WEDNESDAY 15:30PM Seminar: Difference-in-differences and synthetic control methods for random objects

About this event

There is a growing interest in causal inference for non-Euclidean outcomes. However, most existing studies focus on cases where the outcomes are functional data or distributions. In this talk, we propose the Geodesic Difference-in-Differences (GDID) and the Geodesic Synthetic Control Method (GSCM) as extensions of the conventional Difference-in-Differences (DID) and Synthetic Control Method (SCM), respectively, to settings where outcomes take values in a geodesic metric space—a framework that encompasses functional data and distributions as special cases. For GDID, we begin by extending the concept of the Average Treatment Effect on the Treated (ATT) for Euclidean outcomes using geodesic paths, and introduce the Geodesic ATT (GATT). We then generalize the notion of parallel trends using the geodesic transport map and provide an identification result for GATT. Additionally, we present an estimator for GATT and discuss its asymptotic properties. As empirical applications of GDID, we analyze the health impacts of the collapse of the Soviet Union using age-at-death distributions and evaluate the effects of U.S. electricity market liberalization on the composition of electricity generation. For GSCM, we first define the causal effect of interest via geodesics and provide its identification result. We further introduce the Geodesic Synthetic Difference-in-Differences (GSDID), which combines the features of GDID and GSCM. As applications of GSCM, we examine changes in employment composition following the 2011 Great East Japan Earthquake and assess the impact of abortion liberalization policy on fertility patterns in East Germany.