Joint work with Aslan Bakirov and Francesco Del Prato. Under review.
Abstract. How much wage dispersion is visible in characteristics we observe? Using Portuguese matched employer-employee records linked to firm financial data, we sort workers and firms into observable cells and decompose log wages across worker-firm cells. Worker cells account for 35.0% of the variance, firm cells 6.7%, sorting 8.8%, and a worker-firm interaction 6.7%; the remaining 42.8% lies within cells. A second exercise splits the firm component into what firms pay similar workers (pay policy) and whom they employ (workforce composition). Pay policy dominates, accounting for about two-thirds of the firm component’s variance, and the two margins reinforce: higher-paying firms employ higher-wage workforces. Holding observable cells fixed across Portugal’s recovery, the fall in log-wage variance is explained by changing cell wage schedules rather than by workforce reallocation or re-sorting. The two-sided structure usually credited to latent worker and firm effects is thus visible in observed characteristics on the worker side, much less so on the firm side.
Abstract. This paper develops an estimator for quadratic forms in semiparametric models where covariates enter through an unknown function. The leading application is a generalized AKM wage decomposition: we estimate worker and firm variance components and sorting while flexibly partialling out observed worker and firm characteristics. The estimator combines leave-one-out bias correction with series approximation, is robust to heteroskedasticity and many fixed effects, and is consistent when both fixed effects and basis terms grow with sample size under a strengthened smoothness condition. Simulations show large bias reductions relative to plug-in estimators in nonlinear settings. In linked Portuguese employer-employee data, adding rich controls to linear AKM generates large discontinuities, whereas the generalized estimator yields coherent movements across control sets and basis richness, with sorting attenuating toward zero as flexibility increases.