Real national income.

Sefton, James ; Weale, Martin

What do we mean by a country's real income? There are in fact two different approaches here. One, which we address here, is the question of interpreting the existing definition of income. The other is the widespread view that income ought to measure 'sustainable consumption'. The origin of the idea that income should be a measure of sustainable consumption can be traced back to Hicks (1939). He suggests that income should be:

'the maximum amount of money which the individual can spend this week and still expect to be able to spend the same amount in real terms in each ensuing week' (p. 174, op cit).

Despite the current popularity of this idea it is plain that the author was not happy with the concept. For we find later that 'income is a concept which is best avoided' (Hicks, 1939 p. 177).

However, an existing measure of income does not become invalid or wrong simply because. it is not equal to sustainable consumption. In this article we argue that a conventional definition of income is not equal to sustainable consumption but that it can be related to current and future consumption. We discuss a number of practical issues concerning the implementation of this measure before providing estimates of this measure of real income for the United Kingdom in the 20th century. However, we do not discuss any link between income and welfare, and this rather technical issue is covered by Sefton and Weale (1996).

Income in a competitive economy

What then is income equal to? How does it relate to current and future consumption? We can answer this question by observing that growth in income arises first from increases in the capital stock made possible by net saving, and secondly from non-economic factors such as growth in the labour force and exogenous technical progress. In a competitive economy an increase in the real net capital stock of [Delta]K will lead to a permanent increase in income equal to the growth in the capital stock multiplied by the real rate of interest. The real rate of interest is defined as an own-rate of return in consumption goods, and this proposition therefore holds if both income and the increase in capital are measured in terms of consumption goods(1). Both income and the increase in the capital stock have to be measured net of depreciation. In addition, there may be an increase in income arising from technical change and growth in the labour force, which can be described as effects of time. This also has to be taken into account.

The relationship can be expressed formally as

[Delta][Y.sub.t+1] = [r.sub.t][Delta][K.sub.t] + effects of time (1)

The increase in the net capital stock is equal to the amount saved out of income in period t, or to the amount of income which is not consumed. This means that we can write

[Delta][Y.sub.t+1] = [r.sub.t]([Y.sub.t] - [C.sub.t]) + effects of time (2)

This expression allows us to substitute out future levels of income, to produce an expression linking current income to future consumption

[Mathematical Expression Omitted]

If the effects of time are such as to lead to an increase in income independent of saving, then this function indicates the obvious point that future consumption levels can be higher than current income alone would justify.

The expression can be rearranged, to indicate the link between income, current consumption and future changes in consumption

[Mathematical Expression Omitted]

Income Defined

Equation (4) provides a clear definition of real income as it is conventionally measured but defined in terms of consumption goods. In the absence of effects arising purely from the passage of time, real income net of depreciation is equal to the sum of current consumption and the value of all future increases in real consumption discounted at the appropriate real rates of interest. In the presence of income growth arising from the passage of time, the current level of net real income is equal to current consumption plus the discounted value of those increases in consumption which arise only from the effects of net saving.

This definition of income is not, of course, in any sense prescriptive, while the notion that income ought to equal sustainable consumption would be. It is derived simply from the identity that income is either consumed or saved and that the increment to income arising from saving is equal to the real rate of interest multiplied by the amount saved.

One might be tempted to approximate to a situation in which the real rate of interest is constant. In this case equation (3) indicates that income is equal to the real rate of interest multiplied by the present discounted value of all future consumption.. Such a variable could reasonably be called sustainable consumption because it is the rental return on a capital asset which would just buy planned consumption, and this observation provides the basis for the view that income is sustainable consumption.

But the approximation is not as innocent as it seems. If the real rate of interest is constant, then the capital stock must also be constant. If net investment is taking place, an increase in the capital stock will lead to a fall in the real rate of interest measured in terms of consumption goods. The real rate of interest will be constant only if the whole of net income is consumed. In this case income is simply equal to consumption, and current consumption and sustainable consumption are, before taking account of the effects of time, the same thing.

