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Small Bandwidth Asymptotics For Density-Weighted Average Derivatives

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  • Cattaneo, Matias D.
  • Crump, Richard K.
  • Jansson, Michael

Abstract

This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels and the standard errors are "robust" in the sense that they accommodate (but do not require) bandwidths that are smaller than those for which conventional standard errors are valid. Moreover, the results of a Monte Carlo experiment suggest that the finite sample coverage rates of confidence intervals constructed using the standard errors developed in this paper coincide (approximately) with the nominal coverage rates across a nontrivial range of bandwidths.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 30 (2014)
Issue (Month): 01 (February)
Pages: 176-200

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Handle: RePEc:cup:etheor:v:30:y:2014:i:01:p:176-200_00

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  1. Yoshihiko Nishiyama & Peter M. Robinson, 2005. "The Bootstrap and the Edgeworth Correction for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, Econometric Society, vol. 73(3), pages 903-948, 05.
  2. Newey, W.K., 1992. "Kernel Estimation of Partial Means and a General Variance Estimator," Working papers 93-3, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
  4. Kiefer, Nicholas M., 2001. "Heteroskedasticity-Autocorrelation Robust Standard Errors Using the Bartlett Kernel without Truncation," Working Papers 01-13, Cornell University, Center for Analytic Economics.
  5. Newey, W.K., 1991. "The Asymptotic Variance of Semiparametric Estimators," Working papers 583, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Robinson, P M, 1995. "The Normal Approximation for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, Econometric Society, vol. 63(3), pages 667-80, May.
  7. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 18(06), pages 1350-1366, December.
  8. Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000. "Simple Robust Testing of Regression Hypotheses," Staff General Research Papers 1832, Iowa State University, Department of Economics.
  9. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, Elsevier, vol. 75(2), pages 291-316, December.
  10. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, Econometric Society, vol. 57(6), pages 1403-30, November.
  11. Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, Econometric Society, vol. 72(3), pages 947-962, 05.
  12. Y. Nishiyama & P. M. Robinson, 2000. "Edgeworth Expansions for Semiparametric Averaged Derivatives," Econometrica, Econometric Society, Econometric Society, vol. 68(4), pages 931-980, July.
  13. Newey, Whitney K & Stoker, Thomas M, 1993. "Efficiency of Weighted Average Derivative Estimators and Index Models," Econometrica, Econometric Society, Econometric Society, vol. 61(5), pages 1199-223, September.
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Cited by:
  1. Matias D. Cattaneo & Richard K. Crump & Michael Jansson, 2009. "Robust Data-Driven Inference for Density-Weighted Average Derivatives," CREATES Research Papers 2009-46, School of Economics and Management, University of Aarhus.
  2. Hiroaki Kaido, 2014. "Asymptotically efficient estimation of weighted average derivatives with an interval censored variable," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP03/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Dennis Kristensen, 2009. "Semiparametric Modelling and Estimation: A Selective Overview," CREATES Research Papers 2009-44, School of Economics and Management, University of Aarhus.

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