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2.3  Household sector

2.3.1  Private Final Consumption

The consumption decisions of households are assumed to approximate the life-cycle hypothesis developed by Ando and Modiglianli (1963). This approach implies that consumers will spread existing resource to achieve a smooth consumption profile. We therefore derive a consumption function of the form:


Equation (4) states that private consumption (CON) depends upon real income and real non-human wealth, which generates a stream of future income.

There are two major problems encountered in estimating equation (4). The first problem is to find adequate measures for both income and wealth. The second problem is that the sample period of all the available data is not long enough to support a stable long-run relationship.

As it is difficult to find a stable long-run relationship for consumption (see Downing 2001), the income and wealth measures are based on previous work by Murphy (1998). Household income is calculated as the sum of real after-tax labour income and transfers, while non-human wealth includes both financial and real assets. Labour income is preferred to household disposable income in estimating consumption equations because Rae (1996) explains that the use of household disposable income can lead to double-counting of property income. Rae further suggests that disposable income should not be used because it includes the highly volatile entrepreneurial income component. In this model, nominal household income is defined as:


where POL1 is the rate of tax on labour income, W is the nominal wage, NT is total employment, TRPUPR is the nominal transfer from the public sector to the private sector, TROSPR is the nominal transfer from overseas to the private sector and MTRANSFER is the migrant transfer.

As households own all the business capital stock in the model, a theoretically preferred measure of net wealth includes business capital stock (KBF) and housing stock (KH) as real assets. Nominal net wealth is defined as follows:


where B denotes the private sector holdings of public sector bonds, E is the nominal exchange rate, ZPA and ZP are the private sector debt to foreigners contracted in New Zealand currency and in foreign currency respectively, and PYD is the price of the domestic good. The first three terms of equation (6) are classified as financial assets in the model.

Both nominal measures of income and net wealth are then deflated by PYD to derive the real measures of household income and net wealth. To ensure convergence to a balanced growth path, the consumption equation is linear homogenous in real income (RINCOME) and real wealth (RWEALTH). The long-run equilibrium consumption function in real terms is expressed as follows:


PCON is the consumption price index. The last term in equation (7) implies that the higher the relative price of the consumption good, the lower is the level of consumption.

The level of household real income (RINCOME) and real wealth (RWEALTH) are graphed against the level of consumption expenditure in Figures 2 and 3. It appears that the consumption boom around 1995-1997 is associated with slower growth in real wealth during the following period. The rapid rise in private debt to foreigners allowed consumption to grow rapidly during this period. The data might suggest that consumption and real net wealth could be simultaneously determined in the medium run. It could explain why the coefficient on the wealth variable is inconsistent with life cycle theory.

The results of the unit root tests of all the relevant variables are reported in Appendix 3. The results suggest that all the variables are non-stationary and I(1). Using OLS, equation (7) is estimated over the period 1987q2 to 2001q4.

The coefficients from the estimation are presented in Appendix 3. The results suggest that the income elasticity is 0.98 when estimated over the full sample period.[6] This point estimate is higher than was expected. The results of the cointegration test suggest that there is some weak evidence of a long-run equilibrium consumption function. This finding is consistent with at in Downing (2001). The small sample size and the lack of the power of the unit root tests could explain the weak evidence of cointegration.

Another interesting finding is that the income elasticity in equation (7) is only 0.56 if the equation is estimated over a shorter period from 1987q2 to 1996q4. It is clear that the estimates are not very stable and are sensitive to the estimation period. As a result, equation (7) is calibrated in the model and a judgement was made to impose a coefficient of 0.66.

2.3.2  Demand for Housing Services

Households are assumed to maximize utility by choosing an allocation of consumption between housing services (CONH) and other consumption (CONO). The optimal split between consumption of housing services (CONH) and other consumption (CONO) is determined by the ratio of the equilibrium housing services price (PCONH) to the equilibrium price for other consumption. That is, the behavioural equation to be estimated is:


The time trend variable has been included in this long-run equation to capture changes in consumers' preference and changes in the demographic profile of the population. The elasticity of substitution (σ) between housing services (CONH) and other consumption (CONO) items can be derived from the following expression:


Figure 4 shows that the demand for housing services is inversely related to its own relative price. The large increase in the relative price of housing services in the second half of the 1990s coincided with a large decrease in the ratio of the demand for housing services to the demand for other consumption items.

