An Empirical Model of Wage Dispersion with Sorting

By Jesper Bagger and Rasmus Lentz

This paper studies wage dispersion in an equilibrium on-the-job-search model with endogenous search intensity. Workers differ in their permanent skill level and firms differ with respect to productivity. Positive (negative) sorting results if the match production function is supermodular (submodular). The model is estimated on Danish matched employer-employee data. We find evidence of positive assortative matching. In the estimated equilibrium match distribution, the correlation between worker skill and firm productivity is 0.12. The assortative matching has a substantial impact on wage dispersion. We decompose wage variation into four sources: Worker heterogeneity, firm heterogeneity, frictions, and sorting. Worker heterogeneity contributes 51% of the variation, firm heterogeneity contributes 11%, frictions 23%, and finally sorting contributes 15%. We measure the output loss due to mismatch by asking how much greater output would be if the estimated population of matches were perfectly positively assorted. In this case, output would increase by 7.7%.

Denmark is blessed with absolutely fantastic datasets, and this paper exploits this kind of data to reach some very interesting conclusions. In particular, it manages to quantify the sources of wage dispersion and the welfare gain from frictionless matching. With such a large welfare gain, the next step would be to exploit the data to actually step in and do better matches. That would be the ultimate policy experiment. Will that happen?


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