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2  The Steady-state Model

2.1  Introduction

The steady-state version of the NZTM is based on two blocks of estimated equations that are linked by a large number of identities. The first block relates to the supply side of model. There are two types of goods produced by the supply side of the model, which contains the domestic good (YD) and export good (TEXPS). Both goods are modelled in a nested production function format. The third type of goods is imports, which are intermediate inputs to production. This production block has been estimated as a system using Full Information Maximum Likelihood (FIML). For more details on the production block and the estimation methodology see Szeto (2001).

Within the production block, for simplicity, technical progress is assumed to be labour augmenting, that is technical progress is assumed to be Harrod-neutral[2]. When the production block was estimated, the data implied an estimate for labour augmented technical progress of around 2% per annum. This estimate is historically quite high for the NZ economy on a growth accounting basis[3]. Hence, the coefficient has been imposed at 1.5% per annum, which is closer to the historical average for the New Zealand economy.

The second block relates to the demand side of the model is composed of two equations. One equation is related to the long-run consumption equation. This is the key equation in the demand side of the model. It describes how household spending is determined in the long run. The estimation method uses the cointegration approach to test for a long run relationship between consumption (CON), real income (RINCOME) and real wealth (RWEALTH). A cointegration approach is employed as non-stationary is observed in the relevant variables. This approach is similar to recent work on New Zealand consumption equations by Downing (2001).

The second estimated equation describes how consumers allocate total consumption between housing services (CONH) and other consumption (CONO). In the long run, consumption of housing services (CONH) and other consumption (CONO) are a function of the price of CONH relative to the price of CONO.

The model also contains four behavioural sectors. These are the private business sector, the household sector, the external sector and the government sector.

The private business sector determines the levels of inputs and outputs in the production sector. The business sector uses three inputs to produce its output: labour, business fixed capital and imports. It also produces two types of outputs: the domestic good (YD) and export good (TEXPS).

The household sector’s consumption decision is based on household income and wealth. Households supply labour input for the production process and their savings for investment. Households are assumed to allocate their total consumption between housing services and other consumption by maximising their utility.

The external sector introduces international financial flows to the model, which determines the level of the real exchange rate, the level of underlying external capital flows and the level of net foreign debt.

The government sector is a simple entity in the model. Government buys some output and finances this expenditure through tax revenue or borrowing. All government spending decisions are set exogenously in the model, with the tax rate on labour income being endogenously adjusted to achieve a target public debt to GDP ratio.

The model contains 101 equations and therefore includes 101 endogenous variables. There are 49 exogenous variables. A full description of all the variables is included in Appendix 1. Appendix 2 lists all the equations and identities of the model. The following sections provide a brief overview and the relevant theory for each of the four sectors.

2.2  Private business sector

At the heart of NZTM is a theoretical micro-framework determining how firms decide how many goods are produced and what production input to use. Decisions about the quantities of inputs employed and the quantities of outputs produced are based on an optimising process in which firms maximise profits subject to a production function constraint.

The production block combines three inputs (capital KBF, labour N, imports IM[4]) to produce two outputs (domestic good (YD) and export supply (TEXPS)). It is composed of two constant elasticity of substitution (CES) functions and one constant elasticity of transformation (CET) function.

Those CES and CET functions[5] are expressed as follows:




where Y denotes primary factors for production, T total gross output, Trend is a time trend, λ is the rate of labour augmenting technical progress, ρ, δ and θ are the substitution related parameters, π1 and π2 are the trend growth rates to capture changes in import penetration and a more open economy.

Equation (1) and (2) form a nested CES function. Equation (1) represents the value of production contributed by capital and labour. Hence, Y can be interpreted as value added. Value added (Y) is combined in equation (2) with imports in another CES function to yield gross output (T).

A common assumption made in macroeconomic models is that exports and the domestic good are perfectly transformable in production. As New Zealand’s exports are based significantly on primary industries, the assumption of perfect transformation seems inappropriate. Thus, the domestic good (YD) and export supply (TEXPS) are combined in a transformation function described by equation (3).

In the short run, the domestic good (YD) is demand-determined, the cost of inputs (wages and import prices) is fixed, and the capital stock (KBF) is considered a fixed input. With the fixed unit price of exports, firms maximise profits by adjusting employment, the price of the domestic good (PYD), and the levels of both export supply (TEXPS) and imports (IM).

In the long run, employment becomes exogenous to the production block and is determined by labour supply. Wages become endogenous in the long run. The stock of business capital is no longer fixed in the long run and is determined by the rate of return on the business capital stock (AR) which in turn is a function of real interest rates, depreciation rates and the risk premium. Figure 1 shows a simple flow diagram of the production block in the steady-state version of the model.


  • [2]Harrod defines an innovation as neutral if the relative input shares remain unchanged for a given capital/output ratio.
  • [3]There are three possible reasons why the estimate of productivity is higher than that derived from growth accounting. Firstly, the result of the estimation is based on private sector production. Secondly, gross output is used in the estimation and value added is usually used in the growth accounting approach. Imposing a restriction of no substitutability between value added and imports could bias labour productivity estimates downwards. Finally, two trend growth rates are included in the production block allowing for higher the import penetration and more open economy. These two growth rates can also be interpreted as changes in the quality brought about by higher productivity in the tradable sector. Without adjusting higher import penetration, the value added approach could lead to a lower estimate of productivity .
  • [4]All imports are intermediate materials.
  • [5]Constant returns to scale is assumed in the production block.
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