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Optimal Inference in Cointegrated Systems

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  • Phillips, P C B

Abstract

Properties of maximum likelihood estimates of cointegrated systems are studied. Alternative formulations are considered, including a new triangular system error correction mechanism. We demonstrate that full system maximum likelihood brings the problem of inference within the family covered by the locally asymptotically mixed normal asymptotic theory, provided all unit roots have been eliminated by specification and data transformation. Methodological issues provide a major focus of the paper. Our results favor use of full system estimation in error correction mechanisms or subsystem methods that are asymptotically equivalent. They also point to disadvantages in the use of unrestricted VAR's formulated in levels and of certain single equation approaches to estimation of error correction mechanisms. Copyright 1991 by The Econometric Society.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 59 (1991)
Issue (Month): 2 (March)
Pages: 283-306

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Handle: RePEc:ecm:emetrp:v:59:y:1991:i:2:p:283-306

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  1. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
  2. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
  3. Lahiri, Kajal & Schmidt, Peter, 1978. "On the Estimation of Triangular Structural Systems," Econometrica, Econometric Society, vol. 46(5), pages 1217-21, September.
  4. 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.
  5. Lutkepohl, Helmut, 1984. "Linear transformations of vector ARMA processes," Journal of Econometrics, Elsevier, vol. 26(3), pages 283-293, December.
  6. 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.
  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. Sweeting, Trevor, 1983. "On estimator efficiency in stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 15(1), pages 93-98, June.
  9. 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.
  10. Engle, Robert F & Hendry, David F & Richard, Jean-Francois, 1983. "Exogeneity," Econometrica, Econometric Society, vol. 51(2), pages 277-304, March.
  11. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
  12. 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.
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