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.
Highlights
Following a suggestion of Wiener (1956), Granger (1969) introduced a concept of causality in a time series framework
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 a bivariate framework, might not be ‘genuinely’ spurious: they could be reflecting causality from the vector y to x
In this case, it is the non-causality in the trivariate system that is misleading
Summary
Following a suggestion of Wiener (1956), Granger (1969) introduced a concept of causality in a time series framework. If a process y contains information in the past terms that helps in the prediction of the process x, and if this information is contained in no other process used in the predictor, y is said to cause x This notion of Granger causality is used here. The causal links, established in a bivariate setting, seem to be spurious We show that the causal links, in a bivariate framework, might not be ‘genuinely’ spurious: they could be reflecting causality from the vector y to x. In this case, it is the non-causality in the trivariate system that is misleading.
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