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Short and long run causality measures: theory and inference


  • Taamouti, Abderrahim
  • Dufour, Jean-Marie


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.

Suggested Citation

  • Taamouti, Abderrahim & Dufour, Jean-Marie, 2008. "Short and long run causality measures: theory and inference," UC3M Working papers. Economics we083720, Universidad Carlos III de Madrid. Departamento de Economía.
  • Handle: RePEc:cte:werepe:we083720

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    References listed on IDEAS

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    Cited by:

    1. Majid M. Al-Sadoon, 2015. "Testing subspace Granger causality," Economics Working Papers 1495, Department of Economics and Business, Universitat Pompeu Fabra.
    2. 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.
    3. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2017. "A Justification of Conditional Confidence Intervals," Papers 1710.00643,
    4. Diebold, Francis X. & Yilmaz, Kamil, 2015. "Financial and Macroeconomic Connectedness: A Network Approach to Measurement and Monitoring," OUP Catalogue, Oxford University Press, number 9780199338306.
    5. 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.
    6. Al-Sadoon, Majid M., 2014. "Geometric and long run aspects of Granger causality," Journal of Econometrics, Elsevier, vol. 178(P3), pages 558-568.
    7. Zhang, Hui Jun & Dufour, Jean-Marie & Galbraith, John W., 2016. "Exchange rates and commodity prices: Measuring causality at multiple horizons," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 100-120.
    8. repec:cte:werepe:we1212 is not listed on IDEAS
    9. Taoufik Bouezmarni & Abderrahim Taamouti, 2014. "Nonparametric tests for conditional independence using conditional distributions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 697-719, December.
    10. 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.
    11. MAO TAKONGMO, Charles Olivier, 2016. "Government spending, GDP and exchange rate in Zero Lower Bound: measuring causality at multiple horizons," MPRA Paper 79703, University Library of Munich, Germany, revised 02 Jun 2017.
    12. Mariusz Maziarz, 2015. "A review of the Granger-causality fallacy," The Journal of Philosophical Economics, Bucharest Academy of Economic Studies, The Journal of Philosophical Economics, vol. 8(2), May.
    13. Taamouti, Abderrahim & Bouezmarni, Taoufik & El Ghouch, Anouar, 2012. "Nonparametric estimation and inference for Granger causality measures," UC3M Working papers. Economics 14150, Universidad Carlos III de Madrid. Departamento de Economía.
    14. repec:eee:finlet:v:24:y:2018:i:c:p:247-255 is not listed on IDEAS
    15. Hsiu-Hsin Ko, 2015. "On the indirect causality relation from exchange rates to fundamentals," Economics Bulletin, AccessEcon, vol. 35(3), pages 1518-1524.
    16. 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.
    17. Gilbert COLLETAZ & Grégory LEVIEUGE & Alexandra POPESCU, 2016. "Monetary Policy and Long-Run Risk-Taking," LEO Working Papers / DR LEO 2409, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    18. Etesami, Jalal & Habibnia, Ali & Kiyavash, Negar, 2017. "Econometric modeling of systemic risk: going beyond pairwise comparison and allowing for nonlinearity," LSE Research Online Documents on Economics 70769, London School of Economics and Political Science, LSE Library.
    19. Ruiz-Castillo, Javier, 2012. "From the “European Paradox” to a European Drama in citation impact," UC3M Working papers. Economics we1211, Universidad Carlos III de Madrid. Departamento de Economía.
    20. Chang, Tsangyao & Chen, Wen-Yi & Gupta, Rangan & Nguyen, Duc Khuong, 2015. "Are stock prices related to the political uncertainty index in OECD countries? Evidence from the bootstrap panel causality test," Economic Systems, Elsevier, vol. 39(2), pages 288-300.
    21. Ioana Viașu, 2015. "The long-term causality. A comparative study for some EU countries," Computational Methods in Social Sciences (CMSS), "Nicolae Titulescu" University of Bucharest, Faculty of Economic Sciences, vol. 3(2), pages 28-35, December.
    22. repec:eee:dyncon:v:86:y:2018:i:c:p:165-184 is not listed on IDEAS
    23. 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.
    24. Patrick De lamirande & Jason Stevens, 2016. "Predicting events with an unidentified time horizon," Economics Bulletin, AccessEcon, vol. 36(2), pages 729-735.

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    JEL classification:

    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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