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.
Abstract. How much do worker skills, firm pay policies, and their interaction contribute to wage inequality? Standard approaches rely on latent fixed effects identified through worker mobility, but sparse networks inflate variance estimates, additivity assumptions rule out complementarities, and the resulting decompositions lack interpretability. We propose TWICE—Tree-based Wage Inference with Clustering and Estimation—a framework that models the conditional wage function directly from observables using gradient-boosted trees, replacing latent effects with interpretable, observable-anchored partitions. This trades off the ability to capture idiosyncratic unobservables for robustness to sampling noise and out-of-sample portability. Applied to Portuguese administrative data, TWICE outperforms linear benchmarks out of sample and reveals that sorting and non-additive interactions explain substantially more wage dispersion than implied by standard AKM estimates.