The Current Measure of Real Income

The conclusions reached from this theoretical analysis can be contrasted with the published measures of real income. In the United Kingdom two measures of real income are shown in Table 1.1 of the Blue Book.

The first called simply net national product at factor cost, is evaluated as

GDP at market prices - Factor Cost Adjustment + Net property income from abroad - Capital Consumption

all measured at constant prices.

The second, called real national disposable income, is calculated at market prices as

GDP at market prices + Net property and transfer income from abroad + Terms of trade effect.

with GDP and income from abroad measured at constant prices. We discuss the terms of trade effect below.

The Blue Book suggests that the first measure could also be called national income, but we avoid this term in order to prevent confusion with our own suggested measure.

The Blue Book measure of net national product at factor cost is not, in our sense, a measure of income. It reflects the volume of goods and services that the economy produces. It pays due regard to the fact that income from abroad adds to spending power without having any production associated with it, with such income being deflated by the import price index. It does not reflect the fact that changes in the prices of consumption goods relative to those of other goods can affect the well-being of consumers. This latter was an important aspect of our theoretical measure of income, since that was defined in terms of consumption goods.

The Blue Book measure of real national disposable income is gross rather than net of depreciation. Since there is always concern that the depreciation allowances shown in the national accounts are somewhat arbitrary, a gross figure may be preferred on practical grounds. The measure includes all income from abroad, whether the consequence of past saving or simply of transfer payments unconnected with economic activity. This makes sense because both types of income are equally useful for consumption purposes. Finally there is a terms of trade effect. This is an attempt to take account of changes in the country's 'command over resources' arising from changes in prices of imports relative to those of exports.

A simple example demonstrates the reason for the adjustment. In 1973/4 there was a sharp increase in the price of imported oil. Calculated at 1990 prices our balance of payments in 1974 was in surplus by 0.1 per cent of GDP. But since we had to pay for our imports at 1974 prices and not at 1990 prices, this made calculations based on 1990 prices irrelevant for assessing our real spending power. At prices current in 1974 there was a deficit of 5 per cent of GDP. In order to identify the country's command over resources some method of deflation is needed which reflects the actual terms of trade that the country faced and not those given by the 1990 price base.

Hibbert (1975) discussed a number of ways of dealing with this problem and finally advocated the following approach to measuring command over resources. Domestic expenditures at market prices are deflated in the conventional manner to give estimates in base period prices. The net current account balance in current prices (calculated after taking account of net property income and net transfers from abroad) is then deflated by the price index of imports. This means that the contribution of the foreign balance to real income always has the same sign as its contribution in current prices. Deflation by the import price index does not turn the deficit of 1974 into a surplus. Exports and property income are, in effect being assessed in terms of their ability to buy imports. This means that, since the purpose of exporting is presumably to pay for imports, the measure of real income is assessing the economy's command over resources. The terms of trade adjustment is the difference between the contribution of the external sector calculated in this way and the contribution derived through the straightforward use of constant prices.

In the United States a similar variable 'command-based Gross National Product' is calculated. (Survey of Current Business Table 1.11). The methodology in both cases is broadly in line with that suggested by the current System of National Accounts (UN, 1993).

Our objection to these measures is not that they fail to indicate command over resources, but rather that it may be useful to have measures of income which are clearly related to current and future consumption possibilities. The published measures do not fulfil that role; we now discuss the implementation of our own suggested measures.

