Granger Causality and Dynamic Structural Systems

Using a generally applicable dynamic structural system of equations, we give natural definitions of direct and total structural causality applicable to both structural vector autoregressions (VARs) and recursive structures representing time-series natural experiments. These concepts enable us to forge a previously missing link between Granger (G-)causality and structural causality by showing that, given a corresponding conditional form of exogeneity, G-causality holds if and only if a corresponding form of structural causality holds. We introduce a variety of structurally informative extensions of G-causality and provide their structural characterizations. Of importance for applications is the structural characterization of finite-order G-causality, which forms the basis for most empirical work. We show that conditional exogeneity is necessary for valid structural inference and prove that, in the absence of structural causality, conditional exogeneity is equivalent to G noncausality. These characterizations hold for both structural VARs and natural experiments. We propose practical new G-causality and conditional exogeneity tests and describe their use in testing for structural causality. We illustrate with studies of oil and gasoline prices, monetary policy and industrial production, and stock returns and macroeconomic announcements.