Staying on the Dole

market tightness is stable up to time τ and may then change. Hence, λt can take two values: λ0 ,
representing current labor market tightness and λ_τ denoting expected labor market tightness
from time τ until time T . To simplify the notation, we introduce the following aggregated
discount factors.

Note from inspection of equations (4) that a longer working-life increases δT and leaves δτ
unaffected, while longer duration of eligibility for unemployment benefits increases δ_τ and reduces
δ_τ in equal proportions, ∂δ_τ/∂τ = -∂δ_τ/∂τ > 0. With these notational simplifications we can
analyze career decisions conveniently in a h-V -diagram taking the exit time from unemployment
t ∈ {0, τ, T} parametrically. For this purpose we rewrite (1’) — (3’) as

V(h,0) =δτ(1-θ)(h-λ0)+δT(1-θ)(h-λτ)                           (1’)

V(h, τ) = δτb(1 - θ)h - c ∙ e + δτ(1 - θ) [(1 - d)h + e - λτ]               (2’)

V(h, T) =δτb(1-θ)h+δTs.                                               (3’)

The decision to retrain is straightforward. Equation (2’) reveals that life-time income of the
short-term unemployed is higher with retraining (e > 0) than without (e = 0) if the present
value of the labor income gain exceeds the present value of retraining costs. In particular, e > 0
is chosen if

c< (1-θ)δT.                                       (5)

Otherwise, no retraining takes place, i.e. e = 0. Thus, equation (5) suggests that high labor
taxes discourage retraining and that younger workers (i.e. those with higher δT) tend to do
more retraining than older workers. Mitigating human capital degradation is never optimal for
a long-term unemployed because he never reaps the returns of retraining on the labor market.

A natural assumption (which holds for every OECD country, see OECD, 1999) is that the net
market wage is higher than unemployment benefits, i.e. that the replacement rate b is smaller
than 100 percent. Under this condition, life-time income is always more steeply increasing in
human capital for employed persons than for the short-term unemployed (STU). For the STU,
in turn, life-time income increases more steeply in h than for the long-term unemployed (LTU).

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