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THE INCOME OF NATIONS:
MEASUREMENT WITH (WHAT?) THEORY
Michael Harris
Agricultural and Resource Economics
University of Sydney
[email protected]
Environmental Economics Network workshop
Australian National University, May 2005
Abstract
Extensive activity is underway to revise the construction and measurement of national
income statistics. This revision activity is largely motivated by concerns about
environmental quality, resource use and the long run sustainability of development
paths. However, the underlying definitions of income are not settled. At the broadest
level, there is a conflict between income as an economic concept (consumptionrelated, intertemporal) and an accounting concept (output-related, atemporal). More
specifically, the distinction between ex ante income (maintainable consumption) and
ex post income (actual consumption plus capital accumulation) is often blurred, for
example. This raises the issue of the rationale for including capital in measures of
income, and the possible interpretations of such measures as “returns to wealth”.
In the paper, two distinct rationales for adding capital to consumption in an
economically meaningful measure are identified—future consumption postponed
versus current consumption foregone, which differ due to the effect of diminishing
returns in production—and argue that they lead to two distinct interpretations of
income: the stationary-equivalent of future consumption interpretation versus the
stationary-state-equivalent interpretation. I argue that the choice of one or other of
these interpretations has implications for a raft of national accounting issues, such as
the treatment of capital gains, the concept of natural capital, the pricing of investment
goods, and the treatment of technological change. Moreover, it is important to
understand the different perspectives in order to properly resolve differences between
recommendations for expanding the accounts as presented by national accountants
and by economists. The conclusion, that there is not one overriding concept or
measure of income, is emphasised.
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Contents:
1.
Introduction
2.
Preliminaries
3.
Income and Growth: Key Themes
4.
5.
6.
3.1
National accounting themes
3.2
Economic themes
3.3
Growth themes
Income: A Confusion of Definitions
4.1
Terminology
4.2
From personal income to national income
4.3
Relating the themes of income to each other
Income and Capital Goods
5.1
Why include capital in income?
5.2
The growth-theoretic approach
5.3
The atemporal perspective
5.3.1
Examples of “Atemporal perspective” models with investment
5.3.2
Discussion
5.4
Summary
Empirical Implications
6.1
Capital theoretic controversies
a) Technical change
b) Capital gains
c) Natural capital
6.2
7.
Other controversies
Conclusions (followed by Appendix and References)
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1.
Introduction
“Income is a series of events.”
Irving Fisher.1
When Adam Smith wrote the Wealth of Nations, long regarded as the starting point of
modern economics, distinctions between wealth and income were not well
understood. Only much more recently has there been a clear understanding and
acceptance of the underlying stock/flow distinction that characterises modern
discussions of income and wealth at both the personal and the social level. National
income—the definition and systematic measurement thereof through organised
national accounts—has been one of the great practical innovations of twentieth
century economics.
This innovation is still in progress. Revising the national accounts, or discussing how
they should be revised, is a major ongoing activity. The System of National Accounts,
or SNA, has been revised from its 1968 standard and is undergoing further revision
(United Nations 1993, 1998). Individual nations are engaging in accounting exercises
designed to extend the scope and coverage of their accounting systems in line with the
evolving SNA (Oakley 1996; Nordhaus 1999, 2000). Academic and other economists
are engaged in conceptual work and case studies of particular countries, so as to
compare time paths of standard economic growth measures with adjusted measures
(Usher 1980, Eisner 1988, Scott 1989, Nordhaus 1995, and see the overview in Harris
and Fraser 2002), and preparing detailed theoretical treatises on the meaning and
computation of such adjustments (Aronsson, Johansen and Lofgren 1997, Brekke
1997, Hartwick 2000, Perrings and Vincent 2003, Weitzman 2003).
In the first half of the twentieth century, particularly during the decades of the
Depression and Second World War, there was a similar degree of intensity in the
debates and activity concerning national accounting and national income in particular.
Key luminaries in the profession (including Fisher, Lindahl, Hicks, Pigou, and Hayek)
1
Fisher (1930), quoted in Parker and Harcourt (1969), p.33.
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debated the proper notion of income, and its relationship to capital.2 Keynes published
his General Theory (Keynes 1936) exploring the link between aggregate demand and
national income. Experts such as Meade, Stone and Clark began constructing the first
recognisable national income and expenditure accounts (again, see Parker and
Harcourt 1969). There were active debates on definitions, measurements and
interpretations.
One might expect as a result of this pioneering work that the current activity and
debates are essentially “at the margins”—that core ideas of national income are
settled, and that what is still unsettled is how best to extend these core ideas into new
areas: technological change, environmental damage, natural resource use, leisure time
and so on.
This, however, turns out not to be the case. The purpose of this paper is to show that
the area of extended accounting remains heavily contested terrain, as it was in the
1930s and 1940s. The difference now is that there is an expectation that the profession
should know what it is talking about by now; this means that the controversies are
confronted less explicitly than they once were. Key concepts are assumed to be clear
even when, on inspection, it turns out they are not. Key differences in definitions and
assumptions are not well appreciated. The neophyte scholar in the extended national
accounting field would be well justified in feeling lost in a welter of competing
approaches, making estimates hard to compare or interpret.
In this paper I outline the varying ways in which national income is defined,
particularly contrasting the ways in which national accountants view it compared to
economists. I identify how terminology and its connection to an underlying theoretical
framework has become confused between various users, with different concepts of
income being misleadingly conflated. I identify two different conceptual approaches
to accounting for capital goods, one of which reflects the atemporal emphasis of
national accounting practice and one of which reflects the intertemporal focus of
economic theory. I explore the implications of each of these for extended accounting. I
2
See the collection edited by Parker and Harcourt (1969).
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then examine how different authors have drawn on particular assumptions to reach
conclusions about how income should be measured, and the empirical implications of
these assumptions. I include some comments about the ongoing revisions of the
System of National Accounts here too.
2.
Preliminaries
Before proceeding into a discussion of practicalities of national accounting and
national income measurement, some groundwork needs to be covered. Firstly, what is
the simplest static representation we can present of what is an inherently dynamic
concept? Secondly, what interpretation, or interpretations, can be put on both this
simple representation, and on more complex measures of national income, broadly
defined?
To tackle the first problem, assume a simple one period, two good economy. It
possesses a technology for producing each of the two goods, subject to the usual
diminishing returns. We can represent this simple world in Figure 1. The bowed out
curve represents production possibilities in a standard two good economy in a single
accounting period. The diagonal line AD shows relative prices between the two goods
C1 and C2, given by the social optimum at the point of tangency. If the two goods are
consumption goods then the interpretation is straightforward. Using C1 as the
numeraire, OA gives national income in C1–equivalent units. We have derived a
meaningful atemporal measure of social welfare (in this simple example at least).
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C1
A
B
C1 *
C2
C2 *
D
Figure 1
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In fact, we can argue that the national income as measured by OA admits of two
interpretations. First, on the “production” side, by adding up physical units using the
common denominator of the market price ratio (shown here as the marginal rate of
transformation), the magnitude OA equals the value of the economy’s output in this
period. Second, on the “consumption” side, by adding up the units using the marginal
rate of substitution (from the indifference curve, not shown, but assumed to be
tangential to the production frontier BD, at the point (C1*, C2*)), OA gives the
welfare interpretation already alluded to.
Why do the output and welfare interpretations coincide in this representation of the
world? Because only two things matter (consumption of goods 1 and 2, respectively),
and because rates of substitution and transformation are the same. In other words, this
is a first-best world. Market prices are optimal, all utility-generating goods are
included in the index, there are no externalities, and so on. Allow these assumptions
to change to better reflect reality, and the interpretations part company. (This is
distinct from the index number issues that arise in the measurement of economic
growth where changes in productivity and in welfare, in the Fisherian “series of
events” sense, will be measured differently: see the next section.)
There is something of a paradox here, in that it is partly the understanding that the
world is not a first-best one, and that key assumptions that would make an output
measure coincide with a welfare one are violated, that has motivated attempts to
revise accounting procedures such as in the so-called “natural resource accounting”
field. However, the more rigorous the investigation into how to construct and interpret
an ideal index, the more difficult it is to work in a framework that does not rely on
optimising foundations. (This has led to an odd situation in the technical literature on
extended accounting, in which inherently first-best models are used to derive
accounting procedures for applications in the nth-best real world. Models of this nature
are discussed in Section 5.2.)
This static, consumption-only framework also does not allow us to investigate the
inherently dynamic concept of income. In particular, while we can think about output
and welfare in this context, we cannot systematically investigate questions about
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capital formation and sustainable consumption, because this model is not designed to
look at feasible consumption paths over time. Bringing in capital goods necessarily
introduces dynamic considerations, but also necessarily complicates the analysis.
Issues surrounding the inclusion of capital goods in an index of national income are
the subject of Section 5.
However, while we cannot utilise this simple model to analyse some dynamic issues,
we can use it to help define some key concepts. In particular, introducing dynamic
considerations raises issues of “sustainability”. An obvious way to define
sustainability here is to assume that consumption bundle (C1*, C2*) can be consumed
in every subsequent period. This is, by assumption, a simple steady state model in
which the capital stock, labour force and technology that generate output are assumed
constant, so that the production possibility frontier BD does not change. (Implicitly,
neither do preferences, since they define (C1*, C2*) to be the optimal consumption
choice.)
This is a straightforward definition of sustainability—maintenance of consumption
flows over time. A slightly broader condition might be that consumption bundles may
change, but sustainability requires non-declining aggregate utility. In more complex
growth models, sustainability may be defined in terms of either (restrictions on)
changes in instantaneous utility, or, as we shall see, on more generalised present-value
utility measures. But to be able to analyse sustainability issues more effectively, we
will have to move to dynamic models that allow for capital accumulation.
However, this simple example of a static (or steady-state) economy has helped
identify the key issues of interest. National income is firstly a measure of output.
Other interpretations that might be put on an index of income is (i) a measure of
welfare or well being, and (ii) an indicator of sustainable consumption. These three
alternatives—output, welfare, sustainability—will be motivating themes of the
foregoing discussion. In this simple framework, all three interpretations coincide. As
the model becomes more complex, the definitions part company. How to deal with the
fact that the definitions diverge is our task to follow.
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3.
Income and Growth: Key Themes
Having focussed on a simple atemporal representation of the world, what happens
when one moves into more dynamic concepts of national income in which capital
accumulation is taking place? Any discussion of national accounting procedures—and
their appropriateness and adequacy for their stated purposes—should be based on a
coherent and well-defined conception of income. One might expect that such a
fundamental concept in economics as income would be well defined and well
understood within the discipline. This is, however, not the case. Here we will present
alternative views of income in terms of key “themes”: by themes we mean something
more general than definitions, but as shall be seen later, starting with specific
definitions would make things messier rather than clearer.
3.1
National Accounting Themes
The first key theme we explore—national income as an accounting construct—is in
fact the way most beginning economists are exposed to the idea of national income.
That is, we usually first see national income as it arises within the model of the
circular flow of income presented in introductory macroeconomics textbooks.
Viewing income in this way has certain implications. Income is that flow of money
generated by current production of new final goods and services. It is a standard part
of national accounting practice that income arises from current production: the notion
of the circular flow is as an accounting identity that links the value of sales from
production (and total value added associated with the generation of that output) to the
total income earned as a result of generating that production.
The form that national income—gross domestic product (GDP)3—takes from the
accounting perspective is the familiar GDP = C + I. This expression can be extended
in obvious ways to separately account for the government sector and for trade, but in
general we can think of income as the sum of current consumption and gross capital
This is a measure based on the value of production, rather than incomes to factors (“Gross National
Income”), but it is due to the accounting identities that the national accounts are constructed upon that
measuring one is equivalent to measuring the other.
3
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accumulation: appropriate adjustments to the investment term would leave us with an
expression for net product (NDP) instead.
This notion of income as arising from production, and being defined in terms of an
accounting identity, turns out to be of major significance when contemplating how it
should be adjusted, particularly at the official SNA level. The components of income,
in particular consumption and investment, must be appropriately defined so as to
match the value of income as earned by the nation’s citizens. As a result, consumption
and production “boundaries” are drawn around the appropriate flows so as to keep
them consistent in accounting terms with the income being generated.
To sum up income from the accounting perspective:

