TY - JOUR
T1 - On interpreting the regression discontinuity design as a local experiment
AU - Sekhon, Jasjeet S.
AU - Titiunik, Rocío
N1 - Publisher Copyright:
© Copyright 2017 by Emerald Publishing Limited All rights of reproduction in any form reserved.
PY - 2017
Y1 - 2017
N2 - We discuss the two most popular frameworks for identification, estimation and inference in regression discontinuity (RD) designs: the continuitybased framework, where the conditional expectations of the potential outcomes are assumed to be continuous functions of the score at the cutoff, and the local randomization framework, where the treatment assignment is assumed to be as good as randomized in a neighborhood around the cutoff. Using various examples, we show that (i) assuming random assignment of the RD running variable in a neighborhood of the cutoff implies neither that the potential outcomes and the treatment are statistically independent, nor that the potential outcomes are unrelated to the running variable in this neighborhood; and (ii) assuming local independence between the potential outcomes and the treatment does not imply the exclusion restriction that the score affects the outcomes only through the treatment indicator. Our discussion highlights key distinctions between "locally randomized" RD designs and real experiments, including that statistical independence and random assignment are conceptually different in RD contexts, and that the RD treatment assignment rule places no restrictions on how the score and potential outcomes are related. Our findings imply that the methods for RD estimation, inference, and falsification used in practice will necessarily be different (both in formal properties and in interpretation) according to which of the two frameworks is invoked.
AB - We discuss the two most popular frameworks for identification, estimation and inference in regression discontinuity (RD) designs: the continuitybased framework, where the conditional expectations of the potential outcomes are assumed to be continuous functions of the score at the cutoff, and the local randomization framework, where the treatment assignment is assumed to be as good as randomized in a neighborhood around the cutoff. Using various examples, we show that (i) assuming random assignment of the RD running variable in a neighborhood of the cutoff implies neither that the potential outcomes and the treatment are statistically independent, nor that the potential outcomes are unrelated to the running variable in this neighborhood; and (ii) assuming local independence between the potential outcomes and the treatment does not imply the exclusion restriction that the score affects the outcomes only through the treatment indicator. Our discussion highlights key distinctions between "locally randomized" RD designs and real experiments, including that statistical independence and random assignment are conceptually different in RD contexts, and that the RD treatment assignment rule places no restrictions on how the score and potential outcomes are related. Our findings imply that the methods for RD estimation, inference, and falsification used in practice will necessarily be different (both in formal properties and in interpretation) according to which of the two frameworks is invoked.
KW - As-if random assignment
KW - Local experiment
KW - Local randomization
KW - Regression discontinuity
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U2 - 10.1108/S0731-905320170000038001
DO - 10.1108/S0731-905320170000038001
M3 - Article
AN - SCOPUS:85019413033
SN - 0731-9053
VL - 38
SP - 1
EP - 28
JO - Advances in Econometrics
JF - Advances in Econometrics
ER -