Double Robust Bayesian Inference on Average Treatment Effects
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
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2022
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| _version_ | 1866910843423162368 |
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| author | Breunig, Christoph Liu, Ruixuan Yu, Zhengfei |
| author_facet | Breunig, Christoph Liu, Ruixuan Yu, Zhengfei |
| contents | We propose a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. For our new Bayesian approach, we first adjust the prior distributions of the conditional mean functions, and then correct the posterior distribution of the resulting ATE. Both adjustments make use of pilot estimators motivated by the semiparametric influence function for ATE estimation. We prove asymptotic equivalence of our Bayesian procedure and efficient frequentist ATE estimators by establishing a new semiparametric Bernstein-von Mises theorem under double robustness; i.e., the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score and vice versa. Consequently, the resulting Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, our method provides precise point estimates of the ATE through the posterior mean and credible intervals that closely align with the nominal coverage probability. Furthermore, our approach achieves a shorter interval length in comparison to existing methods. We illustrate our method in an application to the National Supported Work Demonstration following LaLonde [1986] and Dehejia and Wahba [1999]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16298 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Double Robust Bayesian Inference on Average Treatment Effects Breunig, Christoph Liu, Ruixuan Yu, Zhengfei Econometrics Methodology Machine Learning We propose a double robust Bayesian inference procedure on the average treatment effect (ATE) under unconfoundedness. For our new Bayesian approach, we first adjust the prior distributions of the conditional mean functions, and then correct the posterior distribution of the resulting ATE. Both adjustments make use of pilot estimators motivated by the semiparametric influence function for ATE estimation. We prove asymptotic equivalence of our Bayesian procedure and efficient frequentist ATE estimators by establishing a new semiparametric Bernstein-von Mises theorem under double robustness; i.e., the lack of smoothness of conditional mean functions can be compensated by high regularity of the propensity score and vice versa. Consequently, the resulting Bayesian credible sets form confidence intervals with asymptotically exact coverage probability. In simulations, our method provides precise point estimates of the ATE through the posterior mean and credible intervals that closely align with the nominal coverage probability. Furthermore, our approach achieves a shorter interval length in comparison to existing methods. We illustrate our method in an application to the National Supported Work Demonstration following LaLonde [1986] and Dehejia and Wahba [1999]. |
| title | Double Robust Bayesian Inference on Average Treatment Effects |
| topic | Econometrics Methodology Machine Learning |
| url | https://arxiv.org/abs/2211.16298 |