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A forward-looking model of aggregate consumption in New Zealand.

An aggregate consumption function is estimated for New Zealand from 1974 to 1995. The instability of previous New Zealand models is addressed by using a broad measure of net wealth and a theoretically more sound measure of income. Households are assumed to be forward-looking, but only partly so. They form rational expectations of next year's real income, but thereafter use a simple rule of thumb: real income will grow at a constant rate. An econometrically stable cointegrating equation is estimated and it performs well out of sample. The main conclusions are that consumption closely follows net wealth over both short and long time horizons; it responds more to expectations of future household income than to current income; there is a strong negative relationship between savings and house prices, but no corresponding link to equity prices; and the impact of real interest rates on savings is positive but weak and possibly insignificant.

1. Introduction

Consumption accounts for approximately two-thirds of total spending in the economy. Although it is the smoothest component of national spending, its size means that consumption changes can have a significant impact on GDP. However, econometric modelling of aggregate consumption in New Zealand has been relatively unsuccessful in the past, making it difficult for forecasters and policymakers to interpret changes in consumption and savings behaviour.

New Zealand is not alone in having difficulty modelling consumption, but significant progress has been made overseas [for a review of international evidence, see Muellbauer (1995)]. In this paper, I attempt to apply recent theoretical developments to improved New Zealand data in order to capture the main trends in aggregate consumption expenditure.

Previous New Zealand research into aggregate consumption has found it difficult to estimate stable consumption equations, partly for data reasons and partly for theoretical reasons. On the data side, the proxies for net financial wealth have typically been inadequate, and consumption was modelled as a function of total disposable income rather than the theoretically more appropriate labour income. In this paper, I attempt to tackle both problems, by constructing a more comprehensive estimate of households' net wealth, and using labour rather than disposable income.

On the theoretical side, it seems intuitively plausible that consumers look to the future when forming their consumption plans. However, it is not obvious just how forward-looking they are. At one extreme lie the inter-temporal optimisation models that assume consumers have rational expectations of their entire future stream of labour income. However, these models have been forcefully criticised by Pemberton (1993) who argues that, in a stochastic framework, these models are unrealistic for most choices of utility function. Many such models cannot be solved even by consumers who have PhDs in economics; the other extreme, hand-to-mouth consumers, seems equally unrealistic. Thus, the extent to which consumers are forward-looking (i.e., the degree of consumption smoothing) is an open empirical question.

In this paper, I work with a compromise between the two extremes. I assume that households have rational expectations of next year's labour income, but after that they use a simple rule of thumb: income will grow at a constant rate. Thus, they are not fully rational, inter-temporally optimising agents. I also explore alternative formulations as part of the sensitivity analysis, including testing whether consumption is related to house price or share price booms. Issues of the number of cointegrating vectors, weak exogeneity, and encompassing are also discussed. The main findings are summarised in Section 10.

2. Previous New Zealand Research

The main consumption research in New Zealand is McDermott (1990) and Corfield (1992, 1993). Each of these papers models household consumption by durability (durables, non-durables, and services). They use the Engle-Granger two-step cointegration approach, modelling consumption as functions of real household disposable income and some proxies for gross wealth. These proxies include the real market value of the housing stock, real

M3 money supply, and real equity prices. Various other variables have been included from time to time, such as nominal interest rates, the inflation rate, and the price of services relative to the price of imported goods.

These studies have faced three problems. The first is that the wealth proxies have typically been inadequate, partly because they are not comprehensive measures of household assets and partly because they have not subtracted off household debt; that is, they measure gross rather than net wealth. A second problem is that consumption is modelled as a function of total household disposable income rather than the theoretically preferred labour income. Apart from being inconsistent with the theory underlying their estimated consumption functions, the use of labour income can lead to the double-counting of property income (once through the disposable income measure, and once through the wealth proxies); it imposes an untested and possibly incorrect restriction that the marginal propensities to consume out of labour and property income are equal; and, at a more practical level, it includes the highly volatile entrepreneurial income component. This latter component is dominated by farm income, and hence by real commodity prices, and again the marginal propensity to consume (NTC) out of this component of income may not be the same as the NTC for wage and salary income. For example, Arndt and Cameron (1957) find that an aggregate consumption function for Australia performs better if farm income is excluded.

The third problem, possibly related to the first two, is that these equations have tended to be unstable. For example, in updating earlier work, Corfield (1993) finds that real disposable income has a minor impact on consumption and that the longrun equations for consumption of non-durables and services depend only on real M3. Real M3 has been the most successful proxy for "wealth" in these studies, but it is likely that this reflects an endogeneity problem. Only a small fraction of real M3 can be regarded as net wealth of the private sector (M3 is predominantly inside money); so the correlation between consumption and M3 is probably due to consumption causing M3 rather than vice versa. For this reason, I use a narrow money aggregate (MO) in my definition of real wealth.

