Risk Preferences in the PSID: Individual Imputations and Family Covariation

1. Risk Preferences in the PSID: Individual Imputations and Family Covariation Miles S. Kimball,University of Michigan, NBERClaudia R. Sahm,Federal Reserve BoardMatthew D. Shapiro,University of Michigan, NBER January 3, 2009 AEA Annual Meeting Session on “New Empirical Approaches to Decision Making Under Uncertainty”

2. 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

3. 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

4. Survey Question 1996 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

5. Distribution of Responses Increasing in risk tolerance • Modal response is to reject all risky jobs • Yet, substantial heterogeneity in sample • Similar to patterns in HRS

6. 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 • similarly, reject downside risk of 1/3  θ  0.50

7. Statistical Model • Assume risk tolerance θlog-normally distributed: • Gamble responses provide noisy signal of risk tolerance: with status quo bias b and transitory error • Response category give bounds for ξandestimate parameters with ordered probit • Not identified with one PSID wave, use HRS panel to correct for survey response error

8. Parameter estimates for PSID Imposed from HRS

9. Individual Imputations • MLE estimates and moment-generating function to impute preference parameters

10. Using Imputations as a Proxy Advantages • Cardinal measure • Controls for response error • Controls attenuation bias in regression analysis

11. 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

12. PSID Intergenerational Application Risk tolerance responses depend on age  Need to control for age in statistical model

13. 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

14. Statistical Model • For example, consider responses from father f and child c: • Covariance driven by preferences not response error • Separate estimation for father-child, mother-child, younger-older sibling, and husband-wife pairs • Age effects controlled for by difference in means

15. 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

16. Conclusions: Imputations • Imputations of preference parameters • Cardinal preference parameter • Adjustments for response error • Substantial heterogeneity in PSID • Age effects substantial

17. Conclusions: Family Correlation • Substantial correlation among family members • Correlation strongest between siblings • Strong correlation  substantial signal in survey • Sources of correlation an open question