Three Essays in Public Economics
by
Sarah Y. Siegel
B.A. Mathematics
Pomona College, 2000
SUBMITTED TO THE DEPARTMENT OF ECONOMICS INPARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY IN ECONOMICS
AT THE
MASSACHUSETTS
INSTITUTE
OF
SEPTEMBER
MASSACHUS'8 INSTUE
TECHNOLOGY
OF TECHNOLOGY
2006
SEP 2 5 2006
@2006
Sarah
Y.
Siegel.
All
rights
LIBRARIES
reserved.
The author hereby grants to MIT permission to reproduce
and to distribute publicly paper and electronic
copies of this thesis document in whole or in part
in any medium now known or hereafter created.
Signature of Author:
/_
..
,
•
Department of Economics
• \
August 11, 2006
Certified by:
Jonathan Gruber
Professor of Economics
Thesis Supervisor
Accepted by:
.
Peter Temin
Elisha Gray II Professor of Economics
Chairman, Committee for Graduate Studies
ARCHAVES
Three Essays in Public Economics
by
Sarah Y. Siegel
Submitted to the Department of Economics
on August 11, 2006 in Partial Fulfillment
of the Requirements for the Degree
of Doctor of Philosophy in Economics
Abstract
This thesis consists of three separate papers. In the first paper, using the Panel Study of
Income Dynamics (PSID), which has measures of both risk preferences and religiosity along
with measures of many risky behaviors, I investigate the implications of the correlations among
risk preferences, religiosity and gender for the observed relationship of each of these variables
with risky behaviors. I conclude that the correlations of risk preferences, religiosity, and gender
with behaviors are all strongly robust to including the others in the regression; although they are
correlated, they have independent relationships with risky behaviors.
The second paper reports the results of a randomized field experiment to study the impact
of choice in charitable giving; in this experiment half of the recipients of a newsletter from a
Dutch NGO were able to choose what program area their donation would be spent on. There is
no difference in either mean response rates or mean donation amounts between the treatment and
control groups; I thus conclude that while most of the treatment group in this experiment did not
value the choice that they were given, the choice also did not make them any less likely to
donate.
In the third paper, a coauthor and I develop a computer model in which individual agents
choose a neighborhood based on preferences over the area's racial composition; this model of
residential segregation is loosely based on the 1971 Schelling model. We find that both the
strength of preferences for diversity, and historical segregation, have strong effects on
equilibrium levels of integration. When we include contemporary discrimination in our model,
however, we find that it increases segregation in an initially unsegregated model, but has no
additional effect on segregation in an initially segregated model. Finally, we examine a simple
social policy that encourages integration, and find that it is successful in creating diversity,
making diversity-seeking agents better off.
Thesis Supervisor: Jonathan Gruber
Title: Professor of Economics
Acknowledgments
I thank my advisors Jonathan Gruber and Esther Duflo for their guidance and advice throughout
the research process, their help was invaluable. I also thank Sendhil Mullainathan for his input
and advice, and Xavier Gabaix for his guidance on Chapter 3.
I thank the National Science Foundation Graduate Research Fellowship for providing primary
financial support. I also thank the MIT Schultz Fund for the travel support required for Chapter
2.
I thank David Abrams, Elizabeth Ananat, Jessica Cohen, and Guy Michaels, for providing a
great arena for comments, criticism, support, and discussion, during the months when that was
most needed. I also thank many friends and officemates who provided moral support, a great
sounding board, constructive criticism, and help throughout the process.
I especially thank Joanna Lahey for her advice, moral support, and proofreading skills, from the
time I began to consider applying to graduate school in economics, during our senior year of
college, through the present. And I thank David Schatten for providing so much support,
encouragement, and humor during my final year of graduate school.
I thank my mentors before graduate school, Gary Burtless, Cecilia Conrad, and Michael
Kuehlwein, for showing me how great economics could be and encouraging me to pursue it.
I thank ICS, especially Machteld Papegaaij and Els Hekstra, for their willingness to perform the
experiment described in Chapter 2 and their work to make it happen; and I thank Jason
Woodard, as well as the other participants at the Santa Fe Institute Complex Systems Summer
School, for comments and suggestions on Chapter 3.
And finally I thank my parents, Daniel and Ruth Siegel, for all of their support, advice, editing,
and words of wisdom at so many times during the last five years.
Chapter 1
The Interaction of Risk Tolerance, Religiosity, and Gender in
Explaining Risky Behaviors
1
INTRODUCTION
11
2
BACKGROUND
12
2.1
Religiosity and Risky Behaviors
12
2.2
Risk Preferences and Risky Behaviors
13
2.3
Risk Preferences and Religiosity
14
2.4
Gender Differences
16
3
DATA
17
3.1
Risk Preferences
19
3.2
Religiosity
20
3.3
Risky Behaviors
21
3.4
Religious Density
22
4
EMPIRICAL APPROACH
23
4.1
Part 1: Relationships among the factors
23
4.2
Part 2: Comparison with the Barsky et al. results
24
4.3
Part 3: Risky Behaviors on Each Factor and Combinations of the Factors
24
4.4
Part 4: Religiosity Instrument
25
5
RESULTS
26
5.1
Relationships among the factors
26
5.2
Comparison with Barsky et al. results for risky behaviors
27
5.3
Risky behaviors on each factor individually and on all three together
28
5.4
Comparison with Barsky et al. results for investment choices
29
5.5
Investment choices on each factor individually and on all three together
30
5.6
Religious Density Instrument
31
6
CONCLUSION
33
REFERENCES
35
TABLES AND FIGURES
37
Chapter 2
The Effect of Choice on Charitable Contributions:
A Field Experiment
1
INTRODUCTION
45
2
EXPERIMENT DESIGN
48
2.1
Design Issue
50
3
DATA
50
4
RESULTS
52
4.1
Targets chosen
52
4.2
Experiment donations
53
4.3
Experiment donations by group
56
4.4
Post-experiment donations
56
5
CONCLUSION
57
REFERENCES
60
TABLES AND FIGURES
62
Chapter 3
Schelling Revisited: Historic Discrimination, the Desire for Diversity,
and Current Segregation
with Elizabeth Ananat
1
INTRODUCTION
71
2
THE MAKINGS OF AMERICAN SEGREGATION
73
3
THE SCHELLING MODEL
75
4
OUR MODEL
77
4.1
Constructing neighborhoods
77
4.2
Constructing preferences
79
4.3
Constructing the simulation
84
4.4
Extension One : Historic Discrimination
84
4.5
Extension Two: Current Discrimination
85
4.6
Extension Three: A Policy Experiment
86
5
THE SIMULATIONS RUN
87
5.1
Main Simulations
87
5.2
Current Discrimination
87
5.3
Subsidy
88
5.4
Percent of each type of agent
88
5.5
Outcomes
89
RESULTS
89
6
6.1
Historical Discrimination
89
6.2
Controls
90
6.3
Current Discrimination
93
6.4
A Policy Experiment
94
7
CONCLUSION
94
REFERENCES
100
TABLES AND FIGURES
102
Chapter 1
The Interaction of Risk Tolerance, Religiosity, and Gender in
Explaining Risky Behaviors
1 Introduction
In this chapter, I look at three factors that have been shown to be strongly correlated with
a person's likelihood of engaging in risky behaviors: risk preferences, religiosity, and gender.
These individual relationships are well-studied; however, there are also strong correlations
among these three factors: women are more risk averse, women are more religious, and people
who are more risk averse are more religious. The gender differences have received a significant
amount of attention, but the direct relationship between risk preferences and religiosity has
received much less attention. I investigate the implications of the correlations among risk
tolerance, religiosity and gender for the observed relationship of each of these variables with
risky behaviors.
The data I use are from the Panel Study of Income Dynamics (PSID), the only broadly
representative dataset that contains measures of both religiosity and risk preferences. The
measure of religiosity I use combines three factors: frequency of attendance at religious services,
number of volunteer hours for religious organizations, and amount donated to religious
organizations. The measure of risk preferences is based on a series of questions about a choice
between a job that guarantees you income for life equal to your current total income and one that
has a 50-50 chance of doubling your income and a 50-50 chance of cutting your income by some
fraction. I also have detailed demographic and socioeconomic data, as well as information on a
number of behaviors such as smoking, drinking, self-employment, and investment decisions.
I show that even though risk preferences, religiosity, and gender are highly correlated,
they each have independent correlations with risky behaviors; for instance, controlling for risk
tolerance does not significantly lower the estimated correlation between religiosity and risky
behaviors. This is true both when the relationship is measured using OLS and when it is
measured using an instrument for religiosity based on religious market density, although the
results from the instrument are only suggestive, as it is a relatively weak instrument. I find strong
associations between each of risk tolerance, religiosity, and gender, and almost all of the risky
behaviors I look at, in the expected directions. Religiosity, risk tolerance, and gender all seem to
have comparable effects, so this research reaffirms both the power of religiosity to affect
behavior and the validity of risk preferences as a measurement of some individual characteristic
that is associated with a wide variety of risky behaviors, as well as the importance of gender in
explaining behaviors even when many other factors are controlled for.
This chapter is laid out as follows: section 2 discusses the background and reviews the
literature; section 3 describes the data used; section 4 lays out the empirical approach; section 5
gives the results; and section 6 concludes.
2
Background
2.1 Religiosity and Risky Behaviors
Iannaccone (1998) provides an excellent summary of the economics of religion literature;
it includes two strains of research that are relevant to this paper: first, research on the
consequences of religion, which includes many papers documenting a relationship between
religion and a wide range of behaviors including drug use, school attendance, and criminal
activity; second, research on the factors that cause a person to be more or less religious.
Iannaccone summarizes research done before 1998 documenting a relationship between
religion and risky behaviors. Since then, the literature has continued to develop, with the most
recent contribution being Gruber (2005); he uses two facts to look at the effect that exogenous
changes in religiosity have on outcomes such as education levels and income. The first fact is
that if a higher fraction of a person's neighbors share that person's religion, that person will
attend religious services more often; higher religious density causes more religious attendance.
The second fact is that religious density of a neighborhood is partly determined by the ethnic mix
of the neighborhood. The religious density of a neighborhood for a certain person can thus be
exogenously predicted using the density of different ethnic groups in the neighborhood, not
including the person's own ethnic group. Using these facts, he finds strong positive effects of
religion on both education and income.
2.2 Risk Preferences and Risky Behaviors
Economists have long assumed that there is a stable, measurable characteristic called
"risk preference" that can be used to predict people's behaviors across a wide variety of domains.
It has also been quite widely assumed that a question which elicits a person's attitude toward
financial risk can create a valid measure of this characteristic. There have been a number of
recent attempts to take a closer look at these assumptions in a variety of ways.
The paper I focus on is Barsky et al. (1997) because the questions used to measure risk
preferences in this paper are almost the same as the ones in the PSID. Barsky et al. look at
measures of risk tolerance, time preference, and intertemporal substitution that were all asked in
wave 1 of the Health and Retirement Study (HRS) in 1992; the measure of risk tolerance I use
from the PSID is based on the measure used in the HRS. In the risk tolerance section, Barsky et
al. look at patterns of risk tolerance with respect to demographic characteristics such as age, sex,
and race. They also look at the relationship between risk tolerance and various risky behaviors
and find significant effects on variables such as smoking, drinking, home ownership, and
investment choices.
The most recent addition to this literature is Dohmen et al. (2005), who make several
important contributions. First, they not only look at the financial risk question, but they also look
at a question that asks people to say how willing they are, generally, to take risks, which is
answered on a scale from 0 to 10. In addition, they compare the answers to these questions not
only to other questions in the survey, but also to behavior in the context of a field experiment.
They find that answers to the financial risk question have predictive power for many, but not all,
of the risky behaviors they study, while the question asking about general attitude towards risk
has predictive power for all behaviors.
2.3 Risk Preferences and Religiosity
There are many reasons risk aversion and religiosity could be correlated. First, it could be
that people who are more risk averse are more likely to be religious because religion provides
insurance. Religion could be thought of as providing several different types of insurance: first, it
can be thought of as providing "spiritual insurance." This idea goes back at least to the
17 th
century French mathematician and philosopher Blaise Pascal. He developed an argument,
referred to as "Pascal's wager," which suggests that you should believe in God (in the Christian
sense,) and act as if you believe, because, if you can't be certain, denying God's existence is too
risky. If you choose not to believe in God but it turns out God does exist, you will spend eternity
in hell; on the other hand, if you believe in God and it turns out there is no God, you have not
lost very much by believing, but if he does exist, you will spend eternity in heaven. Religiosity
can thus be thought of as insurance against the possibility of going to hell.
Two other types of insurance that may be provided by religion are consumption and
happiness insurance. Dehejia et al. (2005) find evidence that some religious organizations
provide consumption insurance and some provide happiness insurance, and Chen (2005) shows
that people who were hit hardest by the Indonesian financial crisis became more religious. Clark
(2005) also finds evidence, using two large-scale European datasets, that religion can act as
happiness insurance in the case of unemployment and divorce.
The causality could also, however, go in the opposite direction: religion could cause
people to be more risk averse. This is slightly less intuitive because a person's risk preferences
are generally thought of as a stable, exogenous characteristic; Stark (2002) discusses evidence
that risk preferences have a physiological basis. However, risk preferences are not always
assumed to be stable: Brunnermeier and Nagel (2004) study whether fluctuations in wealth might
change a person's risk preferences. It is possible that in addition to discouraging particular risky
behaviors, religion, by emphasizing responsibility and planning, for instance, could change a
person's overall level of risk aversion. It must be noted that changing risk aversion is very
different from changing certain behaviors; if religion causes people to be more risk averse, all
risky behaviors will change, even ones, such as investing in stocks, that are not discouraged by
religious leaders. This is very different from changing the behaviors that are regarded as vices
and generally discouraged by religious leaders, such as smoking and drinking.
Finally, it is possible that there is not, in fact, any causal relationship between risk
aversion and religiosity; it could just be a spurious correlation caused by some third factor. In
this paper I do not attempt to differentiate among these different relationships between risk
preferences and religiosity; the different possibilities provide context for my work, and I am
interested in the implications of this relationship for the effects of risk preferences and religiosity
on behavior. I leave it to future work to tease out the causality.
2.4 Gender Differences
Women are less likely to engage in risky behaviors than men are; they have lower rates of
criminality, smoking, drinking, etc. (Byrnes, Miller and Schafer, 1999). They also have lower
risk tolerance, on average (Dohmen et al., 2005). Finally, while the results on the relationships
between religiosity and education and religiosity and age are unclear and not consistent, "the
data are clear: women consistently demonstrate a greater affinity for religion than men," (Spilka
et al., 2003).
Miller and Hoffmnan (1995) argue, using a nationally representative survey of high school
seniors, that controlling for risk tolerance attenuates the gender difference in religiosity. Stark
(2002) also argues that the gender difference in religiosity is related to the gender difference in
risk preferences. He takes it a step further than Miller and Hoffman, however, by arguing that
there is a convincing body of evidence that the gender difference in risk preferences is
physiological, and the gender difference in religiosity is caused by this physiologically based
difference in risk preferences.
3 Data
The data for this study come from the PanelStudy of Income Dynamics (PSID),
specifically the 1996 & 2003 waves, because the module measuring risk tolerance was in the
1996 wave, while a good measure of religiosity was not available until the 2003 wave. The 2003
wave of the PSID is thus the first time that a large, representative survey has been available that
contained good measures of both risk tolerance and religiosity for the same people. The only
other large-scale survey that is now available containing measures of both is the Health and
Retirement Survey (HRS), which includes both the same risk tolerance measure and a question
about attendance at religious services. The HRS, however, is focused on people who were
between the ages of 51 and 61 during the first wave of the study in 1992. The PSID is therefore
the only dataset that allows one to look at the relationship between risk tolerance and religiosity
among a broadly representative sample of individuals.
The survey is asked at the household level, but many of the questions, such as those about
smoking and drinking, are asked of both the head and the wife. I thus create individual-level
observations, so for households headed by a couple I have two observations, one for the husband
and one for the wife. Each observation will also have family-level data such as family income
and wealth. The one variable that I have for at most one person per household is risk tolerance;
the questions in this module were only asked of the survey respondent, who is usually the head
of the household. This is also the only variable that does not come from the 2003 survey--I thus
match the risk tolerance measure with the individual ID for the person who was the survey
respondent in the household in 1996 and use this to merge the information into the 2003 data.
This leaves me with 12,120 observations for most variables, but only 3,499 observations that
include all variables, including risk tolerance.
Table 1 shows the means and standard deviations of all of the variables used in the OLS
regressions except for risk tolerance (whose distribution is shown in Figure 1.) Column 1 uses all
of the data in the 2003 survey, while column 2 uses only the 3,499 observations that contain all
data. Panel A shows the demographic variables; some of these values may appear to be too large,
for instance an average family income of almost $70,000. This is because families headed by
married couples have higher incomes than other families, and these families are counted twice in
the data, because observations are at the individual level, rather than the household level. This
means that there is only have one observation from each single parent household while there are
two observations from each married household. The mean family income using one observation
per family is $60,813, which is in fact below the value estimated from the CPS of $66,970.1
Comparing columns 1 and 2, the means are sometimes significantly different; there are
two reasons for this difference. First, because the module measuring risk preferences was only
used in 1996, this only includes people who were in the survey in both 1996 and 2003. This
means that any families that were formed after 1996 or any people who moved into existing
households after 1996 will not be included. It also means that none of the immigrant sample
added to the survey to make it more representative in 1997 are included. (The survey was
representative of the U.S. population in 1968, and since then has been following those same
people and their offspring and spouses. That means that immigrants who arrived in the U.S. since
1968 are vastly underrepresented. An immigrant sample was thus added into the survey in 1997.)
