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Full-Text Articles in Social and Behavioral Sciences
Vector Autoregression And Causality, Hiro Y. Toda, Peter C.B. Phillips
Vector Autoregression And Causality, Hiro Y. Toda, Peter C.B. Phillips
Cowles Foundation Discussion Papers
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.
The Spurious Effect Of Unit Roots On Exogeneity Tests In Vector Autoregressions: An Analytical Study, Hiro Y. Toda, Peter C.B. Phillips
The Spurious Effect Of Unit Roots On Exogeneity Tests In Vector Autoregressions: An Analytical Study, Hiro Y. Toda, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper analyzes whether inclusion of a statistically independent random walk in a vector autoregression can result in spurious inference. The problem was raised originally by Ohanian (1988). In a Monte Carlo simulation based on the VAR’s estimated by Sims (1980b, 1982), Ohanian found that block exogeneity of the genuine variables with respect to an artificially generated random walk variable was rejected too often. In the present paper we attempt a full analytical study of this problem. It can be shown that if the genuine variables are nonstationary, the Wald statistic for testing the block exogeneity hypothesis does not have …