RDP 2007-01: A Structural Model of Australia as a Small Open Economy 2. A Small-scale Model of Australia

The structural model is in most respects a standard New Keynesian small open economy model. But the model has a number of adjustments to account for some features of the Australian economy that are peculiar compared to many other developed countries. In particular, while international trade for most developed countries appears be driven by benefits that come from specialisation, Australia's external trade appears to be driven more by classical comparative advantage, with exports dominated by primary products, while more than half of imports are manufactured goods.^[3] In the standard model, the demand for a country's exports are determined by the level of world output and the domestic relative cost of production. Australia can be considered to be a price taker in many of its export markets and has little influence over the price of its exports. Exogenous shocks are therefore added to both the volume of export demand as well as the price that exporters receive for their goods.

Australia is also considered a small economy in the model in the sense that macroeconomic outcomes and policy in Australia are assumed to have no discernable impact on world output, inflation and interest rates. These foreign variables are thus modelled as being exogenous to Australia.

2.1 Household Preferences

A continuum of households populate the economy, consume goods and supply labour to firms. Consider a representative household indexed by i ∈ (0,1) that wishes to maximise the discounted sum of its expected utility

where β ∈ (0,1) is the household's subjective discount factor. The period utility function in consumption C_t and labour N_t is given by

and reflects the fact that households like to consume but dislike work. The variable H_t

is a reference level of consumption capturing the notion that households not only care about their own consumption, but also care about the lagged consumption of others. This feature – often referred to as ‘external habits’ or a preference for ‘catching up with the Joneses’ – helps to explain the inertia of aggregate output, since past levels of aggregate consumption are positively related to the marginal utility of current consumption under this set-up.

2.2 The Consumption Bundle

Households' preferences are specified over a continuum of differentiated goods that enter the households' utility function with decreasing marginal weight. Households thus prefer to consume a mixture of differentiated goods rather than consuming just one variety. The consumption bundle C_t is a constant elasticity of substitution (CES) aggregated index of domestically produced and imported sub-bundles and

The domestic price index (CPI) that is consistent with the specification of the utility function is then given by

This specification implies that in steady state, domestichouseholds spend a fraction (1 − α) of their income on domestically produced goods.

2.3 Import Demand

The domestic demand for imported goods can be shown to be

which depends on the relative price of imports τ_t as perceived by the domestic consumer

Thus, the cheaper are imported goods relative to domestic goods, the larger will be the share of imported goods in the consumption bundle. The exogenous shock to the domestic consumers' demand for imported goods is assumed to follow an AR(1) process

The exogenous shock is needed to match the data, but ideally should only explain a small portion of the dynamics of imports.

2.4 The Domestic Budget Constraint and International Financial Flows

The representative household optimises the utility function (1) subject to its flow budget constraint

The variables on the left-hand side are expenditure items and the terms on the right-hand side are income items. B_t(i) and (i) are domestic and foreign bonds, respectively, where both are expressed in real domestic terms. Their respective nominal returns are R_t and . S_t is the nominal exchange rate defined such that an increase in S_t implies a depreciation of the domestic currency. The term is a cost paid by domestic households when they are net borrowers in the aggregate.^[4] This ensures that the net asset position of the domestic economy is stationary and it implies that, ceteris paribus, a highly indebted country will have a higher equilibrium interest rate. Y_t on the right-hand side is real GDP and the term is export income adjusted for exogenous fluctuations in the price of exports (more on this below).