National income reflects the value of current production;

The “circular flow” accounting identity is the basis for both classification
and measurement in the national accounts;

The components of income must be appropriately defined in order to
preserve the accounting identity upon which income is defined (in practice,
this means that the measured components are restricted to those falling
within the market sector);

Income is largely a historical, or atemporal, construct, looking at “what has
just happened”. There is no explicit dynamic interpretation to be placed on
the measure produced.
3.2
Economic Themes
If national accountants think of income as being generated by production and defined
in terms of an accounting identity, is there a contrasting way in which economists
instinctively think of it? If there is one thing common in the economics literature it is
the theme of income as a return to wealth: or, perhaps more precisely, to a stock of
capital. Various definitions of income as a return to wealth are possible, but we will
identify two key themes:

Income as the sum of consumption plus the change in wealth;

Income as a maintainable level of consumption.
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The first of these derives from the public finance literature. Bradford (1990) labels it
the Schanz-Haig-Simons (SHS) measure of income, and we shall as well (although we
shall see that other labels may be applied).
What the SHS concept has in common with the accounting version of income is the
structure they share: both involve adding actual consumption to changes in wealth or
to capital accumulation. We expand on the detailed differences in a later section. For
now we shall make the observation that the boundaries around the consumption and
investment terms in the national accounts are defined to make them consistent with
the overriding accounting identity. For economic interpretations the boundaries are
drawn more to make the income measure consistent with some sort of return to wealth
interpretation. To keep this distinction clear we denote the expression for this theme
of income now as YSHS  C  K , where we use K instead of I to make clear that the
change in the capital stock we are interested here may not be the same as the output of
investment goods counted in conventional GDP or NDP.
The key alternative theme of income that is explored here often appears in the
economics literature associated with Fisher (1930) and Hicks (1946). Instead of
treating income as an accounting concept, something to be constructed empirically,
income is regarded as the answer to a thought experiment about how much can be
consumed without future impoverishment. While there are variations on this theme,
some of which will be explored below, the key point is that income is now
synonymous with consumption rather than being a combination of consumption and
investment (or wealth change).
Bradford (1990, p. 1183) distinguishes between these two themes of income by
describing one as a backward-looking measure (SHS income)—asking “How much
did we produce last year?”—and the other as a forward-looking measure (which we
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shall refer to as Hicksian income, as Bradford does)—asking “At what rate are we
able to produce value?”4
It is important to stress again that we are talking of themes rather than definitions of
income. The subtleties of Hicksian definitions of income, for example, will be
expanded upon in the following section. For now, within what Bradford calls
“Hicksian” income above, two obvious sub-themes are prominent in the literature.
One involves explicitly specifying income as that amount of consumption that does
not diminish future consumption. In this sense, seeing income as a return to wealth
involves defining wealth as the capitalised value of future consumption (Hicks talked
of “receipts”). The second sub-theme involves trying to approximate the first by
defining income as that amount of consumption that keeps wealth constant. In
national accounting terms, wealth here refers to a measurable capital stock.
C
In formal notation, we can write the first of these as YHicks
 max C (t ) s.t. C  0, t ,
K
and the second as YHicks
 max C (t ) s.t. K  0, t . In Nordhausian terminology—see
Nordhaus (1994)—these are, respectively, a “consumption annuity” measure of
income and a “capital intact” measure.
In simple models there is a neat duality to these Hicksian sub-themes. Defining
income as maximal non-declining consumption implies (in certain circumstances)
constant wealth. Defining income as that consumption consistent with constant
wealth, in turn, implies constant consumption. Income is precisely measured as a
return to wealth. Complicate the model—or the world that is being represented by the
model—and this duality breaks down. The first (the consumption annuity measure) is
4
Again, the SHS measure shares an empirical and historical approach with the national accounting
circular flow construct. However, one of the key differences between the philosophy underlying
national accounting calculations of GDP, and how economists use and interpret the SHS expression is
that the accountants intend their measure to be historical—a measure of the economy’s productive
capacity, and by extension, a measure of its income-generating capacity, with the income being what is
generated by that production—while economists instinctively seek to generate a measure that is in some
sense more broadly interpretable and more forward-looking. This tension that arises from using
historical data to generate predictive measures is a feature of the economic literature on national
income, and a key theme of this paper.
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the conceptual ideal, while the second (the capital intact measure) is a measurable
approximation, at least in principle.
As a result of this elegant duality, these two appear often in discussions of income;
sometimes in ways that suggest they are interchangeable. But the second is an
approximation to the first; in a national accounting context, a dictum to maintain
wealth is really an admonition to not consume one’s capital. This may or may not be
equivalent to maintaining consumption possibilities, an issue explored further below.
These economic income themes have obvious return-to-wealth interpretations. But
how do they relate to the criteria of welfare and sustainability, which have been
highlighted as key criteria which extended accounting aggregates should better
measure? Clearly, Hicks was motivated by issues of sustainability, and hence all the
measures associated with what we have labelled Hicksian income themes are
approximations to a measure of sustainability, or at least are intended to be. Can they
also be interpreted as measures of welfare?
The Hicksian ex ante measures define income as consumption so they are welfarerelated by definition. One case in which a precise welfare interpretation is admissible
is the steady state case in which there is a consumption annuity flowing from a


C
K
constant stock of capital; that is, where YHicks
. In this situation, consumption
 YHicks
(income) clearly measures maximum sustainable welfare. That is, it captures
sustainability and welfare in a single measure. Once the economy moves from this
steady state, we may be able to approximately measure sustainability by including
capital accumulation, or else aim for a welfare measure by limiting the focus to
consumption. But only in the strict constant consumption steady state do we get a
measure that accurately captures both.
There is a literature in which income expressions of the YSHS form admit of an
intertemporal welfare interpretation, and this will be covered in Section 5.2.
3.3
Growth Themes
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Things get yet more complex once the (sometimes) neglected issue of index numbers
is raised. To seriously measure economic growth requires the comparison of income at
various points in time. An approximate approach—one consistent with national
accounting practice—is to measure the value of output at two points in time and
adjust for price changes. This measures the value of output using (typically) base
period prices. However, Usher (1980, 1994) reminds us that a meaningful measure of
growth arises as the answer to a thought experiment, and the “change in real income”
measure is at best a rough estimate of more precisely defined growth measures. This
argument is, again, due to Hicks (1940).
What are the thought experiments of interest? There are also at least two distinct
concepts of what is being measured by the concept of “growth”, even in a simple
model with only consumption—no saving or investment—and no inflation (but
allowing for relative price changes). The first measure of growth is a measure of the
welfare change arising from a different production/consumption bundle. The second
measures the change in the economy’s productive capacity.5
The issue of multiple goods has not been explicitly dealt with in our discussions of
dynamic measures of income thus far: once we allow for more than one consumption
good, we are led to the important index number issues that require a detailed
discussion of growth definition and measurement. As expounded by Hicks (1940),
and by Usher (1980, 1994), statistics of real consumption track changes over time in
the location of the production possibility curve (when measuring changes in
productive capacity), or movements of the bundle of goods consumed through the
space of assumedly invariant indifference curves (when measuring welfare).6
Figure 2 shows the two growth measures, in comparison to a “money growth”
measure in which no normalisation of prices is undertaken. Between two consecutive
periods “1” and “2”, technological change (or resource discoveries) result in a shift
5
This distinction was first made clearly by Hicks (1940), in his discussion of market-price vs factorcost measures of income.
6
A whole host of index number and measurement issues regarding welfare, income and output are
presented in Hill (2000), including the divergence between changes in real income and welfare over
time when tastes are not assumed invariant. We do not pursue those issues further here.
14
outward of the production possibilities boundary. Points of tangency with a social
indifference curve indicate the social optimum in each accounting period. Using the
relative price defined by that tangency, we derive money income in each period (YM1
and YM2) as per Figure 1.7
7
Readers should note that the diagram indicates the importance of the choice of numeraire. In this
example, money income increases notably when good 1 is chosen (as shown) but if good 2 were
chosen, income in the scenario shown would not change.
15
C1
YP
2
YU2
YM2
YM1=YU1
=YP1
U1
U2
C1 *
PPF1
PPF2
C2
C2 *
D
Figure 2
16
However, as has been indicated, defining a meaningful measure of growth as opposed
to income generally requires the specification of a set of reference prices. (Standard
practice is to choose the relative price from the base year.) Given this, we construct
the productivity measure YPi for any year i, to represent the largest value of goods that
could be obtained with the technology in that year. Similarly, YUi in year i represents
the value of the cheapest bundle of goods at the given reference prices that would
leave the representative consumer as well off as s/he actually is in that year. The rate
of growth of either measure is then simply the difference between the measured value
in two periods divided by the value in the initial period, that is:
(YP2 – YP1)/ YP1 and (YU2 – YU1)/ YU1
Note also that the use of reference prices is not an issue of inflation adjustment, in
which nominal magnitudes are converted to real ones for purposes of comparison.
Here, attention is paid to a reference relative price, rather than a reference set of
nominal prices. But inflation-adjustment—in which the period 1 relative-price line
runs through through the actual consumption bundle chosen in period 2—is in fact the
“approximate” real growth figure that would be measured in actuality.
What of introducing capital goods into the problem? This adds a whole set of extra
measurement and interpretation issues that shall be covered in Section 5.
4.
Income: A Confusion of Definitions
In this section we examine how the themes of income presented in the previous
section relate to specific definitions used in the literature. In particular, we identify a
slipperiness in terminology, one that can be a barrier to constructive engagement
between analysts. We highlight the important—but under-recognised—differences in
perspective that result by considering income at the national rather than personal level.
Then we attempt to carefully compare and contrast the particular definitions.
As already outlined in the previous section, multiple definitions of income and growth
exist in the economics and national accounting literature. In this section we explore
17
these definitions, and try and resolve some of the resulting confusion and ambiguity,
and highlight both the differences, and the connections, between particular definitions.
4.1
Terminology
It is hard for analysts to discuss and debate how to define and measure income when
there is no agreed terminology to use for the various concepts. Two alternative but
standard concepts or themes of income in the economics literature have already been
stressed in the foregoing, one being the accounting-based measure labelled here as
SHS income, and the other being the consumption-based Hicksian measure. But how
do these themes relate to the definitions individual economists employ in their
discussions of national income? The answers get a little complicated.
Hicks states that the “purpose of income calculations in practical affairs is to give
people an indication of the amount which they can consume without impoverishing
themselves” (p.172). Hence the use of this notion as a key common theme in Hicks’
discussion of income. But within this theme, if we ask what did Hicks actually define
income to be, his definitions are numerous and context specific. For example, his
Income No.1 is “thus the maximum amount which can be spent during a period if
there is to be an expectation of maintaining intact the capital value of prospective
receipts” (p.173); in other words, the keep-wealth-constant dictum, where wealth is
explicitly forward-looking. Allowing for changing interest rates, Hicks’ Income No. 2
is “the maximum amount the individual can spend this week, and still expect to be
able to spend the same amount in each ensuing week.” (p.174). Here, Hicks has
moved from one “Hicksian sub-theme” (constant wealth) to the other (non-declining
consumption). Consideration of price changes leads him to define Income No. 3,
which “must be defined as 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, emphasis in original.) Durable consumption goods add an
extra degree of complication, forcing him “back on the central criterion”, of being as
well off after as before. “By considering the approximations to this criterion, we have
come to see how very complex it is, how unattractive it looks when subjected to
detailed analysis.” (p.176.)
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This negativity about accurate measurement of the central concept pervades Hicks’
writing.
“It seems to follow that any one who seeks to make a statistical calculation of
social income is confronted with a dilemma. The income he can calculate is
not the true income he seeks; the income he seeks cannot be calculated. From
this dilemma there is only one way out; it is of course the way that has to be
taken in practice.” (Hicks 1946, p.178.)
(Modern writers on the subject often seem, it must be said, rather more sanguine about
these difficulties.)
Finally, he concludes by discussing “the way that has to be taken in practice”: he
observes that these measures are conceptual ones, ex ante measures of income,
unmeasurable in general circumstances. The compromise measure he presents, the ex
post approximation to the desired measure (in this case, Income No. 1), is
consumption plus capital accumulation: that is, a measure indistinguishable from the
SHS measure defined above. And this accounting procedure “can only result in a
statistical estimate; by its very nature, it is not the measurement of an economic
quantity.” (p.179.)
The strong impression that can be drawn from Hicks’ discussion of income in Value
and Capital is that he is at pains to distinguish between income as an economic
concept, an answer to a question about how much can be consumed, and income as an
accounting construct, a measured account of what has occurred that can only ever
approximate the economic magnitude he refers to as the “central concept”. He goes to
some lengths to identify different ways in the economic question and answer can be
specified, depending on circumstances, and that different variants of the ex post
formulation will correspond to the particular ex ante version.
Unfortunately, the result has not been a recognition that there is a series of Hicksian
incomes, thematically linked but differing in details; instead there is an almost
arbitrary use of the term “Hicksian income” in the literature to denote a number of
different income concepts or measures, leading Bradford to refer to a “confusion in
19
professional thinking on this subject” (Bradford, 1990, p.1183). This remark came in
the context of an exchange between Eisner (1990), Scott (1990) and Bradford (1990)
on extended accounting and the measures underlying the accounting exercises. Eisner
conflates the ex ante constant consumption definition with the ex post capital
maintenance definition—he refers to it as the “Hicks-Haig-Simons” definition—a
position both Bradford and Scott take issue with. However, Eisner is not alone: in
fact, this mixing up of the two definitions is common practice in the economics
profession. For example, Aronsson, Johansson and Lofgren (1997, pp. 95-6) state
“(Hicks and Lindahl both) defined income as the maximum amount you can consume
and still keep the capital intact (interest on the capital). Intuitively, it equals current
consumption plus net capital accumulation since, as long as net investment is kept
non-negative, the capital is held intact.”8
This tendency to blur the different income concepts is presumably attributable to the
fact that all of these interpretations are variations on the concept of income as a return
to wealth, the predominant theme in economic discussions of income. Yet they all part
ways when the fine details are examined. Bringing them together as a singular
concept, rather than related concepts, over-simplifies Hicks’ careful reasoning: he was
interested, first and foremost, in maintaining consumption possibilities. This raises
two caveats with respect to the above position. Firstly, keeping capital intact satisfies
a non-declining consumption rule in particular circumstances but not universally, as
Hicks recognised. Secondly, even assuming intact capital is sufficient, the “intuitive”
step they then make is between Hicks’ ex ante ideal measure, and the ex post
approximation. They are not identical: the relationship between these is followed up
in subsection 4.3.9
Nordhaus (1995) adopts yet another terminological position. As with Eisner and
Aronsson et al, his definition of the label “Hicksian” is a combination of Hicks’s ex
ante Income No. 1 (maintaining capital intact) with his ex post approximation of this
8
See also the discussion of income in Hartwick and Hagemen (1993).
Further difficulties arise in their interpretation once heterogeneous capital and technological change
are introduced. Some discussion of measurement and interpretive issues concerning technical change
appear later in the paper.
9
20
measure being the sum of consumption plus capital accumulation;10 in this regard he
adopts a quite conventional position. But where these other authors argue (implicitly
or otherwise) that this measure is designed to represent a constant consumption
measure, or at least an approximation to one, Nordhaus takes a different view. For
him, this formulation of “Hicksian income” serves as a production-based measure of
income, much in the way Bradford attributed this characteristic to SHS income.
Nordhaus then describes an alternative utility-based or sustainable-consumption
measure of income, and attributes it to Fisher rather than Hicks. (While Nordhaus
acknowledges that Hicks’ Income No. 3 is similar, he maintains a labelling practice
whereby he substitutes Hicksian for SHS, and Fisherian for Hicksian, in the above
terminology.)
In other words, Nordhaus regards Hicks’ ex ante and ex post definitions regarding
Income No. 1 as being essentially equivalent. In the terminology being used here, the

