Abstract

Much work in causal inference focuses on finite-dimensional targets like average treatment effects. However, many substantively important causal questions involve inherently infinite-dimensional objects, such as counterfactual outcome distributions, heterogeneous treatment effect surfaces, and continuous treatment curves. These targets occupy a hybrid space between classical parameter estimation and nonparametric function estimation. In this talk, I survey some recent work involving these infinite-dimensional causal estimands, highlighting both model-based and model-free nonparametric approaches. I discuss how, despite the impossibility of √n-rate estimation, ideas from semiparametric theory (like double robustness) continue to play a central role. Throughout I emphasize the relevance of these methods in social science applications.