES CITED
Agnew, R. (1992). Foundation for a general strain theory of crime and delinquency*.
Criminology, 30(1):47–88.
Aizer, A. (2010). The gender wage gap and domestic violence. The American Economic
Review, 100(4):1847.
Allen, H. and Panetta, D. (2010). Savings groups: What are they. SEEP Network.
Andersen, M. (2015). Heterogeneity and the effect of mental health parity mandates on
the labor market. Journal of Health Economics, 43:74–84.
Ashe, J. (2009). Saving for change: Low cost, mass-scale, self-replicating and profitable
microfinance for the rural poor. Oxfam America.
Ashe, J. and Neilan, K. J. (2003). In Their Own Hands: How Savings Groups are
Revolutionizing Development. Berrett-Koehler Publishers, Inc.
Banerjee, A., Karlan, D., and Zinman, J. (2015). Six randomized evaluations of
microcredit: Introduction and further steps. American Economic Journal: Applied
Economics, 7(1):1–21.
Barry, C. L. and Busch, S. H. (2008a). Caring for children with mental disorders: do state
parity laws increase access to treatment? The Journal of Mental Health Policy and
Economics, 11(2):57–66.
Barry, C. L. and Busch, S. H. (2008b). New evidence on the effects of state mental health
mandates. INQUIRY: The Journal of Health Care Organization, Provision, and
Financing, 45(3):308–322.
Beaman, L., Karlan, D., and Thuysbaert, B. (2014). Saving for a (not so) rainy day: A
randomized evaluation of savings groups in mali. Technical report, National Bureau
of Economic Research.
Becker, G. S. (2000). Crime and punishment: an economic approach. pages 13–68.
Bilaver, L. A. and Jordan, N. (2013). Impact of state mental health parity laws on access
to autism services. Psychiatric Services, 64(3):967–963.
Blattman, C., Green, E. P., Jamison, J. C., Lehmann, M. C., and Annan, J. (2015). The
returns to microenterprise support among the ultra-poor: A field experiment in
post-war Uganda. American Economic Journal: Applied Economics, 8(2):35–64.
128
Burlando, A. and Canidio, A. (2015). Does group inclusion hurt financial inclusion?
evidence from ultra-poor members of ugandan savings groups. Working Paper.
Cassidy, R. and Fafchamps, M. (2015). Can community-based microfinance groups match
savers with borrowers? evidence from rural malawi. Working Paper.
Dave, D. and Mukerjee, S. (2011). Mental health parity legislation, cost-sharing and
substance-abuse treatment admissions. Health Economics, 20(2):161–183.
Davoli, M., Perucci, C. A., Forastiere, F., Doyle, P., Rapiti, E., Zaccarelli, M., and
D Abeni, D. (1993). Risk factors for overdose mortality: a case-control study within
a cohort of intravenous drug users. International Journal of Epidemiology,
22(2):273–277.
Eitle, D. and Turner, R. J. (2003). Stress exposure, race, and young adult male crime. The
Sociological Quarterly, 44(2):243–269.
Fernandez, J. and Lang, M. (2015). Suicide and organ donors: Spillover effects of mental
health insurance mandates. Health Economics, 24(4):491–497.
FinScope (2010). Results of a national survey on demand, usage and access to financial
services in uganda. Kampala, Uganda, Available at: http://www. fsdu. or.
ug/pdfs/Finscope Report. pdf.
Freeman, R. B. (1999). The economics of crime. Handbook of labor economics,
3:3529–3571.
Gash, M. and Odell, K. (2013). The evidence-based story of savings groups: A synthesis of
seven randomized control trials. A publication of the Savings-led Financial Services
Group at SEEP.
Gossop, M., Stewart, D., Treacy, S., and Marsden, J. (2002). A prospective study of
mortality among drug misusers during a 4-year period after seeking treatment.
Addiction, 97(1):39–47.
Gould, E. D., Weinberg, B. A., and Mustard, D. B. (2002). Crime rates and local labor
market opportunities in the united states: 1979-1997. The Review of Economics and
Statistics, 84(1):45–61.
Greaney, B., Kaboski, J. P., and Van Leemput, E. (2016). Can self-help groups really be
“self-help”? The Review of Economic Studies, pages 1614–1644.
Harris, K. M., Carpenter, C., and Bao, Y. (2006). The effects of state parity laws on the
use of mental health care. Medical care, 44(6):499–505.
Kıbrıs, O¨. (2003). Constrained allocation problems with single-peaked preferences: an
axiomatic analysis. Social Choice and Welfare, 20(3):353–362.
