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March 2021 A regression discontinuity design for ordinal running variables: Evaluating central bank purchases of corporate bonds
Fan Li, Andrea Mercatanti, Taneli Mäkinen, Andrea Silvestrini
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Ann. Appl. Stat. 15(1): 304-322 (March 2021). DOI: 10.1214/20-AOAS1396


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.


The authors are grateful to Federico Apicella, Johannes Breckenfelder, Giovanni Cerulli, Federico Cingano, Riccardo De Bonis, Alfonso Flores-Lagunes, Alessandra Mattei, Fabrizia Mealli, Santiago Pereda Fernández, Stefano Rossi and Stefano Siviero for helpful comments and suggestions. Part of this work was done while AM was a researcher at the Luxembourg Institute of Socio-Economic Research (LISER) and TM was visiting the Einaudi Institute for Economics and Finance (EIEF). The hospitality of these institutions is gratefully acknowledged. FL’s research is partially supported by the Statistical and Applied Mathematical Sciences Institute (SAMSI) through NSF Grant DMS-1638521. The views expressed herein are those of the authors and not necessarily those of Bank of Italy. All remaining errors are ours.


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Fan Li. Andrea Mercatanti. Taneli Mäkinen. Andrea Silvestrini. "A regression discontinuity design for ordinal running variables: Evaluating central bank purchases of corporate bonds." Ann. Appl. Stat. 15 (1) 304 - 322, March 2021.


Received: 1 June 2020; Published: March 2021
First available in Project Euclid: 18 March 2021

Digital Object Identifier: 10.1214/20-AOAS1396

Keywords: Asset purchase programs , augmented estimators , local unconfoundedness , M-estimation , ordered probit , regression discontinuity design , weighting

Rights: Copyright © 2021 Institute of Mathematical Statistics

Vol.15 • No. 1 • March 2021
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