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.
I know nothing about this. But I entered "unemployment human capital deterioration mortensen pissarides" into Google Scholar and clicked the first link (Two Questions about European Unemployment, Ljungqvist and Sargent, Econometrica 2008) and Ljungqvist and Sargent just do the obvious thing.
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.
So this is at least one approach. Do you have a particular reason not to use a Markov chain?
