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Integrated Modified OLS Estimation and Fixed-b Inference for Cointegrating Regressions

  • Vogelsang, Timothy J.

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)

  • Wagner, Martin

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)

This paper is concerned with parameter estimation and inference in a cointegrating regression, where as usual endogenous regressors as well as serially correlated errors are considered. We propose a simple, new estimation method based on an augmented partial sum (integration) transformation of the regression model. The new estimator is labeled Integrated Modified Ordinary Least Squares (IM-OLS). IM-OLS is similar in spirit to the fully modified approach of Phillips and Hansen (1990) with the key difference that IM-OLS does not require estimation of long run variance matrices and avoids the need to choose tuning parameters (kernels, bandwidths, lags). Inference does require that a long run variance be scaled out, and we propose traditional and fixed-b methods for obtaining critical values for test statistics. The properties of IM-OLS are analyzed using asymptotic theory and finite sample simulations. IM-OLS performs well relative to other approaches in the literature.

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File URL: http://www.ihs.ac.at/publications/eco/es-263.pdf
File Function: First version, 2011
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Paper provided by Institute for Advanced Studies in its series Economics Series with number 263.

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Length: 43 pages
Date of creation: Jan 2011
Date of revision:
Handle: RePEc:ihs:ihsesp:263
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  1. Bunzel, Helle, 2006. "FIXED-b ASYMPTOTICS IN SINGLE-EQUATION COINTEGRATION MODELS WITH ENDOGENOUS REGRESSORS," Econometric Theory, Cambridge University Press, vol. 22(04), pages 743-755, August.
  2. Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed-b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 142-162, 01.
  3. Peter C.B. Phillips, 1987. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals via Martingale Approximations," Cowles Foundation Discussion Papers 846, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. 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.
  6. 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.
  7. Vogelsang, Timothy J. & Wagner, Martin, 2011. "A Fixed-b Perspective on the Phillips-Perron Unit Root Tests," Economics Series 272, Institute for Advanced Studies.
  8. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, vol. 53(4), pages 473-95, August.
  9. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation for Research in Economics, Yale University.
  10. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  11. In Choi & Eiji Kurozumi, 2008. "Model Selection Criteria for the Leads-and-Lags Cointegrating Regression," Global COE Hi-Stat Discussion Paper Series gd08-006, Institute of Economic Research, Hitotsubashi University.
  12. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
  13. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  14. Jin, Sainan & Phillips, Peter C.B. & Sun, Yixiao, 2006. "A new approach to robust inference in cointegration," Economics Letters, Elsevier, vol. 91(2), pages 300-306, May.
  15. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests," Working Papers 05-08, Cornell University, Center for Analytic Economics.
  16. Yixiao Sun & Peter C. B. Phillips & Sainan Jin, 2006. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing," Cowles Foundation Discussion Papers 1545, Cowles Foundation for Research in Economics, Yale University.
  17. Davidson, James & de Jong, Robert M., 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii," Econometric Theory, Cambridge University Press, vol. 16(05), pages 643-666, October.
  18. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
  19. 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.
  20. 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.
  21. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
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