Practical Issues of Implementation

A Measure of Real Consumption

There are a number of questions raised by our proposal which should be answered before one could consider putting it into practice. First of all, to talk in terms of a single consumption good is no use since in practice there is a wide range of consumption goods. An obvious solution might be to deflate total consumption (including consumption by Public Authorities) by a suitable price index. But is there any theoretical advice on what is a suitable price index? The answer fortunately is that theory can help. Samuelson and Swamy (1974) prove that provided it is possible to work in terms of a single consumption aggregate (instead of having to define welfare as a function of a vector of individual consumption goods) then the appropriate price deflator is a Divisia price index. This is calculated by defining the percentage change in the price index to equal the sum of the percentage changes in the prices of the goods in question weighted together by their shares in current expenditure. In order to calculate this index exactly it is necessary to monitor prices and expenditures continuously. But a satisfactory approximation can be calculated by taking the year on year percentage changes in goods' prices and weighting them together by the average of the expenditure shares in the two adjacent years(2). The index which results is a chain-linked index and it has the virtue of being calculated with reference to expenditure patterns which are always up to date. It is in fact possible to calculate such a price index retrospectively using the information on consumption in constant and current prices already provided by the Central Statistical Office and we do this in order to provide illustrative figures for the United Kingdom for the period 1900-94. But undoubtedly a more satisfactory picture would be obtained by using a degree of division finer than that published.

The Definition of Net Property Income from Abroad

Secondly there is the question of the measurement of net property income from abroad. This is conventionally measured with reference to property income flows which actually take place. Interest payments on nominal assets and liabilities are affected by inflation. The model which underpins our definition of income requires only flows of real property income to be taken into account. Payments on assets and liabilities denominated in sterling should have deducted from them that component of interest which compensates for the rise in the price level.

More complicated is the question of dealing with securities denominated in other currencies. For short-term assets it would be appropriate to add on to income received any gain arising through changes in the exchange rate and then to deduct the fall in value of the sterling holding of foreign assets arising through an increase in the price level of UK consumption. If exchange rate changes reflect relative movements in the cost of living, then this is equivalent to measuring the real return in terms of the real interest rate paid in local currency; if this is not the case, then this approach generates an assessment of the income earned while keeping the buying power of overseas assets constant. It is less clear how to treat revaluation effects on long-term bonds and equity-type investments denominated in local currency. Further research is needed to identify the most appropriate way of treating erratic price movements in such assets, but in practice the error in using the flow of property income as conventionally measured is not likely to be very great. Certainly, the fact that more research may be needed in this area should not be seen as a reason for abandoning all attempts to produce a consumption-based measure of income.

Factor Cost or Market Prices?

Thirdly, there is the old question whether the calculations should be done using incomes and prices at factor cost or at market prices. Equation (1) is derived from the optimizing behaviour of individual price takers. These price takers are responding to market prices and not to values at factor cost. It follows that the link between income and current and future consumption is to be expected to hold more readily in terms of market prices than in terms of factor cost(3).

The Aggregation Problem

Finally there is the very real issue of aggregation. We have talked about a single consumption price index but the reality is that different people consume different goods and the prices of these goods will not all increase at the same rate. The price index calculated from aggregate data is only some sort of average. Unless the same price index applies to everyone, different people derive different real interest rates from the same nominal market interest rate. In consequence it is not possible to aggregate up the real incomes of individuals to an unambiguous measure of real national income (Gorman, 1953). This aggregation problem is avoided only if each separate consumer spends an identical proportion of her total consumption budget, independently of her income, on each good; in such a situation the same price index does apply to everyone. But it is plain that this is not the case in practice, so that one simply has to hope that the discrepancies are not too large.

This aggregation problem appears in another form. Different countries will have different consumption patterns and different price indices. This means that inflation gains and losses will not add up to zero in the world as a whole. To produce an estimate of world income it would be necessary to use a world consumption price index to deflate world income in money terms. No adjustment would be made for financial assets because the world as a whole cannot be a net debtor or creditor.

Depreciation - A Gross or Net Measure?

The argument that income should be defined in terms of future consumption plainly suggests that a measure net of depreciation should be used. However, because of the uncertainty about the appropriate economic measure of depreciation and in order to give greater comparability with existing practice, we provide measures of both gross and net real income.