3. Theoretical Outline

Consider a standard intertemporal optimisation problem in which a representative consumer, whose rate of time preference is [Delta], chooses a lifetime consumption path, {[C.sub.t]} by maximising the following objective function:


subject to the wealth constraint


In this expression, [W.sub.t] and [H.sub.t] are financial and human wealth respectively, given by

[W.sub.t] = (1 + r)([W.sub.t-1] + [Y.sub.t-1] - [C.sub.t-1]),


where [Y.sub.t] is labour income and r is the real interest rate. Under the assumptions of quadratic preferences or certainty equivalence plus a constant relative risk aversion (CRRA) utility function, the solution to this problem yields a consumption equation of the form:


This standard result implies that consumption is proportional to the sum of financial and human wealth. In general, the constant of proportionality, [K.sub.t], depends on the consumer's expected life span but, in the case of an infinitely lived representative consumer, it is constant and equal to

K = 1 - [(1 + r).sup.-1] [(1 + r)/[(1 + [Delta])].sup.[Rho].

Thus, K depends on the (expected) real interest rate, r, the subjective discount rate, [Delta], and the coefficient of relative risk aversion, [Rho].

An important decision in making equation (3) operational is the appropriate specification of expectations of future labour income, [Y.sub.t+i]. Hendry (1983) emphasises the importance of "reasonable" expectations rather than "rational" expectations and argues that informational requirements would make it too costly for consumers to have fully rational expectations in this case (equivalently, the information gathering and processing costs should be explicitly taken into account in the optimisation problem). Pemberton (1993) makes a similar point and argues that the rational expectations framework cannot be rescued by recourse to a Friedmanite "as-if", argument. The major reason is that the "as-if" argument typically relies on either some form of natural selection (e.g., only "naturally talented" people become expert billiard players) or on some form of practice or learning by doing. However, life-cycle optimisation is a one-shot game that everyone must play. The admittedly ad hoc, but partially tested, solution that I take in this paper is to assume that consumers form a rational expectation of their labour income one period ahead and thereafter expect [Y.sub.t] to grow at some constant average rate, y.(1) A possible motivation for this assumption is that consumers are likely to be able to form a reasonable estimate of next period's income (due, perhaps, to them being on a fixed-term employment contract in which wage increases may be indexed to inflation) but are less likely to be able to forecast labour income further in the future.

With this assumption, the consumption function simplifies to

(4) [C.sub.t] = K[[W.sub.t] + [Y.sub.t] + [(r - [Gamma]).sup.-1] [E.sub.t][Y.sub.t+1]].

Thus, current consumption becomes a function of current financial wealth, current labour income, and the expectation of next-period's labour income. After taking a log-linear approximation, the equation that forms the basis for estimation is

(5) log[C.sub.t] = c + [[Beta].sub.1]log[W.sub.t] + [[Beta].sub.2]log[Y.sub.t] + (1 - [[Beta].sub.1] - [[Beta].sub.2])[E.sub.t]log [Y.sub.t+4] + G + [[Epsilon].sub.t],

where c is a constant, G is a dummy for the introduction of GST, and [[Epsilon].sub.t] is a disturbance term. Note that the adding-up restriction on the coefficients ensures that equation (5) is homogeneous of degree one in its arguments. This restriction is implied by the underlying equation (4).

Several features are worthy of comment. First the estimation is on quarterly data and so the one-period-ahead expectation of labour income is replaced with a one-year-ahead expectation. Thus, I assume that consumers have a decision period of one year. This seems intuitively reasonable and is consistent with the approach in Hendry (1983). In an aggregate sense, however, if individual consumption decisions are not perfectly synchronised then a portion of today's consumption will depend on income one quarter ahead, a portion on income two periods ahead, and so on, depending on when a particular consumer formed her expenditure plans. In this case, we would expect income for all the next four periods to be important. Empirically, however, this seems not to be the case. This is discussed and tested in Section 6.

Second, the interpretation of the coefficients will obviously depend on the underlying theory. An earlier version of this paper assumed that aggregate consumption was a weighted average of two types of households: the forward-looking households discussed above, and hand-to-mouth consumers who simply consume a proportion of their current labour income [see Campbell and Mankiw [[Beta].sub.2] (1991) for a similar model].(2) In such a model, the coefficient on current income, A, becomes a combination of the marginal propensity to consume out of current income for the forward-looking consumers and the proportion of consumers who are liquidity constrained. In New Zealand's case, such a nested model did not add to the explanation of consumption.

Third, I assume that the aggregate value of K, is constant over time. Clearly, this requires a constant real interest rate, r, a constant time preference rate, [Delta], and a constant degree of risk aversion. These parameters may change through time for individual consumers, but, even if they were stable, the "aggregate rate of time preference" and the "aggregate degree of risk aversion" (excuse the abuse of language) may change as the demographic composition of the population changes. These constancy assumptions can be tested in a relatively crude manner, and this is discussed in Section 8.

