Joint work with Francesco Del Prato and Yaroslav Korobka.

Abstract. This paper introduces an estimator for quadratic forms based on the linear parameters of a semi-parametric model. The leading example is the workhorse model of wage determination by Abowd, Kramarz, and Margolis (1999, AKM): our estimator targets standard variance components while allowing for a nonparametric treatment of both worker- and firm-level observable characteristics. We propose a bias-corrected estimator robust to heteroskedasticity that controls for approximating functions of the covariates. We show that this estimator is asymptotically unbiased and consistent when the number of linear parameters (e.g. the AKM fixed effects) is proportional to the sample size. In particular, consistency hinges on a strengthened smoothness condition (which we discuss for the first time) on the nonparametric component’s functional class. In an empirical application, we show that adding a rich set of controls to the standard AKM model yields implausibly large firm effects. Our method addresses this issue, yielding estimates of variance components that aremore robust relative to conventional approaches. Confounding—not functional-form choice—drives the standard model’s instability.

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