Chapter 22 National Income and the Environment⋆

Chapter 22

NATIONAL INCOME AND THE ENVIRONMENT
GEOFFREY HEAL Graduate School of Business, Columbia University, New York, NY 10027, USA BENGT KRISTRÖM Department of Forest Economics, 901 83 Umeå, Sweden

Contents Abstract Keywords 1. Introduction 1.1. Outline

2. Historical background 3. The Keynesian imperative and Lindahl’s alternative 3.1. The accounts of the nation 3.2. Lindahl’s system

4. Welfare interpretations of income and wealth 4.1. Sustainable income: a graphical approach 4.2. Sustainable income and the ideas of Fisher, Lindahl and Hicks 4.3. Sustainable income and the Hamiltonian 4.4. Income and welfare – the separating hyperplane approach 4.5. Taking stock

5. A general dynamic model 6. Measures of income and the Hamiltonian 6.1. Hicksian income and the Hamiltonian

7. National wealth 7.1. Illustration 7.1.1. Hotelling 7.1.2. Stock a source of utility 7.1.3. Renewable resources

8. Income, wealth and NNP 9. Applications and extensions 9.1. Economic growth

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July 2003. For updates on certain issues, see our paper “Income, wealth and sustainable welfare in representative-agent economies”, available at www.ssrn.com.

Handbook of Environmental Economics, Volume 3. Edited by K.-G. Mäler and J.R. Vincent © 2005 Elsevier B.V. All rights reserved DOI: 10.1016/S1574-0099(05)03022-6

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G. Heal and B. Kriström 9.2. Defensive expenditures 9.3. Non-autonomous Hamiltonians 9.4. Non-utilitarian optima 9.4.1. Application to exhaustible resources 9.5. Sustainable revenues and national income

10. Theoretical issues – taking stock 11. Issues in the construction of a green national product 11.1. Valuation of ecological services 11.1.1. Politically determined willingness to pay 11.1.2. Defensive expenditures and similar approaches 11.2. Valuation of stocks 11.2.1. Economic depreciation 11.2.2. El Serafy’s approach 11.3. Transboundary pollution 11.4. A small open economy

12. Expanded social accounting matrices 13. Developments in applied green accounting 13.1. The Nordhaus–Tobin measure of economic welfare (MEW) 13.2. Norwegian resource accounts 13.3. Other developments

14. Selected applications 14.1. The SEEA 14.1.1. The SEEA and valuation 14.1.2. Environmentally adjusted domestic product (EDP) 14.1.3. The SEEA and forest accounting 14.1.4. Applying the SEEA in Mexico 14.2. Sweden 14.3. Indonesia 14.4. Malaysia 14.5. The Philippines 14.6. Genuine savings

15. Conclusions Acknowledgements References

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Abstract In this chapter, we review the concept of national income and the economic theory of national income accounting. There are two building blocks – the ideas of Fisher, Lindahl, Hicks about income as an expenditure level that can be continued into the future, and the concept of income as a welfare measure that emerges from the welfare economics and general equilibrium of the 1950s and 1960s. The former have led to an

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extensive literature on the use of Hamiltonians or their first-order approximations as an income measure. After reviewing this body of theory and the connections between the concepts, we suggest extensions and then consider how various proposed green accounting systems match up to the theoretical desiderata. We also review a number of empirical applications. We devote considerable space to the United Nations’ proposed System of Economic and Environmental Accounts, and to accounting reforms proposed by the statistical offices of various countries.

Keywords welfare measurement, dynamic models, national income, wealth, green accounting JEL classification: C43, D60, D90, E29, M40, Q01

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1. Introduction Green accounting has recently received significant attention from the research community, governments and other organizations. Over the past 30 years several countries have developed green accounting systems via their statistical offices, and international organizations such as the OECD, the World Bank and Eurostat have also contributed to the development of “greener” accounts. The UN, through its statistical office, has developed an extensive System of Environmental and Economic Accounts (SEEA) which complements and extends the System of National Accounts (SNA). A large number of theoretical and applied studies have appeared in recent years, most of them concerned with the welfare properties of linear indices such as the national product. When we ask what has been driving this development, two different strands of thought come to mind. Firstly there is a demand for measures of progress that go beyond traditional measures of income and wealth. In public debate, this appears as an irrepressible demand for a simple indicator of national welfare. In the policy arena, there is also a practical need to evaluate whether and how different activities are contributing to sustainable welfare improvements. In this context, it is important that we have every reason to believe that GDP as traditionally measured is not a robust welfare index, especially if we include environmental and natural resources in the discussion. Secondly, there has been a shift in emphasis within received economic theory regarding the importance of ecological systems for the functioning of the economic system. An increased appreciation of the environmental resource base as a fundamental capital asset has led to important theoretical developments in economics, including a deeper understanding of the links between the economy and our natural resources and environments. In addition, the Brundtland Commission1 has played an important role in propelling green accounting into its current prominence, by popularizing the notion of sustainable development and marshalling a comprehensive approach to links between the environment and the economy. The practical uses of green accounting systems are bounded only by our imaginations, although what we need at the most basic level is a consistent database for the analysis and evaluation of policy. It is important to note that green accounting is a comprehensive economic information system within which “green” measures of income and other indices play important roles. This view is consistent with the standard view of national accounting systems such as the SNA. The most important single statistic that comes out of the SNA is undoubtedly the Gross Domestic Product (GDP), but it is the ingenious structure of the entire system of accounts that helps analysts to form pictures of the entire economy and its development in many dimensions. While green accounting in monetary terms has come play a dominant role in recent literature, it is important to note that resource accounts can be developed in monetary terms and in physical terms.

1 World Commission on Environment and Development (1987).

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Physical accounts are a prerequisite for monetary accounts, although our focus here is on the latter.2 The literature on green accounting is large and no survey can do full justice to it, this review being no exception. For example, Vincent and Hartwick (1997) review of green forest accounting includes an assessment of the developments in over 100 countries. A significant part of the material is also in the “grey” literature, in government reports and in other outlets that are sometimes difficult to access.3 An important purpose of this review is to try to tie together some of the empirical and theoretical literature. There is a gap between theory and practice: empirical studies are not always backed up by sound theory. A closer look at the empirical literature reveals that there is no shortage of definitions of fundamental concepts such as “green” national product: indeed, there is a surfeit of riches in this respect, sadly with little overlap with the concepts proposed in the theoretical literature. There are, of course, several reasons why empirical studies cannot fulfill the ideals set forth in theoretical constructions. The challenges to the empirical researcher are many and perhaps greater here than in most areas of economics. Even so, the lack of a common framework may reflect a deeper issue, namely that the questions that the empirical studies seek to answer are interpreted differently in different studies. There may even be a lack of clarity and of agreement about the true nature of these questions. The theoretical literature suggests that there is little need for such disagreement or ambiguity, although, perhaps surprisingly, it is still possible to find some different views among theorists about just what we should measure. There is, however, little disagreement among economists about the appropriate theoretical base, as the usefulness of viewing environmental and natural resource concerns through the lens of capital theory is clear: environmental concerns can almost always be traced back to some stock. This is clearly true for renewable and exhaustible resources per se, but the argument holds true in the more general sense as well. Indeed, concerns expressed about global warming and the ozone layer are based on stocks that we can think of as atmospheric quality indices. The gaseous composition of the atmosphere and the ozone layer are renewable resources. Thus, with a suitably general interpretation of economic assets, capital theory is a natural starting point for discussion of the ideas in the green accounting literature. It will, nevertheless, be incumbent upon us to answer clearly the question: what is it that we want to measure? Possibilities include sustainability indices and measures of welfare change. We may use green accounts to shed light on whether or not current changes in consumption and production increase our level of well-being. Alternatively, we may seek to inquire into the sustainability of current patterns of economic activity. There are other useful measures: the bottom line is that the construction of a

2 One can also complement the information system by way of a comprehensive system of environmental

indices, using ecological pressure indices or other environmental indices. Official indicators are published, e.g., in Britain, see Custance and Hillier (1998) for a discussion of some of the issues. 3 Gernot Wagner keeps an updated bibliography at http://www.gwagner.net.

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well-functioning green accounting system must rest on the twin pillars of clearly defined objectives and a sound theoretical base. Without these, the summary statistics that emerge may be, indeed are likely to be, completely devoid of economic significance. 1.1. Outline We begin with a brief review in Section 2 of the development of the concepts used in national income accounting. This is revealing: it shows many of today’s topical issues and approaches to be a part of a long historical tradition. It also shows the many strands of economic analysis that have contributed to our present understanding. This goes some way to explaining some of the ambiguities we find today. Concepts developed by Keynes and his associates for macroeconomic management, and those arising from theoretical welfare economics, have acquired the same or similar names and are often used interchangeably. We discuss the Keynesian imperative as well as the less well-known Lindahl alternative to national accounting in Section 3. We proceed by exploring the links between (sustainable) welfare and income or wealth measures in Section 4. To fix ideas and obtain some intuition, we start out by using a simple graphical approach to illustrate the main ideas that lies behind sustainable income. A key point is that there are two quite distinct traditions at play here. One is the concept of (sustainable) income as the return on wealth, which with a centurylong intellectual ancestry through the work of Fisher, Lindahl and Hicks has recently been rediscovered in the guise of a sustainability measure. The other is the concept of income changes as indicators of welfare changes, a concept firmly embedded in the welfare economics and general equilibrium theory of the 1950s and 1960s. These income measures were developed in an atemporal framework: their dynamic analog is a wealth measure. This seems more robust, and theoretically better founded, than the sustainable income concept, though the two are closely related. In Section 5, we begin the process of formalizing these insights in a consistent model that will allow us to explore and compare the different concepts and investigate their robustness. We introduce a general dynamic model of which many standard models used in the environmental and resource economics literature are special cases. We use the general model in Section 6 to develop measures of sustainable income via the Hamiltonian. Section 7 has a rigorous discussion of the wealth concept using a separating hyperplane approach. We then integrate the income and wealth discussion in Section 8 and show how measures of sustainable income and wealth are related: the change in Hicksian income is shown to be the real return on the change in wealth. In Section 9, we apply the theory to two cases of immediate interest and extend the discussion to more general cases. Thus, we show how endogenous growth fits our measurement proposals and provide tools for consistent handling of so-called defensive expenditures in an accounting framework. We discuss nonautonomous Hamiltonians (as arise for example with exogenous technological progress) and explore nonutilitarian objectives and zero discount rates. A summary of the theoretical issues appears in Section 10, where we try

