Causal Inference With Noisy Covariates: Heteroscedastic Measurement Error and Differential Privacy

Abstract

We study causal inference with high-dimensional covariates, observed with various types of heteroscedastic noise. Our main assumption is that the true covariates are low rank, which we empirically evaluate with plots and interpret as approximate repeated measurements. This assumption delivers semiparametric inference on the causal parameter, as precisely as if the true covariates were available. A methodological contribution is to introduce an error-in-variable balancing weight for estimation and inference on cross-sectional causal parameters with heterogeneous effects.