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

Author

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  • Otávio 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.

Suggested Citation

  • Otávio Bartalotti, 2013. "Theory and Practice of Inference in Regression Discontinuity: A Fixed-Bandwidth Asymptotics Approach," Working Papers 1302, Tulane University, Department of Economics, revised Nov 2013.
  • Handle: RePEc:tul:wpaper:1302
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    File URL: http://repec.tulane.edu/RePEc/pdf/tul1302.pdf
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    References listed on IDEAS

    as
    1. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs," Econometrica, Econometric Society, vol. 82, pages 2295-2326, November.
    2. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    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. Lee, David S. & Card, David, 2008. "Regression discontinuity inference with specification error," Journal of Econometrics, Elsevier, vol. 142(2), pages 655-674, February.
    5. Jinyong Hahn & Petra Todd & Wilbert Van der Klaauw, 1999. "Evaluating the Effect of an Antidiscrimination Law Using a Regression-Discontinuity Design," NBER Working Papers 7131, National Bureau of Economic Research, Inc.
    6. Guido Imbens & Karthik Kalyanaraman, 2012. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 933-959.
    7. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, Fall.
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    More about this item

    Keywords

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

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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