Estimating Risk Tolerance From the 1996 PSID

By Ming-Ching Luoh and Frank Stafford

In questions M1-M5 (page 138 on the paper mock-up of the questionnaire, employed respondents are asked how willing they are to take jobs with different income prospects. These questions are similar to ones used in the Health and Retirement Study, but here they indicate that the new job will be equally good, having the same non-monetary attributes as their current job. All answers to these questions offer a 50-50 chance to double income or to cut income in different proportions. (Note: The mock-up questionnaire has a typo. The actual question asked of respondents in the CATI application starts with a 50-50 chance of doubling income and spending, or a 50-50 chance of reducing income and spending power by a third.)

If the respondent is willing to take a chance and answers yes, the next question branches into a query about their willingness to accept a doubling on the up side, combined with a cut to one half. If the respondent answers yes again, they are asked how willing they would be to accept a cut of 75 percent. If, however, the respondent answers no to the initial double or one-third option, the question branches into a query about their willingness to accept a 20 percent cut on the downside. If they answer no here, they are asked about their willingness to accept only a 10 percent cut on the downside.

Based on responses to these questions, we can arrange people into six groups with an exact risk tolerance range, and four groups with larger ranges due to item non-response along some of the branches.

To convert these answers into a single, quantitative index of risk tolerance (see Barsky, Juster, Kimball and Shapiro, Quarterly Journal of Economics, May 1997), suppose the utility function is U(c) = (1/(1-1/q) )c ^1-1/q. Our task is to estimate q. Assume that q is log-normally distributed, then X = ln (q) is a normal distribution. However, X is unobservable. What we observe is X*, which is in one of the ten groups according to the following process:

X* in group i, if B_i-1< x < B_i

Where B_i is the cutoff point on X determined by the design of the survey questions, indicated above.

The likelihood function then is the product of each individual's probability of being in that particular group. We can estimate mean m and standard deviation s_x by maximizing the likelihood function. We can then recover q for each group by computing the expected e^x conditional on being in that group.

The estimated m is -1.27, while the estimated s_x = 1.579. The conditional means of q are as follows for each group.

Group

Sample

Percent

HRS (a)

Reject (b)

Accept (c)

Range of q 

E(q |X*)

11

365

6.5

(3.8)

None

1 / 4 

[3.2706, Infinity]

8.295

22

760

13.5

(7.1)

1 / 4 

1 / 2

[1,3.2706]

1.758

33

829

14.8

(14.2)

1 / 2 

2 / 3

[.5,1]

.711

44

861

15.3

(12.9)

2 /3 

4 /5 

[.2607,.5] 

.369

55

1009

18.0

(17.4)

4/ 5

9 /10

[.1329, .2607]

.193

66

1741

31.0

(44.5)

9/10 

None

[0,.1329]

.062

12

5

.1

1 / 2 

[1, Infinity]

3.619

13

15

.3

2 / 3

[.5, Infinity]

2.424

46

20

.4

2 / 3

[0,.5]

.171

56

9

.2

4 /5 

[0,.2607]

.107

00(d)

2903

A risk tolerance file is available which shows the difference between the risk tolerance estimates and the tolerances after measurement errors have been corrected. The first variable in the comparison file is the 1996 Family ID. The second variable, Risk Tolerance, is estimated from 1996 PSID questions M1-M5 without correcting for measurement error. In the third variable, Risk Tolerance 1, measurement errors are corrected based on both HRS waves I and II. Data for Risk Tolerance 1 are taken from the last column of Table 1 in Barsky, Juster, Kimball and Shapiro (Quarterly Journal of Economics, May 1997). Fields without numbers indicate that the head was not in the labor force, or that the question was unanswered.