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to take stock and offer our judgment on the gradual process of convergence that we are beginning to see in the theoretical literature. For example, there are strong assumptions needed to justify an interpretation of green NNP as sustainable income; a focus on the stocks as “sufficient statistics” seems to offer more robustness towards perturbations of the underlying assumptions. Having explored these conceptual issues, we turn to the problems that arise in applying these concepts. There are, of course, many, measurement and valuation being primary amongst them. Section 11 offers a compact summary of issues encountered when constructing green income measures. We cover valuation of flows and stocks, how to handle transboundary pollution and some accounting issues relevant for the small “resource-rich” open economy. We then return in Section 12 to the social accounting matrix described in Section 3 and discuss extensions of it. Finally we turn to applications. Section 13 provides a brief review of developments in the applied literature, while Section 14 details a number of useful applications. We review two types of applications. Firstly we look at suggested revisions of the national income accounting measures to incorporate a more accurate picture of the impact of economic activity on the environment and the impact of this on economic welfare and the sustainability of current practices. One of the suggested revisions we consider is that proposed by the UN as the SEEA (System of Economic and Environmental Accounts). Secondly we look at applications of some of these suggested revisions to the accounts of particular countries, in an attempt to estimate the errors in their conventional GDP measures. We also discuss the genuine savings measured proposed by the World Bank. Section 15 has conclusions and final remarks.

2. Historical background The systematic compilation of economic data into national accounts ranks among the most important innovations in the social sciences. With roots in Quesnay’s tableau économique and William Petty’s 17th century assessments of England’s national income, the current systems of national accounts integrate a wealth of information pertaining to the economic state of a nation. Its importance in today’s economic life cannot be overestimated, as it remains the basis for the construction, evaluation, and comparison of economic performance throughout the world. While the early work on social accounting was to some extent motivated by an interest in the potential tax base and war finance, our current accounting systems enable us to shed light on a rich array of issues, amongst these the connections between the economy and the environment. The development of social accounting has often been closely related to pressing social issues. Thus the current focus on green accounting is really not surprising. While we cannot cover the history of social accounting to any extent in this paper the origins of the SNA are of interest because its history is reflected in the structures that are often

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a basis for current applications of green accounts. The reader interested in the development of national accounting should consult the book by Studentski (1958) for a detailed historical perspective. For a compact summary of the early developments of national accounting, see also Kendrick (1995).

3. The Keynesian imperative and Lindahl’s alternative In John Hick’s last paper [Hicks (1990)], he writes (p. 528) “If we define macroeconomics as beginning with Keynes, it is more than his General Theory of 1935 that we should be meaning. . . . This is his booklet How To Pay for the War [Keynes (1940)].” Intriguingly, a distant precursor to Keynes’ work on the second world war was the compilation of crude national income accounts by Gregory King in 1696 in the context of the war between France and members of the League of Augsburg (including England, Dutch Netherlands and other countries). King showed that this war could not go on beyond 1698 without substantial changes in the economy (such as an increase in the national income). Consistent with King’s predictions, the Peace of Ryswick ended the war in 1697.4 Keynes came to focus on the central problems of war finance in the autumn of 1939 and his booklet came out in 1940, focussing mainly on inflation. Keynes set out to form a structure that lies at the root of current national accounting systems. His attempts led to a demand for official estimates of the national income and its components. James Meade began this task in the summer of 1940 and was joined by Richard Stone, then a student of economics at Cambridge. Under the supervision of Keynes, Stone and Meade wrote a White Paper (An analysis of the sources of war finance and an estimate of the national income and expenditure in 1938 and 1940), which came out in a technical version in the Economic Journal in 1941. It came to be the basis for the Accounts of the Nations, to be further developed and refined with the development of the SNA. Thus, Stone prepared a manuscript in 1947 and chaired a group at the League of Nations that subsequently published the 1952 edition of the SNA. Eventually, Stone’s achievement led to his being awarded the 1984 Alfred Nobel Memorial Prize in Economic Sciences “for having made fundamental contributions to the development of systems of national accounts and hence, greatly improved the basis for empirical economic analysis.” A key contribution by Stone was the close attention to having a consistent accounting system, by way of a double-entry book-keeping system.5 4 See Stone (1988) for a fascinating account of King’s work. Stone (1988) replicates King’s analysis for

WWII, but abstains from making predictions about when the war would have ended. Incidentally, Stone correctly predicted the day when Italy would enter WWII (using statistics on oil cargo ships). 5 While the development of social accounts are mainly associated with Stone, similar developments were under way in other countries (e.g., in Norway, Denmark and The Netherlands). For an account of the Scandinavian development, see Aukrust (1992).

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The theoretical underpinnings of the system that Stone and his co-workers developed were naturally Keynesian. Key components of the simplest Keynesian model include exogenously determined real investment, government expenditure on goods and services, exports, as well as consumption and imports (determined within the model). Those components of final demand were also chosen as categories of expenditures on final output in the accounts. Thus, the accounts were suitable for empirical macroeconomic analysis from the Keynesian perspective. However, as pointed out in the motivation for Stone’s Nobel prize: “Although it was primarily the Keynesian revolution in economics which gave the strongest impulse towards the construction of national account systems, these systems may today be regarded as ‘neutral’ from both the analytical and the ideological point of view.” 3.1. The accounts of the nation It is useful to think about national accounting in terms of how one can systematically summarize the economic activities of the nation. In a national accounting system, the most important economic aggregates are assembled and organized into several different accounts. This opens the scope for a wide variety of useful analyses. The national accounts have traditionally been given four tasks: (1) To describe economic activity in a country during a given period of time. (2) To portray how income and its changes affect consumption and other economic activities. (3) To make possible structural analyses of the economy. (4) To make possible national budgets and various forecasts necessary for economic policy. The most important single number that comes out of the national accounts is GDP, although it is important to remember that the accounts comprise a consistent system, in which useful information about the economy is stored. The national accounts consists of four main accounts: the production account, the account for consumption and income, savings and investment and trade. These accounts describe, in turn: production, the income generated by production and how income is used for investment and saving and trade with other countries. The four accounts are split in several sub-accounts, permitting a detailed picture of, let us say, a certain industrial sector. A basic principle of an accounting system is the fact that each transaction is entered twice. We can picture this principle in a convenient way by using a matrix, because we then cut the number of items in the system by 50%. Each number is entered only once, but we interpret the number in two ways, depending on whether we read along a row or down a column. A social accounting matrix, SAM, is a way of summarizing the national accounts in this way. Each column in a SAM represent payments from a sector, while a row details payments to a sector. A SAM usefully summarizes a substantial information about the economy. SAMs play an important role in computable general equilibrium models, in which connections

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G. Heal and B. Kriström Table 1 A social accounting matrix (numerical example) Institutions Institutions Factors Production Savings/investment RoW

Factors

Production

Savings/investment

RoW

30

5 5

100 100 80 20

5 10

between economic agents are analyzed. There are several ways to represent a SAM, here is a simple numerical example of a SAM.6 Begin with the number 100 in the first row of Table 1. When we read along a row, we think of payments to a sector, as explained above. Thus, households, companies and the public sector have received a total income of 100. This is the return on the factors that they own. Reading down the column, we find the payments from a particular sector. Consequently, the first column tells us that 80 is used for consumption and 20 is used for savings/investment. The second row displays factor income, which is equal to 100 in this example. The corresponding outlays are found in the second column, and we interpret this simply as the income factor owners receive. In the third row, we find that production is allocated to consumption (80), savings and investment (30) and exports (5). In the third column, we find the corresponding outlays: production factors (100), depreciation (5) and imports (10). The fourth row and column depicts investment and saving activities. In the fourth column, we find that 30 units was spent on buying equipment from the producing sector, while the fourth row explains how investments were financed. Hence, 20 units were saved among the institutions, 5 units come from depreciation and 5 units appears as a saving in other countries (hence the current account is negative). Finally, the last row and column shows trade with rest of the world. Payments to the account is interpreted as the expenditures importers have made (10). “Foreigners” have used those resources for buying our exported goods (5), but they have also lent us 5 units, since we have not been able to pay for all imports with exported goods. In general terms, the basic SAM for the national accounts is in Table 2. The first column and row suggest that the Net National Product (NNP) is equal to consumption (C) and net saving (S). Proceeding to the third column and row, we find 6 We choose here the simplest possible representation, which is based on a fundamental separation of the economy into factors, activities and institutions [see Stone (1951)]. Factors include resources available to the economy in the form of labor, real capital and natural resources. By activity is meant the transformation of resources into products in a general sense; a useful disaggregation of this concept is (i) production, (ii) consumption, and (iii) adding to wealth. The institutions of the economy is an aggregate of the actors of the economy, e.g., households, firms and the government. In Table 1, we view Savings/investment as one particular activity and the rest of the world (RoW) as one particular institution. A fundamental property of a SAM is that the sums of corresponding columns and rows always match, which is another way of expressing the fundamental idea of a double-entry book-keeping system.

