Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Survey

Abstract

Individuals' preferences underlying most economic behavior are likely to display substantial heterogeneity. This paper reports on direct measures of preference parameters relating to risk tolerance, time preference, and intertemporal substitution. These experimental measures are based on survey respondents' choices in hypothetical situations. The questions are constructed with as little departure from the theorist's concept of the underlying parameter as possible. The individual measures of preference parameters display substantial heterogeneity. The majority of respondents fall into the least risk-tolerant group, but a substantial minority display higher risk tolerance. The individual measures of intertemporal substitution and time preference also display substantial heterogeneity. The mean risk tolerance is 0.25; the mean elasticity of intertemporal substitution is 0.2. Estimated risk tolerance and the elasticity of intertemporal substitution are essentially uncorrelated across individuals. Because the risk tolerance measure is obtained as part of the main questionnaire of a large survey, it can be related to a number of economic behaviors. Measured risk tolerance is positively related to a number of risky behaviors, including smoking, drinking, failing to have insurance, and holding stocks rather than Treasury bills. Although measured risk tolerance explains only a small fraction of the variation of the studied behaviors, these estimates provide evidence about the validity and usefulness of the measures of preference parameters.

Full text

PREFERENCE PARAMETERS AND BEHAVIORAL
HETEROGENEITY:
AN EXPERIMENTAL APPROACH IN THE HEALTH AND
RETIREMENT STUDY*
R
OBERT
B
.
B
ARSKY
F
.
T
HOMAS
J
USTER
M
ILES
S
.
K
IMBALL
M
ATTHEW
D
.
S
HAPIRO
This paper reports measures of preference parameters relating to risk toler-
ance, time preference, and intertemporal substitution. These measures are based
on survey responses to hypothetical situations constructed using an economic the-
orist’s concept of the underlying parameters. The individual measures of prefer-
ence parameters display heterogeneity. Estimated risk tolerance and the
elasticity of intertemporal substitution are essentially uncorrelated across indi-
viduals. Measured risk tolerance is positively related to risky behaviors, including
smoking, drinking, failing to have insurance, and holding stocks rather than Trea-
sury bills. These relationships are both statistically and quantitatively signifi-
cant, although measured risk tolerance explains only a small fraction of the
variation of the studied behaviors.
I. I
NTRODUCTION
A recurrent theme in Amos Tversky’s remarkable output is
the description of individual preferences and their relation to
choice behavior. In particular, Tversky’s work is concerned with
achieving a better match between theory and empirical evidence
with respect to behavior toward risk.
1
Tversky was most con-
cerned with situations in which the evidence seems to contradict
expected utility theory. While in this paper we adhere to an ex-
pected utility benchmark, Tversky’s concern with explaining indi-
vidual behavior in a variety of situations also impels our work.
This paper describes the results of an experimental attempt
to elicit individual preference parameters by means of direct
questions closely derived from economic theory, and to study
the behavioral implications of heterogeneity in the measured
*This research was supported by a program project grant from the National
Institute of Aging, “Wealth, Saving, and Financial Security Among Older House-
holds,” PO1 AG10179-03. Barsky and Shapiro also acknowledge the support of
the Alfred P. Sloan Foundation. Carlos Quintanilla and Lisa Sanchez provided
excellent research assistance. We gratefully acknowledge the constructive and
critical comments of John Campbell, Lawrence Katz, Robert Shiller, Richard Tha-
ler, anonymous referees, and numerous seminar and conference participants.
1. See, for example, Kahneman and Tversky [1979, 1981, 1982].
q1997 by the President and Fellows of Harvard College and the Massachusetts Institute
of Technology.
The Quarterly Journal of Economics, May 1997.
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parameters across individuals. Participants in the Health and
Retirement Study were asked to respond to hypothetical situa-
tions specifically designed to elicit information about their risk
aversion, subjective rate of time preference, and willingness to
substitute intertemporally. These three parameters are essential
to individual choices about wealth accumulation, retirement,
portfolio allocation, and insurance, as well as to policy choices
that are dependent on this behavior.
Despite the analytic importance of these preference parame-
ters, econometric studies have not fully resolved issues involving
even their mean values. Indeed, even when the underlying pa-
rameter is constant across individuals, econometric estimation
often relies on problematic identifying restrictions. The econome-
trician typically needs to posit a functional form. Instrumental
variables are needed to control for potential endogeneity. The sur-
vey approach addresses these issues by constructing a survey in-
strument that is designed precisely to elicit the parameter of
interest while asking the respondent to control for differences in
economic circumstances that confound estimation. While the sur-
vey approach introduces other problems—for example, whether
the respondents are giving accurate answers—it can provide a
potentially important source of information about these parame-
ters in addition to econometric evidence.
Econometric estimation of preference parameters may be
particularly inadequate when heterogeneity of preferences in the
population is important. In this case it may be desirable to have
an estimate of the parameters of interest for each individual in a
cross section, not just the average value of that parameter in the
population. In a cross section one would be able to study the co-
variation between the estimated parameters and observed behav-
ior with regard to saving, portfolio choice, labor supply, insurance
purchases, etc. Absent enough data to estimate the econometric
model for each individual (i.e., a long panel), the standard econo-
metric approaches cannot assign values of parameters to spe-
cific individuals.
The underlying purpose of our research is to explore the pos-
sibility of obtaining information about theoretically important
parameters from direct questions involving choice in hypothetical
situations, with as little departure from the theorist’s concept of
a parameter as possible. We obtain our measure of risk aversion
by asking respondents about their willingness to gamble on life-
time income. By contrast, experiments in the existing literature
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typically involve stakes that have little impact on lifetime re-
sources. A gamble whose outcome is uncorrelated with consump-
tion should not require a risk premium.
We obtain our measures of intertemporal substitution and
time preference by asking respondents to choose consumption
profiles implicitly associated with different rates of return. Ac-
cording to the relevant economic theory, the two parameters are
the solution of two equations in two unknowns. The questions
typically asked about time preference in the literature do not
properly distinguish between the subjective discount rate and the
market rate of interest. As we emphasize in Section II, the rate
at which individuals are willing to trade off present and future
consumption depends on both. By asking for the preferred con-
sumption path at more than one interest rate, we are able in prin-
ciple to separate time preference from the market interest rate.
The organization of the paper is as follows. In Section II we
spell out our methods for measuring risk preference, intertempo-
ral substitution, and time preference. In Section III we report our
results for the questions about risk preference. In Section IV we
apply these results to the equity premium puzzle. In Section V
we report our results for questions about preferred consumption
paths. In Section VI we discuss some caveats about the survey
and extensions of the modeling of the results. In Section VII we
present our conclusions.
II. M
ETHODOLOGY
A. Measuring Risk Aversion
The principal requirement for the question aimed at measur-
ing risk aversion is that it must involve gambles over lifetime
income. After considerable testing,
2
in which the precise nature
of the hypothetical circumstances was refined several times to
minimize misunderstandings and additional complications envi-
sioned by respondents, we arrived at the following question.
3
2. We tested preliminary versions of the survey instruments on two groups.
Versions of the questions were first given to undergraduate economics students.
Based on the student responses, we refined the questions. They were then tested
as part of the standard Survey Research Center procedure for testing survey in-
struments. This phase of testing is meant to uncover difficulties respondents
might have in interpreting the questions.
3. The questions ask about income rather than spending or consumption.
After pretesting, we concluded that survey respondents would better understand
income than consumption lotteries. Given the low levels of financial wealth of
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most respondents, permanent labor income and permanent income are not that
different. We investigate (see below) the extent to which high-wealth and older
individuals respond differently to the questions. See question L14 of the Health
and Retirement Study, Wave I (page 162 of the survey instrument).
Suppose that you are the only income earner in the family, and you
have a good job guaranteed to give you your current (family) income
every year for life. You are given the opportunity to take a new and
equally good job, with a 50–50 chance it will double your (family)
income and a 50–50 chance that it will cut your (family) income by
a third. Would you take the new job?
If the answer to the first question is “yes,” the interviewer
continues:
Suppose the chances were 50–50 that it would double your (family)
income, and 50–50 that it would cut it in half. Would you still take
the new job?
If the answer to the first question is “no,” the interviewer
continues:
Suppose the chances were 50–50 that it would double your (family)
income and 50–50 that it would cut it by 20 percent. Would you then
take the new job?
The questions separate the respondents into four distinct risk
preference categories, depending on the answers to two ques-
tions. The categories can be ranked by risk aversion without hav-
ing to assume a particular functional form for the utility function.
The categorical responses (labeled I, II, III, and IV) are summa-
rized in the first column of Table I.
The categorical responses can be thought of as resulting from
the following expected utility calculation. Let Ube the utility
function and cbe permanent consumption. An expected utility
maximizer will choose the 50–50 gamble of doubling lifetime in-
come as opposed to having it fall by the fraction 1 2lif
(1)
1
2
2Uc Uc Uc() () (), +
1
2
λ≥
that is, the expected utility of the income stream offered by the
gamble exceeds the expected utility of having the current income
stream with certainty.
If one is willing to assume that relative risk aversion 1/u5
2c
?
U99/U9is constant over the relevant region, the categorical
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TABLE I
R
ISK
P
REFERENCE
S
URVEY
D
ESIGN
Expectation
conditional
Relative risk aversion Relative risk tolerance on survey
(1/u)(u)
response
c
Upper Lower Lower Upper
Gamble
a
bound bound Mean
b
bound bound Mean
b
1/uu
I. Reject both one-third ∞3.76 15.8 0 0.27 0.11 15.7 0.15
and one-fifth
II. Reject one-third but 3.76 2 2.9 0.27 0.5 0.36 7.2 0.28
accept one-fifth
III. Accept one-third but 2 1 1.5 0.5 1 0.68 5.7 0.35
reject one-half
IV. Accept both one-third 1 0 0.7 1 ∞1.61 3.8 0.57
and one-half
a. Gambles all have a 50 percent probability of doubling lifetime income and a 50 percent probability of losing half, one-third, or one-fifth of lifetime income.
b. These columns report the mean if the true value is between the lower and upper bounds.
c. These columns give the expected value of relative risk tolerance and relative risk aversion conditional on observing response I, II, III, or IV. This conditional expectation takes
into account measurement error in the survey response. This baseline case assumes lognormality, no status quo bias, and no persistent measurement error. (See text for details and
Table XIV for other cases.)
