The role of seasonality in economic time series: Reinterpreting money–output causality in U.S. data

While empirical evidence on the relationship between money and income has mainly been presented using seasonally adjusted data, seasonally unadjusted data are used in this paper to examine the time series behaviour of money, real GNP and industrial production, at both the seasonal and zero frequencies, based on tests of cointegration and seasonal cointegration. Two important conclusions are reached in the paper. First, although the univariate time series properties of M1 and real GNP appear to be very similar at both the seasonal and zero frequencies, seasonal comovements of M1 and real GNP turn out to be different from long-run comovements. Second, when seasonally unadjusted data are used, there appears to be no long-run relationship between money (M1 or M2) and output in the sense that the null of no cointegration cannot be rejected. Moreover, there is evidence of some feedback from output to money so that money is not necessarily exogenous. Consequently, as we might lose a possibly important chain of causation from money to income by ignoring the information concerning seasonal fluctuations, this paper provides further evidence that researchers should use raw data instead of seasonally adjusted data for inference and forecasting purposes.