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Table 2 A basic social accounting matrix Institutions Institutions Factors Production Savings/investment RoW

Factors

Production

Savings/investment

RoW

I

X B

NNP NNP C S

D M

that C + I + X = NNP + D + M: consumption plus investment (I ) plus exports (X) equals NNP plus depreciation (D) plus imports (M). The fourth row and column shows that gross savings plus the current account deficit (B) is equal to investments. The last row and column implies that when imports exceed exports there is a positive current account deficit. Combining the last two identities we find that I = (S + D) + (M − X). In other words, investments are financed via domestic savings and the current account deficit. This basic structure lends itself easily to generalizations, the most direct being various disaggregations of the accounts. Each box in the matrix can be disaggregated, one important example of this being the input–output matrix. By suitable reinterpretations, we can include environmental resources and services in this structure, as we will discuss later. 3.2. Lindahl’s system While the Keynesian imperative rightfully plays a dominant role in the development of social accounting, several other contributions deserve mention. The choice is to some degree a matter of taste, but it is not unreasonable to single out some Scandinavian contributions to the early literature, in particular the contributions by Erik Lindahl, since they have gone largely unnoticed.7 Lindahl is probably best known to economists for his contribution to the literature on public economics, even though he played a major role in the estimation of national income. He was a major contributor to “The National Income of Sweden”, a monumental work on estimates of Swedish National income from 1860–1930. His direct contributions to national accounting are less well-known, perhaps because the only complete source we are aware of is in Swedish [Lindahl (1954), a shorter version in English appears in Lindahl (1939)]. He set out to describe a complete accounting system, based on a detailed theoretical model, and applied it to national accounting data for Sweden in 1950.

7 Ragnar Frisch set out to develop his own national accounting system, which he tested for Norwegian 1935 data for selected sectors.

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We will not describe his system here, but some of his ideas are worth reiterating, in particular, one that is related to the demarcation between different purposes of a national accounting system. Lindahl (1954, p. 88) was critical of ideas that implied that one accounting system is suitable for income estimates, another for productivity analysis, a third for analysis of the business cycle and so on. Ohlsson (1953), in one of the classic contributions to the national accounting literature, had previously argued at length to the opposite effect, namely that the intended purpose of the accounts should have an influence on the solutions chosen. For example, the choice of production boundary and the sectoral design could be allowed to vary depending on the purpose of the accounting system. Lindahl, however, claimed to have developed a “general purpose system” that would respond to several different needs. Do we need to develop a different accounting system for green accounting, or is there a general purpose system that can cater for all needs? The accounts stemming from the work of Keynes, Meade and Stone were after all primarily intended to provide tools for macroeconomic management. In this sense, it is possible that green accounting and national accounting serve different purposes. Is it therefore correct, as implied by Ohlsson’s (1953) ideas, that they require different accounting systems? If what we seek is a single number measuring the economic well-being of a society within the utilitarian framework, it seems likely that there is a single correct measure and a single correct procedure for arriving at this. In principle, this could differ from a measure of sustainable welfare, though we shall see below that they actually coincide. There is an additional interesting point about the Lindahl system of national accounts. We will define later a concept of income which is best called Fisher–Lindahl–Hicks income (known in the literature as Hicksian income). Lindahl provided a theoretical concept of income as return the nation’s capital, which is very similar to the concepts proposed by Fisher and Hicks. However, Lindahl seemed reluctant to use this concept of income in his national income accounts. He preferred to use a concept of income which is quite similar to the current definition of net national product (which he calls national income).

4. Welfare interpretations of income and wealth We now return to a central issue in national income accounting – what exactly is a one-dimensional construct such as national income seeking to measure? What information should it convey? The Keynesian approach, as we have seen, was rooted in the imperatives of macroeconomic management. It was not really seeking to produce a one-dimensional measure of the success of the economy – which is what gross national product is usually taken to be – but rather a set of numbers to be used for evaluating the economy’s macroeconomic posture and the merits of alternative policy measures. The alternative approach to the definition and measurement of national income is rooted in an attempt to construct an index number with clear welfare significance. The bulk of the recent (and quite complex) theoretical literature on green accounting focuses

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on the links between welfare and various concepts of income, such as national product.8 We begin the discussion of income within the realm of a perfect market economy, so that we can later add complications that stem from welfare implications of adding in the ecological system explicitly. Within the context of theoretical work on income and welfare, there are again two distinct sub-traditions, although we shall show that they are closely linked. One focuses on income as sustainable consumption, and the other on income as a welfare measure. We look first at the concept of income as sustainable consumption, as this is more closely associated with the environmental literature, and also the older of the two interpretations. Although environmentalists have claimed it as their own, it pre-dates the present round of environmental concerns by at least three quarters of a century. 4.1. Sustainable income: a graphical approach Before becoming immersed in technical details, let us think intuitively about the Fisher– Lindahl–Hicksian (FLH) concepts of income (we shall return to Fisher, Lindahl and Hicks in a moment). Consider a Robinson Crusoe economy in which corn is produced with land and labor. The part of total output which we can consider to be income is the part which remains after we have set aside seeds for production next year. If more is consumed today than the maximum sustainable consumption, the economy will necessarily produce less next year. In the short run, we can consume more than this income, but the costs are borne by future generations. Conversely, if we consume less than the maximum sustainable consumption, then future generations may enjoy the fruits of our savings. In general, consider consumption vectors along a 45-degree ray from the origin in a diagram picturing consumption in different periods (consumption is equal in every period along the ray). We could then define an optimal path and consider constant consumption vectors that yield the same utility as the optimal path, or alternatively focus on consumption vectors that give the same wealth as that associated with the optimal path at its supporting prices. FLH income is simply the consumption vector where the ray giving equal consumption in all periods intersects the production boundary. We explain these ideas in more detail below. This discussion brings out the point that sustainable income is but one of many ways of thinking about income. As noted, it may be the case that we would like to consume less than the maximum sustainable consumption today, in order to enjoy the fruits of our savings in future periods. In Figure 1, we consider a two-period world (present and future) with c1 and c2 being the consumption levels in the two periods. Society has a transformation frontier between

8 Summaries of this literature, from various perspectives, appears in Aronsson, Johansson and Löfgren (1997), Aronsson and Löfgren (1998), Asheim (2000), Dasgupta and Mäler (2000) and Weitzman (2000, 2003).

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Figure 1. Fisher–Lindahl–Hicks income.

these two periods represented by the concave curve in Figure 1. The FLH concept of income can, as noted, be interpreted as the maximum consumption level in period 1 that is consistent with the same level in period two. Clearly this is the horizontal coordinate of the intersection of the frontier with the line c1 = c2 . We show the FLH income in the first period as cH . 4.2. Sustainable income and the ideas of Fisher, Lindahl and Hicks Having set out the basics, let us now turn to a more detailed discussion of the concept of income and how it relates to welfare in certain settings. A good beginning is with the question: What is income? This straightforward question has many answers, depending upon the context.9 For example, for tax purposes, income is defined by existing tax codes;10 in macroeconomic analysis, GDP is often the most natural concept for analysis, while the income concepts we are studying here are linked to notions of welfare.11 Fisher (1906) defines income abstractly as “a series of events”.12 According to Tobin (1987, p. 372) “Perhaps the most remarkable feature is Fisher’s insistence that ‘income’ 9 According to Samuelson (1951), a search for the meaning of income is a meaningless endeavor. In his view, a question like “what is income?” is similar to old pseudo-questions like “How do we know that Uranus is really Uranus?” 10 The so-called Haig–Simons concept income is one of the earliest definitions of income used for tax purposes. 11 From an accounting perspective, Gross national product (GNP = GDP + net factor income from abroad) may be viewed as an income measure, while GDP may be viewed as a product measure. 12 Fisher describes how he first came to think of the fundamental distinction between capital and income in the following way “It suddenly occurred to me while looking at a watering trough with its in-flow and outflow, that the basic distinction needed to differentiate[d] capital and income was substantially the same as the distinction between water in the trough and flow into or out of it” [as quoted in Nordhaus (1995, p. 4)].

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is consumption, including of course consumption of the services of durable goods. In principle, he says, income is psychic, the subjective utility yielded by goods and services consumed.” Fisher argued that adding investments to consumption would involve double counting. The return from investments would yield consumption later, and hence should be counted as income only when it contributed directly to subjective utility. Fisher defined income as the services from all the stocks of the economy, which is a basic tenet of the modern theory of green accounting, and is also central to Hicks’ definition. In the current literature on sustainable development, the concept of Hicksian income plays a dominant role, although, as we have indicated, Fisher–Lindahl–Hicks income is a more appropriate name. Hicks (1939) himself states that13 “Income No. 3 must be defined as the maximum amount of money which an individual can spend this week, and still expect to be able to spend the same amount in real terms in each ensuing week.”14 Hicks goes on to say that “We ask . . . how much he would be receiving if he were getting a standard stream of the same present value as his actual expected receipts. This amount is his income.”15 So income is the expenditure which if kept constant would yield the same present value as a person’s actual future receipts. This concept has the advantage of being explicitly dynamic. Formalized by Weitzman (1976), the concept has subsequently been developed further by, among others, Solow (1994), Asheim (1994, 1996a, 1996b), Hartwick (1994, 2000), Dasgupta (1993a, 1993b) and Dasgupta, Kriström and Mäler (1995). Lindahl (1932) discusses a concept of income which is, in effect, very similar. After reviewing four alternative concepts of income (income as consumption, interest, earnings and produce), Lindahl (1932, p. 407) concludes “The result of this investigation is, then, that for a certain period of time forward the anticipated interest, and for a period reckoned backward the produce in the sense of realized interest, is the most adequate expression of the income idea.” Lindahl went on to use this concept of income in his “Studies in the Theory of Money and Capital,” where he clarifies his position further. He argues that “(a consistent definition of income is) . . . that of a stream of interest on the capital values of these resources (“economic resources of all kinds”) arising from the economic value of the time factor,” Lindahl (1939, p. 144). As Fisher had seen earlier, Lindahl clearly recognized that social income is a comprehensive measure that should be based on a broad interpretation of capital. 4.3. Sustainable income and the Hamiltonian Weitzman (1976) showed that in the special case when utility is linear in consumption the Hamiltonian of an optimal growth problem can be interpreted as “Hicksian” consumption, i.e., as a constant consumption level giving a present value utility equal to that 13 We are very much indebted to Geir Asheim for a most instructive discussion of Hick’s concept of income. 14 Page 174 of Hicks (1939). 15 Page 184 of Hicks (1939). Pigou and Hayek also contributed to the early literature on real income mea-

surement.

