This paper adds two-sided ex-ante heterogeneity and a production technology inducingsorting to the canonical Diamond-Mortensen-Pissarides (DMP) search and matchingmodel. Ex-ante heterogeneity and sorting have important implications for the dynamicproperties of the model. The modifications solve the problem that standard DMP modelsdo 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 endogenouslygenerated wage rigidity, which is of reasonable magnitude given empirical evidencefrom the U.S. labor market. Additionally, endogenous matching sets fluctuate inresponse to shocks and amplify job-creation. Using a standard Nash sharing rule, I showthat the surplus function of the model, which depends on both workers' and firms' outsideoptions, exhibits an asymmetry in equilibrium that stems from unequal bargainingpowers. Using the standard calibration of the model, the firms' matching sets are widerin equilibrium than the workers' matching sets and fluctuate more in response to shocks.