IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v149y2009i2p118-135.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • Kurozumi, Eiji & Hayakawa, Kazuhiko, 2009. "Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors," Journal of Econometrics, Elsevier, vol. 149(2), pages 118-135, April.
  • Handle: RePEc:eee:econom:v:149:y:2009:i:2:p:118-135
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(08)00211-X
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-143, January.
    2. 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.
    3. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    4. Donggyu Sul & Peter C. B. Phillips & Chi-Young Choi, 2005. "Prewhitening Bias in HAC Estimation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(4), pages 517-546, August.
    5. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 631-653.
    6. 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.
    7. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Oxford University Press, vol. 57(1), pages 99-125.
    8. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    9. Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 51-60, January.
    10. Peter C. B. Phillips & Mico Loretan, 1991. "Estimating Long-run Economic Equilibria," Review of Economic Studies, Oxford University Press, vol. 58(3), pages 407-436.
    11. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    12. 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.
    13. 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.
    14. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    15. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    16. Montalvo, Jose G., 1995. "Comparing cointegrating regression estimators: Some additional Monte Carlo results," Economics Letters, Elsevier, vol. 48(3-4), pages 229-234, June.
    17. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
    18. Kitamura, Yuichi & Phillips, Peter C. B., 1997. "Fully modified IV, GIVE and GMM estimation with possibly non-stationary regressors and instruments," Journal of Econometrics, Elsevier, vol. 80(1), pages 85-123, September.
    19. 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.
    20. 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.
    21. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
    22. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
    23. 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.
    24. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marcel Aloy & Gilles De Truchis, 2012. "Estimation and Testing for Fractional Cointegration," Working Papers halshs-00793206, HAL.
    2. Marcel Aloy & Gilles Truchis, 2016. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems and the Co-persistence Analysis of Stock Market Realized Volatilities," Computational Economics, Springer;Society for Computational Economics, vol. 48(1), pages 83-104, June.
    3. 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.
    4. Stapleton, Lee & Sorrell, Steve & Schwanen, Tim, 2016. "Estimating direct rebound effects for personal automotive travel in Great Britain," Energy Economics, Elsevier, vol. 54(C), pages 313-325.
    5. Arize, Augustine C. & Malindretos, John & Ghosh, Dilip, 2015. "Purchasing power parity-symmetry and proportionality: Evidence from 116 countries," International Review of Economics & Finance, Elsevier, vol. 37(C), pages 69-85.
    6. J. Isaac Miller, 2010. "Cointegrating regressions with messy regressors and an application to mixed-frequency series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 255-277, July.
    7. Marcel Aloy & Gilles De Truchis, 2013. "Optimal Estimation Strategies for Bivariate Fractional Cointegration Systems," Working Papers halshs-00879522, HAL.
    8. 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.

    More about this item

    Keywords

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

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:149:y:2009:i:2:p:118-135. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.