Out-of-sample tests for Granger causality

Clive W.J. Granger has summarized his personal viewpoint on testing for cau sality in numerous articles over the past 30 years and has outlined what he considers to be a useful operational version of his original definition of Granger causality, which he notes is partially alluded to in the Ph.D. dis sertation of Norbert Wiener. This operational version of Granger causality is based on a comparison of the one-step-ahead predictive ability of compet ing models. However. Granger concludes his discussion by noting that it is common practice to test for Granger causality using in-sample F-tests. The practice of using in-sample type Granger causality tests continues to be pr evalent. In this paper we develop simple (nonlinear) out-of-sample predicti ve ability tests of the Granger non-causality null hypothesis, In addition, Monte Carlo experiments are used to investigate the finite sample properit es of the test. An empirical illustration shows that the choice of in-sampl e versus out-of-sample Granger causality tests can crucially affect the con clusions about the predictive content of money for output.