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responses bound the values of relative risk aversion. Table I gives
the upper and lower bounds on relative risk aversion correspond-
ing to the choices I, II, III, and IV. For most of the analysis we
work with the reciprocal of relative risk aversion, called “relative
risk tolerance” in the finance literature. Risk tolerance, unlike
risk aversion, aggregates linearly. Table I also gives the ranges of
relative risk tolerance uconsistent with the choices. The lower
bound on relative risk tolerance is the reciprocal of the upper
bound on relative risk aversion and vice versa. Table I includes
the mean relative risk aversion and tolerance corresponding to
these ranges. This mean depends on the distribution of the pref-
erence parameter in the population. We discuss in the next sec-
tion how we estimate this distribution and how we construct the
estimates in the last two columns of Table I.
4
One important criticism of this survey question is that re-
spondents might value their current job for reasons other than
the income flow associated with it and therefore might be reluc-
tant to switch jobs even for a high expected increase in income.
This “status quo bias” would tend to reduce the estimate of risk
tolerance because it gives a reason in addition to risk aversion
for individuals to express an unwillingness to accept the gamble.
In Section VI of the paper we address the issue of status quo bias
by offering a quantitative assessment of its potential impact on
our results and a suggestion for eliminating status quo bias in
future surveys.
B. Measuring Time Preference and the Elasticity of
Intertemporal Substitution
Our experimental survey also sought to develop estimates of
the desired slope of the path of consumption over time and the
willingness of individuals to alter the slope of the consumption
path in response to changes in the interest rate. These choices
relate to two preference parameters: the rate of time preference
and the elasticity of intertemporal substitution. To estimate these
parameters, we attached an experimental set of questions to
Wave I of the Health and Retirement Study (designated Module
K). In contrast to the questions about gambles over lifetime in-
4. The numerical results are not that sensitive to the choice of a constant
relative risk aversion parameterization. For example, with constant absolute risk
aversion the bounds on risk tolerance consistent with the responses would be 0.30,
0.55, and 1.04 instead of the values of 0.27, 0.5, and 1.0 given in Table I for con-
stant relative risk aversion.
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come, which are part of the main Health and Retirement Study
questionnaire, the questions in the modules were asked only of a
small subset of respondents.
The basic behavioral equation underlying our survey design
for capturing time preference and intertemporal substitution is
(2)
∆log( ) ( ),csr =−ρ
where cis consumption, ris the real interest rate, ris the subjec-
tive discount rate, and sis the elasticity of intertemporal substi-
tution. Equation (2) says that if the real interest rate is greater
than the rate of time preference, consumption will be growing
over time. If the rate of time preference is less than the interest
rate, agents start out with relatively low consumption in order to
save and take advantage of the high rate of return. This effect
will be larger the larger is s, which measures the strength of the
willingness to intertemporally substitute in consumption. Given
rand s, the larger is r, the less upward-sloping will be the chosen
consumption path, as households discount the future more heav-
ily. If r,r, the interest rate is not high enough to overcome the
subjective discounting of the future, and agents choose consump-
tion paths that (in expectation) fall as they age.
5
In the module we first posed a hypothetical set of circum-
stances that are meant to control for heterogeneity in economic
and demographic conditions facing the household. (In particular,
respondents were told to assume no inflation and that they would
have no uninsured health expenses.) Then the respondents were
shown charts with different profiles of consumption with constant
present value at a zero interest rate and were asked to choose the
preferred path. In subsequent questions they were asked to
choose among constant present value consumption paths with in-
terest rates of 4.6 and 24.6 percent per year. From the slopes of
the preferred paths and how the slopes change when the interest
rate changes, one can estimate the rate of time preference and
the elasticity of intertemporal substitution. Appendix 3 contains
the exact wording of the question and the charts containing the
consumption profiles from which the individuals chose.
5. Equation (2) is nominally the same Euler equation routinely estimated on
time series data by macroeconomists [Hansen and Singleton 1983; Mankiw 1981;
Hall 1988]. It can be derived by assuming a time-separable, constant relative risk
aversion utility function, so that uequals s. Our survey design does not depend
on a particular maximization problem. In particular, uneed not equal s. Indeed,
we will compare the results of the risk preference and intertemporal substitution
questions to test this restriction.
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C. The Survey Instrument
The questions were included in Wave I of the Health and Re-
tirement Study (HRS), administered to a large cross section of
households in 1992.
6
The target respondents were between the
ages of 51 and 61 in 1992. The survey also includes their spouses.
The full survey, which takes about two hours, was conducted face-
to-face in the field. Respondents are paid for their participation.
The HRS asks a wide range of questions concerning health sta-
tus, retirement decisions, income, and assets. It also asks a num-
ber of behavioral questions, such as whether the individual
smokes or drinks. In the case of couples, questions that pertain
to individuals—including our questions on risk preference and
intertemporal consumption preferences—are asked of both.
Questions pertaining to the household as a whole, e.g., about
wealth, are asked only of a primary respondent. The primary re-
spondent is the member of the couple “most knowledgeable”
about the family’s assets, debts, and retirement planning.
7
The survey yielded 11,707 responses to the risk preference
questions, 7278 from primary respondents and 4429 from second-
ary respondents. Appendix 1 gives some summary statistics. The
average age of 55.6 years reflects the sampling frame. Primary
respondents, who are disproportionately male, are a little older
and have a little more education.
8
The experimental intertempo-
ral consumption preference questions were given only to a very
small subsample, yielding only 198 observations.
The risk preference questions were also included in one of
the modules of Wave II of the Health and Retirement Study,
which was conducted by telephone. This module was asked of
roughly 10 percent of the sample, most of whom responded to the
questions on Wave I. We use the multiple responses to the ques-
6. The HRS is a representative sample within this age group, except that
blacks, Hispanics, and residents of Florida are 100 percent oversampled. See Jus-
ter and Suzman [1995] for an overview of the survey. Further information and
public-release data are available on the worldwide web at http://www.
umich.edu/∼hrswww.
7. The first person contacted is asked to identify the most knowledgeable
member of the family. There is a slight propensity for the first person contacted
to overreport himself or herself as the most knowledgeable. For this point, and
for a general analysis of this feature of the HRS, see Hill [1993]. Members of
couples need not be married. In our sample, one-third of the secondary respon-
dents are males (see Appendix Table I).
8. The fraction of respondents who are black and Hispanic represents the
oversampling of these groups in the HRS. Further demographic breakdowns are
given in the tables below where we report the results for the risk preference
question.
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tion to estimate the measurement error associated with the
responses.
III. P
REFERENCE OVER
L
IFETIME
I
NCOME
G
AMBLES
We find substantial heterogeneity in the estimates of risk
preference.
• The response exhibiting least risk tolerance is strongly
modal. Hence, low risk tolerance characterizes most of the
population.
• Nonetheless, there is substantial heterogeneity in risk tol-
erance. A significant fraction of the sample exhibited willing-
ness to undertake substantial gambles over lifetime income.
• The measured risk tolerance has predictive power for
choices over risky behaviors—the decisions to smoke and
drink, to buy insurance, to immigrate, to be self-employed,
and to hold stock. The behaviors studied are, nevertheless,
very noisy and difficult to explain; the incremental predictive
power of risk tolerance is never very high.
In this section we present tabulations, cross tabulations, and re-
gressions that establish these findings.
A. The Distribution of True and Measured Risk Tolerance
The survey groups the respondents into the four risk toler-
ance categories detailed in Table I. The survey response is, how-
ever, likely to be subject to noise. In this subsection we describe
a procedure for estimating the distribution of the true parameter
and the distribution of the noise.
9
This procedure is possible be-
cause a subset of respondents answered the risk tolerance ques-
tions in both Wave I and Wave II of the Health and Retirement
Study.
10
By studying how the responses correlate across waves,
we can quantify the signal and noise in the survey responses.
Consider the following model of relative risk tolerance, de-
noted u
j
. Let
(3)
x
jj
=log( )θ
be the logarithm of individual j’s true relative risk tolerance, and
let «
jk
be an independent error associated with the individual’s
9. See Kimball and Shapiro [1996] for a more complete discussion of this
statistical issue.
10. We do not use any other information from Wave II.
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response to the survey k(k5Wave I or Wave II). The true pa-
rameter is assumed to remain constant. The realized log risk
tolerance,
(4)
yx
jk j jk
+ ,=ε
equals the true log risk tolerance plus the error. Let B
i
be the
range of log risk tolerance for category i5I, II, III, and IV.
We assume that an individual will choose response iif y
jk
[
B
i
. That is, there is noise in how an individual will report his or
her risk tolerance on a given day, but given the noise, the individ-
ual calculates correctly which gamble to accept.
11
Note that this
model is quite different from the standard latent variable model.
In the standard model the latent variable x
j
and the cutoffs defin-
ing B
i
are based on an arbitrary index. In contrast, our latent
variable is a cardinal preference parameter, and the cutoffs are
known numbers.
To identify the statistical model requires strong assump-
tions. In particular, the estimation scheme presumes that the
persistent component of responses represents true preferences.
In Section VI we relax this assumption to allow for a persistent
component to the error in the responses.
With one response per individual we would have been able
to estimate only the distribution of y
jk
, not the distribution of the
true parameter x
j
. But 717 individuals responded to the risk pref-
erence questions on both waves. Appendix 2 gives the joint distri-
bution of responses to both waves.
12
This empirical distribution
allows us to estimate the distribution of the true parameter and
to quantify the noise. To implement this statistical model, we as-
sume that u
j
is distributed lognormally across individuals.
13
The
maximum likelihood estimate of the mean of log risk tolerance x
j
is -1.96. The estimated standard deviation of xis 1.03 and of «is
1.39.
14
These parameter estimates yield a mean true risk toler-
11. An alternative would be that there is no noise in the preference parame-
ter, but the individual uses noisy cutoffs. The former interpretation implies some
noise in preferences. The latter places the noise in interpreting the questions.
These two interpretations yield the same statistical model.
12. The univariate distributions in the two waves are nearly identical.
Hence, for example, risk tolerance is not drifting as the panel ages.
13. The estimation uses all the observations, including those individuals who
answer only one of the two waves. The likelihood is constructed from the trivari-
ate normal distribution of x
j
,y
j1
, and y
j2
and the bivariate normal distribution of
x
j
and y
jk
for those who answered only k5Wave I or Wave II. Those who answer
only one wave help us estimate the distribution of y, while those who answer both
allow us to identify the distributions of xand «. The distributions are integrated
over the truncation intervals B for yto yield the likelihood.
14. Standard errors of the estimated parameters are approximately 0.01.
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ance uof 0.24. The estimated correlation of 0.60 between the true
(x) and reported (y) log risk tolerance is quite high.
Based on these assumptions, the last two columns of Table I
report the expectation of relative risk aversion (1/u) and relative
risk tolerance (u) conditional on an individual responding I, II,
III, or IV to the risk preference questions in Wave I.
15
Table I also
reports the means of the ranges for the true choices I, II, III, and
IV. If there were no measurement error, the means of the ranges
would be equal to the conditional expectations. Because of the
measurement error, the conditional expectation of the preference
parameter given the survey response reverts toward the uncondi-
tional mean.
