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Exogeneity in Vector Error Correction Models with Purely Exogenous Long‐Run Paths

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  • Jacqueline Pradel
  • Christophe Rault

Abstract

Existing exogeneity conditions of literature are only sufficient and imply ‘overly strong’ constraints on long‐run parameters. This paper presents some new results on exogeneity in vector error correction models. A key concept of the analysis is the ‘purely exogenous long‐run path’, i.e. a cointegrating vector only including ‘exogenous’ variables. Extending earlier results of Johansen, S. (1992). ‘Cointegration in partial systems and the efficiency of single‐equation analysis’, Journal of Econometrics, Vol. 52, pp. 389–402 and of Toda and Phillips (1991). Vector Autoregressions and Causality, Cowles Foundation Discussion Paper, No. 977 among others, we propose a framework based on two canonical representations of the long‐run matrix, which can constitute a suitable basis to formulate a necessary and sufficient condition for non‐causality as well as a condition for strong exogeneity. An interesting property is that the statistics involved in the sequential procedures for testing these conditions are distributed as χ2 variables and can, therefore, easily be calculated with the usual statistical computer packages, which makes our approach fully operational, empirically. Finally, the power and size distortions of the sequential test procedures are analysed using Monte Carlo experiments.

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  • Jacqueline Pradel & Christophe Rault, 2003. "Exogeneity in Vector Error Correction Models with Purely Exogenous Long‐Run Paths," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(5), pages 629-653, December.
    • Handle: RePEc:bla:obuest:v:65:y:2003:i:5:p:629-653
    DOI: 10.1111/j.1468-0084.2003.00065.x
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    1. Rault, Christophe, 2005. "Further Results on Weak Exogeneity in Vector Error Correction Models," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 25(2), November.
    2. Imed Drine & Christophe Rault, 2007. "Fluctuations de Change et Performances Economiques," Brussels Economic Review, ULB -- Universite Libre de Bruxelles, vol. 50(4), pages 427-444.
    3. Christophe Rault, 2011. "Long-run strong-exogeneity," Economics Bulletin, AccessEcon, vol. 31(1), pages 1-8.
    4. Parent, Antoine & Rault, Christophe, 2004. "The Influences Affecting French Assets Abroad Prior to 1914," The Journal of Economic History, Cambridge University Press, vol. 64(2), pages 328-362, June.
    5. Yannick L’Horty & Christophe Rault, 2005. "The Impact of Growth, Labour Cost and Working Time on Employment: Lessons from the French Experience," LABOUR, CEIS, vol. 19(3), pages 595-620, September.
    6. Christophe Rault, 2007. "Une synthèse de l'exogénéité dans les modèles vectoriels à correction d'erreurs," Post-Print halshs-00202651, HAL.
    7. Poomthan Rangkakulnuwat & Sung Ahn & Holly Wang & Susan He, 2010. "Extended generalized purchasing power parity and optimum currency area in East Asian countries," Applied Economics, Taylor & Francis Journals, vol. 42(4), pages 497-513.

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    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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