The Impact of Individual Investment Behavior for Retirement Welfare: Evidence from the United States and Germany

individual’s characteristics—over the life cycle. Based on this model, hypotheses for
the econometric analyses are formulated in section 5.1.

3.1 The Individual’s Problem

For our normative analysis, we use the workhorse for solving intertemporal
allocation problems, discounted utility. The individual maximizes the expected utility
of consumption C (all monetary variables are stated in nominal terms) over his or her
stochastic life span. The intertemporally separable utility function U(C) is defined as:

τ - x   ( t 1

U ( C )=∑ δ l∏ pI U, ( C, ) .                      (1)

t=0    \ i=0    J

T denotes the maximum life span, x the current age, δ the subjective discount factor,
and p_t the probability of the individual to survive from period t - 1 to t. We assume
no bequest motives; thus, the one-period CRRA-utility function Ut(Ct), with γ as the
coefficient of relative risk aversion, is given by:
as long as the individual lives and 0 otherwise. Ct stands for nominal consumption at
time t and is adjusted for inflation at rate π.

At each point in time t, the individual decides how much to consume (implicitly
determining savings) and how to allocate savings. Financial wealth at time t is
denoted by Wt, henceforth called “cash on hand” (Deaton, 1991). Savings St are
allocated to both a risk-free investment and a risky investment. The proportion of
savings invested riskily each period, αt, earns the risky return Rt whereas the rest (1 -
αt) is compounded at the risk-free return Rf . We assume that the individual cannot
borrow money or short-sell stocks. The individual earns stochastic labor income Lt

<<   7   8   9   10   11   12   13   >>

More intriguing information