Uncertainty Quantification in Synthetic Controls with Staggered Treatment Adoption

Abstract We propose principled prediction intervals to quantify the uncertainty of a large class of synthetic control predictions (or estimators) in settings with staggered treatment adoption, offering precise non-asymptotic coverage probability guarantees. From a methodological perspective, we provide a detailed discussion of different causal quantities to be predicted, which we call causal predictands, allowing for multiple treated units with treatment adoption at possibly different points in time. We illustrate our methodology with an empirical application studying the effects of economic liberalization on real GDP per capita for Sub-Saharan African countries. Companion software packages are provided in Python, R, and Stata.