# Limitless Regression Discontinuity

5/9/19 | 4:15pm | E51-325
Reception to follow.

Ben Hansen

Associate Professor
University of Michigan

Abstract

In a regression discontinuity design (RDD), assignment to treatment versus a control condition is determined by the value of a particular baseline variable, $R$. In one recent RDD, $R$ is the average of a student's grades in his first year at university; the treatment condition is academic probation, forced upon a student if his $R$ falls below a threshold; and downstream effects of the academic probation regime are estimated with ordinary least squares.  The RDD setup can be used to estimate deaths attributable to a natural disaster, for example Hurricane Maria, by contrast of mortality series before and after the catastrophic event.

Some recent RDD methods contrast limits of $\mathrm{E}(Y|R=r)$ as $r$ approaches a cut-point, $c$, from either side; this conceptualization is ill suited to natural disaster applications, where it is necessary to estimate excess mortality over specific periods of non-negligible duration. Other RDD methodology avoids passing to limits by supposing that in sufficiently narrow neighborhoods of the threshold, there is random assignment.  Both frameworks are difficult to reconcile with examples such as the academic probation study, where running-variable-manipulation tests find the experimental analogy to be at its weakest in the immediate vicinity of the cut-point.

"Limitless regression discontinuity" avoids these limitations by using formulating a relaxed variant of the classical RDD model within the Neyman-Rubin causal framework, then estimating that model with the help of M-estimators of regression enjoying certain specific robustness properties.  The model is equally comfortable with discrete and continuous running variables; the method is straightforward to implement, at least in R or Stata.  It is uniquely equipped to meet a significant, somewhat misunderstood threat associating with sample contamination, and it appears to remedy in dramatic fashion a known vulnerability of the classical approach, in realistic scenarios reducing those methods' RMSEs by factors upwards of 100.

This is joint work with Adam C. Sales, University of Texas-Austin

Bio: Dr. Hansen is Associate Professor of Statistics at the University of Michigan, as well as a faculty affiliate of the Survey Research Center and the Population Studies Center. He holds an M.A. in Statistics and a Ph.D. in Logic and the Methodology of Science, both from the University of California-Berkeley. His research interests include matching, sensitivity analysis and distribution-free methods for quasi-experiments and experiments, and applications in education, health and social science.

2019 - 16:15