Staying on the Dole

Appendix: Comparative Statics without STU

If life-time incomes intersect in a way that STU is never the best choice as in Figure 3, human
capital endowment h^B separates employment and LTU. The relevant derivatives are

∂hB _    δτhB

~∂b = δτ (1 - b)+ δτ

^δ f^λ0 ^{- λ}τ ^- Tj ⁺ + ^hB ^b^ yzj ιΛ ∣ с

1 - θ         δ_τ(1 - b) + δT

∂hB _        δτ

∂s = (1 - θ) [⅛_r (1 - b) + δτ ]

∂hB            δτs

~∂θ~ = (1 - θ)2 [δτ (1 - b) + δτ]
∂h^B ∂h^B
0
∂d ∂c

∂hB = ( s  - hB\          1

∂δτ   V - θ 7(1 - θ)[δτ (1 - b)+ δτ ]2

∂hB        δτ            ∂hB        δτ

дЮ = δτ (1 - b) + δτ > ^, W = δτ (1 - b) + δτ

In principle, the effects on employment and LTU are the same as for the non-generate case
discussed in the text. Sometimes, of course, there are no partial effects observable. Because the
LTU will never be at work again they are not affected by retraining costs and do not suffer from
(further) increasing skill degradation. This is not the same as saying that there are no effects
at all. The parameter variation can be so large that LTU is affected because STU turns out to
be worthwhile and the degenerate case ceases to exist.

The sign of ∂hB/∂δ_τ is undetermined and only unambiguously positive in the absence of
current labor market tightness (λ0 = 0). In this case LTU is decreasing with δT, i.e. younger
workers are less afflicted with unemployment. The sign of ∂hB/∂τ is also ambiguous. It includes
a degenerate case where longer eligibility for unemployment benefits leads to lower unemploy-
ment. In order to provide an intuition, we assume that labor market frictions are structural

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