Theory and Practice of Inference in Regression Discontinuity: A Fixed-Bandwidth Asymptotics Approach
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.
|Date of creation:||Jan 2013|
|Date of revision:||Nov 2013|
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- 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.
- Imbens, Guido W. & Lemieux, Thomas, 2008.
"Regression discontinuity designs: A guide to practice,"
Journal of Econometrics,
Elsevier, vol. 142(2), pages 615-635, February.
- Guido Imbens & Thomas Lemieux, 2007. "Regression Discontinuity Designs: A Guide to Practice," NBER Working Papers 13039, National Bureau of Economic Research, Inc.
- Guido Imbens & Thomas Lemieux, 2007. "Regression Discontinuity Designs: A Guide to Practice," NBER Technical Working Papers 0337, National Bureau of Economic Research, Inc.
- Imbens, Guido W. & Kalyanaraman, Karthik, 2009.
"Optimal Bandwidth Choice for the Regression Discontinuity Estimator,"
IZA Discussion Papers
3995, Institute for the Study of Labor (IZA).
- 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.
- Guido Imbens & Karthik Kalyanaraman, 2010. "Optimal bandwidth choice for the regression discontinuity estimator," CeMMAP working papers CWP05/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Guido Imbens & Karthik Kalyanaraman, 2009. "Optimal Bandwidth Choice for the Regression Discontinuity Estimator," NBER Working Papers 14726, National Bureau of Economic Research, Inc.
- Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
- 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.
- 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.
- Hashimzade, Nigar & Vogelsang, Timothy, 2006.
"Fixed-b Asymptotic Approximation of the Sampling Behavior of Nonparametric Spectral Density Estimators,"
06-04, Cornell University, Center for Analytic Economics.
- Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed-b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 142-162, 01.
- Lee, David S. & Card, David, 2008.
"Regression discontinuity inference with specification error,"
Journal of Econometrics,
Elsevier, vol. 142(2), pages 655-674, February.
- David S. Lee & David Card, 2006. "Regression Discontinuity Inference with Specification Error," NBER Technical Working Papers 0322, National Bureau of Economic Research, Inc.
- Pagan,Adrian & Ullah,Aman, 1999.
Cambridge University Press, number 9780521355643, November.
- McCrary, Justin, 2008. "Manipulation of the running variable in the regression discontinuity design: A density test," Journal of Econometrics, Elsevier, vol. 142(2), pages 698-714, February.
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