Publication Type
Journal Article
Version
submittedVersion
Publication Date
2-2024
Abstract
We study how to improve efficiency via regression adjustments with additional covariates under covariate-adaptive randomizations (CARs) when subject compliance is imperfect. We first establish the semiparametric efficiency bound for the local average treatment effect (LATE) under CARs. Second, we develop a general regression-adjusted LATE estimator which allows for parametric, nonparametric, and regularized adjustments. Even when the adjustments are misspecified, our proposed estimator is still consistent and asymptotically normal, and their inference method still achieves the exact asymptotic size under the null. When the adjustments are correctly specified, our estimator achieves the semiparametric efficiency bound. Third, we derive the optimal linear adjustment that leads to the smallest asymptotic variance among all linear adjustments. We then show the commonly used two stage least squares estimator is not optimal in the class of LATE estimators with linear adjustments while Ansel, Hong, and Li's (2018) estimator is. Fourth, we show how to construct a LATE estimator with nonlinear adjustments which is more efficient than those with the optimal linear adjustment. Fifth, we give conditions under which LATE estimators with nonparametric and regularized adjustments achieve the semiparametric efficiency bound. Last, simulation evidence and empirical application confirm efficiency gains achieved by regression adjustments relative to both the estimator without adjustment and the standard two-stage least squares estimator.
Keywords
Randomized experiment, Covariate-adaptive randomization, High-dimensional data, Local average treatment effects, Regression adjustment
Discipline
Econometrics
Research Areas
Econometrics
Publication
Review of Economics and Statistics
First Page
1
Last Page
45
ISSN
0034-6535
Identifier
10.1162/rest_a_01417
Publisher
Massachusetts Institute of Technology Press
Citation
JIANG, Liang; LINTON, Oliver B.; TANG, Haihan; and ZHANG, Yichong.
Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance. (2024). Review of Economics and Statistics. 1-45.
Available at: https://ink.library.smu.edu.sg/soe_research/2633
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://doi.org/10.1162/rest_a_01417