This explains why the percent Hispanic (and hence percent Catholic) is so much lower in the
restricted data. Second, the risk tolerance module in only asked of respondents if they are
employed, so the restricted data has higher income, education, etc. and fewer women.
'From http://pubdb3.census.gov/macro/032003/faminc/new07_000.htm
3.1 Risk Preferences
The series of questions used to measure risk tolerance are the same as the ones that
Barsky et al. use from the HRS; see Barsky et al. (1997) for the logic behind its development.
The first question in the series is:
Suppose you had a job that guaranteed you income for life equal to your current, total
income. And that job was (your/your family's) only source of income. Then you are
given the opportunity to take a new, and equally good, job with a 50-50 chance that it
will double your income and spending power. But there is a 50-50 chance that it will cut
your income and spending power by a third. Would you take the new job?
A respondent who answers no is then asked about a 50-50 chance of income being cut by
a fifth; a respondent who answers yes is asked about a 50-50 chance of income being cut by a
half. So far, this is exactly the same as the module in the HRS. However, while the HRS
questions stop at a fifth, in the PSID if a respondent answers no to income being cut by a fifth,
the survey goes on to ask about a tenth; if the respondent answers yes to income being cut by a
half, the survey goes on to ask about it being cut by 75%. Because of the phrasing of this
question, it is only asked of individuals who are currently employed. This series of questions has
the advantage of being about an amount of money that scales by income, so there shouldn't be
much variation in the measurement of risk aversion by income level. (And I do not, in fact, find
very much variation.)
The HRS, like the PSID, is a panel survey, and the risk tolerance module was asked of
everyone for wave 1, and repeated in wave 2 for 10% of the sample. Barsky et al. use the
repeated sample to estimate the measurement error in the risk tolerance values and use that to
generate a better estimate of risk tolerance. See Barsky et al. (1997) for the details; because the
PSID question is so similar but is only asked once, the PSID uses the Barsky et al. calculations
for the values of risk tolerance. This means that some information is lost, because the
information from the questions about income being cut by a tenth or 75% is dropped and only
the information from the questions about income being cut by a third and a fifth is used. This
means I lose some variation (although I have the same number of observations); however, the
results generated from using the corrected values are much more precise, so I use those data.
Figure 1 shows the resulting values of risk tolerance; almost half of the sample (49%) chooses
the lowest value, and the other half of the sample is very evenly divided among the other three
values (16%, 16%, and 20%.)
3.2 Religiosity
The PSID contains 3 potential measures of religiosity: frequency of attendance at
religious services, amount donated to religious organizations, and hours spent volunteering for
religious organizations. Gruber (2004) used variation in tax rates to show that attendance and
giving are substitutes, so combining them should give a more complete measure of religiosity.
(Whether giving and volunteering are substitutes or complements, in general or in the religious
context, remains an open question (Carlin, 2001), but including volunteering in addition to
giving should create an even more complete measure of religious involvement.)
Unfortunately, none of these measures of religiosity are distributed normally. Their
distribution is much closer to lognormal, but there are many zeros in each of them, so using logs
will cut the sample significantly. Figures 2 and 3 show this visually; they are kernel densities of
attendance at religious services (times per year) and the log of attendance at religious services,
respectively, neither of them including zeros, which are 27% of the observations. Figure 2
shows a distribution where the vast majority of the observations are clustered very close to zero
and there is a very, very long tail; figure 3 gives a much clearer view of the distribution-the
large peak is at attendance once a week, although there is still a fairly long tail.
Also, combining these three separate measures into one index of religiosity requires
measuring each of them in a comparable way. As a result, I have chosen to translate each one
into a percentile; all zeros are given a percentile of .01 and the highest 1% are given a percentile
of 1.0. The religious index is then the average of the attendance percentile, the giving percentile
and the volunteering percentile. Translating each into a percentile allows me to keep all the
observations without being concerned about outliers and at the same time allows me to combine
the three measures of religiosity. The means of both the original variables and the percentiles are
shown in Panel B of Table 1. The average of the percentiles are all well under .5; in fact the
mean volunteering percentile is only 0.15. This is because there are so many zeros and they all
have a percentile of 0.1.
3.3 Risky Behaviors
I follow Barsky et al. in my choice of outcomes to examine in order to allow direct
comparison to their results. As a result, the risky behaviors studied are whether individuals have
ever smoked and whether they smoke now; whether they drink now and the number of drinks
they have per day; the number of years of education they have completed; whether they are selfemployed; whether anyone in their family has had health insurance over the last 2 years; and
whether they own their home. The number of drinks per day is not the exact number but a
categorical variable where 1 represents less than 1 drink a day, 2 is 1-2 drinks per day, 3 is 3-4
drinks per day, and 4 is 5 or more drinks per day.
I also follow Barsky et al. in looking at investment behaviors. The PSID questions divide
financial wealth into four categories.: stocks, savings, etc., IRAs, and other assets. The stocks
category includes "any shares of stock in publicly held corporations, mutual funds, or investment
trusts-not including stocks in employer-based pensions or IRAs." The savings, etc. category
includes "any money in checking or savings accounts, money market funds, certificates of
deposit, government savings bonds, or treasury bills-not including assets held in employerbased pensions or IRAs." The IRAs category includes IRAs and private annuities. Finally, other
assets includes "any other savings or assets, such as bond funds, cash value in a life insurance
policy, a valuable collection for investment purposes, or rights in a trust or estate." The sum of
these four categories is considered to be a family's total financial assets, and the outcome
variables of interest are the fraction of financial wealth that is in each category. Panel C shows
the means of all of these outcome variables.
3.4 Religious Density
I use local religious density as an instrument for religiosity, following the approach of
Gruber (2005) as well as is possible given my data. The PSID's ethnicity data are not as detailed
as the ethnicity data in the survey he used, the General Social Survey (GSS)-the PSID
categories are Western Europe, Eastern Europe, Africa, etc., which are much too broad to be
used for this purpose. As a result, I use religious density directly rather than using ethnicity as a
proxy; one's religious density is the fraction of people in one's state who share one's religion.
Following Gruber (2005), I use the categorization of Christian denominations defined in Roof
and McKinney (1987), but I combine categories that have fewer than 100 observations in my
data, which leaves the categories Catholic, Jewish, Episcopalian, Presbyterian, Methodist,
Lutheran, Christian (Disciples of Christ), Northern Baptist, black Methodist, black Northern
Baptist, black Southern Baptist, Southern Baptist, Pentecostal, other Protestant, other Christian,
unknown religion, and no religion.
I measure religious density at the state level, and I drop all states for which I have fewer
than 100 observations; this results in dropping 6.6% of my observations. I follow Gruber in using
religious attendance as my measure of religiosity for this section, because the literature says (and
my work supports) that higher religious density increases religious attendance (Phillips, 1998
and Olson, 1998), while it decreases charitable giving (Zaleski and Zech, 1995, and Perl and
Olson, 2000). Even though I use attendance only for the instrument, I use the religiosity index
for the OLS results; using attendance only would give very similar but less precise results.
4 Empirical Approach
4.1 Part1: Relationships among the factors
The first step is to examine the relationship among the three factors by running these
regressions :
(1)
REL, = P, + P 2R
(2)
RT =
(3)
REL, = P, + A 2F + A3X, + e
1
+f
2Fj
+ P3X, +
+
3 Xi
6
+
where REL5 is the religiosity of individual i, RTj is the risk tolerance of individual i, FJ is a
dummy for whether the individual is female, and X, is my vector of controls. These are each of
the possible pairwise regressions of each of the factors on each other and controls, to establish
these relationships among the factors before looking at the relationships of these factors with
behavior. The controls used are age (35-44, 45-54, 55-64, 65 and above), race (black, Hispanic,
other), female, education (high school, some college, college, more than college), religion
(Catholic, other Christian, Jewish, other, unknown, none) family income decile, family wealth
decile (excluding home equity), and home equity decile.
4.2 Part2: Comparison with the Barsky et al. results
The second step is to compare the results I find with the PSID to the Barsky et al. results
using the HRS. For this section I repeat their regressions:
(4)
Yi
=f
+
fl 2RTI + fl 3X,
+
Here, Yi is one of my measures of risky behaviors or investment choices, and X, contains only
my controls for age, race, sex, and religion, as those are the controls used by Barsky et al.
4.3 Part 3: Risky Behaviors on Each Factorand Combinations of the Factors
This section discusses regressions of the form
(5)
Yi = P +f 2Ri + Pf3Xi + e
where Y. is one of my measures of risky behaviors or investment choices for individual i; R1 is
either religiosity, risk tolerance, gender, or some combination of these factors; and X, is a vector
of controls. The controls used are the same used in part 1: age, race, female, education, religion,
family income decile, family wealth decile (excluding home equity), and home equity decile.
First three separate regressions are run: one with risk tolerance and controls; one with
religiosity and controls; and one with gender and controls. These are followed by three
regressions that each contain a pair of the factors: one on risk tolerance, religiosity, and controls;
one on risk tolerance, gender, and controls; and one on religiosity, gender, and controls. Finally,
I run a regression on risk tolerance, religiosity, and gender combined.
Following Barsky et al., the observations for the regressions of financial assets are
limited in two ways: first, they are limited to those families who have at least $1000 of financial
wealth. Second, because these variables are very much at the family-level, as opposed to the
individual level, only household heads are used in these regressions.
4.4 Part4: Religiosity Instrument
I look more closely at causation by instrumenting for religiosity. Of the three factors I
study, religiosity is the primary one that may not be exogenous: gender is clearly exogenous, and
risk tolerance is also generally considered to be a stable, exogenous characteristic, while the
same things that change risky behaviors could change religiosity at the same time. Instrumenting
for religiosity thus allows me to look more carefully at the causal effects of each of the three
factors on behavior. The regressions I run are thus
(2)
Y, =/
1
+
f 2A, +
3X,
+
4
reli + Areg, + E
where A. is attendance, instrumented with religious density, X, are individual-level controls,
rel, are religion dummies and reg, are region dummies. I have a dummy for each of the 17
religious categories that I calculate religious density based on, and 4 region dummies: northeast,
north central, south, and west. (The final regional category is Alaska and Hawaii, but those
states both have fewer than 100 observations, so they are both dropped.)
As discussed in Gruber (2005), the choice of this instrument is based on a few studies
which have found that higher religious density is associated with more religious attendance;
however, he discusses several measurement issues that lead to concerns about the exogeneity of
this instrument. The issue that will be of concern to me is that more religious people may be
more likely to move to areas where there are more people who share their religion. Gruber is able
to look at people who move and find that this would, in fact, bias against finding the positive
effects that he finds.
5 Results
5.1 Relationshipsamong the factors
Table 2 shows the relationships among risk tolerance, religiosity, and gender; it shows the
results of the regressions described in equations 1, 2, and 3. Panel A shows the results of
regression 1 (religiosity on risk tolerance) and panel B, columns 1-4 show the results of
regression 3 (religiosity on female). Each column of columns one to four has a different
measure of religiosity as the dependent variable; attendance, volunteering, donations, and the
overall index.
Looking at Panel A, the coefficient on risk tolerance is approximately -0.1 in each
column. This means that, because the difference between the highest and lowest values of risk
tolerance is 0.42, the least risk tolerant people have a religiosity index that is 4 percentage points
higher than the most risk tolerant. This is larger than the difference between men and women of
2.9 percentage points, and as women's higher degree of religiosity is well established in the
sociology literature, the fact that risk tolerance has as strong an association as gender indicates
the importance of risk tolerance.
Column 3, the regression of donations to religious organizations, stands out because it is
the only one where the coefficients are not significant. I do not take this, however, to mean that
there is in fact no relationship; rather, this is a data issue. While risk tolerance, gender, religious
attendance, and religious volunteering are measured at the individual level, donations are
measured at the household level; it is thus not surprising that the relationship is weaker with
donations than with the other measures of religiosity.
The final column, column 5 in panel B, shows that women are less risk tolerant than men,
by .026, from a modal value, as seen in figure 1, of 0.15.
5.2 Comparison with Barsky et al. resultsfor risky behaviors
Next I examine the relationship between risk tolerance and a variety of risky behaviors.
Table 3, Panel A shows my regressions of equation (4) replicating the Barsky et al. results in the
PSID, while Panel B shows the original Barsky et al. results. My results are generally very
similar to the Barsky et al. results, and so serve to validate this measure of risk tolerance, as it is
strongly correlated with many risky behaviors; the effect of risk tolerance is significant at the 1%
level on a dummy for drinking, number of drinks per day, a dummy for self-employment, a
dummy for someone in the household having health insurance.2
2 Ideally,
for comparison purposes, I would limit my sample to the same age range as in the HRS; however, this
cuts
the sample so much that the coefficients are no longer significant and the standard errors are too large to generate
any useful insights.
My results are broadly similar to the Barsky et al. results. One significant difference is
that Barsky et al. find that more risk tolerant people are more likely to smoke now and to have
ever smoked, while I find no significant effects and the point estimate on smokes now is
negative, though insignificant. Although this is inconsistent with Barsky et al., it is consistent
with Dohmen et al. (2005), who find no relationship between current smoking and the response
to their financial measure of risk preferences but find a strong, positive relationship between
current smoking and their general measure of willingness to take risks. I also find a strong,
significant relationship with self-employment, whereas Barsky et al. did not. I also find slightly
larger effects on drinking and self-employment, and smaller effects on home ownership; my
results are stronger in some cases and weaker in others, but broadly similar, and upholding the
conclusion that risk tolerance is associated with a broad range of risky behaviors.
5.3 Risky behaviors on each factor individually and on all three together
The columns of Table 4 are the same as in Table 3; the heading of each one gives the
risky behavior that is the dependent variable of the regressions whose results are listed in that
column. Panel A is almost exactly the same as Panel A of Table 3, the only difference being that
these regressions use my control variables, which are a somewhat broader set than those used in
Barsky et al, encompassing income, wealth, and education in addition to race, sex, age, and
religion. The coefficients remain very similar, although with the additional controls risk
tolerance now does have a significant, positive effect on whether a person has ever smoked; the
coefficient in the "smokes now" regression, however, remains small, negative, and insignificant.
More risk tolerant people are more likely to have ever smoked, to drink now, to have more drink
per day, to be self-employed, and to lack health insurance, and less likely to own a home.
Panel B shows these same dependent variables on religiosity and controls, and Panel C
shows these same ones on gender. The coefficients on religiosity are always the opposite sign of
the coefficients on risk tolerance, as long as both are significant. This means that more religious
people are less likely to behave in risky ways-the only exception to this is self-employment,
which is not significantly related to religiosity. The coefficients on the female dummy, however,
are all significant and all in the opposite direction from risk tolerance-women are less likely to
engage in all of these risky behaviors.
Panel D uses the same observations used in panels A-C and risk tolerance, religiosity and
gender are all combined into one regression. The coefficients all remain very similar to what they
were in panels A - C, although all coefficients which were significant in panels A - C decrease
slightly in absolute value in panel D. (Because the results in panel D are so similar to those in
panels A-C the results of the regressions on each pair of factors are not shown; they are each
very similar as well.) Looking at the magnitudes of the coefficients, we can see that religiosity is
the factor with the strongest correlations with behaviors. For instance, consider whether a person
drinks now. The most risk tolerant people are 7.9 percentage points more likely to drink than the
least risk tolerant people, while people at the
9 0 th
percentile of the religiosity distribution are
18.9 percentage less likely to drink than the people at the
10th
percentile of the religiosity
distribution, and women are 10.7 percentage points less likely to drink than men; although these
are all quite large effects, the religiosity effect is certainly the largest.
5.4 Comparisonwith Barsky et al. resultsfor investment choices
In Table 5 I again run regressions that can be compared with the Barsky results, but now
with investment choices. Unfortunately, the questions about investments are quite different in the
PSID and the HRS, so that it is more difficult to directly compare the two sets of regressions;
nevertheless, my results are broadly similar to the Barsky et al. results. The categories that are
the same across the two samples, stocks, and IRAs, have very similar results; the coefficient for
stocks is about 0.09, while the coefficient for IRAs is very close to zero and insignificant. The
category of savings, etc. in the PSID includes bonds, savings, checking, and t-bills, and the
coefficient on this category is within the range set out by the coefficients on these categories by
the Barsky et al. results; it is not surprising that this one is not significant at 5%because it
combines such disparate categories, some of which have a positive and some a negative
relationship with risk tolerance, so the resulting standard error is large.
5.5 Investment choices on eachfactor individually and on all three together
In table 6, the dependent variables are the fraction of financial wealth in each of four
different categories: stocks; savings, etc.; IRAs; and other assets. In Panel A the regressions are
run on risk tolerance and controls, in Panel B they are on religiosity and controls, and Panel C on
gender and controls. In Panel D the regression is run on all three together. Once again,
combining the three together in one regression changes the coefficients very little. These
regressions are slightly less straightforward to interpret than the ones of risky behavior, because
financial wealth is measured at the family level, while the variables of interest are at the
individual level. Because I only use family heads, this looks at the effects of characteristics of the
family head.
The results for risk tolerance are as expected: more risk tolerant heads put more of their
wealth into stocks, the riskiest investment, and less into savings, the safest. While in the context
of other risky behaviors, religiosity had the opposite effect from risk tolerance, here it is more
complicated; both more risk tolerant and more religious people put less in savings accounts, but
while risk tolerant people put that money into stocks instead, religious people put it into IRAs.
