A Comparison of Alternative Causality and Predictive Accuracy Tests in the Presence of Integrated and Cointegrated Economic Variables

Abstract

A number of variants of seven procedures designed to check for the absence of causal ordering are summarized. Five are based on classical hypothesis testing principles, including: Wald F-tests designed for stationary and di®erence stationary data; sequential Wald tests that account for coin- tegration; surplus lag regression type tests; and nonparametric fully modied vector autoregressive type tests. The other two are based on model selection techniques, and include: complexity penal- ized likelihood criteria; and ex-ante model selection based on predictive ability. In addition, various other approaches to checking for the causal order of economic variables are brie°y discussed. A small set of Monte Carlo experiments is carried out in order to assess empirical size, and it is found that although all tests perform well in the environments where the true lag dynamics and cointe- grating ranks are \accurately estimated, simple surplus lag type tests of the variety discussed by Toda and Yamamoto (1995) and Dolado and LA utkepohl (1996)), and model selection type proce-

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