Association for Public Policy Analysis & Management

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
satises 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.