@article{58dd436172f14168b5a05319bc8e637d,
title = "Two-step estimation and inference with possibly many included covariates",
abstract = "We study the implications of including many covariates in a first-step estimate entering a two-step estimation procedure. We find that a first-order bias emerges when the number of included covariates is “large” relative to the square-root of 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 automatic bias-corrected two-step point estimator. The jackknife also consistently estimates the standard error of the original two-step point estimator. 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, policy evaluation, and other applied microeconomics settings. In particular, we discuss production function and marginal treatment effect estimation in detail.",
keywords = "Bias correction, M-estimation, Many covariates asymptotics, Resampling methods, Robust inference",
author = "Cattaneo, {Matias D.} and Michael Jansson and Xinwei, {M. A.}",
note = "Funding Information: Acknowledgments. This article encompasses and supersedes our previous paper titled “Marginal Treatment Effects with Many Instruments”, presented at the 2016 NBER summer meetings. We specially thank Pat Kline for posing a question that this article answers, and Josh Angrist, Guido Imbens and Ed Vytlacil for very useful comments on an early version of this article. We also thank the Editor, Aureo de Paula, three anonymous reviewers, Lutz Kilian, Whitney Newey and Chris Taber for very useful comments. M.D.C. gratefully acknowledges financial support from the National Science Foundation (SES 1459931). M.J. gratefully acknowledges financial support from the National Science Foundation (SES 1459967) and the research support of CREATES (funded by the Danish National Research Foundation under grant no. DNRF78). Disclaimer: This research was conducted with restricted access to Bureau of Labor Statistics (BLS) data. The views expressed here do not necessarily reflect the views of the BLS. Funding Information: This article encompasses and supersedes our previous paper titled ?Marginal Treatment Effects with Many Instruments?, presented at the 2016 NBER summer meetings. We specially thank Pat Kline for posing a question that this article answers, and Josh Angrist, Guido Imbens and Ed Vytlacil for very useful comments on an early version of this article. We also thank the Editor, Aureo de Paula, three anonymous reviewers, Lutz Kilian, Whitney Newey and Chris Taber for very useful comments. M.D.C. gratefully acknowledges financial support from the National Science Foundation (SES 1459931). M.J. gratefully acknowledges financial support from the National Science Foundation (SES 1459967) and the research support of CREATES (funded by the Danish National Research Foundation under grant no. DNRF78). Publisher Copyright: {\textcopyright} The Author(s) 2018.",
year = "2019",
month = may,
day = "1",
doi = "10.1093/restud/rdy053",
language = "English (US)",
volume = "86",
pages = "1095--1122",
journal = "Review of Economic Studies",
issn = "0034-6527",
publisher = "Oxford University Press",
number = "3",
}