Manipulation of the Running Variable in the Regression Discontinuity Design: A Density Test
Standard sufficient conditions for identification in the regression discontinuity design are continuity of the conditional expectation of counterfactual outcomes in the running variable. These continuity assumptions may not be plausible if agents are able to manipulate the running variable. This paper develops a test of manipulation related to continuity of the running variable density function. The methodology is applied to popular elections to the House of Representatives, where sorting is neither expected nor found, and to roll-call voting in the House, where sorting is both expected and found.
I thank Jack Porter, John DiNardo, and Serena Ng for discussion, Jonah Gelbach for computing improvements, and Ming-Yen Cheng for manuscripts. Any errors are my own. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.