Money-Income Granger-Causality in Quantiles

The causal relationship between money and income (output) has been an important topic that has been extensively studied. However, those empirical studies are almost entirely on Granger-causality in the conditional mean. Compared to conditional mean, conditional quantiles give a broader picture of a variable in various scenarios. In addition, under some asymmetric loss functions, conditional quantiles (rather than conditional mean) may be optimal forecasts. In this paper, we explore whether forecasting the conditional quantile of output growth may be improved using money. We compare the check (tick) loss functions of the quantile forecasts of output growth with and without using the past information on money growth, and assess the statistical significance of the loss-differential of the unconditional and conditional predictive abilities. As conditional quantiles can be inverted to the conditional distribution, we also test for Granger-causality in the conditional distribution (via using a nonparametric copula function). Using U.S. monthly series of real personal income and industrial production for income, and M1 and M2 for money, for 1959-2001, we find that out-of-sample quantile forecasting for output growth, particularly in tails, is significantly improved by accounting for money. On the other hand, money-income Granger-causality in the conditional mean is quite weak and unstable. These empirical findings in this paper have never seen in the money-income literature. The new results have an important implication on monetary policy, showing that the effectiveness of monetary policy has been underestimated by merely testing Granger-causality in mean. Money does Granger-cause income more strongly than it has been known and therefore the information on money growth can (and should) be more utilized in implementing monetary policy