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Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models

  • Phillips, Peter C B

The author derives some exact finite sample disbibutions and characterizes the tail behavior of maximum likelihood estimators of the cointegrating coefficients in error correction models. The reduced rank regression estimator has a distribution with Cauchy-like tails and no finite moments of integer order. The maximum likelihood estimator of the coefficients in a particular triangular system representation has matrix t-distribution tails with finite integer moments to order T - n + r, where T is the sample size, n is the total number of variables, and r is the dimension of cointegration space. This helps explain some recent simulation studies where extreme outliers occur more frequently for the reduced rank regression estimator than for alternative asymptotically efficient procedures based on triangular representation. Copyright 1994 by The Econometric Society.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 62 (1994)
Issue (Month): 1 (January)
Pages: 73-93

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Handle: RePEc:ecm:emetrp:v:62:y:1994:i:1:p:73-93
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  1. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  2. 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.
  3. Park, J.Y. & Ogaki, M., 1991. "Inference in Cointegrated Models Using VAR Prewhitening to Estimate Shortrun Dynamics," RCER Working Papers 281, University of Rochester - Center for Economic Research (RCER).
  4. Peter C.B. Phillips, 1988. "Reflections on Econometric Methodology," Cowles Foundation Discussion Papers 893, Cowles Foundation for Research in Economics, Yale University.
  5. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  6. Allan W. Gregory, 1991. "Testing for Cointegration in Linear Quadratic Models," Working Papers 811, Queen's University, Department of Economics.
  7. Phillips, P. C. B., 1989. "Spherical matrix distributions and cauchy quotients," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 51-53, May.
  8. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
  9. 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.
  10. Hiro Y. Toda & Peter C.B. Phillips, 1991. "Vector Autoregression and Causality: A Theoretical Overview and Simulation Study," Cowles Foundation Discussion Papers 1001, Cowles Foundation for Research in Economics, Yale University.
  11. repec:oup:restud:v:58:y:1991:i:3:p:407-36 is not listed on IDEAS
  12. Peter C.B. Phillips, 1984. "The Exact Distribution of the Wald Statistic," Cowles Foundation Discussion Papers 722, Cowles Foundation for Research in Economics, Yale University.
  13. 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.
  14. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  15. Peter C.B. Phillips, 1983. "The Exact Distribution of LIML: II," Cowles Foundation Discussion Papers 663, Cowles Foundation for Research in Economics, Yale University.
  16. Peter C.B. Phillips, 1985. "The Distribution of FIML in the Leading Case," Cowles Foundation Discussion Papers 739, Cowles Foundation for Research in Economics, Yale University.
  17. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
  18. Peter C.B. Phillips, 1985. "Fractional Matrix Calculus and the Distribution of Multivariate Tests," Cowles Foundation Discussion Papers 767, Cowles Foundation for Research in Economics, Yale University.
  19. repec:cup:etheor:v:7:y:1991:i:1:p:1-21 is not listed on IDEAS
  20. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  21. Constantine, A. G. & Muirhead, R. J., 1976. "Asymptotic expansions for distributions of latent roots in multivariate analysis," Journal of Multivariate Analysis, Elsevier, vol. 6(3), pages 369-391, September.
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