A1395
Title: Robust inference for the variance of the CATE in randomized experiments using machine learning
Authors: Alejandro Sanchez Becerra - Emory University (United States) [presenting]
Abstract: Machine learning tools are increasingly used to estimate the conditional average treatment effect function (CATE). We propose an efficient estimator of its unconditional variance, the VCATE, which measures the overall effect heterogeneity explained by covariates. First, we introduce a novel way of interpreting VCATE as a bound for the gains of policy learning. We show that the incremental welfare of policies targeted using CATE over policies without targeting has a sharp upper bound equal to root-VCATE/2. Second, we propose novel adaptive confidence intervals (CIs). We start by showing that off-the-shelf CIs with normal critical values and standard errors derived from the efficient influence function have issues covering VCATE. We explain the boundary problem that arises when the treatment effects are homogeneous; this manifests even for simple two-step estimators of VCATE assuming a linear CATE. For the regression case, we prove that the second-step limiting distribution is a generalized chi-square and construct CIs with exact coverage. We then show how to (i) extend these intervals to a class of efficient, debiased, machine learning estimators with a regression step, and (ii) construct variational extensions with conservative coverage that account for sample splitting uncertainty. We document excellent performance in simulations using LASSO.
