Reproducing Kernel Methods for Nonparametric and Semiparametric Treatment Effects.

We propose a family of reproducing kernel ridge estimators for nonparametric and semiparametric policy evaluation. The framework includes (i) treatment effects of the population, of subpopulations, and of alternative populations; (ii) the decomposition of a total effect into a direct effect and an indirect effect (mediated by a particular mechanism); and (iii) effects of sequences of treatments. Treatment and covariates may be discrete or continuous, and low, high, or infinite dimensional. We consider estimation of means, increments, and distributions of counterfactual outcomes. Each estimator is an inner product in a reproducing kernel Hilbert space (RKHS), with a one line, closed form solution. For the nonparametric case, we prove uniform consistency and provide finite sample rates of convergence. For the semiparametric case, we prove root n consistency, Gaussian approximation, and semiparametric efficiency by finite sample arguments. We evaluate our estimators in simulations then estimate continuous, heterogeneous, incremental, and mediated treatment effects of the US Jobs Corps training program for disadvantaged youth.