4. Data

All data are from the NBNZ-DEMONZ database (Rae, 1996), are quarterly, and have been seasonally adjusted using X-11. The data were adjusted because the seasonal pattern of many New Zealand variables has been unstable and including seasonal dummies in equations has proved to be a poor way of modelling seasonality (Sims, 1993). The drawback is that it becomes more difficult to reject non-cointegration because seasonal adjustment lowers the power of unit root tests (Ghysels, 1990).

The consumption series used in this study is based on the official real consumption series with an adjustment for the consumption of housing services (imputed rent). The adjustment is made so that imputed rent follows the stock of dwellings more closely. Households' real net wealth is approximated by financial assets (MO, or currency), private sector holdings of government bonds, the portion of the business sector's capital stock that is owned by New Zealanders, and the stock of houses, all net of the private sector's net foreign debt. An important empirical question is whether to value assets at factor cost or market price. Based on the econometric evidence below, the stock of capital is valued at factor cost, while houses are valued at market price.

Real after-tax labour income is the sum of compensation of employees and government transfer payments (net of tax), minus other taxes levied on households. Other taxes are residual taxes that are not accounted for in the rest of the NBNZ-DEMONZ model. Netting off "other taxes" induces a large amount of volatility to the labour income series, and the impact of this is checked as part of the sensitivity tests in Section 8. Where relevant, the variables are measured in per capita terms. Further details are in the Appendix.

5. Descriptive Analysis

Table 1 shows that consumption growth is only a quarter as variable as labour income growth, and, even when the volatile "other taxes" component is not netted off labour income, consumption growth is still significantly smoother thin income growth.(3) The finding that consumption is smoother than income is consistent with most international evidence, but whether it should be so smooth depends on the data generating process for income. For example, if labour income is a martingale then, under the rational-expectations permanent-income hypothesis (REPIH), consumption and income should be equally smooth. A positively autocorrelated non-stationary income process should see consumption being less smooth than income (Deaton, 1987).
Table 1. Consumption, Income, and Wealth Volatility

 Standard deviation
 per cent)

Consumption 1.8
Labour income 7.4
- without other taxes 2.2
Wealth 1.8

Consumption may be smooth in New Zealand because aggregate labour income appears to be negatively autocorrelated. Figure 1 shows the correlogram of income growth. There is a strong negative correlation at the first lag, and little else. This suggests a negative MA(1) process, which is consistent both with a significant fraction of income changes being transitory and with significant measurement error. The negative autocorrelation does not appear to be caused by the volatile "other taxes" component as the univariate processes for the two income measures are similar.


The level of consumption since June 1973 is shown in Figures 2 and 3, graphed against income(4) and wealth. Several periods stand out. The first is the enormous consumption boom during the "golden years" of 1973 and 1974. In these two years consumption grew by 21 per cent, while income grew "only" 15 per cent. The consumption boom was associated with a significant rise in the terms of trade, to a level 30 per cent higher than anything New Zealand has experienced since. There were also related booms in immigration and in the housing market The second period is the acceleration in consumption from (approximately) 1983 to 1988, interrupted by a flicker caused by the introduction of GST in 1986. Over most of this period, per capita labour income was relatively static. The rapid rise in unemployment from 1988 to 1991 led to a large drop in after-tax labour income. Consumption fell, but by significantly less than the fall in income. The strong consumption recovery from its trough in 1992 occurred in advance of the rise in labour income, but was accompanied by a rise in wealth.


Figures 2 and 3 suggest that consumption may be more closely related to wealth than to current labour income. The ratio of consumption to wealth has shown no long-run trend, suggesting some form of mean reversion between the two variables.(5) However, the consumption-wealth ratio is marginally non-stationary at the 10 per cent level, suggesting that factors other than wealth are important for determining consumption. In contrast, the ratio of consumption to labour income appears distinctly non-stationary. It trends down from 1973 to 1981, then trends up for the rest of the sample.

The short-term link between consumption and income is also weak.(6) The simple correlation between the quarterly change in consumption and the quarterly change in income is 0.03. Even looking at annual changes, the correlation is only 0.19. In contrast, the corresponding correlations between consumption and wealth are 0.34 and 0.65.

6. Estimation Results

The estimation method uses the Engle-Granger two-step approach of estimating the long-run equation, testing for cointegration, then estimating a short-run dynamic error-correction equation. Because equation (5) contains a forward-looking variable, it is estimated using the General Method of Moments (GMM) estimator. The properties of the GMM estimator using non-stationary data are unknown. However, my intuition is that, provided the equation forms a valid cointegrating relationship, the parameter estimates will be consistent. They may also inherit the super-consistency results that apply to OLS estimation.(7) However, the standard errors will be unreliable (the t-values will be biased upwards). It is unknown whether GMM's test of over-identifying restrictions is valid with I(1) variables(8) but it is reported anyway.