Assuming a zero net supply of domestic bonds we can write the flow budget constraint as a difference equation describing the evolution of the net foreign asset position

where the change in the net foreign asset position is the difference between income received for exports and expenditure on imports plus valuation effects from inflation and changes in the nominal exchange rate and the net debtor cost . Households choose consumption subject to the flow budget constraint given by Equation (12). Optimally allocating consumption over time yields the standard consumption Euler equation

where U_c(C_t) is the marginal utility of consumption in period t. Households also choose between allocating their savings to bonds denominated in the domestic and foreign currency. Equating the marginal expected return on foreign and domestic bonds yields the uncovered interest rate parity (UIP) equilibrium condition

where is a time-varying ‘risk premium’ that is assumed to follow the AR(1) process

The time-varying and persistent risk premium is usually necessary to account for the observed deviations of the exchange rate from that implied by the UIP condition. There is no consensus in the literature on the causes of the deviations and the interpretation of the risk premium shock does not have to be literal.^[5]

2.5 Firms

The domestic economy is populated by two types of firms: producers and importers. Domestic producers indexed by j use labour as the sole input to manufacture differentiated goods with a linear technology

where a_t is a sector-wide exogenous process that augments labour productivity assumed to follow

In addition to the production sector, there is a sector that imports differentiated goods from the world and resells them domestically.

Firms have some market power over the price of the goods that they are selling since consumers prefer a mixture of differentiated goods rather than consuming just one variety. Unlike the case when all goods are perfect substitutes, this means that consumers will not switch consumption away completely from a slightly more expensive good. In this monopolistically competitive environment firms charge a mark-up over marginal cost.

Quantities sold in a given period are demand-determined in the sense that firms are assumed to set prices in domestic currency terms and then supply the amount of goods that are demanded by consumers at that price. Both importers and domestic producers set prices according to a discrete time version of the Calvo (1983) mechanism whereby a fraction θ^d of firms producing domestically and a fraction θ^m of importing firms do not change prices in a given period. A fraction ω of both the domestic producers and importers that do change prices, use a rule of thumb that links their price to lagged inflation (in their own sector). This is a two-sector generalisation of Galí and Gertler (1999) that yields two Phillips curves of the following form

and

where is the marginal cost of the domestic producers and , defined as

is the real unit cost at the dock of imported goods. The shock is a cost-push shock common to both sectors. The parameters in the Phillips curves are given by

and domestic CPI inflation is simply the weighted average of inflation in the two sectors

2.6 Export Demand

As mentioned above, a large share of Australian exports are commodities that are traded in markets where individual countries have little market power. The standard specification of export demand is amended to reflect the fact that Australian exports and export income depend on more than just the relative cost of production in Australia and the level of world output, as would be the case in a standard open economy model. Two shocks are added to the model. The first shock captures variations in exports that are unrelated to the relative cost of the exported goods and the level of world output. Export volumes are then given by

where is world output and is an exogenous shock that follows the AR(1) process

We also want to allow for ‘windfall’ profits due to exogenous variations in the world market price of the commodities that Australia exports. We therefore add a shock to the export income equation, which in domestic real terms is given by

The shock is thus a shock to real income (expressed in real domestic currency terms) received for the goods that Australia exports. It is assumed to follow the AR(1) process

It is worth emphasising here the different implication of a shock to export demand, as opposed to a shock to export income, : the former leads to higher export incomes and higher labour demand, while the latter improves the trade balance without any direct effects on the demand for labour by the exporting industry.

2.7 The World Economy

The log of world output, inflation and interest rates, denoted , is assumed to follow an unrestricted vector auto regression

The rest of the world is assumed to be unaffected by the Australian economy, and the coefficients in M and the covariance matrix of the world shock vector can therefore be estimated separately from the rest of the model.

2.8 Monetary Policy

A simple way to represent monetary policy that has been found to fit central bank behaviour quite well is to let the short interest rate follow a variant of the Taylor rule, letting the interest rate be determined by a reaction function of lagged inflation, lagged output and the lagged interest rate:

where is a transitory deviation from the rule with variance . This completes the description of the structural model.^[6]

Footnotes

See Department of Foreign Affairs and Trade (2005). [3]

See Benigno (2001). [4]

See, for instance, Bacchetta and van Wincoop (2006) for an explanation based on information imperfections. [5]

Readers who want a detailed derivation of open economy models are referred to Corsetti and Pesenti (2005). [6]