The results of the unit root test suggest that both series are nonstationary. Estimation of (8) by OLS over the full sample period yields an estimate of the elasticity of substitution of 5.3, which is relatively high. Like the consumption equation, there is evidence of unstable coefficients. When we re-estimated the equation over the period of 1991q1 to 2001q4, the elasticity of substitution was 0.63. A judgement was made again to impose the elasticity of substitution at 0.83. The estimation results are presented in Appendix 4.

2.3.3  Labour Supply

In the steady-state, the labour market is in equilibrium. The unemployment rate is equal to the NAIRU when firms and workers expectation of the behaviour of wages and prices are realised. The NAIRU and the participation rate are set exogenously in the steady-state model.

2.4  External sector

Edwards (1987, 1989) developed an intertemporal framework to investigate how policy induced disturbances and other exogenous shocks affect the path of equilibrium relative prices in an economy. The equilibrium exchange rate is reached when the economy attains both internal and external equilibrium. Internal equilibrium means that the non-tradable goods market clears in all periods. External equilibrium means that current account balances are consistent with long-run sustainable capital flows.

The external structure of NZTM developed in this paper is similar to the general equilibrium intertemporal model described by Edwards (1989). The key difference is that in NZTM imports are included as an intermediate input. When there is significant variability in the terms of trade, it is not appropriate to treat tradables as a single composite good. In this context, there are two relevant real exchange rates. One is the relative price of importables to non-tradables (RPM). The other is the relative price of exportables to non-tradables (RPTEX). For more discussion on the theoretical framework for the real exchange rates used in this model, refer to Szeto and Gardiner (2001).

The key structure of the external sector can be represented by the following equations:



Equation (10) simply states that the level of the net real household financial wealth (FRWEALTH) is determined by a ratio of net household financial wealth to real GDP (PAGDPR). The private financial wealth variable is composed of domestic bonds and foreign assets (RPFDEBT). The steady state solution for government foreign debt (RGFDEBT) is set exogenously in the model. Equation (11) states that net foreign debt is a sum of household foreign debt and government foreign debt.


At the steady state, the level of underlying capital inflows (RDOS) is equivalent to a proportion of net foreign debt (RFDEBT) as specified by Equation (12) after adjusting for migrant transfers (RMTRANSFER). The proportion is determined by the natural growth rate of the economy (GR-1).

The following equation is the balance of payments equation:


where RTROSPR denotes real transfers from overseas to the private sector, RTRPUOS real transfers from the public sector to overseas, RYOSPR net real investment income from overseas to the private sector and RYOSPU net real investment income from overseas to the public sector.

Equation (13) states that the underling capital inflow is equal to the current account and the equilibrium real exchange rates (RPM or RPTEX) are defined as the rate at which equation (13) holds.

2.5  Government sector

The government sector is composed of a set of accounting identities. The role of the government is to provide public services such as health and education and provide a safety net for those who are in need. The government’s activity consists of purchasing goods and services and making transfer payments and financing these expenses and transfers. Government spending can be financed in two ways: taxing and borrowing from the private sector.

In NZTM, five tax flows are modelled. They include income tax, consumption tax on non-housing, consumption tax on housing, import tax and lump sum tax related to capture a combination of taxes on company income and interest income.

A range of transfer payments, including superannuation, unemployment benefits, and other benefits are included

The steady-state level for real public liability to RGDP ratio and government expenditure are set exogenously. The tax rate on labour income is then endogenously adjusted to ensure that public debt is restored to its target.


  • [6]The empirical literature often refers to the income elasticity as the marginal propensity to consume (MPC).
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