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A Simple MLE of Cointegrating Vectors in Higher Order Integrated Systems

  • James H. Stock
  • Mark W. Watson

An MLE of the unknown parameters of co integrating vectors is presented for systems in which some variables exhibit higher orders of integration, in which there might be deterministic components, and in which the co integrating vector itself might involve variables of differing orders of integration. The estimator is simple to compute: it can be calculated by running GLS for standard regression equations with serially correlated errors. Alternatively, an asymptotically equivalent estimator can be computed using OLS. Usual Wald test statistics based on these MLE's (constructed using an autocorrelation robust covariance matrix in the case of the OLS estimator) have asymptotic x2 distributions.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0083.

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Date of creation: Dec 1989
Date of revision:
Publication status: published as Econometrica, vol 61, no 4, (July 1993), p. 783-820
Handle: RePEc:nbr:nberte:0083
Note: EFG ME
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  1. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
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  6. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Estimation and Inference in Models of Cointegration: A Simulation Study," Cowles Foundation Discussion Papers 881, Cowles Foundation for Research in Economics, Yale University.
  7. Hoffman, Dennis L & Rasche, Robert H, 1991. "Long-Run Income and Interest Elasticities of Money Demand in the United States," The Review of Economics and Statistics, MIT Press, vol. 73(4), pages 665-74, November.
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  9. Banerjee, Anindya, et al, 1986. "Exploring Equilibrium Relationships in Econometrics through Static Models: Some Monte Carlo Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 253-77, August.
  10. 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.
  11. Campbell, John Y, 1987. "Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis," Econometrica, Econometric Society, vol. 55(6), pages 1249-73, November.
  12. 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.
  13. West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
  14. Peter C.B. Phillips & Bruce E. Hansen, 1988. "Statistical Inference in Instrumental Variables," Cowles Foundation Discussion Papers 869R, Cowles Foundation for Research in Economics, Yale University, revised Apr 1989.
  15. Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1987. "Stochastic Trends and Economic Fluctuations," NBER Working Papers 2229, National Bureau of Economic Research, Inc.
  16. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  17. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
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  19. 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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