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on an optimal path. Another way of saying this is that the Hamiltonian is a weighted average of future consumption levels along the optimal path, the weights being the discount factors. Solow (1994) and Asheim (1994) extended the analysis from the case of linear utilities. Weitzman’s insight shed light on a problem posed by Samuelson (1961), in his analysis of social income. Samuelson had looked at various income measures and argued that we cannot obtain a meaningful welfare index from these; rather, he claimed, we need a wealth-like measure. In retrospect, as we shall see later, Samuelson may have been correct. Weitzman and those who extended his initial analysis beyond the linear case showed that in a certain class of models income and wealth are merely “different sides of the same coin”. However, as we will show below, the class of models is limited and there is a wealth concept that seem to be more robust and general in various dimensions, such as the underlying assumptions about discounting the future. Weitzman’s result and its generalizations are in fact a simple application of the classical Hamilton–Jacobi equation of nineteenth century physics. The Hamilton–Jacobi equation relates the potential at points in a field to the energy in the field, and in effect the Weitzman-type results just tell us that wealth is under certain conditions the potential function for income. This is, in physical terms, the insight of Fisher, Lindahl and Hicks. 4.4. Income and welfare – the separating hyperplane approach Now we switch to the second of the concepts of income arising from welfare economics rather than from macroeconomics. This is income as a measure of welfare, rather than as a measure of sustainable consumption. The income measure relevant here is the value of equilibrium output at supporting prices. An important result in welfare economics connects national income and Pareto preferred projects. For example, if an allocation of goods is potentially Pareto preferred to a current equilibrium allocation, then national income measured in current prices must be higher in the new allocation (in a perfect market economy). This is the basis for cost-benefit analysis, since if a project, measured in current prices, lowers national income, then this project cannot provide an allocation of goods that is potentially Pareto preferred to the current allocation. This result is proved inter alia in Varian (1992, p. 407). Under standard convexity assumptions, it is intuitively clear that the converse result is not necessarily true. There are projects which increase national income, but at the same time may not lead to a potentially Pareto preferred allocation. However, if the change is small enough, the converse result is true: a “small enough” project, valued at current prices will also increase welfare, if it increases national income. Varian (1992, p. 408) points out that changes in utility are proportional to changes in income, if the changes are “small enough”. To explain the basic idea in a more rigorous way, consider the following simple model. Let u(c1 , c2 ) denote an individual’s utility function, where c1 and c2 are consumption goods with prices p1 and p2 , which is maximized subject to income m = p1 c1 + p2 c2 . This is NNP in this simple static economy. Differentiating the utility function totally and substituting the first-order conditions ∂u/∂ci = λpi , i = 1, 2,

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shows that u/λ = p1 c1 + p2 c2 is a linear index of welfare change. In other words, the value of the change of NNP is proportional to the underlying welfare change. In a dynamic world, m is the present value of consumption and the prices are present value prices; the welfare interpretation of the change in wealth follows immediately. We can now make our intuition from Figure 1 more exact. In a static model, any increase in national product – interpreted as above as the value of equilibrium output at supporting prices – will be a sign-preserving measure of the underlying welfare change, provided that prices are constant. In a dynamic model, the production possibility frontier pictures the efficient consumption levels in each of two periods (in the simplest case). It is obvious from this that in any economy, and so specifically in a dynamic economy, the appropriate welfare measure depends upon the objectives of the economy, on its maximand. It depends on the social indifference curves. It thus depends on the discount rate and on the nature of the economy’s intertemporal objective function in the dynamic case, as indicated in detail in Section 9. Until we have specified our valuation of future generations, we cannot define dynamic welfare measures. Intuitively this makes sense. Consider an economy endowed with a large number of very long-lived environmental assets each of which will provide a small flow of services indefinitely: it is rich if one takes a very long-term view but poor if one focuses mainly on the near future. This is a very real issue as many environmental assets [such as watersheds and biodiversity, see Chichilnisky and Heal (1998) and Heal (2000)] are capable of providing a flow of services indefinitely into the future, in contrast to physical and human capital. This highlights the importance in practical applications of assessing whether market prices reflect adequately social attitudes towards the future. By way of illustration, the services provided to New York City by the Catskills watershed could be replaced by a filtration plant at a capital cost of $8 billion [Chichilnisky and Heal (1998), Heal (2000) and National Research Council (2000)]. This would have a life of a few decades, and would then need replacing, whereas the watershed could continue for ever, as it has for the last few millennia. So the total cost of the replacement, an upper bound on the value of the natural asset as a watershed,16 is the present value of an indefinite sequence of $8 billion investments, clearly very sensitive to the discount rate. Let us now explain the separating hyperplane approach to income and wealth measurement in more detail. The transformation frontier in Figure 2 shows alternative combinations of labor and consumption available to an economy. CE is a competitive equilibrium, with SIC being the social indifference curve corresponding to the individual indifference curves attained at the equilibrium.17 pp is a hyperplane separating the set bounded by the social indifference curve from the feasible set. The normal to this line represents the equilibrium price vector: national income is defined as the value of 16 It may play other roles, such as biodiversity support or provision of recreational facilities. 17 This social indifference curve is the lower boundary of the set-theoretic sum of the individual preferred-

or-indifferent sets corresponding to equilibrium consumption levels. For more discussion and a review of the literature on this topic, see Chichilnisky and Heal (1983).

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Figure 2. The separating hyperplane.

equilibrium consumption at these prices. Any small move from CE which has a positive value at pp will move the economy above the social indifference curve through CE and is potentially Pareto improving. This is the concept of national income underlying cost-benefit analysis and was referred to in Heal (1998) as national welfare or national wealth. In a dynamic context, it is the present value of incomes in all periods, the righthand side of the intertemporal budget constraint in a world of complete markets. Figure 2 suggests that changes in wealth serve as the appropriate indicator of underlying welfare changes. But wealth is inherently difficult to measure, so it is natural to ask if currently measured income provides the same information about the economy as does the wealth concept. This is a subtle issue and subject to much current debate, see, e.g., the exchange between Dasgupta and Mäler (1999) and Weitzman (1999). We will suggest below that the wealth measure of welfare seems more fundamental and in some ways more robust: it works for variable discount rates, zero discount rates, and the cake eating problem, whereas the sustainable income concept associated with the Hamiltonian has problems in these cases. The wealth measure also works for nonutilitarian objectives such as overtaking, the Chichilnisky criterion and the Green Golden Rule, whereas the sustainable income measure does not. 4.5. Taking stock We have discussed two approaches to welfare measurement in dynamic economies. While there are still divergent views upon whether wealth and income are “two sides of the same coin”, the theoretical literature on income and wealth has converged to a key insight in the green accounting literature. This is that an accurate description of the economy’s stocks is a prerequisite for obtaining useful welfare measures. The Catskills watershed example illustrates this point rather well. Furthermore, in his 1995 Arrow lectures, Mäler (1995) argues: “That all economies depend on their natural resources,

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such as soil and its cover, water, forests, animals, and fisheries should be self-evident: ignore the environmental-resource base, and we are bound to obtain a misleading picture of productive activity in the economy.” Take as an example the development of U.S. agriculture between 1950 and early 1990. Significant productivity increases along with lower consumer prices suggest that consumers have been made better off. According to Crosson (1993), however, erosion-induced losses of soil productivity and “mining” of groundwater for irrigation, as well as recreation values not reflected in commodity prices, “excites unease” about future productivity levels. The importance of stocks extends to the recent literature on endogenous growth, which pinpoints the crucial importance of human capital and of technological knowledge for future economic growth. While the framework we develop in this paper is in principle very general, we focus the environmental stocks.

5. A general dynamic model Next we begin the process of formalizing all these insights in a consistent model that will allow us to explore and compare the different concepts and investigate their robustness. As noted, we place particular emphasis on the role of stocks of environmental assets and their contributions to welfare and to productivity. This allows us to structure our discussion about the links between welfare measurement and the construction of resource accounts. The purpose here is to arrive at an index that is proportional to some measure of current or sustainable human welfare, and to associate this with an accounting framework. As has come to be standard in this literature, the Ramsey (1928) model is a workhorse for the developments to follow. Let the vector c(t) ∈ m be a vector of flows of goods consumed and giving utility at time t, and s(t) ∈ n be a vector of stocks at time t, also possibly but not necessarily sources of utility. Each stock si (t), i = 1, . . . , n, changes over time in a way which depends on the values of all stocks and of all flows:
 . si (t) = di c(t), s(t) , i = 1, . . . , n. (1) We begin with a relatively simple case in which the economy’s preferences are represented by the discounted sum of utilities, a case, we should note, that many environmentalists regard as inappropriate in terms of the present-future balance that it strikes. The economy’s objective is to maximize the discounted (at discount rate δ) integral of utilities (2):  ∞
 max (2) u c(t), s(t) e−δt dt 0

subject to the rate-of-change Equations (1) for the stocks. The utility function u is assumed to be strictly concave and the reproduction functions di (c(t), s(t)) are assumed to be concave. This is a very general and flexible formulation, and in the following we

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shall frequently specialize it to simple and more familiar cases. This general formulation makes it possible to include human capital and other assets, as well as to address issues that are not directly relevant for green accounting per se. Note that if u = u(c) . and s = f (s) − c, then we have the Solow model. In the context of resource economics, . when u does not depend on s and if (1) takes the form si (t) = −ci (t) then we have the Hotelling model. This formulation captures the possible contributions of environmental stocks to consumer utility and to productive efficiency. To solve this problem, we construct a Hamiltonian which takes the form n 

