Free Discontinuity Design (joint w/ David van Dijcke)

Abstract:
Regression discontinuity design (RDD) is a quasi-experimental impact evaluation method ubiquitous in the social- and applied health sciences. It aims to estimate average treatment effects of policy interventions by exploiting jumps in outcomes induced by cut-off assignment rules. Here, we establish a correspondence between the RDD setting and free discontinuity problems, in particular the celebrated Mumford-Shah model in image segmentation. The Mumford-Shah model is non-convex and hence admits local solutions in general. We circumvent this issue by relying on well-known convex relaxations based on the calibration method to generate global solutions. We derive deterministic and statistical convergence properties of this convex relaxation and demonstrate the utility of the resulting free discontinuity design (FDD) estimator in two empirical applications. Unlike canonical RDD estimators, our FDD estimator (i) extends to settings with running variables of any dimension, most notably the spatial setting; (ii) does not require the location of the boundary (the cut-off) to be known precisely, but rather estimates it jointly with the response function; (iii) does not depend on bandwidth selection rules.

Bio:
Florian Gunsilius is an Assistant Professor of Econometrics at the University of Michigan, Ann Arbor. He graduated from Brown University with a PhD in economics, receiving the Joukowsky family foundation dissertation award in the social sciences. Before joining the faculty at the University of Michigan, he spent one year as a Visiting Postdoctoral Associate at the Department of Economics at MIT. His work focuses on nonparametric approaches to statistical identification, estimation, and inference. His current focus is on developing geometric methods for causal inference.