Finally, families with female heads, controlling for everything else, have less in savings and
more in "other assets." This is difficult to interpret because this is not an effect of gender but the
effect of the gender of the household head, and it is unclear what the other assets are here.
The only variable here that risk tolerance, religiosity, and gender are all significantly
associated with is the fraction of the household's financial wealth that is in savings and checking
accounts and other relatively safe assets. Comparing the coefficients in column 2 of panel D, we
see that the percentage of financial wealth in these safe assets is 5.4 percentage points lower for
the most risk tolerant people than the least risk tolerant people, 4.9 percentage points lower for
people at the 9 0th percentile of the religiosity distribution than people at the 10th percentile, and
6.1 percentage points lower for women then men. So here, the magnitudes of the effect are very
comparable, and are all a little more than a 10% change from a mean of 46%.
5.6 Religious Density Instrument
As discussed earlier, the instrument may not be perfectly exogenous; as a result, the
instrumented regressions are merely suggestive. Table 7 shows the first stage results, and
columns one to three show, as found in earlier results, that religious density is quite strongly
positively related to religious attendance, and while it is also related to religious donations and
volunteering, attendance is the strongest. These results support Gruber's use of attendance as a
measure of religiosity, so in the following IV results I use religious density to instrument for
religious attendance. In columns 5, 6, and 7, I add in controls. Column 5 adds in income controls,
column 6 adds region dummies, and column 7 adds in state dummies. The first stage is strongest
in column 6, using all controls other than the state dummies, so I run the instrumental regressions
using this specification.
Table 8, Panel A shows the regressions of all of the risky behaviors on instrumented
attendance.3 The coefficients are somewhat larger here than in the OLS results, but the standard
errors are so much larger as well so I cannot reject the hypothesis that the coefficients are the
same as in the OLS regression. However, despite the large standard errors, some of the effects
are significant, and all of the significant ones go in the expected direction. Instrumented
religiosity decreases the likelihood that one currently drinks and the number of drinks per day
and increases the likelihood that one owns a home; these effects are significant at the 5%level.
Table 8, Panel B shows the regressions on instrumented attendance using only
observations that have observations for risk tolerance. This drastically cuts the number of
observations, and the standard errors increase enough that only one coefficient is now
significant; religiosity now seems to decrease self-employment, which is surprising, as this is one
of the few results that was not significant in the OLS results. Panel C shows these regressions
where risk tolerance and gender are also included, and once again, the coefficients on attendance
stay quite similar when these variables are included.
Table 9 shows the instrumented regressions for investment behavior. Here, none of the
coefficients are even significant at 10% even using all observations. Especially when the sample
is limited, in panels B and C,to only observations containing risk tolerance values, even using
the strongest specification the instrument is simply too weak to uncover the effects on financial
wealth, with standard errors at least 0.26 and expected effect sizes (judging by the OLS results)
of no more than 0.1.
3 Ideally, I would use state dummies so that I would be identified only off of religion*state interactions. However,
using state dummies soaks up much of my variation in religious density; my results are much more precise if I only
control for region.
6 Conclusion
There is a large literature showing a strong association between religiosity and the level
of risky behaviors, between risk tolerance and the level of risky behaviors, and between gender
and the level of risky behaviors. However, literature on the relationships among religiosity, risk
tolerance, and gender is highly speculative; I use the fact that I have measures of risk tolerance,
religiosity, gender, and risky behaviors to look carefully at these relationships. It has been
suggested that higher risk aversion causes more religiosity; I find that risk preferences are
correlated with religiosity, although I cannot speak to the causality. It has also been suggested
that women's higher level of religiosity is caused by the fact that women are more risk averse. I
find that this is not true: the gender difference is in fact even larger when risk preferences are
controlled for.
In general, I conclude that the effects of religiosity, risk tolerance, and gender on risky
behaviors are in fact completely independent; adding the other two variables as controls does not
affect the coefficient on the third. I find that risk tolerance, as measured in the PSID, is correlated
with many types of behavior, including drinking, health insurance coverage, and investment
decisions, which validates this measure of risk preferences as measuring a personal characteristic
that has predictive power in many different contexts. Similarly, religiosity is correlated with
these behaviors as well, and controlling for risk aversion does not lower the coefficients on
religiosity; this reaffirms that religiosity itself is correlated with behaviors, through a channel that
is independent of risk aversion. Finally, even when risk aversion and religiosity are controlled
for, the gender differences in behavior remain; these gender differences must thus be caused by
other factors. Instrumenting for religiosity provides suggestive evidence that the effects of
religion are causal, although the instrument is too weak to make strong conclusions.
Many risky behaviors, such as smoking and drinking, can have negative externalities, and
are therefore of concern to policy-makers. However, we do not have a good understanding of
what determines a person's likelihood of engaging in risky behaviors; as a result, we cannot
confidently predict the effects of policies on these behaviors. My results further our
understanding of these behaviors by showing that risk preferences, religiosity, and gender each
have powerful and independent correlations with risky behaviors; this implies that it is important
to include them all in studies of these behaviors whenever possible. In addition, they show that
even though women are more religious and more risk averse, controlling for religiosity and risk
preferences increases the estimated impact of gender on risky behaviors, rather than lessening it.
This implies that there is another difference between men and women that accounts for their
different behaviors, and understanding this gender difference could provide insight into what
causes people to engage in risky behaviors.
References
Azzi, Corry and Ronald Ehrenberg (1975). "Household allocation of time and church
attendance," JournalofPoliticalEconomy 83: 27-56.
Barsky, Robert B. et al. (1997). "Preference Parameters and Behavioral Heterogeneity: An
Experimental Approach in the Health and Retirement Study," QuarterlyJournalofEconomics,
112 (2): 537-579.
Byrnes, James P., David C. Miller and William D. Schafer (1999). "Gender Differences in Risk
Taking: a Meta-analysis," PsychologicalBulletin, 125 (3): 367-383.
Carlin, Paul S. (2001). "Evidence on the Volunteer Labor Supply of Married Women," Southern
Economic Journal,67 (4): 801-824.
Chaves, Mark and Philip Gorski (2001). "Religious Pluralism and Religious Participation,"
Annual Review of Sociology, 27: 261-281.
Chen, Daniel (2005). "Economic Distress and Religious Intensity: Evidence from Islamic
Resurgence During the Indonesian Financial Crisis," mimeo, University of Chicago.
Clark, Andrew (2005). "Deliver us from Evil: Religion as Insurance," mimeo, PSE.
Dehejia, Rajeev, Thomas DeLeire and Erzo F. P. Luttmer (2005). "Insuring Consumption and
Happiness Through Religious Organizations," mimeo, Harvard University.
Dohmen, Thomas et al. (2005). "Individual Risk Attitudes: New Evidence from a Large,
Representative, Experimentally-Validated Survey, " IZA DiscussionPaperSeries, No. 1730.
Donkers, Bas, Bertrand Melenberg, and Arthur van Soest (2001). "Estimating Risk Attitudes
using Lotteries: A Large Sample Approach." JournalofRisk and Uncertainty, 22 (2): 165-195.
Ellison, Christopher (1991). "Religious Involvement and Subjective Well-Being," Journalof
Health and Social Behavior, 32: 80-99.
Francis, L. J., S.H. Jones, C.J. Jackson, and M. Robbins (2001). "The feminine personality
profiles of male Anglican clergy in Britain and Ireland," Review of Religious Research 43:14-23.
Gruber, Jonathan (2004). "Pay or Pray: The Impact of Charitable Subsidies on Religious
Attendance," Journalof PublicEconomics, 88: 2635-2655.
Iannaccone, Laurence (1998). "Introduction to the Economics of Religion," Journalof Economic
Literature, 36: 1465-1496.
Levin, Jeffrey S. (1994). "Religion and Health: Is There an Association, Is it Valid, and Is It
Causal?," Social Science and Medicine, 38: 1475-1482.
Miller, Alan S. and John P. Hoffman (1995). "Risk and Religion: An Explanation of Gender
Differences in Religiosity," Journalfor the Scientific Study ofReligion 34: 63-75.
Miller, Alan S. and Rodney Stark (2002). "Gender and Religiousness: Can Socialization
Explanations Be Saved?," American JournalofSociology, 107 (6): 1399-1423.
Phillips, Rick (1998). "Religious Market Share and Mormon Church Activity," Sociology of
Religion, 59: 117-130.
Roof, Wade C. and William McKinney (1987). American Mainline Religion: Its Changing
Shape andFuture. New Brunswick and London: Rutgers University Press.
Sherkat, Darren E. and Christopher G. Ellison (1999). "Recent Developments and Current
Controversies in the Sociology of Religion," Annual Review of Sociology, 25: 363-394.
Spilka, Bernard et al., (2003). The Psychology of Religion: An EmpiricalApproach. New York:
Guilford Press.
Stark, Rodney (2002). "Physiology and Faith: Addressing the 'Universal' Gender Difference in
Religious Commitment," Journalfor the Scientific Study ofReligion, 41 (3): 495-507.
Wallace, John, and David Williams (1997). "Religion and Adolescent Health-Compromising
Behavior," in J. Schulenberg, J.L. Maggs, and K. Hurrelman, eds., Health Risks and
Developmental TransitionsDuringAdolescence. Cambridge, UK: Cambridge University
Press, 444-468.
Figure 1: Risk tolerance values
2nnA
O
00U0 - i
1500 -
•-1000 '-
0
0
500-
E
z
0
0.15
0.15
I
I 0.35
0.28
value
0.28tolerance 0.35
Risk
-
0.57
Risk tolerance value
Figure 2: Kernel density of attendance at religious services
CO
O -
CO
oO
0-
oI
5000
I
10000
Attendance at religious services
I
15000
I
20000
Figure 3: Kernel density of log of attendance at religious services
C -1
CD -
01
(0
Nu-
0-
·
·
·
I
6i
I
24 of attendance at religious
6 services
Log
38
·
8
I1
10
Table 1: Means (with standard errors) of all variables
(1)
All data
(2)
Restricted Data
PanelA: Demographics
Female
Black
Hispanic
Other Race
Catholic
Protestant
Other Christian
Jewish
Other Religion
Unknown Religion
No religion
Education (years)
Age
Family income ($1,000s/year)
Wealth, excluding home equity ($1,000s)
Home equity ($1,000s)
0.54 (0.007)
0.095 (0.003)
0.069 (0.003)
0.14 (0.005)
0.27 (0.006)
0.54 (0.007)
0.016 (0.002)
0.037 (0.003)
0.068 (0.003)
0.017 (0.002)
0.052 (0.003)
13.19 (0.037)
47.64 (0.21)
0.46 (0.011)
0.10 (0.006)
0.019 (0.004)
0.067 (0.006)
0.23 (0.010)
0.60 (0.011)
0.017 (0.003)
0.040 (0.005)
0.038 (0.004)
0.0063 (0.002)
0.061 (0.006)
13.82 (0.051)
47.33 (0.25)
67.67 (1.35)
78.56 (1.98)
208.45 (13.68)
86.87 (2.12)
253.48 (27.05)
39.98 (3.58)
22.60 (2.40)
915.78 (42.08)
0.42 (0.004)
38.74 (5.06)
26.50 (4.90)
96.08 (3.38)
PanelB: Religiosity
Religious attendance (times/year)
Religious volunteering (hours/year)
Religious donations ($/year)
Religious attendance percentile
Religious volunteering percentile
Religious donations percentile
Religiosity index percentile
0.15 (0.005)
0.38 (0.006)
0.32 (0.004)
980.42 (55.56)
0.41 (0.007)
0.17 (0.008)
0.40 (0.009)
0.32 (0.007)
Panel C: Outcome behaviors
Ever smoked
0.47 (0.007)
0.49 (0.011)
Smoke now
0.20 (0.006)
0.21 (0.009)
Drink now
0.62 (0.007)
0.68 (0.010)
Drinks per day
0.81 (0.011)
0.91 (0.018)
Self-employment
0.11 (0.004)
0.14 (0.008)
No health insurance
0.064 (0.003)
0.047 (0.004)
Home ownership
0.71 (0.006)
0.78 (0.009)
Fraction in stocks
0.17 (0.006)
0.17 (0.008)
Fraction in IRAs, etc.
0.23 (0.007)
0.27 (0.010)
Fraction in savings, etc.
0.50 (0.008)
0.46 (0.012)
Fraction in other assets
0.10 (0.005)
0.10 (0.007)
Observations
12,120
3,499
Weighted individual means, dollar figures are in 2002 dollars. Restricted data includes only those observations that
have non-missing values for risk tolerance. The final four variables are calculated only on family heads with at least
$1,000 of wealth, so only use 4,764 (all data) or 1,759 (restricted data) observations.
Table 2: Relationships Among the Factors
(1)
Attendance
(2)
Volunteering
(3)
Donations
Panel A: Religiosity regressed on risk tolerance
Risk
-0.106
-0.106
-0.078
Tolerance
(0.031)**
(0.036)**
(0.040)
(4)
Religiosity
index
(5)
Risk
tolerance
-0.100
(0.028)**
Panel B: Religiosity and risk tolerance regressed on gender
Female
0.059
0.038
-0.016
0.029
-0.026
(0.010)**
(0.012)**
(0.013)
(0.010)**
(0.005)**
Standard errors in parentheses. Regressions include controls for age, race, religion, income, education, wealth, and
home equity; only the coefficient for sex is shown. The regressions of attendance and the religiosity index have
3,499 observations and volunteering and donations have 3,550. Dependent variables in columns 1-4 are percentiles
which vary from 0.01 to 1.
* significant at 5%; ** significant at 1%
Table 3: Risky behavior on risk tolerance, comparison with the Barsky et al. results
(3)
(2)
(1)
Ever
Smokes Drinks
smoked
now
now
Panel A: PSID (author's calculations)
Risk
0.068
-0.055
0.218
Tolerance
(0.052)
(0.043)
(0.048)**
Panel B: HRS (Barsky et al. calculations)
Risk
0.092
0.068
0.099
Tolerance
(0.030)** (0.028)*
(0.030)**
(6)
No health
insurance
(7)
Home
ownership
(4)
Drinks per
day
(5)
Selfemployment
0.335
(0.083)**
0.102
(0.035)**
0.071
(0.027)**
-0.127
(0.045)**
0.256
(0.053)**
0.021
(0.020)
0.196
(0.031)**
-0.153
(0.024)**
Standard errors in parentheses. Regressions include controls for age, sex, race, and religion. Every
regression in panel A uses 5,012 observations. All dependent variables except for drinks per day
(a categorical variable described in the data section) are dummies. Panel B are the results from Barsky
et al. (1997) using the HRS. Each regression in panel B has 11,707 observations except health
insurance, which only has 8,642.
* significant at 5%; ** significant at 1%
Table 4 : Risky behaviors on each factor, and then all three
(1)
Ever
smoked
(2)
Smokes now
(3)
Drinks
now
(4)
Drinks per
day
(5)
Selfemployment
(6)
No health
insurance
(7)
Home
ownership
Panel A: Risk preferences only
Risk
0.128
-0.036
Tolerance
(0.052)*
(0.043)
0.238
(0.050)**
0.422
(0.089)**
0.101
(0.035)**
0.087
(0.026)**
-0.113
(0.041)**
Panel B: Religiosity only
Religiosity
-0.197
(0.030)**
-0.206
(0.023)**
-0.252
(0.029)**
-0.495
(0.046)**
0.022
(0.021)
-0.033
(0.011)**
0.141
(0.022)**
Panel C: Gender only
Female
-0.075
(0.017)**
-0.042
(0.014)**
-0.118
(0.017)**
-0.337
(0.029)**
-0.038
(0.011)**
-0.034
(0.008)**
0.038
(0.013)**
Panel D: Risk preferences, religiosity, and gender together
Risk
0.093
-0.066
0.188
0.299
0.095
0.076
-0.091
Tolerance
(0.052)
(0.043)
(0.049)**
(0.085)**
(0.035)**
(0.026)**
(0.041)*
Religiosity
-0.188
-0.205
-0.236
-0.457
0.029
-0.028
0.135
(0.030)**
(0.023)**
(0.029)**
(0.045)**
(0.021)
(0.011)*
(0.022)**
Female
-0.068
-0.038
-0.107
-0.317
-0.036
-0.031
0.032
(0.017)**
(0.014)**
(0.016)**
(0.028)**
(0.011)**
(0.008)**
(0.013)*
Standard errors in parentheses. Regressions include controls for age, race, religion, income, education, wealth, and
home equity. Dependent variables are dummy variables except for drinks per day, which is categorical. There are
3,499 observations.
* significant at 5%; ** significant at 1%
Table 5 : Investment behavior on risk tolerance, comparison with the Barsky et al. results
(1)
Stocks
(2)
Bonds
(3)
Saving,
Checking
(4)
T-bills
Panel A: PSID (my calculations)
Risk
0.086
tolerance
(0.040)*
Panel B: HRS (Barsky et al. calculations)
Risk
0.097
0.015
tolerance
(0.029)**
(0.008)*
(5)
Savings,
etc.
-0.094
(0.054) +
-0.128
(0.041)**
-0.055
(0.024)*
(6)
IRAs
(7)
Other assets
0.038
(0.048)
-0.030
(0.037)
-0.006
(0.037)
0.076
(0.025)**
Standard errors in parentheses. Regressions include controls for age, sex, race, and religion. Every regression in
panel A uses 1,833 observations. All dependent variables except for drinks per day (a categorical variable described
in the data section) are dummies. Panel B are the results from Barsky et al. (1997) using the HRS. Each regression in
panel B has 5,012 observations.
