Exponential family model improves synthetic controls for causal effects
Exponential Family Synthetic Controls
Machine Learning
Summary
Synthetic controls help estimate what would have happened without a treatment or event, usually by averaging similar data. This paper develops a new method called exponential family synthetic controls (EFSC) that models full data distributions, not just averages. The authors use a flexible probabilistic model to better capture changes in data and test their approach on various datasets. Their method can also identify effects even with messy data and was applied to study health insurance changes in the US.
What this means in practice
- •For health policy analysts: Provide detailed estimates of distributional impacts of policy changes like Medicaid expansion across regions using probabilistic synthetic controls.
- •For business intelligence teams: Identify causal effects on customer behavior distributions following market interventions with a probabilistic approach to synthetic controls.
Authors
Hector Rodriguez-Deniz, David M. Blei
Abstract
We develop exponential family synthetic controls (EFSC), a distributional version of synthetic controls for a panel of datasets. Each cell of the panel corresponds to a dataset drawn from an exponential family whose natural parameters factorize probabilistically across units and times. We estimate the latent factors using black-box variational inference. This replaces the usual weighted-average view of synthetic controls with a flexible probabilistic model that operates on full distributions. We propose causal estimands based on divergences between pre- and post-intervention distributions induced by the posterior of the natural parameters, together with distributional placebo tests to support causal inference and assess the significance of the estimated effects. We validate the proposed framework on synthetic and real data. Across a variety of exponential-family distributions, EFSC accurately recovers causal effects induced by exponential tilts, together with the corresponding divergences between treated and counterfactual distributions. The framework also captures effects induced by structural perturbations of the latent factors and by heavy-tailed noise contamination. Finally, we apply EFSC to study the expansion of Medicaid under the Affordable Care Act (ACA) and its impact on the distribution of health insurance coverage across U.S. states. Code is available at https://github.com/blei-lab/efsc.