Staying on the Dole

The model predicts that workers with low human capital degradation (d) and old workers (small
δT ) are particularly responsive to changes in unemployment benefits.

3.2. Duration of Eligibility for Unemployment Benefits. The effects of an increase in the
duration of eligibility for unemployment benefits are less straightforward. An increased duration
of unemployment benefits increases LTU if it discourages (low-skill) STU to retrain. An increased
duration increases total unemployment under some conditions (in particular when labor markets
are tight and taxes are high). To simplify the notation, we define δ' ≡ ∂δ_τ/∂τ > 0 and recall
that ∂δτ/∂τ = -δ. We obtain the following effects of increasing the duration of eligibility for
unemployment benefits (τ).

∂hA         ceδ'       >       ∂hC   (δ_τ + δ_τ)λ₀(1 — θ)d — φ ∙ e _z

∂τ δT(1 — θ)(1 — d) ^^ ^, ∂τ (1 — θ)[δ_τ(1 — b) + δ_τd]2

φ ≡ [(1 — θ)δT — c] (1 — b) + (1 — θ)(1 — b)δτ + cd > 0,

where the positivity of φ follows from the retraining condition (5).

Suppose unemployment is not used for retraining (e = 0). In this case, longer eligibility for
unemployment benefits does not affect LTU (these workers prefer to stay on the dole anyway).
It increases STU because some workers in the higher range of the education spectrum find a
short spell in unemployment attractive (∂hC/∂τ > 0 for e = 0). This will in particular be the
case when current labor market frictions are large. Without labor market frictions (λ0 = 0) and
without retraining, there is no effect of benefit eligibility on STU because the replacement rate
is smaller than one (i.e. 1 — θ — b > 0).

If workers retrain, their option to upgrade skills is the dominant motive for being STU (rather
than to collect unemployment benefits). In this case, our simplified model which treats retrain-
ing as a one-time event that happens instantly (by paying the retraining cost) may imply a
degenerate reaction to longer eligibility of unemployment benefits. Having used the STU spell
for retraining, workers actually strive for a new job because the payoff of the newly acquired
skills in terms of higher wages occurs only after re-employment.

An (exogenous) extension of the unemployment period τ has thus the negative effect of delay-
ing re-employment. The delay devaluates retraining such that some workers with intermediate
skills who would have retrained with a shorter duration now decide against retraining. Without
retraining, they find a permanent stay on the dole attractive and as a consequence LTU increases

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