K
capital-intact Hicksian income YHicks
is (i) interchangeable with the YSHS measure,
and (ii) it is a productivity-oriented measure with its roots in national accounting
practice and hence unrelated to sustainability measurement. This second component is
an eclectic interpretation. Other authors explicitly write in these terms in order to
address sustainability themes. For Nordhaus, it is what he calls Fisherian income—the

C
consumption-annuity measure we have labelled YHicks
—that is of interest in the
context of sustainability. How does he distinguish the two in practice, given Hicks’
scepticism regarding the measurement of true sustainable consumption? Nordhaus
conceptually bases his Fisherian measure on a growth model presented by Weitzman
(1976) (this model will be discussed in detail in Section 5.2, including its relevance as
a sustainability measure); empirically it is distinguished by having a much broader
measure of capital than the produced capital measure used in the national accounts, or
some narrowly defined extensions to it. Most importantly in Nordhaus’s eyes is
knowledge capital (capitalised technical change).
10
See his quote on p.3 (Nordhaus 1995) in which he combines two different definitions of income from
Hicks’ book.
21
The end result of this selective review of labelling practices in the literature is, quite
clearly, that there exists a confusion in terminology that exacerbates a confusion in
conceptual clarity, and leads to inconsistent methods and interpretations. At one
extreme is the strict national accounting measure GDP = C + I, and at the other
extreme is an economic measure based on Hicks’ “central criterion”, which is
C
formally defined here as YHicks
 max C (t ) s.t. C  0, t . The difficult and contested
area is virtually everywhere in between. Economists writing on national income
definition and measurement move somewhat arbitrarily from these extremes to the

K
varieties of compromise measures we have labelled YHicks
and YSHS , choosing their
own labels and specific emphases on what should be included and how the resulting
measures should be interpreted.
4.2
From Personal Income to National Income
Definitions and concepts are affected by the degree of aggregation involved. The
circular flow version of income is explicitly a measure of aggregate income. By
contrast, the economic themes were explored initially as measures of income for an
individual. This distinction has important implications. There are definitional issues
and aggregation issues that arise once one moves from the individual level to the
social level. Bos (1997) has argued forcefully that national accounting practice and
economic principles operate in different directions: while they use similar terminology
and what may look like similar conceptual apparatus, the interpretations and
applications of these terms and tools can often be significantly different from one to
the other. One reason he argues these discrepancies have arisen is that economists
started out thinking about how to define income for an individual, then generalised
this reasoning to the national level. In doing so, they impose their reasoning of what
income should be a measure of, onto the national accountants’ conception of what
national income is a measure of.
The Schanz-Haig-Simons formulation of income (consumption plus the change in
wealth) is essentially a public finance concept in origin, with income being defined as
a basis for taxation. The intuition here is that income is the accretion to a person’s
wealth, regardless of how it is then used (Musgrave and Musgrave 1982, Ch.16). The
22
intent, in this literature, is to define income as the base for personal taxation, and in
that regard “All accretion should be included, whether it be regular or fluctuating,
expected or unexpected, realized or unrealised.” (Musgrave and Musgrave 1982,
p.344.)
While national income identities are structured along similar lines, being the sum of
consumption items and investment items, national accounting practice draws
boundaries around consumption and production activities that may not match how
they are drawn for personal taxation purposes. Moreover, while “all accretions should
be included” in personal income as a tax base, what constitutes capital in the national
accounts is considerably different. At the personal level, SHS income involves adding
consumption to an individual’s change in wealth, while at the national level it refers to
the change in a country’s capital stock. In the first instance, as already noted, the
public finance principle is to include all accretions in income; at the national
accounting level, it is orthodox practice to exclude all anticipated capital gains.11
Once we move into examining Hicksian themes, we find further difficulties in
translating the concept(s) from the personal to the social level. In particular, the

K
relationship between the capital-constant version YHicks
and the consumption-annuity

C
version YHicks
changes with the level of analysis. There are several reasons for this.
First, what is the “capital” being held constant in each case? Hicks writes of “the
capital value of prospective receipts” as we saw in the discussion of terminology. This
is essentially a partial equilibrium perspective, where the receipts themselves can be
regarded in the first instance as essentially exogenous, with the total capital value only
being influenced by consumption decisions. At the macro level, the value of capital is
endogenous (at the margin as well as in the aggregate), as is the rate of return.
11
In part, this reflects the shift to general equilibrium considerations implied by considering income at
a national scale: a capital gain accruing to me can be realised by me acting in isolation in the year in
which it occurs, and therefore represents a change in my immediate consumption possibilities (personal
income). However, if the stock market booms during a year and personal incomes increase for all
shareholders, they cannot all realise the capital gains simultaneously without driving the asset values
back down. Thus, the capital gains do not represent an immediate increase in consumption possibilities
to the nation. Moreover there are aggregation issues: in a closed economy, if gains to me come at the
expense of someone else, gains at the individual level thus represent transfers at the national level. This
is taken up in Section 6.1 (part b).
23
Nordhaus (1994) raises the issue of differing time horizons at each level, noting that
with the finite time horizon of the individual (as opposed to the infinite time horizon
that can be assumed in the first instance for a nation or society), the individual’s final
period consumption (income) must just equal their wealth.12 However, that
observation itself does not isolate the problem in switching perspectives.
If we think of wealth as a stock to be drawn upon, and to which there is a given rate of
return, the appropriate consumption-annuity income in this instance would involve a
degree of capital consumption in each period. With constancy and complete certainty
over the lifetime, a consumption annuity would be computed for the entire length of
the individual’s life, with the final period’s income consisting entirely of capital
consumption, as Nordhaus noted. But why this matters is that it breaks the symmetry

