Bayesian Matrix Completion Approach to Causal Inference with Panel Data
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This study proposes a new Bayesian approach to infer average treatment effect. The approach treats counterfactual untreated outcomes as missing observations and infers them by completing a matrix composed of realized and potential untreated outcomes using a data augmentation technique. We also develop a tailored prior that helps in the identification of parameters and induces the matrix of the untreated outcomes to be approximately low rank. While the proposed approach is similar to synthetic control methods and other relevant methods, it has several notable advantages. Unlike synthetic control methods, the proposed approach does not require stringent assumptions. Whereas synthetic control methods do not have a statistically grounded method to quantify uncertainty about inference, the proposed approach can estimate credible sets in a straightforward and consistent manner. Our proposal approach has a better finite sample performance than the existing Bayesian and non-Bayesian approaches, as we show through a series of simulation studies.
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