A Regression Discontinuity Design for Ordinal Running Variables: Evaluating Central Bank Purchases of Corporate Bonds Fan Li Andrea Mercatanti Taneli M¨ akinen Andrea Silvestrini 1 ABSTRACT We propose a regression discontinuity design which can be employed when assignment to treat- ment 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 employ- ing 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 Cen- tral Bank on bond spreads. KEY WORDS: asset purchase programs, balance, local unconfoundedness, ordered probit, re- gression discontinuity design, weighting 1 FL is associate professor, Department of Statistical Science, Duke University, Durham, NC, 27708 (email: fl35@duke.edu); AM is researcher (andrea.mercatanti@liser.lu), Bank of Italy and Luxembourg Institute of Socio-Economic Research; TM (email: taneli.makinen@bancaditalia.it) and AS (email: an- drea.silvestrini@bancaditalia.it) are researchers, Bank of Italy. The authors are grateful to Federico Apicella, Jo- hannes Breckenfelder, Federico Cingano, Riccardo De Bonis, Alfonso Flores-Lagunes, Frank Li, Fabrizia Mealli, Santiago Pereda Fern´ andez, Stefano Rossi and Stefano Siviero for helpful comments and suggestions. Part of this work was done while TM was visiting the Einaudi Institute for Economics and Finance, whose hospitality is gratefully acknowledged. The views expressed herein are those of the authors and not necessarily those of Bank of Italy. All remaining errors are ours. 1 arXiv:1904.01101v1 [stat.ME] 1 Apr 2019