Indian Buffet process factor model for counterfactual analysis

This article proposes a factor model-based counterfactual analysis. We explicitly estimate the underlying factor structure of the outcome variables and estimate the counterfactual values of the unit subject to an intervention. With the help of the non-parametric Bayesian Indian Buffet Process prior, our approach is capable of exploring heterogeneous factor exposures, and the number of latent factors is endogenously determined in the estimation process. The flexible Markov Chain Monte Carlo algorithm utilizes the maximal intervention-free information provided by the data, whereas the original synthetic control only uses pre-intervention data. The counterfactual values are estimated by simulating from the posterior predictive distribution so that we can integrate out any parameter estimation uncertainty. We also calculate the posterior predictive upper- and lower-quantile bounds for inference. The two applications, namely California’s Tobacco Control Program and the West German Reunification, demonstrate the usefulness of our approach compared to the synthetic control method and the elastic net model. The Monte Carlo simulation study also shows the robustness of our approach with respect to nonlinear dynamics in the underlying factor process.