The Sources of Wage Variation: 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 wage earners over a little more than two decades. The variation in log real hourly wages is decomposed into different components related to worker, firm, and job title characteristics (both observed and unobserved) and a residual component. It is found that worker permanent heterogeneity is the most important source of wage variation (36.0 percent) and that the unobserved component plays a more important role (21.0 percent) than the observed component (15.0 percent) in explaining wage differentials. Firm permanent effects are less important overall (28.7 percent) and are due in almost equal parts to the unobserved component and the observed component. Job title effects emerge as the least important dimension but they still explain close to 10 percent of wage variation. We found definitive evidence of positive assortative matching.