+significant at 10%; * significant at 5%; ** significant
at 1%
Table 6: Investment behavior on each factor, and then all three
(1)
Fraction in
stocks
(2)
Fraction in
savings, etc.
(3)
(4)
Fraction in
IRAs
Fraction in
other assets
Panel A: Risk preferences only
Risk
0.072
-0.097
Tolerance
(0.041) +
(0.056) +
0.040
(0.049)
-0.015
(0.038)
Panel B: Religiosity only
Religiosity
-0.013
(0.022)
-0.057
(0.031) +
0.065
(0.028)*
0.005
(0.022)
Panel C: Gender only
Female
-0.002
(0.016)
-0.060
(0.024)*
0.026
(0.021)
0.035
(0.018)*
Panel D: Risk preferences when religiosity and gender are controlled for
Risk
0.071
-0.108
0.050
-0.012
Tolerance
(0.041) +
(0.056) +
(0.049)
(0.038)
Religiosity
-0.010
-0.061
0.067
0.005
(0.022)
(0.031)*
(0.028)*
(0.022)
Female
-0.001
-0.061
0.027
0.035
(0.016)
(0.024)**
(0.021)
(0.018)*
Standard errors in parentheses. Regressions include controls for age, race, religion,
income, education, wealth, and home equity. The dependent variables are shares
of assets in total financial wealth. There are 1,759 observations.
+significant at 10%; * significant at 5%; **significant at 1%
Table 7: First stage for religious density instrument
(7)
(6)
(5)
(3)
(2)
(1)
Attendance
Donations
Volunteering Attendance
Attendance
Attendance
Religious
0.258
0.169
0.061
0.265
0.323
0.290
Density
(0.034)**
(0.045)**
(0.036)
(0.033)**
(0.035)**
(0.038)**
Basic controls
Yes
Yes
Yes
Yes
Yes
Yes
Income controls
No
No
No
Yes
Yes
Yes
Region dummies
No
No
No
No
Yes
No
State dummies
No
No
No
No
No
Yes
Robust standard errors in parentheses .There are 10,985 observations in columns 1 and 4; 11,263 in columns 2 and
3; and 10,176 in columns 6 and 7. Basic controls are age, race, and religion. Income controls are income education,
wealth, and home equity.
* significant at 5%; ** significant at 1%
Table 8 : Instrumented regressions of risky behaviors
(3)
(2)
(1)
Ever
Smokes now Drinks
smoked
now
Panel A: Attendance only, using all observations
Attendance
-0.295
-0.201
-1.197
(0.381)
(0.314)
(0.476)*
(4)
Drinks per
day
(5)
Selfemployment
-1.494
(0.711)*
-0.169
(0.245)
Panel B: Attendance only, using only observations with risk tolerance
Attendance
-0.265
-0.196
-0.380
-0.933
-0.515
(0.344)
(0.274)
(0.323)
(0.581)
(0.260)*
(6)
No health
insurance
(7)
Home
ownership
0.230
(0.213)
0.309
(0.143)*
0.173
(0.144)
0.104
(0.256)
Panel C: Attendance, risk preferences, and gender together
Attendance
-0.242
-0.210
-0.341
-0.859
-0.507
0.196
0.081
(0.350)
(0.280)
(0.328)
(0.583)
(0.265) +
(0.149)
(0.261)
Risk
0.083
-0.087
0.141
0.190
0.035
0.086
-0.101
Tolerance
(0.060)
(0.049) +
(0.058)*
(0.098) +
(0.045)
(0.030)**
(0.048)*
Female
-0.058
-0.026
-0.092
-0.276
-0.009
-0.044
0.027
(0.025)*
(0.021)
(0.024)**
(0.043)**
(0.019)
(0.011)**
(0.019)
Standard errors in parentheses. Regressions include controls for age, race, religion, income, education, wealth, and
home equity, and region dummies. Dependent variables are dummy variables except for drinks per day, which is
categorical. There are 10,176 observations used in panel A and 3,247 in panels B and C.
+significant at 10%; * significant at 5%; ** significant at 1%
Table 9: Instrumented regressions of investment behavior
(1)
Fraction in
stocks
(2)
Fraction in
savings, etc.
(3)
Fraction in
IRAs
Panel A: Attendance only, using all observations
Attendance
-0.213
0.969
-0.895
(0.359)
(0.620)
(0.548)
(4)
Fraction in
other assets
0.139
(0.351)
Panel B: Attendance only, using only observations with risk tolerance
Attendance
0.043
-0.188
0.048
0.097
(0.368)
(0.278)
(0.351)
(0.254)
Panel C: Attendance, risk preferences, and gender together
Attendance
0.057
-0.227
0.069
0.101
(0.285)
(0.379)
(0.360)
(0.261)
Risk
0.051
-0.133
0.075
0.008
Tolerance
(0.050)
(0.070) +
(0.063)
(0.048)
Female
-0.011
-0.042
0.014
0.038
(0.018)
(0.027)
(0.025)
(0.020) +
Standard errors in parentheses. Regressions include controls for age, race, religion,
income, education, wealth, and home equity. The dependent variables are shares
of assets in total financial wealth. There are 4,029 observations used in panel A and
1,635 in panels B and C.
+significant at 10%; * significant at 5%; ** significant at 1%
Chapter 2
The Effect of Choice on Charitable Contributions:
A Field Experiment
1 Introduction
Economists and policy makers have long been interested in the determinants of charitable
giving. Economists have, in recent years, performed many field and laboratory experiments on
this topic. Some of these experiments look at the importance of social distance and anonymity
(Soetevent, 2004; Breman and Granstrom, 2005), and of empathy (Batson et al., 1995; Fong,
2004) in the donation decision. Some test the effect of changing the "appeals scale," the list of
suggested donation amounts (Desmet and Feinberg, 2003) or the extent of crowding out (Eckel,
Grossman, and Johnston, 2005). Several compare the effects of different sorts of subsidies,
including matching grants, seed money, and rebates, on fundraising (List and Lucking-Reiley,
2002; Eckel and Grossman, 2003; Falk 2004; Eckel and Grossman, 2005; Meier, 2005; Karlan
and List, 2006). Landry et al.(2005) tests the effect of a lottery incentives in door-to-door
fundraising.
Variation in the extent of choices available to potential contributors, however, has not
been investigated in the literature. This is surprising because existing theory and evidence
generate ambiguous predictions for the effects of the availability of choice on the welfare of
potential contributors, as well as their willingness to donate. Economic theory generally
considers choice to be welfare enhancing, and extensive psychology research has focused on
enumerating the beneficial effects of choice (e.g. Cordova & Lepper, 1996); however, recent
research has cast doubt on the idea that choice is invariably positive (e.g. Iyengar and Lepper,
2000).
This paper is a first attempt to fill this gap: using a randomized field experiment, it tests
the effect on donations of having an expanded set of options. A randomly selected half of the
recipients of a newsletter from a Dutch NGO had the option of choosing what program area their
donation should be spent on: health, education, or wherever most needed. (Health and education
are this charity's major program areas.)
There are two reasons to expect an increase in donations from this experiment. First,
there is the rational reason: people who are given the opportunity to donate to something they
care more about will be more likely to donate, and will donate more. A person who values health
much more than education will have a higher marginal utility of donations to health than of
donations to the organization as a whole, and thus will be more likely to donate and/or will
donate a larger amount. Second, there is the psychological explanation. Psychologists have
repeatedly found that people have greater "intrinsic motivation" when they are allowed to make
choices for themselves, and this is true even when the choice is fairly indirectly related to their
goal ( e.g. Lewin, 1952; Deci, 1981; Deci and Ryan, 1985; Cordova and Lepper, 1996).
Charitable giving depends strongly on intrinsic motivation, as there are unlikely to be any strong
external forces pushing a person to make a donation; much of the psychology research would
thus lead one to predict an increase in donations.
Recent research, however, has produced ample evidence that in certain cases, choice can
in fact be demotivating (Shafir, Simonson, and Tversky,1993; Redelmeier and Shafir, 1995;
Iyengar and Lepper, 2000; Bertrand et al., 2005; Roswarski and Murray, 2006). Iyengar and
Lepper (2000) performed a field experiment in a grocery store where jams were put on display
for sampling, and found that while 30% of the people who stopped to look at a display of 6
different jams bought some of that jam, only 3% of the people who stopped to look at a display
of 24 jams bought any. Bertrand et al. (2005) performed a field experiment that involved sending
out mailings advertising a variety of loans. They found that potential loan recipients who saw a
simple table of loan choices were much more likely to respond to the advertisement than those
who were shown a more complete display of their options; the size of the table was unrelated to
the number of options that were in fact available, which were described in the text of the letter.
These papers show the potential negative effects of choice; they indicate that when a
choice seems complicated or difficult, people may postpone choosing or may end up not
choosing at all. Although the choice of where to target the donation is not very complicated, it is
more complicated than the usual decision a donor faces; it is thus easy to imagine a donor seeing
the choice and thinking to himself or herself "Oh, I can choose where I want my money to go.
Interesting. I wonder what I should do? I will have to think about that later, when I have more
time." The donor will then put the donation form back in his or her pile of things to do, and may
or may not ever return to it. This could be expected to decrease the response rate among the
treatment group; however, it should not change the donation amount conditional on giving,
except through compositional effects.
There is also evidence that an experiment which has direct effects on donation rates can
have intertemporal effects (Meier, 2005). There are several ways this could occur: if the
experiment increased the response rate, it could increase future donations, by drawing more
people into becoming regular donors. If it increased donations by generating positive feelings
towards ICS, among the donors, because they appreciate the chance to target their donations, this
could carry over into the future, and thus increase future donations. In addition, if it increases
either the response rate or mean donation in the experiment, that could also decrease future
donations, if it causes intertemporal substitution. If the experiment decreases donations,
however, any of these effects could occur in the opposite direction; a lower response rate could
reduce the number of future donors, choice could generate negative feelings towards ICS that
carry over, and there could be positive future intertemporal substitution.
Based on previous research and the experimental design, there are thus reasons to expect
the donation rate and donation amount conditional on donation to increase or to decrease. In this
case, the provision of choice seemed to have zero impact: both the donation rate and amount are
remarkably similar between the treatment and control groups. This is not because the recipients
did not understand that they had the opportunity to choose; over half of the people in the
treatment group did take the opportunity to make a choice. However, a striking result is that 80%
of those choose "wherever is most needed" rather than targeting the money to a particular target
area. This suggests that choice was not particularly valued by those recipients, which may
explain the absence of and effect; the option of not choosing remained a natural 'default' option
which allowed them to avoid thinking about the issue.
The remainder of this chpater is organized as follows: section 2 describes the experiment
design; section 3 discusses the data used; section 4 gives the results; and section 5 concludes.
2 Experiment Design
This project entailed modifying one of the regular mailings sent out by International
Child Support (ICS). ICS is a Dutch charity that provides aid programs, focused on children, in
five developing countries in Africa and Asia. They were founded over 25 years ago and in 2005
they received donations totaling almost C2 million. Although international aid makes up only 2%
of the philanthropic sector in the U.S., it is one of the largest areas of philanthropy in the
Netherlands; the Dutch gave C5.2 billion to charity in 2003 (1.1% of GDP), and 12% of this went
to international aid organizations such as ICS (AAFRC, 2003; Geven in Nederland, 2003).
Figure 1 shows the newsletter ICS sent on Sept 14, 2004 to 19,122 of the people on their
mailing list; it describes some of their projects in Africa, and on the final page it discusses the
retirement of one of their employees, and the crisis in Darfur, Sudan. ICS used their standard
process to determine who to send this newsletter to: they mailed it to their regular donors who
receive every newsletter and then added a few other subsets, who receive the mailings less often.
The newsletter recipients were then divided into treatment and control groups using a
randomization based on their unique IDs. ICS then sent this mailing to the entire list; the
newsletters were identical for the treatment and control groups, so that the sole difference
between the mailings received by the two groups was on the donation form. Figure 2 shows the
donation form; this is the standard form used to make a donation in the Netherlands. Instead of
writing a check, donors use this form (which already has the account number of ICS written on
it), write in their account information and send it to their bank. The bank then transfers the
money from the donor's account to the charity's account.
The control group received this standard form, and for people in the treatment group,
there is a slight addition: in the upper right comer of the form (the bottom right comer of figure
2, because the picture is rotated 90 degrees) there is text asking what program area they want
their money to go to: health, education, or wherever is most needed. When the donations were
received, ICS also received the donation forms of the donors who were able to target their
donations, and the donors' choices were recorded.
2.1 Design Issue
Because the choice was presented in small print on the donation form only, and was not
discussed elsewhere in the newsletter, many people may not have noticed it. Also, as many
donors likely did not look at the donation form until they were filling it out, they may not have
noticed the choice until after they had decided to donate. The intervention would thus have
possible impacts on donations on the intensive margin, but the extensive margin would not be
affected.
3
Data
The analysis makes use of two donation databases. The first one lists the 303,928
potential donors; it includes names and addresses as well as other administrative information and
calculations such as the total amount donated each of the past 4 years. A quarter of the people in
this database have donated at least once, and 1.5% of them participate in the child sponsorship
program (KAP), meaning they donate £20.50 each month. This database also identifies addresses
that are churches or schools, regular donors who receive every newsletter, and cold rentals
(meaning addresses that, although they may have received mailings from ICS in the past, have
never donated.)
The second database lists each donation ICS has received from January 1 1996, until
September 16, 2005, almost 1.2 million donations in total. For each donation this database says
who it is from, the date, the amount, what newsletter or other donation request it was donated in
response to, whether it was given as part of the child sponsorship program, and some other
administrative data. I use these data to create three variables: the total donations since 2001; the
donations given in response to the experimental newsletter; and the donations given after the
experiment. Total donations since 2001 is the total amount donated between Jan 1 2001 and Sept
14, 2004, the day the experimental newsletter was mailed; donations given after the experiment
is the total donations given after the day the experimental newsletter was sent out that were not
given in response to the newsletter.
I use the Statistics Netherlands urban/rural definition and merge their list of
municipalities in urban regions and with the donor list; by this definition 56% of the Dutch
population lives in urban areas. The Netherlands also has an area that is more religious than the
rest of the country called the bijbelgordel, or bible belt. I define this area using zip codes based
on a list given to me by ICS; approximately 25% of the Dutch population lives in the
bijbelgordel. Finally, I can determine gender for a limited number of people on the mailing list;
this is, unfortunately, not entirely straightforward, because one difference between the
Netherlands and the U.S. is that they are more likely to use first initials rather than names. This is
partly, I believe, because they use more names, so the database has first initials and last name,
for example T. M. J. de Graaf. This means I cannot use names to determine donors' gender. I
can assign a gender to those names that have the title Mr. or Mrs., but that leaves me with only
44% of my sample.
Table 1 shows summary statistics for the treatment and control groups. The
randomization was successful; there are no significant differences between the two groups in
pre-experiment characteristics. The first variable here is total post-experiment donations-the
mean is E50, although the mean of the log is only 1.69, which is the log of 65.42. The next
variable is whether the prior donations since 2001 are above zero, and this shows that 46% of the
sample has donated since 2001. The sample is 31% urban, 31% in the bible belt; this is much
more rural than the overall Dutch population and slightly more likely to live in the bible belt.
12% are churches or schools, 0.08% take part in the child sponsorship program, 30% are regular
donors and 44% are cold rental addresses.
4 Results
Figure 3 shows a kernel density graph of the donations in the experiment without zeros.
Even without zeros, the donations are heavily concentrated at numbers under £100 but there is a
very long tail, with very few donations above €100 but one observation at £1,000. Figure 4 then
shows the distribution of the log of the donation amount; this is much closer to a normal density
with the one difference that there are large spikes at certain numbers; the largest ones occur at
€log(5) and Clog(10). This is because many people donate round numbers such as £5 or £10 but
fewer donate anything between those two amounts.
Table 2 shows the basic results of the experiment: the donation amounts and response
rates for the treatment group and the control group. It shows that whether you look at donation
amount, response rate, the amount donated, log of donation conditional on giving, or the log of
post-experiment donations, there are no significant mean differences between the treatment and
control groups. The response rate is 11% and the mean log donation amount conditional on
giving is 2.11 (which is the log of £8.25.)
4.1 Targets chosen
Table 3 shows the choices made by the treatment group. The first three rows show the
number of people who chose each of education, health, and wherever most needed, and their
average donation amounts. Out of the over 1,000 people in the treatment group who made
donations, only 59 of them chose education and 29 chose health, while over 400 chose wherever
is most needed. Overall, of those in the treatment group who made a donation, there are more
who made some choice (495) than who didn't make a choice (404); this means that despite the
inconspicuousness of the choice, most people did notice it. The mean donation to education is
significantly higher than the mean donation to health, but row 5 shows that if health and
education are combined together, their mean donation is almost exactly the same as "wherever
most needed", and because the number of people choosing education and health are both so low,
the difference in donation amounts among the people choosing each of these are not
economically significant. However, row 7 shows the average donation amounts of those who
made any choice, and comparing these numbers to those in row 4 shows that those who made a
choice donated more than those who did not make a choice, and this difference is highly
significant (t = 4.18) for log donations. Comparing these numbers to row 3 of table 2 shows that
while those in the treatment group who made a choice donated about the same amount as the
control group, those who failed to make a choice donated less than the control group. This
implies that not only did people not value the choice, but some donors, those who did not make a
choice, may have disliked having the choice, and donated less as a result.
