Estimating slim-majority effects in US state legislatures with a regression discontinuity design under local randomization assumptions

Regression discontinuity design could be a valuable tool for identifying causal
effects of a given party holding a legislative majority. However, the variable ‘number
of seats’ takes a finite number of values rather than a continuum and, hence, it is not suited as a running variable. Recent econometric advances suggest the necessary assumptions and empirical tests that allow us to interpret small intervals around the cut-off as local randomized experiments. These permit us to bypass the assumption that the running variable must be continuous. Herein, we implement these tests for US state legislatures and propose another: whether a slim-majority of one seat had at least one state-level district result that was itself a close race won by the majority party.