Causality and separability

Following Wold (1954), a causal relationship from a vector y of economic variables towards a vector x should be interpreted through a fictive controlled experiment. At least one factor y(i) component of y should have an impact on x when other factors y(j  ), j≠ij≠i, are kept constant. It is arguably a logical weakness of the causality concept when this interpretation breaks down, due to common factors between the components of y. We provide a general separability condition between causal factors to restore their causal interpretation. This general approach can be applied to most of the commonly used causality concepts in modern econometrics.