4.2 Experiment donations
The first specification is
(1) D, = P,
+ P2
+ P3 P
+
4 4 PG, + PSX,
+ E,
where D, is the donation amount given by donor i, T is a dummy variable that is equal to one
for donors in the treatment group, JP is the level of previous donations since 2001 of donor i,,
PG, is a dummy variable that is equal to 1 if P, is greater than zero and Xi is two controls: bible
belt and urban. This specification is shown in the second column of table 4; the first column is
simply the donation amount regressed on the treatment dummy. In both of these regressions, the
coefficient on the treatment dummy is very small and insignificant. Also, the r-squared of the
regression with only choice is 0.00, while adding in the other variables increases it to 0.2; the
treatment dummy does not seem to explain any of the variation in donation amounts, although
the controls do.
In the second specification, I add in an interaction term between choice and prior
donations, and an interaction term between choice and the non-zero prior donations dummy, to
begin to see whether there may be distribution effects even though there are no mean effects.
(2)D i = , +• 21T +33 3 + P4Ti *P+ flPGi +f6Ti *PG, +/ 7Xi +,•i
This specification is shown in column 3 of table 4. This shows a very large, positive, interaction
effect with prior donation amounts and a significant negative interaction effect with the positive
previous donations dummy. In column 4, however, just one observation, the donation of C1,000,
is removed, and the results change very significantly. Although the main effects of choice,
previous donations, and the positive previous donations dummy are all very similar, the
interaction effect with previous donations is now only about one-fifteenth as large and the
interaction effect with the previous donations dummy is only one-eighth as large as they were in
column 3. Column 5 shows this same regression using a log specification, as I demonstrated
above that this was the more appropriate approach. These regressions use the log of both the
experimental donation amount and the previous donations, except the zeros are left in as zeros.
(There are 6 observations where either the experimental or the previous donation amounts were
between zero and one; these were replaced with zeros.)
Both the main effect of choice and the interaction effects are insignificant and very close
to zero in this regression. I have also ran this regression transforming both the previous donations
and the experimental donations into percentiles, and the results are similar to the results with
logs. The apparent effects in columns 3 and 4 thus are most likely a result of the larger donations
having an unduly large impact on the results, because of the lognormal distribution of donations.
Table 5 takes a closer look at different sections of the donation distribution, to determine
if choice has different impacts at different parts of the distribution. The specification here is:
(3) COU
= , 1 + f 1T
2 + 83 log(P) + ,84T. * log(Pi) + S
5PG1
+ f6T * PG, +P7X, + ,6
where CO
i is a dummy for whether individual i donated an amount above the given cutoff, Ci is
again a dummy variable that is = 1 for donors in the treatment group, log(PD
5 ) is the log of the
prior donations of person i, including zeros, and NZ, is a dummy variable indicating whether the
prior donations of individual i are nonzero. The cutoffs I use are response (whether the donor
responded to the newsletter, i.e. had a donation amount greater than zero), at least C5, at least
£10, at least £15, at least £20, and at least £25.
This reinforces the conclusions from the previous regressions. Although previous
donations strongly predict donation amounts, the main effect and interaction of choice are both
almost always zero. The is one significant interaction effect, however-the interaction is
negative in the regression of whether the donor gave at least £10. The results remain very similar
if these regressions are run as probits instead of linear probability regressions.
4.3 Experiment donations by group
There are two unique subgroups among the newsletter recipients; 12% of them are
schools and churches, and 44% are cold rental addresses. Table 7 shows how different these two
groups are from the other largest category, the regular donors. While the churches and schools,
and the cold rental addresses, both have response rates under 1%, the regular donors have a
response rate of 31%. Table 8 shows the same specifications shown above without the churches
and schools and the cold rentals; this results in dropping many of the zeros, and it also drops all
of the observations who had zero previous donations. The results are very similar; the previous
donations remain the only highly significant variable, and neither choice or the interaction term
are ever significant. The results thus do not change when the less involved newsletter recipients
are dropped from the analysis. This means that the more involved donors do not seem to behave
significantly differently from those who are less involved; it also means that it is probably not all
the zeros that are driving the results, because dropping over 60% of the zeros does not change the
results.
4.4 Post-experimentdonations
Table 9 is the same as table 4, (the specifications from equations 1 and 2), except now
the dependent variable is post-experiment donations; these are the donations sent by donors who
were in the experiment sample, in the year following the experiment. The conclusions from this
are the same as the conclusions from table 4: looking at the regressions in levels with the
interaction term, in columns 2 and 3, there appears to be a treatment effect, but when the
regressions are run in logs instead, these results disappear. Table 10 is the same as table 5 but
with post-experiment donations; it uses the specification of equation 3, but the cutoff points have
been shifted somewhat, as the donation totals are higher here. The regressions are all quite
similar to the ones in table 5; again, one of the 12 interaction effects is significant.
One difference, however, between tables 9 and 10 and the earlier results, is that the rsquareds are much higher here. The final regression of table 9 has an r-squared of 0.47, while the
final one in table 4 is only 0.22; in table 10 the r-squareds range from 0.1 to 0.42, whereas they
ranged from 0.04 to 0.21 in table 5.This may be because the total donations over several
previous years are an even better predictor of the total donations over the year than they were of
the donation amount given in response to one particular newsletter.
5 Conclusion
In this paper I discuss a field experiment that studies choice in charitable giving. Half of
the recipients of a charity's regular newsletter were given the opportunity to target their donation
to either health, education, (the two major program areas of the charity,) or wherever it was most
needed. It was a priori unclear, from the psychology and economics literature, what effect this
intervention would have on donation rates and amounts. A first glance at the mean donation rates
and amounts of the treatment and control groups indicates that the experiment, in fact, had no
effects; more careful examination of interactions and the distribution of donations support this
conclusion.
There are several ways of explaining this zero effect. One possibility is that the sample
size was simply not large enough; the power of this experiment is such that a 5%change in either
donation rates or donation amounts would have been detectable at the 95% confidence level in
the simple comparison of means. This appears to be significant power as many charitable giving
experiments have found much larger effects than that from their manipulations, e.g. Karlan and
List (2006) increase the donation rate by 20%, Landry et al. (2005) increase it by 100%,, and
Soetevent (2005) increases total donations by 10% . Another explanation is that the choice was
simply not salient enough for donors to notice it or respond to it; however, the majority of donors
in the treatment group did select one of the three choices, and the average donation of those who
made a choice was the same as the average donation of the control group. The final explanation
is that the donors did not value the choice given, which is supported by the fact that 80% of the
people who made a choice picked "wherever is most needed." More evidence for this comes
from the fact that the people who made no choice donated less than either the control group or
the people who made a choice, which implies that they may have been put off by the offer of a
choice.
Why would these donors fail to value this choice? Why did so many of the people who
took the time to make a choice choose to leave the decision to ICS? One possibility is that much
of the literature regarding choice comes from experiments performed on Americans, and the
Dutch may be different from Americans. Americans place a particularly high value on choice,
independence, and personal control, so it is possible that the results would have been different if
this experiment had been done on Americans.
Alternatively, maybe it is the particular choice provided that was not valued. This could
be because people realized that the money was quite fungible, so where their personal money
went would have no effect on the overall services provided by ICS, which made it essentially a
meaningless choice. Or it could be because they trust ICS to choose where their money should
go and do not want to make the choice themselves. Finally, it could be because it simply doesn't
matter to them which projects ICS spends the money on; what is important to them is giving
money to ICS, and the exact work it goes towards is unimportant. More research is needed to
distinguish among these competing explanations.
References
AAFRC Trust for Philanthropy (2003). Giving USA 2003. Indianapolis, IN: Author.
Batson, Daniel C. et al. (1995). "Empathy and the Collective Good: Caring for One of the Others
in a Social Dilemma." JournalofPersonalityand SocialPsychology, 68 (4): 619-631.
Bertrand, Marianne et al. (2005). "What's Psychology Worth? A Field Experiment in the
Consumer Credit Market." Working paper, Harvard University.
Breman, Anna and Ola Granstrom (2005). "Altruism without Borders?" Working paper,
Stockholm School of Economics.
Cordova, Diana I. and Mark R. Lepper (1996). "Intrinsic Motivation and the Process of
Learning: Beneficial Effects of Contextualization, Personalization, and Choice." Journalof
EducationalPsychology, 88 (4): 715-730.
Deci, Edward L. (1981). The psychology of self-determination. Lexington, MA: Heaths.
Deci, Edward L., and Richard M. Ryan (1985). Intrinsic motivation and self-determination in
human behavior. New York: Plenum Press.
Desmet, Pierre and Fred M. Feinberg (2003). "Ask and Ye Shall Receive: The Effect of the
Appeals Scale on Consumers' Donation Behavior." Journalof Economic Psychology, 24: 349376.
Eckel, Catherine C. and Phillip J. Grossman (2003). "Rebate versus Matching: Does How We
Subsidize Charitable Contributions Matter?" JournalofPublic Economics, 87: 681-701.
Eckel, Catherine C., Phillip J. Grossman, and Rachel M. Johnston (2005). "An Experimental
Test of the Crowding Out Hypothesis." Journalof PublicEconomics, 89: 1543-1560.
Falk, Armin (2004). "Charitable Giving as a Gift Exchange: Evidence from a Field
Experiment." Working PaperSeries, Institute for Empirical Research in Economics. University
of Zurich.
Fong, Christina M. (2004). "Empathic Responsiveness: Evidence from a Randomized
Experiment on Giving to Welfare Recipients." Working paper, Carnegie Mellon University.
Geven en Nederland (2005). "Kemcijfers 'Geven in Nederland 2005."'
www.geveninnederland.nl
Iyengar, Sheena S. and Mark Lepper (1999). "Rethinking the value of choice: a cultural
perspective on intrinsic motivation." Journalof Personalityand Social Psychology, 76: 349-366.
Iyengar, Sheena S. and Mark Lepper (2000). "When Choice is Demotivating: Can One Desire
too Much of a Good Thing?." Journalof Personalityand Social Psychology, 79: 995-1006.
Karlan, Dean and John List (2006). "Does Price Matter in Charitable Giving? Evidence from a
Large-Scale Natural Field Experiment." Working paper, Yale University.
Kingma, Bruce R. (1989). "An Accurate Measurement of the Crowd-out Effect, Income Effect,
and Price Effect for Charitable Contributions." Journalof PoliticalEconomy, 97 (5): 1197-1207.
Landry, Craig, et al. (2005). "Toward an Understanding of the Economics of Charity: Evidence
from a Field Experiment." Working paper, University of Maryland.
Lewin, Kurt (1952). "Group decision and social change," in Guy E. Swanson, Theodore M.
Newcomb, and Eugene L. Hartley, eds., Readings in socialpsychology. New York: Henry Holt,
459-473.
List, John and David Lucking-Reiley (2002). "The Effects of Seed Money and Refunds on
Charitable Giving: Experimental Evidence from a University Capital Campaign." Journalof
PoliticalEconomy, 110, 215-233.
Madrian, Brigitte C. and Dennis F. Shea (2001). "The Power of Suggestion: Inertia in 401(k)
participation and savings behavior." QuarterlyJournalofEconomics, 116: 1149-1187.
Meier, Stephan (2005). "Do Subsidies Increase Charitable Giving in the Long Run? Matching
Donations in a Field Experiment." Working paper, University of Zurich.
Redelmeier, Donald A., and Eldar Shafir (1995). "Medical Decision Making in Situations that
Offer Multiple Alternatives," Journalof the American Medical Association, 273: 302-305.
Roswarski, Todd Eric and Michael D. Murray (2006). "Supervision of Students May Protect
Academic Physicians from Cognitive Bias: A Study of Decision Making and Multiple Treatment
Alternatives in Medicine." MedicalDecision Making, 26(2): 154-161.
Sethi-Iyengar, Sheena, Gur Huberman, and Wei Jiang (2004). "How Much Choice is Too Much?
Contributions to 401 (k) Retirement Plans" in Olivia S. Mitchell and Stephem P. Utkus (Eds.),
Pension Design and Structure: New Lessons from Behavioral Finance. Oxford University Press,
New York, NY pp.83-95.
Shafir, Eldar, Itamar Simonson and Amos Tversky (1993). "Reason-Based Choice." Cognition,
49, 11-36.
Soetevent, Adriann R. (2005). "Anonymity in Giving in a Natural Context-a Field Experiment
in 30 Churches." Journalof PublicEconomics, 89: 2301-2323.
Figure 1: The Newsletter
WV•L Dapn
* c~~r
h~ighb~smiwH Ilrili
n*
bq,,,wild
I "o
JK+*
Ortdorwis
In
K*W
idWr
*
~8r
lu
kL~
Ho. 1v,4-ift.A.
moo Voa~truao*r)O
~
&V,L, At4,*,
~~hc~r Výflý
4gkýW-kotv,*
D"wbtomtmijý
m·b4UtgE
*
k~opMI·k~lrMI
DrJ
.k~
-A 0,4".uslp
E~i~r
S-k-
-,Ov*J~phot m-ocHýIL
dm*
ý" " bwo!l
d*4-
554(
wk1,A4-n
k..hwý4.
W -r
anýkut
04-
iiaaQ~5rnoCBLFLý,iu:-::
AUW
X1. "Wdomn
.. Oketn 7O:
tO.
~OS
Figure 2: The donation form
::
I
a
r
C
.i
4
C
1
r:i
it
t
ii-
iCl
C
H
£5~
Sti
I
Figure 3: Distribution of donations (kernel density)
00
Co
0-
(D
o-
O-
200
400
600
donation amount
Figure 4: Distribution of log donations (kernel density)
-2
0
Log of Donation Amount
800
1Idoo
Table 1: Newsletter recipient pre-experiment characteristics (variable means)
(1)
(2)
Prior donations (since
2001, in 1,000s)
Log (prior donations
since 2001)
Prior donations greater
Control
0.053
(0.002)
1.71
(0.021)
0.46
Treatment
0.054
(0.002)
1.74
(0.021)
0.47
than zero (dummy)
(0.005)
(0.005)
0.27
(0.007)
0.31
0.27
(0.007)
0.31
(0.005)
(0.005)
Female
Urban
Bible belt
Church or school
Child sponsor
Regular donor
Cold rental
0.31
(0.005)
0.12
(0.003)
0.0008
(0.0003)
0.30
(0.005)
0.44
(0.005)
0.31
(0.005)
0.12
(0.003)
0.0006
(0.0003)
0.31
(0.005)
0.43
(0.005)
Standard errors in parentheses. There are 9,561 observations
for each cell with the exception that the variable Female has
only 3,852 observations in the control group and 3,859 in the
treatment group.
Table 2: Basic experiment results
Donation amount
Response
Amount conditional on
Giving
Log of donation
Amount
(1)
Control
1.29
(0.064)
0.11
(2)
Treatment
1.31
(0.12)
0.11
11.99
(0.47)
2.11
12.28
(1.09)
2.07
(0.025)
(0.025)
(0.003)
(0.003)
Log of post-experiment
3.07
3.04
donation amount
(0.023)
(0.023)
There are 9,561 observations for each cell in rows 1&2,
in rows 3&4 there are 1,027 observations in column 1
and 1,022 observations in column 2.
Table 3: Target areas chosen among treatment group
(2)
(1)
(1)
Education
(2)
Health
(3)
Number of
Donors
59
29
Wherever
407
most needed
(4) No choice
404
Made
(5) Unknown
125
Choice
._
(6) Education or
88
Health
(7) Any choice
495
Made
The first five rows are mutually
Is rows 1, 2 and 3 together.
(3)
(4)
Percent of
total donors
5.7%
Mean
Mean log
Donation
Donation
13.63
2.27
(1.96)
(0.10)
2.8%
7.40
1.74
(0.88)
(0.16)
39.8%
11.93
2.15
(0.59)
(0.039)
39.5%
10.44
1.92
(1.08)
(0.040)
12.0%
19.82
2.26
__Q._5) ...........
JO-074)_
8.6%
11.58
2.10
(1.23)
(0.091)
48.4%
11.86
2.14
(0.54)
(0.036)
exclusive, row 6 is rows 1 and 2 together, and row 7
Table 4: Basic regressions with interactions
(1)
Donation
amount
Choice
Prior donations
0.025
(0.139)
(2)
Donation
amount
0.010
(0.124)
21.296
(0.322)**
(3)
Donation
amount
-0.019
(0.162)
7.017
(0.471)**
(4)
Donation
amount
-0.019
(0.119)
7.012
(0.345)**
Log of prior
Donations
Prior donations
greater than zero
Choice * Prior
Donations
Choice * Log prior
donations
Choice * Prior don.
greater than zero
(5)
Log donation
amount
-0.002
(0.012)
0.244
(0.007)**
0.172
(0.130)
1.781
(0.177)**
25.067
(0.624)**
-2.817
(0.249)**
1.788
(0.130)**
1.655
(0.491)**
-0.333
(0.183)
-0.437
(0.028)**
-0.014
(0.009)
0.037
(0.039)
0.26
0.09
0.22
0.00
0.20
R-squared
Standard errors in parentheses. All regressions include the urban and bible belt dummies as controls. In column 1
donation amount is regressed on choice, in column 2 total prior donations since 2001 is added to the regressors, and
in column 3 the interaction of choice and prior donations is added as a regressor. Column 4 is the same as column 3
with one outlier dropped. Columns 5 and 6 are the same as column 3 except column 5 is in logs and column 6 is in
logs except for the zeros, which are left as zeros. There are 19,122 observations in every regression except column 4,
which has only 19,121.
