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Vector Autoregression And Causality: A Theoretical Overview And Simulation Study, Hiro Y. Toda, Peter C.B. Phillips
Vector Autoregression And Causality: A Theoretical Overview And Simulation Study, Hiro Y. Toda, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper provides a theoretical overview of Wald tests for Granger causality in levels vector autoregressions (VAR’s) and Johansen-type error correction models (ECM’s). for VAR models the results for inference are not encouraging. The limit theory typically involves nonstandard distributions and nuisance parameters, and there is no sound statistical basis for testing causality in such a framework. Granger causality tests in ECM’s also suffer from nuisance parameter dependencies asymptotically and nonstandard limit theory. But, in spite of these difficulties Johansen-type ECM’s do offer a sound basis for empirical testing of the rank of the cointegration space and the rank of …
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.