Semiparametric Bayesian doubly robust causal estimation

Yu Luo, Daniel J. Graham and Emma J. McCoy

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Frequentist semiparametric theory has been used extensively to develop doubly robust (DR) causal estimation. DR estimation combines outcome regression (OR) and propensity score (PS) models in such a way that correct specification of just one of two models is enough to obtain consistent parameter estimation. An equivalent Bayesian solution, however, is not straightforward as there is no obvious distributional framework to the joint OR and PS model, and the DR approach involves a semiparametric estimating equation framework without a fully specified likelihood. In this paper, we develop a fully semiparametric Bayesian framework for DR causal inference by bridging a nonparametric Bayesian procedure with empirical likelihood via semiparametric linear regression. Instead of specifying a fully probabilistic model, this procedure is only realized through relevant moment conditions. Crucially, this allows the posterior distribution of the causal parameter to be simulated via Markov chain Monte Carlo methods. We show that the posterior distribution of the causal estimator satisfies consistency and the Bernstein–von Mises theorem, when either the OR or PS is correctly specified. Simulation studies suggest that our proposed method is doubly robust and can achieve the desired coverage rate. We also apply this novel Bayesian method to a real data example to assess the impact of speed cameras on car collisions in England.

Keywords: Bayesian estimation; causal inference; double robustness; empirical likelihood; propensity score adjustments; semiparametric inference (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 17 pages
Date: 2023-07-01
New Economics Papers: this item is included in nep-ecm
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Published in Journal of Statistical Planning and Inference, 1, July, 2023, 225, pp. 171 - 187. ISSN: 0378-3758

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:117944

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