Comparing alternative tests of causality in temporal systems: Analytic results and experimental evidence

This paper discusses eight alternative tests of the absence of casual ordering, all of which are asymptotically valid under the null hypothesis in the sense that their limiting size is known. Their behavior under alternatives is compared analytically using the concept of approximate slope, and these results are supported by the outcomes of Monte Carlo experiments. The implications of these comparisons for applied work are unambiguous: Wald variants of a test attributed to Granger, and a lagged dependent variable version of Sim's test introduced in this paper, are equivalent in all relevant respects and are preferred to the other tests discussed.