The Distinction between GDP and Real Income

With this definition of income we can identify the implications of changes in relative prices for national income. Output can be measured in the traditional way, as gross domestic product deflated by the GDP deflator. The latter is a price index for the whole economy but it can also be thought of as an index of costs. Real income can move differently from real GDP for a number of reasons. First of all the nominal aggregates can diverge - either because of a change in net property income from abroad or because of a change in the importance of depreciation. Secondly the GDP deflator can move differently from the consumption deflator. If the price of capital goods increases faster than the price of consumption goods, then real GDP will increase by less than real income. The increased price of capital goods is implicitly reflecting their greater ability to produce consumption goods in the future and thus faster growth in future consumption. This effect is completely neglected in the conventional analysis of real income. If the price of exports rises faster than that of consumption goods then real income will increase faster than real GDP. And an increase in the price of imports, which with no other changes would lead to a fall in the GDP deflator, will have no effect on real income. Only if it leads to an increase in the price of consumer goods will real income fall. And if the rise in import prices is entirely passed on as an increase in consumption prices, then real income will fall while real GDP is unchanged. This is an example of the terms of trade effect. These observations mean that we can decompose the changes in real national income into changes in output, changes in net property income, changes in the relative price of capital goods and terms of trade effects.

Real National Income in the United Kingdom, 1900-1994

Table 1(4) presents estimates of UK real national income calculated both using the method we describe (both gross and net of depreciation) here and also using the official method (gross of depreciation only). Movements in real GDP are also shown and the differences between growth of that and of real income are decomposed.

From Table 1 we can see that there are sometimes significant differences between the movement of the CSO's series for real national disposable income and that generated by the approach set out here. Between 1990 and 1994 the CSO measure grew by 5.8 per cent while the National Institute measure grew by only 2.6 per cent. The impact of using a Divisia-type deflator rather than a conventional deflator was almost negligible; the difference arises mainly because our measure looks at income in terms of consumption goods, while the CSO measure looks at command over resources.

The statistical cause of the difference is straightforward to identify. Table 2 shows the price deflators for the components of domestic expenditure.

The price of investment goods actually fell over the period and fell substantially relative to consumption goods. Thus any assessment of income in terms of consumption is bound to show much slower growth than a measure of command over resources would indicate. The CSO measure of growth in real national disposable income shows an increase of 5.8 per cent. This is larger than the growth in GDP (3.6 per cent) largely because of a surge in net property income from abroad in 1994. There has also been a positive contribution from the terms of trade effect identified by the CSO. However, by taking into account the implications of the movement in the relative price of capital goods and a small effect arising from the use of a Divisia index, the growth in our measure of gross real income is reduced to 2.6 per cent. This measure is still gross of depreciation. When we make an allowance for depreciation, the rate of growth of real net income is raised to 3.8 per cent over the period. More by coincidence than anything else, the various adjustments to GDP offset each other almost completely, so that, between 1990 and 1994 the growth in GDP is much the same as the growth in real national income.

Final 1995 figures are not yet available and are thus not included in Table 1. However, based on the projections presented in the chapter on the UK economy, we expect a rise in net national income in 1995 of about 1.7 per cent. This is substantially below the growth in GDP of 2.6 per cent both because the price of investment goods continued to rise more slowly than that of consumption goods and because we expect that the final figures will show a fall in net investment income from abroad relative to the very high level of 1994. A look at income growth rather than output growth makes it easy to understand why the recovery is not leading to a general increase in feelings of economic well-being.

In 1996 we do see real national income growing at a rate slightly faster than the growth of GDP, but looking at the period since 1990 it is likely to remain the case that gross income growth has been slower than output growth. This helps to explain the feeling of 'joyless recovery'.

Conclusion

This exercise suggests that more thought could be given to the definition of income variables in the national accounts. We are unable to see any strong case for retaining the existing measures as the sole indicators of movements in real income. We demonstrate that it is possible to produce estimates of a measure of national income related to current and future consumption. Such a measure should form a useful addition to the current range of economic statistics.

