A Regression Discontinuity Design for Categorical Ordered Running Variables with An Application to Central Bank Purchases of Corporate Bonds

We propose a regression discontinuity design which can be employed when assignment to a treatment is determined by an ordinal variable. The proposal first requires an ordered probit model for the ordinal running variable to be estimated. The estimated probability of being assigned to a treatment is then adopted as a latent continuous running variable and used to identify a covariate-balanced subsample around the threshold. Assuming the local unconfoundedness of the treatment in the subsample, an estimate of the effect of the programme is obtained by employing a weighted estimator of the average treatment effect. We apply our methodology to estimate the causal effect of the corporate sector purchase programme of the European Central Bank on bond spreads