COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 977

"Vector Autoregression and Causality"

Hiro Y. Toda and Peter C.B. Phillips

May 1991

This paper develops a complete limit theory for Wald tests of Granger causality in levels vector autoregression (VAR's) and Johansen-type error correction models (ECM's) allowing for the presence of stochastic trends and cointegration. Earlier work by Sims, Stock and Watson (1990) on trivariate VAR systems is extended to the general case, thereby formally characterizing the circumstances when these Wald tests are asymptotically valid as chi-square criteria. Our results for inference from unrestricted levels VAR are not encouraging.

Keywords: Error correction model, exogeneity, Granger causality, vector autoregression

JEL Classification: C32, C12, C52