Extrapolating Treatment Effects in Multi-Cutoff Regression Discontinuity Designs

Abstract

Abstract–In nonexperimental 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. Supplementary materials for this article are available online.

Keywords:

• Causal inference
• Extrapolation
• Regression discontinuity

Acknowledgments

We are very grateful to Fabio Sanchez and Tatiana Velasco for sharing the dataset used in the empirical application. We also thank Josh Angrist, Sebastian Calonico, Sebastian Galiani, Nicolas Idrobo, Xinwei Ma, Max Farrell, and seminar participants at various institutions for their comments. We also thank the co-editor, Regina Liu, an associate editor, and a reviewer for their comments.

Additional information

Funding

Cattaneo and Titiunik gratefully acknowledge financial support from the National Science Foundation (SES 1357561).