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Johansen’s Reduced Rank Estimator Is GMM

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  • Bruce E. Hansen

    (Department of Economics, University of Wisconsin, Madison, WI 53706, USA)

Abstract

The generalized method of moments (GMM) estimator of the reduced-rank regression model is derived under the assumption of conditional homoscedasticity. It is shown that this GMM estimator is algebraically identical to the maximum likelihood estimator under normality developed by Johansen (1988). This includes the vector error correction model (VECM) of Engle and Granger. It is also shown that GMM tests for reduced rank (cointegration) are algebraically similar to the Gaussian likelihood ratio tests. This shows that normality is not necessary to motivate these estimators and tests.

Suggested Citation

  • Bruce E. Hansen, 2018. "Johansen’s Reduced Rank Estimator Is GMM," Econometrics, MDPI, vol. 6(2), pages 1-9, May.
    • Handle: RePEc:gam:jecnmx:v:6:y:2018:i:2:p:26-:d:147870
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    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Adrian, Tobias & Crump, Richard K. & Moench, Emanuel, 2015. "Regression-based estimation of dynamic asset pricing models," Journal of Financial Economics, Elsevier, vol. 118(2), pages 211-244.
    3. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    4. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    5. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    6. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    7. Goldberger, Arthur S & Olkin, Ingram, 1971. "A Minimum-Distance Interpretation of Limited-Information Estimation," Econometrica, Econometric Society, vol. 39(3), pages 635-639, May.
    8. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
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    Cited by:

    1. Luca Nocciola, 2022. "Finite Sample Forecast Properties and Window Length Under Breaks in Cointegrated Systems," Advances in Econometrics, in: Essays in Honor of M. Hashem Pesaran: Prediction and Macro Modeling, volume 43, pages 167-196, Emerald Group Publishing Limited.
    2. Rocco Mosconi & Paolo Paruolo, 2022. "Celebrated Econometricians: Katarina Juselius and Søren Johansen," Econometrics, MDPI, vol. 10(2), pages 1-4, May.

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    Keywords

    GMM; VECM; reduced rank;
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