 λi (t)e−δt di c(t), s(t) , H (t) = u c(t), s(t) e−δt +

(3)

i=1

where the λi (t) are the shadow prices of the stocks. Two features of this formulation may be worth commenting upon. First, note that the Hamiltonian is in some sense a utility function. It suggests that there is a trade off between the current and the future; consumption “now” provides instant utility as measured by u(c(t), s(t)), which is traded-off against a smaller net investment in this period. Second, if we insert the Solow model in the Hamiltonian, we obtain a definition of net national income (in utility terms). If the utility function is linear in c, the correspondence to net national income is direct.18 The first-order conditions for optimality can be summarized as  ∂di (c(t), s(t)) ∂u(c(t), s(t)) =− λi,t ∂cj ∂cj

(4)

n . ∂u(c(t), s(t))  ∂dk (c(t), s(t)) − λk (t) . λi (t) − δλi (t) = − ∂si ∂si

(5)

n

i=1

and

k=1

We shall make use of the state valuation function V (s), which we define in the usual manner:  ∞ . V (s0 ) = max u(c, s)e−δt dt, si,t = di (ct , st ), i = 1, . . . , n, s0 given. {ct }

0

This function gives the maximum present value utility obtainable from the initial stock vector s0 . By standard results, ∂V = λi ∂si

(6)

18 There is some controversy in the literature on the interpretation of a “linearized Hamiltonian”. See

Aronsson, Johansson and Löfgren (1997), Asheim (1999) and Dasgupta and Mäler (1999) for different viewpoints. Papers exploring expanded version of NNP include Mäler (1991), Dasgupta and Mäler (1995), Dasgupta, Kriström and Mäler (1995, 1997a, 1997b), Dasgupta and Mäler (2000) and Hartwick (1990, 2000).

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so that the shadow price of the ith stock is the marginal social productivity of that stock. It immediately follows that  . dV λi si . = dt

(7)

i

Note that (7) tells us something of interest: it states that the rate of change of the state valuation function along an optimal path is positive if and only if the value of stocks at shadow prices is increasing. Formally, P ROPOSITION 1. Future welfare rises along an optimal path if and only if investment is positive at current shadow prices. This result is in Heal (1998), Dasgupta and Mäler (2000) and Pemberton and Ulph (2001), as well as Asheim and Weitzman (2001). We can now obtain a second expression for the rate of change of the state valuation function, by differentiating under the integral sign in the definition:  ∞ dV u(c, s)e−δt dt. = −u(c, s) + δ dt 0 Equating the two expressions for dV /dt gives δV = H

(8)

so that the Hamiltonian can be seen as “interest” on the state valuation function, where the interest rate is the discount rate. This result is a special case of the well-known Hamilton–Jacobi equation of classical physics, see Ekeland and Turnbull (1983).

6. Measures of income and the Hamiltonian We now use this general framework to develop different welfare measures of income, specializing to various case as required. We begin with income in the Hicksian tradition. Throughout this section we assume that the Hamiltonian is autonomous, which essentially means that the accounting system is complete (the Hamiltonian contains all necessary information for evaluating the future). We discuss the nonautonomous case separately. 6.1. Hicksian income and the Hamiltonian Let {c∗ (t), s ∗ (t)} be the solution to the problem of maximizing (2) subject to (1). Also let CH(t) be the Hamiltonian corresponding to this problem, not discounted to time zero: CH(t) is the current value Hamiltonian. Then we have the following generalization of Weitzman (1976):

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P ROPOSITION 2. For any date t,  ∞ 
 CH(t) c∗ (t), s ∗ (t) e−δ(τ −t) dτ = t

∞


 u c∗ (τ ), s ∗ (τ ) e−δ(τ −t) dτ.

t

In words, a utility stream from t to infinity of a constant value equal to the Hamiltonian evaluated on the optimal path at t has the same present value as the utility stream from t to infinity associated with a solution to the problem of maximizing (2) subject to (1). P ROOF. This result follows almost trivially from (8). Note that  ∞ V = H /δ = H e−δt dt.




0

The Hamiltonian is thus a measure of the “equivalent constant utility level” associated with an optimal path, and, as we have noted, it is a natural candidate for a measure of Hicksian national income. It is sometimes referred to as a “sustainable” utility level, but this is in fact inaccurate [see Heal and Kriström (2000)]: it is an average future utility level, but not necessarily a utility level that can be maintained for ever. This leaves open the issue of whether an increase in the Hamiltonian is an increase in welfare as measured by the objective function of the optimal growth problem, or whether it is a potential Pareto improvement. We return to this later, showing that in general neither of these propositions is true: the welfare implications of an increase in the Hamiltonian are limited to those just stated. The Hamiltonian is denominated in an ordinal utility metric, so for practical measurement purposes we need to find a way of translating this metric into something that we can measure, i.e., money. This transformation is, in general, not trivial [see Dasgupta and Mäler (2000) and Weitzman (2000) for differing views]. Before proceeding, it might be useful to pause for the moment and reflect upon the usefulness of the Hamiltonian formalism that currently dominates the theoretical green accounting literature. Besides posing clearly the question of what it is we want to measure, the Hamiltonian formalism helps avoid double counting when devising (linear) welfare indices. Stocks and flows are handled correctly in the welfare sense. Furthermore, the Hamiltonian is useful in the construction of accounts. We will give a few direct illustrations of the power of this approach when we discuss empirical studies in Section 14. We also provide an indirect illustration of its usefulness, as we penetrate the UN-system of environmental accounting, the SEEA, in Section 14.1. There, the accounts are based on expanded versions of the SNA identities and not on the Hamiltonian formalism.

7. National wealth Turn now to the second approach to defining national income, that portrayed in Figure 2 and associated with the use of the prices defining a separating hyperplane to judge

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whether a change is an increase in welfare. This is in many respects an approach that is more in keeping with the standard approach to project evaluation in applied welfare economics: it is in the mainstream tradition of welfare economics established in the 1950s and 1960s. It draws on the standard theory of static welfare economics and extends it to a dynamic context via the time-dated commodity approach of Arrow and Debreu: it does not, however, address the task of computing a static equivalent to future consumption levels and so has no direct connection with the issues underlying the conventional interpretations of sustainability. It lends itself naturally to the discussion of long-run issues, in fact more so than the Hamiltonian-based approach, and so in this sense is useful for answering questions about sustainability. There is an irony here: an approach devised specifically to grapple with sustainability and its interpretation is in the end less well-adapted to this than a more generic approach sanctioned by traditional theory. Next we set out the basic principles of measuring national welfare via the separating hyperplane approach in the context of the general model in Equations (1) and (2). The first-order conditions for optimality were given in (4) and (5). The use of arguments about separating hyperplanes in problems involving infinite time horizons is mathematically quite delicate, so we need to be precise about the framework to be used. We shall assume that the functions di (c(t), s(t)), i = 1, . . . , n are such that the set of feasible paths for cj (t) and si (t) is bounded: reasonable conditions sufficient for this are presented for the specific models used here in Heal (1998).19 A hyperplane which supports the optimal path is one that separates the set of paths preferred to an optimum from those which are feasible (for a formal definition see the previous footnote). This is a time path of prices for stocks and flows pc,j (t) and ps,i (t) which satisfies two conditions: any path at least as good as the optimum has a value at these prices at least as great as the optimal path, and any feasible path costs no more than the optimum.20 D EFINITION 3. A set of prices pc,j (t) and ps,i (t) supporting the optimal path will be called optimal prices and will be used to define national wealth as follows: national wealth along the optimal path is  ∞     pc (t), c∗ (t) + ps (t), s ∗ (t) e−δt dt. 0 19 Under this assumption, the paths of all variables, including utilities, are such that their integrals against a discount factor with a positive discount rate are finite. Formally, for any i and j , 0∞ cj (t)e−δt dt < ∞, ∞ −δt dt < ∞ where c (t) and s (t) are real-valued functions of time. We can therefore regard the j i 0 si (t)e space of possible paths of consumptions levels and stocks as a weighted l∞ space, with the norm f (t) = supt |f (t)e−δt | and the inner product of two functions f (t) and g(t) being f, g = 0∞ f (t)g(t)e−δt dt.

A supporting hyperplane for a set S is then given by a function h(t) such that everything in the set is above it in the sense of having at least as great a value at the prices defining the hyperplane:  ∞   s(t)h(t)e−δt dt  0 ∀s(t) ∈ S. s(t), h(t) = 0

If the function s(t) is a n-vector-valued function defined on the real numbers, then likewise h(t) :  → n and s(t)h(t) is interpreted as the inner product of two vectors in n . 20 For a formal definition, see Heal and Kriström (2000).

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Here pc (t), c∗ (t) represents the inner product of the price vector pc (t) with the consumption vector c∗ (t). This entire expression is just the inner product of consumption and stock paths over time with the path of supporting prices, a generalization of Figure 2. By analogy with Figure 2, we want to establish that any small change which increases this measure is a welfare improvement. In the next proposition, we characterize a set of prices which are optimal prices in the sense of the above definition. These prices are quite intuitive: they are the marginal utilities of the stocks and flows along an optimal path. So price ratios are just marginal rates of substitution as usual. In effect, these marginal utilities define ∞ the marginal rates of substitution between the different arguments of the maximand 0 u(c, s)e−δt dt, and are natural candidates for the role of defining a separating hyperplane. P ROPOSITION 4. The sequence of prices defined by the derivatives of the utility function along an optimal path, i.e.,

   ∂u(c∗ (t), s ∗ (t)) ∂u(c∗ (t), s ∗ (t)) , ∀j, i, t pc,j (t), ps,i (t) = ∂cj (t) ∂si (t) form a set of optimal prices in the sense of Definition 3. We have now established that the derivatives of the utility function with respect to stocks and flows on an optimal path can be used to define a hyperplane which separates the set of paths preferred to an optimal path from the set of feasible paths. They can therefore be used to define a price system at which national income in the national welfare sense can be computed. It is of course immediate that any small change in a path which has a positive present value at these optimal prices will increase welfare: ∞ ∗ ∗ C OROLLARY 5. A variation {c(t), s(t)}∞ t=0 on optimal path {c (t), s (t)}t=0 has ∞ positive present value at the optimal prices {pc,j (t), ps,i (t)}t=0 and so is an increase in NW if and only if the implementation of this variation leads to an increase in welfare.

