Adaptive Estimation of the Regression Discontinuity Model
AbstractIn 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.
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Bibliographic InfoPaper provided by EconWPA in its series Econometrics with number 0506003.
Length: 41 pages
Date of creation: 07 Jun 2005
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Adaptive estimator; local cross validation; local polynomial; minimax rate; optimal bandwidth; optimal smoothness parameter;
Find related papers by JEL classification:
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
- C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
- C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
- C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
- C5 - Mathematical and Quantitative Methods - - Econometric Modeling
- C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
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- 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.
- Sandra E. Black, 1997.
"Do better schools matter? Parental valuation of elementary education,"
9729, Federal Reserve Bank of New York.
- 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.
- 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.
- 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.
- 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.
- 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.
- Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
- 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.
- Hall, Peter & Schucany, William R., 1989. "A local cross-validation algorithm," Statistics & Probability Letters, Elsevier, vol. 8(2), pages 109-117, June.
- 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.
- Ganong, Peter & Jäger, Simon, 2014. "A Permutation Test and Estimation Alternatives for the Regression Kink Design," IZA Discussion Papers 8282, Institute for the Study of Labor (IZA).
- Guido Imbens & Thomas Lemieux, 2007.
"Regression Discontinuity Designs: A Guide to Practice,"
NBER Working Papers
13039, 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 Technical Working Papers 0337, National Bureau of Economic Research, Inc.
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