Assessment of resampling methods for causality testing: A note on the US inflation behavior

Different resampling methods for the null hypothesis of no Granger causality are assessed in the setting of multivariate time series, taking into account that the driving-response coupling is conditioned on the other observed variables. As appropriate test statistic for this setting, the partial transfer entropy (PTE), an information and model-free measure, is used. Two resampling techniques, time-shifted surrogates and the stationary bootstrap, are combined with three independence settings (giving a total of six resampling methods), all approximating the null hypothesis of no Granger causality. In these three settings, the level of dependence is changed, while the conditioning variables remain intact. The empirical null distribution of the PTE, as the surrogate and bootstrapped time series become more independent, is examined along with the size and power of the respective tests. Additionally, we consider a seventh resampling method by contemporaneously resampling the driving and the response time series using the stationary bootstrap. Although this case does not comply with the no causality hypothesis, one can obtain an accurate sampling distribution for the mean of the test statistic since its value is zero under H(0). Results indicate that as the resampling setting gets more independent, the test becomes more conservative. Finally, we conclude with a real application. More specifically, we investigate the causal links among the growth rates for the US CPI, money supply and crude oil. Based on the PTE and the seven resampling methods, we consistently find that changes in crude oil cause inflation conditioning on money supply in the post-1986 period. However this relationship cannot be explained on the basis of traditional cost-push mechanisms.