# RDP 7703: Price and Quantity Responses to Monetary Impulses in a Model of a Small Open Economy 3. A Model of the Australian Economy

July 1977

Any model which aims to address the questions discussed above should meet several criteria, most of which are mentioned or implicit in the critical discussion of Brainard and Cooper (1975). The model should have sensible steady state properties. It must allow for the major channels for monetary and budgetary policy. To allow treatment of the reverse causation problem, the model needs to include an endogenous money supply, with appropriate allowance for feedback via policy reaction. It should be estimated in a way which ensures that simultaneous equation bias is not an important problem, and which takes account of the fact that, while macroeconomic processes are probably more or less continuous, data are discrete. Although a rigorous and explicit derivation of the equations of a macroeconomic model from a microtheoretic basis is probably not feasible at present, the equations of the model should be consistent with an integrated macroeconomic theory. Among other things, this is likely to mean that simple adaptive expectations theories of the formation of expectations should be replaced or supplemented by theories which utilize more information about the structure of the economy.

The RBA76 model used in the current paper is more satisfactory than most others which are available in the above respects.^{[22]} In obtaining the benefits of recent developments in macroeconometric modelling, however, some costs have been incurred. In particular, there are places in which the theoretical specification has been simplified to keep the model reasonably small, and a linearized version of the model has been estimated and used for the simulation analysis of the current paper.^{[23]} The general features of the model are discussed, then its treatment of expectations, and then the channels for the transmission of monetary and budgetary impulses; the appendix sets out the equations of the model.

#### 3.1 General features

A basic feature of the model is its representation of economic processes as reflecting partial adjustment towards a moving equilibrium determined by a set of long run behavioural schedules. Thus, for example, desired consumption is determined by disposable income and interest rates, business fixed investment by a desire to equate the marginal product of capital with the cost of capital, desired imports and domestic output by sales and the price of imports relative to that of domestic output. Actual consumption, investment, imports, output, etc. are in general assumed to adjust towards desired levels with a first order adjustment process, although adjustment is also importantly influenced by the gap between actual and desired levels of buffer stocks. The buffer stocks, consisting of money in the case of households and inventories of goods in the case of firms, allow smoothing of the relevant path in the face of unexpected disturbances, and play an important role in the dynamics of the model. The actual quantity of each buffer stock is determined residually in the short run, reflecting its role as a shock absorber. Thus, for example, the stock of money is determined as the net outcome of all private and government decisions, as indicated by equation 18 in the model.

The desired levels of the buffer stocks of real money balances and of inventories of goods are respectively assumed to be a function of income and a vector of interest rates and a function of total sales. It is assumed that the gap between actual and desired levels of the buffer stocks produces adjustment of consumption, prices and wages in the case of money, and of output in the case of inventories of goods – which produce indirect convergence of actual and desired levels of the buffer stocks through the whole model reactions to disequilibrium. As argued in Jonson, Moses and Wymer (1976) with respect to the buffer stock role of money, this particular approach is based on decision rules which produce satisfactory outcomes in a world of uncertainty and imperfect information.

Another general feature of the model is the way in which it endogenises interest rate and exchange rate policy, by the inclusion of policy reaction functions rather than market reaction functions for the relevant variables.^{[24]} Equations 20 and 21 explain an interest rate on government securities and the $US exchange rate respectively, and the corresponding financial quantities (the net value of government securities held by the non-bank sector and the level of international reserves) are determined by the relevant demand functions ((equation 12) for government securities and the functions entering the balance of payments equation (equation 17)). The policy reaction functions include terms representing the usual stabilization policy objectives, but also dummy variables capturing the timing of several of the major changes, particularly in the exchange rate, which have occurred in recent times.^{[25]}

One other general feature of the model, which distinguishes it from most of the large econometric models mentioned in the introduction, is its specification in a way which gives sensible steady state properties. At present, this has involved the imposition of constraints, such as the unitary income elasticities of demand throughout, which ensure that the model has a solution in which all nominal variables grow at the same rate and in which. all real variables also grow at a common rate. When it is possible to solve for the steady state levels of each variable, either analytically or numerically, further constraints will be available to increase the efficiency of the estimates.

