  This study proposes a new Bayesian approach to infer binary treatment
effects. 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 untreated outcomes to be approximately low rank.
Posterior draws are simulated using a Markov Chain Monte Carlo sampler. While
the proposed approach is similar to synthetic control methods and other related
methods, it has several notable advantages. First, unlike synthetic control
methods, the proposed approach does not require stringent assumptions. Second,
in contrast to non-Bayesian approaches, the proposed method can quantify
uncertainty about inferences in a straightforward and consistent manner. By
means of a series of simulation studies, we show that our proposal has a better
finite sample performance than that of the existing approaches.
