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Econometrics 2017, 5(4), 46; https://doi.org/10.3390/econometrics5040046

Non-Causality Due to Included Variables

Department of Information Engineering, Computer Science and Mathematics University of L’Aquila, 67100 Coppito, Italy
Academic Editor: Marc S. Paolella
Received: 25 May 2017 / Revised: 5 October 2017 / Accepted: 5 October 2017 / Published: 15 October 2017
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Abstract

The contribution of this paper is to investigate a particular form of lack of invariance of causality statements to changes in the conditioning information sets. Consider a discrete-time three-dimensional stochastic process z = ( x , y 1 , y 2 ) . We want to study causality relationships between the variables in y = ( y 1 , y 2 ) and x. Suppose that in a bivariate framework, we find that y 1 Granger causes x and y 2 Granger causes x, but these relationships vanish when the analysis is conducted in a trivariate framework. Thus, the causal links, established in a bivariate setting, seem to be spurious. Is this conclusion always correct? In this note, we show that the causal links, in the bivariate framework, might well not be ‘genuinely’ spurious: they could be reflecting causality from the vector y to x. Paradoxically, in this case, it is the non-causality in trivariate system that is misleading. View Full-Text
Keywords: Granger causality; Hilbert spaces; time series Granger causality; Hilbert spaces; time series
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Triacca, U. Non-Causality Due to Included Variables. Econometrics 2017, 5, 46.

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