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The income of nations

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Michael Harris

Agricultural and Resource Economics

University of Sydney

Environmental Economics Network workshop

Australian National University, May 2005


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 (consumption-related, 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.

1. Introduction
2. Preliminaries
3. Income and Growth: Key Themes

3.1 National accounting themes

3.2 Economic themes

3.3 Growth themes

4. 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

5. 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
6. Empirical Implications

6.1 Capital theoretic controversies

a) Technical change

b) Capital gains

c) Natural capital

6.2 Other controversies

7. Conclusions (followed by Appendix and References)

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) 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 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).








Figure 1

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 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.
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 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:

  1. National income reflects the value of current production;

  2. The “circular flow” accounting identity is the basis for both classification and measurement in the national accounts;

  3. 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);

  4. 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:

  1. Income as the sum of consumption plus the change in wealth;

  2. Income as a maintainable level of consumption.

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 , where we use 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 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.
In formal notation, we can write the first of these as , and the second as . 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 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 welfare-related 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 constant stock of capital; that is, where . In this situation, consumption (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 form admit of an intertemporal welfare interpretation, and this will be covered in Section 5.2.
3.3 Growth Themes

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 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








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