A regression discontinuity design for ordinal running variables: Evaluating central bank purchases of corporate bonds

Regression discontinuity (RD) is a widely used quasi-experimental design for causal inference. In the standard RD the assignment to treatment is determined by a continuous pretreatment variable (i.e., running variable) falling above or below a prefixed threshold. Recent applications increasingly feature ordered categorical or ordinal running variables which pose challenges to RD estimation due to the lack of a meaningful measure of distance. This paper proposes an RD approach for ordinal running variables under the local randomization framework. The proposal first estimates an ordered probit model for the ordinal running variable. The estimated probability of being assigned to treatment is then adopted as a latent continuous running variable and used to identify a covariate-balanced subsample around the threshold. Assuming local unconfoundedness of the treatment in the subsample, an estimate of the effect of the program is obtained by employing a weighted estimator of the average treatment effect. Two weighting estimators-overlap weights and ATT weights-as well as their augmented versions are considered. We apply the method to evaluate the causal effects of the corporate sector purchase programme (CSPP) of the European Central Bank which involves large-scale purchases of securities issued by corporations in the euro area. We find a statistically significant and negative effect of the CSPP on corporate bond spreads at issuance.