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INVESTING RETIREMENT WEALTH: A LIFE-CYCLE MODEL – Time parameters and preferences 2

The estimation controls for family-specific fixed effects. To control for education the sample is split into three groups: households without high school education, a second group with high school education but without a college degree, and finally college graduates. This sample split is intended to accommodate the well-established finding that age profiles differ in shape across education groups (Attanasio 1995, Hubbard, Skinner and Zeldes 1994). For each education group the function f (t, ~t) is assumed to be additively separable in t and Zit. The vector Zit of personal characteristics, other than age and the fixed household effect, includes marital status and household composition. Household composition equals the additional number of family members in the household besides the head and (if present) his spouse.
Ideally one should also control for occupation. Using PSID data this is problematic because from the 1975 wave onwards the majority of the unemployed report no occupation, and are categorized together with people who are not in the labor force. But modelling unemployment as a switch in occupation is inappropriate as the possibility of unemployment through layoff is one of the main sources of labor income risk. We explore this in greater detail in Section 4 below.
To obtain age profiles suitable for the simulation model of life-cycle portfolio choice, we fit a third-order polynomial to the age dummies estimated from the PSID. The resulting income profiles are similar to those used in Gourinchas and Parker (1996), Attanasio (1995), and Carroll and Summers (1991). They are plotted in Figure 1 along with the underlying age dummies for each of the three educational groups.
To estimate the variances of permanent and temporary shocks to labor income, we follow Carroll and Samwick (1997). Defining Y* as
Formula 13-14

We estimate j and j by running an OLS regression of Var(log(Y*t+d ) — log(Yit)) on d and a constant term. We find that groups with lower education tend to have more variable transitory income shocks, but less variable permanent shocks, than groups with higher education. Table 1 reports these variances.
We use a similar procedure to estimate the correlation between labor income shocks and stock returns, p^. The change in log(Y*) can be written as
Formula 15
Averaging across individuals gives
Formula 16
The correlation coefficient is then easily computed from the OLS regression of A log(Y*) on demeaned excess returns:

Formula 17

Table 1: Baseline Parameters

Description Parameter Value
Retirement age (K) 65
Discount factor (B) .96
Risk aversion (7) 5
Variance of transitory shocks (j)
No high school .1056
High school .0738
College .0584
Variance of permanent shocks (j)
No high school .0105
High school .0106
College .0169
Sensitivity to stock returns (q)
No high school .0956
High school .0627
College .0733
Correlation with stock returns (p^)
No high school .3280
High school .3709
College .5155
Riskless rate (Rp — 1) .02
Mean excess return on stocks (>) .04
Std stock return (j) .157
Fixed cost (8) 0 or 10000
Social Security tax rate (W) .10


Figure 1 – Labor Income Profiles (age dummies and fitted polynomials)