The presence of a four-quarter-ahead expectations variable induces an MA(3) error process and this is accounted for in the estimation. Valid instruments for the estimation include current and lagged aggregate variables. The chosen instruments are current values of the exogenous variables, a one-quarter lag of consumption, the lagged unemployment rate, a time trend, and the GST dummies. The instruments are logged where appropriate. A reduced-form regression of log [Y.sub.t+1] against the instruments produces an [R.sup.2] of 0.41.

Column (1) of Table 2 shows the results of estimating equation (5). Although t-values are inconsistent when dealing with non-stationary variables, they are reported in the table as an informal check. The table also gives the equation standard error, [Sigma], the test of the over-identifying restrictions, and an ADF cointegration test.(9) The estimate of [[Beta].sub.1] implies that the MPC out of net wealth is approximately two-thirds, while the MPC out of expected future income is around one-third The MPC out of current income, A, is small and seemingly insignificant. The higher elasticity on wealth than on labour income is consistent with the graphical evidence in Section 5. The equation has a reasonable fit given that dynamics are omitted at this stage, and the ADF provides strong evidence of cointegration at the 1 per cent level.
Table 2. Long-Run Consumption Function

 (1) (2) (3)
 [[Beta].sub.2] = 0 Net property

[[Beta].sub.1] 0.665 0.663 -0.362
 (27.2) (26.7) (0.76)

[[Beta].sub.1] -0.010 0 0.107
 (0.22) (0.50)

[Sigma] 0.028 0.028 0.10

[R.sup.2] 0.78 0.79 0.01
DW 1.44 1.43 0.85
OIR 7.63 7.58 12.0(*)
ADF -7.15(**) -7.05(**) -2.21

 (4) (5)
 Current Annual
 income income

[[Beta].sub.1] 0.709 0.673
 (22.9) (25.8)

[[Beta].sub.1] -0.038

[Sigma] 0.029 0.023

[R.sup.2] 0.80 0.85
DW 1.29 0.88
OIR 12.7(*) 9.42
ADF -3.41 -5.03(**)

Notes: "t-values" in parentheses. [Sigma] is the equation's standard error. OIR is GMM's test of over-identifying restrictions (Chi-square test). ADF is Augmented Dickey-Fuller cointegration test; critical values from MacKinnon (1991). Tests marked (*) and (**) mean rejection at 5 per cent and 1 per cent levels respectively. Estimation period is 1974:1 to 1995:3. Constants and GST dummies are not reported.

The next four columns of Table 2 test a variety of hypotheses about the model. Column (2) restricts [[Beta].sub.2] to zero; i.e., it tests whether households respond to current income at all. In all these tests, standard statistical tables cannot be used because the regression involves I(1) variables. Consequently, I take the informal approach of checking whether the restriction "worsens the equation significantly": does it alter the remaining parameter estimates, does it reduce the equation's accuracy, and, most importantly, does it alter the cointegration test? In this case, restricting [[Beta].sub.2] to zero has an almost imperceptible impact on the equation.

A further empirical issue is whether the relationship between consumption and wealth is best modelled in terms of stocks or flows. Column (3) of Table 2 replaces the stock of net wealth with the flow of net property income ([Y.sub.prop]). That is, the following equation is estimated:

log[C.sub.t] = c + [[Beta].sub.1] log [Y.sub.prop,t] + [[Beta].sub.2] log [Y.sub.t] + (1-[[Beta].sub.1]-[[Beta].sub.2]) [E.sub.t] log [Y.sub.t+4] + G + [[Epsilon].sub.t].

This alternative formulation is strongly rejected. In some respects, that should not be surprising. To the extent that asset prices incorporate information about expected future income flows, the stock of wealth implies a degree of forward-looking behaviour that is not captured in the current period's flow of property income.

Column (4) tests whether consumers genuinely are forward-looking. That is, it tests whether consumption responds to expected future labour income one year ahead, or to current labour income. To test this, [E.sub.t](log[Y.sub.t+4]) is removed from the equation. Although the parameter estimates do not change appreciably, the resulting equation does not cointegrate. The forward-looking aspect seems important when modelling aggregate consumption.

There is more than one interpretation of this result. The interpretation that is consistent with the theoretical derivation in Section 3 is that consumers face no borrowing restrictions and are five to access capital markets so that they can consume out of expected lifetime resources, rather than out of current income. In other words, it implies an absence of liquidity constraints. An alternative and perhaps more plausible interpretation is that consumers are liquidity constrained, and that is why they look only one year ahead. Models in which assets are used as a buffer-stock show that liquidity constraints have the effect of reducing a consumer's effective planning horizon. In particular, the planning horizon is the period until the assets run out. This may be a few years rather than a whole lifetime (Deaton, 1992).

