Liang Jiang, Liyao Li, Ke Miao, Yichong Zhang
arXiv 17 Apr 2023 · Econometrics · publishedJournal of Econometrics (2025)
arXiv:2304.08184 · PDF · DOI · OpenAlex · Extracted main text
Our paper discovers a new trade-off of using regression adjustments (RAs) in causal inference under covariate-adaptive randomizations (CARs). On one hand, RAs can improve the efficiency of causal estimators by incorporating information from covariates that are not used in the randomization. On the other hand, RAs can degrade estimation efficiency due to their estimation errors, which are not asymptotically negligible when the number of regressors is of the same order as the sample size. Ignoring the estimation errors of RAs may result in serious over-rejection of causal inference under the null hypothesis. To address the issue, we construct a new ATE estimator by optimally linearly combining the estimators with and without RAs. We then develop a unified inference theory for this estimator under CARs. It has two features: (1) the Wald test based on it achieves the exact asymptotic size under the null hypothesis, regardless of whether the number of covariates is fixed or diverges no faster than the sample size; and (2) it guarantees weak efficiency improvement over estimators both with and without RAs.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Cattaneo, M. D., M. Jansson, and W. K. Newey (2018) Inference in linear regression models with many covariates and heteroscedasticity | 1.000 | 11 | 4 | 100% |
| 2 | Ye, T., Y. Yi, and J. Shao (2022) Inference on the average treatment effect under minimization and other covariate-adaptive randomization methods | 1.000 | 11 | 4 | 100% |
| 3 | Bugni, F. A., I. A. Canay, and A. M. Shaikh (2019) Inference under covariate-adaptive randomization with multiple treatments | 1.000 | 8 | 5 | 100% |
| 4 | Chiang, H. D., Y. Matsushita, and T. Otsu (2023) Regression adjustment in randomized controlled trials with many covariates | 1.000 | 8 | 4 | 100% |
| 5 | Lei, L. and P. Ding (2021) Regression adjustment in completely randomized experiments with a diverging number of covariates | 1.000 | 8 | 4 | 100% |
| 6 | Kline, P., R. Saggio, and M. Slvsten (2020) Leave-out estimation of variance components | 1.000 | 5 | 3 | 100% |
| 7 | Jochmans, K (2022) Heteroscedasticity-robust inference in linear regression models with many covariates | 0.950 | 7 | 4 | 86% |
| 8 | Liu, H., F. Tu, and W. Ma (2023) Lasso-adjusted treatment effect estimation under covariate-adaptive randomization | 0.928 | 4 | 3 | 100% |
| 9 | Lu, X., F. Yang, and Y. Wang (2024) Debiased regression adjustment in completely randomized experiments with moderately high-dimensional covariates | 0.874 | 8 | 2 | 100% |
| 10 | Chong, A., I. Cohen, E. Field, E. Nakasone, and M. Torero (2016) Iron deficiency and schooling attainment in Peru | 0.874 | 6 | 2 | 100% |
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| 1 | Covariate Adjustment in Randomized Experiments Motivated by Higher-Order Influence Functions | 0.874 | 6 | 2 |
| 2 | Assumption-lean covariate adjustment under covariate adaptive randomization when $p = o (n)$ | 0.737 | 3 | 2 |
| 3 | An Improved Inference for IV Regressions | 0.405 | 1 | 1 |