2  Modelling Approach

2.1  Model specification

The approach taken here is the error correction model (ECM) approach employing the Engle-Granger two-step procedure. The ECM was first used by Sargan (1964), but became popular in the consumption literature after it was used by Davidson et al. (1978) to model consumption expenditure in the United Kingdom. A major advantage of the ECM approach is that the long-run effects are distinguished from the short-run effects, with specification of the long-run effect drawing on economic theory while allowing the short-run to be in dis-equilibrium.

The intuition behind the ECM approach is that households adjust their consumption towards the long-run equilibrium, as defined by the long-run consumption function. However, in the short-run households’ consumption may deviate from equilibrium, which they correct for in the long-run. The Engle-Granger two-step procedure is used to include the lagged residuals from the long-run equation as an explanatory variable in the short-run equation. The Engle-Granger procedure takes advantage of the super consistency property of ordinary least squares (OLS) estimates of a single cointegrating relation by treating these super consistent parameter estimates as fixed in the short-run regression.

As a first step, the long-run consumption function is estimated in the following form:

(1)    

where c is consumption, y is income, w is wealth, and ecm is the independent and identically distributed residual term. Equation (1) is consistent with a range of consumption functions including Modigliani and Brumburg’s (1954) life-cycle hypothesis and Friedman’s (1957) permanent income hypothesis.[1] The central theme of most consumption functions is that households divide their consumption between the present and the future based on estimates of their ability to consume in the long-run (ie households try to smooth their consumption over time and workers save to spend in retirement). Households choose their level of consumption based on their overall stock of wealth, which includes human capital wealth as well as financial and non-financial wealth. However, human capital wealth is unobservable and the most common approach is to assume that human wealth is proportional to current income, hence the specification of equation (1) of consumption as a function of current income and current wealth.

The wealth variable in equation (1) can be expressed either as an aggregate net wealth variable w (defined as total assets less total liabilities), or disaggregated into net non-financial wealth nfw (defined as total housing assets less mortgages) and net financial wealth nf (defined as the balance of w less nfw). Muellbauer (1994) favours separating net wealth into liquid and illiquid assets, on the grounds that the marginal propensities to consume vary depending on liquidity.

In the second step, the short-run consumption function is estimated in the following form:

(2)     

where z is a vector of other possible determinants of consumption over the short-run, and ecm is the residual from the long-run equation (1), or also known as the error correction term. Including lagged growth rates of income, wealth and consumption help to capture additional short-run dynamics in the reactions of these variables to transitory shocks that do not affect the long-run level of consumption (Davis and Palumbo, 2001). The existing consumption literature is relied upon in choosing the appropriate variables for z.[2]

Past researchers have sought to capture the influence of uncertainty on consumption by using proxies, since uncertainty is not directly observable. The most common proxies is the unemployment rate and the rate of inflation, although consumer sentiment measures have become popular recently. Despite a growing empirical literature on the usefulness of consumer sentiment measures in forecasting consumption, starting with Acemoglu and Scott (1994) and Carroll et al (1994), the evidence to date has been mixed. For this reason, and also for reasons of practicality (to our knowledge, there are no forecasts of consumer sentiment), measures of consumer sentiment are excluded. The unemployment rate is used to capture uncertainty.

Another variable used for z is the real interest rate, which is commonly used to model the short-run behaviour of consumption. The use of the real interest rate variable is to reflect substitution effects, which can be thought of as the time preference of households to consumer now or at some time in the future.

Financial liberalisation in New Zealand from the mid-1980s may have eased liquidity constraints facing households, raising the short-run variations in consumption. Fernandez-Corugedo and Price (2002) found that several different liberalisation proxies have been used in the literature. Since the composition of New Zealand households’ wealth is strongly biased towards housing (Thorp and Ung, 2000), mortgage equity withdrawal is used as a proxy for increases in liquidity, as it is essentially borrowing that is secured on the housing stock but not invested in it. Therefore, it represents additional funds available for reinvestment or to finance consumption spending. Because it is a form of household borrowing, mortgage equity withdrawal can be thought of as an alternative to personal loans, overdraft facilities and credit card borrowing. As such, some elements of mortgage equity withdrawal may be driven by the same influences as other forms of household borrowing. Although some housing equity may be withdrawn with the specific purpose of funding consumption, the funds could also be put to a variety of other uses, such as the purchase of financial assets, investment in businesses, transfers abroad, or to pay off other higher interest debts. Conversely, mortgage equity injection lowers the amount of money available for consumption.

One variable not used in any existing consumption study, but which could be a significant determinant of New Zealand consumption, is migrant transfers. Due to New Zealand’s small population base, net migration has a large effect on overall population growth. Since the late 1980s, net migration has accounted for between –0.3% and 0.8% of the population base in New Zealand. Migrant transfers are the funds that immigrants bring with them to New Zealand and emigrants take to other countries. The net migrant transfers amount (incoming transfers by immigrants less outgoing transfers by emigrants) can be regarded as an additional injection of funds into the country, available for investment or consumption. Over the last two decades, net migrant transfers have fluctuated from between –0.7% to 4% of total household disposable income.