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Short and long run causality measures: Theory and inference

  • Dufour, Jean-Marie
  • Taamouti, Abderrahim

The concept of causality introduced by Wiener [Wiener, N., 1956. The theory of prediction, In: E.F. Beckenback, ed., The Theory of Prediction, McGraw-Hill, New York (Chapter 8)] and Granger [Granger, C. W.J., 1969. Investigating causal relations by econometric models and cross-spectral methods, Econometrica 37, 424-459] is defined in terms of predictability one period ahead. This concept can be generalized by considering causality at any given horizon h as well as tests for the corresponding non-causality [Dufour, J.-M., Renault, E., 1998. Short-run and long-run causality in time series: Theory. Econometrica 66, 1099-1125; Dufour, J.-M., Pelletier, D., Renault, É., 2006. Short run and long run causality in time series: Inference, Journal of Econometrics 132 (2), 337-362]. Instead of tests for non-causality at a given horizon, we study the problem of measuring causality between two vector processes. Existing causality measures have been defined only for the horizon 1, and they fail to capture indirect causality. We propose generalizations to any horizon h of the measures introduced by Geweke [Geweke, J., 1982. Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association 77, 304-313]. Nonparametric and parametric measures of unidirectional causality and instantaneous effects are considered. On noting that the causality measures typically involve complex functions of model parameters in VAR and VARMA models, we propose a simple simulation-based method to evaluate these measures for any VARMA model. We also describe asymptotically valid nonparametric confidence intervals, based on a bootstrap technique. Finally, the proposed measures are applied to study causality relations at different horizons between macroeconomic, monetary and financial variables in the US.

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Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 154 (2010)
Issue (Month): 1 (January)
Pages: 42-58

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Handle: RePEc:eee:econom:v:154:y:2010:i:1:p:42-58
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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  1. Ben Bernanke, 1990. "The Federal Funds Rate and the Channels of Monetary Transnission," NBER Working Papers 3487, National Bureau of Economic Research, Inc.
  2. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Smooth Functions of Slope Parameters and Innovation Variances in VAR (∞) Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 309-332, May.
  3. Francis X. Diebold & Lutz Kilian, . "Measuring Predictability: Theory and Macroeconomic Applications," CARESS Working Papres 97-19, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  4. Deirdre N. McCloskey & Stephen T. Ziliak, 1996. "The Standard Error of Regressions," Journal of Economic Literature, American Economic Association, vol. 34(1), pages 97-114, March.
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  6. Peter N. Ireland, 2005. "The monetary transmission mechanism," Working Papers 06-1, Federal Reserve Bank of Boston.
  7. Dufour, J.M. & Renault, E., 1995. "Short-Run and Long-Rub Causality in Time Series: Theory," Cahiers de recherche 9538, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
  9. Boudjellaba, B. & Dufour, J.M. & Roy, R., 1991. "Testing Causality Between Two Vectors in Multivariate Arma Models," Cahiers de recherche 9119, Universite de Montreal, Departement de sciences economiques.
  10. Boudjellaba, H. & Dufour, J.M. & Roy, R., 1992. "Simplified Conditions for Non-Causality Between Vectors in Multivariate Arma Models," Cahiers de recherche 9236, Universite de Montreal, Departement de sciences economiques.
  11. Jeremy Berkowitz & Lutz Kilian, 1996. "Recent developments in bootstrapping time series," Finance and Economics Discussion Series 96-45, Board of Governors of the Federal Reserve System (U.S.).
  12. Hsiao, Cheng, 1982. "Autoregressive modeling and causal ordering of economic variables," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 243-259, November.
  13. Gourieroux,Christian & Monfort,Alain, 1997. "Time Series and Dynamic Models," Cambridge Books, Cambridge University Press, number 9780521411462, September.
  14. DUFOUR, Jean-Marie & PELLETIER, Denis & RENAULT, Éric, 2003. "Short Run and Long Run Causality in Time Series : Inference," Cahiers de recherche 14-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  15. David A. Pierce & Larry D. Haugh, 1977. "Causality in temporal systems: characterizations and a survey," Special Studies Papers 87, Board of Governors of the Federal Reserve System (U.S.).
  16. Geweke, John, 1984. "Inference and causality in economic time series models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 19, pages 1101-1144 Elsevier.
  17. Kapetanios, G. & Pagan, A. & Scott, A., 2007. "Making a match: Combining theory and evidence in policy-oriented macroeconomic modeling," Journal of Econometrics, Elsevier, vol. 136(2), pages 565-594, February.
  18. repec:wop:ubisop:0088 is not listed on IDEAS
  19. K. D. Patterson, 2007. "Bias Reduction through First-order Mean Correction, Bootstrapping and Recursive Mean Adjustment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 23-45.
  20. Ben S. Bernanke & Ilian Mihov, 1995. "Measuring monetary policy," Working Papers in Applied Economic Theory 95-09, Federal Reserve Bank of San Francisco.
  21. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
  22. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
  23. DUFOUR, Jean-Marie & TAREK, Jouini, 2005. "Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form," Cahiers de recherche 2005-09, Universite de Montreal, Departement de sciences economiques.
  24. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  25. Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May.
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