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.