Abstract: This paper proposes a Bayesian synthetic control method (a.k.a., the latent multifactor model approach) for causal inference with observational time-series cross-sectional (TSCS) data. We develop a state-space latent factor model and make dynamic and multilevel extensions to the widely-applied difference-in-differences estimator, the synthetic control approach, and latent factor models. We adopt a fully Bayesian prior-to-posterior approach to parameter estimation and counterfactual prediction. Compared with existing frequentist approaches, our method has several advantages. First, it assigns unit- and time-specific weights to outcomes and features of the donor pool to flexibly model the response surface and exploits high-order relationships between treated and control time series. Secondly, by combining dense modeling with latent factor analysis and sparse modeling with Bayesian shrinkage, the method achieves a good balance between correcting bias and avoiding overfitting. Thirdly, based on Bayesian posterior distributions of counterfactuals, the proposed method generates easily interpretable finite-sample inference for causal quantities at an individual, group, or global level, which has long been a challenge for the synthetic control method and its extensions. As a model-based semi-parametric approach, the proposed method is highly flexible and relax restrictive requirements on the data structure. We test the method with Monte Carlo simulations and apply it to several empirical studies to illustrate how to implement the method and to compare it with some widely-applied alternative approaches. Those applications demonstrate that the proposed method can help the researcher test causal effect generated by complicated causal mechanisms and with substantively important and methodologically thorny timing issues.