* significant at 5%; ** significant at 1%
Table 5: Whether gave above cutoffs
(6)
(5)
(4)
(3)
(2)
(1)
Response
At least 65
At least 610 At least 615 At least 620 At least 625
Choice
-0.001
-0.001
-0.000
0.000
0.000
0.000
(0.005)
(0.005)
(0.004)
(0.003)
(0.002)
(0.002)
Log of previous
0.092
0.093
0.073
0.039
0.024
0.019
Donations
(0.003)**
(0.003)**
(0.002)**
(0.002)**
(0.001)**
(0.001)**
Choice*Log of
-0.005
-0.004
-0.009
-0.001
0.003
0.000
Prev. donations
(0.004)
(0.004)
(0.003)**
(0.002)
(0.002)
(0.002)
Donated before
-0.120
-0.155
-0.153
-0.096
-0.060
-0.050
(0.012)**
(0.011)**
(0.009)**
(0.007)**
(0.005)**
(0.005)**
Choice*Donated
0.020
0.014
0.019
0.003
-0.008
-0.002
Before
(0.017)
(0.016)
(0.013)
(0.009)
(0.007)
(0.006)
Observations
19122
19122
19122
19122
19122
19122
R-squared
0.21
0.20
0.15
0.08
0.06
0.04
These are linear probability regressions of donating an amount above the given cutoff amount (0, 65, 610, 615, 620,
or 625) on choice; the log of previous donations since 2001 (except with zeros, which are coded as zeros rather than
missing); the interaction of choice and the log of previous donations; a dummy for previous donations being greater
than zero; and the interaction of choice and this dummy. Standard errors are in parentheses.
* significant at 5%; ** significant at 1%
Table 7: Donation rates and amounts by group
5798
(2)
Response
rate
0.31
(3)
Average log
donation
2.07
2263
0.009
3.84
(1)
Number
Regular
Donors
Churches &
Schools
Cold rentals
Cold rentals are
a donation.
8312
0.004
2.11
newsletter recipients who have never made
Table 8: Excluding churches, schools, and cold rentals
(6)
(5)
(4)
(3)
(2)
(1)
Response
At least C5
At least £10 At least £15 At least 620 At least £25
Choice
0.012
0.005
0.015
0.002
-0.012
-0.003
(0.024)
(0.026)
(0.019)
(0.014)
(0.011)
(0.009)
Log of previous
0.103
0.103
0.081
0.043
0.026
0.020
Donations
(0.005)**
(0.004)**
(0.003)**
(0.002)**
(0.002)**
(0.002)**
-0.004
Choice * Log of
-0.002
-0.008
-0.001
0.003
0.000
prev. donations
(0.006)
(0.006)
(0.005)
(0.003)
(0.003)
(0.002)
Constant
-0.145
-0.180
-0.176
-0.107
-0.064
-0.051
(0.019)**
(0.017)**
(0.014)**
(0.010)**
(0.008)**
(0.007)**
Observations
8139
8139
8139
8139
8139
8139
R-squared
0.11
0.12
0.11
0.07
0.05
0.04
This table excludes all churches, schools, and cold rentals (newsletter recipients who have never made a donation).
The dependent variables are whether the experimental donation was above the given cutoff amount (0, £5, £10, £15,
£20, or 625) and the regressors are choice, the log of total previous donations since 2001, and the interaction of these
two variables. Standard errors are in parentheses.
* significant at 5%; ** significant at 1%
Table 9: Basic regressions of donations made in the year after the experiment
Choice
Prior donations
Log of prior
Donations
Prior donations
greater than zero
Choice * Prior
Donations
(1)
Donation
amount
0.057
(0.610)
(2)
Donation
amount
-0.041
(0.503)
115.175
(1.307)**
(3)
Donation
amount
0.569
(0.679)
147.109
(1.968)**
0.640
(0.010)**
4.127
(0.527)**
1.118
(0.741)
-56.059
(2.608)**
Choice * Log prior
donations
Choice * Prior don.
greater than zero
(4)
Log donation
amount
-0.001
(0.019)
5.122
(1.041)**
-0.977
(0.044)**
-0.004
(0.015)
0.014
(0.062)
0.47
0.32
0.34
R-squared
0.00
Standard errors are in parentheses. There are 19,122 observations in each column.
* significant at 5%; ** significant at 1%
Table 10: Whether gave above cutoffs after the experiment
(3)
Any donation
Choice
-0.000
(0.006)
0.140
Log of previous
Donations
(0.003)**
0.002
Choice*Log ofprev.
Donations
(0.005)
-0.062
Donated before
(0.014)**
Choice*Donated
-0.001
Before
(0.020)
-0.002
Constant
(0.005)
19122
Observations
0.42
R-squared
Standard errors in parentheses
* significant at 5%; ** significant at 1%
At least 65
-0.000
(0.006)
0.150
(0.003)**
0.000
(0.005)
-0.118
(0.014)**
0.003
(0.019)
-0.001
(0.005)
19122
0.42
At least 610
-0.001
(0.006)
0.167
(0.003)**
0.001
(0.004)
-0.250
(0.013)**
0.002
(0.018)
-0.000
(0.005)
19122
0.42
(4)
At least 625
-0.000
(0.005)
0.146
(0.003)**
-0.002
(0.004)
-0.336
(0.011)**
0.008
(0.015)
0.001
(0.004)
19122
0.34
(5)
At least 650
-0.000
(0.004)
0.093
(0.002)**
-0.007
(0.003)**
-0.243
(0.008)**
0.018
(0.012)
0.002
(0.003)
19122
0.22
(6)
At least 6100
0.000
(0.002)
0.040
(0.001)**
-0.003
(0.002)
-0.113
(0.005)**
0.007
(0.008)
0.002
(0.002)
19122
0.10
Chapter 3
Schelling Revisited: Historic Discrimination, the Desire for Diversity,
and Current Segregation
with Elizabeth Ananat
1 Introduction
In the United States, residential areas are overwhelmingly segregated by race. This fact
has been blamed for many economic phenomena, including higher rates of poverty and
joblessness among African-Americans (cf. Kain, 1968; 1992) and poor education (cf. Orfield and
Eaton, 1996). Segregation is also, however, an economically interesting fact in its own right,
because the existing racial distribution of neighborhoods does not offer the integrated areas for
which a significant number of Americans express preferences. What, then, causes segregation?
Is segregation a market failure, in which the play of individual preferences cannot create the
equilibrium that individuals prefer? Is it a result of inertia, caused by a past in which institutions
created and maintained segregation? Does it result from contemporary discrimination by some
market agents, who prevent others from realizing their preferences?
In what follows, we create a model of this process of segregation in order to answer these
questions. Thomas Schelling's now canonical model of segregation predicts that if people have
(even quite mild) preferences to live with some people like themselves, they will end up quite
severely segregated from people who are unlike themselves. The vastly increased computing
power (and data on preferences) that has become available since 1971 allows us to study the
effects of different preferences, of past discrimination, and of current discrimination in creating
the high levels of segregation we see today by expanding on Schelling's model. It also allows us
to study the impact of a potential government policy designed to foster integration.
We find that accounting for the effects of past discrimination decreases the amount of
integration in equilibrium by almost half. This effect, in general, dominates the effects of varying
preferences and the fraction of the population with given characteristics and preferences. In the
absence of historical discrimination, current discrimination also has powerful effects on the level
of integration in equilibrium. Combining current and historical discrimination leads to a very
interesting conclusion: historical discrimination has caused such high levels of current
segregation that current discrimination has very little effect. This is because segregation was so
severe in 1970 that 70% of neighborhoods were at least 99% white, and in our model blacks do
not want to move into any of those neighborhoods, so the fact that they would be discriminated
against if they wanted to buy a house there is unimportant. Finally, we examine a potential
policy and find that it increases the ability of those who desire integration to form integrated
neighborhoods, thereby increasing utility.
By expanding upon Schelling's original model, we are thus able to learn a great deal
more about residential racial segregation, and the role of current and historical discrimination
and people's changing preferences for segregation and integration in maintaining segregation. In
contrast to Schelling, we find that rather than being the natural outcome of market forces, the
severe levels of segregation we see today are the result of sub-optimally high levels of
segregation imposed by historic discrimination. In addition, eliminating current discrimination
will not be sufficient to get the nation out of this high-segregation equilibrium; an activist policy
would be necessary to create the higher level of integration that would have resulted from a wellfunctioning market in the absence of historical discrimination.
The paper is laid out as follows: section 2 discusses the history of discrimination, section
3 describes the Schelling model, section 4 shows how our model builds on the Schelling model,
section 5 describes the simulations, section 6 gives the results, and section 7 concludes.
2 The Makings of American Segregation
In 1890, African-Americans in the northern U.S. were only slightly more segregated from
native-born whites than were European immigrants. Using a dissimilarity index, a conventional
measure of segregation that ranges from 0 to 100 and on which 60 is considered high, neither
blacks, at an average of 46, nor foreign-born whites faced highly segregated conditions in
h
19t
century northern cities. And in the South, where blacks lived in alleys and byways interspersed
between blocks of white-owned mansions, segregation was even lower. Moreover, in 1890 place
of residence was determined by class and not race. The two were of course highly correlated,
but those African-Americans who did amass wealth took residence in neighborhoods of other
wealthy people, meaning for the most part neighborhoods that were predominantly white
(Massey and Denton 1993).
By 1940, however, the northern dissimilarity index averaged around 80, nearly double
what it had been 50 years earlier; southern cities experienced similar increases in segregation.
Cutler, Glaeser, and Vigdor (1999) find that by their definition only one city (Indianapolis) had a
"ghetto" in 1890; in 1940, 55 cities did. And segregation ceased to be a function of economic
class (Sims, 1999). What happened to cause such dramatic increases in the separation of blacks
and whites?
In their 1993 book American Apartheid, Douglas Massey and Nancy Denton explain in
compelling detail how this radical shift occurred. In the first two decades of the 2 0th century, as
significant numbers of blacks migrated to Northern cities in search of industrial jobs and greater
civil liberties, whites responded with riots and murders targeting African-Americans who lived
outside black areas. After the violence exhausted itself, whites turned heavily to the nonviolent
but perhaps more effective "restrictive covenant," a type of collective agreement that prevented
whites in a neighborhood from selling houses to blacks. By the time such agreements were ruled
unenforceable by the Supreme Court in 1948, the federal government had institutionalized
segregation through its lending practices: the Federal Housing Administration, which both made
loans and set norms for private lenders, had instituted the practice of "redlining," in which
almost no loans went to neighborhoods with even small percentages of black residents;
moreover, the government still afforded no protection for victims of explicit housing
discrimination.
In 1968 the civil rights movement brought about the Fair Housing Act, and the housing
market became for the first time, if in many ways only ostensibly, a place where individual
preferences determined outcomes. But by that time, 70 years of implicit and explicit government
policy of enforcing segregation had left its very visible mark on the composition of
neighborhoods throughout the United States.
Subsequently, segregation has changed very little. The average metropolitan
dissimilarity index for African-Americans, which hovered around an average of 80 in 1970
(Cutler et al. 1999), had fallen to about 65 by 2000-still highly segregated-but that fall was
driven almost entirely by cities with very low black populations. The cities where the majority
of blacks live tend also to be those that are the most segregated, and in those cities the
segregation indexes not only were higher at the beginning of the ostensibly free housing market,
but also have fallen by much less (Mumford, 2001).
This stagnation does not appear to be driven by an African-American preference for selfsegregation, however. The modal ideal neighborhood among African-Americans has been 50%
white ever since the question was first asked in the 1976 Detroit Area Study (Farley and
Schuman, 1976). Moreover, according to results from the 1994 Multi-City Study of Urban
Inequality (Bobo et al., 1994), some 20% of African-Americans would be unwilling to move into
an all-black neighborhood, while some 40% would be willing to move into an all-white
neighborhood. And the major explanatory factor for black unwillingness to move into all-white
neighborhoods is concern about white intolerance (Krysan and Farley, 2002).
Over the same time period, white attitudes have become consistently more prointegration. White support for the right of whites to keep blacks out of their neighborhoods if
they want has fallen from 47% in 1970 to 13% in 1996. On the level of personal preferences, in
1976 58% of whites stated a preference for living in a mostly- or all-white neighborhood, while
20 years later that figure had fallen to 43% (Schuman et al., 1997).
Nonetheless, there is still substantial evidence of discrimination against AfricanAmericans. This includes institutional discrimination, in the form of discriminatory lending
(Goering and Wienk, 1996) and real estate marketing practices (Galster 1992) as well as
preference-based decentralized discrimination, in the form of the premium paid by whites to
avoid living in black areas (Cutler et al, 1999).
3 The Schelling Model
In 1971, Thomas Schelling developed several models with similar implications that
became the canonical economic wisdom on segregation. In the simplest of these, using nickel
and penny "agents" on a table, he demonstrated that, given random initial conditions, agents with
relatively modest preferences for being with at least some agents like themselves would soon be
severely segregated from those unlike themselves. He intended this model to be general enough
that it could be applied to many types of segregation, but in the paper he applied it specifically to
racial segregation in housing in the U.S.
In his model, each nickel or penny represented a household: one type of coin represented
whites, the other blacks. A household was either happy or unhappy, depending on the color of its
immediate neighbors. If some portion of its neighbors were the same color as it, it was happy.
Schelling randomly placed nickels and pennies on a grid, leaving 25 to 30 percent of the spaces
empty. He then went through the grid and moved each unhappy household to the nearest empty
space where it would be happy. He continued the moving process until nobody was movingi.e., either every household was happy or unhappy households could not be made happy in any
vacant spot.
Figure 1, a replication of Schelling, shows the severe segregation that results from ingroup preferences of 50% enacted in an initially random, well-integrated grid. Here, many
people have no neighbors of the opposite color at all, so the average household has many more
neighbors of their own color than they require to be happy.
Figure 1.
Schelling's finding has frequently been taken by economists to mean that American racial
segregation results from the market expression of reasonable individual preferences, and thus
that there is little economics to justify policy intervention in housing. To the extent that
economists have viewed segregation as a problem, then, their focus tends to be either on
continuing institutional discrimination (either in lending or in real estate markets) or on waiting
for neighborhoods to change as in-group preferences erode.4
4 Our Model
Our basic model differs from the Schelling model in two basic ways: the definition of
neighborhood and the description of preferences. We then expand upon this basic model to
explore the effects of both past and current discrimination, and to evaluate a policy proposal.
4.1 Constructing neighborhoods
In the Schelling model, as in most agent-based models, an agent's neighborhood consists
solely of immediate neighbors. By contrast, in our model we define neighborhoods as fixed
squares composed of 100 homes, because survey data indicate that this is how respondents view
neighborhoods. Lee and Campbell (1997) conclude, in their study of survey respondents'
neighborhood definitions, that "[m]ost people use the word [neighborhood] to refer to a
territorial unit." Moreover, they find that the vast majority of urban residents identify their
4 In general, there has not been much attention paid to empirically testing the Schelling model and its implications;
we are aware of only one macro (rather than case-study) examination. Easterly (2003) uses U.S. data to test the
tipping point implication of the mathematical version of Schelling's model, which allows for a continuum of nonisolation preferences; he finds little support for simple tipping as a description of neighborhood racial change in the
U.S.
neighborhood using a modal neighborhood name (e.g. SoHo or Beverly Hills)-regardless of
where in that neighborhood they live. Such an understanding of neighborhoods also underlies the
questions asked in MCSUI, where preferences are assumed to depend on non-adjacent houses.
Prior to our current set of simulations, we tested the effect of this change on an otherwise
classic Schelling model with in-group preferences of 50%. Figure 2 shows the result of basing
utility on fixed neighborhood composition-here, agents' utility is a function of the composition
of the quadrant of the grid in which they reside. This leads to complete segregation, even more
severe than in the classic model.
Figure 2.
With milder in-group preferences, the model becomes much more sensitive to initial conditions:
for some preferences stability is reached either at complete segregation or at complete
integration, depending on the initial random distribution. Such extreme results and severe
dependence on initial conditions do not mirror what we see in the real world, so on its own this
modification does not make the predictions of the Schelling model more realistic.
4.2 Constructingpreferences
Schelling's model assumed that people were indifferent between a neighborhood that was
100% in-group and one that was 50% in-group: the only thing Schelling agents care about is
being with enough members of their own group. They get no value out of living with out-group
members. Put yet another way, in the Schelling model no one places value on diversity; thus, it
is not surprising that the resulting neighborhoods are not diverse. However, this model of
preferences is belied by all available survey data. As discussed in section II, the modal preferred
neighborhood for African-Americans is 50% white. Moreover, a significant minority of white
Americans would be unwilling to move into an all-white neighborhood, preferring
neighborhoods with a non-zero black presence.
Because of this, we update the preferences in the model, basing them on data from the
Multi-City Study of Urban Inequality (Bobo et al., 1994). MCSUI is a study of more than 8,500
households in Boston, Detroit, Atlanta, and Los Angeles that asked whites and blacks about their
preferences over neighborhood racial composition. They were each shown a set of flashcards
depicting 15 houses-three rows of five-with the middle house in the middle row indicating
their home and with each other house colored either white or black to depict the race of its
residents. Unfortunately, whites and blacks were not shown flashcards with the same series of
white/black ratios, nor were they asked the same questions about their preferences; nonetheless,
we have been able to construct a reasonable set of preferences from the available data.
Whites were shown one card with each of the following racial compositions: 14 white
houses, 13 white houses and one black house, 11 white houses and three black houses, 9 white
and 5 black, and 6 white and 8 black. They were asked:
Suppose you have been looking for a house and have found a nice one you can
afford. This house could be located in several different types of neighborhoods,
as shown on these cards. Would you consider moving into any of these
neighborhoods?