Comparing the last two columns of Table I illustrates the im-
portance of Jensen’s inequality. The expectation of the reciprocal
is substantially greater than the reciprocal of the expectation.
The following subsections report results for the risk prefer-
ence survey questions. When we report mean risk tolerance or
include risk tolerance as a regressor, we use the conditional ex-
pectations shown in the last column of Table I.
16
We also present
cross tabulations based on the categorical responses. These do
not depend on the functional form of the utility function or our
statistical model for the measurement error.
B. Heterogeneity in Individuals’ Risk Tolerance
Table II gives the fraction of all respondents who fall into
risk tolerance groups I, II, III, and IV. Most respondents are in
category I, but a significant minority are in the higher risk toler-
ance categories.
17
Based on the estimated underlying lognormal
15. This expectation is computed by integrating e
2x
or e
x
over the joint proba-
bility distribution of xand y. It is also possible to compute the expectation condi-
tional on the survey response. We use these values below in the regression
analysis.
16. When an individual responded to both Wave I and Wave II, we condition
on both responses to assign the expected risk tolerance.
17. Shiller, Boycko, and Korobov [1992] report the results of a survey ques-
tion similar to ours. They asked a small sample of respondents from different
countries whether they would be willing to take a job at a 50 percent higher wage
than their current job if there were a 50-50 chance of failing at the job. In the
event of failure the respondent would get his or her old job back “after some time.”
Since the bad outcome entails only a temporary loss, this proposition is much less
risky than ours. (The aim is to elicit job-market flexibility, not risk tolerance.)
They find that 50 to 80 percent of respondents would take the new job, with Rus-
sians and West Germans less willing to take the new job than those in the United
States. The unwillingness of many to face even a temporary income loss for the
chance of a large, permanent gain would imply a high level of risk aversion.
Binswanger and Sillers [1983] report the results of experiments where parti-
cipants faced relatively large risks, ranging from 2.5 to 143 weeks of wages, but
are still small relative to lifetime resources. Absent enough information to calcu-
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TABLE IIA
R
ISK
T
OLERANCE BY
P
RIMARY AND
S
ECONDARY
R
ESPONDENTS
Percent choosing response Number of Mean risk
Respondent I II III IV responses tolerance
a
All respondents 64.6 11.6 10.9 12.8 11707 0.2412
Primary respondent 64.8 11.4 10.7 13.0 7278 0.2413
Secondary respondent 64.3 11.8 11.2 12.5 4429 0.2410
The p-value for the hypothesis that the mean risk tolerance is equal across primary and secondary
respondents is 0.92.
a. The mean risk tolerance is computed using the baseline parametric model.
density, the mean risk tolerance is 0.24, and the standard devia-
tion is 0.33.
18
Table II also gives the results separately for the
primary and secondary respondents. The distribution of re-
sponses across the four risk tolerance categories and mean risk
tolerance are nearly identical for the two groups.
TABLE IIB
P
RIMARY VERSUS
S
ECONDARY
R
ESPONDENTS
Percent choosing response
(column percent)
Primary respondent
Secondary Number of
respondent I II III IV responses
I 68.8 57.4 56.3 55.1 2692
II 10.8 17.5 11.6 11.8 494
III 9.4 12.4 18.7 12.8 466
IV 10.9 12.6 13.2 20.1 521
Number of
responses 2721 508 438 506 4173
Sample is limited to households with both a primary and secondary respondent. Columns give secondary
respondent’s risk tolerance conditional on primary respondent’s risk tolerance.
late the respondents’ marginal propensities to consume, it is impossible to directly
relate these estimates to ours. Indeed, Binswanger and Sillers emphasize the role
of credit constraints in interpreting their results. Our questions about lifetime
resources are designed to circumvent the need to know the marginal propensity
to consume.
18. The fractiles of the distribution of relative risk tolerance (u) are as
follows:
Fractile 0.05 0.10 0.25 0.50 0.75 0.90 0.95
u0.03 0.04 0.07 0.14 0.28 0.53 0.77.
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The second part of Table II shows the distribution of re-
sponses of the secondary respondent conditional on the response
of the primary respondent. The diagonal elements are substan-
tially larger than the unconditional distribution shown in the
first part of the table. The simple correlation of relative risk toler-
ance across household members is only 0.12, but is strongly sig-
nificant (t-statistic of 7.8).
19
Table III examines how risk preference varies by demo-
graphic group. There are substantial differences by age in esti-
mated risk tolerance. The youngest and the oldest cohorts are
TABLE III
R
ISK
T
OLERANCE BY
D
EMOGRAPHIC
G
ROUPS
Percent choosing response Number of Mean risk
Demographic group I II III IV responses tolerance
a
Age under 50 years 58.5 14.4 13.8 13.1 1147 0.2542
50 to 54 years 61.9 12.0 12.2 13.7 3800 0.2486
55 to 59 years 66.0 11.5 9.8 12.5 4061 0.2372
60 to 64 years 69.3 9.5 9.4 11.6 2170 0.2301
65 to 69 years 66.6 12.0 9.2 12.0 390 0.2331
Over 70 years 68.3 6.4 9.3 15.8 139 0.2432
Female 65.1 11.8 11.0 11.9 6448 0.2383
Male 64.0 11.2 10.7 13.9 5259 0.2448
White 64.9 12.5 10.7 11.8 8508 0.2377
Black 66.7 9.1 10.6 13.3 1884 0.2402
Other 62.3 10.0 13.7 13.7 109 0.2462
Asian 57.9 10.3 11.1 20.6 126 0.2762
Hispanic 59.3 9.2 12.6 18.7 1054 0.2666
Protestant 66.2 11.5 10.8 11.4 7404 0.2350
Catholic 62.3 10.8 11.4 15.3 3185 0.2514
Jewish 56.3 13.2 11.1 19.2 197 0.2683
Other 61.6 14.3 9.6 14.3 900 0.2498
The p-value for the hypothesis that the mean risk tolerance is equal across age groups is 0.0001, that it
is equal across sexes is 0.015, that it is equal across races is 0.0001, and that it is equal across religions
is 0.0001.
a. The mean risk tolerance is computed using the baseline parametric model.
19. This correlation is based on the conditional expectations from our para-
metric model of risk tolerance. The rank correlation, which is independent of our
parametric model, is 0.13. Some of this correlation arises from one spouse having
heard the other’s response to the same question. On the other hand, correcting
for measurement error would increase the estimated correlation. We have no
strong prior belief about the degree of correlation of the preference parameters of
married individuals. It is not clear that risk tolerance would be a key variable
upon which there is assortative mating.
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the most risk tolerant, with cohorts in the middle being less risk
tolerant. The groups under 55 years old choose the least risk tol-
erant option (I) relatively infrequently; the group over 70 chooses
the most risk tolerant option (IV) relatively frequently. Ages 55
to 70 are relatively risk intolerant. We can reject with a high de-
gree of confidence (p-value of 0.0001) that the mean risk toler-
ance of these age groups is equal.
There are also differences in risk tolerance by sex. Males are
somewhat more risk tolerant than females, with the biggest dif-
ference being in males’ propensity to choose the most risk-
tolerant option (IV). Again, the differences are statistically
significant.
There are noticeable differences in risk tolerance by the race
and religion of the respondent. Whites are the least risk tolerant,
blacks and Native Americans somewhat more risk tolerant, and
Asians and Hispanics the most risk tolerant. Again, the differ-
ences are easiest to see in the columns I and IV giving the ex-
treme responses. For example, Asians are seven percentage
points less likely than whites to choose the least risk-tolerant re-
sponse and are nine percentage points more likely to choose the
most risk-tolerant response. Risk tolerance also varies signifi-
cantly by religion. Protestants are the least risk tolerant, and
Jews the most. In risk tolerance Catholics are about halfway be-
tween Protestants and Jews.
C. Is Risk Tolerance Related to Behavior?
In this subsection we examine the extent to which measured
risk tolerance predicts risky behavior. Showing that our measure
of risk tolerance predicts behavior in the way one would expect
partially validates the survey measure. Psychologists studying
the conceptualization and measurement of personality traits
have been interested in what Mischel [1971] calls the issue of
“behavioral specificity.” Do individuals tend to show similar re-
sponses to all risky situations (e.g., financial, social, and health
risks), or is risk taking in one setting nearly independent of risk
taking behavior in other settings? Slovic cites a dozen studies ap-
parently showing that “the majority of the evidence argues
against the existence of risk-taking propensity as a generalized
characteristic of individuals.” (See Slovic [1972a, 1972b].) More
recently, however, questions measuring the characteristics of
“harm avoidance,” “novelty seeking,” and “reward dependence”—
no doubt closely related to risk aversion—have formed the basis
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of the much used Cloninger tridimensional personality scale. (See
Cloninger, Przybeck, and Svrakic [1991].) Some researchers in
neurology and psychiatry [Menza, Golbe, Cody, and Forman
1993] have reported evidence of a biological basis for particular
responses on the Cloninger scales, which suggests that they mea-
sure stable personality traits with some constancy across set-
tings. The results of this section can be used to evaluate whether
our survey measure captures a parameter that similarly has ex-
planatory power across behaviors.
Moreover, the relationship of measured risk tolerance with
various behaviors is something of interest in its own right. We
stop far short of constructing a complete theory of all the behav-
iors that are potentially related to risk preference. Rather, we
present cross tabulations analogous to the ones in the previous
subsection. We also estimate some simple, linear regressions in
an attempt to control for some correlates of risk preference.
The risk tolerance measure does predict risky behaviors—
including smoking, drinking, not having insurance, choosing
risky employment, and holding risky assets. These results are
often strongly significant statistically and are associated with
quantitatively significant coefficient estimates. We can decisively
reject the null that the measured preference parameters are un-
related to behavior. The fraction of the variance of the various
behaviors that our survey instrument explains is, however,
quite small.
20
Smoking and Drinking. The first three panels of Table IV
show the distribution of risk tolerance conditional on smoking
and drinking—behaviors that increase health risk.
21
The corre-
sponding regression estimates are reported in the first rows of
Table V. Individuals who have ever smoked are more risk tolerant
than those who never smoked and those who smoke now are more
risk tolerant than those who do not smoke now. Of particular in-
terest are those who say they once smoked, but do not smoke now.
The sample is largely composed of middle-aged to older individu-
als. Hence, those who quit smoking would have done so during a
20. Psychologists typically find that survey measures explain only a small
fraction of individual behavior. Mischel, in connection with his discussion of the
“personality coefficient,” notes that the fraction of cross-sectional variation in a
specific behavior that can be accounted for by responses to a survey questionnaire
typically ranges from .04 to .09 (see Mischel [1971], pp. 147–48).
