Christoph Breunig, Ruixuan Liu, Zhengfei Yu
arXiv 29 Nov 2022 · Econometrics · publishedEconometrica (2025) · 6 citations (OpenAlex)
arXiv:2211.16298 · PDF · DOI · OpenAlex · Extracted main text
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].
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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 | J. Hahn (1998) On the role of the propensity score in efficient semiparametric estimation of average treatment effects | 0.855 | 8 | 5 | 62% |
| 2 | C. Rassmusen and C. Williams (2006) Gaussian processes for machine learning | 0.843 | 4 | 3 | 75% |
| 3 | K. Ray and A. van der Vaart (2020) Semiparametric bayesian causal inference | 0.821 | 38 | 10 | 55% |
| 4 | A. Abadie and G. W. Imbens (2011) Bias-corrected matching estimators for average treatment effects | 0.811 | 4 | 2 | 100% |
| 5 | A. van der Vaart (1998) Asymptotic statistics | 0.737 | 5 | 4 | 40% |
| 6 | D. Benkeser, M. Carone, M. v. D. Laan, and P. Gilbert (2017) Doubly robust nonparametric inference on the average treatment effect | 0.737 | 3 | 2 | 100% |
| 7 | R. H. Dehejia and S. Wahba (1999) Causal effects in nonexperimental studies: Reevaluating the evaluation of training programs | 0.737 | 3 | 2 | 100% |
| 8 | R. J. LaLonde (1986) Evaluating the econometric evaluations of training programs with experimental data | 0.737 | 3 | 2 | 100% |
| 9 | K. Ray and B. Szabó (2019) Debiased bayesian inference for average treatment effects | 0.737 | 3 | 2 | 100% |
| 10 | R. K. Crump, V. J. Hotz, G. W. Imbens, and O. A. Mitnik (2009) Dealing with limited overlap in estimation of average treatment effects | 0.693 | 5 | 1 | 100% |
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