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.

τ-1

δτ Σ δt =

t=0


1 - δτ


T-1

δτ δt = δτ
t=τ


1 - δτ-τ

1 - δ


(4)


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 δτ and reduces
δ
τ in equal proportions, ∂δτ/∂τ = -∂δτ/∂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 δ
T) 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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