K
at every point in time between the capital-intact measure YHicks
and the consumption
C
annuity measure YHicks
.13
4.3
Relating the Themes of Income to Each Other
The previous subsection contained some suggestions as to how various measures of
income may be related to one another, and how strong that relationship may be. We
address the relationships between alternative measures more precisely here.
The initial definition of income introduced was the one arising from the circular flow
of income construct. Here, income is equivalent (by construction) to the value of
production. This is done by defining the components of national income (consumption
It can be thought of the following way. The final period’s consumption entails consumption of all
remaining wealth. With consumption in all periods equal, this means that consumption in each period
before the last will involve some combination of “pure harvest” and “capital consumption”, with capital
consumption increasing over time and harvest reducing to zero in the final, but aggregate consumption
for the individual remaining constant.
13
Hicks, in writing of “maintaining intact the capital value of prospective receipts”, seems to have an
infinite time horizon in mind. It may be that with the uncertainty of the end-date of a lifetime, or the
possibility of a bequest motive, it is a sensible approximation to work on the basis of maintaining the
capital value intact for an individual. The argument above presumed the final time period is known in
advance, and no bequests are given.
12
24
and investment) in such a way as to correspond conceptually with aggregate factor
incomes.
Constructing income as the sum of consumption and investment leads naturally to the
next definition, the one we have referred to as YSHS . By construction, SHS income and
circular-flow income appear identical. However, there has been a subtle but vital
shifting in conceptual gears from one to the other. Firstly, as already noted, SHS
income is a measure of personal income that then gets aggregated—with “person”
being replaced by “economy” (albeit often only implicitly)—in discussions of national
income, whereas the circular-flow constructs of GDP and NDP are explicitly
aggregate, deliberately designed to measure activity in a national economy. The latter
accounting measures are constrained in their design and construction by accounting
identities, whereas thinking in economic terms involves thinking of income as a
return to wealth; not as an accounting construct designed to match the value of
production. Because of these differences, each involves conceptually different
measures of consumption and capital, in ways that have already been discussed.
Bos (1997) is a useful reference for readers wishing to examine this issue further. He
points out, for example, that valuation at market prices by national accountants is
purely descriptive: no normative content is assumed or implied by such valuation.
Economists typically think in terms of shadow prices and net present values—that is,
in optimising and forward-looking terms—that do not fit within the national
accountants’ methodology. This distinction is crucial: prices of capital goods to
national accountants are taken as exchange prices, not capitalised values of future
streams of returns.
This does not mean national accountants do not want their constructions interpretable
in economic terms. On the contrary, there is a general consensus that if depreciation
can be measured accurately, something approaching a sensible economic magnitude
has been calculated. Examples from the national accounting literature are not hard to
find. Harrison (1993, pp.23-4), for example, notes that:
“(National) Income in this case is not as Hicks defined it, namely, the amount
that can be spent and still leave one as well off at the end of the period as one
25
was at the beginning. …Hicks’s income can be approximated by deducting an
allowance for the consumption of fixed capital from primary income. The
resulting aggregate is known as net domestic product (NDP).”
Fraumeni (1997, p.9) in turn remarks on sustainable income “where depreciation is
subtracted from GDP to derive net domestic product and net domestic income—a
rough measure of that level of income or consumption that can be maintained while
leaving capital intact.”
However it is clear that the accounting nature of conventional NDP—where capital
and consumption are defined to conform to the requirements of the respective
accounting identities and valued using market rather than shadow prices, etc.—
renders it only a crude approximation to the economic concept of Hicksian ex post
income, or YSHS . This in turn is only an approximation of Hicks’ “central criterion”.
To which we now turn: how are the Hicksian consumption (or utility-based) themes of
income related to YSHS ? Or, using different terminology, how is Hicksian ex ante
income related to Hicksian ex post income? We base our discussion here on the
premise that Hicksian income concepts are underpinned by concerns about
sustainability. Both Scott (1990) and Eisner (1990), while disagreeing about how to
define income, agree that sustainability is the core concern in their attempts to revise
how it is measured. Moreover, the blurring of the distinction between Hicksian and
SHS income, by, for example, Eisner and Aronsson et al., is (presumably) motivated
by the view that the consumption-plus-capital-accumulation measure provides a
suitable approximation to a sustainable consumption measure. That is, that ex post
income, using Hicks’ labels, is a useful approximation to the desired ex ante income.
At the very least, it provides an indication of whether capital is being accumulated,
maintained, or consumed.
In terms of the notation and terminology being employed here, recall the distinction


K
C
between YHicks
and YHicks
. A number of analysts seem to treat YSHS as a close
K
approximation to YHicks
. The argument is that at the very least, the K term in YSHS
26

K
enables us to see whether we are above or below YHicks
. From this, we can draw and
inference regarding sustainability, based on whether we are “consuming our capital”
or simply living off it.
However, the difficulties with taking too literal a sustainability interpretation of this
approximate measure have already been identified. Hicks himself departed from the
constant-wealth version (Income No. 1) to allow for the effects of changing interest
rates and prices: only with these held constant will constant wealth necessarily imply a
constant stream of consumption. And even then, for reasons discussed in the previous
subsection, the capital must be defined, measured, and valued appropriately in order
for the sustainability interpretation to be admissible. Not only does this not reflect
national accounting methodology, but convincingly achieving such a measure of
national capital represents a major task for those proposing to amend the national
accounts in order to strengthen their interpretation along sustainability lines.
In conclusion, if we can reliably convert GDP to NDP as per the existing national
accounts—that is, if we can accurately calculate depreciation of the measured capital
stock—we are still some distance from a measure of YSHS that economists would
regard as meaningful. This in turn would only be an approximation to a constant


K
K
capital measure of income, YHicks
. Finally, YHicks
needs key assumptions to hold for it

C
to be equivalent to the consumption annuity measure YHicks
.
In other words, the distance between the conventionally accepted accounting measures
of GDP and NDP, and the economic “central criterion” of sustainable consumption, is
potentially vast.
5.
Income and Capital Goods
5.1
Why Include Capital in Income?
A key distinction between our two key themes of income ( YHicks or ex ante, versus
YSHS or ex post) is between a consumption only measure, and one that includes capital
accumulation. Whether we are interested in extending conventional GDP to be a
27
better measure of welfare, or an improved indicator of sustainability, the key variable
in either case is consumption. Capital accumulation is only ever a means to an end.
“Repeatedly and unabashedly the national income statistician calculates a
number he calls net national product by adding in the value of the nation’s net
investment to its consumption. What does this single figure measure? The
usual welfare interpretation of index numbers can perhaps be used to excuse
combining apples and oranges, but it falls short of providing an adequate
justification for NNP. Economic activity has as its ultimate end consumption,
not capital formation.” (Weitzman 1976, p.156.)
There are really two main options in the interpretation of investment in terms of
consumption opportunities. They are, in turn, treating investment goods as (i)
consumption opportunities foregone today, or as (ii) consumption opportunities
increased tomorrow. We shall investigate these in turn, and in a later section assess
their respective implications for particular accounting practices and interpretations of
the results.
To appreciate this issue, refer again to Figure 1. The welfare interpretation in the case
of two consumption goods has already been outlined. However, if C2 is a capital good
(so that C 2*  K * ) that—by definition—is used to produce future consumption goods
at the expense of being available for present consumption, this interpretation becomes
problematic. The amount OA no longer measures current consumption equivalents
using a single numeraire. OA only represents consumption possibilities if we could (i)
devote all available resources to the production of consumption goods, and (ii)
transform them at the rate at which they are transformed locally at the optimum.14 As
Weitzman (1976) notes, diminishing returns imply that the lower amount OB
measures the total amount of consumption goods that the economy can actually
produce given its resource endowments and its technology.
The question then is, what is the justification for (and thus, the economic significance
of) combining today’s capital accumulation with today’s consumption into a
seemingly atemporal index called “national income”? How does capital investment
today relate to current welfare and/or future welfare and/or the potential to maintain or
14
The transformation ratio given by the slope of AD.
28
increase consumption levels? In other words, what broader interpretation can be given
to income expressed in its ex post (or SHS) form?
We present and contrast two alternatives, the intertemporal interpretation and the
atemporal one. Presenting the former first, we turn to Weitzman (1976).
5.2
The Growth-Theoretic Approach
One way of regarding Weitzman’s paper is as an attempt to reconcile the measured
form of income that combines consumption and capital goods ( YSHS ) with the

C
conceptual ideal, the consumption-annuity measure YHicks
. (Strictly speaking,
Weitzman refers to what the national accountant produces, implying conventional
NDP/GDP aggregates, but his analysis and interpretation require a more extended
economic measure of YSHS that goes beyond conventional accounting practice. In
particular, all consumption must be attributable to an underlying capital stock and thus
all changes in the capital stock must be appropriately defined and measured.)
In order to reconcile these measures, Weitzman in effect compares two hypothetical
economies. One—“Growthland”—experiences consumption C G changing over time,
driven by capital accumulation K G (positive or negative), while the other—
“Hicksville”—maintains constant consumption C H over an infinite time horizon. Let
both economies start at time zero with equal national income so that
Y G (0)  C G (0)  K G (0)  Y H (0)  C H .15
Weitzman demonstrated that the present value of Hicksville’s constant consumption
path C H over an infinite horizon was just equal to the present value of Growthland’s


actual optimal consumption path C G (0),....., C G () . NDP in a growing economy
thus indicates the level of consumption which, if maintained at a constant level
forever from “today”, would generate a present value of welfare equal to that of the
competitive trajectory from today to the infinite future. Put another way, current
15
By income here, we refer to conventional GDP. However, by virtue of a series of simplifying
assumptions, GDP, NDP and SHS income are all equivalent.
29
income, expressed as the Hamiltonian function of the underlying dynamic
optimisation problem, just represents the “return to wealth” of the economy, where
wealth equals discounted future consumption, and investment can legitimately be
added to consumption in its capacity as an exact measure of the present value of future
consumption.
Other authors such as Hartwick (1990) and Maler (1991) have generalised
Weitzman’s analysis. In particular these authors generalised the objective function and
explicitly modeled the use and measurement of items outside the conventional
national accounts such as natural resources and environmental amenities. Where
Weitzman relied on a linear objective function U(C) = C, to show that the
Hamiltonian of the intertemporal optimisation problem was equivalent to the return to
wealth, other authors present a more general utility function U(C), and then linearised
using U(C) = UC.C.
The Hamiltonian of this problem is of the form H  U (C )  K . (Here,  is the
shadow value of capital. Note that the variables in this expression are functions of
time, e.g. U C (t ) , but here the time notation has been suppressed.)
Using the linear approximation U (C )  U C .C and the first order condition   U C ,
we can see the “national income” form of the normalised Hamiltonian as follows.
NDP 
H
 C  K
UC
While typically derived in the literature as NDP (or NNP) this is not a standard
national accounting measure if the model includes elements in the consumption or
capital terms that are not part of the standard definition of national income. In order to
keep the distinction clear, we shall denote the Hamiltonian expression as
*
YWHM
 C *  K * (where WHM refers to Weitzman/Hartwick/Maler16, and the
16
The choice of these three authors to name this particular version of income is perhaps arbitrary.
Solow (1986) arguably brought Weitzman’s result to the attention of authors who have since pursued
30
asterisk denotes optimal values of this variable according to the optimisation problem
defined by the Hamiltonian). Note that in most current models of this nature, the
return to wealth interpretation is now one in which today’s income is a return to future
utility, rather than the value of future consumption.
The Hamiltonian approach has inspired an extensive literature in which issues of
extended accounting have been explored, in particular in the field of natural resource
accounting. Recent surveys and extensions of this literature, and its potential
implications for revised national accounting procedures, are contained in Aronsson,
Johansson and Lofgren (1997), Hamilton (1994), Atkinson, Dubourg, Hamilton,
Munasinghe, Pearce and Young (1997) and Hartwick (2000).
What is important to note about the Hamiltonian approach to income definition is that
it admits a welfare interpretation, not a sustainability one. While it appears to provide
a rigorous means by which income in its SHS form can be regarded in quite precise
terms as a return to wealth (seemingly a very Hicksian interpretation), we note that the
Hicksian themes discussed up to now concerned income as sustainable consumption,
not income as consumption plus investment. As Aaheim and Nyborg (1995) point out,
Weitzman’s result does not reveal a feasible consumption level that can be maintained
in perpetuity; what it shows is the hypothetical constant consumption path that has
equivalent present-value-of-welfare implications to the actual consumption path the
economy is following.17 What this means is that in practice there is no guarantee that
consumption will be sustained at current levels even by following the accounting
revisions suggested by analysts using this framework. All that can be asserted is that
current income is proportional to discounted future utility.
this modelling strategy. But Hartwick and Maler both generalised Weitzman’s model and explored its
implications for national accounting practice, which is our concern here, hence the choice of their
names.
17
Several authors have presented Weitzman’s result as though it held in strict sustainable-consumption
terms. This error appears for example in Musu and Sinisalco (1996, p.28, emphasis added) where they
incorrectly assert that “if the NNP of each period is defined as the sum of the consumption and of the
net investment value when the relative price is efficient … then the NNP thus defined can be interpreted
as the maximum consumption which can be indefinitely maintained from each period onwards.” It also
seems to be what Nordhaus (1999, p.47, emphasis added) is saying when he remarks “when population
is constant, when the national accounts include all stocks of capital and other dynamic features that
affect production, and when market prices accurately capture the social value of economic activity …
the sum of total consumption and net capital formation is equal to the maximum sustainable level of per
capita consumption that an economy can maintain indefinitely.”
31
Of course, the potential for sustainability can be analysed within this framework;
examples of this include Solow (1986), Asheim (1994, 1997), Hartwick (1994, 1996)
and Pezzey and Withagen (1997). Such studies use the growth-theoretic framework of
Weitzman but incorporate reinvestment rules and/or international trade in order to
allow for capital maintenance; in this way they can examine how consumption is
related to constant capital (national wealth). Summaries of results in this area are
contained in Toman, Pezzey and Krautkraemer (1995) and Hanley (1999).
Weitzman (1997) positions himself in a terminological middle ground, referring to
sustainability in the context of his model as concerning a “generalised power of the
economy to consume”, as opposed to its ability to maintain a specific consumption
flow. By referring to sustainability in this way, no a priori restrictions are imposed on
changes in consumption over time. There is certainly no strong injunction to prevent
consumption declining over time as features in the Rawlsian-based sustainability
literature.
*
Finally, how does the measure YWSHM
compare to the measures previously presented?


