Table 1: Parameter Calibration for the Benchmark Model
--- put Table 1 here ---
The optimization problem (3)-(6) is solved backward via stochastic dynamic
programming. Further details are given in Appendix A.
3.3 Asset Allocations According to the Benchmark Model
In this section, we show how individual optimal asset allocations—that is, the
percentage share of savings invested into the risky asset—are influenced by the
various input parameters. The results will serve as hypotheses for the empirical
estimations in section 5 and build the basis for analyzing welfare effects in section 6.
We describe the impact of risk aversion, the subjective discount factor, the survival
probability, age, education, gender, the capital market environment, cash on hand,
and expected labor income. We begin with an explanation of the effect of cash on
hand and expected labor income, because some of the other effects depend on the
ratio of expected labor income to cash on hand.
Whereas in a model without labor income the individual’s risky asset share is age,
time, and cash on hand invariant, here, the risky asset share increases in the labor
income-to-cash on hand ratio, because labor income serves partially as a risk-free
asset (Viceira, 2001; Cocco, Gomes, and Maenhout, 2005) and due to diversification
effects (Gollier, 2001). Note that the CRRA feature of the one-period utility function
still can result in an asset allocation that is invariant with respect to some fixed value
of the labor income-to-cash on hand ratio, if the cash on hand and labor income are
perfectly scaled. This means that, for example, while doubling cash on hand and
expected labor income, the asset allocation stays constant, if expected labor income
is doubled in all future periods.11
11 Note that, if leaving, for example, the discounted value of expected labor income constant
but changing the shape of the life-cycle income profile over the life cycle would, in
general, result also in a change in asset allocation, because the likelihood of binding no-
short-sale or borrowing constraints in future periods is changed.
13