The final column of Table 2 considers whether the proxy for future income is adequate. In particular, it replaces expected income four quarters ahead, [E.sub.t](log[Y.sub.t+4]), with an average of labour income over the next four quarters. Although the fit of the equation improves, the evidence in favour of cointegration is less strong. The equation still cointegrates at the 1 per cent level, but further tests reveal that the dynamic error correction model based on this long-run equation suffers from parameter instability. Overall, the four-quarter-ahead income figure is the preferred proxy for future labour income. In short, some form of forward-looking behaviour appears necessary but the evidence is not conclusive on the precise form that it should take.

To sum up, the equation represented by column (2) of Table 2 appears a tentatively adequate long-run cointegrating equation for New Zealand. It is more parsimonious than the equation in the first column at little cost in terms of data congruency; hence, for further work [[Beta].sub.2] is restricted to zero and consumption is modelled as a function of real net wealth and expected labour income one year ahead. I refer to this as the "baseline" model.

7. The Valuation of Net Wealth

An interesting policy question is whether consumption responds to variations in relative house prices and share prices. The appropriate valuation of wealth is addressed in Table 3. For reference, the "baseline" model is repeated in column (1). Column (2) shows the results if the housing stock is valued at replacement cost rather than current market value. Replacement cost is proxied by the price of domestic output, pyd. Valuing houses in this way significantly worsens the equation: the standard error doubles, the [R.sup.2] falls from 0.79 to 0. 16, and it no longer cointegrates. The equation performs poorest when house prices near a peak or trough. This suggests a strong negative link between house prices and the aggregate savings rate.
Table 3. Alternative Wealth Measures

 (1) (2) (3)
 Baseline House prices Business capital

[[Beta].sub.1] 0.663 0.714 0.331
 (26.7) (10.4) (5.13)

[Sigma] 0.028 0.063 0.073
[R.sup.2] 0.79 0.16 0.37
DW 1.43 0.19 0.95
OIR 7.58 13.1 13.2
ADF -7.05(**) -2.26 -5.15(**)

Notes: See notes to Table 2.

The final column of Table 3 looks at the valuation of the business sector's capital stock. The market value of the capital stock is proxied by the NZSE40 sharemarket index. Valuing capital at market price significantly reduces the fit of the equation and, in fact, reduces the coefficient on wealth ([[Beta].sub.1]) by a half. Cointegration is stiff accepted, but the evidence is not as strong as for the baseline model.

The finding that consumers respond to increases in the value of their houses but not of their share portfolio is consistent with some international evidence, e.g., Bosworth, Burtless and Sabelhaus (1991) for the US. A possible explanation is that it may be easier to borrow using a house as collateral rather than using equities. Furthermore, many households own their equities indirectly through superannuation funds and therefore may not count them as wealth. Alternatively, direct stockholders, who tend to be high-net-worth individuals, may have low marginal propensities to consume.

From a theoretical point of view, the role of wealth, and housing wealth in particular, is complex. Real house prices may have several different impacts on consumption. The first is the obvious wealth impact on homeowners. The second is that rises in real house prices redistribute wealth from young to old households. If old households have a higher marginal propensity to consume out of wealth, because they are closer to retirement or death, this will add to the simple wealth effect. Furthermore, if households can borrow against a house but not against other assets (including human capital), a rise in house prices may ease credit constraints and therefore lower the savings rate (Miles, 1992). This implies that the estimated wealth elasticity may fall following financial liberalisation. This was tested by allowing the coefficients of equation (5) to vary over time but no evidence of parameter instability was found. Miles (1993) discusses implications of house prices in a theoretical consumption model based on intertemporal optimisation. He finds that a rise in house prices will have an ambiguous effect on aggregate consumption in general. However, if the price (user cost) elasticity of demand for housing is unity then a rise in house prices will unambiguously raise aggregate consumption.(10) Even so, the overall impact may be small unless households' planning horizons are short. These results depend on fully rational intertemporally optimising behaviour. It is not clear whether the conclusions would change if the model allowed for imperfect capital markets or "irrational" behaviour.

8. Sensitivity Tests

8.1 Real Interest Rates

International empirical evidence on the impact of real interest rates on consumption has revealed coefficients that are small and unstable (Deaton, 1992, Chapter 2.2). This may reflect the theoretical ambiguity in the sign of the relationship (Deaton, 1991, pp. 60-63) and may also reflect the possible importance of liquidity constraints in determining consumption. I proxy the real interest rate by the 10-year bond rate less the annual rate of CPII(11) inflation (excluding the impact of GST). This may be an inadequate proxy because of the period of financial regulation during which measured real rates were negative. Hence, I also add to the regression a dummy variable that takes the value 1 before 1985:1 and 0 thereafter. In effect, the dummy variable "shifts up" the measured real rate over the period that it was negative.