21. Smoking and drinking have complicated effects on the distribution of fu-
ture income. Smoking and immoderate drinking reduce mean life expectancy, and
hence have a negative effect on expected income. They also increase income vari-
ance by increasing the probability that an individual will have a serious disease.
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TABLE IV
R
ISK
T
OLERANCE BY
B
EHAVIORS
Percent choosing response Number of Mean risk
Behavior I II III IV responses tolerance
a
Never smoked 66.3 11.2 10.9 11.4 4276 0.2353
Quit smoking 63.9 11.9 11.2 12.9 4276 0.2425
Smokes now 63.3 11.6 10.4 14.5 3155 0.2474
Does not drink 68.0 9.4 10.2 12.1 4584 0.2344
Drinks 62.4 12.9 11.3 13.2 7123 0.2456
Zero drinks per day 68.0 9.4 10.2 12.1 4584 0.2344
Between zero and one 63.2 12.9 11.5 12.2 5317 0.2418
Between one and two 59.5 13.4 11.5 15.4 1187 0.2549
Between two and five 61.9 11.7 9.0 17.2 441 0.2573
More than five 57.3 12.3 10.1 20.2 178 0.2689
Less than 12 years of 65.7 8.9 10.8 14.4 3320 0.2448
education
12 years 67.7 11.4 10.5 10.2 4130 0.2294
13 to 16 years 61.9 13.4 11.2 13.3 3158 0.2463
Over 16 years 57.6 14.6 11.7 15.9 1099 0.2598
Self-employed 63.9 10.4 11.1 14.4 1374 0.2461
Employee 66.0 12.0 10.5 11.3 6397 0.2349
Not working 62.5 11.2 11.4 14.7 3936 0.2497
Nonwesterner 65.5 11.2 10.7 12.4 9811 0.2388
Westerner 59.8 13.1 11.9 14.9 1896 0.2538
Nonimmigrant 65.0 11.9 10.8 12.2 10568 0.2389
Immigrant 61.2 8.2 11.7 18.7 1139 0.2630
The p-value for the hypothesis that mean risk tolerance is equal among smokers. quitters, and those
who never smoked is 0.0017. The p-values for the hypothesis of no difference in risk tolerance according to
the other behaviors (drinks, drinks per day, years of education, employment status, region, or immigrant
status) are each less than 0.0001.
a. The mean risk tolerance is computed using the baseline parametric model.
period of increasing public awareness of the risks associated with
cigarette smoking. Those who quit smoking are somewhat more
risk tolerant than those who never smoked, but less risk tolerant
than current smokers.
Whether an individual drinks or not is also related to mea-
sured risk tolerance. Risk tolerance is higher for those who drink
than for those who do not drink. The difference in risk tolerance
between drinkers and nondrinkers is about the same as between
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TABLE V
D
OES
M
EASURED
R
ISK
T
OLERANCE
P
REDICT
B
EHAVIOR?
R
EGRESSIONS OF
B
EHAVIORS
ON
R
ISK
T
OLERANCE AND
D
EMOGRAPHIC
V
ARIABLES
Mean of Regression Standard
dependent coefficient of error of
Dependent variable variable risk tolerance estimate R
2
Ever smoke 0.635 0.092 0.469 0.054
(0.030)
Smoke now 0.269 0.068 0.441 0.011
(0.028)
Drinks 0.608 0.099 0.472 0.065
(0.030)
Drinks per day 0.831 0.256 0.835 0.073
(0.053)
Education (years) 12.083 0.265 2.920 0.172
(0.184)
Self-employed 0.117 0.021 0.318 0.024
(0.020)
Immigrant 0.097 0.027 0.248 0.303
(0.016)
No health insurance 0.272 0.196 0.422 0.100
(0.031)
No life insurance 0.294 0.155 0.439 0.073
(0.028)
Owns home 0.805 20.153 0.383 0.066
(0.024)
The dependent variables are (0,1) except for drinks per day and years of education. The estimated regres-
sions include the following covariates whose estimated coefficients are not reported: constant, age, sex, reli-
gion (Catholic, Jewish, other), and race (black, Hispanic, Asian, other). The mean of the dependent variables
is given in the second column. The regression coefficient of relative risk tolerance uis reported in the third
column (with standard errors in parentheses). Relative risk tolerance conditional on the survey responses is
assigned to each respondent using the baseline statistical model. The last two columns give the standard
error and R
2
of the regressions. The regressions are based on 11,707 individuals’ responses with two excep-
tions. For health insurance the sample is the 8642 households not eligible for Medicare. For life insurance
the sample is only 11,561 households owing to missing data.
smokers and nonsmokers. Moderate drinking is not generally be-
lieved to be a health risk. Table IV shows risk tolerance by drinks
per day. Those who take less than one drink per day have a will-
ingness to accept the moderate gambles (II and III) relatively of-
ten. As drinks per day increase, there is a monotonic increase in
mean risk tolerance. For heavy drinkers, risk tolerance—mea-
sured either by willingness to choose gamble IV or by mean risk
tolerance—is substantially above average.
The regressions reported in Table V show that the risk toler-
ance measure predicts smoking and drinking even after control-
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ling for the demographic variables. Moreover, the risk tolerance
measure has a substantial quantitative role in predicting these
behaviors. For example, the most risk tolerant respondents are
over three and a half percentage points more likely to have ever
smoked than the least risk-tolerant respondents (0.0922 times
the 0.42 difference between the expected risk tolerances of a re-
spondent in categories I and IV). Risk tolerance is also a signifi-
cant explanatory variable for drinking behavior. Moving from the
lowest to highest response for risk tolerance is associated with a
4 percent increase in the probability of drinking (t-statistic of 3)
and a 0.1 drink increase in the number of drinks per day
(t-statistic of 4–1/2).
22
Education and Employment Status. The fourth panel of
Table IV shows a U-shaped relationship between years of school-
ing completed and the measure of risk tolerance. Individuals with
exactly twelve years of schooling are the least risk tolerant. In-
deed, the mean risk tolerance of 0.229 and average propensity to
choose response IV of 10.2 percent are the lowest we found for
any group that we categorized. Those with less than twelve or
from thirteen to sixteen years of schooling have slightly greater
than average risk tolerance. Those with some post-college educa-
tion (years greater than sixteen) have substantially greater than
average risk tolerance. In the multivariate analysis in Table V,
the number of years of schooling is not associated with risk toler-
ance—in part because of the nonlinearity we found in the cross
tabulation.
Among the biggest risks voluntarily taken by a large seg-
ment of the population is self-employment. The self-employed
generally face a riskier overall income stream than their wage-
earning or salaried counterparts (see Friedman 1957 and Carroll
[1994]). Thus, one would expect risk tolerance to be positively as-
sociated with the decision to undertake self-employment. The
fifth panel of Table IV shows that the self-employed are more risk
22. Researchers have studied attitudes about health-related risk and exam-
ined how these interact with economic choices. The relationship between our risk
tolerance measure and smoking and drinking corroborates the findings that indi-
viduals translate health risks into pecuniary values. Viscusi and Evans [1990]
estimate that workers show rather smooth, concave trade-offs between occupa-
tional health and safety risks and consumption. Fuchs [1982] shows that the sub-
stantial heterogeneity in responses to questions about money or commodities now
versus the corresponding desiderata in the future has predictive power for the
decision to smoke, and that some, but not all of this is mediated through
education.
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tolerant than employees.
23
The multivariate analysis shows
that the most risk-tolerant respondents are about one percentage
point more likely to select self-employment than the least
risk tolerant respondents. Given that the probability of self-
employment is less than 12 percent, this is a quantitatively large
effect, but it is not statistically significant (t-statistic of 1.1).
Region and Immigrant Status. An epic risk is to move to a
new country in search of a better life. The idea that immigrants
are more daring than the average person is part of the American
mythology. Migration within the United States could also entail
significant risks. The western United States has in the past been
an internal frontier to which one might argue the more daring
have migrated. Some of the attitudes from that frontier past may
have persisted to the present.
Both region of residence and immigrant status are signifi-
cantly predicted by risk tolerance. Residents of the western
United States are more risk tolerant than residents of other re-
gions. Immigrants are also substantially more risk tolerant than
natives. They are especially likely to be in category IV (see
Table IV).
Given that many recent immigrants are Hispanic and Asian
and that Hispanics and Asians have high risk tolerance (see Ta-
ble III), it is important to check that immigrant status is not con-
founded with ethnicity. The positive association of risk tolerance
and immigrant status survives controlling for the demographic
factors, but has a t-statistic of only one and three-quarters
(Table V).
Health and Life Insurance. Anyone with positive risk aver-
sion should be fully insured against purely financial risks when
insurance is actuarially fair. In the presence of a load factor, how-
ever, those who are most risk averse should be most willing to
buy insurance against financial risks. A complication arises (as
with smoking and drinking) because the kinds of insurance pur-
chases on which we have information are health and life insur-
ance, where the risks are not purely financial—the marginal
utility of wealth potentially depending on health status, for in-
stance. We appeal to financial responsibility for the support of
others as the basis of our a priori expectation that the (finan-
23. There is no obvious prediction about the risk tolerance of those not work-
ing—mainly retired individuals and spouses not in the labor force.
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cially) more risk averse are more likely to purchase both medical
and life insurance.
24
Table VI examines our measure of risk tolerance according
to whether or not the individual has health insurance. We do
separate tabulations for employees, the self-employed, and those
not working. To focus on those who have the option of having in-
surance or not, this tabulation excludes those in the Medicare-
eligible age group.
For each of the three employment classes, more risk tolerant
individuals are less likely to have health insurance. For those
employed, measured risk tolerance seems to be an important fac-
tor sorting individuals into jobs with health insurance. For the
not employed, risk preference is a powerful determinant of the
propensity to be insured. The effect of risk tolerance on the pro-
pensity to be insured is smaller among the self-employed than
among the unemployed. Between groups, the self-employed have
a higher risk tolerance and have much lower average propensity
TABLE VI
R
ISK
T
OLERANCE BY
H
EALTH
I
NSURANCE
C
OVERAGE AND
E
MPLOYMENT
S
TATUS
Percent choosing
response
Employment Health Number of Mean risk
status insurance I II III IV responses tolerance
a
Self-employed Yes 63.5 10.0 12.3 14.0 763 0.2459
No 63.0 10.3 10.0 16.6 319 0.2529
Employee Yes 66.9 11.8 10.5 10.6 4186 0.2317
No 58.4 11.4 13.4 16.6 638 0.2643
Not employed Yes 63.8 11.9 10.9 13.2 1343 0.2424
No 59.8 10.1 12.0 18.0 1393 0.2647
Tabulation for health insurance excludes Medicare-eligible individuals. The p-value for the hypothesis
that mean risk tolerance does not differ according to whether or not the respondent has health insurance is
0.4953 for the self-employed, 0.0001 for employees, and 0.0002 for those not employed.
a. The mean risk tolerance is computed using the baseline parametric model.