There is also the question of the stability properties of the model, which can be investigated analytically by calculation of the eigenvalues of the estimated model. As indicated by Jonson, Moses and Wymer (1976, p.24), the existing model has well defined cycles with periodicities of approximately four, eight and nine years, with one (small) positive root occurring in some specifications.^{[26]} The stability properties of the model will be the subject of a future paper, but the simulations presented below provide further information about its dynamic properties.

#### 3.2 The role of expectations

As indicated above, expectations about changes in prices and in the exchange rate are likely to be important for the dynamic response to monetary impulses. In neither case has it so far been possible to integrate direct measures of expectations into the RBA76 model, and so it is necessary to rely on supplementary hypotheses about the formation and influence of price and exchange rate expectations.

With respect to price expectations, the wage-price sector of the model (equations 6 and 9) is built around a wage-price interaction which is intended to allow for the effects of both past and expected price changes. Money wages adjust with a lag to bring real wages into line with the marginal product of labour, while prices adjust to a mark up over unit labour costs. This specification ensures that the effects of __past__ price changes are built into wages and that wage rises feed in turn into prices (in each case with allowance for movements in productivity). Within the framework of the model, however, information about __future__ price movements is provided by the level of real money balances relative to desired real money balances, and our results to date suggest that there are numerically important and statistically significant direct effects of excess money balances upon price and wage dynamics.^{[27]} In addition, labour market disequilibrium is in the wage equation, to represent the Phillips effect of demand pressure in the labor market, and deviations of real award wages from trend are assumed to influence wage expectations and therefore wages.^{[28]}

In the case of the exchange rate, expectations are assumed to depend on the factors determining policy induced changes in the rate; that is, the important determinants of exchange rate changes are assumed to also influence exchange rate expectations, and the assumed determinants of exchange rate expectations are in the asset demand functions of the model. This version of “sensible” expectations seems to work quite well in the RBA76 model, and the variables which seem to perform best as proxies for exchange rate expectations are the ratio of domestic to world prices and a dummy variable representing the extent to which the sizeable major changes in the exchange rate were anticipated.^{[29]} There is also evidence that in recent Australian conditions the monetary growth rate directly influences exchange rate expectations. Although this evidence is not firm enough to allow for such an effect in estimating the model, it could be allowed for by simulations in which the monetary impulse is accompanied by a parametric change in exchange rate expectations.

It should be noted that the treatment of price and exchange rate expectations in the model is suggestive rather than definitive, and considerable further work in this area will be undertaken in the future.

#### 3.3 Channels for the effects of monetary and budgetary changes

The major way in which the RBA76 model differs from those discussed in Section 2 is perhaps the direct effects of the quantity of money in the model. The hypothesis that money is a buffer stock for the private sector suggests that the gap between actual and desired money balances has an important direct impact upon private consumption. This effect is to some extent analagous to that of liquid asset effects in conventional consumption functions, but it is argued that the specification of this effect in terms of a disequilibrium adjustment mechanism accords more precisely with economic theory.^{[30]} The estimates of the effect of the term in RBA76 give a larger influence than conventional results suggest.^{[31]}

Because of the role of money as a buffer stock, monetary disequilibrium yields information about __future__ price movements and hence is included in the wage and price equations, as discussed above. This yields a direct price effect of monetary disequilibrium, which is absent from most conventional models.^{[31]}

Other channels for the effects of monetary policy in the standard version of the model, the interest rate effects upon consumption and investment decisions, are fairly conventional,^{[33]} although the representation of interest rate determination by a policy reaction function is somewhat unusual. The standard channels for the effects of budgetary policy are also present. Real government spending on goods and services adds to aggregate demand and therefore is assumed to raise output and imports with a fairly short lag.^{[34]} Cash benefits to persons add to disposable income and personal income taxes reduce it. The money supply identity (equation 18) includes the government budget constraint, and this equation thus captures the consequent interdependencies of monetary and budgetary policies.

Although the model is formally a one-sector model, the factor demand functions have been altered from the standard specification to allow for the fact that government and private reactions are likely to differ. In the business fixed investment equation current government spending, a proxy for government output, is deducted from total output in defining the marginal product of capital, as it would be in a 2-sector model with different production functions in each sector. In the labour demand function, the level of public consumption expenditure relative to trend is included to allow in a simple way for the fact that the government sector production function is likely to be more labour intensive than that in the private sector. Therefore, fluctuations in the growth of government are likely to exercise a disproportionate effect on the demand for labour.

