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Two-step estimation and inference with possibly many included covariates

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Two-step estimation and inference with possibly many included covariates. / Cattaneo, Matias D.; Jansson, Michael; Xinwei, M. A.

In: Review of Economic Studies, Vol. 86, No. 3, 01.01.2019, p. 1095-1122.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Harvard

Cattaneo, MD, Jansson, M & Xinwei, MA 2019, 'Two-step estimation and inference with possibly many included covariates', Review of Economic Studies, vol. 86, no. 3, pp. 1095-1122. https://doi.org/10.1093/restud/rdy053

APA

Cattaneo, M. D., Jansson, M., & Xinwei, M. A. (2019). Two-step estimation and inference with possibly many included covariates. Review of Economic Studies, 86(3), 1095-1122. https://doi.org/10.1093/restud/rdy053

CBE

MLA

Cattaneo, Matias D., Michael Jansson and M. A. Xinwei. "Two-step estimation and inference with possibly many included covariates". Review of Economic Studies. 2019, 86(3). 1095-1122. https://doi.org/10.1093/restud/rdy053

Vancouver

Cattaneo MD, Jansson M, Xinwei MA. Two-step estimation and inference with possibly many included covariates. Review of Economic Studies. 2019 Jan 1;86(3):1095-1122. https://doi.org/10.1093/restud/rdy053

Author

Cattaneo, Matias D. ; Jansson, Michael ; Xinwei, M. A. / Two-step estimation and inference with possibly many included covariates. In: Review of Economic Studies. 2019 ; Vol. 86, No. 3. pp. 1095-1122.

Bibtex

@article{122ed60b0d764e26b6add3276dd5a7b4,
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.}",
year = "2019",
month = jan,
day = "1",
doi = "10.1093/restud/rdy053",
language = "English",
volume = "86",
pages = "1095--1122",
journal = "The Review of Economic Studies",
issn = "0034-6527",
publisher = "Oxford University Press",
number = "3",

}

RIS

TY - JOUR

T1 - Two-step estimation and inference with possibly many included covariates

AU - Cattaneo, Matias D.

AU - Jansson, Michael

AU - Xinwei, M. A.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Bias correction

KW - M-estimation

KW - Many covariates asymptotics

KW - Resampling methods

KW - Robust inference

UR - http://www.scopus.com/inward/record.url?scp=85068539007&partnerID=8YFLogxK

U2 - 10.1093/restud/rdy053

DO - 10.1093/restud/rdy053

M3 - Journal article

AN - SCOPUS:85068539007

VL - 86

SP - 1095

EP - 1122

JO - The Review of Economic Studies

JF - The Review of Economic Studies

SN - 0034-6527

IS - 3

ER -