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Asymptotic Properties of the Efficient Estimators for Cointegrating Regression Models with Serially Dependent Errors

  • Eiji Kurozumi
  • Kazuhiko Hayakawa

In this paper, we analytically investigate three efficient estimators for cointegrating regression models: Phillips and Hansen's (1990) fully modified OLS estimator, Park's (1992) canonical cointegrating regression estimator, and Saikkonen's (1991) dynamic OLS estimator. First, by the Monte Carlo simulations, we demonstrate that these efficient methods do not work well when the regression errors are strongly serially correlated. In order to explain this result, we assume that the regression errors are generated from a nearly integrated autoregressive (AR) process with the AR coefficient approaching 1 at a rate of 1/T , where T is the sample size. We derive the limiting distributions of the three efficient estimators as well as the OLS estimator and show that they have the same limiting distribution under this assumption. This implies that the three efficient methods no longer work well when the regression errors are strongly serially correlated. Further, we consider the case where the AR coefficient in the regression errors approaches 1 at a rate slower than 1/T . In this case, the limiting distributions of the efficient estimators depend on the approaching rate. If the rate is slow enough, the efficiency is established for the three estimators; however, if the approaching rate is relatively fast, they have the same limiting distribution as the OLS estimator. This result explains why the effect of the efficient methods diminishes as the serial correlation in the regression errors gets stronger.

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File URL: http://hi-stat.ier.hit-u.ac.jp/research/discussion/2006/pdf/D06-197.pdf
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Paper provided by Institute of Economic Research, Hitotsubashi University in its series Hi-Stat Discussion Paper Series with number d06-197.

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Date of creation: Dec 2006
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Handle: RePEc:hst:hstdps:d06-197
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  1. James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
  2. 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.
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  5. 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.
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  8. 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.
  9. 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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  11. Montalvo, Jose G., 1995. "Comparing cointegrating regression estimators: Some additional Monte Carlo results," Economics Letters, Elsevier, vol. 48(3-4), pages 229-234, June.
  12. 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.
  13. Phillips, Peter C B & Loretan, Mico, 1991. "Estimating Long-run Economic Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 407-36, May.
  14. 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.
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  17. 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.
  18. 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.
  19. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  20. 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.
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  25. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
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