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Short and long run causality measures: theory and inference

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  • Jean-Marie Dufour

    ()

  • Abderrahim Taamouti

    ()

Abstract

The concept of causality introduced by Wiener (1956) and Granger (1969) is defined in terms of predictability one period ahead. This concept can be generalized by considering causality at a given horizon h, and causality up to any given horizon h [Dufour and Renault (1998)]. This generalization is motivated by the fact that, in the presence of an auxiliary variable vector Z, it is possible that a variable Y does not cause variable X at horizon 1, but causes it at horizon h > 1. In this case, there is an indirect causality transmitted by Z. Another related problem consists in measuring the importance of causality between two variables. Existing causality measures have been defined only for the horizon 1 and fail to capture indirect causal effects. This paper proposes a generalization of such measures for any horizon h. We propose nonparametric and parametric measures of unidirectional and instantaneous causality at any horizon h. Parametric measures are defined in the context of autoregressive processes of unknown order and expressed in terms of impulse response coefficients. On noting that causality measures typically involve complex functions of model parameters in VAR and VARMA models, we propose a simple method to evaluate these measures which is based on the simulation of a large sample from the process of interest. We also describe asymptotically valid nonparametric confidence intervals, using a bootstrap technique. Finally, the proposed measures are applied to study causality relations at different horizons between macroeconomic, monetary and financial variables in the U.S. These results show that there is a strong effect of nonborrowed reserves on federal funds rate one month ahead, the effect of real gross domestic product on federal funds rate is economically important for the first three months, the effect of federal funds rate on gross domestic product deflator is economically weak one month ahead, and finally federal fundsrate causes the real gross domestic product until 16 months.

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Bibliographic Info

Paper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we083720.

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Date of creation: Jul 2008
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Handle: RePEc:cte:werepe:we083720

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Keywords: Time series; Granger causality; Indirect causality; Multiple horizon causality; Causality measure; Predictability; Autoregressive model; Vector autoregression; VAR; Bootstrap; Monte Carlo; Macroeconomics; Money; Interest rates; Output; Inflation;

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References

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  1. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
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  3. Peter N. Ireland, 2005. "The monetary transmission mechanism," Working Papers 06-1, Federal Reserve Bank of Boston.
  4. Jean-Marie Dufour & Denis Pelletier & Éric Renault, 2003. "Short Run and Long Run Causality in Time Series: Inference," CIRANO Working Papers 2003s-61, CIRANO.
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Citations

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Cited by:
  1. Diebold, Francis X. & Yılmaz, Kamil, 2014. "On the network topology of variance decompositions: Measuring the connectedness of financial firms," Journal of Econometrics, Elsevier, vol. 182(1), pages 119-134.
  2. Javier Ruiz-Castillo, 2012. "From the “European Paradox” to a European Drama in citation impact," Economics Working Papers we1211, Universidad Carlos III, Departamento de Economía.
  3. Taamouti, Abderrahim & Bouezmarni, Taoufik & El Ghouch, Anouar, 2014. "Nonparametric estimation and inference for conditional density based Granger causality measures," Journal of Econometrics, Elsevier, vol. 180(2), pages 251-264.
  4. Majid Al-Sadoon, 2013. "Geometric and Long Run Aspects of Granger Causality," Working Papers 682, Barcelona Graduate School of Economics.
  5. repec:cte:werepe:we1212 is not listed on IDEAS
  6. Abderrahim Taamouti & Taoufik Bouezmarni & Anouar El Ghouch, 2012. "Nonparametric estimation and inference for Granger causality measures," Economics Working Papers we1217, Universidad Carlos III, Departamento de Economía.
  7. Hui Jun ZHANG & Jean-Marie DUFOUR & John W. GALBRAITH, 2013. "Exchange Rates and Commodity Prices : Measuring Causality at Multiple Horizons," Cahiers de recherche 14-2013, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Francis X. Diebold & Kamil Yilmaz, 2013. "Measuring the Dynamics of Global Business Cycle Connectedness," PIER Working Paper Archive 13-070, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  9. Ren, Yunwen & Xiao, Zhiguo & Zhang, Xinsheng, 2013. "Two-step adaptive model selection for vector autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 349-364.
  10. Matilla-García, Mariano & Marín, Manuel Ruiz & Dore, Mohammed I., 2014. "A permutation entropy based test for causality: The volume–stock price relation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 280-288.

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