On the duality between long-run relations and common trends in the i(1) versus(2)model.an application to aggregate money holdings

Long-run relations and common trends are discussed in terms of the multivariate cointegration model given in the autoregressive and the moving average form. The basic results needed for the analysis of I(1) and 1(2)processes are reviewed and the results applied to Danish monetary data. The test procedures reveal that nominal money stock is essentially I(2). Long-run price homogeneity is supported by the data and imposed on the system. It is found that the bond rate is weakly exogenous for the long-run parameters and therefore act as a driving trend. Using the nonstationarity property of the data, “excess money” is estimated and its effect on the other determinants of the system is investigated. In particular, it is found that “excess money” has no effect on price inflation.