If they say yes, they are then asked to hand to the interviewer the cards for all the neighborhoods
they would be willing to move into. We used a very strict measure for identifying white
respondents as "integrationists": they not only had to be willing to move into neighborhoods with
non-zero proportions of African-Americans, they had to be unwilling to move into an all-white
neighborhood. That is, we required that their utility be clearly increasing over some range of
African-American presence. Three percent of white respondents met this criterion.
However, this approach does not take into account that utility may also increase over
some range of African-American presence among those who would be willing to live in an allwhite neighborhood-a group that includes not only those who say they would be unwilling to
live in neighborhoods with high proportions of African-Americans, but also those who state that
they would be willing to live in all of the neighborhoods shown. Eighty-seven percent of
respondents, for example, stated that they would be willing to move into a neighborhood with 1
black and 13 white houses; 42 percent would be willing to move into the highest percentageblack neighborhood they were shown.
Certainly it is unlikely that all of these respondents have increasing utility over some
range of African-American presence; it seems equally unlikely, however, that none of these
respondents do. We thus make for our model the quite conservative assumption that half of
integrationists reveal themselves through our mechanism and half do not-i.e., that the true
percentage of whites who are integrationist is 6%.
Among integrationist whites, preference patterns bifurcate. Recall that white respondents
were asked about neighborhoods that range from 0/14 to 8/14 black; for half (50.7%) of
integrationists, as the proportion black starts to increase they become willing to enter the
neighborhood, but at higher proportions they become unwilling. The other half, however, never
become unwilling over the observed range. Based on their responses to a separate, "ideal
neighborhood" question, we impute that their preferences mirror those of black integrationists,
whose preferences we observe over the full range of neighborhoods.
Thus in our model we have two types of white integrationists: those whose utility
declines prior to the midpoint of the racial distribution we call "mild integrationists," and those
whose preferences look like those of black integrationists we call "full integrationists." The
utility function of mild integrationists is based on taking the median of the length of the interval
of neighborhoods that the integrationist whites are willing to move into, and assuming that their
ideal neighborhood is halfway between the endpoints of that interval. Their utility thereby peaks
at 4.5 black neighbors, and is higher for no black neighbors than for more than 9. As with all of
our agents, their utility is normalized to have a minimum of 0 and a maximum of 1 and is
assumed to be piecewise linear. Figure 3 shows the preferences we generated for mild
integrationists.
Figure 3.
Utility of Mild Integrationists
I
0.8
0.6
0.40.2A
v
1
Race
% Same Race
%
Same Race
% Same
lOO
100
10
Black respondents were shown one card with each of the following racial compositions:
14 black houses, 10 black houses and 4 white houses, 7 black houses and 7 white houses, 2 black
and 12 white, and 14 white. They were asked:
Suppose you have been looking for a house and have found a nice one you can
afford. This house could be located in several different types of neighborhoods,
as shown on these cards. Would you look through the cards and rearrange them
so that the neighborhood that is the *most* attractive to you is on top, the next
most attractive second, and so on down the line with the least attractive on the
bottom.
Roughly one-quarter (22.5%) of African-American respondents placed the all-black
neighborhood first. Among these respondents, the average ranking of each other neighborhood
fell as the percentage black in that neighborhood fell--we classify these respondents as
isolationist blacks. Isolationists, both white and black, have preferences that are monotonically
decreasing over percent other race. Figure 4 shows the utility function that we assigned them.
Figure 4
Utility of Isolationists
1
0.8
0.6
0.4
0.2
0
%Other Race
100
Among the black respondents who did not rank the all-black neighborhood first, the 7
black:7 white neighborhood had the highest average ranking, the 10:4 neighborhood ranked
second, the 2:12 neighborhood third, the 14:0 neighborhood fourth, and the 0:14 neighborhood
fifth. We only know the relative rankings of these 5 neighborhoods from these responses, and the
relative utility of the differently ranked points turn out to affect the results of our model. Thus in
our simulations we vary the values of X and Y, where X is the utility of a neighborhood that is
1/14 the other race and Y is the utility of a neighborhood that is 13/14 the other race.
In Figure 5 are two examples of full integrationist utility functions showing different
pairs of X, Y values. On the left, X is much higher than Y, so that neighborhoods with very low
percentages other race will be preferred to those with compositions even slightly over 50% other
race. On the right, X is quite close to Y, so that neighborhoods closer to the midpoint tend to be
preferred to neighborhoods with more same-race residents. In our simulations, we allow the X
value to vary between .35 and .75, while the Y value varies between .3 and .65; Y is constrained
to be less than or equal to X. The X and Y values of the white full integrationists vary
independently from the X and Y values of the black integrationists.
Figure 5.
Utility of Integrationists, Version
Utility of Integrationists, Version
1
I
1
I-
0.8
0.8 -
0.6
0.6 -
0.4
0.4 -
0.2
0.2 -
0
1
% Other Race
I
100
X
Y
0
I
1
% Other Race
100
4.3 Constructingthe simulation
At the beginning of a simulation, 1750 agents are randomly assigned a type. They have a
3% probability of being an isolationist black, a 9% probability of being an integrationist black, a
2.64% chance of being a full integrationist white, a 2.64% chance of being a mild integrationist
white, and an 82.7% chance of being an isolationist white. They are then randomly assigned to a
neighborhood.
Once all of the agents have been created and assigned a home, they begin to move. In
each period, agents are randomly assigned a move order, and the period ends when each agent
has had the opportunity to move. Moving is costless, and agents always move to the
neighborhood that offers them the highest utility and has a space available, unless no
neighborhood offers higher utility than their current neighborhood. The simulation ends when an
entire period passes where no agent has moved-i.e., each agent's utility is maximized over
current vacancies and neighborhood compositions, so the simulation has stabilized. (For a more
detailed explanation of the simulations, see the Appendix.)
4.4 Extension One : Historic Discrimination
The Schelling model and our basic model assume that preferences play out within an
initially random racial distribution. However, we know that the residential distribution in
1970-around the time that individual preferences were first allowed to have relatively free reign
in the housing market-was anything but random. Rather, as discussed in section II, decades of
financial discrimination, restrictive covenants, and intimidation had created a highly stratified
system of neighborhoods. We thus extend our model to explore the impact of past discrimination
by assigning agents to their initial houses according to the 1970 U.S. metropolitan distribution of
racial compositions, as shown in the Appendix in Table A.1, rather than randomly; we refer to
this as the "historical distribution."
4.5 Extension Two: CurrentDiscrimination
The basic model also abstracts away from any current discrimination that may exist, so
we extend our model to include the possibility that discrimination remains in the housing market.
In the baseline model, there are no limits on which neighborhood agents can move into--they
simply move to the neighborhood that maximizes their utility. In reality, however, people can be
kept out of neighborhoods: the Urban Institute recently conducted two studies for the
Department of Housing and Urban Development that both found significant discrimination in
housing markets by real estate and rental agents as well as loan officers (Turner et. al. 2002a,
Turner et. al. 2002b).
In particular, the realtor study illustrates a discriminatory mechanism that is
straightforward to incorporate into our model. That study, which took place in 2000, involved
sending one minority and one white person to pose as otherwise identical homeseekers while
visiting realtors. The auditors faced discriminatory treatment in both the rental market and the
sales market--whites received more information, had more opportunities to inspect apartments
and homes, and were more likely to be shown houses in predominantly white neighborhoods. In
fact, geographic steering was found to have increased since the last study in the series, which
occurred in 1989.
We model this process by giving black agents who attempt to move to majority-white
neighborhoods a probability of being rejected. As shown in Figure 6, this probability starts at
zero, for neighborhoods that are 50% white, and increases quadratically with the percentage
white. We vary Z, the probability that a black agent is rejected from an all-white neighborhood,
from 10% to 100%; in the simulations that assume no current discrimination, Z is implicitly set
to O.
Figure 6
Probability a Black Agent is Rejected
1
0.8
Z
0.6
0.4
0.2
0
1
%White
100
4.6 Extension Three: A Policy Experiment
Suppose if a neighborhood contains at least 25% blacks and 25% whites the government
considers it to be an integrated neighborhood, and the government gives all integrated
neighborhoods a payment of some sort. They might do this by subsidizing the construction and
running of a community center or some other good that everyone can use. And suppose that a
neighborhood that switches from being integrated to being segregated immediately loses the
subsidy.
In this set of simulations, we model such a policy by assuming that this subsidy increases
the utility of everyone in every integrated neighborhood by an equal amount S.5 Such a subsidy
will make the integrated neighborhoods much more desirable. We do not want the subsidy to be
5 This assumption may not be very believable in the case of a community center. It would apply better to a
subsidy that would be given to every resident, such as a refundable tax credit. We would not expect a policy of
giving money directly to people simply because they live in the right kind of neighborhood to be politically
palatable, however. Subsidizing a community center would seem to be a more feasible policy.
so large, however, that isolationists will want to live in integrated neighborhoods. It is optimal
for the isolationists to stay in their isolated neighborhoods, since that is where their utility has its
optimum that is where they want to be; the purpose of the policy is simply to encourage the
creation of integrated neighborhoods for those who desire them. The difference in an
isolationist's utility of a completely segregated neighborhood and one that is 25% other race is
0.523, so the levels of subsidy we examine range from zero to 0.5.
5 The Simulations Run
5.1
Main Simulations
The main set of simulations comprise 42,665 runs, and some summary statistics for them
are shown in column 1 of Table 1. The first statistic here shows that exactly half of the
simulations are run from an initially random distribution and half from the segregated
distribution that takes into account institutionalized racism before 1970. We run simulations fully
exploring the effects of variation in the preference parameters within each type; each Y value
varies independently between 0.3 and 0.65 and each X value varies independently between .35
and 0.75.
5.2 CurrentDiscrimination
Column 2 of Table 1 shows that these simulations were done mainly in the context of
historical discrimination, although ¼ of them were done from an initially random distribution.
Current discrimination varied from 0 to 1, concentrated more in the lower end of this range,
generating an average discrimination level of 0.25. Panel A shows that, as discussed above, we
restricted ourselves to conservative parameter values after exploring the full range in the main
body of simulations, so here the Y value remains at the minimum value, .3, while the X value
varies within the top end of the range, 0.65 to 0.75, which means we restrict our full
integrationists to have relatively weak desire for integration.
5.3 Subsidy
Now looking at column 3 of Table 1 we can see that all of the subsidy simulations were
done using the segregated initial distribution, current discrimination varies evenly between 0 and
1, and the subsidy level varies evenly between 0 and 0.5. Just as for the discrimination
simulations, the Y value is fixed at 0.3 and the X values vary within the upper range, although in
this case it is a slightly broader range, from 0.6 to 0.75, which once again means we restrict our
full integrationists to have relatively weak desire for integration.
5.4 Percentof each type of agent
In our model, we designed the simulations to be 82.7% isolationist whites, 2.64% mild
integrationist whites, 2.64% full integrationist whites, 9% integrationist blacks, and 3%
isolationist blacks. Panel B of table 1 shows that the numbers are not exactly as planned: we have
the right number of mild integrationist whites and of both integrationist and isolationist blacks,
but there are slightly too many full integrationist whites and slightly too few white isolationists.
The problem is most severe for the subsidy simulations but exists in each of the three datasets;
this imbalance results from a small mistake in the computer code which needs to be corrected,
and we will take this error into account in the discussion of the results.
5.5 Outcomes
Our outcome variables are the percentages of integrationist agents who find stably
integrated neighborhoods to live in. A neighborhood is defined as stably integrated if it contains
at least one white and one black household at the end of the simulation. Any neighborhood that
contains at least one of each will contain significant numbers of each, because none of our agents
are very happy in a neighborhood where the overwhelming majority are of the other race. Table
2 shows some summary statistics for these outcomes: in the main simulations, which incorporate
past but not current discrimination, 70% of full integrationists live in integrated neighborhoods,
and almost 20% of mild integrationists do. This is a much higher percentage than would have
been predicted by Schelling's original models. The percentages are much lower in the other
columns; this is partially because they incorporate current as well as past discrimination, and
partly because they make more conservative assumptions regarding desire for integration. We
identify the effects of each of these variables below.
6 Results
6.1 HistoricalDiscrimination
Table 3 shows the coefficient on whether the simulation began from the historical initial
condition in eight different regressions. Columns 1 and 2 show regressions where the dependent
variable is the percentage of white mild integrationists who live in integrated neighborhoods,
columns 3 and 4 show the percentage of white full integrationists, columns 5 and 6 show the
percentage of black full integrationists, and columns 7 and 8 show the percentage of all
integrationist agents. Columns 1, 3, 5, and 7 show the regressions without controls, and columns
2, 4, 6, and 8 show the regressions with controls. (The controls will be described in detail in the
following section.)
Columns 1 and 2 show that including the controls changes the coefficient on the initial
distribution from a very significant positive to a very significant negative for the white mild
integrationists; controlling for the other variables is very important to understanding the impact
of past discrimination on mild integrationists. In addition, with all controls, the historic
discrimination only lowers the percent of mild integrationists living in integrated neighborhoods
by 1.28 percentage points. Both of these results contrast with the results in columns 3 to 6, where
we see that the past discrimination lowers the percentage of full integrationists who are able to
live in integrated neighborhoods by over 30 percentage points, although adding all of the
controls does lower the coefficient significantly (in absolute value). This is an almost 50%
reduction from the mean of 70% of full integrationists living in integrated neighborhoods.
6.2 Controls
Table 4 shows the effects of each of our control variables. Panel A shows the effects of
the preference parameters on their own, and then the ratio of the X value to the Y value-a
higher X-Y ratio means a higher preference for a neighborhood that is a majority of your race
over a neighborhood that is a majority the other race. Panel B shows the effect of the percent of
each type of agent, where the omitted category is white isolationists. Panel C shows the effect of
the squares of these percentages. Panel D shows the effect of the interactions of the percent of
each of the full integrationist types and their X- and Y-values.
There are several conclusions that can be drawn from this table. First, the control
variables all have almost exactly the same effect of the percent of full integrationist blacks and
the percent of full integrationist whites who live in integrated neighborhoods; there are no
statistically significant differences in the coefficients in columns 3 and 4. So we can talk about
the effect of a variable on the percentage of full integrationists who live in integrated
neighborhoods, rather than discussing blacks and whites separately.
Second, in almost all of the variables in this table have a significant effect on the
percentage integrated of full integrationists; the squares and interactions are highly significant, so
the simple linear regression would have given a very inadequate picture of the process. However,
the importance of these nonlinear functions of the variables makes it difficult to directly interpret
the coefficients. We have thus created table 4a to show the effects more transparently; it shows
what happens when each variable is increased a small amount from its mean and all others are
kept at their mean. The values shown are the percentage point change in the percent living in
integrated neighborhoods; the percent of white mild integrationists in column 1 and of black full
integrationists in column 2.
The first four rows show the effect of increasing each preference parameter by 0.1 from a
mean of either 0.62 (X) of 0.43 (Y). The white preference parameters have a much larger impact
than the black preference parameters, and they all have larger impacts on the full integrationists
than on the mild integrationists. In increase of 0.1 in the white X value decreases the percentage
of black full integrationists living in integrated neighborhoods by over 1 percentage point and an
increase in the white Y value increases it by over 1 percentage point. Both of these mean, not
surprisingly, that the more integrationist the integrationist whites are, the more agents will be
able to live in integrated neighborhoods.
The last four rows show the effect of increasing the percent of each type, other than white
isolationists, by their standard deviation, and decreasing the percent of white isolationists by the
same amount; this is the effect of switching some agents from white isolationists to these other
types. The type that has by far the largest impact per percentage point change is white full
integrationists-the overall impact is somewhat larger for black integrationists, but since this is a
much larger group, their standard deviation is over double any of the others. Switching 0.6
percent of the agents from being white isolationists to being white full integrationists increases
the percent of white mild integrationists living in integrated neighborhoods by 2.4 percentage
points but decreases the percent of black full integrationists living in such neighborhoods by 7.8
percentage points. This means that as the number of white full integrationists increase, the
integrated neighborhoods have enough white agents in them that they draw in the mild
integrationists and thus push out many full integrationists. Since in our simulations we
accidentally created too many full integrationist whites and not enough isolationist whites,
putting those two back to where they should be would decrease the percent of white mild
integrationists living in integrated neighborhoods but increase the percent of full integrationists
in integrated neighborhoods.
Finally, the control variables impact the fraction of white mild integrationists who get
integrated very differently than the fraction of either full integrationist types. In panel A, only
the white agents' preference parameters change the white mild integrationist percent integrated,
the black preferences don't matter, while for the full integrationists they are all important. On the
other hand, panel B shows that only the percent of each black types matters for the mild
integrationists, while the percent of all types matter for the full integrationists. This may be
because the important factor is whether there are enough black integrationists that there are some
who will not fit in the fully integrationist neighborhood(s) with the full integrationist whites and
are thus willing to form a somewhat integrated neighborhood with a majority of mild
integrationist whites. The black integrationist exact preferences do not matter as much, because
they will almost always prefer living in a neighborhood with a mix that will make the mild
integrationists happy to living in an all-black neighborhood.
6.3 CurrentDiscrimination
Table 5 shows the effect of current discrimination in two cases: starting from a random
initial distribution of households, and starting from a segregated distribution of households. First
focusing on the results when the simulation is run with the random initial distribution, current
discrimination appears to be even more powerful than past discrimination-the highest level of
discrimination (when the parameter Z = 1) results in, on average, over 80 percentage points
fewer of the full integrationist households living in integrated neighborhoods. From a mean of
70%, this essentially brings it down to zero. The effects are of a similar relative magnitude for
the white mild integrationists and all integrationists overall, and this is true whether or not the
controls are included.
