External Validity in Fuzzy Regression Discontinuity Designs

Abstract

Fuzzy regression discontinuity designs identify the local average treatment effect (LATE) for the subpopulation of compliers, and with forcing variable equal to the threshold. We develop methods that assess the external validity of LATE to other compliance groups at the threshold, and allow for identification away from the threshold. Specifically, we focus on the equality of outcome distributions between treated compliers and always-takers, and between untreated compliers and never-takers. These equalities imply continuity of expected outcomes conditional on both the forcing variable and the treatment status. We recommend that researchers plot these conditional expectations and test for discontinuities at the threshold to assess external validity. We provide new commands in STATA and MATLAB to implement our proposed procedures.

Keywords:

• key words: Exogeneity; External validity; Fuzzy regression discontinuity designs; Potential outcomes; Treatment effects

ACKNOWLEDGMENTS

We are grateful for comments by Joshua Angrist, Brigham Frandsen, and Arthur Lewbel on an earlier version of this paper. We thank two anonymous referees for valuable suggestions, Wei Qian for research assistance, Brian Jacob, Lars Lefgren, and Jordan Matsudaira for making available the data used in this article.

Notes

1 We use the compliance terminology of Imbens and Angrist (1994) extended to the FRD case by HTV.

2 Available at www.nd.edu/∼mbertanh.

3 Matsudaira (2008) did not disclose the name of the school district as part of an agreement to use the data.

Additional information

Funding

Bertanha: gratefully acknowledges the financial support received from: ISLA-Notre Dame, CORE-UcLouvain, and as a B.F. Haley and E.S. Shaw Fellow at SIEPR-Stanford.