This result, though immediate given what precedes it, is important: it tells us that any other index indicates a small increase in welfare if and only if it agrees locally with NW, which is therefore the benchmark for welfare indices. An alternative measure of wealth, used inter alia by Dasgupta and Mäler (2000), is the value of stocks at shadow prices, W = i λi si . Note from Proposition 1 and from Equation (7) that the rate of change of the state valuation function is the rate of change of W at constant prices. Building on this and the earlier definitions we can establish an important relationship between the rates of change of national wealth NW and the state valuation function V : they are equal up to a first-order approximation. Differentiating NW with respect to time, dNW dV = δNW − pc c − ps s = δNW + − δV + R(2), dt dt

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so  d
d
−δt  + R(2) NWe−δt = Ve dt dt and, for t = 0 or for all t if NW(0) = V (0), dNW dV = + R(2), dt dt so that dNW/dt = dV /dt plus terms of the second order in u(c, s). From this and Equation (7) we immediately have the following proposition. P ROPOSITION 6. The rate of change of national wealth NW equals the rate of change of wealth measured as the value of stocks at shadow prices W while prices are constant.21 The rate of change of NW also equals to a first order the rate of change of the state valuation function. This implies that of the two approaches to measuring wealth, as the present value of consumption at shadow prices or as the value of stocks at shadow prices, the former tracks welfare changes better. Wealth as the value of stocks only tracks welfare if stock prices are constant. We return to this issue later in more detail. 7.1. Illustration 7.1.1. Hotelling To illustrate the workings and the essential simplicity of these ideas, consider briefly the present value of national wealth in the case of the classical formulation due to Harold ∞ ∞ Hotelling. In this case, we seek to max 0 u(c)e−δt dt subject to 0 c dt = s0 . Denoting the optimal path of consumption by an asterisk, the present value national welfare ∞ would in this case be measured by NW = 0 c∗ u (c∗ )e−δt dt. Noting that u (c∗ )e−δt is a constant by the first-order conditions characterizing an optimal path, equal to the initial value of the shadow price λ0 , this is simply the initial stock of the resource multiplied by the initial shadow price: NW = λ0 s0 . This is an extremely simple and natural measure of wealth: the welfare the economy can attain depends on its stock and the social value of this.22 In this case, two wealth measures are identical: national wealth as the value of consumption over time at supporting prices is the same as the value of stocks at shadow prices. It follows that the change in NW resulting from a change in the stock is clearly NW = λ0 s0 . 21 This result is similar to one contained in Dasgupta and Mäler (2000), who show that welfare increases if

wealth at constant prices increases: this is Proposition 1. 22 This result is closely related to the Hotelling Valuation Principle, which has been used to test the Hotelling

model empirically, see Krautkraemer (1998) for a survey of this literature.

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7.1.2. Stock a source of utility Next we set out in detail the implications of Proposition 6 and the foregoing analysis to a slightly more complex model of natural resource use which is a special cases of the general framework set out above. The model is as follows: 

∞

max

u(c, s)e−δt dt

0



∞

subject to

c dt  s0 ,

0

where s0 is a given initial stock. The Hamiltonian will be H = u(c, s) − λc and using the first-order condition for maximization of the Hamiltonian with respect to the level of consumption, a linear approximation to a change in this is LI = sus (c, s), where LI (for linear index) may be interpreted as Hicksian national income. So consumption flows net out and the value of LI at t is just the change in the value of the flow of services from the resource stock, valued at the marginal utility of the stock. The change in the flow of utility from depleting the resource makes no contribution to LI: the value of the flow cuc (c, s) is exactly offset by a term λc accounting for the depletion of the stock. Only the stock counts: if the stock were not valued in our economy, as in the Hotelling case, then LI would be zero. Any change in the stock, through discoveries or through sales, must be recorded in LI and valued (in a stationary state) at the shadow price of the flow times the discount rate. For more on this, see the discussion in Section 11.4, where we include trade possibilities in a cake-eating economy. At a stationary solution s ∗ , the marginal utility will satisfy us = δuc .23 With this relationship we can rewrite LI at a stationary state s ∗ as LI = δs ∗ λ

(9)

which is just the shadow value of the stock multiplied by the discount rate. This is, of course, the traditional definition of income: the flow of services from a capital stock. Away from a stationary state, the corresponding equation is . λ λs LI = δ − λ

(10)

which expresses the change in LI as the real return on the change in wealth. A similar conclusion is immediate from linearization.

23 See Heal (1998).

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7.1.3. Renewable resources Similar results hold in the case of renewable resources, using the model above with the . constraint s = r(s) − c. The Hamiltonian is now H = u(c, s) + λ{r(s) − c} so that     LI = cuc (c, s) + sus (c, s) + uc sr (s) − ct . As before, the terms in the flow c net out, so that once again, only terms relating to the stock appear in the expression for LI: .

  λ LI = s us (c, s) + uc r (s) = sλ δ − λ and in a stationary solution LI = δλs. A linearization approach gives, using consumption as the numeraire (suppressing the implicit  operator), the following linear index: . LI = c + ps s + s

(11)

which is consumption plus the net change in the resource stocks, to which we add the “existence” value of the stock (as for example in the case of blue whales). Return now to national welfare measures. A change in national welfare is measured by  ∞   uc (c∗ , s ∗ )c + us (c∗ , s ∗ )s e−δt dt. NW = 0

How does this compare with the Hicksian equivalent? For the same problem, the Hicksian measure is .

λ . LI = sλ δ − λ Using the first-order conditions for optimality, the instantaneous national welfare measure NW can be expressed as

. λ NW t = cλ + sλ δ − r − . λ

(12)

The difference between NW t and LI is cλ − λsr (s), which is the change in the flow of consumption minus the change in the return on the stock, evaluated at the marginal productivity of the stock in generating consumption flows. Clearly these two measures are quite different, and are measuring different characteristics of the economy. . The difference arises from the inclusion in Hicksian income of the term −λs reflecting . stock changes, as −λs = λc − λsr .

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8. Income, wealth and NNP It is now time to pull several strands of our discussion together. How are the income and wealth measures we have derived related to conventional indexes such as NNP? Let us first explore how conventional NNP is related to our wealth measure and to the Hamiltonian. This is most conveniently done in the simplest possible dynamic model. Thus, assume the scalar case for a prototype dynamic model (and assume that stocks do not appear in the utility function): . H = u(c) + λs = δV . Taking the time derivative, we have dV dH . .. .. = λc + λs + λs = δ . dt dt The conventional definition of NNP is . NNP = c + s.

(13)

(14)

Note that this is (essentially) the same as the LI defined above in Equation (11). Taking the time-derivative of (14) and using (13) we find that . dH d δ dV λ. dt = NNP + s = λ dt λ λ dt and consequently, . dV δ λ. d NNP = − s (15) dt dt λ λ therefore the change in NNP is not equal to change in V and the signs need not even be the same. Consequently, if we estimate the change in NNP over the years, an increase in NNP is not necessarily a sign of welfare increase (not even in the perfect market economy). It now follows [recall Equation (7)] that dtd NNP is the real return on the change in the capital stock .

λ d . NNP = s δ − . (16) dt λ Thus, there seems to be merit in focusing on wealth-based measures following Samuelson’s original ideas. The simple example above spelled out a problem that arises when interpreting conventional NNP as a welfare change measure. At the same time, it suggested advantages with the wealth-based measures. Thus, it is natural to ask how the wealth-based measure stands up in a more general model, where we include many stocks and flows, including the possibility that one or more stock is a source of utility. In Proposition 7, we propose a linear index in the “green” NNP tradition and tie it together with our national wealth measure.

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. P ROPOSITION 7. Consumption (λ.c + us s) plus investment (λ.si ) valued at shadow prices equals interest on national wealth NW computed at the discount rate δ: . λ.c + us s + λ.si = δNW. ∞ P ROOF. By definition, V (s0 ) = 0 u(c∗ , s ∗ )e−δt dt and  ∞  ∞ (cuc + sus )e−δt dt = (pc c + ps s)e−δt dt, NW(s0 ) = 0 0  ∞ dNW (pc c + ps s)e−δt dt = −(cuc + sus ) + δNW. = −(cuc + sus ) + δ dt 0 Also note that as NW is a first-order approximation to V then from Proposition 6 . dNW/dt = dV /dt and we know already that dV /dt = λi si so that  . λi si = −(cuc + sus ) + δNW or λc + us s +



. λi si = δNW.




. This measure λc +us s + λi si is not the first-order approximation to a change in the Hamiltonian resulting from a policy change. A significant point is that consumption and investment are observable contemporary variables whereas NW is not. Whether shadow prices are observable is a debatable point to which we return in Section 11. To sum up: the correct welfare measure is V (or NW) so that i si λi or λc + us s + . λi si are the preferred instantaneous welfare indices. The former is referred to by the World Bank as “genuine savings” – see Section 14.6.

