Abstract
We propose a family of estimators based on kernel ridge regression for nonparametric dose response curves and semiparametric treatment effects. Treatment and covariates may be discrete or continuous, over a broad variety of domains. We reduce causal estimation and inference to combinations of kernel ridge regressions, which have closed form solutions and are straightforward to compute by matrix operations. This computational simplicity allows us to extend the framework to several settings: (i) heterogeneous effects and distribution shift; (ii) instruments and proxies; (iii) mediation and dynamic effects; (iv) sample selection and data fusion. For dose responses, we prove uniform consistency with finite sample rates. For treatment effects, we prove root-n consistency, Gaussian approximation, and semiparametric efficiency with a new double spectral robustness property.