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Estimation of Cointegration Vectors with Linear Restrictions

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  • Saikkonen, Pentti

Abstract

A general approach for the estimation of cointegration vectors with linear restrictions is described. In the special case of zero restrictions, the cointegration relations of the paper are formally similar to the structural form of a traditional simultaneous equation model. The proposed estimation procedures require a conventional rank condition of identification but no exogeneity assumption. In place of exogenous variables there are series that are not cointegrated and can therefore describe the common trends in the system. The estimators of the paper are flexible and simple to use. They can be combined with several recent estimators developed for cointegration regressions which in the present context are formally similar to the reduced form of a simultaneous equation model. After the coefficient matrix of a cointegration regression has been estimated, the estimators of the paper can be obtained by simple generalized least squares. Both single equation estimators and more efficient system estimators are developed. The asymptotic distributions of the estimators are shown to be mixed normal so that Wald tests with asymptotic chi-square distributions under the null hypothesis can be obtained in the usual way. Convenient test procedures for checking the validity of overidentification restrictions are also provided.

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  • Saikkonen, Pentti, 1993. "Estimation of Cointegration Vectors with Linear Restrictions," Econometric Theory, Cambridge University Press, vol. 9(1), pages 19-35, January.
    • Handle: RePEc:cup:etheor:v:9:y:1993:i:01:p:19-35_00
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    1. Vicente Esteve & Cecilio Tamarit, 2018. "Public debt and economic growth in Spain, 1851–2013," Cliometrica, Springer;Cliometric Society (Association Francaise de Cliométrie), vol. 12(2), pages 219-249, May.
    2. Bauer, Dietmar & Wagner, Martin, 2005. "Autoregressive Approximations of Multiple Frequency I(1) Processes," Economics Series 174, Institute for Advanced Studies.
    3. Mosconi, Rocco & Paruolo, Paolo, 2017. "Identification conditions in simultaneous systems of cointegrating equations with integrated variables of higher order," Journal of Econometrics, Elsevier, vol. 198(2), pages 271-276.
    4. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.
    5. Ulph, A. & Valentini, L., 1998. "Is environmental dumping greater when firms are footloose?," Discussion Paper Series In Economics And Econometrics 9819, Economics Division, School of Social Sciences, University of Southampton.
    6. M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 49-87.
    7. Mukerji, S., 1995. "A theory of play for games in strategic form when rationality is not common knowledge," Discussion Paper Series In Economics And Econometrics 9519, Economics Division, School of Social Sciences, University of Southampton.
    8. Cook, S., 1996. "Econometric methodology II: the role of the philosophy of science," Discussion Paper Series In Economics And Econometrics 9619, Economics Division, School of Social Sciences, University of Southampton.
    9. Pesaran, M. Hashem & Shin, Yongcheol, 1996. "Cointegration and speed of convergence to equilibrium," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 117-143.
    10. Rayner, J., 1992. "Identification of structural VARs," Discussion Paper Series In Economics And Econometrics 9219, Economics Division, School of Social Sciences, University of Southampton.
    11. Nelson C. Mark & Masao Ogaki & Donggyu Sul, 2005. "Dynamic Seemingly Unrelated Cointegrating Regressions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 797-820.
    12. Hall, Stephen & Mizon, Grayham E. & Welfe, Aleksander, 2000. "Modelling economies in transition: an introduction," Economic Modelling, Elsevier, vol. 17(3), pages 339-357, August.
    13. In Choi, 2012. "Panel Cointegration," Working Papers 1208, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    14. Allison Zhou & Carl Bonham & Byron Gangnes, 2007. "Modeling the supply and demand for tourism: a fully identified VECM approach," Working Papers 200717, University of Hawaii at Manoa, Department of Economics.
    15. MacLeod, W.B. & Malcomson, J.M., 1993. "Motivation, markets and dual economies," Discussion Paper Series In Economics And Econometrics 9319, Economics Division, School of Social Sciences, University of Southampton.
    16. Gomez-Biscarri, Javier & Hualde, Javier, 2015. "Regression-based analysis of cointegration systems," Journal of Econometrics, Elsevier, vol. 186(1), pages 32-50.
    17. Boswijk, H. Peter, 1995. "Efficient inference on cointegration parameters in structural error correction models," Journal of Econometrics, Elsevier, vol. 69(1), pages 133-158, September.
    18. Mourmouras, I.A. & Ghosh, S., 1997. "Fiscal policies and the terms of trade in an endogenous growth model with overlapping generations," Discussion Paper Series In Economics And Econometrics 9719, Economics Division, School of Social Sciences, University of Southampton.
    19. Bonham, Carl & Gangnes, Byron & Zhou, Ting, 2009. "Modeling tourism: A fully identified VECM approach," International Journal of Forecasting, Elsevier, vol. 25(3), pages 531-549, July.
    20. Mosconi, Rocco & Paruolo, Paolo, 2014. "Rank and order conditions for identification in simultaneous system of cointegrating equations with integrated variables of order two," MPRA Paper 53589, University Library of Munich, Germany.
    21. Qizilbash, M., 1994. "Corruption, temptation and guilt: moral character in economic theory," Discussion Paper Series In Economics And Econometrics 9419, Economics Division, School of Social Sciences, University of Southampton.

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