Testing for Granger's Full Causality

Abstract-A procedure is proposed to test for the existence
of a fully causal relationship between two variables. The
method involves contrasting the probabilistic forecasting performance
of a univariate and bivariate specification for the
same variable Y. If there exists some theory or belief that X
causes Y, and the addition of a variable X to the information
set of a prequential forecasting system for a variable Y reduces
miscalibration and/or the level of forecast uncertainty
with respect to Y's distribution for the next period, then a
fully causal effect running from X to Y may be inferred.
Vector autoregression allows testing for feedback. The method
is applied to the issue of causality between the live cattle
futures market and a major slaughter cattle cash market.

GRANGER (1980), noting the absence of a
universally accepted definition for causality,
offered a probabilistic definition which he suggested
might be useful in econometric research.
Granger (1980) further proposed two operational
definitions which he derived from his general
one. The first he referred to as causality-in-mean.
The second he referred to as full causality or
causality-in-distribution. Full causality is preferred
to mean causality when decision-making
populations are characterized by non-linear utility
functions (Bessler and Kling, 1990).