# Short and long run causality measures: Theory and inference

*Jean-Marie Dufour* () and
*Abderrahim Taamouti* ()

*Journal of Econometrics*, 2010, vol. 154, issue 1, 42-58

**Abstract:**
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 theÂ US.

**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 (search for similar items in EconPapers)

**Date:** 2010

**References:** View references in EconPapers View complete reference list from CitEc

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Working Paper: Short and long run causality measures: theory and inference (2008)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:econom:v:154:y:2010:i:1:p:42-58

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