K
K
The closest analogue is YHicks
in that in ideal circumstances, YHicks
is interpretable as a
*
return on social wealth, defined as the national capital stock K, while YWSHM
represents
a return to social wealth defined as discounted consumption/utility. But the

K
circumstances where YHicks
is a return to capital are precisely those where


K
C
YHicks
= YHicks
. Thus, in principle, the two “return to wealth” concepts differ by virtue
of the different concepts of capital/wealth they refer to. In terms of practical
implication they differ in that one is meant to yield an actual consumption annuity,
while the other yields only the stationary equivalent of a consumption annuity.
5.3
The Atemporal Perspective
Weitzman’s neat result creates something of a quandary that has gone almost entirely
unremarked in the literature thus far. National accounting has already been argued to
be a form of historical scorekeeping, unconcerned with what will happen in the future.
32
Even Hicks, whose conceptual definitions were explicitly based on intertemporal
reasoning, stressed that in measuring income what mattered was what had happened,
not what would (or might) happen.
This emphasis on history has the effect of turning the conventional injunction in
economics to ignore the past—“let bygones be bygones”—on its head. In the
conventional approach to measuring income it is the future, or expectations of it, that
should be ignored: the dictum seems to be to “let maybes be maybes”.18 In this
atemporal view, how are we to justify the addition of capital goods to consumption
goods in an aggregate index that is meant to capture more than simply the value of
total output? A representative example is Scott (1990, p.1174, emphasis added) who
writes (with no reference to the Hamiltonian literature): “Generally it would be a
reasonable first approximation to assume that a dollar of investment thus switched
could provide a dollar of consumption. That, at any rate, must be the justification for
estimating income as the sum of consumption and investment.” Using this
justification, the dollar for dollar addition of consumption goods and investment
goods is based on an “as if” argument: capital goods are treated as if they are
equivalent to an equal amount of foregone consumption today. The diminishing
returns argument presented in Figure 1 has to be assumed away in order for this
interpretation to be admissible.
Weitzman’s (1976) analysis clearly breaks with this tradition. Building on
Samuelson’s (1961) interpretation of income as a “wealth-like magnitude”—clearly a
forward-looking interpretation—Weitzman spelt out the relationship between current
income and future consumption, and in doing so inspired an explicitly forwardlooking literature on national accounting. This distinction between the atemporal and
intertemporal perspectives still resonates in the literature today. Its implications for
income measurement will be followed up below.
5.3.1
18
Examples of “Atemporal-Perspective” Growth Models With Investment
Or perhaps: “Whatever will be, will be.”
33
Weitzman’s model and result has been used to motivate an intertemporal approach to
national accounting. What model might be representative (or at least indicative) of an
analysis within the atemporal accounting perspective? One useful example is that
presented in Usher (1980). We have already noted that Usher stressed the index
number issues originally raised by Hicks, and their practical implications. In
particular, in a model with only consumption goods, there are several possible
measures of growth, one measuring changes in productive capacity and one measuring
changes in welfare.19
The introduction of capital goods into the picture unsurprisingly makes things even
more complex when considering these alternatives. Usher argues that, in the context
of growth, the introduction of savings and investment to the analysis leads to an added
and important dimension (or distinction) in how we think about the change-in-welfare
and the change-in-productive-capacity measures of growth. This is that for the
productive capacity measure, distinctions between the end-uses of goods are
unimportant, whereas for the welfare measure such distinctions are crucial.
Given this, Usher advocates focussing on a welfare-based rather than a productivitybased concept of growth. In order to move his measurement in this direction, he
carefully distinguishes various ways in which capital and investment can be defined:
these include what he regards as welfare and productive capacity measures. From here
he attempts to relate the various possibilities back to an underlying (Hicksian) income
concept.
Usher (1980) raises four possible interpretations of investment from an accounting
point of view. They are respectively the change in wealth; the output of new capital
goods; the increase in the capital stock; and real saving. (For details on how Usher
distinguishes between these measures, see Usher 1980, Ch. 3) In contrast to the
Weitzman intertemporal model where measurement of capital is (in principle)
straightforward, Usher’s model present various ways in which capital can be
19
This seems to coincide with the general distinction we have been drawing between income measures
that are production based versus those that are consumption or utility based. Note however that in the
34
measured, with each measure corresponding to a different underlying measure of
income. Thus a key feature of Usher’s approach is that the nature of the income
measure depends on the capital measure used to underpin it.20
Usher’s preferred measure is the income measure based on the fourth interpretation of
investment (real saving), and emphasises the sacrifice of current consumption goods
involved in producing capital goods. This is precisely the atemporal view of
investment as consumption foregone today rather than consumption postponed, and
hence increased in the future.
Scott (1989) has also been cited as an advocate of the atemporal approach, and his
approach, like Usher’s, emphasises the complexity of measuring (changes in) capital.
He, like Usher, argues that we should proceed “as if” today’s investment could be
converted to an equivalent value of consumption, and that the task of calculating
income is to measure the “sustainable-consumption-equivalent” level of output (Scott
1990). Scott does this in two steps: first he divides conventional investment
expenditures into what he calls “maintenance” expenditures—those devoted to
restoring and maintaining the productivity of the capital stock—and “investment”
expenditures—those that increase the productivity of capital—and he classifies the
former as intermediate spending. Second, he justifies adding the latter magnitude
(investment) to consumption on the basis that with a fully maintained capital stock,
we can treat the extra output of investment goods as if it were increased consumption,
and regard the total as a yield on the capital stock. This does entail redefining what
counts as investment expenditure and, as noted previously, deflating it using a
consumption-goods price index. Scott is critical of the notion that exogenous technical
change can add to consumption growth: in his view the conventional “residual”
reflects a mis-definition or miscalculation of investment.21
5.3.2 Discussion
consumption-goods-only context, this distinction arises purely from index number considerations, not
from the specification of a point in time income measure.
20
In the standard growth theory model, capital is assumed to be homogenous.
35
Conventional one-sector growth models, often used in discussions of income
measurement and economic growth, express output in growth in terms of
consumption goods. Once differences between consumption goods—or between
capital and consumption goods—are allowed, then index number issues arise that are
often neglected in discussions of national income. Another problem that arises in a
multi-good context is the issue of diminishing returns between capital and
consumption goods. Acknowledging these issues—the index number problem, and the
existence of diminishing returns—then forces the analyst to frame the specific
question they think should be answered by the practice of national accounting: which
question you would like answered will then drive the choice of the preferred measure
to be used. These questions resolve around issues of output, welfare or sustainability
(and appropriate measures of the changes in these magnitudes over time).
An examination of different approaches to measuring these magnitudes has revealed a
tension between atemporal approaches—in which what happens this year is what
counts—and intertemporal approaches—in which magnitudes representing capitalised
values of things in future years can legitimately be added to consumption goods this
year.
How do these approaches relate to the objectives we highlighted earlier, namely
welfare (which could be regarded as an atemporal concept) and sustainability (an
explicitly intertemporal one)? It might be thought that the atemporal approach to
income measurement was a welfare-oriented one while the intertemporal approach to
income was aimed at being sustainability-oriented. This is a tempting conclusion to
reach, but mistaken. As noted already, Weitzman’s model is avowedly intertemporal.
In his view the very reason for adding consumption goods to capital goods in a
measure of national income is the fact that (in his model) investment embodies the
discounted value of increased future consumption. And yet, income in Weitzman’s
analysis does not admit of a sustainability interpretation: it is intertemporal welfare
that is the benchmark. In his words, “Net national product is what might be called the
21
This is an important point because it conflicts with much of growth theory, and with the practice of
analysts like Usher (1980) who use exogenous technical change as a litmus test to weigh the properties
of different measures of income. See Section 6 (and the appendix) for further discussion of this.
36
stationary equivalent of future consumption, and this is its primary welfare
interpretation.” (Weitzman, 1976, p.160.)
Regarding the possible interpretation of an atemporal measure, both Scott and Usher
appear to have a conventional Hicksian concept in mind. Usher’s stated interpretation
of his own preferred “real savings” measure of income is as follows: income measures
“the amount of consumption that could be obtained in the stationary state that would
arise if technical change, net investment and population growth ceased today”. (Usher
1980, p.92.)
What are the significant elements of Usher’s definition? Firstly, it is explicitly a
Hicksian (steady state) concept. Secondly, key variables are assumed constant.
Population growth is the easiest to “assume away”, and it would also be easy to handle
this variable differently; by, for example, recasting income in per capita terms and
then assuming that population growth remained constant. The assumption that
technical change has ceased represents the traditional, atemporal emphasis of Usher’s
analysis. (In the next section, we shall see that allowing for capitalised technical
change takes us into the realm of intertemporal measures.) Assuming net investment
is zero in the steady state is equivalent to Scott’s rationale that investment is added to
consumption “as if” it represented, dollar for dollar, the value of foregone
consumption.
The fundamental issue to be resolved is revealed as being the conflict between
economic concepts of income that are steady-state in nature (maintainable
consumption), and the actual measurement of income in a growing economy, in which
consumption flows and capital stocks are changing over time. Clearly, Weitzman and
Usher, as two representative authors, have resolved this conflict in different ways.
The two approaches identified above, atemporal and intertemporal, essentially involve
different ways of approximating steady states in dynamic contexts. Weitzman’s quote
above identifies the intertemporal approach as measuring a stationary equivalent
(present value) of future consumption. By contrast, Usher advocates what we might
label a stationary state equivalent in which, by treating capital accumulation as
37
present consumption foregone (thus making current investment a proxy for what could
be additionally consumed), it is as if the economy is on a constant consumption path.
5.4
Summary
In this paper we have seen that one single and central concept in economics, national
income, is open to a variety of conceptual definitions. These definitions provide in
turn a range of implications for the definition and measurement of the components of
income (particularly consumption and investment) and the interpretations of the
resulting aggregates. Moreover, conceptual confusion and idiosyncratic approaches to
terminology have led to some disagreements being over-emphasised22, with others
being perhaps underplayed or their significance under-appreciated.23
If the difference between the national accountants’ approach to income and the
economists’ approach can be summarised succinctly, it is probably in the following
way: national accountants view income as a measure of the value of production while
economists view income as some form of return to wealth. In the latter view, the
nature of national wealth, the connection between wealth and income, and the
rationale for combining capital and consumption goods into a single index are topics
for which there is as yet no consensus. For example, the standard SHS measure treats
wealth as current capital, and income is an approximation to the return to that wealth,
depending on whether net investment is positive, negative or zero. Hicksian income,
as defined thus far, is defined in consumption units as an exact return to wealth
(which can be thought of as a capital stock or as capitalised future receipts). Income in
Weitzman’s terms is the sum of consumption and investment, measured as a return to
capitalised future utility.
The result of all these different perspectives is a confusion in the literature between
those who advocate (or assume) a welfare emphasis or a sustainability emphasis in the
interpretation of a proposed idealised measure; not to mention a difference—
important but largely unrecognised—in possible conceptual frameworks, between an
22
For example, is adding capital gains into a forward-looking measure of income any more problematic
than adding the net output of investment goods?
38
atemporal perspective in which income is strictly a “this-year” phenomenon, versus an
intertemporal perspective in which “present value” magnitudes are legitimately added
to magnitudes representing current output. Both of these frameworks represent ways
that economists have tried to get “Hicksian” (or return to wealth) interpretations from
accounting-derived measures of national income.
The interpretations of these two frameworks or perspectives in terms of the objectives
(welfare and sustainability) is one key distinction. Two key authors in the atemporal
tradition, Usher and Scott, seem to be intent on constructing measures that reflect the
Hicksian “consumption annuity” measure presented earlier. If the economy was in
such a steady state that consumption and the capital stock were both constant, then an

