The Role of Fiscal Policy in a Financially Disaggregated Macroeconomic Model: Comment

Abstract

In analyzing stability of a macroeconomic model with 100 percent money financing of the government budget, Darrel Cohen and J. Stuart McMenamin [3] (henceforth C&M), claimed that in the absence of the Pigou effect in saving, it is likely that no long-run equilibrium exists, since the determinant of the dynamic matrix DM vanishes. This is stated as their Proposition Sb. This note makes three points about C&M. One is to elaborate further on the consequences of the vanishing determinant of the dynamic matrix. We show that the economy, when disturbed off the long-run equilibrium, will return to a onedimensional subspace under a mild sign condition on EK (effect of changes in the capital stock on its real market value), so that the deviations in the money and capital stocks need not both go to zero with time but instead maintain a linear relation. The second point is to show that certain policy reaction functions, or automatic rules for adjusting policy instruments, can make such a seemingly anomalous state disappear and the long-run equilibrium state stable even with the vanishing determinant of the dynamic matrix. Finally, we suggest a procedure for carrying out stability analysis of a steady state (balanced growth) time path in a growth framework, the desirability of such analysis being mentioned by C&M. We take up these points in sequence. First, the vanishing determinantDM is caused by the existence of one zero eigenvalue. We show that the zero eigenvalue is caused by deviation of the investment being proportional to deviation of real net national product in the absence of the Pigou effect. Furthermore, the presence of zero eigenvalue indicates that the dimension of the system being addressed is actually lower than that of the matrix DM. To see these facts, consider the homogeneous part of the dynamic equation which governs the deviational variables about the stationary state of the model, while holding B and G fixed at the equilibrium values. Denoting the deviation from the equilibrium values by bM = M M*, and AK = K K*, where * denotes the long-run equilibrium or stationary state value, these deviational variables are governed by the differential equation given by