Two-step estimation and inference with possibly many included covariates

Matias D. Cattaneo, Michael Jansson, M. A. Xinwei

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1095-1122
Number of pages28
JournalReview of Economic Studies
Issue number3
StatePublished - May 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • Bias correction
  • M-estimation
  • Many covariates asymptotics
  • Resampling methods
  • Robust inference


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