Risk Preferences in the PSID: Individual Imputations and Family Covariation

January 3, 2009AEA Annual Meeting

Session on “New Empirical Approaches to Decision Making Under Uncertainty”

Miles S. Kimball, University of Michigan, NBER

Claudia R. Sahm, Federal Reserve Board

Matthew D. Shapiro, University of Michigan, NBER

Overview: Risk Tolerance in the PSID

• Measure survey responses to a hypothetical gambles over lifetime income (Barsky, Kimball, Juster, and Shapiro QJE 1997)

• Use statistical model to impute individual risk tolerance (BKJS 1997, Kimball, Sahm, Shapiro JASA 2008)

• Examine covariation in risk preferences between family members

Lessons from Survey-Based Measurement of Preferences

• Survey measures explain actual behavior

• Survey measures subject to response errors: Need to model noise

• Guidance for use of imputations in regressions

Survey Question1996 PSID asks working family respondents:

Suppose you had a job that guaranteed you income for life equal to your current, total income. And that job was (your/your family's) only source of income.

Then you are given the opportunity to take a new, and equally good, job with a 50-50 chance that it will double your income and spending power. But there is a 50-50 chance that it will cut your income and spending power by a third.

Would you take the new job?

Follow-up questions with downside risks of 10, 20, 50, and 75 percent, assign to 1 of 6 response categories

1 30.9 2 18.2 3 15.6 4 15.0 5 13.7 6 6.6

5,466 PSID respondents

Response Category

Percent of Respondents

Distribution of Responses

• Modal response is to reject all risky jobs• Yet, substantial heterogeneity in sample• Similar to patterns in HRS

Increasing in risk

tolerance

Mapping to Preferences Parameters• Gamble response categories have a cardinal interpretation under expected utility theory and CRRA

For example, category 3:

• accept downside risk of 1/5:

Coefficient of relative risk tolerance θ 0.27

1/-1C U(C)where

)())5/11((5.0)2(5.01/-1

CUCCU

• similarly, reject downside risk of 1/3 θ 0.50

Statistical Model

itqit

itiit

eb

log

• Assume risk tolerance θ log-normally distributed:

• Gamble responses provide noisy signal of risk tolerance:

• Response category give bounds for ξ and estimate parameters with ordered probit

• Not identified with one PSID wave, use HRS panel to correct for survey response error

2log ~ ,i i xx N

with status quo bias b and transitory error 2,0~ eNe

Parameter estimates for PSID

Log of risk tolerance Mean -1.05

Standard deviation x 0.87

Status-quo bias b -0.21

Response error Standard deviation e 1.30

Imposed from HRS

1 -1.60 0.27 6.7 2 -1.18 0.40 4.2 3 -0.98 0.49 3.5 4 -0.77 0.60 2.8 5 -0.50 0.79 2.2 6 -0.08 1.22 1.4

Log Risk Tolerance

Risk Tolerance

Risk Aversion

Note: Imputations use MLE estimates from the PSID gambles that are adjusted for response error and status quo bias using estimates from the HRS.

Response Category

Individual Imputations

• MLE estimates and moment-generating function to impute preference parameters

Using Imputations as a Proxy

Advantages• Cardinal measure• Controls for response error• Controls attenuation bias in regression analysis

Using Imputations as a Proxy

Cautions• Imputations based on survey response alone

do not account for all heterogeneity in preferences

• In multivariate regressions, imputation error may be correlated with regressors

• KSS give procedures for handling covariates

20-29 30-39 40-49 50-59 60-69 1 22.7 27.8 30.5 44.6 60.6 2 18.7 18.5 18.8 16.9 13.4 3 15.9 16.1 16.5 13.3 9.3 4 17.8 16.3 15.5 8.0 6.5 5 17.3 13.9 13.0 11.6 4.9 6 7.6 7.4 5.6 5.5 5.3Note: Unweighted tabulations of PSID gamble respondents.

Response Category

Percent by Age Group

Risk tolerance responses depend on age

PSID Intergenerational Application

Need to control for age in statistical model

Family Covariation• Use family members responses to explore source

of heterogeneity in preferences

• Compare responses from parents and adult children, siblings, (PSID), and spouses (HRS)

• Positive covariation within family as in other studies (Charles and Hurst JPE 2003 and Dohmen, Falk, Huffman, and Sunde WP 2008)

• Sets upper bound on the degree variation due to idiosyncratic (persistent) response errors

Statistical Model• For example, consider responses from father f and child c:

• Covariance driven by preferences not response error

),(~log 2 fffff N

),(~log 2 ccccc N

2Cov , (log , log )f c f c fcCov

• Separate estimation for father-child, mother-child, younger-older sibling, and husband-wife pairs

•Age effects controlled for by difference in means

Father Mother Child 1 Child 2Father 0.76 0.41 0.14 0.14

(0.07)Mother 0.32 0.76 0.23 0.23

(0.13) (0.07)Child 1 0.11 0.18 0.76 0.48

(0.13) (0.11) (0.03)Child 2 0.11 0.18 0.37 0.76

(0.13) (0.11) (0.06) (0.03)

Variance-Covariance \ Correlation

Covariation in Log Risk Tolerance

• Mother-child correlation twice as large as father-child

• Sibling correlation is considerably stronger than parent-child• Spouse correlation nearly as high as sibling correlation

• Imputations of preference parameters– Cardinal preference parameter– Adjustments for response error

• Substantial heterogeneity in PSID

• Age effects substantial

Conclusions: Imputations

• Substantial correlation among family members

• Correlation strongest between siblings

• Strong correlation substantial signal in survey

• Sources of correlation an open question

Conclusions: Family Correlation