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Theory and Practice of Inference in Regression Discontinuity: A Fixed-Bandwidth Asymptotics Approach

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  • Ot�vio Bartalotti

    ()
    (Department of Economics, Tulane University)

Abstract

In regression discontinuity design (RD), researchers use bandwidths around the discontinuity. For a given bandwidth, one can estimate asymptotic variance based on the assumption that the bandwidth shrinks to zero as sample size increases (the traditional approach) or, alternatively, that the bandwidth is fixed. The main theoretical results for RD rely on the former, while most applications in the literature treat the estimates as parametric. This paper develops the "fixed-bandwidth" alternative asymptotic theory for local polynomial estimators, bridging the gap between theorists and practitioners and shedding light on implicit assumptions on both approaches. The fixed-bandwidth approach provides alternative formulas, i.e. alternative approximations, for the bias and variance of RD estimators. Simulations indicate that fixed-bandwidth approximations are usually better than traditional approximations, and improvements are nontrivial when there is heteroskedasticity. When there is no heteroskedasticity, both approximations are shown to be equivalent under some additional mild conditions. Feasible estimators of fixed-bandwidth standard errors are easy to implement and improve coverage of confidence intervals compared to the traditional approach, especially in the presence of heteroskedasticity. Fixed-bandwidth approximations are akin to treating RD estimators as locally parametric, providing theoretical justification for the common empirical practice of using heteroskedasticity-robust standard errors in RD settings.

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File URL: http://econ.tulane.edu/RePEc/pdf/tul1302.pdf
File Function: Second Version, January 2013
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Bibliographic Info

Paper provided by Tulane University, Department of Economics in its series Working Papers with number 1302.

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Length: 61 pages
Date of creation: Jan 2013
Date of revision: Nov 2013
Handle: RePEc:tul:wpaper:1302

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Keywords: regression discontinuity design; average treatment effect; fixed bandwidth asymptotics; local polynomial estimators;

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  1. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, October.
  2. Guido Imbens & Thomas Lemieux, 2007. "Regression Discontinuity Designs: A Guide to Practice," NBER Working Papers 13039, National Bureau of Economic Research, Inc.
  3. Fan, Yanqin, 1998. "Goodness-Of-Fit Tests Based On Kernel Density Estimators With Fixed Smoothing Parameters," Econometric Theory, Cambridge University Press, vol. 14(05), pages 604-621, October.
  4. Hashimzade, Nigar & Vogelsang, Timothy, 2006. "Fixed-b Asymptotic Approximation of the Sampling Behavior of Nonparametric Spectral Density Estimators," Working Papers 06-04, Cornell University, Center for Analytic Economics.
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