that life-time labor market income V (0) increases with human capital endowment and the length
of remaining working life. This implies that V (0) decreases with the worker’s age.
The cost of being unemployed is that human capital degrades during unemployment. This
may, for example, be the case because the unemployed do not benefit from on-the-job training,
because human capital erodes when not familiarized with the current state-of-the-art technology,
or simply because they are not used to work anymore.1 The unemployed may mitigate human
capital degradation or actually improve skills by incurring costly educational efforts (e.g. by
taking a computer course). These efforts are valuable because they increase human capital, and
thus future wages. To keep the analysis of skill deterioration and retraining tractable, we assume
that a fraction d of human capital depreciates during short-term unemployment and that an
unemployed person can spend c ∙ e units of income on retraining which increases their human
capital by e > 0 units. Alternatively, they may let their human capital erode and do not retrain
(e = 0).
A short-term unemployed (STU) receives unemployment benefits b ∙ (1 — θ)h from unem-
ployment insurance for τ periods. STU leave unemployment at time τ and receive a wage of
wt = (1 — θ)[(1 — d)h + e — λt] per period t for the rest of their working life. Thus the present
value of an STUs life-time income is given by
τ-1 T-1
V(h, τ) = ^ δtb(1 — θ)h — c ∙ e + ^ δt(1 — θ) [h(1 — d) + e — λt], (2)
t=0 t=τ
where c denotes unit costs of retraining (in present value terms).
If people are still unemployed after τ periods, they become long-term unemployed (LTU) and
receive tax-exempt social benefits s per period until time T . The present value of an LTU’s
life-time income is
τ-1 T-1
V (h,T ) = ∑ δtb(1 — θ)h + ∑ δts. (3)
t=0 t=τ
A person’s life-time income V(h, t) can be understood as a function of his human capital and
the time t at which he leaves unemployment. To keep the analysis simple, we assume that labor
1 Topel (1990) estimates that in the US in the 1970s and 1980s workers losing a job suffered on average a wage
reduction of between 15 and 40 percent by the time they found a new job. Jacobsen et al. (1993) find similar
results. Keane and Wolpin (1997) estimate that blue-collar skills depreciate by about 10 percent in a year absent
from work, while white-collar workers lose about 30 percent of their skills during one year of unemployment.
Thus, a more realistic model would tie the depreciation rate itself to the level of human capital. In any case,
however, human capital degradation is of non-negligible magnitude.