129
Klick, J. and Markowitz, S. (2006). Are mental health insurance mandates effective?
evidence from suicides. Health Economics, 15(1):83–97.
Klick, J. and Stratmann, T. (2006). Subsidizing addiction: Do state health insurance
mandates increase alcohol consumption? The Journal of Legal Studies,
35(1):175–198.
Ksoll, C., Lilleør, H. B., Lønborg, J. H., and Rasmussen, O. D. (2015). Impact of village
savings and loans associations: evidence from a cluster randomized trial. Journal of
Development Economics, 120:70–85.
Lang, M. (2013). The impact of mental health insurance laws on state suicide rates.
Health economics, 22(1):73–88.
LaVallee, R. A. and Yi, H. Y. (2011). Apparent per capita alcohol consumption: National,
state, and regional trends, 1977-2009 (surveillance report 92). US Department of
Health of Human Services, National Institutes of Health, Bethesda, MD. Archived by
WebCite at http://www. webcitation. org/695Mj1yIO. Accessed July, 11:2012.
Linn, M. W., Sandifer, R., and Stein, S. (1985). Effects of unemployment on mental and
physical health. American Journal of Public Health, 75(5):502–506.
Maclean, J. C., Cantor, J. H., and Pacula, R. L. (2013). Economic downturns and
substance abuse treatment: Evidence from admissions data. Technical report,
National Bureau of Economic Research.
Madensen, T. D. and Eck, J. E. (2008). Violence in bars: Exploring the impact of place
manager decision-making. Crime Prevention & Community Safety, 10(2):111–125.
Minnesota Population Center (2016). National historical geographic information system:
Version 11.0 [database].
Mino, A., Bousquet, A., and Broers, B. (1999). Substance abuse and drug-related death,
suicidal ideation, and suicide: a review. Crisis: The journal of crisis intervention
and suicide prevention, 20(1):28.
Mocan, H. N. and Bali, T. G. (2010). Asymmetric crime cycles. The Review of Economics
and Statistics, 92(4):899–911.
Mocan, H. N. and Rees, D. I. (1999). Economic conditions, deterrence and juvenile crime:
Evidence from micro data.
Paulozzi, L. J., Kilbourne, E. M., and Desai, H. A. (2011). Prescription drug monitoring
programs and death rates from drug overdose. Pain Medicine, 12(5):747–754.
Raphael, S. and Winter-Ebmer, R. (2001). Identifying the effect of unemployment on
crime. Journal of Law and Economics, 44(1):259–283.
130
Reifler, L. M., Droz, D., Bailey, J. E., Schnoll, S. H., Fant, R., Dart, R. C., and
Bucher Bartelson, B. (2012). Do prescription monitoring programs impact state
trends in opioid abuse/misuse? Pain Medicine, 13(3):434–442.
Scott, M. S. and Dedel, K. (2006). Assaults in and Around Bars 2nd, Edition.
Washington, DC: Office of Community Oriented Policing Services.
Substance Abuse and Mental Health Services Administration (2014). Treatment Episode
Data Set – Admissions (TEDS-A). United States Department of Health and Human
Services. Substance Abuse and Mental Health Services Administration. Center for
Behavioral Health Statistics and Quality. Inter-university Consortium for Political
and Social Research (ICPSR) [distributor].
Swensen, I. D. (2015). Substance-abuse treatment and mortality. Journal of Public
Economics, 122:13–30.
Thomson, W. (2014). Fully allocating a commodity among agents with single-peaked
preferences. Working paper.
United States Department of Justice (2017). Uniform crime reporting program data:
Arrests by age, sex, and race 1960-2015. Federal Bureau of Investigation. Ann Arbor,
MI: Inter-university Consortium for Political and Social Research [distributor].
Vanmeenen, G. (2010). Savings and Internal Lending Communities (SILC), voices from
Africa: The benefits of integrating SILC into development programming.
Walley, A. Y., Xuan, Z., Hackman, H. H., Quinn, E., Doe-Simkins, M., Sorensen-Alawad,
A., Ruiz, S., and Ozonoff, A. (2013). Opioid overdose rates and implementation of
overdose education and nasal naloxone distribution in massachusetts: interrupted
time series analysis. BMJ, 346:f174.
World Health Organization (1992). International classification of diseases
(icd-10)[organizacio´n mundial de la salud, clasificacio´n internacional de enfermedades
(de´cima edicio´n)(cie-10)].
131