On Extrapolation of Treatment Effects in Multiple-Cutoff Regression Discontinuity Designs (2412.04265v2)

Abstract: Regression discontinuity (RD) designs typically identify the treatment effect at a single cutoff point, which may not always be the primary interest. When and how, then, can we learn about treatment effects away from the cutoff? This paper addresses this question within a multiple-cutoff RD framework. We begin by examining the plausibility of the constant bias assumption proposed by Cattaneo, Keele, Titiunik, and Vazquez-Bare (2021) through the lens of rational decision-making behavior. We argue that this assumption is indeed plausible when the groups defined by different cutoffs consist of similar agents and the running variable is effort-invariant, that is, not influenced by the agents' effort (e.g., family income level). However, this positive conclusion no longer holds when the running variable is effort-contingent, meaning it depends on agents' effort (e.g., test scores). In such settings, extrapolated effects based on the constant bias assumption can be biased, even when all other features remain identical except for the cutoff position. To address this issue, we introduce an alternative set of assumptions grounded in empirical motivations and develop a novel partial identification strategy. We illustrate the usefulness and practical relevance of the proposed bounds through empirical examples. In this application, we also find that extrapolation under the constant bias assumption performs reasonably well when the running variable is effort-invariant and some similarity between groups is expected.