Semiparametric Bayesian Difference-in-Differences
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915344737632256 |
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| author | Breunig, Christoph Liu, Ruixuan Yu, Zhengfei |
| author_facet | Breunig, Christoph Liu, Ruixuan Yu, Zhengfei |
| contents | This paper studies semiparametric Bayesian inference for the average treatment effect on the treated (ATT) within the difference-in-differences (DiD) research design. We propose two new Bayesian methods with frequentist validity. The first one places a standard Gaussian process prior on the conditional mean function of the control group. The second method is a double robust Bayesian procedure that adjusts the prior distribution of the conditional mean function and subsequently corrects the posterior distribution of the resulting ATT. We prove new semiparametric Bernstein-von Mises (BvM) theorems for both proposals. Monte Carlo simulations and an empirical application demonstrate that the proposed Bayesian DiD methods exhibit strong finite-sample performance compared to existing frequentist methods. We also present extensions of the canonical DiD approach, incorporating both the staggered design and the repeated cross-sectional design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04605 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semiparametric Bayesian Difference-in-Differences Breunig, Christoph Liu, Ruixuan Yu, Zhengfei Econometrics Machine Learning This paper studies semiparametric Bayesian inference for the average treatment effect on the treated (ATT) within the difference-in-differences (DiD) research design. We propose two new Bayesian methods with frequentist validity. The first one places a standard Gaussian process prior on the conditional mean function of the control group. The second method is a double robust Bayesian procedure that adjusts the prior distribution of the conditional mean function and subsequently corrects the posterior distribution of the resulting ATT. We prove new semiparametric Bernstein-von Mises (BvM) theorems for both proposals. Monte Carlo simulations and an empirical application demonstrate that the proposed Bayesian DiD methods exhibit strong finite-sample performance compared to existing frequentist methods. We also present extensions of the canonical DiD approach, incorporating both the staggered design and the repeated cross-sectional design. |
| title | Semiparametric Bayesian Difference-in-Differences |
| topic | Econometrics Machine Learning |
| url | https://arxiv.org/abs/2412.04605 |