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Testing identifying assumptions in fuzzy regression discontinuity designs

Arai, Y; Hsu, Y-C; Kitagawa, T; Mourifié, I; Wan, Y; (2019) Testing identifying assumptions in fuzzy regression discontinuity designs. (cemmap working paper 10/19). Institute for Fiscal Studies (IFS): London, UK. Green open access

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Abstract

We propose a new specification test for assessing the validity of fuzzy regression discontinuity designs (FRD-validity). We derive a new set of testable implications, characterized by a set of inequality restrictions on the joint distribution of observed outcomes and treatment status at the cut-off. We show that this new characterization exploits all the information in the data useful for detecting violations of FRD-validity. Our approach differs from, and complements existing approaches that test continuity of the distributions of running variables and baseline covariates at the cut-off since ours focuses on the distribution of the observed outcome and treatment status. We show that the proposed test has appealing statistical properties. It controls size in large sample uniformly over a large class of distributions, is consistent against all fixed alternatives, and has non-trivial power against some local alternatives. We apply our test to evaluate the validity of two FRD designs. The test does not reject the FRD-validity in the class size design studied by Angrist and Lavy (1999) and rejects in the insurance subsidy design for poor households in Colombia studied by Miller, Pinto, and Vera-Hernández (2013) for some outcome variables, while existing density tests suggest the opposite in each of the cases.

Type: Working / discussion paper
Title: Testing identifying assumptions in fuzzy regression discontinuity designs
Open access status: An open access version is available from UCL Discovery
DOI: 10.1920/wp.cem.2019.1019
Publisher version: https://www.cemmap.ac.uk/publication/testing-ident...
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Fuzzy regression discontinuity design, nonparametric test, inequality restriction, multiplier bootstrap
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/10087222
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