Empirical likelihood for regression discontinuity design

Abstract

This paper proposes empirical likelihood based inference methods for causal effects identified from regression discontinuity designs. We consider both the sharp and fuzzy regression discontinuity designs and treat the regression functions as nonparametric. The proposed inference procedures do not require asymptotic variance estimation and the confidence sets have natural shapes, unlike the conventional Wald-type method. These features are illustrated by simulations and an empirical example which evaluates the effect of class size on pupils' scholastic achievements. Furthermore, for the sharp regression discontinuity design, we show that the empirical likelihood statistic admits a higher-order refinement, so-called the Bartlett correction. Bandwidth selection methods are also discussed.

Second order expansions of estimators in nonparametric moment conditions models with weakly dependent data

“…One possibility is to follow the ad hoc procedure suggested by Otsu et al's( 2015) and use least squares cross-validation to estimate the bandwidth and then multiply the resulting bandwidth by a power of the sample size that is consistent with undersmoothing. In this paper, we consider another method, that is, similar to the ad hoc cross-validation method of Otsu et al (2015) but is less computationally intensive. Specifically, we consider a twofold cross-validation procedure, which consists of computing for a random subset of the sample, the training set S v with 0 < v < 1, and a pilot bandwidth b p…”

“…To investigate this issue further, we consider the second order asymptotic properties of both the LLGEL and LLGMM estimators under a standard undersmoothing condition. Undersmoothing is often used in nonparametric estimation and inference (see for example Chen (1996), Lewbel (2007), Lewbel (2007), Fang et al (2011), Chen and Qin (2000) and Otsu, Xu, and Matsushita (2015) among others); it is practically useful, as it removes the need to estimate the asymptotic bias resulting from the local estimation, and theoretically interesting as it produces confidence intervals (regions) with more accurate coverage (see Hall (1992) for a theoretical justification of the merit of undersmoothing over direct bias estimation).…”

Regression Discontinuity Designs in the Econometrics Literature

“…McCrary ( 2008) developed a test for the null hypothesis of no discontinuity in the density of the forcing variable that should be performed any time someone does a rdd analysis. See also Otsu et al (2015) for an alternative version of the test. Note that, for the purpose of estimating the difference in the conditional means of the outcome on the right and the left of the threshold, there is formally no need for the marginal density of the forcing variable to be continuous at that point.…”

Uniform Inference on Quantile Effects under Sharp Regression Discontinuity Designs

“…More recent contributions include those on distributional treatment e¤ects (Frölich and Melly, 2010, Frandsen, Frölich, and Melly, 2012, and Shen and Zhang, 2016, alternative estimation procedures (Porter, 2003, Lee, Moretti, and Butler, 2004, and Otsu, Xu, and Matsushita, 2015, graphical methods (Calonico, Cattaneo, and Titiunik, 2015), methods for bandwidths selections (Ludwig andMiller, 2007, Imbens andKalyanaraman, 2012), robust inference (Calonico, Cattaneo, and Titiunik, 2014), speci…cation analysis (McCrary, 2008, andCard, 2008), and kink designs (Dong, 2012, Card, Lee, Pei, and Weber, 2015, and Chiang and Sasaki, 2016. A comprehensive survey can be found in Imbens and Lemieux (2008).…”