[TABULAR DATA FOR TABLE 1 OMITTED]

Table 2. Movements in price deflators: 1991-94

 1990 = 100

 Consumers' Public Gross fixed
 expenditure authorities' capital
 current formation
 expenditure

1990 100 100 100
1994 119.3 121.7 100
% increase 19.3 21.7 0

NOTES

(1) In this competitive economy differences in the physical marginal products of different capital goods will be offset by movements in their relative prices. Scott (1993) also argues that income should be measured in terms of consumption, although not for the reasons we set out here.

(2) The United States has just adopted this approach to the calculation of the GDP deflator, Survey of Current Business, September 1995.

(3) As quite a separate exercise, one may wish to carry out project evaluation or some other sort of cost-benefit analysis. In such circumstances valuation should take place using shadow prices rather than market prices (Dasgupta, 1994). It may be that these are better approximated by means of factor cost valuations.

(4) The data used to construct Table 1 are provided by Feinstein (1972), Sefton and Weale (1995) and the Blue Book (1995).

REFERENCES

Dasgupta, P. (1993), An Inquiry into Well-being and Destitution, Chapter 7, Clarendon Press. Oxford.

Feinstein, C.H. (1972), National Income, Expenditure and Output of the UK 1855-1965, Cambridge University Press.

Gorman, W. (1953), 'Community preference fields', Econometrica, vol. 21. pp. 63-80.

Hibbert, J. (1975), 'Measuring changes in the nation's real income', Economic Trends, no. 255, pp. 23-35.

Hicks, J.R. (1939), Value and Capital, Clarendon Press, Oxford, Chapter 12.

Samuelson, P. A. and Swamy S. (1974), 'Invariant economic index numbers and canonical duality: survey and synthesis', American Economic Review, Vol 64, no. 4, pp. 566-593.

Scott, M. Fg. (1993). 'Explaining economic growth', American Economic Review Papers and Proceedings, vol. 83, no. 2, pp. 421-430.

Sefton, J.A. and Weale M.R. (1995), The Reconciliation of National Income and Expenditure: Balanced Estimates of National Income for the United Kingdom, 1920-1990, Cambridge University Press.

Sefton J.A. and Weale M.R. (1996), 'Natural resources in the net national product - the case of foreign trade', Journal of Public Economics, forthcoming.

RELATED ARTICLE: Box A. Income and sustainable consumption

We can demonstrate diagramatically that the conventional definition of income is not normally equal to sustainable consumption. Consider an economy which can produce combinations of a consumption and an investment good. The production possibility frontier, which shows that combination of the two goods that can be produced, is itself a function of the existing stock of capital. If the economy is producing investment goods as well as consumption goods then in future it will be able to choose between more investment goods and more consumption goods. It is producing output equal to sustainable consumption only when its output of net investment goods is zero. This is the only economic decision that preserves the capital stock at its present level and therefore maintains the same consumption possibilities in the next week.

This situation can be represented on the diagram. If the economy is competitive and is producing at the point marked A, then the price of investment goods in terms of the consumption good is represented by the slope of the line tangent to the production possibility frontier at point A. The value of output measured in terms of the consumption good is given by the point at which this line cuts the consumption axis, Y1. This is conventionally equal to the income generated in such an economy.

If, however, the economy is functioning on a sustainable basis, production of the net investment good will be zero. This means that the output of the consumption good and the total value of all output will be given by Y2 which is plainly lower than the value of output when the economy is producing both consumption and investment goods. In this economy, then, income is normally greater than sustainable consumption. In fact the value of output would be equal to sustainable consumption only if one value the production of investment good not at the prices commanded in the market but instead at the prices which would rule if production actually took place at Y2. In any other situation the equation of income to sustainable consumption involves the use of prices for the investment good different from market prices. In this example the maximum level of achievable consumption is equal to sustainable consumption. When net investment is taking place current consumption is lower and income is higher than sustainable consumption.