24. Researchers have used choices about insurance to elicit estimates of risk
aversion. Friedman [1973] used data on choices regarding health insurance, and
obtained an estimate of about 10. Szpiro [1986] returns to the idea of gauging risk
aversion by studying the demand for insurance. He looks at households’ willing-
ness to pay a load factor in order to obtain insurance, using insurance company
data on premiums and claims. Using these data, along with the Goldsmith data
on total household wealth, Szpiro reports estimates of the coefficient of relative
risk aversion between one and two. While these studies are clearly related to our
results, their method is to estimate risk aversion from purchase of insurance
while our survey creates an independent measure of risk aversion, which can then
be related to purchase of insurance.
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to be insured than employees. Similarly, Table VII shows that
individuals without life insurance are substantially more risk tol-
erant than those with it.
The results in the cross tabulations for health and life insur-
ance carry over when the demographic factors are controlled for
in the regressions reported in Table V. The most risk tolerant re-
spondents are 8.2 percentage points more likely not to have
health insurance and over six and one-half percentage points
more likely to forgo life insurance than the least risk-tolerant
respondents. Both results are highly statistically significant
(t-statistics in excess of 5) and are quantitatively important.
Income and Wealth. Tables VIII and IX show risk tolerance
by quintiles of income and wealth. Risk tolerance decreases with
income and wealth until the middle of the distributions, and then
increases. Note that the pattern of risk tolerance by income and
wealth is similar to that for age. Risk tolerance rises at the high
end of the wealth, income, and age distributions.
25
Home equity is the major component of wealth for most indi-
viduals. The 20 percent of individuals who do not live in houses
they own are substantially more risk tolerant than those who
own their homes. The most risk-tolerant individuals are over 6
percent less likely to own homes than the least risk tolerant indi-
25. Older and high wealth individuals might interpret the survey questions
differently from most respondents because labor income is a smaller fraction of
their current resources. We checked for this possibility by grouping the responses
by both age and wealth quintile. These groupings do not lead to the conclusion
that the highly risk-tolerant respondents are either old or wealthy. Moreover, we
reran the regressions in Table V including the logarithms of income and wealth
as regressors. Controlling for income and wealth raises some coefficient of risk
tolerance and lowers others, but overall has little qualitative impact on the find-
ings. (We report the regressions without wealth and income in Table V, owing to
concern about the endogeneity of those variables.)
TABLE VII
R
ISK
T
OLERANCE BY
L
IFE
I
NSURANCE
C
OVERAGE
Percent choosing response
Life Number of Mean risk
insurance I II III IV responses tolerance
a
Yes 66.1 11.6 10.5 11.6 8162 0.2353
No 61.0 11.5 11.7 15.7 3399 0.2548
The p-value for the hypothesis that mean risk tolerance does not differ according to whether or not the
respondent has life insurance is 0.0001.
a. The mean risk tolerance is computed using the baseline parametric model.
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TABLE VIII
R
ISK
T
OLERANCE BY
F
AMILY
I
NCOME
Percent choosing response
Income Number of Mean risk
quintile I II III IV responses tolerance
a
1st 62.2 9.3 12.3 16.1 2415 0.2556
2nd 66.7 10.5 10.5 12.1 2321 0.2366
3rd 66.9 11.6 10.5 10.8 2289 0.2310
4th 67.2 12.3 9.1 11.2 2356 0.2312
5th 59.9 14.4 12.1 13.7 2326 0.2511
Cutoffs for the income quintiles are $18,980, $33,200, $49,000, and $72,200. The p-value for the hypothe-
sis that mean risk tolerance does not differ according to income is 0.0001.
a. The mean risk tolerance is computed using the baseline parametric model.
TABLE IX
R
ISK
T
OLERANCE BY
F
AMILY
W
EALTH
Percent choosing response
Wealth Number of Mean risk
quintile I II III IV responses tolerance
a
1st 61.5 9.1 12.0 17.2 2402 0.2601
2nd 65.0 12.0 10.7 12.1 2320 0.2381
3rd 67.4 11.5 10.2 11.2 2335 0.2318
4th 65.7 12.7 11.4 10.0 2319 0.2319
5th 63.4 13.1 10.0 13.3 2331 0.2435
Cutoffs for the wealth quintiles are $21,000, $70,000, $139,000, and $285,000. Net worth includes hous-
ing wealth. The p-value for the hypothesis that mean risk tolerance does not differ according to wealth
quintile is 0.0001.
a. The mean risk tolerance is computed using the baseline parametric model.
viduals (see the last line of Table V). It is not obvious what corre-
lation one would expect a priori. Although house prices are
volatile and houses are often highly leveraged, owning a house
insulates individuals from local changes in the cost of shelter, and
thus provides some consumption insurance.
Financial Assets. Studying the demand for risky assets is an
important application of our risk preference measures. Table X
presents regressions of portfolio shares on the demographic vari-
ables, risk tolerance, wealth, and income for a subsample that
has positive financial assets. Many households have little or no
financial wealth. We limit this analysis to households that have
at least $1000 in financial wealth. This criterion excludes about
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TABLE X
D
OES
M
EASURED
R
ISK
T
OLERANCE
P
REDICT
P
ORTFOLIO
S
HARES?
R
EGRESSIONS OF
P
ORTFOLIO
S
HARES ON
R
ISK
T
OLERANCE AND
D
EMOGRAPHIC
V
ARIABLES
Regression coefficients of
risk tolerance
Dependent
variable: Mean of Primary minus Standard
Portfolio dependent Primary secondary error of
share variable (R1) (R1 2R2) estimate R
2
Stocks 0.140 0.097 20.023 0.244 0.060
(0.029) (0.027)
Bonds 0.014 0.015 20.010 0.068 0.040
(0.008) (0.008)
Saving and 0.416 20.128 0.018 0.348 0.153
checking (0.041) (0.039)
Treasury bills 0.095 20.055 0.050 0.201 0.013
(0.024) (0.022)
IRA and Keogh 0.248 20.006 0.020 0.312 0.033
(0.037) (0.035)
Other assets 0.086 0.076 20.056 0.215 0.017
(0.025) (0.024)
The dependent variables are shares of assets in total financial wealth. The estimated regressions include
demographic covariates (see note to Table VII) plus the logarithms of income and wealth. The third column
reports the estimated coefficient of the primary respondent’s (R1) relative risk tolerance. The fourth column
gives that of the difference between the primary and secondary respondents’ (R1 2R2) relative risk toler-
ance. Relative risk tolerance conditional on the survey responses is assigned to each respondent using the
baseline statistical model. The regressions are based on 5012 households’ responses.
one-sixth of the households. Since asset ownership depends sub-
stantially on income and wealth, we include these as controls in
the regressions of portfolio variables.
26
The questions about assets apply to the household. In the
Health and Retirement Study, they are answered by the “knowl-
edgeable respondent”—the member of the household with the
best knowledge of the household’s assets. The assets are charac-
teristics of the household (there is no information on asset owner-
ship within the household), while risk preference is a feature of
individuals. Recall that the risk tolerance measure is positively,
but not strongly, correlated within couples (Table II). To study the
26. Some of the portfolio shares are zero. Tobin’s Separation Theorem im-
plies, however, that they should all be positive. The zero shares may result from
a fixed cost of holding a particular asset, which would imply jumps from zero to
strictly positive portfolio shares.
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role of potentially conflicting risk tolerances within the family, we
enter the risk tolerance of members of couples separately. Hence,
the regressions include the risk tolerance of the primary respon-
dent (R1) and the difference between the risk tolerance of the
primary and secondary respondent (R1 2R2).
27
The risk tolerance measure has significant predictive power
for stock ownership. In households where the primary respondent
gave the most risk-tolerant response, the fraction of financial
assets held in equities is 4.1 percentage points higher on average
than in those where the primary respondent gave the least risk-
tolerant response. Since the average fraction of portfolios in
stocks is only 14 percent, this effect is substantial. It is also
strongly statistically significant. If the secondary respondent is
less risk tolerant than the primary respondent, the stock share
is lower, although this result is not statistically significant.
28
Similarly, relatively safe assets—Treasury bills and savings
accounts—make up more of the portfolios of the less risk-tolerant
respondents. Bonds are too small a share of portfolios for the re-
sults to be decisive (1.4 percent of portfolios on average), although
there is a marginally significant positive relationship between
bond holding and risk tolerance. Ownership of other assets
(trusts, collections held for investment) is powerfully related to
risk tolerance.
29
Therefore, for assets at opposite ends of the risk
spectrum—stocks at one end versus Treasury bills and savings
accounts at the other end—the risk tolerance measure has sub-
stantial explanatory power for portfolio demands.
Yet, the relationship between risk tolerance and the holding
of risky assets is much weaker than theory suggests it should be.
27. If there is no secondary respondent, we code the difference as zero. If the
secondary respondent did not answer the risk tolerance question, we also code
the difference as zero. If the primary respondent did not answer, we exclude the
household from the sample. The values of the other individual-specific covariates
refer to the primary respondent.
28. The regression coefficient of 0.097 corresponds to a squared correlation of
0.02 between the risk tolerance measure and the stock portfolio share—somewhat
below the range commonly reported in the psychological literature for the fraction
of variance explained by a battery of survey measures. We also estimated the
portfolio share equations by Heckman’s two-step, Tobit estimator. As would be
expected, the Heckit estimates are larger than the OLS estimates. Indeed, for the
equation for the stock share, the coefficient of relative risk tolerance is twice the
OLS estimate.
29. The Health and Retirement Study fails to provide any information about
the asset composition of retirement accounts, so we do not know their riskiness.
Given the growing importance of retirement accounts and defined contribution
pension plans, it is important that future surveys provide information about the
composition of these accounts.
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30. Kandel and Stambaugh [1991] argue for precisely this interpretation of
the equity premium puzzle.
In the standard capital asset pricing model, portfolio shares
equal the product of risk tolerance and covariance-scaled excess
returns. Hence, the elasticity for the share of each risky asset
with respect to risk tolerance should be one. When the estimated
coefficients of risk tolerance in Table X are expressed as elasticit-
ies, the elasticity of the stock portfolio share with respect to risk
tolerance is estimated to be 0.17; the elasticities of the bond share
and of other assets are estimated to be 0.25 and 0.21. Conse-
quently, there is inadequate sensitivity of portfolio shares to risk
tolerance compared with the prediction of the standard model.
