Semiparametric Bayesian Estimation for Marginal Parametric Potential Outcome Modeling: Application to Causal Inference

Abstract

We propose a new semiparametric Bayesian model for causal inference in which assignment to treatment depends on potential outcomes. The model uses the probit stick-breaking process mixture proposed by Chung and Dunson (2009), a variant of the Dirichlet process mixture modeling. In contrast to previous Bayesian models, the proposed model directly estimates the parameters of the marginal parametric model of potential outcomes, while it relaxes the strong ignorability assumption, and requires no parametric model assumption for the assignment model and conditional distribution of the covariate vector. The proposed estimation method is more robust than maximum likelihood estimation, in that it does not require knowledge of the full joint distribution of potential outcomes, covariates, and assignments. In addition, the method is more efficient than fully nonparametric Bayes methods. We apply this model to infer the differential effects of cognitive and noncognitive skills on the wages of production and nonproduction workers using panel data from the National Longitudinal Survey of Youth in 1979. The study also presents the causal effect of online word-of-mouth on Web site browsing behavior. Supplementary materials for this article are available online.

KEY WORDS:

• Dirichlet process mixture
• Factor analysis
• Probit stick-breaking process mixture
• Selection bias
• Word-of-mouth

Acknowledgments

This work was presented at a regular meeting of Bayesian analysis section of the Japan Statistical Society. The author appreciates the participants, in particular Professor Kazuo Shigemasu (Univeristy of Tokyo/Teikyo University) and Professor Nojomu Matsubara (University of Tokyo/Sei-Gakuin University), for valuable comments and suggestions that benefit the earlier draft of the article. The authors sincerely appreciate the anonymous reviewers, associate editor, and editor for insightful comments to improve the article. The authors greatly thank Video Research Interactive Inc. for allowing them to use the Internet Audience Data. This work was supported by JPSP KAKENHI(23680026).