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A labor market model under search frictions is developed, where participants are heterogeneous in productivity and the decision of which type of agents to match with is endogenized. Two applications are studied. It is observed that countries with high (low) unemployment tend to exhibit low (high) wage dispersion. And there is evidence showing that individual and firm characteristics have more explanatory power for the French than for the American wage data. Matching patterns can account for these two observations. In the absence of a minimum wage, I thus provide a theory of endogenous wage compression.