A Regression Discontinuity Design for Ordinal Running Variables: Evaluating Central Bank Purchases of Corporate Bonds

Abstract

We propose a regression discontinuity design which can be employed when assignment to treatment is determined by an ordinal variable. The proposal first requires estimating 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. Three types of balancing weights---overlap weights, inverse probability weights and ATT weights---are considered. An empirical M-estimator for the variance of the weighting estimator is derived. We apply the method to evaluate the causal effect of the Corporate Sector Purchase Programme of the European Central Bank on bond spreads.