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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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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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