We first observe that a variation in income leads to results opposite those found for
U.S. individuals. Lower income (comparing different curves for given levels of net
worth) is associated with larger welfare losses. Here the effect that with higher
income savings and thus potential deviations from optimal asset allocation are lower,
is stronger than the other effects described for U.S. individuals. Although the—
opposed to the normative benchmark model—negative sign of the coefficient for the
log of labor income leads to greater deviations from the optimal asset allocation for
high income individuals, their lower savings overcompensate for this. The combined
effect of a change in savings and the change in the gap to the optimal asset allocation
explains the hump-shaped welfare loss curves. First, due to the relatively large
income, savings are zero and thus welfare losses are also zero. Then, with increasing
net worth, savings increase, as does the impact of the asset allocation gap. For larger
levels of net worth, the empirical asset allocation comes closer to the 100% optimal
result of the normative benchmark (given certain levels of income and wealth), thus
decreasing the welfare gap. For very large levels of net worth (not shown in Figure
8), this should reverse again, because optimal asset allocation goes below 100% risky
assets, whereas the empirical asset allocation still increases.
In the German data, women generally experience higher welfare losses. First, for any
given current income, the expected discounted value of future labor income is lower,
due to the gender-specific German calibration of the life cycle income profiles.
Consequently, women save more, making deviations work on a larger amount
invested. Additionally, for many parameter constellations, the optimal asset
allocation is 100% risky. Thus, the negative coefficient for the gender dummy
variable increases the gap in asset allocation for women, leading to a higher welfare
loss.
The effects of a change in the assumption about relative risk aversion or the subject
discount factor confirm U.S. results and thus are not shown here.
The impact of a variation in education is shown in Figure 9.
28
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