IV. H
ETEROGENEOUS
R
ISK
P
REFERENCES AND THE
E
QUITY
P
REMIUM
P
UZZLE
In this section we discuss how to aggregate our estimates of
individuals’ risk tolerance in a way that informs the demand for
stockholding. The “equity premium puzzle” [Grossman and
Shiller 1981; Mehra and Prescott 1985] is a mismatch between
the low levels of risk tolerance (high levels of risk aversion) re-
quired to explain empirical facts about mean asset returns and
the range of values for risk tolerance that seem reasonable to
most economists. We ask whether the answer to the equity pre-
mium puzzle might simply lie in the fact that the average individ-
ual is more risk averse than an economist might have expected,
as indicated by the high percentage of respondents in the least
risk-tolerant category.
30
We demonstrate here that our findings
are in fact not consistent with this story. Although most individu-
als are quite risk averse, there are enough risk-tolerant individu-
als to hold the outstanding supply of equity at far less than the
historically observed risk premium. Equivalently, because fi-
nance theory implies that in aggregating preferences across indi-
viduals the least risk averse receive the greatest weight, the
effective risk aversion of the representative investor is actually
rather low. These statements are robust to different ways of
treating nonstockholders.
The literature on the equity premium puzzle finds that ag-
gregate risk aversion must be in excess of 30—and possibly as
high as 100—in order to explain the six percentage-point-per-
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year mean excess return of equities above the Treasury bill rate
over the last century or so (see Mankiw and Zeldes [1991]). What
is the appropriate way to use our estimate of the population dis-
tribution of preferences to aggregate the heterogeneous individu-
als and construct a single number for use in an asset demand
equation? One might be tempted to take a simple (weighted or
unweighted) arithmetic average of risk aversion over all individ-
uals. But in the aggregation of a capital asset pricing model,
those with greater willingness to bear risk ought to receive
greater weight, since they tend to take large positions in risky
assets. More specifically, individual asset demands—which can
be aggregated by simple addition—involve a term that is propor-
tional to risk tolerance. In the consumption capital asset pricing
model, the level of asset demand is implicitly determined by the
covariance of consumption with the return on the asset (see
Breeden [1979)]. Let c
i
be an individual’s level of consumption, Z
the return on any asset in excess of the safe rate of return, and
u
i
the individual’s risk tolerance. The consumption capital asset
pricing model says that
(5)
EZ Z c c
titii
( ) / )cov ( , . ()/=1θ∆
Consumption c
i
is known at time t, so one can multiply through
by c
i
u
i
and sum over all households to get
(6)
EZ c Z c
ti
i
it
i
i
( ) cov ( , . )
∑∑
=θ∆
Denote aggregate consumption as C, and define aggregate risk
tolerance by the consumption-weighted average Q5S
i
(c
i
/C)u
i
.
Then
(7)
EZ Z CC
tt
( ) ) cov ( , ) (1/ /=Θ ∆
because covariance is a linear operator. Equation (7) has the
same form as equation (5), but with aggregate consumption and
risk tolerance replacing the individual values.
In the first column of Table XI, we show average relative risk
tolerance, computed using the numerical assignments and with
the theoretically mandated consumption weights proxied by
equal weights, income weights, and wealth weights, respectively.
In the second column we show the arithmetic weighted average
of relative risk aversion. Jensen’s inequality is strongly operative.
The difference between mean risk tolerance and the reciprocal of
mean risk aversion is substantial. For the entire sample (top
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TABLE XI
M
EAN
R
ISK
P
REFERENCE AND
S
TOCK
O
WNERSHIP
Relative risk Relative risk
Respondents Weighting tolerance aversion
All Unweighted 0.2391 12.1193
Income-weighted 0.2417 11.9928
Wealth-weighted 0.2441 11.9781
All, with nonstockholders Unweighted 0.0738 . . .
getting zero risk tolerance Income-weighted 0.1079 . . .
Wealth-weighted 0.1418 . . .
Stockholders only Unweighted 0.2435 11.8904
Income-weighted 0.2480 11.7279
Wealth-weighted 0.2485 11.8346
11,136 observations (3,377 observations for stockholders only). Relative risk tolerance and aversion con-
ditional on the survey responses is assigned to each respondent using the baseline statistical model.
panel of Table XI), the reciprocal of the mean risk tolerance of
0.24 equals 4.2, while mean risk aversion is 12.1. This result is
not very sensitive to the weighting. Hence, the heterogeneity we
find implies a dispersion in risk preferences that is large enough
to make the difference between the arithmetic mean of risk aver-
sion (12.1) and the harmonic mean of risk aversion (4.2) an im-
portant one. These levels of risk aversion are not high enough to
explain the level of the equity premium.
A large group of individuals do not hold stock at all. If these
individuals hold zero net positions because of fixed costs of being
in the stock market or constraints on short sales (rather than
because their unconstrained optimum for stockholding is pre-
cisely zero), they require special treatment. Formally, using Q
˜to
represent the consumption-weighted average of risk tolerance
where nonstockholders have their risk tolerance replaced by zero,
(8)
EZ Z CC
tt
() ˜
)cov ( , ) (1/ /=Θ ∆
if nonstockholders have consumption that is uncorrelated with
the stock return Z. If nonstockholders on average have consump-
tion that is positively correlated with stock returns, as Mankiw
and Zeldes [1991] find—thereby having an implicit position in
equities through the correlation of equities with macroeconomic
events—then the right-hand side of (8) is an upper bound for
E
t
(Z).
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In the middle panel of Table XI, we repeat our previous calcu-
lations, assigning nonstockholders zero risk tolerance, to get an
estimate of Q
˜. (In the last panel of Table XI, we show risk toler-
ance for stockholders only. These calculations fairly closely repli-
cate the numbers for all respondents without special treatment
of nonstockholders.) Although the precise risk tolerance esti-
mates are two to three times larger for the whole sample than
they are when nonstockholders are assigned zero risk tolerance,
the qualitative conclusions above continue to hold. Aggregate risk
tolerance is low enough so that the equity premium remains a
puzzle.
V. P
REFERENCES OVER
C
ONSUMPTION
P
ATHS
In this section we report the results of our experimental sur-
vey questions designed to elicit estimates of the preference
parameters governing intertemporal substitution and time pref-
erence. As with the other experimental modules, Module Kwas
administered to a very small subset of the HRS respondents:
there are 198 respondents. In contrast, there are more than
11,000 responses to the risk preference questions discussed in the
previous sections. In light of the small sample, the results should
be regarded as tentative. Nonetheless, we can characterize our
results broadly as follows:
• Most individuals have low elasticities of intertemporal
substitution. Our point estimate for the average elasticity of
intertemporal substitution is 0.18. Virtually no respondents
have intertemporal substitution as elastic as that implied by
log utility.
• Although the mean elasticity of intertemporal substitution
is only slightly less than the mean risk tolerance, there is
essentially no relationship between individuals’ estimated
elasticity of intertemporal substitution and relative risk
tolerance.
• At a zero interest rate the modal time preference is for a
flat consumption path, but an upward slope is chosen more
often than a downward slope. Hence, the mean preference is
for an upward sloping consumption path.
The remainder of this section presents these results in more de-
tail and discusses some of the problems that arose in the experi-
mental survey.
Unlike the risk preference questions, the questions about the
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slope of the consumption path had possible responses that are
either uninformative about the elasticity of intertemporal substi-
tution or are inconsistent with utility maximization. For ex-
ample, respondents who—regardless of the interest rate—chose
either the extreme positive slope or the extreme negative slope
could have any elasticity of intertemporal substitution. Since
they are at a corner (given the range of choices we present), we
do not learn anything about their willingness to substitute inter-
temporally when confronted with different interest rates. Of the
198 respondents to the module, 24 (12 percent) gave such unin-
formative responses. Since they convey no information about in-
tertemporal substitution, they are left out of those tabulations.
The set of possible responses to the questions on the module
left open the possibility of responses that were inconsistent with
utility maximization. While we leave these out of the tabulations,
it is important to examine the nature and extent of these incon-
sistent answers. The first question offered three consumption
profiles. This was meant as a warm-up to familiarize the respon-
dents with the form of the questions. The second question offered
the same three choices plus two intermediate possibilities. Six-
teen (8 percent) of the respondents made inconsistent choices. We
eliminated these respondents from the tabulation even if their
subsequent responses were otherwise consistent. Another 42 re-
spondents (21 percent) displayed other inconsistencies in the sub-
sequent choices. Specifically, these involved changing the slope of
the desired consumption path in the direction opposite to the
change in the interest rate. There was, in particular, some ten-
dency for respondents to react perversely when moving to a nega-
tive real rate, implying a negative elasticity of intertemporal
substitution, although not one very different from zero. We ex-
cluded these observations. Including these observations in an
analysis allowing for response noise would pull down the already
low estimate of the elasticity of intertemporal substitution.
Intertemporal Substitution. Excluding the responses that are
either uninformative about intertemporal substitution or are in-
consistent, we are left with 116 useful observations. Just as with
the risk preference question, the discrete nature of the survey
questions leads to responses that correspond to ranges of prefer-
ence parameters. Because we present the respondents with a
fairly rich set of consumption profiles, the responses cannot be
categorized into a few, nonoverlapping groups, as they were for
the risk preference questions. The respondents are presented five
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slopes for each of the three interest rates (zero, positive, and
negative).
For each valid response we calculate the range of possible
elasticities of intertemporal substitution and most-desired slopes
of the consumption path at a zero interest rate that are consistent
with the responses. These calculations are analogous to the
ranges for the risk preference parameters given in Table I. Table
XII summarizes the preference parameters of the respondents.
The first row gives the elasticity of intertemporal substitution.
The second row gives time preference as measured by the slope
of the desired consumption path at a zero interest rate. For each
respondent’s answers to the questions in the module, we calculate
the lower bound and the upper bound of both parameters. The
averages across respondents of these lower and upper bounds are
reported in the first two columns of Table XII. The third column
reports the average of the midpoints between these upper and
lower bounds.
The average of the estimated lower bounds of the intertem-
poral elasticity of substitution is very close to zero. The average
of the estimated upper bounds is 0.36. The average midpoint is
0.18. The average lower bound is as low as it is because the re-
sponses for most households (103 of the 116 valid responses) are
consistent with a zero elasticity of intertemporal substitution. In-
deed, the most common response was to choose a flat consump-
tion profile regardless of whether the interest rate was zero,
positive, or negative. The next most common response was to
choose the moderately upward sloping path for each interest rate.
Eighty-four (72 percent) of the valid responses fell into these two
groups. Because the interest rate is varying across the paths,
these responses provide a fairly tight upper bound on the elastic-
ity of intertemporal substitution. For those always preferring a
TABLE XII
P
REFERENCE
P
ARAMETERS FOR
C
ONSUMPTION
P
ATHS (EXPERIMENTAL MODULE)
Lower Upper
Parameter bound bound Midpoint
Intertemporal substitution elasticity 0.007 0.36 0.18
Consumption growth at zero interest 0.28 1.28 0.78
rate (percent per year)
116 observations.
