Wage rigidity and labor market dynamics with sorting

This paper adds two-sided ex-ante heterogeneity and a production technology inducing sorting to the canonical Diamond-Mortensen-Pissarides (DMP) search and matching model. Ex-ante heterogeneity and sorting have important implications for the dynamic properties of the model. The modifications solve the problem that standard DMP models do not generate enough volatility in response to shocks, also known as the "Shimer Puzzle" (Shimer, 2005). Amplification to overcome the volatility puzzle stems from an endogenously generated wage rigidity, which is of reasonable magnitude given empirical evidence from the U.S. labor market. Additionally, endogenous matching sets fluctuate in response to shocks and amplify job-creation. Using a standard Nash sharing rule, I show that the surplus function of the model, which depends on both workers' and firms' outside options, exhibits an asymmetry in equilibrium that stems from unequal bargaining powers. Using the standard calibration of the model, the firms' matching sets are wider in equilibrium than the workers' matching sets and fluctuate more in response to shocks.