Search and (In-)Elastic Rest Unemployment: An Analytical Framework

This paper develops a tractable quantitative framework for analyzing sectoral labor reallocation and unemployment. The framework features analytical solutions for sectoral wages, employment and unemployment dynamics, as well as aggregate unemployment, which allows fast model estimation from labor market transition data and convenient counterfactual exercises to quantify the impact of sectoral shocks and the relevant labor market institutions. In particular, the framework accommodates two important features of the data: (i) heterogeneous response of sectoral labor market dynamics to shocks; and (ii) persistent unemployment accompanied by persistently depressed wages for certain sectors. I apply the framework to test the sectoral shifts hypothesis and find that a 1% increase in sectoral shock dispersion would raise aggregate unemployment by 0.55%. The result is consistent with the observation of slow employment recovery post recent recessions with job polarization.