# Unemployment: Human Capital Deterioration

I am looking for Macro-Labor models that include deterioration of human capital. The mechanism is simple: The longer you were unemployed, the more human capital you are losing.

However, this is backward-looking: Your human capital today depends on the length of unemployment - i.e. the periods $t-1$, $t-2$, .... Hence, keeping track of this issue in a macroeconomic model appears to be nontrivial, and I am wondering how and whether the literature was dealing with this fact so far.

Employed and unemployed workers experience stochastic accumulation or deterioration of skills, respectively. There is a finite number of skill levels with transition probabilities from skill level $h$ to $h'$ denoted by $\mu_u(h, h')$ and $\mu_e(h, h')$ for an unemployed and an employed worker, respectively. That is, an unemployed worker with skill level $h$ faces a probability $\mu_u(h, h')$ that his skill level at the beginning of the next period is $h'$, contingent on not retiring. Similarly, $\mu_e(h, h')$ is the probability that an employed worker with skill level $h$ sees his skill level change to $h'$ at the beginning of the next period, contingent on not being exogenously laid off. In the event of an exogenous layoff, the transition probability is $\mu_l(h, h')$. After the initial period coinciding with an exogenous layoff, the stochastic skill level of an unemployed worker is again governed by the transition probability $\mu_u(h, h')$. All newborn workers begin with the lowest skill level.