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

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  • Eiji Kurozumi
  • Kazuhiko Hayakawa

Abstract

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.

Suggested Citation

  • Eiji Kurozumi & Kazuhiko Hayakawa, 2006. "Asymptotic Properties of the Efficient Estimators for Cointegrating Regression Models with Serially Dependent Errors," Hi-Stat Discussion Paper Series d06-197, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hst:hstdps:d06-197
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    References listed on IDEAS

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    1. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-143, January.
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    Citations

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    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.
    9. J. Isaac Miller, 2016. "Conditionally Efficient Estimation of Long-Run Relationships Using Mixed-Frequency Time Series," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 1142-1171, June.

    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

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