benchmark in each period. Thus, our results measure only the welfare effects that
arise from choosing a suboptimal asset allocation.19
To calculate the welfare effects, we chose a certain subsample to avoid extremely
long computation times (the SCF and EVS data sets contain 11,658 total cases). For
this, we chose three ages: 30, 50, and 65. For each age group, cash on hand (net
worth) is varied continuously,20 whereas for labor income, the 25%, 50%, and 75%
age-specific quantiles as given by the data are assigned to the individuals.21 Next, the
welfare measure is calculated for these individuals assuming a relative risk-aversion
parameter γ of 2 and a subjective discount factor δ of 0.97 for different values of
gender (male, female) and education (low, middle, high). Furthermore, the
preference parameters γ and δ are varied according to the calibrations shown in Table
1.
The analysis of our results begins with the outcome of the model calibrated with U.S.
data. After this, we discuss the German results. Finally, we compare both countries
and draw general conclusions. In general, U.S. and German individuals invest too
little in risky assets. Thus, losses in welfare are significantly influenced by the size of
the (positive) gap between the optimal and the empirical investment share of the
risky asset.
6.1 Results for U.S. Individuals
Figure 3-SCF shows how the loss in welfare is influenced by net worth, labor
income, and gender:
19 Savings adequacy is addressed in Scholz, Seshadri, and Khitatrakun (2006). Furthermore,
the SCF data set does not provide information on consumption and savings.
20 For this we can utilize the CRRA feature of the value function with respect to Wt.
21 Precisely, we also included the neighbouring age groups (e.g., 29 and 31 in case of age
30) to calculate the quartiles in order to avoid too much distortion due to a low amount of
cases in some age groups.
23
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