9. Applications and extensions This section contains applications of the theory to two cases of immediate interest and provides extensions beyond autonomous Hamiltonians and discounted utilitarianism. Thus, we begin applying the ideas developed above to a simplified model that draws on some of the ideas developed in the literature on endogenous growth theory [Aghion and Howitt (1997)]. Next we take on defensive expenditures. They are notorious for creating confusion regarding their place in measures of national product. Should resources expended at cleaning up an oil spill really show up in GDP? The answer depends on the purpose of measurement and we show what the answer is from a welfare-theoretic perspective. We then turn to immediate extensions of the framework. The main departures in the literature from the framework we have reviewed so far are two fold: placing more emphasis on the welfare of future generations, via nonutilitarian objectives and zero discount rates, and allowing for technical progress. There have also been attempts

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to introduce uncertainty and unemployment into the analysis. Such extensions complicate the basic framework, in the sense that measurement of sustainable income becomes rather more difficult. As we shall see, the wealth measures we have discussed are more robust towards perturbations of the standard assumptions. 9.1. Economic growth We consider an economy whose output depends on the investments made in technological knowledge and in human capital. We assume the utility level u at each date to depend on consumption c and on the amount of leisure, which is expressed as the total time available l minus labor in production l1 and minus time in education l2 : u(c, l − l1 − l2 ). Production depends on the state of technological knowledge T and on the stock of human capital which we represent by hl1 where h is human capital per person, so that y = f (T , hl1 ). We can allocate output y to increasing both the stock of technological knowledge and that of human capital, so that y = f (T , hl1 ) = c + e + I where e and I are investments in human capital and technology respectively. The rate of change of . human capital per person is h = E(e, l2 ) where e is the output invested in human capital and l2 the population working in education. The stock of knowledge changes at the rate . I : T = I . In this framework, the optimal growth problem is  ∞ u(c, l − l1 − l2 )e−δt dt max 0

s.t.

c = f (T , hl1 ) − e − I

. and h = E(e, l2 ).

The Hamiltonian is
 H = u(c, l − l1 − l2 )e−δt + λe−δt f (T , hl1 ) − e − c + µe−δt E(e, l2 ) and by applying the first-order conditions we can readily show that a linear approximation is given by T λf1 + hλf2 l1 or at a stationary solution: δ[T λ + hµ]. This implies that at a stationary solution NW = T λ + hµ. So we can express the change in wealth resulting from a variation about an optimal policy as the change in value of stocks, with no other terms needed. 9.2. Defensive expenditures Defensive expenditures are those that people undertake to neutralize the impact of negative externalities – for example, double glazing to reduce traffic noise or installing air

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filters to reduce pollution. There has been extensive debate about how these expenditures should be treated in national income accounts. For example, if there is a disastrous oil-spill, such as the Exxon Valdez 1989 spill, resources will go into the clean-up and, it is argued, this will be recorded as an increase in GDP. Under full employment this is not the case, of course, since labor resources will be crowded out from other sectors that at the margin have equal value. Under unemployment, the issue is more subtle and it might happen that total production, as measured by GDP, increases. In so far, as total production increases, GDP should signal this, because GDP is a measure of production. If we seek a welfare-adjusted national product, then the wage bill should not be included [Dasgupta, Kriström and Mäler (1995)] and the issue is moot. Let utility depend on consumption and on a variable z that depends on the state of the environment Q and the defensive expenditures g undertaken to improve this: u(c, z), where z = h(g, Q). Output is just a function of the capital stock, y = f (k), and can be . consumed, invested or allocated to defensive expenditures: y = c + k + g. The state of the environment Q evolves positively (α  0) according to investment in defensive expenditures and the current state and negatively with output (β  0):24 . Q = αh(g, Q) + βf (k). Given this formulation and the objective of maximizing the discounted integral of utilities, the Hamiltonian is
     H = u c, h(g, Q) e−δt + λ f (k) − c − g + µ αh(g, Q) + βf (k) and by conventional arguments we can derive the approximation kλf + Qh2 [u2 + µα] = kδλ + Qh2 δµ in a stationary state. The key point about this equation – apart from the now-familiar formulation in terms of stocks – is that the levels of defensive expenditures do not appear in national wealth or its changes. Nor do wage payments: all that is needed is the changes in the stocks that drive economic well-being, k and Q. We return to defensive expenditures in Section 11.1.2, albeit from a different perspective, as we discuss whether or not they can be used to approximate the value of ecological services. 9.3. Non-autonomous Hamiltonians The Hamiltonian represent two aspects of welfare in the standard formulation: u(c) . measures instantaneous welfare, while λs provides information about future welfare. If there is exogenous technological progress, the very passage of time provides future utility, since production possibilities increase from period to period without the input of any scarce resources. The value of this “gift” must be added to the Hamiltonian, 24 If one thinks of Q as noise and of g as double glazing or some other form of insulation, then α = 0. If Q

is pesticide or fertilizer in agriculture and g represents wetlands then α > 0.

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to represent the present value of future technological progress, if we want to measure the present value of future welfare correctly. More formally, as already noted, if the Hamiltonian is autonomous then a basic theorem from physics states that H = δV , which translates to the statement that the Hamiltonian is the return on social welfare. This correspondence is broken if the Hamiltonian depends explicitly on time. Aronsson (1998) shows that the introduction of unemployment has two implications for the measurement of sustainable income: (i) the wage provides no information about the value of leisure time, and (ii) the present value of future changes in unemployment must be included in the welfare measure. A similar result is obtained by Aronsson and Löfgren (1993) regarding the impact of exogenous technological progress on the measurement of sustainable income. For a useful discussion of the interpretation of the Hamiltonian as return on wealth when exogenous technological progress is allowed, see Aronsson, Johansson and Löfgren (1997) and Usher (1994). There is also a subtle difference between interpretations of the Hamiltonian as an indicator of sustainable welfare and the Dasgupta–Mäler perturbation approach in this context. Dasgupta and Mäler (1999, p. 24) claim that “. . . one can confirm that the discussion in Section 7 on the evaluation of policy reform remains unchanged in the presence of technical change.” By contrast, Aronsson, Johansson and Löfgren (1997) argue (p. 63) “In the case of technological progress, another term, representing (an approximation of) the present value of marginal technological progress along the optimal path, has to be added (to the linear welfare measure).” The reconciliation between these seemingly contradictory statements is now familiar. The authors are interested in two different characteristics of the economy. The Dasgupta–Mäler approach aims at welfare measurement over short intervals of time, while the papers in the Weitzman tradition focus on sustainability indicators, necessarily long-term in their orientation. 9.4. Non-utilitarian optima We now extend our discussion beyond the discounted utilitarian case. The new cases may capture better current concerns for sustainability. In many of the more general cases, a Hamiltonian approach to the definition of national income is clearly inapplicable as the welfare integrals diverge or the underlying optimization model cannot be solved by standard control theoretic or variational techniques. The former is true of von Weizäcker’s overtaking criterion [von Weizäcker (1967)], which gives a partial ordering of alternative consumption plans that is not representable numerically: the latter is true of the criterion introduced by Chichilnisky. We focus first on the case of an economy which defines optimality according to Chichilnisky’s criterion of sustainability [Chichilnisky (1993, 1996)], which involves the weighted average of an integral of utilities and a term depending on long-run or sustainable utility levels. We shall focus on the case of exhaustible resources. Consider the optimal use problem in the simplest

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version of this case:25  ∞ max α u(ct , st )e−δt dt + (1 − α) lim u(ct , st ), t→∞

0

. st = −ct and st  0 ∀t.

The FLH income measure cannot be computed for this case, as this problem cannot be solved by standard Hamiltonian-based techniques [see Heal (1998)], so we have to work with the national wealth measure. Let (ct∗ , st∗ ) be the optimal path for this problem. Then using an obvious generalization from the utilitarian case national welfare is now defined as  ∞ 

 ct uc ct∗ , st∗ + st∗ us ct∗ , st∗ e−δt dt NW = 0 

 + lim ct uc ct∗ , st∗ + st us ct∗ , st∗ . (17) t→∞

Marginal utilities are again used as prices, as in Definition 3. The definition of wealth now contains two elements: one the integral term, as in the case of the discounted utilitarian approach, and an extra element arising from the value placed by the objective on the limiting utility level. In this, the limiting stock values and consumption levels are valued at limiting prices. The value assigned to a path depends both on the time path over finite horizons, via the present value term, and also on the limiting or sustainable values along the path.26 With Chichilnisky’s definition of optimality, the price system contains undiscounted terms because of the limiting term in the definition. So national welfare is measured in (17) as a present value plus a term reflecting long-run or sustainable welfare. This term is not discounted: apart from this it has the same form as the other terms, namely stocks and flows evaluated at prices given by marginal valuations along an optimal path. The presence of this extra term is important, because it gives a reason for using in the measurement of national welfare prices which relate to the distant future yet are nevertheless not discounted. This possibility has been discussed by several authors including Cline (1992) and Broom (1992), but in the context of using only undiscounted valuations, rather than a combination of discounted and undiscounted values. By analogy with Figure 2, we now want to establish that any small change which increases this welfare measure is a welfare improvement. T HEOREM 8. Let a small variation {ct , st } about an optimal path {ct∗ , st∗ } increase NW as defined in (17). Then the implementation of this variation leads to an increase in welfare. 25 For the solution of this problem, see Heal (1998). 26 Formally, we are now defining the value of a sequence of consumption and stock levels (c(t), s(t)) at

prices pc (t), ps (t), or equivalently defining the inner product of the consumption and stock sequences with the price sequences. We define a supporting hyperplane for a set S of paths (c(t), s(t)) of consumption and of the resource stock as functions pc (t), ps (t) such that  ∞     c(t)pc (t) + s(t)ps (t) e−δt dt + lim c(t)pc (t) + s(t)ps (t)  0 ∀(ct , st ) ∈ S. 0

t→∞

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In summary, the definition of national income implied by Chichilnisky’s criterion of intertemporal optimality involves the use of prices to assign value to a path of the economy: the value will have two components, one a present value computed at a discount rate in the conventional fashion, and one an undiscounted value associated with the very long-run properties of the path. 9.4.1. Application to exhaustible resources With this criterion of optimality, national welfare is defined by (17). With the exhaustible resource model used in the previous illustrations, the instantaneous value of this expression at any point in time is exactly as for the previous welfare measure, namely {c∗ uc (c∗ , s ∗ ) + s ∗ us (c∗ , s ∗ )}. However, there is a big difference from the previous national welfare case, which is that in this context the total national welfare along a path is not the present value of all instantaneous welfare levels, but exceeds this by the limiting terms limt→∞ {c∗ uc (c∗ , s ∗ ) + s ∗ us (c∗ , s ∗ )} reflecting sustainable welfare levels. There is no instantaneous welfare measure that reflects accurately the total contribution of the current configuration to the welfare value of a path. In evaluating any change, we have to consider both the effect on current welfare (and on future welfare levels at finite dates, which are captured in shadow prices) and the effect on limiting or sustainable welfare levels. 9.5. Sustainable revenues and national income Suppose now that the economy is very future-oriented, in that the objective is to achieve the maximum sustainable utility. Consider in this case the renewable resource model used by Beltratti, Chichilnisky and Heal (1993, 1995) to define the Green Golden Rule: . max lim u(ct , st ) subject to st + ct = r(st ). t→∞

