Abstract
AbstractThis paper proposes a Bayesian alternative to the synthetic control method for comparative case studies with a single or multiple treated units. We adopt a Bayesian posterior predictive approach to Rubin’s causal model, which allows researchers to make inferences about both individual and average treatment effects on treated observations based on the empirical posterior distributions of their counterfactuals. The prediction model we develop is a dynamic multilevel model with a latent factor term to correct biases induced by unit-specific time trends. It also considers heterogeneous and dynamic relationships between covariates and the outcome, thus improving precision of the causal estimates. To reduce model dependency, we adopt a Bayesian shrinkage method for model searching and factor selection. Monte Carlo exercises demonstrate that our method produces more precise causal estimates than existing approaches and achieves correct frequentist coverage rates even when sample sizes are small and rich heterogeneities are present in data. We illustrate the method with two empirical examples from political economy.
Highlights
With the introduction of the synthetic control method (SCM) (Abadie and Gardeazabal 2003; Abadie, Diamond, and Hainmueller 2010), comparative case studies using time-series crosssectional (TSCS) data, or long panel data, are becoming increasingly popular in the social sciences
In each Markov Chain Monte Carlo (MCMC) iteration, the algorithm samples a model consisting of the parameters that successfully escape the shrinkage, and posterior distributions of parameters generated by the stochastic search algorithm are based on a mixture of models in a continuous model space
We develop an MCMC algorithm to estimate a DM-latent factor models (LFMs)
Summary
With the introduction of the synthetic control method (SCM) (Abadie and Gardeazabal 2003; Abadie, Diamond, and Hainmueller 2010), comparative case studies using time-series crosssectional (TSCS) data, or long panel data, are becoming increasingly popular in the social sciences. We adopt the Bayesian causal inference framework (Rubin 1978; Imbens and Rubin 1997; Rubin et al 2010; Ricciardi, Mattei, and Mealli 2020) to estimate treatment effects in comparative case studies This framework views causal inference as a missing data problem and relies on the posterior predictive distribution of treated counterfactuals to draw inferences about the treatment effects on the treated. Compared with the SCM or LFMs, our method is most suitable when one of the following is true: (1) the uncertainty measures bear important policy or theoretical implications; (2) researchers suspect the latent factor structure is complex, the number of factors is large, or some of the factors are relatively weak; (3) many potential pre-treatment covariates are available and their relationships with the outcome variable may vary across units or over time; or (4) researchers have limited knowledge of how to select covariates for counterfactual prediction. We develop an R package bpCausal, whose core functions are written in C++, for researchers to efficiently implement this method
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