Alternative Assumptions to Identify LATE in Fuzzy Regression Discontinuity Designs
| Published date | 01 October 2018 |
| Date | 01 October 2018 |
| DOI | http://doi.org/10.1111/obes.12249 |
| Author | Yingying Dong |
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©2018 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 80, 5 (2018) 0305–9049
doi: 10.1111/obes.12249
AlternativeAssumptions to Identify LATE in Fuzzy
Regression Discontinuity Designs
Yingying Dong†
†Department of Economics, University of California Irvine, Irvine, CA 92697, USA (e-mail:
yyd@uci.edu) http://yingyingdong.com/
Abstract
There exist two alternative assumptions to identify local average treatment effects (LATE)
in fuzzy regression discontinuity (RD) designs: local independence (LI) and local smooth-
ness (LS). Together with the usual LATE assumptions requiring existence of a first-stage
and treatment monotonicity, either of these two assumptions is sufficient to identify RD
LATE. I discuss the practical (and testable) implications of these alternative assumptions,
and show that weakening LI by LS might be empirically relevant. However, when LI does
hold, there are some practical implications one may explore. Numerical and empirical
examples are briefly presented.
I. Introduction
Regression discontinuity (RD) designs have been widely used in many areas of empirical
research. There exist twoalternative assumptions to identify local average treatment effects
(LATE)in fuzzy RD designs: local independence (LI) and local smoothness (LS). Together
with the usual LATE assumptions requiring existence of a first-stage and treatment mono-
tonicity, either of these two assumptions is sufficient to identify RD LATE.1This paper
discusses these alternative assumptions, and show that weakening LI by LS might be em-
pirically relevant. However, when LI does hold, there are some practical implications one
may explore.
LI requires that individual treatment effects and potential treatment status are jointlyin-
dependent of the running variable in the neighbourhood of the RD cut-off (Hahn, Todd and
van der Klaauw, 2001, hereafter HTK). It is a local version of the independence assump-
tion proposed in the LATEframework (Imbens and Angrist, 1994 and Angrist, Imbens and
Rubin, 1996). In contrast, LS only requires that the conditional means (or distributions) of
potential outcomes and potential treatment status are smooth near the RD cut-off (see, e.g.
Frandsen, Frolich and Melly, 2012; Dong, forthcoming; Dong and Lewbel, 2015), which
can be seen as a smooth parallel of the LATE independence assumption.
JEL Classification numbers: C21, C25.
1This paper focuses on fuzzy RD designs, with sharp design following as a special case.
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