TSCS Causal Inference Using Bayesian Dynamic Multilevel State-Space Models

• In Event: New Directions in Political Methodology

Abstract

Most existing methods for TSCS causal inference with time heterogeneities are based on multivariate factor analysis. However, TSCS data are multilevel and clustered data, and there are more sources of time-heterogeneities in TSCS data than the unobserved factors. Time-varying effects, structural breaks, and time decaying dependency all introduce heterogeneities over time.

This research proposes a Bayesian approach for causal inference with continuous and discrete Time-Series Cross-Sectional Data on the basis of a Bayesian dynamic multilevel state-space model to predict the treated counterfactuals in the post-treatment period. The Bayesian method gives high flexibility for model specifications with a full consideration of the intrinsic TSCS data structure. We develop a hybrid Markov Chain Monte-Carlo algorithm to estimate the parameters with observations under the control condition, and then conduct Bayesian predictive posterior simulation to estimate the treated counterfactuals only conditional on observed data by integrating out all the unknown parameters using their posterior draws. The simulation provides fully Bayesian time-series cross-sectional estimates of the pointwise treatment effects on the treated. And inferences about point-wise, average, running average, and cumulative treatment effects on the treated can be easily drawn with posterior predictive simulation. To achieve the most appropriate synthetic control, this paper adopts Bayesian averaging to weight multiple relevant models according to their posterior probabilities to model the counterfactuals. We also extend the proposed Bayesian method to binary TSCS data by using a Bayesian data augmentation approach, given the fact that discrete TSCS outcomes are common in Political Science studies.

We conduct Monte Carlo simulation studies to evaluate the performance of the proposed method and compare it with competing approaches. Then we demonstrate how to practically apply the method with two empirical applications in Political Science. An R package will be developed for practitioners to implement the proposed approach for causal inference with TSCS data.

Authors

• Xun Pang, Tsinghua University

• Licheng Liu, Tsinghua University