The results are shown in column (2) of Table 4. The real rate has a plausible negative sign and the coefficient implies that a rise of one percentage point in the real rate will lower consumption by 0. 15 per cent. However, it is of marginal significance (based on the low "t"-value and the minor impact that it has on the rest of the equation). Partly in the interests of parsimony, and partly because the error-correction model (ECM) corresponding to this equation is unstable, the real interest rate is excluded from the consumption function.


The theoretical section pointed out that the coefficient, [K.sub.t] in equation (3) depended inter alia on the real rate, r. Hence, including r as a regressor in the consumption equation may not be sufficient to capture all the variation that it may potentially have on the model. In particular, the equation's reduced-form coefficients may depend on r (this is the Lucas critique). To test this, I specified the parameters as linear functions of r (for example, the coefficient on wealth became [Beta.sub.11] + [Beta.sub.12]r). There was no evidence that the estimated parameters depended on the real interest rate (e.g., [Beta.sub.12] was "insignificant", in the sense defined above).

8.2 Inflation

There are several reasons why inflation may affect consumption. The first is a measurement issue, although it should not be relevant to this study. National accounts typically include an estimate of real property income as part of the real disposable income statistics. However, it is calculated as a nominal return on net assets deflated by some price index. A rise in inflation will raise nominal interest rates by much more than it will raise the current price level, and so real disposable income will appear to rise even though nothing has changed in real terms. This is one of the key reasons for using real non-property income in a consumption function, rather than using real disposable income (Lattimore, 1995).

A second reason concerns uncertainty. The variance of inflation appears to be positively related to the level of inflation; Rae (1993) shows that this is true for New Zealand. To the extent that the variance is a reasonable proxy for inflation uncertainty, higher inflation should lead prudent consumers to save more (Juster and Wachtel, 1972). A third possibility is discussed by Deaton (1977). Inflation may imply misperceptions of the price level. If households have trouble distinguishing relative from general price movements, then unanticipated inflation will be interpreted as a rise in the relative price of the goods that they are currently buying. Thus, households will consume less.

Column (3) of Table 4 shows that the impact of inflation, as measured by the annual rate of change of the CPII, has a negligible impact on consumption. The inflation rate is insignificant has a small coefficient with the "wrong" sign, and barely alters the equation diagnostics. This is consistent with the findings of Corfield (1992), but not with Corfield (1993), although this later work, estimated from 1980:1 onwards, gives inflation an implausibly high weight. However, Corfield (1993) uses disposable rather than labour income in his specification, suggesting that the significance of inflation is due to the spurious measurement problem discussed above.

8.3 Productivity and Population Growth

A prediction of the life-cycle model is that aggregate saving and productivity growth should be positively related. In a growing economy the young are wealthier than their parents were at the same age. Because the young typically are savers and the old are dis-savers, aggregate savings in a growing economy will be positive. The faster the growth rate the higher the savings rate. A similar effect flows from population growth. A growing population will mean more young people than old (relative to the steady-state or stationary population) and their saving will outweigh the dis-saving of the old. This induces a positive relationship between population growth and aggregate per capita savings. Note that both these results are due to aggregation; they are not expected to hold at the micro level.

These hypotheses are tested in columns (4) and (5) of Table 4. Both variables have the "wrong" sign and appear insignificant in the sense that their overall impact on the consumption function is small.

8.4 Demographic Profile

The theoretical derivation assumed a representative consumer through time. However, the demographic profile of New Zealand's population has changed through time. The population of working age (15-64) as a proportion of the total population has risen from 68 per cent in 1974 to 75 per cent in 1995. Because workers are typically net savers, a rise in this proportion should increase savings and decrease consumption, all other factors equal. This is tested by adding the ratio of working age to total population as an extra variable in the consumption equation. The result is shown in column (6). The coefficient is estimated to be negative and including the age ratio appears to improve the fit of the equation with no deleterious impact on the cointegration result. It seems that this equation may be a useful candidate for further analysis in Section 9.

8.5 Uncertainty

Uncertainty will encourage a prudent consumer (i.e., one with u... [is greater than 0) to tilt her lifetime consumption profile downwards (save more while young) and thus increases the growth rate of consumption. This relationship is tested in column (7). As a proxy for income uncertainty I use the change in the unemployment rate. This is an imperfect measure but is suggested by Muellbauer and Murphy (1993). The variable has the anticipated sign, but has a small overall impact on the consumption function.

8.6 "Other" Taxes

The final sensitivity check is to consider whether the treatment of "other taxes" in the definition of labour income significantly alters the results. Column (8) shows the results from using a labour income measure that does not net off other taxes. The standard error of the equation falls but this is to be expected as the alternative income measure is substantially less volatile on a quarter-to-quarter basis. However, the cointegration test worsens and it is this result in combination with a preference for the more comprehensive (if more volatile) income measure, that leads me to prefer the equation that uses the broader income measure.

