Econometrica: May, 1982, Volume 50, Issue 3

The General Equivalence of Granger and Sims Causality

https://doi.org/0012-9682(198205)50:3<569:TGEOGA>2.0.CO;2-H
p. 569-582

Gary Chamberlain

Linear predictor definitions of causality are not adequate for discrete data. The paper extends the Granger and Sims definitions by using conditional independence instead of linear predictors. The extended definition of "y does not cause x" is that x is independent of past y conditional on past x. This is stronger than the strict exogeneity condition that y be independent of future x conditional on current and past x. Under a weak regularity condition, however, if y is independent of future x conditional on current and past x and past y, then y does not cause x.