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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. Bernanke, Ben S. & Mihov, Ilian, 1995. "Measuring Monetary Policy," Economics Series 10, Institute for Advanced Studies.
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  4. Francis X. Diebold & Lutz Kilian, 1998. "Measuring Predictability: Theory and Macroeconomic Applications," Working Papers 98-16, New York University, Leonard N. Stern School of Business, Department of Economics.
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  8. Boudjellaba, H. & Dufour, J.M. & Roy, R., 1992. "Simplified Conditions for Non-Causality Between Vectors in Multivariate Arma Models," Cahiers de recherche 9236, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  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. 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.
  11. Bernanke, Ben S & Blinder, Alan S, 1992. "The Federal Funds Rate and the Channels of Monetary Transmission," American Economic Review, American Economic Association, vol. 82(4), pages 901-21, September.
  12. 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.
  13. Jean-Marie Dufour & Eric Renault, 1998. "Short Run and Long Run Causality in Time Series: Theory," Econometrica, Econometric Society, vol. 66(5), pages 1099-1126, September.
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  17. DUFOUR, Jean-Marie & PELLETIER, Denis & RENAULT, Éric, 2003. "Short run and long run causality in time series: Inference," Cahiers de recherche 2003-16, Universite de Montreal, Departement de sciences economiques.
  18. Peter N. Ireland, 2005. "The Monetary Transmission Mechanism," Boston College Working Papers in Economics 628, Boston College Department of Economics.
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  25. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
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