Publication Type
Working Paper
Version
publishedVersion
Publication Date
2-2023
Abstract
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.
Keywords
Experiment, matched pairs, covariate adjustment, randomized controlled trial, treatment assignment, LASSO
Discipline
Econometrics
Research Areas
Econometrics
First Page
1
Last Page
77
Citation
BAI, Yuehao; JIANG, Liang; ROMANO, Joseph P.; SHAIKH, Azeem M.; and ZHANG, Yichong.
Covariate adjustment in experiments with matched pairs. (2023). 1-77.
Available at: https://ink.library.smu.edu.sg/soe_research/2684
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://arxiv.org/abs/2302.04380