The Sources of Wage Variation: A Three-Way High-Dimensional Fixed Effects Model

This paper estimates a wage equation with three high-dimensional fixed effects – worker, firm, and job title – 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 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 effects are less important overall (28.7 percent) and are due in roughly equal parts to the unobserved component (14.6 percent) and the observed component (14.0 percent). Job title effects emerge as the least important factor but they still explain 9.7 percent of wage variation, with the observed fixed effects component playing a more important role (7.9 percent versus 1.9 percent for the unobserved fixed component) while improving the precision of the estimates of the other sources of wage variation. Finally, and importantly given the lingering ambiguity in the wider empirical literature, there is material evidence of positive assortative matching.