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Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors

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  • Kurozumi, Eiji
  • Hayakawa, Kazuhiko

Abstract

In this paper, we analytically investigate three efficient estimators for cointegrating regression models: Phillips and Hansen's [Phillips, P.C.B., Hansen, B.E., 1990. Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57, 99-125] fully modified OLS estimator, Park's [Park, J.Y., 1992. Canonical cointegrating regressions. Econometrica 60, 119-143] canonical cointegrating regression estimator, and Saikkonen's [Saikkonen, P., 1991. Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7, 1-21] dynamic OLS estimator. We consider the case where the regression errors are moderately serially correlated and the AR coefficient in the regression errors approaches 1 at a rate slower than 1/T, where T represents the sample size. We derive the limiting distributions of the efficient estimators under this system and find that they depend on the approaching rate of the AR coefficient. If the rate is slow enough, efficiency is established for the three estimators; however, if the approaching rate is relatively faster, the estimators will have the same limiting distribution as the OLS estimator. For the intermediate case, the second-order bias of the OLS estimator is partially eliminated by the efficient methods. This result explains why, in finite samples, the effect of the efficient methods diminishes as the serial correlation in the regression errors becomes stronger. We also propose to modify the existing efficient estimators in order to eliminate the second-order bias, which possibly remains in the efficient estimators. Using Monte Carlo simulations, we demonstrate that our modification is effective when the regression errors are moderately serially correlated and the simultaneous correlation is relatively strong.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 149 (2009)
Issue (Month): 2 (April)
Pages: 118-135

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Handle: RePEc:eee:econom:v:149:y:2009:i:2:p:118-135

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Cointegration Second-order bias Fully modified regressions Canonical cointegrating regressions Dynamic ordinary least squares regressions;

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References

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  1. Peter C.B. Phillips & Tassos Magdalinos, 2004. "Limit Theory for Moderate Deviations from a Unit Root," Cowles Foundation Discussion Papers 1471, Cowles Foundation for Research in Economics, Yale University.
  2. Nunzio Cappuccio & Diego Lubian, 2001. "Estimation And Inference On Long-Run Equilibria: A Simulation Study," Econometric Reviews, Taylor & Francis Journals, vol. 20(1), pages 61-84.
  3. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  4. Peter C.B. Phillips & Tassos Magadalinos, 2005. "Limit Theory for Moderate Deviations from a Unit Root under Weak Dependence," Cowles Foundation Discussion Papers 1517, Cowles Foundation for Research in Economics, Yale University.
  5. Kejriwal, Mohitosh & Perron, Pierre, 2008. "Data Dependent Rules For Selection Of The Number Of Leads And Lags In The Dynamic Ols Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1425-1441, October.
  6. Liudas Giraitis & Peter C.B. Phillips, 2004. "Uniform Limit Theory for Stationary Autoregression," Cowles Foundation Discussion Papers 1475, Cowles Foundation for Research in Economics, Yale University.
  7. Donggyu Sul & Peter C.B. Phillips & Choi, Chi-Young, 2003. "Prewhitening Bias in HAC Estimation," Cowles Foundation Discussion Papers 1436, Cowles Foundation for Research in Economics, Yale University.
  8. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  9. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  10. Saikkonen, Pentti & L tkepohl, Helmut, 1999. "Local Power Of Likelihood Ratio Tests For The Cointegrating Rank Of A Var Process," Econometric Theory, Cambridge University Press, vol. 15(01), pages 50-78, February.
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  12. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  13. 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.
  14. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
  15. Yuichi Kitamura & Peter C.B. Phillips, 1994. "Fully Modified IV, GIVE and GMM Estimation with Possibly Non-Stationary Regressions and Instruments," Cowles Foundation Discussion Papers 1082, Cowles Foundation for Research in Economics, Yale University.
  16. Mohitosh Kejriwal & Pierre Perron, 2006. "Data Dependent Rules for the Selection of the Number of Leads and Lags in the Dynamic OLS Cointegrating Regression," Boston University - Department of Economics - Working Papers Series WP2006-035, Boston University - Department of Economics.
  17. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  18. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-78, September.
  19. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  20. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
  21. Inder, Brett, 1993. "Estimating long-run relationships in economics : A comparison of different approaches," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 53-68.
  22. Christou, Christina & Pittis, Nikitas, 2002. "Kernel And Bandwidth Selection, Prewhitening, And The Performance Of The Fully Modified Least Squares Estimation Method," Econometric Theory, Cambridge University Press, vol. 18(04), pages 948-961, August.
  23. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  24. Montalvo, Jose G., 1995. "Comparing cointegrating regression estimators: Some additional Monte Carlo results," Economics Letters, Elsevier, vol. 48(3-4), pages 229-234, June.
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Citations

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Cited by:
  1. Marcel Aloy & Gilles De Truchis, 2013. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems," Working Papers halshs-00879522, HAL.
  2. Hirukawa, Masayuki, 2011. "How useful is yet another data-driven bandwidth in long-run variance estimation?: A simulation study on cointegrating regressions," Economics Letters, Elsevier, vol. 111(2), pages 170-172, May.
  3. Jair Ojeda-Joya & José E. Gómez-González, 2012. "The Term-Structure of Sovereign Default Risk in Colombia and its Determinants," Borradores de Economia 709, Banco de la Republica de Colombia.
  4. Marcel Aloy & Gilles de Truchis, 2012. "Estimation and Testing for Fractional Cointegration," AMSE Working Papers 1215, Aix-Marseille School of Economics, Marseille, France.

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