On Extrapolation of Treatment Effects in Multiple-Cutoff Regression Discontinuity Designs

TL;DR

This paper examines how to accurately estimate treatment effects away from cutoffs in multiple-cutoff regression discontinuity designs, highlighting when common assumptions hold and proposing a new partial identification method.

Contribution

It introduces a novel partial identification approach for extrapolating treatment effects and develops a uniform inference procedure for multiple-cutoff RDDs.

Findings

Parallel-trend assumption holds under random cutoff assignment and non-manipulable running variables.

Extrapolations can be biased when the running variable is manipulable.

The proposed partial identification method provides robust bounds for treatment effects.

Abstract

We investigate how to learn treatment effects away from the cutoff in multiple-cutoff regression discontinuity designs. Using a microeconomic model, we demonstrate that the parallel-trend type assumption proposed in the literature is justified when cutoff positions are assigned as if randomly and the running variable is non-manipulable (e.g., parental income). However, when the running variable is partially manipulable (e.g., test scores), extrapolations based on that assumption can be biased. As a complementary strategy, we propose a novel partial identification approach based on empirically motivated assumptions. We also develop a uniform inference procedure and provide two empirical illustrations.