9. Short-Run Dynamic Model

Two potential long-run cointegrating relationships have been identified: the "baseline" model and the specification that includes the proportion of the population that is of working age. In this section, I estimate a short-run ECM using the general-to-specific approach. The estimation period is 1974:4 to 1993:3, leaving 8 quarters for an out-of-sample forecasting test. Two lags of each variable were originally included, and the dynamic structure was trimmed by deleting insignificant lags. Lags of various other variables were also included to test for some of the effects discussed in Section 3. These were changes in: nominal interest rates, the inflation and unemployment rates, population, the age ratio, and (smoothed) productivity.

The lagged residuals from the two long-run equations were initially included, with the result that the residual from the model that included the age ratio was insignificant. Thus, the data are more congruent with the baseline cointegrating relationship. After removing insignificant lags, the final short-run equation was estimated to be:

[Delta]logC=-0.290[(logC - log C*).sub.-1], +0.1939 [Delta] logW - 0.9033 [Delta]Urate+GST dummies

(4.49) (2.06) (1.93)

[R.sup.2] = 0.5532 DW = 2.33 [Sigma]= 0.0152

AR(1-5) F(5, 65) = 0.6556 [0.40]

Standard errors are heteroscedastic consistent

where (logC - logC*) is the residual from the long-run equation. The error-correction term is significant, and its t-value provides an additional test that the long-run equation cointegrates at the 1 per cent level [based on the critical values tabulated in Banerjee, Dolado and Mestre (1993)]. The coefficient on the lagged residual implies that three-quarters of the disequilibrium term will be corrected within a year. The equation was tested against parameter instability, autocorrelation, non-normality, heteroscedasticity, and mis-specification and failed none of the tests. It also passes the two-year out of sample parameter constancy and forecasting tests.

Short-run diagnostics are presented in graphical form in Figures 4 and 5. The main trends in AlogC appear to be adequately captured although some of the early quarter-by-quarter volatility is missed. However, the residual plot reveals no obvious pattern to the residuals except for a period around 1982 when the equation over-predicted consumption growth. The out-of-sample forecasts appear reasonable, with an average absolute error of 0.46 per cent and no consistent over- or under-prediction.


Figure 5 shows the recursive estimates of the parameters. They are relatively stable, although the coefficient on changes in the unemployment rate appears to have reduced over time. The error-correction coefficient appears reasonably stable. One-step-ahead residuals and Chow tests remain within the 5 per cent confidence bounds throughout the sample.

In summary, given the degree of structural change that the economy has experienced, and the significant changes in the quality of the data, the short-run equation appears to be a tentatively adequate, if not perfect, description of the data. What instability there is appears in the dynamics rather than in the long-run part of the equation.

The interpretation of the consumption function's coefficients depends on two further issues. I have assumed the existence of a single cointegrating vector amongst the variables (Y, C, W) and normalised the equation on consumption. The inferences derived above may be invalid if either assumption is incorrect. The number of cointegrating; vectors can be tested using Johansen's framework, albeit without the forward-looking component of income. The results are not reported here but indicate that there is only one cointegrating vector amongst the variables [see O'Donovan, Rae and Grimes (1997) for similar tests in a system that included advertising expenditures]. This suggests that the coefficients are not an amalgam of the coefficients from more than one underlying long-run equation. More generally, the issue of the weak exogeneity of income and wealth with respect to the long-run parameters can be tested by including the error-correction term in short-run equations for [Delta]Y and [Delta]W. The weak exogeneity of labour income may be important in this context because income is partially a choice variable. It depends on hours worked and participation decisions. The results, not reported here, are that the error-correction term is insignificant in the equations for [Delta]Y and [Delta]W, indicating that both variables are weakly exogenous with respect to the long-run parameters. Hence, it is statistically valid to take them as given and condition on them when estimating the long-run consumption function. Finally, the fact that the error-correction term is significant in the short-run consumption equation suggests that we are dealing with a consumption function rather than an incorrectly normalised income or wealth equation.

A second issue is whether this model encompasses its rivals. This is difficult to test formally because the main alternative studies (Corfield, 1992, 1993) model consumption at the level of durables, non-durables, and services. These models were discussed in Section 2 and were found to be unstable and to place "too much" weight on real M3. Furthermore, they used poor proxies for net wealth and used disposable rather than labour income. Even so, some progress can be made by comparing these models to the model estimated above. I was able to approximately replicate Corfield's equations for durables and non-durables but unable to replicate the services equation (my attempt resulted in a "conventional" equation that depends largely on disposable income, whereas Corfield's model was a function of real M3 only).(12) I then re-estimated these equations over a longer sample (1965:3 to 1995:3) and extracted the error-correction terms. These were then added to the short-run equation estimated above and found to be jointly and individually insignificant (t-values were 1.1, 1.0, and 0.6 for durables, non-durables, and services respectively). This is not a formal test for encompassing but does suggest that the rival models contain no useful information that has not already been captured in the model estimated above.