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flat consumption profile, the upper bound is 0.23; the upper
bound is 0.29 for those always preferring the moderately upward
sloping profile.
The remaining 28 percent of the valid responses did not fall
into tight groupings. Many showed a higher elasticity of inter-
temporal substitution—with a midpoint as high as 1.08 for one
respondent. Yet, even among those for whom intertemporal sub-
stitution is bounded away from zero, preferences are rarely as
elastic as log utility. Only 2.5 percent of respondents had an up-
per bound of elasticity of intertemporal substitution greater than
or equal to one.
Time Preference. Table XII also gives results for the time
preference parameter. The overall average slope of the desired
consumption path at a zero interest rate is 0.78 percent per
year.
31
Thus, we confirm the findings by experimental and cogni-
tive psychologists that there is some evidence for a negative time-
discount rate: on average, people prefer an upward sloping con-
sumption profile, even when the interest rate is zero.
32
Intertemporal Substitution versus Risk Tolerance. Many ap-
plications assume that a representative consumer maximizes a
time- and state-separable utility function with the period-by-
period function having the constant elasticity functional form. In
this context, relative risk tolerance (the reciprocal of relative risk
aversion) equals the elasticity of intertemporal substitution.
Selden [1978] and Epstein and Zin [1989] have discussed
preferences where the individual’s elasticity of intertemporal
substitution is not equal to risk tolerance. Weil [1990], Hall
[1988], and Barsky [1989] explore the implications of such prefer-
ences for consumption and asset pricing while Kimball and Weil
[1992] discuss the implications of these preferences for precau-
tionary saving.
33
For the respondents to our experimental survey,
31. Because sis close to zero, we focus on the estimate of -s?r instead of
dividing by sto get an estimate of r. See equation (2).
32. See Loewenstein [1987], Loewenstein and Prelec [1991, 1992],
Loewenstein and Thaler [1989], Maital [1988], and Maital and Maital [1977]. In
contrast, the econometric evidence (e.g., Hausman [1979] and Lawrance [1991])
finds downward sloping profiles. Future research is needed to explain why the
econometric and experimental evidence arrive at different conclusions. One pos-
sible explanation of the finding of high subjective discount rates in the economet-
ric work is the difficulty of controlling for features of the economic environment
facing agents, such as liquidity constraints and the need for precautionary
savings.
33. Certain utility functions that display habit formation or consumption ex-
ternalities also can break the link between risk tolerance and intertemporal sub-
stitution. This is an important feature of Campbell and Cochrane’s [1995]
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we can test directly whether there is a relationship between risk
tolerance and intertemporal substitution.
Table XIII tabulates the consumption path parameters by
the four responses to the risk preference question. There is no
significant relationship, either statistically or economically, be-
tween risk tolerance and intertemporal substitution. Similarly, if
we regress the estimated elasticity of intertemporal substitution
(measured by the midpoint of the range of possible values for
each respondent) on the mean risk tolerance, we get a coefficient
of 0.01 with a standard error of 0.02. Under the usual assumption
that risk tolerance equals the elasticity of intertemporal substitu-
tion, the regression coefficient should be one. Hence, it appears
that there is no relationship between measured intertemporal
substitution and measured risk tolerance even though their
means are similar.
Given the scant number of observations from this module,
we do not consider tabulations with the demographic and behav-
ioral variables.
VI. E
XTENSIONS AND
Q
UALIFICATIONS
Our analysis of the survey responses is based on several pre-
sumptions. First, we make assumptions about how the individu-
als interpret the questions. Second, in the case of the risk
tolerance survey responses, we use identifying assumptions to
TABLE XIII
C
ONSUMPTION
P
ATH
P
REFERENCE
P
ARAMETERS AND
R
ISK
T
OLERANCE
R
ESPONSES
Response to risk
tolerance question
Midpoint parameter I II III IV p-value
Intertemporal substitution elasticity 0.18 0.21 0.15 0.20 0.28
Consumption growth at zero 0.80 1.10 0.53 0.53 0.87
interest rate (percent per year)
116 observations. The table gives mean parameter value conditional on response to risk tolerance survey.
The p-value is for the null hypothesis of no correlation with relative risk tolerance assigned to each respon-
dent using the baseline statistical model.
analysis. Andrew Abel’s discussion of that paper at the October 1994 NBER Eco-
nomic Fluctuations meeting clarified this point for us. Laibson [1996] uses a novel
form of the utility function which also has the effect of breaking this link.
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estimate a parametric model of relative risk tolerance. In this
section we investigate the robustness of the results under depar-
tures from some of these assumptions. In particular, we investi-
gate how a preference for an existing job might cause respondents
to give responses that understate their risk tolerance and how
our assumption of no persistent response error would lead to an
overstatement of risk tolerance. Instead of simply noting the di-
rection of these offsetting biases, we attempt to quantify them.
This quantification requires further parametric specification.
A. Status Quo Bias
The survey question asks whether the respondent would
switch to a job that is “equally good” except for the income risk.
Nonetheless, the survey respondents might imagine that there is
a cost to switching jobs, might have a nonpecuniary value to their
job, or might simply have an excess propensity to decline the
gamble because doing so preserves the status quo. This status
quo bias would cause our results to understate risk tolerance to
the extent that individuals are disinclined to accept the gambles
for reasons other than their preference toward risk.
34
Status quo bias can be analyzed using the theoretical model
developed above. Suppose that individuals place a premium on
their current job above the consumption flow that it allows them
to sustain. That is, we can imagine individuals responding to the
survey based on whether
(9)
1
2
2Uc Uc U() () + ( ),
1
2
λφ≥c
where fparameterizes the status quo bias in terms of consump-
tion flows. fequal to one is our baseline case of no status quo
bias. If fis greater than one, the respondents will accept a gam-
ble that also entails switching jobs if it delivers an expected util-
ity strictly in excess of the current job.
In Table XIV we present results for various values of f. The
top line gives the results for our baseline specification of no status
quo bias. The next two lines show how the estimated distribution
of relative risk tolerance changes if it takes a 5 percent (f51.05)
or 10 percent (f51.1) consumption premium to make the re-
spondent indifferent between his or her current job and a differ-
34. See Samuelson and Zeckhauser [1988] for a study of status quo bias.
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TABLE XIV
E
XPECTED
V
ALUE OF
R
ELATIVE
R
ISK
T
OLERANCE (
u
)
C
ONDITIONAL ON
S
URVEY
R
ESPONSES FOR
A
LTERNATIVE
P
ARAMETRIC
M
ODELS
Expectation conditional on
Statistical model response
c
Status quo Fraction of true parameter Standard Adjustment to
bias, f
a
in persistent variance, t
b
Mean
c
deviation
c
I II III IV regression coefficients
d
1.0 1.0 0.241 0.334 0.150 0.279 0.353 0.569 1.0
1.05 1.0 0.299 0.426 0.184 0.347 0.442 0.729 0.77
1.1 1.0 0.396 0.667 0.221 0.455 0.729 1.087 0.48
1.0 0.5 0.185 0.155 0.150 0.208 0.234 0.294 2.91
1.05 0.5 0.227 0.195 0.184 0.257 0.290 0.369 2.27
1.1 0.5 0.283 0.277 0.220 0.324 0.494 1.540 1.54
This table reports statistics relating to the estimated distribution of relative risk tolerance under different assumptions about status quo bias and the presence of permanent
measurement error. The case in the first row (no status quo bias, no permanent measurement error) provides the basis for the results in the main tables of the paper. The other cases
are discussed in Section VI. (See text for details.)
a. This column gives different cases of the utility premium, f, that the respondent places on the current job relative to the expected utility of the job in the gamble. fequals 1.0
is no status quo bias. (See equation (9).)
b. This column gives different cases of the fraction tof the persistent variance of yowing to the true preference parameter. (See equation (10).)
c. These columns give the estimated mean and standard deviation of the unconditional distribution of relative risk tolerance and the expectation of relative risk tolerance
conditional on the four possible responses to the survey.
d. This column gives the multiplicative adjustment to the regression coefficients in Tables V and X warranted by the various cases of the statistical model.
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ent job with a certain level of income. Allowing for 5 percent
status quo bias raises the estimate of mean risk tolerance from
0.241 to 0.299. It also increases the estimated dispersion substan-
tially. Allowing for 10 percent status quo bias raises mean risk
tolerance further, to 0.396. As status quo bias increases, respon-
dents expressing a willingness to switch jobs are assigned sub-
stantially higher risk tolerance conditional on their survey
response; i.e., they must be quite risk tolerant if their willingness
to undertake the income gamble more than compensates for a
general unwillingness to switch jobs.
Because we do not have an estimate of f, the results of Table
XIV are conjectural.
35
It would be straightforward to reword the
question to eliminate the status quo bias in future surveys. In-
stead of asking about the current job versus a different job with
risky lifetime income as we did in the first two waves of the HRS,
one could ask about preferences between two new jobs, one with
a certain income stream the same as the current job and the other
with the risky income stream. Hence, the choice set would man-
date a change in job regardless of risk preference, and the re-
sponses would be free from the bias owing to a preference for the
existing job.
We are proposing to ask this status quo bias free question on
future waves of the HRS. Moreover, we have conducted a pilot
study of status quo bias free questions using a sample of Univer-
sity of Michigan undergraduates. Half the students were given
the question with the original wording (choice between a hypo-
thetical current job and a risky new job); half were given the re-
worded question (choice between two new jobs with current or
risky income). Using the conditional expectations estimated for
the HRS respondents, the mean relative risk tolerance for those
responding to the original question was 0.26, remarkably close
to what we found for the HRS sample. For those answering
the reworded question, the mean was 0.34. Hence, status quo
bias does appear to lead our results to understate the level of
35. Samuelson and Zeckhauser [1988] quantify the extent of status quo bi-
ases. They asked student survey respondents their opinions about various public
policies and their responses to hypothetical economic decisions. They pose the
questions with and without status quo bias. Samuelson and Zeckhauser find that
respondents were 17 percentage points more likely to choose an option that was
presented as the status quo than if it was expressed neutrally. They also report
that status quo bias appears to be not just a phenomenon of survey responses,
but to affect economic decisions such as selection of health plans and retirement
portfolios. Therefore, some of the unwillingness to make risky job changes that we
find in the survey might reflect actual behavior, but not be due to risk tolerance.
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risk tolerance.
