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Reduced rank regression using generalized method of moments estimators

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Author Info
Kleibergen, F. (Tilburg University, Center for Economic Research)

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Abstract

Generalized Method of Moments (GMM) Estimators are derived for Reduced Rank Regression Models, the Error Correction Cointegration Model (ECCM) and the Incomplete Simultaneous Equations Model (INSEM). The GMM (2SLS) estimators of the cointegrating vector in the ECCM are shown to have normal limiting distributions. Tests for the number of unit roots can be constructed straightforwardly and have Dickey-Fuller type limiting distributions. Two extensions of the ECCM, which are important in practice, are analyzed. First, cointegration estimators and tests allowing for structural shifts in the variance (heteroscedasticity) of the series are derived and analyzed using both a Generalized Least Squares Estimator and a White Covariance Matrix Estimator. The resulting cointegrating vectors estimators have again normal limiting distributions while the cointegration tests have identical limiting distributions which differ from the Dickey-Fuller type. Second, cointegrating vector estimators and tests are derived which allow for structural breaks in the cointegrating vector and/or multiplicator. The limiting distributions of the estimators are again shown to be normal and the limiting distributions of the cointegration tests differ from the Dickey-Fuller type.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 20.

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Date of creation: 1996
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Handle: RePEc:dgr:kubcen:199620

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Keywords: regression;

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
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  2. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Kleibergen, F. & Franses, P.H., 1995. "Direct Cointegration Testing in Periodic Vector Autoregressive Models," Papers 9518/a, Erasmus University of Rotterdam - Econometric Institute.
  6. Kleibergen, F.R. & Van Dijk, H.K., 1993. "On the Shape of the Likelyhood/Posterior in Cointegration Models," Papers 9315-a, Erasmus University of Rotterdam - Econometric Institute.
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  7. 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. [Downloadable!] (restricted)
  8. Peter C.B. Phillips, 1992. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Cowles Foundation Discussion Papers 1039, Cowles Foundation, Yale University. [Downloadable!]
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  9. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May. [Downloadable!] (restricted)
  10. Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516 Elsevier. [Downloadable!] (restricted)
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  11. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March. [Downloadable!] (restricted)
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  12. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March. [Downloadable!] (restricted)
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  13. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  14. Kleibergen, Frank & van Dijk, Herman K., 1994. "Direct cointegration testing in error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 61-103, July. [Downloadable!] (restricted)
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  1. J.J.J. Groen & F. Kleibergen, 2001. "Likelihood-Based Cointegration Analysis in Panels of Vector Error Correction Models," WO Research Memoranda (discontinued) 646, Netherlands Central Bank, Research Department. [Downloadable!]
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  2. Kleibergen, Frank & Paap, Richard, 1996. "Priors, posterior odds and Lagrange multiplier statistics in Bayesian analyses of cointegration," Econometric Institute Report 37, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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