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Optimal Inference in Cointegrated Systems

This paper studies the properties of maximum likelihood estimates of co-integrated systems. Alternative formulations of such models are considered including a new triangular system error correction mechanism. It is shown that full system maximum likelihood brings the problem of inference within the family that is covered by the locally asymptotically mixed normal asymptotic theory provided that all unit roots in the system have been eliminated by specification and data transformation. This result has far reaching consequences. It means that cointegrating coefficient estimates are symmetrically distributed and median unbiased asymptotically, that an optimal asymptotic theory of inference applies and that hypothesis tests may be conducted using standard asymptotic chi-squared sets.

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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 866R.

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Length: 28 pages
Date of creation: 1988
Date of revision: Aug 1989
Publication status: Published in Econometrica (March 1991), 59(2): 283-306
Handle: RePEc:cwl:cwldpp:866r
Note: CFP 777.
Contact details of provider: Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Phillips, P.C.B., 1988. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals Via Martingale Approximations," Econometric Theory, Cambridge University Press, vol. 4(03), pages 528-533, December.
  2. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
  3. Hendry, David F, 1986. "Econometric Modelling with Cointegrated Variables: An Overview," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 201-12, August.
  4. Lutkepohl, Helmut, 1984. "Linear transformations of vector ARMA processes," Journal of Econometrics, Elsevier, vol. 26(3), pages 283-293, December.
  5. 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.
  6. Lahiri, Kajal & Schmidt, Peter, 1978. "On the Estimation of Triangular Structural Systems," Econometrica, Econometric Society, vol. 46(5), pages 1217-21, September.
  7. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
  8. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(03), pages 468-497, December.
  9. Engle, Robert F & Hendry, David F & Richard, Jean-Francois, 1979. "Exogeneity," The Warwick Economics Research Paper Series (TWERPS) 162, University of Warwick, Department of Economics.
    • Engle, Robert F & Hendry, David F & Richard, Jean-Francois, 1983. "Exogeneity," Econometrica, Econometric Society, vol. 51(2), pages 277-304, March.
    • ENGLE, Robert F. & HENDRY, David F. & RICHARD, Jean-François, . "Exogeneity," CORE Discussion Papers RP 516, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
  11. Sweeting, Trevor, 1983. "On estimator efficiency in stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 15(1), pages 93-98, June.
  12. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
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