K
C
accurate measure of income, defined as YHicks
, would represent a measure of
 YHicks
maximum sustainable welfare, since in a pure Hicksian steady state welfare and
sustainability are not distinct. This explains why some extended measures of income
have been explicitly titled “measures of sustainable economic welfare” (see for
example Stockhammer, Hochreiter, Obermayr and Steiner 1997). Given that the
atemporal-perspective measures can only be approximations in a dynamic setting to
the steady state consumption annuity measure, it is not clear how closely these
measures approximate the underlying concepts they are intended to measure. And
clearly, away from the steady state, one indicator cannot successfully measure both
welfare and sustainability simultaneously.
The effect of this is that the atemporal (stationary-state equivalent) approach blurs
welfare and sustainability by claiming to approximate a maximum-sustainableeconomic-welfare program. By contrast, it becomes clear with the intertemporal
approach that welfare and sustainability considerations need to be explicitly
distinguished.24
23
For example, the repeated blurring of the distinction between ex-post and ex-ante Hicksian income
definitions.
24
In the context of explicitly intertemporal models, Asheim (2000) and Pezzey (2004) have
categorised a series of concepts of income based on sustainable consumption, on several versions of
returns to wealth/welfare (as capitalised consumption, and as capitalised utility, with alternate
approaches to discounting), and on net output. This “family” of income measures is distinguished for
different reasons than (say) Usher’s alternatives, which were distinguished by different underlying
39
TABLE 1 AROUND HERE
6.
Empirical Implications
6.1
Capital Theoretic Controversies
The two alternative theoretical perspectives we have identified in national income
analysis have been shown to be differentiated by the role played by the future.
Discounted future consumption is the exact measure of wealth (or capital) used in the
“return to wealth” measure proposed by Weitzman, and (as we shall see) changes in
future consumption prospects then have implications for current income. Usher, by
contrast (as one example), follows national accounting practice by explicitly
disavowing any effects of future changes on the current measure he is constructing.
Clearly, different concepts of capital are at play here, and there are measurement
consequences arising from which perspective one chooses to adopt.
As remarked already, the motivation for “atemporalists” like Usher and Scott for
adding investment goods to consumption goods is that, diminishing returns
notwithstanding, it is “as if” the economy had potential current consumption prospects
available to it equivalent to the total output of current consumption and capital goods.
One implication of this is that both these authors are critical of the standard practice of
deflating the price of investment goods over time by a price deflator defined in terms
of investment goods. To promote the desired interpretation of investment as
consumption foregone, they advocate using a consumption-goods price index to
deflate the nominal value of investment.
This is not necessarily in conflict with the intertemporal perspective: the shadow price
of capital in a Hamiltonian model is a relative price of capital and consumption goods.
But the assumed homogeneity of capital in many of these stylised models has meant
concepts of capital and investment, and Pezzey shows clearly that the choice of measure used, even in
simple deterministic settings, has empirical significance.
40
that such issues have received little attention by authors working in this area. Recent
work in this vein with multiple capital goods requires complex restrictions on prices
(using, say, Divisia price indices) to maintain the basic interpretation.
a)
Technical Change
An area where differences become more marked is that of technical change. Usher
opposes the incorporation of any effects of future technical change on a measure of
current income, to the point of choosing one measure of capital (and hence income)
over another based on the fact that it did not capitalise future technical change.25
Intertemporalists, by contrast, are much more enthusiastic about accounting for
technical progress. As remarked previously, this is more consistent with economic
principles than it is with standard national accounting. Nordhaus (1995) argues for its
inclusion in his measure of “Fisherian income”. Weitzman (1997) does a back of the
envelope calculation to compute the likely magnitude of technical change on social
wealth (and hence potential consumption). Both Nordhaus and Weitzman draw the
conclusion that the potential upside, in sustainability terms, of ongoing technical
change can dwarf any sustainability threat resulting from resource depletion and
environmental degradation.26
b)
Capital Gains
Another controversial issue involving capitalisation of expected changes in the future
concerns capital gains. Conventional national accounting wisdom here is clear: capital
gains do not represent income from current production and thus do not count in
national income.27 Employing an intertemporal perspective, as Weitzman and others
Usher (1980, Ch. 3) notes the similarity between his “real saving” measure of income and the
“change in real wealth” measure, which derive from slightly different interpretations of investment. He
regards their main difference as being in their response to technical change; namely, the real wealth
version capitalises (anticipated) technical change while the real saving version does not. Based on the
presumption that we do not wish to say real income today is higher simply because we expect technical
change tomorrow, Usher endorses the latter.
26
It should be noted that Scott, an atemporalist, takes a distinctly heterodox position with regard to the
appropriate measurement of investment and the effects of technical change. He is particularly
concerned with appropriate measurement of technological change ex post, arguing that the conventional
“Solow residual” represents statistical mismeasurement, not the effects of technical change. Readers
should consult Scott (1988) and subsequent writings for details.
27
Note that this is another issue where the personal-versus-national perspective is an issue. Defining
and measuring personal income, as per the public finance literature, typically involves measuring all
changes in personal wealth including those arising from capital gains.
25
41
do, complicates this. However, the first authors in the Hamiltonian literature to
explicitly address the issue of capital gains maintained a position consistent with
national accounting orthodoxy. In considering depreciation of the (natural) capital
stock, Maler (1991) for example draws clearly the distinction between measuring the
value of the change in the stock as opposed to the full change in the value of the
stock. The full change in value includes both depreciation and capital gains and is,
Maler argues, an inappropriate measure of depreciation. Usher (1994), in an
evaluation of the Hamiltonian approach to defining income, maintains that the
inclusion of capital gains in income violates what he calls the “this yearness” of
national income.
Yet the very nature of the intertemporal perspective brought to bear on the analysis of
national income via the use of optimal control methods calls into question the
traditional concept of national income in which “this yearness” is a defining
characteristic of elements to be included. Bradford (1990) makes this clear when he
presents the argument against the incorporation of capital gains in income as follows:
“I think the traditional objection to inclusion of revaluations … in a measure of
national output goes something like: ‘The extra value is not really “output” this year;
it is the present value of “output” that will appear in the future.’” (Bradford 1990,
p.1186)
In the intertemporal perspective, this reasoning applies similarly to the interpretation
(and inclusion) of new capital goods, and to technical change as well. To make the
point as obviously as possible, consider the argument against inclusion of capital
gains, namely that aggregate capital gains cannot be converted to increases in
aggregate consumption simultaneously. If the share market rises in value for instance,
not all of these gains can be realised instantaneously—a mass decision by
shareholders to sell all their higher-valued shares simultaneously will result in share
prices being driven back down again. This is simply another aspect of Bradford’s
observation that revaluations represent capitalised changes in future consumption
possibilities, not an equivalent amount of current consumption possibilities.
42
Yet this is exactly as true of capital goods as it is of capital gains, and it is precisely
the motivation for Weitzman’s stationary-equivalent interpretation of a national
income measure combining capital and consumption goods. One can no more turn the
entire capital stock (or even the addition to it, the investment goods that are counted in
this year’s income) into an equivalent value of consumption goods today than one can
with, say, stock market gains. It was the problem of diminishing returns between
current consumption and current investment that led Weitzman to take a forwardlooking approach to defining and interpreting income. Investment in Weitzman’s
formulation is regarded as the capitalised value of increases in consumption over the
optimal path—yet this is precisely the argument raised against inclusion of gains as
pointed out by Bradford. Bradford argues that capital gains might be validly included
in a forward-looking measure of income: to the extent they represent a capitalised
value of future consumption increases—that is, they cannot be converted into
immediate increases in aggregate consumption but they can be converted into
increased consumption over an optimal trajectory—they have as much legitimacy (in
principle) in a forward-looking measure of income as do investment goods. Hartwick
(2000) deals with capital gains explicitly in an optimal control context and also
explores how they might be counted on the income, as opposed to the product, side of
the accounts.
A neglected distinction thus far is between anticipated and unanticipated capital
gains: the previous discussion is on the context of a deterministic economy where
capital gains occur over some predictable (optimal?) path. Unexpected events cause
unanticipated gains, and it tends to be argued that such gains should not be counted in
income. As an example, small resource-rich economies can experience large
fluctuations in national income, based on the outcomes of exploration or simply
changes in world market conditions. Hill and Hill (2003) look at concepts of Hicksian
income in a stochastic setting to determine appropriate rules for treating capital gains
in national accounting. 28
c)
Natural Capital
28
Hartwick (2000) also discusses unanticipated gains—windfalls—and suggests an appropriate
treatment is to count only the interest on unanticipated gains as an addition to income.
43
Clearly, capital-theoretic considerations loom large; different opinions on how to
define and measure stocks and flows of capital are a critical element in debates on
income. This is, of course, nothing new. The valuable collection of articles on income
collected by Parker and Harcourt (1969) contains three papers from the 1940s, by
Pigou, Hayek, and Hicks respectively, on the notion of the maintenance of the capital
stock as part of the definition of income. The emphasis then was on the distinction
between maintenance of physical versus economic capital, and in particular the impact
of obsolescence. More recently, debates have turned to issues such as those discussed
above—technical change, capital gains—as well as broadening the definition of
capital to include elements of “natural capital” such as pools of oil or values for
biodiversity.
The idea of natural capital raises its own controversies, from the particular to the
general. A particular, and important, controversy involves the appropriate treatment of
non-renewable resources, but before we explore the details, some background is worth
outlining. The easiest (in principle), and most consistent (both with standard economic
reasoning and the principles of national accounting), way of undertaking so-called
natural resource accounting is to take a capital-theoretic approach: expand our
category of capital so as to include resources such as timber, oil, fish stocks, and so
on, and then adjust the accounts for changes in stocks and flows as would be done for
produced capital. This produces an adjusted net product measure in the YSHS vein that

