Joint work with Francesco Del Prato and Yaroslav Korobka.

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.

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