1485 - 6441 Testing for Two - step Granger Noncausality in Trivariate VAR Models

Granger’s (1969) popular concept of causality, based on work by Weiner (1956), is typically defined in terms of predictability for one period ahead. Recently, Dufour and Renault (1998) generalized the concept to causality at a given horizon h, and causality up to horizon h, where h is a positive integer that can be infinite (1≤h<∞); see also Sims (1980), Hsiao (1982) and Lütkepohl (1993a) for related work. They show that the horizon h is important when auxiliary variables are available in the information set that are not directly involved in the noncausality test, as causality may arise more than one period ahead indirectly via these auxiliary variables, even when there is one period ahead noncausality in the traditional sense. For instance, suppose we wish to test for Granger noncausality (GNC) from Y to X with an information set consisting of three variables – X, Y and Z, and suppose that Y does not Granger cause X, in the traditional one-step sense. This does not preclude two-step Granger causality, which will arise when Y Granger causes Z and Z Granger causes X; the auxiliary variable Z enables predictability to result two periods ahead. Consequently, it is important to examine for causality at horizons beyond one period when the information set contains variables that are not directly involved in the GNC test.