Title: Two-step estimation and inference with possibly many included covariates
Authors: Matias Cattaneo - University of Michigan (United States)
Michael Jansson - UC-Berkeley (United States)
Xinwei Ma - University of Michigan (United States) [presenting]
Abstract: The implications of including many covariates in a first-step estimate entering a two-step estimation procedure are studied. We find that a first order bias emerges when the number of covariates is ``large'' relative to the sample size, rendering standard inference procedures invalid. We show that the jackknife is able to estimate this ``many covariates'' bias consistently, thereby delivering a new fully automatic bias-corrected two-step point estimator. The jackknife also consistently estimates the standard error of the original two-step point estimator (prior jackknife bias-correction). For inference, we develop a valid post-bias-correction bootstrap approximation that accounts for the additional variability introduced by the jackknife bias-correction. We find that the jackknife bias-corrected point estimator and the bootstrap post-bias-correction inference perform excellent in simulations, offering important improvements over conventional two-step point estimators and inference procedures, which are not robust to including many covariates. We apply our results to an array of distinct treatment effect and policy evaluation settings. In particular, we discuss in detail Marginal Treatment Effect (MTE) and Local Average Response Function (LARF) estimation in instrumental variables settings: our results are the first to offer valid estimation and inference when many instruments/covariates are included in non-linear settings with heterogeneous treatment effects.