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Spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix

  • Kim, Min Seong
  • Sun, Yixiao

This paper considers spatial heteroskedasticity and autocorrelation consistent (spatial HAC) estimation of covariance matrices of parameter estimators. We generalize the spatial HAC estimator introduced by Kelejian and Prucha (2007) to apply to linear and nonlinear spatial models with moment conditions. We establish its consistency, rate of convergence and asymptotic truncated mean squared error (MSE). Based on the asymptotic truncated MSE criterion, we derive the optimal bandwidth parameter and suggest its data dependent estimation procedure using a parametric plug-in method. The finite sample performances of the spatial HAC estimator are evaluated via Monte Carlo simulation.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 160 (2011)
Issue (Month): 2 (February)
Pages: 349-371

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Handle: RePEc:eee:econom:v:160:y:2011:i:2:p:349-371
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Russell Davidson & Emmanuel Flachaire, 2001. "The Wild Bootstrap, Tamed at Last," Working Papers 1000, Queen's University, Department of Economics.
  2. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  3. Timothy Conley & Francesca Molinari, 2005. "Spatial correlation robust inference with Errors in Location or Distance," CeMMAP working papers CWP10/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Yixiao Sun & Peter C.B. Phillips, 2008. "Optimal Bandwidth Choice for Interval Estimation in GMM Regression," Cowles Foundation Discussion Papers 1661, Cowles Foundation for Research in Economics, Yale University.
  5. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Wiley Blackwell, vol. 61(4), pages 631-53, October.
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  8. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  9. Gonçalves, Sílvia & Vogelsang, Timothy J., 2011. "Block Bootstrap Hac Robust Tests: The Sophistication Of The Naive Bootstrap," Econometric Theory, Cambridge University Press, vol. 27(04), pages 745-791, August.
  10. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2002. "Heteroskedasticity-Autocorrelation Robust Testing Using Bandwidth Equal To Sample Size," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1350-1366, December.
  11. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2008. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Econometrica, Econometric Society, vol. 76(1), pages 175-194, 01.
  12. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  13. Kelejian, Harry H. & Prucha, Ingmar R., 2007. "HAC estimation in a spatial framework," Journal of Econometrics, Elsevier, vol. 140(1), pages 131-154, September.
  14. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
  15. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
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