K
is (intended to be) a closer approximation to a capital-constant YHicks
measure by
virtue of incorporating a more complete measure of capital than traditional measures
of net product.
Both theorists and practitioners have proceeded in this direction. Repetto (1988?), a
leading advocate of natural resource accounting in developing countries, has argued
that the overuse of natural resource endowments in such countries is directly
attributable, at least in part, to depletion of resource stocks being measured as
increases in income rather than reductions in wealth. Weitzman (1976) presents a
model in which all growth is attributable to (changes in) an underlying capital stock.
44
In both of these instances, the issue is one of defining capital appropriately and then
correctly accounting for changes in the capital stock.
Thus it seems that a natural approach to accounting for non-renewable natural
resources is by treating them as capital, and measuring resource depletion as
depreciation or capital consumption. Practitioners like Repetto and colleagues, and
theorists like Hartwick and Maler have all followed this depreciation approach,
sometimes called the “net price” approach as it involves calculating a figure for priceless-marginal-extraction-cost to be used in computing the depreciation allowance.
But one striking implication of this approach is that a Kuwait-type economy that lives
off a rich resource endowment would have, in the absence of trade, a net product of
zero, in that gross income is just cancelled out by depreciation. A country with a
meagre but renewable endowment will have positive income (net product) compared
to a country with a generous but non-renewable endowment, which will in turn have
the same income, being zero, as a country with virtually no endowment at all. In
response to this, El Serafy (1989) has proposed an alternative method for accounting
for exhaustible resources. He explicitly disavows the notion of treating such resources
as capital for which a depreciation allowance can be calculated. Instead he advocates
calculating the maintainable income stream that could be generated from the proceeds
of the resource depletion. He also argues that, as this is not an adjustment to net
capital, it does not represent an adjustment from gross product (GDP/GNP) to net
product (NDP/NNP). Instead he argues that his method more correctly counts the
value-added from resource depletion, which makes it part of the gross product
measure itself, since gross product is a measure of value added in the economy.
Hartwick and Hagemen (1993) have argued that El Serafy’s measure is theoretically
reconcilable with a capital-theoretic depreciation measure. Notwithstanding this,
many empirical studies have calculated both a conventional depreciation-adjusted
income measure, as well as a measure adjusted for El Serafy’s “user cost” method,
with the results often being starkly in contrast. Common and Sanyal (1998) make this
point forcefully in regard to measurement of resource use in Australia; Neumeyer
45
(2000) similarly contrasts the differences in results from each method in a critique of a
sustainability study undertaken by the World Bank.
Butterfield (1992) criticises El Serafy for confusing product and income measures.
The depreciation method, based on the adjustment of one product measure (gross
product) to another (net product), is quite consistent in principle with basic ideas of
national accounting. But El Serafy’s method grafts an adjustment based on
sustainable income to an initial measure based on gross product, a position Butterfield
argues is inconsistent. (This is an example of the accounting-identity concept of
income clashing with the sustainable-consumption concept.)
One further point remains to be remarked upon. The nature-as-capital argument
depends upon the idea of all capital being, fundamentally, fungible. The focus of a
discussion in these terms can then turn to ends (consumption) rather than means or
specific resources (maintenance of given levels of environmental amenity or resource
stocks, for example). In policy terms, the implication is that maintenance of a total
stock of capital is an appropriate focus for discussion of income (in particular, for the
sustainability of income); the component elements of the capital stock are, in
principle, irrelevant. This underlies the analytical approach of authors like Hartwick
(1977) and Solow (1986), and the use of measures such as Genuine Savings
(Hamilton and Clemens 1999).
David Pearce and colleagues (see e.g. Pearce, Markandya and Barbier 1989) have
since distinguished two capital-stock maintenance rules that can serve (in principle) as
operational guidelines for sustainability policy. The first is an aggregate capital
maintenance condition, which they refer to as “weak sustainability”: this is a common
underpinning, often implicit, to many neoclassical analyses of economic growth. The
second, a stronger condition, requires maintenance of a given stock of natural capital;
this is labelled “strong sustainability”. (For a critique of the capital-theoretic approach
to ecological sustainability, see e.g. Stern 1997. For counterexamples of the
proposition that non-declining wealth always implies non-declining consumption, see
Asheim 1994 and Pezzey and Withagen 1997.)
46
6.2
Other Controversies
Various other issues remain contentious in discussions of extended—particularly
environmental and natural resource—accounting. Space precludes an extended
discussion, but some points of controversy can be quickly touched on.
One such point is that environmental valuation techniques are typically designed for
use in cost-benefit analyses. They measure values, not price-equivalents. Incorporating
them into national accounting aggregates introduces elements of consumers’ surplus
which are not components of any other parts of national income. (See Harris and
Fraser 2002.)
Another area at issue relates to the clash between accounting and economic
conceptions of income as outlined earlier. The United Nations, overseeing the revision
of national accounting standards for international use, have been struggling to balance
the desire to broaden the coverage of the accounts for elements that have hitherto been
neglected, with the desire to maintain a comprehensible and easily comparable set of
definitions of national income in the spirit of the original. The solution has been to
maintain a set of “core” accounts, designed and constructed according to traditional
national accounting principles, and then to construct satellite accounts that contain
elements not within the market sector or otherwise not included in the core accounts.
(See United Nations 1993, 1998.) The same philosophy has been applied to revisions
of particular national systems of accounts such as the United States (see Nordhaus
1999, 2000).
The questions of what comparisons are intended to be made also looms as an issue of
concern. The Hamiltonian approach is perhaps best suited to intertemporal
comparisons, being based as it is on the solution to a dynamic optimisation problem.
Another branch of the literature, specifically designed to generate international
comparisons, is the index number approach typified by (for example) Dowrick and
Quiggin (1998), and reviewed by Hill (2000). This literature takes an atemporal
approach, providing point-in-time comparisons of standards of living across countries
(rather than a time series indicator for a particular country), but has an implicitly
47
intertemporal element in that capital goods are typically included as proxies for
discounted consumption.29
A final controversial area has been the estimation of much broader time-series
indicators that include not only conventional indicators of national income or output,
but measures of losses in environmental amenities and resource stocks, and (more
controversially) broader measures of “social capital” such as changes in income
distribution. Such measures of “gross national progress” or so-called “sustainable
economic welfare” (e.g. Stockhammer et al 1997, or Hanley, Moffatt, Faichney, and
Wilson 1999) are, compared to more conventional accounting aggregates, empirically
broader and theoretically ad hoc. The sense in which they capture “sustainable
economic welfare” is not exposited from first principles.
7.
Conclusions
7.1
Economists and national accountants use different “default” conceptual
frameworks to think about the concept of income.
In national accounting, income is a static measure, defined as the value of current
production and derived from the relevant accounting identities. Economists, by
contrast, think of income in dynamic terms, being a flow from an underlying stock
that may or may not be being held constant. (In the simplest benchmark or steady state
case the stock is maintained, neither declining nor growing.) The two concepts are, of
course, reconcilable in principle but they are not identical in their construction. The
implication of this is that when proposing revisions to how income is defined and
measured in practice, accountants and economists often come from quite different
directions, with accountants concerned to maintain the integrity of the relevant
identities, and economists attempting to broaden the definition of the capital base
from which income is presumed to flow, sometimes in ways that violate the
output/income identity. At the official level, this is reflected in the reluctance of the
United Nations to tamper too much with the “core” market-sector accounts in their
revisions of the System of National Accounts.
29
Arguably, this brings into question the significance of their point-in-time welfare comparisons based
on consumption when not all of the output of the countries being compared is of consumption goods.
48
7.2
Income ex post (consumption plus capital accumulation) and income ex ante
(maintainable consumption) are distinct concepts, but often conflated into a
single one.
Some statements of “Hicksian” income refer to a measure combining consumption
plus capital accumulation as if it is also an indicator of that amount of consumption
that can be had without future impoverishment. Hicks himself distinguished clearly
between ex ante consumption measures—his central criterion—and ex post
approximations to it. He was not confident in his assessment of how good an
approximation these ex post measures would be. In fact, his pessimism shows in just
clarifying what the central criterion ex ante was, given the complications due to price
changes, interest rate changes, consumer durables and so on. Once it came to
measuring these concepts in practice, his tone became even more gloomy. Yet many
modern writers treat the ex ante measure as being well defined, and as being virtually
interchangeable with the ex post measure. As recently as 1990, David Bradford
reasserted the distinction between the two, referring to ongoing “professional
confusion” on the subject.
7.3
Proposals to modify income measures are typically aimed at re-defining a
measure constructed along ex post, or backward-looking, lines, into one that is
interpretable in forward-looking terms.
Standard national accounting is oriented to identifying “where we are” (or have
recently been). The usual aim in revising the accounts is to re-orient the measures we
produce into a more forward-looking direction. In particular, the motivation is often
one of measuring the sustainability of our consumption; in other words, are we putting
ourselves at future risk of declining living standards?
The problem turns on how one recasts an ex post measure (consumption plus capital
accumulation) into a measure interpretable in terms of consumption. This requires
measuring investment goods in terms of a “consumption counterfactual”, the
implications of which lead us to the next conclusion.
7.4
There are two distinct ways in which ex post income measures have been
presented in terms of a sustainable consumption measure, corresponding to
49
two different ways in which investment goods are “converted” to consumption
units. Each way has different implications for defining, measuring and
interpreting the income measure that results.
As presented here, two approaches or traditions have emerged in getting “Hicksian
income” measures from modified national income statistics. One—that I have labelled
the stationary-state equivalent approach—treats investment goods as current
consumption foregone, in line with the atemporal focus of standard national
accounting that treats the appropriate focus of the national accounts as being what
happened this year rather than what might happen in future. The other—labelled the
stationary equivalent approach—takes the intertemporal (present value) perspective
more familiar to economists, with investment being treated as future consumption
postponed. This latter approach, prevalent since the 1990s, is popular with economists
schooled in growth theory. The atemporal approach is perhaps more old-fashioned,
and more closely associated with analysts schooled in national accounting principles
as well as dynamic economics.
The problem of presenting an ex post measure as somehow equivalent to a
consumption-only measure can be re-expressed as the problem of presenting the
measurement of output in a dynamic economy as though the economy were in a steady
state. The atemporal approach treats the economy as if it were in an actual steady state
(hence, stationary-state equivalent), while the intertemporal approach treats the
economy as being the present-value equivalent of a constant-consumption economy
(hence, stationary equivalent).
7.5
The analysis of welfare and sustainability is often oversimplified (sometimes
misleadingly) in the literature given the divergence of the actual economy from
the steady-state proxy economy analysed in each of the concepts presented in
7.4
Note that another problem is presented by the fact that our key analytic construct
(typically referred to as Hicksian income) is based on the idea of a steady state while
the world may not actually be in such a state. In a steady state economy, with a
constant income flow off an unchanging stock of wealth, current welfare is
50
unchanging, and is sustainable. In fact, the situation is a textbook one of consumption
(income) signifying maximum sustainable welfare.
Out of a steady state, however, current welfare (actual consumption) and sustainable
consumption will typically take different values. Getting a measure of whether
standards of living are changing, and by how much, becomes a different question than
assessing whether current standards of living are maintainable. In the intertemporal
Hamiltonian models this tends to be clearer: one must either define sustainability
more weakly, such as Weitzman’s “generalized power to consume”, or be explicit
about the consumption path that is being solved for and whether it is possible for
consumption to decline given the parameters of the model.
In the vaguest (theoretically speaking) models, such as those that purport to present
measures of “sustainable economic welfare”, it is not clear how the numbers presented
relate to either welfare or to sustainability.
7.6
Both economic approaches to revising income—stationary equivalent and
stationary-state equivalent—contain measurement error problems. Neither
can be thought of as “exact”.
The approach of treating investment as if it were equivalent to current consumption
foregone has the problem that it ignores the diminishing returns that are evident in
Figure 1. Weitzman’s development of the Hamiltonian-based model of national
income with its associated (and novel) intertemporal interpretation was motivated by
the observation that feasible present consumption and actual national income were
two different magnitudes for that very reason. However, the intertemporal approach
linearises the Hamiltonian to get a linear income measure and hence suffers some
approximation error in turn. The Hamiltonian measure seeks to cast current income as
being proportional to discounted future welfare: but to be able to add consumption to
investment in dollar units requires a linearisation that removes any consumers’
surplus. This loss of consumers’ surplus is appropriate from a national accounting
perspective, but the exact proportional correspondence with future welfare is lost.
51
7.7
The applied literature, such as the natural resource accounting studies
proliferating in recent years, often do not proceed with clear reference to firstprinciples models.
The examination of first-principles models in the first few sections of this paper
showed them to be assumption-specific, with no one model that covered every
situation or allowed a robust and generally applicable interpretation. It suggests that
any attempt to empirically recalculate a measure of national or regional income should
proceed with regard to a particular model and interpret its results in that light.
This is not in fact what happens. Many studies appear to proceed with the intention of
producing some modified version of a YSHS measure. This is turn seems motivated by
the general notion that maintaining capital intact is a good idea—in other words that a
modified measure of YSHS will be a good approximation to a constant capital measure


