Publication Type
Working Paper
Version
publishedVersion
Publication Date
1-2022
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
First Page
1
Last Page
79
Citation
JIANG, Liang; LINTON, Oliver B.; TANG, Haihan; and ZHANG, Yichong.
Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance. (2022). 1-79.
Available at: https://ink.library.smu.edu.sg/soe_research/2633
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.