This paper develops a theory of optimal unemployment insurance (UI) in matching models. The optimal UI replacement rate is the conventional Baily-Chetty replacement rate, which solves the tradeoff between insurance and job-search incentives, plus a correction term, which is positive when an increase in UI pushes the labor market tightness toward its efficient level. In matching models, most wage mechanisms do not ensure efficiency, so tightness is generally inefficient. The effect of UI on tightness depends on the model: increasing UI may raise tightness by alleviating the rat race for jobs or lower tightness by increasing wages through bargaining.
Figures 4: The effect of UI on labor market tightness differs across matching models. The effect can be measured by the wedge between the macroelasticity ($\epsilon^M$) and microelasticity ($\epsilon^m$) of unemployment with respect to UI.
Landais, Camille, Pascal Michaillat, and Emmanuel Saez. 2018. “A Macroeconomic Approach to Optimal Unemployment Insurance: Theory.” American Economic Journal: Economic Policy 10 (2): 152–181. https://doi.org/10.1257/pol.20150088 .