The sources of wage variation and the direction of assortative matching: Evidence from a three-way high-dimensional fixed effects regression model

This paper estimates a wage equation with three high-dimensional fixed effects, using a longitudinal matched employer-employee dataset covering virtually all Portuguese private sector wage earners over a 26-year interval. First, the variation in log real hourly wages is decomposed into three components reflecting worker, firm, and job title characteristics and a residual element. It is found that worker permanent heterogeneity is the most important source of wage variation accounting for one third of the wage variance, while firm permanent effects contribute one fourth. Job title fixed effects still explain a considerable one fifth of wage variance. Second, having established that high-wage workers tend to match with high-paying firms, worker fixed effects from the wage equation are next correlated with firm fixed effects from sales and value-added production equations to provide unambiguous evidence on the sign and strength of assortative matching. The correlations are positive and large, indicating that higher productivity workers tend to match with higher productivity firms.