Regression Discontinuity Designs Lecture

Regression Discontinuity Designs Lecture -...

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Unformatted text preview: Imbens/Wooldridge, Lecture Notes 3, NBER, Summer ’07 1 What’s New in Econometrics NBER, Summer 2007 Lecture 3, Monday, July 30th, 2.00-3.00pm R e gr e ssi on D i sc ont i n ui ty D e si gns 1 1. Introduction Since the late 1990s there has been a large number of studies in economics applying and extending Regression Discontinuity (RD) methods from its origins in the statistics literature in the early 60’s (Thisthlewaite and Cook, 1960). Here, we review some of the practical issues in implementation of RD methods. The focus is on five specific issues. The first is the importance of graphical analyses as powerful methods for illustrating the design. Second, we suggest using local linear regression methods using only the observations close to the discontinuity point. Third, we discuss choosing the bandwidth using cross validation specifically tailored to the focus on estimation of regression functions on the boundary of the support, following Ludwig and Miller (2005). Fourth, we provide two simple estimators for the asymptotic variance, one of them exploiting the link with instrumental variables methods derived by Hahn, Todd, and VanderKlaauw (2001, HTV). Finally, we discuss a number of specification tests and sensivitity analyses based on tests for ( a ) discontinuities in the average values for covariates, ( b ) discontinuities in the conditional density of the forcing variable, as suggested by McCrary (2007), ( c ) discontinuities in the average outcome at other values of the forcing variable. 2. Sharp and Fuzzy Regression Discontinuity Designs 2.1 Basics Our discussion will frame the RD design in the context of the modern literature on causal effects and treatment effects, using the potential outcomes framework (Rubin, 1974), rather than the regression framework that was originally used in this literature. For unit i there are two potential outcomes, Y i (0) and Y i (1), with the causal effect defined as the difference 1 These notes draw heavily on Imbens and Lemieux (2007). Imbens/Wooldridge, Lecture Notes 3, NBER, Summer ’07 2 Y i (1)- Y i (0), and the observed outcome equal to Y i = (1- W i ) · Y i (0) + W i · Y i (1) = braceleftbigg Y i (0) if W i = 0 , Y i (1) if W i = 1 , where W i ∈ { , 1 } is the binary indicator for the treatment. The basic idea behind the RD design is that assignment to the treatment is determined, either completely or partly, by the value of a predictor (the forcing variable X i ) being on either side of a common threshold. This predictor X i may itself be associated with the potential outcomes, but this association is assumed to be smooth, and so any discontinuity in the conditional distribution of the outcome, indexed by the value of this covariate at the cutoff value, is interpreted as evidence of a causal effect of the treatment. The design often arises from administrative decisions, where the incentives for units to participate in a program are partly limited for reasons of resource constraints, and clear transparent rules...
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Regression Discontinuity Designs Lecture -...

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