36
The results of the pilot study can be expressed
in terms of our model given in equation (9). Based on the statis-
tical model estimated with the HRS data, the difference of
the responses of the two groups of students is consistent with a
status quo premium of between 5 and 10 percent of lifetime
consumption.
B. Persistent Measurement Error
Our statistical model of the survey responses attributes all
the correlation in responses across waves to the true preference
parameter. Put differently, we assume that all randomness in re-
sponses is temporary. While the model is not identified if the per-
sistence of the measurement error is a free parameter, it is
possible to calculate its implications for different assumptions
about the persistence of measurement error. Consider a modifi-
cation to the statistical model (equation (4)),
(10)
yx
jk j j jk
+ + =ηε,
where h
j
is a persistent error component. Define t5s
2
x
/(s
2
x
1s
2
h
),
that is, the fraction of variance of the persistent component of the
response due to the true preference parameter.
In our baseline model, there is no h
j
term, so t51. The
fourth line of Table XIV presents a reestimation of the model
where half of the persistent signal is error (t50.5). The persis-
tent measurement error reduces the estimate of mean risk toler-
ance from 0.241 in the baseline model to 0.185. Moreover, it pulls
the expectations conditional on the survey response toward the
unconditional mean.
37
In the limit as tapproaches zero, the sur-
vey would contain no information about the heterogeneity of risk
tolerance, although it could still provide information about mean
risk tolerance. The last two lines of Table XIV present results
with both status quo bias and persistent measurement error. For
the parameters in the table, the two have substantially offsetting
effects on the estimated distribution of risk tolerance.
36. This survey was conducted in the fall of 1996 in an intermediate macro-
economic theory class. We gratefully acknowledge the collaboration of James An-
drew Kovacs in conducting this survey. It is difficult to extrapolate the results
based on the students to the sample of older individuals in the HRS. In particular,
status quo bias might be more severe for the HRS respondents because they are
likely to have actually been in their current jobs for a long time. Yet, the extent
of status quo bias that we find in our pilot is quite close to that reported by Sam-
uelson and Zeckhauser [1988]. In particular, 14 percent of respondents declined
to take any gamble in the survey with status quo bias while only 3 percent de-
clined any gamble in the status quo bias free survey.
37. This reduction in variance also reduces the wedge between the arithmetic
and harmonic means of risk aversion arising from Jensen’s inequality.
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C. Discussion
The previous two subsections discuss status quo bias and
persistent measurement error. We are able to quantify the effect
of these biases on the estimated distribution of relative risk toler-
ance. The biases are offsetting: correcting for status quo bias
raises the estimate of relative risk tolerance while correcting for
persistent measurement error lowers it. The survey does not con-
tain enough information to estimate the extent of either of these
biases, so the quantification is based on conjectured values of the
relevant parameters. Based on a pilot study, we have some infor-
mation on the extent of status quo bias. This pilot study suggests
that the estimate of relative risk tolerance implied by our base-
line model should be adjusted upward substantially. Future re-
search, such as asking the risk tolerance question on future
waves of the HRS in the status quo bias free form, is needed to
get better estimates of the relevant parameters.
As the discussion in this section and the results of Table XIV
make clear, the estimates of the distribution of relative risk toler-
ance—based on our parametric model of the utility function and
the statistical distribution of its parameter—are quite sensitive
to the assumptions needed to implement it. Yet, we hasten to add
that many of the results of the paper do not depend on the para-
metric model. The qualitative information on the distribution of
risk tolerance and how it relates to demographic characteristics
and behaviors reported in Tables II through IV and VI through
IX does not depend on the parametric model. Moreover, our find-
ing that the estimate of the elasticity of intertemporal substitu-
tion is independent of the risk tolerance response (Table XIII)
does not depend on the parametric model.
Moreover, the modest explanatory power of the risk tolerance
responses for the behaviors reported in the regressions is not af-
fected by the choice of parametric model. The conditional expecta-
tions of relative risk tolerance according to the survey response
are approximately linear across the various rows of Table XIV.
The last column gives the adjustment factor by which the results
of the baseline model should be multiplied in each case. Choice of
parametric model will change the regression coefficient of rela-
tive risk tolerance by the factor reported in Table XIV, but will
not change the t-statistic or the goodness of fit of the regressions.
The regressions reported in Table V are simply prediction
equations. A linear transformation of the risk tolerance measure
has no effect on the prediction for behavior of being in one of the
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risk tolerance categories versus another. The regressions re-
ported in Table X, however, have a structural interpretation that
depends on the level of risk tolerance. As noted above, the coeffi-
cient of 0.097 for risk tolerance in the equation for stock (Table
X) implies an elasticity of stock demand with respect to risk toler-
ance of 0.17, less than its theoretically mandated level of one.
Based on the mean risk tolerances and adjustment factors re-
ported in Table XIV, correcting for status quo bias of 5 percent
and 10 percent reduces this elasticity to 0.16 and 0.13, respec-
tively. Correcting for persistent measurement error makes a big-
ger difference. Assuming tequal to 0.5, the estimated elasticity
of the share of stocks becomes 0.37 assuming no status quo bias,
0.36 assuming a 5 percent status quo bias, and 0.30 assuming a
10 percent status quo bias. The elasticities for the other risky
assets would be modified by the same factors. In essence, if one
believes in substantial persistent measurement error, some frac-
tion of the difference between the theoretically mandated elastic-
ity and that estimated in the baseline model can be seen as a
consequence of the persistent measurement error.
VII. C
ONCLUSION
This paper reports the results of experimental questions de-
signed to elicit measures of risk tolerance, the elasticity of inter-
temporal substitution, and time preference. The measures
concern preferences over behaviors that are central to macroeco-
nomics and finance, namely willingness to take gambles over life-
time income and to substitute consumption over long periods. The
parameters are estimated as part of the Health and Retirement
Study. Estimating the preference parameters as part of a large-
scale survey has several advantages. First, the estimated prefer-
ence parameters can be related to the behaviors that they should
predict. The economics profession is skeptical about subjective
questions and answers. Being able to relate the subjectively esti-
mated preference parameters to tangible behavior should ad-
dress some of this skepticism. Second, to the extent that the
estimated parameters do predict behavior, they might be useful
in many applications of the survey database.
We find that there is substantial heterogeneity in preference
parameters. Although most of our respondents are in our least
risk-tolerant category, many are substantially more risk tolerant.
Theory predicts very different behavior toward risk for agents
with these varying degrees of risk tolerance. We have some suc-
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cess in relating these estimates to different behaviors. For ex-
ample, the risk tolerance measure is related in the way one would
expect to whether a respondent smokes, drinks heavily, has no
health or life insurance, or holds stocks and other risky assets.
Indeed, for virtually every behavior we investigate, the risk toler-
ance measure made qualitatively correct predictions. The regres-
sion coefficients are large in their implications for behavior. Yet,
there is tremendous variability in the behaviors, so only a small
fraction of their variance is explained by risk tolerance (or any
covariate). This finding of a common factor in behavior, but one
that leaves most of the differences between individuals unex-
plained, is common in the psychological literature.
A
PPENDICES
APPENDIX
1
:
S
UMMARY
D
EMOGRAPHIC
C
HARACTERISTICS,
HRS W
AVE
IR
ESPONDENTS
All Primary Secondary
Characteristic respondents respondents respondents
Average age (years) 55.6 56.1 54.7
Average education (years) 12.1 12.2 11.9
Fraction male (percent) 44.9 51.7 33.8
Fraction black (percent) 16.1 18.4 12.2
Fraction Asian (percent) 1.1 1.0 1.1
Fraction Hispanic (percent) 9.0 9.2 8.7
Number of respondents 11707 7278 4429
For couples the primary respondent is the one reported to be most knowledgeable about family finances.
A
PPENDIX
2
:
D
ISTRIBUTION OF
R
ESPONSES TO
R
ISK
P
REFERENCE
Q
UESTION ACROSS
W
AVES
Percent choosing response
(column percent)
Wave I Number of
Wave II I II III IV responses
I 68.4 57.3 48.2 36.8 436
II 12.7 18.0 10.6 14.9 96
III 11.8 18.0 21.2 19.5 105
IV 7.0 6.7 20.0 28.7 80
Number of 456 89 85 87 717
observations
Distribution of responses for the subset of individuals who answered risk tolerance questions on both
waves of the HRS.
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A
PPENDIX
3
:
M
ODULE
K
:
S
PENDING AND
S
AVING
P
REFERENCES
Module K is a set of questions asked of a small subset of HRS
Wave I respondents designed by us to elicit preferences about the
path of consumption. The interviewer began the module by read-
ing the following introduction to the respondents:
Now I have a few questions about your preferences for spending and
saving as you get older. To make the questions comparable for all
respondents in the survey, let’s suppose that you are now 50 years
old, that you [and your (husband/wife)] will live to be 80. Further
suppose that future health care costs are fully covered by insurance,
that there will be no inflation, and the income after taxes is guaran-
teed to be $3000 each month from age 50 to age 80.
The interviewer then gives a card to the respondent showing two
equal present value consumption profiles with different slopes.
The interviewer describes the card as follows:
[The card] contains several possible patterns of monthly spending
before retirement, the striped bars, and after retirement, the solid
black bars. By saving part of your income before retirement, you
can have more to spend after retirement, as in choice E. Or you
could borrow and spend more before retirement, spending less and
repaying the loan after retirement, as in choice A. Or you could just
spend your income each month, as in choice C. Thus, you can afford
any of the spending patterns shown on [the card]. Which pattern do
you like the most?
The interviewer first presents the respondent card I (not repro-
duced). It is the same as card II (reproduced as Figure I), except
it presents only options A, C, and E. (We meant this first card to
acquaint the respondents with the format of the questions.) The
interviewer then gives card II to the respondent and states, “Here
are the same patterns as before, with two additional choices.
Which do you prefer?” (If the respondent chooses choice C (flat
consumption path), the interviewer offers the choices on card III
(not reproduced), with slopes of the consumption path between
those represented by choice B and D.)
To this point in the module, the consumption paths have a
zero interest rate. To estimate the elasticity of intertemporal sub-
stitution, we then offer the respondents choices with a nonzero
interest rate. That the interest rate is positive is not stated ex-
plicitly. The interviewer instead gives the respondent card IV (re-
produced as Figure II) and reads the following:
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F
IGURE
I
F
IGURE
II
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Here is another card with 5 more spending patterns for before and
after retirement. As before, by saving part of your income before
retirement, you can have more to spend after retirement. Assuming
that you can afford any of the spending patterns on Card IV, which
pattern do you like the most?
Finally, the interviewer asks the respondent to choose among
paths on card V (not reproduced), which are constructed using a
negative interest rate.
U
NIVERSITY OF
M
ICHIGAN AND
N
ATIONAL
B
UREAU OF
E
CONOMIC
R
ESEARCH
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