The results for the simulations run from the segregated initial distribution are very
different: here, discrimination is never significant. It seems that when past discrimination has
already created a significant number of highly segregated neighborhoods, whether or not there is
currently any discrimination is unimportant; thus, in the absence of government intervention, this
model suggests that sub-optimally high levels of segregation, imposed by past institutionalized
discrimination, will remain.
6.4 A Policy Experiment
There are many possible policies that could correct for the effects of past discrimination
and allow the creation of optimal levels of integration. Our model has limited scope for studying
the impact of such policies, but one policy that we can evaluate takes the form of a subsidy to
integrated neighborhoods. Table 6 shows the effects of this subsidy. Comparing the coefficients
here to the values in Table 3 shows that the effects of the maximum subsidy, 0.5, almost exactly
counteract the effects of historical discrimination (except for in the case of white mild
integrationists, who are more likely to be able to live in an integrated neighborhood with the
presence of the full subsidy than they would have been in the absence of both the subsidy and
past discrimination.) This suggests that there may in fact be government policies that could
correct for the negative effects of past discrimination on people's ability to achieve their desired
level of racial integration.
7 Conclusion
By extending and modifying the simple framework developed by Thomas Schelling, we
have created a model of U.S. residential segregation that has several important implications. We
find that the strength of preferences for integration and the number of agents of each racial and
integration preference type have complex effects on the percent of integrationists who are able to
live in integrated neighborhoods. One simple result is that the more integrationist the full
integrationist whites are, the more agents will be able to live in integrated neighborhoods; the
preferences of the integrationist whites have a much stronger impact than those of the
integrationist blacks. Another is that the more white full integrationist whites there are, the lower
the percent of full integrationists (both white and black) who find integrated neighborhoods to
live in, but higher the percent of white mild integrationists who do; this is because when there are
more integrationist whites, the integrated neighborhoods will be a higher fraction white, so the
mild integrationists will be more comfortable there. Unfortunately, this means they push out
some full integrationists.
In addition, we find that historic segregation impedes diversity-seeking agents from
achieving the integration they desire. Indeed, the legacy of past discrimination is such a
powerful force against integration that it appears to make current discrimination somewhat
irrelevant in maintaining segregation. Because this legacy is in part the result of past government
action, and because this high level of segregation is sub-optimal both for individual preferences
and for many social outcomes, government action to counter the effects of past segregation
appears appropriate. We studied one simple version of possible government action, and found
that it could be successful in facilitating integration in historically segregated environments,
making individuals better off.
Appendix: Executing the Simulations
Our model was written using Repast, a set of Java libraries made to be used in developing
agent-based models in Java. Each agent in the model is one of five types: white isolationist,
white mild integrationist, white full integrationist, black isolationist and black full integrationist.
Each agent lives on a 50 x 50 grid of squares, where each square represents a house. This grid is
divided into a 5 x 5 grid of neighborhoods, each of which is made up of a 10 x10 grid of houses.
Each type is given piecewise linear preferences as shown in Figure 2. If the x-axis gives
percent other race in the agent's neighborhood, we can describe the utility of isolationists with 3
points: (0,1), (21.4,0.5) and (100,0). Mild integrationist preferences are defined by (0,
0.313),(21.4, 0.5), (32.1, 1), (42.9, 0.5) and (100, 0); full integrationist preferences are defined by
(0, 0.25), (7.1, X), (50, 1), (85.7, Y), (100,0). X and Y are the parameters described on page 13.
There are 2500 houses and the vacancy rate is 30% (following Schelling), so there are
1750 agents. Each agent gets a randomly generated x-coordinate (not to be confused with their
assigned utility value X) and a randomly generated y-coordinate. If there is already an agent at
that point then a different point is generated; if not, the agent is placed at that point. There are
two ways these agents are then given identities: random and historic. In the random distribution,
88% of the agents are white and 12% are black. In the historic distribution each neighborhood is
randomly assigned a value for percent black based on the distribution in Table A. 1, which comes
from the racial distribution of metropolitan census tracts in 1970 (U.S. Census, 1970). The table
divides the interval [0% black, 100% black] into 13 sub-intervals and shows the percentage of
neighborhoods which had a percent black in that interval:
Table A.1
Percent Percent of
Black Neighborhoods
0
40.9
(0,1]
29.7
(1, 10]
7.3
(10,20]
5.5
(20,30]
2.9
(30, 40]
1.8
(40, 50]
1.4
(50, 60]
1.3
(60, 70]
1.3
(70, 80]
1.3
(80, 90]
1.8
(90, 100)
4.5
100
0.4
On the micro level, each agent is then randomly assigned a race based on the macro racial
distribution assigned to the agent's initial neighborhood. In both setups, each white agent then
has a 94% chance of being isolationist, a 3% chance of being mildly integrationist and a 3%
chance of being fully integrationist; each black agent has a 25% chance of being isolationist and
a 75% chance of being fully integrationist.
The body of the program then consists of the agents moving. In each period, each agent
has a chance to move, in a random order. A move consists of three steps. First, the agent
determines its current utility, which is the utility for that agent's type given the racial
composition of the agent's current neighborhood. Second, the agent looks at the other
neighborhoods and determines how many of the other neighborhoods it would be happier in. If it
would not be happier in any other neighborhood, it stays where it is. If it would be happier in at
least one other neighborhood, it picks a neighborhood to move to. (If it would be happier in more
than one other neighborhood, it chooses randomly among them.) Third, the agent randomly
chooses a vacant spot in that neighborhood to move to. If there is no vacant spot it does not
move.
We explore the impact of discrimination by modifying this process. In the second step of
the modified moving process, a white agent is able to consider every neighborhood and choose
the best one. A black agent, however, may not be allowed to choose some of the majority white
neighborhoods. When a black agent is evaluating the neighborhoods, the program generates a
random number between 1 and 100 for each majority white neighborhood. If that number is less
than f(p), where f(p) is an increasing function of the fraction p of whites in the neighborhood,
then the agent is not allowed to consider that neighborhood.. We chose f(p) = 100*4/3*Z(p*p.25) for p >= .5 where Z is the discrimination parameter. This function has the general shape
shown in figure 6; it is always 0 at .5 and increases quadratically until it reaches Z at 1.
The simulation continues, with each agent getting one chance to move during each
period, until there is a period where no agent moves, which is a stable distribution. The data is
then collected for that simulation: number of agents of each type, number of integrated
neighborhoods, percent of each type living in an integrated neighborhood, average utility of each
type, and number of periods necessary to reach stability.
When we run simulations for discrimination and subsidy we don't run through all the
values of X and Y because we have already explored their effects; we want to study the effects of
discrimination and policy in the most realistic context possible. For these sections, we leave Y at
0.3 and vary X from .6 to .75 in steps of .05. These are also the most conservative values to use,
because a low Y and a high X makes the agents less integrationist.
Because the definition of an integrated neighborhood that is used in the policy simulation
is different from the definition used in the data (at least 25% each race, rather than at least one
agent of each race), we cannot calculate from the data collected exactly how many agents receive
the subsidy at the end of the simulation. For each integrationist type, we took the percent
integrated and multiplied that by the subsidy to get an estimate of the average subsidy received
by an agent of that type. This is an upper bound estimate, because it assumes that all agents who
live in neighborhoods containing at least one agent of each race live in neighborhoods where at
least 25% of the residents are of each race and thus receive subsidies; some of these agents might
not receive the subsidy, so this is an overestimate of the average subsidy.
References
Bobo, L,, J. Johnson, M. Oliver, R. Farley, B. Bluestone, I. Browne, S. Danziger, G. Green, H.
Holzer, M. Krysan, M. Massagli, C. Charles, J. Kirschenman, P. Moss, and C. Tilly, 1994.
Multi-City Study of Urban Inequality. Ann Arbor, MI: Inter-University Consortium for Political
and Social Research Study #2535.
http://data.fas.harvard.edu
Cutler, David, Edward Glaeser, and Jacob Vigdor, 1999. "The Rise and Decline of the American
Ghetto," Journalof PoliticalEconomy 107(3): 455-506.
Farley, R. and H. Schuman, 1976. Detroit Area Study, 1976: A Study of Metropolitan and
Neighborhood Problems. Ann Arbor, MI: Inter-University Consortium for Political and Social
Research Study #7906. http://data.fas.harvard.edu
Galster, G., 1992. The Metropolis in Black and White. New Brunswick, NY: Center for Urban
Policy Research.
Goering, J. and R. Wienk (eds.), 1996. MortgageLending, RacialDiscriminationandFederal
Policy. District of Columbia: Urban Institute Press.
Kain, J., 1968. "Housing Segregation, Negro Employment, and Metropolitan Decentralization,"
QuarterlyJournalofEconomics 82:175:97.
Kain, J., 1992. "The Spatial Mismatch Hypothesis: Three Decades Later." Housing Policy
Debate 3(2):371-460.
Krysan, Maria and Reynolds Farley, 2002. "The Residential Preferences of Blacks: Do They
Explain Persistent Segregation?" Social Forces 80(3): 937-980.
Lee, B.A. and K.E. Campbell. "Common ground? Urban neighborhoods as survey respondents
see them." Social Science Quarterly 78.4 (1997): 922-936.
Lewis Mumford Center. "Ethnic Diversity Grows, Neighborhood Integration Lags Behind."
MetropolitanRacial andEthnic Change- Census 2000. 2001. 22 Jul 2002
<http://mumford1.dvndns.org/cen2000/WholePop/WPreport/page1 .html>
Massey, D. and N. Denton, 1988. "Residential Segregation of Blacks, Hispanics, and Asians by
Socioeconomic Status and Generation," Social Science Quarterly69.
Massey, D. and N. Denton, 1993. American Apartheid: Segregation and the
Making of the Underclass. Cambridge: Harvard University Press.
Orfield, G. and S. Eaton, 1996. DismantlingDesegregation:The Quiet Reversal of Brown v.
Board ofEducation. New York, NY: W.W. Norton and Company.
100
Schelling, T.C. "Dynamic Models of Segregation." Journalof MathematicalSociology 1(1971):
143-186.
Sims, Mario, 1999. "High-Status Residential Segregation among Racial and Ethnic Groups in
Five Metro Areas, 1980-1990," Social Science Quarterly80(3): 556-73.
St. John, Craig and Robert Clymer, 2000. "Racial Residential Segregation by Level of
Socioeconomic Status," Social Science Quarterly81(3): 701-15.
Turner, Margery Austin, et. al., 2002a. Discriminationin Metropolitan HousingMarkets:
NationalResults from PhaseI HDS 2000. Washington, DC: The Urban Institute.
Turner, Margery Austin, et. al., 2002b. All Other Things Being Equal: A PairedTesting Study of
MortgageLending Institutions. Washington, DC: The Urban Institute.
Yinger, John. 1995. "Opening Doors: How to Cut Discrimination by Supporting Neighborhood
Integration." Syracuse University Center for Policy Research Policy Brief No. 3/1995.
101
Table 1: Summary statistics for each of the three sets of simulations-parameters and randomized variables
Historical
discrimination
Current
discrimination
Subsidy
(1)
Main
Simulations
0.50
(0.002)
(2)
Current
discrimination
0.76
(3)
111
Subsidy
1
(0.006)
(0)
0.25
(0.003)
0.5
(0.003)
0.25
(0.002)
PanelA: Preferenceparameters
White X
Black X
White Y
Black Y
White X-Y ratio
Black X-Y ratio
0.62
(0.0005)
0.62
(0.0005)
0.43
(0.0005)
0.43
(0.0005)
1.48
(0.002)
1.48
(0.002)
0.69
0.67
(0.0009)
(0.0006)
0.69
0.3
0.66
(0.0005)
0.3
(0)
(0)
(0)
(0)
(0.0009)
0.3
0.3
PanelB: Percentof each type of agent
Pct white
Isolationists
Pct white mild
integrationists
Pct white full
integrationists
Pct black
Isolationists
Pct black
integrationists
82.26
(0.016)
2.64
(0.002)
3.03
(0.005)
3.02
(0.005)
9.05
(0.013)
81.91
81.70
(0.051)
2.63
(0.004)
(0.064)
2.64
(0.006)
3.29
(0.009)
3.04
(0.018)
9.11
(0.051)
3.51
(0.005)
3.04
(0.014)
9.12
(0.041)
Observations
42,665
4,660
9,240
For each variable used, this shows the mean for each of the three sets of simulations,
with standard errors in parentheses
102
V
oC
o
0)
00
m
0
6Z
,
0
00,
0
O
0-.
0
z
o
C4
co
I--
Cl%
tr)
00
C-
.0
0
ci
Ro
C'
Z
0
0
0
.,
G.O0
0nOvf
C; 00
Mv W)C1
6t M
c
-
-
-4
-
, t , f) "' I..
06400600
N
0N
00
W.-
0
Z
'
Ud
..
o
.8
.L
.,
tz8
0
Ud
u-
0a
S0
103
U'Dc
;m.5
Table 4: Effects of controls on the percentage of each type of integrationist agent living in integrated
neighborhoods, in simulations with historic discrimination
(1)
Overall
PanelA: Preferenceparameters
White X
-19.042
Black X
White Y
Black Y
White X-Y
Ratio
Black X-Y
Ratio
(2.471)**
8.881
(1.508)**
28.843
(2.633)**
-9.575
(1.781)**
4.507
(0.444)**
-3.245
(0.445)**
(3)
(4)
White mild
White full
Black full
48.804
(15.545)**
-13.754
(9.548)
-123.836
(18.731)**
-127.446
(18.644)**
79.672
(11.375)**
185.763
(19.860)**
-89.181
(13.433)**
32.315
(3.348)**
-28.336
(3.358)**
(2)
-34.528
(16.525)*
15.420
(11.234)
5.280
(2.782)
0.036
(2.819)
PanelB: Percentof each type of agent
Pct white mild
0.727
-3.612
Integrationists
(1.105)
(6.925)
Pct white full
-5.593
-7.238
Integrationists
(1.110)**
(6.955)
Pct black
2.050
-28.900
Isolationists
(1.202)
(7.526)**
Pct black
2.314
-34.211
Integrationists
(1.189)
(7.450)**
Panel C: Percent of each type of agent,squared
Pct white
0.011
-0.138
isolationists, sq
(0.040)**
(0.006)
Pct white mild
0.172
-3.542
integrationists, sq
(0.142)
(0.887)**
Pct white full
1.102
-1.284
integrationists, sq
(0.081)**
(0.508)*
Pct black
-0.075
0.814
(0.034)*
(0.215)**
isolationists, sq
Pct black
-0.028
0.443
integrationists, sq
(0.008)**
(0.051)**
PanelD: Interactions
White X * Pct white
full integrationists
White Y * Pct white
full integrationists
Black X * Pct black
full integrationists
Black Y * Pct black
full integrationists
-1.895
(0.615)**
0.640
(0.615)
0.213
(0.085)*
-0.258
(0.088)**
-24.032
(3.872)**
28.068
(3.857)**
0.908
(0.537)
-1.444
(0.551)**
82.527
(11.505)**
183.488
(19.912)**
-84.585
(13.537)**
30.438
(3.352)**
-27.242
(3.397)**
18.733
(8.345)*
-53.500
(8.380)**
31.995
(9.069)**
29.290
(8.977)**
22.803
(8.343)**
-46.923
(8.378)**
34.458
(9.070)**
31.117
(8.974)**
0.174
0.187
(0.048)**
(0.048)**
1.207
(1.068)
11.034
(0.612)**
-0.821
(0.259)**
-0.183
(0.061)**
1.027
(1.068)
10.676
-15.353
(4.665)**
8.462
(4.648)
1.045
(0.646)
-1.772
(0.664)**
(0.608)**
-0.811
(0.259)**
-0.205
(0.061)**
-18.091
(4.640)**
10.989
(4.638)*
1.440
(0.639)*
-1.434
(0.665)*
21216
20795
Observations
20797
21216
0.1864
0.2056
0.1356
0.2371
R-squared
The dependent variable is the percent of each type of integrationist agent who live in
integrated neighborhoods. All observations are from the main set of simulations and
were run from an initially segregated distribution. Standard errors are in parentheses.
* significant at 5%; ** significant at 1%
104
U,
04
0
t
0
o
I
I
t
00 00
I
V0
-4
0-0
roo\rc
•75 ~
.;N•
t~vl
4..-
o
• eC'J •
00
rn1;
og
a0
0O
Cd
Cd0
4-
105
0
Q)
ou
0
~o
;-
0o
so oo
ag)
106
9
Table 6: The effect of subsidies on the percent of integrationist agents who live in integrated neighborhoods
Subsidy
Current
Discrimination
Controls
(1)
White mild
67.234
(1.803)**
-1.215
(0.974)
(2)
White full
60.322
(1.893)**
-1.347
(1.022)
(3)
Black full
59.753
(1.842)**
-3.363
(0.995)**
(4)
Overall
9.268
(0.252)**
-0.305
(0. 136)*
Yes
Yes
Yes
Yes
Observations
9240
9240
9239
9240
R-squared
0.2216
0.1713
0.2080
0.1491
The dependent variable is the percent of each type of integrationist agent who live in integrated
neighborhoods. Each regression includes controls for preference parameters and percentages of
each type of agent. These regressions are run using the third set of simulations, which focus on
the subsidy. Standard are errors in parentheses.
* significant at 5%; ** significant at 1%
107