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

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Listed:
  • 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 chi-squared 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. Copyright 2003 Blackwell Publishing Ltd.

Suggested Citation

  • 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
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    References listed on IDEAS

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    1. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-1393, November.
    2. J.-F. Richard, 1980. "Models with Several Regimes and Changes in Exogeneity," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 1-20.
    3. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    4. Ericsson, Neil R & Hendry, David F & Mizon, Grayham E, 1998. "Exogeneity, Cointegration, and Economic Policy Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 370-387, October.
    5. Urbain, Jean-Pierre, 1992. "On Weak Exogeneity in Error Correction Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(2), pages 187-207, May.
    6. Yannick L'horty & Christophe Rault, 2003. "Why Is French Equilibrium Unemployment So High?," Journal of Applied Economics, Universidad del CEMA, vol. 6, pages 127-156, May.
    7. Mosconi, Rocco & Giannini, Carlo, 1992. "Non-causality in Cointegrated Systems: Representation Estimation and Testing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 54(3), pages 399-417, August.
    8. Ericsson, Neil R., 1995. "Conditional and structural error correction models," Journal of Econometrics, Elsevier, vol. 69(1), pages 159-171, September.
    9. Urbain, Jean-Pierre, 1995. "Partial versus full system modelling of cointegrated systems an empirical illustration," Journal of Econometrics, Elsevier, vol. 69(1), pages 177-210, September.
    10. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    11. Rault, Christophe, 2000. "Non-causality in VAR-ECM models with purely exogenous long-run paths," Economics Letters, Elsevier, vol. 66(1), pages 7-15, January.
    12. Davidson, James E H, et al, 1978. "Econometric Modelling of the Aggregate Time-Series Relationship between Consumers' Expenditure and Income in the United Kingdom," Economic Journal, Royal Economic Society, vol. 88(352), pages 661-692, December.
    13. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    14. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 211-244.
    15. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    16. Psaradakis, Zacharias, 1994. "A comparison of tests of linear hypotheses in cointegrated vector autoregressive models," Economics Letters, Elsevier, vol. 45(2), pages 137-144, June.
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    Cited by:

    1. repec:sbe:breart:v:25:y:2005:i:2:a:2503 is not listed on IDEAS
    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. 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.
    5. Christophe Rault, 2007. "Une synthèse de l'exogénéité dans les modèles vectoriels à correction d'erreurs," Post-Print halshs-00202651, HAL.

    More about this item

    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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