2. The Model
Consider a person who loses his job but could get a new job immediately or anytime in the
future (we abstract from job search frictions). The person can either accept the job, earn a
wage that depends on his productivity and current labor market conditions, and pay taxes
on his wage income. Alternatively, the person can remain unemployed. We call a person
remaining unemployed for less than τ periods a short-term unemployed (STU), and a person
who remains unemployed beyond τ periods a long-term unemployed (LTU). The STU receive
unemployment benefits depending on their last (net) wage for a limited time of τ periods. Long-
term unemployed persons receive social benefits (welfare assistance) which are independent of
their last wage until the end of their working life. The cost of being unemployed is that human
capital erodes, i.e. the unemployed face skill degradation. We assume that the unemployed can
retrain at some cost to mitigate skill degradation.
The decision maker thus faces two decisions: when to exit unemployment (i.e. to be employed,
STU or LTU) and, if unemployed, whether to mitigate human capital degradation by retrain-
ing. As shown in detail below, our model predicts that some (those with high productivity)
find it profitable to accept the job and to be employed, some may find it attractive to obtain
unemployment benefits for some periods and use the STU spell for retraining, and some (often
those with low skills), may find it profitable to let human capital erode and remain on the dole
permanently. These decisions often depend in subtle ways on labor market institutions, personal
characteristics and labor market tightness.
Consider a currently unemployed person with human capital (productivity) h who could get a
job at a gross wage wt = h - λt. The parameter λt represents current labor market tightness, i.e.
exogenous shocks to labor market income. We assume that labor income is taxed at a constant
rate θ.
It pays for a person with human capital h to exit unemployment immediately (i.e. at time
t = 0) if the present value of life-time labor market income
T-1
V(h, 0) = ∑ δt(1 - θ)(h - λt) (1)
t=0
dominates all other possible income streams. We assume that future income is discounted at
factor δ < 1, and that the person retires from working life after T periods. Equation (1) shows