RDP 7903: Monetary Rules: A Preliminary Analysis 2. Some General Considerations

The RBA79 model is based on the assumption that the economy is generally in disequilibrium. That is, prices are sticky and do not instantaneously change to equate long-run demands and supplies of assets, goods and labour following a change in an exogenous variable. Short-run equilibrium is achieved mainly by changes in quantities, although prices move over time in response to the relevant excess demands as part of a movement to long-run equilibrium. The short-run changes in quantities are possible because of the existence of buffer stocks – of money, goods and labour.

Both quantities and prices move in response to the gap between actual and desired values of the buffer stocks. A particularly important role is played by the excess demand or supply of money, which influences directly the adjustment of household expenditure (and thus of output), prices, and non-monetary assets and liabilities. The transmission mechanism in RBA79 thus gives an important direct role to changes in the quantity of money, although real and nominal interest rates have their usual influence in the demand functions for goods and assets.

RBA79 is a complex dynamic non-linear model which consists of twenty-six first-order differential equations. For estimation and for some analytic exercises, including the present one, the model is made linear in the logarithms of variables by linearizing the relevant relationships (mainly identities) about a quasi-steady state growth path. The properties of the linearised model can be examined by analytic methods as well as with simulations. If the estimated model is stable, with all real eigenvalues negative and with negative real parts of complex eigenvalues, the steady-state properties of the linearised model will provide a good guide to the equilibrium property of the non-linear model. The short-run responses of the linearised model are likely to provide a reasonable guide to the dynamic properties of the non-linear model.^[5]

The current version of RBA79 is stable. It has ten real eigenvalues, with values ranging from −3.56 to −0.01. It has eight pairs of complex eigenvalues, representing cycles with periodicities ranging from two years to eighty-two years.^[6] Of these, there is a dominant cycle^[7] with a period of ten years.

The properties of a stable system of linear differential equations are such that a sustained change to the level of an exogenous variable may permanently change the levels, but not the rates of growth, of the endogenous variables. Such a shock may, for example, permanently change the level of the money supply, of prices, of output, etc but not their rates of growth. During the adjustment process, of course, there will be changes to both levels and rates of growth of endogenous variables.^[8]

These points are illustrated in the following section. In each case, the diagrams show the impact effect of the shock, the steady state (or permanent) effect and the adjustment path for the first decade.

Footnotes

See Bergstrom and Wymer (1974) and Appendix C for discussions of the various technical matters covered here. [5]

The very long cycle has a very short damping period and therefore has little effect on the dynamics. In any case, it is considerably longer than the sample period and thus must be interpreted with caution. [6]

A dominant cylce is one with a damping period which is long relative to its period. [7]

Changes to the rate of growth of the exogenous variables can change the equilibrium rates of growth of endogenous variables. As such changes can be considered as a series of changes to the levels, they are not considered further in this paper. [8]