Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs

TL;DR

This paper presents a new design-based method for extrapolating treatment effects in regression discontinuity designs with multiple cutoffs, enabling estimation beyond local effects.

Contribution

It introduces a novel extrapolation technique for RD effects using multiple cutoffs and a common trends assumption, expanding the scope of causal inference in RD studies.

Findings

Applied method to Colombian loan program data

Estimated effects for students away from cutoff scores

Demonstrated feasibility of extrapolation in RD designs

Abstract

In non-experimental settings, the Regression Discontinuity (RD) design is one of the most credible identification strategies for program evaluation and causal inference. However, RD treatment effect estimands are necessarily local, making statistical methods for the extrapolation of these effects a key area for development. We introduce a new method for extrapolation of RD effects that relies on the presence of multiple cutoffs, and is therefore design-based. Our approach employs an easy-to-interpret identifying assumption that mimics the idea of "common trends" in difference-in-differences designs. We illustrate our methods with data on a subsidized loan program on post-education attendance in Colombia, and offer new evidence on program effects for students with test scores away from the cutoff that determined program eligibility.