Conventional tests of the regression discontinuity design’s identifying restrictions can perform poorly when the running variable is discrete. This paper proposes a test for manipulation of the running variable that is consistent when the running variable is discrete. The test exploits the fact that if the discrete running variable’s probability mass function satisfies a certain smoothness condition, then the observed frequency at the threshold has a known conditional distribution. The proposed test is applied to vote tally distributions in union representation elections and reveals evidence of manipulation in close elections that is in favor of employers when Republicans control the NLRB and in favor of unions otherwise.
The McCrary tests in the simulations were implemented using the Stata software program DCdensity.ado available at http://emlab.berkeley.edu/ jmccrary/DCdensity/. All default options were maintained except the bin width of the discrete random variable was specified. The manipulation test for discrete running variables proposed in this paper is available as a Stata command .ado file from the author upon request.
Frandsen, B.R. (2017), "Party Bias in Union Representation Elections: Testing for Manipulation in the Regression Discontinuity Design when the Running Variable is Discrete", Regression Discontinuity Designs (Advances in Econometrics, Vol. 38), Emerald Publishing Limited, Bingley, pp. 281-315. https://doi.org/10.1108/S0731-905320170000038012
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