Risk Preferences in the PSID: Individual
Imputations and Family Covariation
Miles S. Kimball,
University of Michigan, NBER
Claudia R. Sahm,
Federal Reserve Board
Matthew D. Shapiro,
University of Michigan, NBER
January 3, 2009
AEA Annual Meeting
Session on “New Empirical Approaches to Decision Making Under Uncertainty”
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 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
Distribution
of ofResponses
Response
Percent
Category
1
2
3
4
5
6
Respondents
30.9
18.2
15.6
15.0
13.7
6.6
Increasing
in risk
tolerance
5,466 PSID respondents
• Modal response is to reject all risky jobs
• Yet, substantial heterogeneity in sample
• Similar to patterns in HRS
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:
0.5U (2C )  0.5((1  1 / 5)C )  U (C )
1-1/
C
where U(C) 
1 - 1/
 Coefficient of relative risk tolerance θ  0.27
• similarly, reject downside risk of 1/3  θ  0.50
Statistical Model
• Assume risk tolerance θ log-normally distributed:
log i  xi ~ N   ,  x2 
• Gamble responses provide noisy signal of risk tolerance:
 it  log  i   it
 it  bq  eit
2
with status quo bias b and transitory error e ~ N 0, e 
• 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
Parameter estimates for PSID
Log of risk tolerance
Mean

-1.05
Standard deviation
x
0.87
Status-quo bias
Response error
Standard deviation
b
-0.21
e
1.30
Imposed
from HRS
Individual Imputations
Response
Category
1
2
3
4
5
6
Log Risk
Tolerance
-1.60
-1.18
-0.98
-0.77
-0.50
-0.08
Risk
Tolerance
0.27
0.40
0.49
0.60
0.79
1.22
Risk
Aversion
6.7
4.2
3.5
2.8
2.2
1.4
Note: Imputations use MLE estimates from the PSID gambles
that are adjusted for response error and status quo bias using
estimates from the HRS.
• 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
PSID Intergenerational Application
Risk tolerance responses depend on age
Response
Category
1
2
3
4
5
6
20-29
22.7
18.7
15.9
17.8
17.3
7.6
Percent by Age Group
30-39
40-49
50-59
27.8
30.5
44.6
18.5
18.8
16.9
16.1
16.5
13.3
16.3
15.5
8.0
13.9
13.0
11.6
7.4
5.6
5.5
60-69
60.6
13.4
9.3
6.5
4.9
5.3
Note: Unweighted tabulations of PSID gamble respondents.
 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:
 f  log  f   f ~ N ( f , 2f )
c  log  c   c ~ N (c ,  c2 )
Cov  f , c   Cov (log  f ,log  c )   2fc
• Covariance driven by preferences not response error
• Separate estimation for father-child, mother-child, youngerolder sibling, and husband-wife pairs
•Age effects controlled for by difference in means
Covariation in Log Risk Tolerance
Father
Mother
Child 1
Child 2
Variance-Covariance \ Correlation
Father
Mother
Child 1
Child 2
0.76
0.41
0.14
0.14
(0.07)
0.32
0.76
0.23
0.23
(0.13)
(0.07)
0.11
0.18
0.76
0.48
(0.13)
(0.11)
(0.03)
0.11
0.18
0.37
0.76
(0.13)
(0.11)
(0.06)
(0.03)
• 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
Conclusions: Imputations
• Imputations of preference parameters
– Cardinal preference parameter
– Adjustments for response error
• Substantial heterogeneity in PSID
• Age effects substantial
Conclusions: Family Correlation
• Substantial correlation among family members
• Correlation strongest between siblings
• Strong correlation  substantial signal in
survey
• Sources of correlation an open question