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Short and long run causality measures: theory and inference

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  • Taamouti, Abderrahim
  • Dufour, Jean-Marie

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.

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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    More about this item

    Keywords

    Time series;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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