Covariate adjustment in experiments with matched pairs

This paper studies inference on the average treatment effect in experiments in which treatment status is determined according to “matched pairs” and it is additionally desired to adjust for observed, baseline covariates to gain further precision. By a “matched pairs” design, we mean that units are s...

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Main Authors: BAI, Yuehao, JIANG, Liang, ROMANO, Joseph P., SHAIKH, Azeem M., ZHANG, Yichong
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Language:English
Published: Institutional Knowledge at Singapore Management University 2023
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Online Access:https://ink.library.smu.edu.sg/soe_research/2684
https://ink.library.smu.edu.sg/context/soe_research/article/3683/viewcontent/2302.04380.pdf
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spelling sg-smu-ink.soe_research-36832023-08-11T06:52:53Z Covariate adjustment in experiments with matched pairs BAI, Yuehao JIANG, Liang ROMANO, Joseph P. SHAIKH, Azeem M. ZHANG, Yichong This paper studies inference on the average treatment effect in experiments in which treatment status is determined according to “matched pairs” and it is additionally desired to adjust for observed, baseline covariates to gain further precision. By a “matched pairs” design, we mean that units are sampled i.i.d. from the population of interest, paired according to observed, baseline covariates and finally, within each pair, one unit is selected at random for treatment. Importantly, we presume that not all observed, baseline covariates are used in determining treatment assignment. We study a broad class of estimators based on a “doubly robust” moment condition that permits us to study estimators with both finite-dimensional and high-dimensional forms of covariate adjustment. We find that estimators with finite-dimensional, linear adjustments need not lead to improvements in precision relative to the unadjusted difference-in-means estimator. This phenomenon persists even if the adjustments are interacted with treatment; in fact, doing so leads to no changes in precision. However, gains in precision can be ensured by including fixed effects for each of the pairs. Indeed, we show that this adjustment is the “optimal” finite-dimensional, linear adjustment. We additionally study two estimators with high-dimensional forms of covariate adjustment based on the LASSO. For each such estimator, we show that it leads to improvements in precision relative to the unadjusted difference-in-means estimator and also provides conditions under which it leads to the “optimal’ nonparametric, covariate adjustment. A simulation study confirms the practical relevance of our theoretical analysis, and the methods are employed to reanalyze data from an experiment using a “matched pairs” design to study the effect of macroinsurance on microenterprise. 2023-02-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2684 https://ink.library.smu.edu.sg/context/soe_research/article/3683/viewcontent/2302.04380.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Experiment matched pairs covariate adjustment randomized controlled trial treatment assignment LASSO Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Experiment
matched pairs
covariate adjustment
randomized controlled trial
treatment assignment
LASSO
Econometrics
spellingShingle Experiment
matched pairs
covariate adjustment
randomized controlled trial
treatment assignment
LASSO
Econometrics
BAI, Yuehao
JIANG, Liang
ROMANO, Joseph P.
SHAIKH, Azeem M.
ZHANG, Yichong
Covariate adjustment in experiments with matched pairs
description This paper studies inference on the average treatment effect in experiments in which treatment status is determined according to “matched pairs” and it is additionally desired to adjust for observed, baseline covariates to gain further precision. By a “matched pairs” design, we mean that units are sampled i.i.d. from the population of interest, paired according to observed, baseline covariates and finally, within each pair, one unit is selected at random for treatment. Importantly, we presume that not all observed, baseline covariates are used in determining treatment assignment. We study a broad class of estimators based on a “doubly robust” moment condition that permits us to study estimators with both finite-dimensional and high-dimensional forms of covariate adjustment. We find that estimators with finite-dimensional, linear adjustments need not lead to improvements in precision relative to the unadjusted difference-in-means estimator. This phenomenon persists even if the adjustments are interacted with treatment; in fact, doing so leads to no changes in precision. However, gains in precision can be ensured by including fixed effects for each of the pairs. Indeed, we show that this adjustment is the “optimal” finite-dimensional, linear adjustment. We additionally study two estimators with high-dimensional forms of covariate adjustment based on the LASSO. For each such estimator, we show that it leads to improvements in precision relative to the unadjusted difference-in-means estimator and also provides conditions under which it leads to the “optimal’ nonparametric, covariate adjustment. A simulation study confirms the practical relevance of our theoretical analysis, and the methods are employed to reanalyze data from an experiment using a “matched pairs” design to study the effect of macroinsurance on microenterprise.
format text
author BAI, Yuehao
JIANG, Liang
ROMANO, Joseph P.
SHAIKH, Azeem M.
ZHANG, Yichong
author_facet BAI, Yuehao
JIANG, Liang
ROMANO, Joseph P.
SHAIKH, Azeem M.
ZHANG, Yichong
author_sort BAI, Yuehao
title Covariate adjustment in experiments with matched pairs
title_short Covariate adjustment in experiments with matched pairs
title_full Covariate adjustment in experiments with matched pairs
title_fullStr Covariate adjustment in experiments with matched pairs
title_full_unstemmed Covariate adjustment in experiments with matched pairs
title_sort covariate adjustment in experiments with matched pairs
publisher Institutional Knowledge at Singapore Management University
publishDate 2023
url https://ink.library.smu.edu.sg/soe_research/2684
https://ink.library.smu.edu.sg/context/soe_research/article/3683/viewcontent/2302.04380.pdf
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