K
K
. In turn, the presumption must be that YHicks
is a good approximation to the
YHicks

C
ideal sustainable consumption measure, a.k.a. Hicks’ “central criterion”, YHicks
. In
some cases, when pressured to pay lip service to theory, authors may make a general
appeal to the foundations provided by the Hamiltonian literature; the problem is that
this implies a forward-looking interpretation in the vein of YW HM , which does not in

C
general serve as a proxy for the steady-state measure YHicks
.
7.8
Income is not one concept to be defined in one single all-encompassing way.
Following Hicks, various context specific measures, complete with
approximation errors, are likely to be required. This requires analysts in the
field of national income measurement and empirical economic growth to
understand the limitations of their respective measures, and the limits to their
interpretations. Welfare and sustainability interpretations arise from
particular assumptions made about the “steady-stateness” of the economy,
and being explicit about those assumptions is vital to drawing appropriate
conclusions from empirical analyses.
Two leading economists have both contended that interpreting national income figures
depends on the purpose with which we have constructed them.
52
“Sharpening our conception of what we want the accounts to tell us seems a
matter well worth further professional attention.” (Bradford, 1990, p.1186)
“Ultimately the meaning of national income is inherent in the purposes of the
national accounts.” (Usher, 1994, p.124)
The problem faced by all attempts at measurement of economically meaningful
magnitudes boils down to the fact that the key economic interpretations are intended
to describe steady states, but the measurement is typically occurring in the context of
a growing economy. The atemporal approach aims, in effect, to mimic a steady-state
(consumption-annuity) economy; in doing so, the sustainability and welfare emphases
coincide, in that the steady-state they purport to describe is one in which the economy
is generating maximum sustainable economic welfare. The problem is that the link
between welfare and sustainability here is an artificial and forced one, given that
capital goods are included in the index. A sustainability interpretation may be
admissible (for k  0 ) using these measures if we make appropriate capital-theoretic
assumptions, but current welfare is mismeasured.
Alternatively, the intertemporal approach aims to provide a more general and rigorous
welfare interpretation, in which income and welfare are expressed in present value
rather than “instantaneous” terms. However, the trade-off is that sustainability is also
only interpretable in such present value terms as well—what Weitzman (1997) refers
to as the generalised capacity of the economy to consume.
The result of all these different perspectives is a confusion in the literature between
those who advocate (or assume) a welfare emphasis or a sustainability emphasis in the
interpretation of a proposed idealised measure (and whether the measure they may
propose provides the interpretation they claim it does); not to mention a difference in
an atemporal perspective in which income is strictly a “this-year” phenomenon, versus
an intertemporal perspective in which “present value” magnitudes are legitimately
added to magnitudes representing current output.
53
TABLE 1—DIFFERENT THEMES OF INCOME
Income Theme
Form
National Accounting
GDP/NDP
Y=C+I
Schanz-Haig-Simons
YSHS
Y = C + K
Hicksian

K
YHicks
Y = max C s.t. K = 0
(constant capital)
or
C
YHicks
(consumption annuity)
Income is generated by production.
Historical perspective.
Consumption and investment determined
by “boundaries” (market sector) according
to circular flow relationships.
 Return to wealth underpinning.
 Historical but broadening it in principle
can make it more forward-looking.
C and I (denoted K to highlight the
capital stock K from which income is
presumed to flow) may vary in definition
(not only from national accounting
measure, but between individual economic
studies), depending on level of analysis
and what is presumed to contribute to
current and future utility.
 Crude sustainability interpretation based

on non-negative K .
 Stricter return to wealth interpretation,
with income now consumption only.
 “Constant capital” measure generally
regarded as the measurable analogue of the
“consumption annuity” measure.
 C and I can be defined similarly as for
YSHS, which is sometimes taken as an
Y = max C s.t. C = 0
approximation for the
K = 0 version.

Hamiltonian
(Weitzman-HartwickMaler)
YWHM
Interpretation



*
YWHM
 C *  K *
Income is now return to wealth
(sometimes strictly so) but is not
consumption only!
 Explicitly intertemporal interpretation,
and derived from optimising model (*
denotes optimal value).
 Wealth is taken to be PV of all
consumption – in contrast with treating
wealth as the value of the actual capital
stock in interpretation of
YSHS for
example.
Investment presumed to be PV of extra
consumption.
 Admits welfare rather than sustainability
interpretation, in contrast to above
definitions, and even that is conditional.

54
Appendix
On the treatment of depreciation, deterioration and obsolescence in Maurice
Scott’s work on measuring economic growth.
Maurice Scott has proposed a radically different view from the “orthodox” view of
national accounting and income measurement. It is worth covering it in a little bit of
detail.
Scott (1989), like Usher, argues that we should proceed “as if” today’s investment
could be converted to an equivalent value of consumption, and that the task of
calculating income is to measure the “sustainable-consumption-equivalent” level of
output (Scott 1990). Scott does this in two steps: first he divides conventional
investment expenditures into what he calls “maintenance” expenditures—those
devoted to restoring and maintaining the productivity of the capital stock—and
“investment” expenditures—those that increase the productivity of capital—and he
classifies the former as intermediate spending. Second, he justifies adding the latter
magnitude (investment) to consumption on the basis that with a fully maintained
capital stock, we can treat the extra output of investment goods as if it were increased
consumption, and regard the total as a yield on the capital stock. This does entail
redefining what counts as investment expenditure and, as noted previously, deflating it
using a consumption-goods price index. Scott is critical of the notion that exogenous
technical change can add to consumption growth: in his view the conventional
“residual” reflects a mis-definition or miscalculation of investment
(He also questions whether diminishing returns empirically justify the rejection of the
atemporal approach (pers. comm..))
Here is a summary of how key parts of his approach compare to the “orthodoxy”.
1. The conventional view of depreciation and productivity in economics:
-
depreciation is akin to physical deterioration (“reduction”) in the capital stock
-
as such it is associated with loss of productivity in the economy
55
-
economic growth is associated with (or determined by) the net change in the
capital stock
-
the income/product identity is maintained by deducting depreciation from
profit on the income side, to match the loss on the product side
-
unexplained growth (not accounted for by conventional labour and capital) is
the "residual" reflecting technical change.
2. Scott's view of depreciation-as-obsolescence:
-
most actual depreciation results from obsolescence, not physical decay
-
no loss of productivity is associated with obsolescent capital goods (only a loss
of value)
-
depreciation thus not associated with a reduction in output
-
any "restorative" capital expenditure that offsets actual wear and tear should be
labelled maintenance and not investment spending (conceptually different and
should be classified and measured elsewhere)
-
economic growth associated with the total (or gross) rate of investment, not
the net change in the capital stock
-
on the income side of the accounts (with product not declining based on
obsolescent but still-productive capital equipment), losses to capital owners
are offset by increases in income to labour
-
the conventional "residual" is a result of mismeasurement. If we assume
obsolescence results in reduced productivity when it doesn't, then we
underestimate growth, and mistakenly attribute the "excess" growth to an
unmeasured activity. Correct accounting should eradicate the residual.
READINGS IF INTERESTED:
Scott, M. (1989), A New View of Economic Growth, Oxford University Press, Oxford.
Scott, M. (1990), “Extended Accounts for National Income and Product: A
Comment”, Journal of Economic Literature, 28, September, pp. 1172-1179.
56
Dension, E (1991), “Scott's A New View of Economic Growth: A Review Article”,
Oxford Economic Papers; 43(2), pp.224-36.
Scott, M. (1991), “A Reply to Denison”, Oxford Economic Papers, 43(2), pp.237-44.
Scott, M. (1991), “A New Theory of Endogenous Economic Growth”, Oxford Review
of Economic Policy; 8(4), Winter, pp.29-42.
Oulton, N. (1995), “Depreciation, Obsolescence and the Role of Capital in Growth
Accounting”, Bulletin of Economic Research; 47(1), pp.21-33.
Scott, M, (1995a), “Depreciation, Obsolescence and the Role of Capital in Growth
Accounting: A Reply”, Bulletin of Economic Research; 47(1), pp.35-38.
Scott, M, (1995b), “What Sustains Economic Development?”, in Goldin, Ian,
Winters, L. Alan, eds. The Economics of Sustainable Development.
Cambridge; New York and Melbourne: Cambridge University Press, pp. 83105.
Scott, M, (1984), “Maintaining Capital Intact”, Oxford Economic Papers, N. S.;
36(0), Supp. Nov. 1984, pages 59-73, reprinted in Collard, D. A., et al., eds.
Economic Theory and Hicksian Themes. Oxford; New York; Toronto and
Delhi: Oxford University Press Clarendon Press, 1984, pp.59-73.
57
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