Adaptive Estimation of the Regression Discontinuity Model
In order to reduce the finite sample bias and improve the rate of convergence, local polynomial estimators have been introduced into the econometric literature to estimate the regression discontinuity model. In this paper, we show that, when the degree of smoothness is known, the local polynomial estimator achieves the optimal rate of convergence within the Hölder smoothness class. However, when the degree of smoothness is not known, the local polynomial estimator may actually inflate the finite sample bias and reduce the rate of convergence. We propose an adaptive version of the local polynomial estimator which selects both the bandwidth and the polynomial order adaptively and show that the adaptive estimator achieves the optimal rate of convergence up to a logarithm factor without knowing the degree of smoothness. Simulation results show that the finite sample performance of the locally cross-validated adaptive estimator is robust to the parameter combinations and data generating processes, reflecting the adaptive nature of the estimator. The root mean squared error of the adaptive estimator compares favorably to local polynomial estimators in the Monte Carlo experiments.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hall, Peter & Schucany, William R., 1989. "A local cross-validation algorithm," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 109-117, June.
- Kenneth Y. Chay & Michael Greenstone, 2005.
"Does Air Quality Matter? Evidence from the Housing Market,"
Journal of Political Economy,
University of Chicago Press, vol. 113(2), pages 376-424, April.
- Kenneth Y. Chay & Michael Greenstone, 1998. "Does Air Quality Matter? Evidence from the Housing Market," NBER Working Papers 6826, National Bureau of Economic Research, Inc.
- Erich Battistin & Enrico Rettore, 2002. "Testing for programme effects in a regression discontinuity design with imperfect compliance," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(1), pages 39-57.
- ANDREWS, DONALD W & Sun, Yixiao X, 2002.
"Adaptive Local Polynomial Whittle Estimation of Long-Range Dependence,"
University of California at San Diego, Economics Working Paper Series
qt9wt048tt, Department of Economics, UC San Diego.
- Donald W. K. Andrews & Yixiao Sun, 2004. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Econometrica, Econometric Society, vol. 72(2), pages 569-614, 03.
- Donald W.K. Andrews & Yixiao Sun, 2002. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Cowles Foundation Discussion Papers 1384, Cowles Foundation for Research in Economics, Yale University.
- Hahn, Jinyong & Todd, Petra & Van der Klaauw, Wilbert, 2001. "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, Econometric Society, vol. 69(1), pages 201-09, January.
- Sandra E. Black, 1999.
"Do Better Schools Matter? Parental Valuation Of Elementary Education,"
The Quarterly Journal of Economics,
MIT Press, vol. 114(2), pages 577-599, May.
- Sandra E. Black, 1997. "Do better schools matter? Parental valuation of elementary education," Research Paper 9729, Federal Reserve Bank of New York.
- Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
- Giraitis, Liudas & Robinson, Peter M. & Samarov, Alexander, 2000. "Adaptive Semiparametric Estimation of the Memory Parameter," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 183-207, February.
- Hurvich, Clifford M. & Moulines, Eric & Soulier, Philippe, 2002. "The FEXP estimator for potentially non-stationary linear time series," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 307-340, February.
- Joshua D. Angrist & Victor Lavy, 1999. "Using Maimonides' Rule To Estimate The Effect Of Class Size On Scholastic Achievement," The Quarterly Journal of Economics, MIT Press, vol. 114(2), pages 533-575, May.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpem:0506003. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.