Figure 2: Involuntary Unemployment
LTU STU Employed
invol. LTU invol. STU
retrain), the present-biased value of life-time income becomes
T-τ
Vτ-ι(h, τ) = b(1 - θ)h - kτ-1 ∙ c ∙ e + β ∑ δs(1 - θ)
s=1
(1 - d)h +
(S‘ ■)
(13)
implying that they will retrain if
c < β(1 — τ)δτ.
(14)
(15)
They will not retrain if the costs of retraining fulfill
β<δτ < ---< < δ>τ.
1-θ
If condition (15) holds, present-biased agents do not retrain when they lose eligibility for un-
employment benefits although they originally planned to use the STU spell to upgrade their
skills.
Figure 2 illustrates the consequences of a failed retraining episode depending on the worker’s
initial skill level. Because retraining was, in principle, worthwhile, failed retraining shifts life-
time income V(h,τ) downwards. At the upper end of the education spectrum, between h'C
and hC , we find those workers who would have preferred to be employed had they known
19
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