10. Conclusions

The aim of this paper was to build a stable model of aggregate consumption in New Zealand, incorporating forward-looking elements where appropriate and using better estimates of consumption, income, and wealth than had been used in the past. The main conclusions of the paper are as follows. First, per capita consumption follows net wealth closely, both in the short term and over periods of several years. In fact, consumption follows wealth more closely than it does labour income. Second, consumers appear to base their consumption decisions on expected labour income one year ahead, rather than on current income. Third, changes in house prices have a significant negative impact on aggregate savings, while changes in equity prices have no discernible impact. Fourth, the inflation rate does not appear to affect saving behaviour if labour income (as opposed to disposable income) is used in the consumption function. Fifth, the model developed in this paper appears to be an improvement over previous work in the sense that the main rival model contains no extra information, and the rival model does not appear to be stable. Finally, there is some tentative evidence that the demographic profile may influence the aggregate savings rate, but further work would be needed before this could be confirmed.

Clearly, all these conclusions are suggestive only and may be subject to the impact of data revisions. Even so, the consumption function appears to be an improvement over previous New Zealand work, is relatively stable, and forecasts reasonably well out of sample. (1) At this stage I am being deliberately vague about how long "one period ahead" actually is

(2) Hand-to-mouth consumption is often regarded as an approximation to behaviour by liquidity-constrained consumers (Deaton, 1991).

(3) For simplicity, and unless otherwise stated, "consumption", "income", and "wealth" will be short-hand for aggregate real per capita consumption, income, and wealth. It will usually refer to the logarithms of these variables. (4) To reduce volatility, income has been smoothed by taking a centered 9-quarter moving average.

(5) Carroll's (1997) buffer stock model provides a theoretical rationale for a constant target ratio of consumption to wealth.

(6) The figures in this paragraph are based on a GST-adjusted consumption series.

(7) This is also the intuition of Neil Ericsson (personal communication).

(8) This may also be true if the ADF cointegration tests, which are based on residuals from a GMM estimation.

(9) Up to 3 lags were included in the test and the lag structure trimmed down by the removal of insignificant lags. Because this is a test of equation residuals, neither a constant nor a trend is included. (10) O'Donovan and Rae (1997) find that this elasticity is close to unity for New Zealand.

(11) CPII is the CPI excluding interest, and conforms to the convention used by the Reserve Bank. (12) Details are available on request.


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Appendix: The Data

All data are from the NBNz-DEMONZ model database, are quarterly, and, where appropriate, are seasonally adjusted using X-11. Consumption is real household consumption (per capita), except that the owner-occupied dwellings component has been replaced with the following estimate: CONH = 0.024KDP, where CONH is consumption of housing services and KDP is the real stock of dwellings of the private sector. Real labour income is defined as:

Y = [(1 - twr)(ycez + unb + gswo) - glumps]/cpii,

where ycez = compensation of employees, unb = unemployment benefit payments, gswo = other social welfare transfers, twr = average tax rate on wages, salaries, and transfers, glumps = "other" taxes levied on households, and cpii = CPl excluding interest.

Unit root tests reveal that y is integrated of order 1, 1(1). The alternative measure of y, which does not subtract off glumps, is also I(1). Other taxes consist of all tax revenue except for: taxes on wages and salaries, indirect taxes (sales tax, customs duty), company tax, and taxes on government transfers.

Real wealth is defined as:

W = [M0 + bonds + pyd(kp - kpf) + ped.kdp - debtp]/[cpii/(1 + pgst)],

where M0 = notes and coins in the hands of the public, bonds = stock of government bonds held by private sector, pyd = price of domestic output, kp = private sector stock of business capital, kpf = foreign owned part of kp, ped = price of existing dwellings (Valuation NZ series), kdp = stock of dwellings, pgst = impact of GST on price level (Reserve Bank estimate), and debtp = private sector's net overseas debt (based on cumulated current account deficits, with various adjustment for other flow components). Wealth is I(1).

Net property income is from the Household Income and Outlay Accounts. The unemployment rate is from the Household Labour Force Survey.

David Rae, The National Bank of New Zealand Ltd, Wellington.

My thanks go to my colleagues, three referees, and the Editor for their comments. Many of their suggestions led to substantial improvements in the paper. David Rae, The National Bank of New Zealand Ltd, Wellington.

My thanks go to my colleagues, three referees, and the Editor for their comments. Many of their suggestions led to substantial improvements in the paper.
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Author:Rae, David
Publication:New Zealand Economic Papers
Date:Dec 1, 1997
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