Generalized Kernel Ridge Regression for Nonparametric Structural Functions and Semiparametric Treatment Effects

We propose a family of estimators based on kernel ridge regression for nonparametric structural functions (also called dose response curves) and semiparametric treatment effects. Treatment and covariates may be discrete or continuous, and low, high, or infinite dimensional. We reduce causal estimation and inference to combinations of kernel ridge regressions, which have closed form solutions and are easily computed by matrix operations, unlike other machine learning paradigms. This computational simplicity allows us to extend the framework in two directions: from means to increments and distributions of counterfactual outcomes; and from parameters of the full population to those of subpopulations and alternative populations. For structural functions, we prove uniform consistency with finite sample rates. For treatment effects, we prove $\sqrt{n}$ consistency, Gaussian approximation, and semiparametric efficiency with a new double spectral robustness property. We conduct simulations and estimate average, heterogeneous, and incremental structural functions of the US Jobs Corps training program.