The control solution of the model is broadly the same as that of the standard version presented by Jonson, Moses and Wymer (1976), although the fit is rather closer.^{[35]} In particular, there has been some increase in the model's ability to track output cycles and the model tracks moderately well in 1975, although it overestimates inflation and underestimates real product in 1976.

## Footnotes

The model is in the tradition, of those developed at the International Monetary Research program at the London School of Economics. It is discussed more fully in Jonson, Moses and Wymer (1976). [22]

In the future, it is intended to examine the effects of these analytic constraints by selective disaggregation and by simulation of the non-linear version of the model. It is impossible at present to estimate the non-linear model consistently. [23]

The exchange rate equation is included to allow for a variable rate in policy simulations, even though the rate was pegged for much of the period. Jonson and Taylor (1977, pp.9–11) provide a discussion of the treatment of this and other policy variables in the model. [24]

Much of the variance in the exchange rate equation is “explained” by the exogenous timing variables however, which means that the exchange rate, is fairly “sticky” in the simulations of the current paper. In future work alternative exchange rate regimes will be examined, including more flexible exchange rates. [25]

Although the current model is somewhat different to the basic model discussed in the earlier paper, its stability properties are very similar. [26]

Further discussion of this issue is provided by Jonson (1976a); the discussion of Laidler (1974) is also of relevance. The approach is intended to capture in a simple way the contribution of the literature on rational or “sensible” expectations, although, since the approach does not require that economic agents have information about the money supply process, it is an alternative to rational expectations as usually applied. [27]

See Jonson, Moses and Wymer (1976) for a further discussion of the wage-price sector, and in particular of the influence of award wage increases. In the current version of the model, the price equation (no. 6) has been modified to replace real product by the production function in defining the target price. This is equivalent to replacing the denominator of unit labor costs by a normalized variable, and has the effect of substantially increasing the fit of the price equation even though the commodity market disequilibrium term was no longer significant. [28]

The latter variable also enters the trade equations. This dummy consists of geometrically increasing weights which build up prior to each of the several exchange rate changes in the period; this approach is based on that developed by Black (1973). [29]

The basic point is that regarding liquid assets as a proxy for net wealth of the private sector as in the standard approach is open to the objection that most money is inside money, and the asset value of this is offset by a corresponding liability in the aggregate. If government securities are included in an extended definition of private sector wealth, then the asset value is in theory offset by the discounted future tax liabilities required to service the government debt. A disequilibrium real balance effect would be expected even if “money”, however defined, is not net wealth, provided the private sector desires to hold money in proportion to transactions, income, etc. (with the proportion depending upon the opportunity cost of holding money). See Jonson (1976a) for a more detailed discussion. [30]

Whether this is due to the specification of the model, the use of a full information maximum likelihood estimation technique or appropriate accounting for the fact that, while the theoretical model is assumed to be continuous the data are discrete, (or all three factors) remains to be determined. [31]

The RBA1 model of the Australian economy, discussed in Norton and Henderson (1972) and Henderson and Norman (1975), captures such an effect to some extent in its equation for price expectations. [32]

Though the details of the specification differ from those in conventional models. [33]

In conventional models the determination of output is somewhat different. Typically, GDP is determined by an identity, so that aggregate output is assumed to respond directly to an increase in aggregate demand of which government spending is a part. A corresponding identity determines inventory changes in the RBA76 model, consistent with a notion that inventories of goods are a buffer stock for firms, and output is determined as part of an aggregate supply function. (See equations 4, 5 and 19.) [34]

Apart from the changes discussed above, there are also several minor ways in which the model has been modified, although these changes have little influence on its simulation properties. An aggregate required asset ratio has been introduced into the equation for total bank advances, and derivative reactions have been allowed for in the policy reaction functions. There is an increase in the coverage of indirect taxes, and a consequent change in the specification of the equation, to allow for the influence of payroll tax receipts; a minor change in the specification of the equation explaining the price of goods consumed by the government sector has also been introduced. [35]