Timothy B. Armstrong, Michal Kolesár
arXiv 13 Dec 2017 · Statistics — Applications · publishedEconometrica (2021) · 33 citations (OpenAlex)
arXiv:1712.04594 · PDF · DOI · OpenAlex · Extracted main text
We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates. Given nonparametric smoothness and/or shape restrictions on the conditional mean of the outcome variable, we derive estimators and confidence intervals (CIs) that are optimal in finite samples when the regression errors are normal with known variance. In contrast to conventional CIs, our CIs use a larger critical value that explicitly takes into account the potential bias of the estimator. When the error distribution is unknown, feasible versions of our CIs are valid asymptotically, even when $\sqrt{n}$-inference is not possible due to lack of overlap, or low smoothness of the conditional mean. We also derive the minimum smoothness conditions on the conditional mean that are necessary for $\sqrt{n}$-inference. When the conditional mean is restricted to be Lipschitz with a large enough bound on the Lipschitz constant, the optimal estimator reduces to a matching estimator with the number of matches set to one. We illustrate our methods in an application to the National Supported Work Demonstration.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Abadie, A. and Imbens, G. W (2006) Large sample properties of matching estimators for average treatment effects | 0.874 | 5 | 2 | 100% |
| 2 | Abadie, A. and Imbens, G. W (2011) Bias-corrected matching estimators for average treatment effects | 0.811 | 4 | 2 | 100% |
| 3 | Efron, B., Hastie, T., Johnstone, I. M., and Tibshirani, R. J (2004) Least angle regression | 0.737 | 3 | 3 | 67% |
| 4 | Armstrong, T. B. and Kolesár, M (2018) Finite-sample optimal estimation and inference on average treatment effects under unconfoundedness self | 0.644 | 2 | 2 | 100% |
| 5 | Khan, S. and Tamer, E (2010) Irregular identification, support conditions, and inverse weight estimation | 0.644 | 2 | 2 | 100% |
| 6 | Noack, C. and Rothe, C (2020) Bias-aware inference in fuzzy regression discontinuity designs | 0.644 | 2 | 2 | 100% |
| 7 | Kallus, N (2020) Generalized optimal matching methods for causal inference | 0.644 | 2 | 2 | 100% |
| 8 | Robins, J., Tchetgen, E. T., Li, L., and van der Vaart, A. W (2009) Semiparametric minimax rates | 0.644 | 2 | 2 | 100% |
| 9 | Rothe, C (2017) Robust confidence intervals for average treatment effects under limited overlap | 0.644 | 2 | 2 | 100% |
| 10 | Donoho, D. L (1994) Statistical estimation and optimal recovery | 0.630 | 12 | 3 | 25% |
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