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Title: Robust MM estimation for imperfect regression discontinuity designs Authors:  Adam Sales - University of Texas - Austin (United States)
Ben Hansen - University of Michigan (United States) [presenting]
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 using ordinary least squares. Some cutting-edge RDD methods contrast limits of $\mathrm{E}(Y|R=r)$ as $r$ approaches a cut-point, $c$, from either side; others avoid 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 tests for manipulation of the running variable find the experimental analogy to be at its weakest in the immediate vicinity of the cut-point. Our method addresses these challenges with a combination of tactics: weakening the local randomization assumption; decontaminating the sample with the aid of specification tests; and robust MM-estimation. The MM-estimators' insensitivity to contamination imparts a unique robustness to leading validity threats facing RDDs.