Granger causality and dynamic
structural systems
Halbert
White and Xun Lu, Department of Economics,
University of California San Diego
Using a generally applicable dynamic structural system of equations, we
give
natural definitions of direct and total structural causality applicable
to
both structural 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. Of
importance for applications is the structural characterization of
finite-order G-causality, which forms the basisfor 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 non-causality. We provide practical new
G-causality and conditional exogeneity tests and describe their use in
testing for structural causality.
[
NIPS 2009 Causality and Time Series
Mini-Symposium]