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

Fan Li, Andrea Mercatanti+2 more|arXiv (Cornell University)|Apr 1, 2019

Advanced Causal Inference Techniques44 references57 citations

TL;DR

The paper develops a regression discontinuity design (RD) approach for ordinal running variables using an ordered probit model to create a latent continuous running variable, and applies it to evaluate the ECB’s CSPP on corporate bond spreads at issuance.

ABSTRACT

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 pre-fixed threshold. In the case 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, such a threshold can be defined in terms of an ordinal running variable. This feature poses challenges to RD estimation due to the lack of a meaningful measure of distance. To evaluate such program, 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 effect of the CSPP and find a statistically significant and negative effect on corporate bond spreads at issuance.

Motivation & Objective

• Motivate and address causal inference challenges when the running variable is ordinal rather than continuous or discrete with distance.
• Propose a three-step RD approach within a local randomization framework using a latent continuous running variable.
• Estimate causal effects under local overlap, local SUTVA, and local unconfoundedness, with covariate balancing in a covariate-balanced subsample.
• Provide robust estimators (overlap and ATT weighting, with augmented outcome models) and valid variance estimation for the RD analysis.

Proposed method

• Postulate an ordered probit model for the ordinal running variable to obtain a latent continuous running variable via the estimated probability of being assigned to treatment.
• Identify a covariate-balanced subpopulation around the threshold using the estimated latent running variable and balance checks.
• Within the balanced subpopulation, estimate a weighted average treatment effect using overlap weights (ATO) or ATT weights, with augmented outcome regression models for robustness.
• Derive M-estimator (sandwich) variance estimators accounting for uncertainty from both the design (propensity scores) and analysis stages.
• Define target populations via tilting function h(x) and use weighted estimators to obtain the estimands (ATO and ATT).
• Describe subpopulation selection through a data-driven bandwidth search based on covariate balance (balancing tests) around the threshold.

Experimental results

Research questions

• RQ1 How can RD inference be conducted when the running variable is ordinal rather than continuous, and distance to threshold is ill-defined?
• RQ2 Can a latent continuous running variable derived from an ordered probit model provide valid local randomization-like inference around the RD threshold?
• RQ3 What is the effect of the CSPP eligibility on bond spreads at issuance when estimated with covariate-balanced, overlap-weighted RD around the threshold?
• RQ4 Do augmented (doubly robust) weighting estimators improve efficiency and robustness in RD with ordinal running variables?

Key findings

• The method yields a statistically significant and negative effect of CSPP eligibility on corporate bond spreads at issuance.
• The three-step RD approach using an ordered probit latent running variable successfully identifies a covariate-balanced subsample around the threshold.
• Overlap weighting (ATO) and ATT weighting with augmentation are feasible to estimate causal effects in this ordinal-RD setting.
• Augmented estimators provide double robustness and improved efficiency in the RD context, with variance estimators accounting for design and analysis uncertainty.
• Bond ratings, used as the ordinal running variable, can be modeled to reflect a latent continuous process that governs eligibility for CSPP purchases.