Causation Delays and Causal Neutralization for General Horizons: The Money-Output Relationship Revisited

In this paper, we develop a parametric test procedure for multiple horizon "Granger" causality and apply the procedure to the well established problem of determining causal patterns in aggregate monthly U.S. money and output. As opposed to most papers in the parametric causality literature, we are interested in whether money ever "causes" (can ever be used to forecast) output, when causation occurs, and how (through which causal chains). Our tests are based on new recursive parametric characterizations of causality chains which help to distinguish between mere noncausation (the total absence of indirect causal routes) and causal neutralization, in which several causal routes exists that cancel each other out such that noncausation occurs. In many cases the recursive characterizations imply greatly simplified linear compound hypotheses for multi-step ahead causation, and permit Wald tests with the usual asymptotic ÷²-distribution. A simulation study demonstrates that a sequential test method does not generate the type of size distortions typically reported in the literature, and null rejection frequencies depend entirely on how we define the "null hypothesis" of non-causality (at which horizon, if any). Using monthly data employed in Stock and Watson (1989), and others, we demonstrate that while Friedman and Kuttner's (1993) result that detrended money growth fails to cause output one month ahead continues into the third quarter of 2003, a significant causal lag may exist through a variety of short-term interest rates: money appears to cause output after at least one month passes, although in some cases using recent data conflicting evidence suggests money may never cause output and be truly irrelevant in matters of real decisions.multiple horizon causation; multivariate time series; sequential tests