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

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  • Phillips, Peter C B

Abstract

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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Bibliographic Info

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. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  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. Phillips, P. C. B., 1989. "Spherical matrix distributions and cauchy quotients," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 51-53, May.
  4. 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.
  5. 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.
  6. Phillips, P C B, 1986. "The Exact Distribution of the Wald Statistic," Econometrica, Econometric Society, vol. 54(4), pages 881-95, July.
  7. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  8. Gregory, Allan W, 1994. "Testing for Cointegration in Linear Quadratic Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 347-60, July.
  9. Phillips, P C B, 1986. "The Distribution of FIML in the Leading Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 239-43, February.
  10. Phillips, Peter C B, 1985. "The Exact Distribution of LIML: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 21-36, February.
  11. Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
  12. 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.
  13. repec:cup:etheor:v:7:y:1991:i:1:p:1-21 is not listed on IDEAS
  14. 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.
  15. Phillips, P C B, 1988. "Reflections on Econometric Methodology," The Economic Record, The Economic Society of Australia, vol. 64(187), pages 344-59, December.
  16. Bowden,Roger J. & Turkington,Darrell A., 1990. "Instrumental Variables," Cambridge Books, Cambridge University Press, number 9780521385824.
  17. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January.
  18. 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).
  19. 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.
  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. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
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