The solution is described in Figure 3: it involves moving to a point (c∗ , s ∗ ) in the c–s plane at which the graph of r(s) is tangent to an indifference curve of the utility function. We expect intuitively to be able to support such a point by facing agents with relative prices for the two commodities (the stock and the flow in this case) equal to the common slope of both sets at their point of tangency. Applying this in the present context, we could normalize the price of consumption to be unity, and set the price of the stock to be p = r (s ∗ ). Maximizing c + ps,

where p = r (s ∗ )

(18)

over the set of c–s points that can be maintained for ever (i.e., that form stationary solutions with c = r(s)) will lead to the Green Golden Rule. In the renewable resource context, think of the following example. The owner of a resource stock can sell a flow generated from this, and is also paid a “rent” for maintaining the stock. The stock might be a forest: then the flow would be derived by cutting and selling a part of this, while

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Figure 3. The Green Golden Rule.

the rental payment on the stock could be payments made by people using the forest for recreational purposes, a payment in recognition of the forest’s carbon sequestration or biodiversity support roles. Then if the rent relative to the price of the flow is r (s ∗ ), the combination of stocks and flows which maximizes total receipts is the Green Golden Rule. There is a difficult point here, relating to the time dimension. The diagram and the analysis relate to a one-period framework: however we are interested in behavior which supports the Green Golden Rule for ever. We would like to say that choosing (c∗ , s ∗ ) maximizes the sum of revenues from the resource over the long run, but we cannot say this, as this sum is clearly infinite, and there are many other feasible (c, s) combinations which will also give an infinite value. And we cannot say that (c∗ , s ∗ ) maximizes the present discounted value of revenues form the resource, because it does not: for any positive discount rate, the policy which maximizes the present value of profits will be nonstationary. What then can we say? We can say that the Green Golden Rule leads to the highest indefinitely maintainable level of revenues from the use of the resource: it maximizes “sustainable” or limiting or long-run revenues. There is an important conclusion here: if society is so future-oriented as to wish to support the highest sustainable utility level, i.e., the Green Golden Rule, then we need correspondingly future-oriented behavior on the parts of agents in the economy. We need firms to seek the highest sustainable profits (i.e., the maximum value of profits that can be maintained for ever) and resource

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owners to manage their resources so as to yield the highest sustainable revenues from the resources. Formally: T HEOREM 9. Consider the economy described by
 . max lim u c(t), s(t) s.t. s(t) = r(s) − c(t), t→∞

s(t)  0 ∀t.

Then there exists a price for the flow of the resource and a rental for the stock such that the Green Golden Rule values of consumption and the resource stock lead to the maximum sustainable profits from the use of the resource. How do these observations relate to the previous discussions of national income in its several interpretations? As we have noted elsewhere, with a zero discount rate the Hicksian national income is not well-defined and the Hamiltonian-based analysis cannot be applied (except to Ramsey’s formulation of the optimal growth problem). What we are using here is again the separating hyperplane approach, but now instead of the price system consisting of two parts, one defining a present value via an integral and the other reflecting the limiting behavior of the path, we now have only the latter term. The national wealth measure corresponding to this price system is now limt→∞ {cuc (c∗ , s ∗ ) + sus (c∗ , s ∗ )} which can be rewritten as limt→∞ {c + ps}, where p = r (s ∗ ) = us (c∗ , s ∗ )/uc (c∗ , s ∗ ). This is precisely the price system introduced above in (18), which we can now see as a particular form of our earlier concept of national welfare. Note that Hicksian national income is not applicable here, as there is no Hamiltonian to work with.

10. Theoretical issues – taking stock Several important points emerge from this review of the theory of national income accounting. Some are rather obvious, but nevertheless benefit from reiteration. In this category is the statement that how you should construct national income depends on what you want to measure and on how you want to use the measure. In addition, the right measure depends on society’s preferences – whether utilitarian or not, and if so, on their discount rate. Society’s welfare measure must reflect the extent to which it is forward-looking. This means, of course, that societies with different preferences may rank the same physical changes differently. Clearly this is not surprising, but bears restatement to emphasize that there is no universal measure of social welfare and so none of national income. We have reviewed many different approaches to the measurement of economic welfare. In spite of the extent of the literature and the occasional debates between contributors, there is substantial agreement on many major issues and there is a gradual process of convergence under way. It seems to us likely that the convergence will eventually lead to the following consensus. There are a number of weakness with green NNP, specifically the strong assumptions needed to justify an interpretation of this as sustainable

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income or welfare. The standard interpretation of NNP as a welfare measure used in cost benefit analysis is more robust (provided that prices are constant). What also seems to be very robust is the conclusion that changes in the values of stocks are “sufficient statistics” for welfare changes, and these are of course a measure of the change in wealth. They are also sufficient to measure changes in the linearized Hamiltonian. So via a circuitous route we seem to be agreeing with Samuelson and others who have argued for wealth-based measures in a dynamic context.

11. Issues in the construction of a green national product Having set the stage by formulating a series of potentially useful conceptual approaches to welfare measurement in the context of social accounting, we are now ready to discuss particular issues that arise in practice. In this section, we discuss three issues which seem particularly strategic in the context of implementing green accounting procedures:27 • valuation of ecological services; • valuation of stocks; • transboundary pollution. Subsequently, we turn to specific attempts to reformulate national income accounts – such as the UN’s proposed System of Economic and Environmental Accounts – and to applications to particular countries. We also discuss the genuine savings approach by the World Bank. 11.1. Valuation of ecological services One of the stumbling blocks in applying green accounting is the valuation of nonpriced goods and services. The practical measurement problems are considered so difficult that in some countries, for example in Norway, the environmental accounts are constructed in purely physical terms. Despite the significant improvement in our understanding of valuation methods in recent decades (as described elsewhere in this Handbook), the implied level of aggregation poses unique measurement problems in this context. Indeed, the direct and indirect methods for valuation of nonmarket goods were basically developed for micro level project analysis. It is altogether another matter to use such methods at a national scale. Nevertheless, there are a number of potentially useful approaches available and we begin by discussing those that have been developed mainly in the context of national income accounting. We refer to other chapters of this Handbook for discussion of other methods such as contingent valuation, the travel cost method and the hedonic pricing approach.

27 We will not discuss the treatment of labor further in this paper. See Dasgupta, Kriström and Mäler (1995)

and Hartwick (2000) for further discussion.

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11.1.1. Politically determined willingness to pay An approach that we here will term “politically determined willingness to pay” is based on the assumption that democratically elected representatives of the government are able to make decisions that reflect perfectly voters’ willingness to pay for environmental improvements. This implies that we can analyze the costs of various politically determined environmental goals to estimate the shadow prices. For example, if reducing the emission of some substance by y tonnes n years from now is an agreed political goal, then we can use the cost of the reduction in pollution required to reach the goal as an approximation to what the public is willing to pay for the change. This procedure is theoretically consistent, although based on a stringent assumption. The basic idea is illustrated in Figure 4. The x-axis depicts the level of an emission and the y-axis is given in a monetary unit. The downward sloping line shows the marginal costs of emission reductions, while the upwards sloping line summarizes the marginal benefits. Assume that the current level of emission is 6 units and the goal is to reduce emissions to 5 units, which is a level of emissions where marginal benefits and costs are equalized. The benefits of this policy are given by the area bounded by the marginal benefits curve, which will be approximated by the costs of reaching the goal – the area below the marginal costs schedule. It follows that the costs for reaching the political goals will be correlated with the benefits, although the approximation may not be very good. There are a number of practical problems with this approach. It assumes that political goals exist, which may only be true for a subset of the ecological services that one wants to value. It may also be difficult at times to define exactly what the goal is, since shortand long-run goals may exist simultaneously. Note also that when aspirations change dramatically upwards, the measured costs of pollution will increase proportionally. If environmental taxes or emission markets are in place, then this approach is considerably simplified. We can then make the argument that the tax or the price of a permit reflects the politically determined willingness to pay for a marginal reduction.

Figure 4. Politically determined willingness-to-pay.

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Hence, we can simply use the tax or the permit price as an approximation of the shadow price.28 11.1.2. Defensive expenditures and similar approaches Another approach to valuation, one that has led to considerable debate, is the use of defensive expenditures, which we discussed above in terms of a theoretical model. Within that model it was clear that such expenditures should not be included in a welfare index. What remains has to do with the classification of certain expenditures in the national accounts, i.e., whether or not they should be considered part of final demand or intermediate demand. Some commentators have argued that expenditures on police force and military should not be considered a part of final demand. Yet others have argued that expenditures on medication and other necessary inputs for quality of life should not be considered components of final demand. Clearly such arguments, quite apart from what theory implies, could lead to a reductio ad absurdum; any good consumed can, under certain arguments, be viewed as intermediate input. For example, food could be considered as a defensive expenditure against starvation. Such lines of reasoning may eventually lead to the conclusion that the national product is zero. Apart from the classification issue, there is a second, and for our purposes in this section, more relevant discussion about defensive expenditures. Can expenditures on a marketed good approximate the willingness to pay for environmental quality improvements? This depends on the assumptions about substitutability and complementarity of the environmental and market goods under scrutiny, as explained by Bockstael and Freeman (2005). They give an example where the quality of drinking water is produced by two perfectly substitutable goods: the “purity of public drinking water” and “increasingly effective filtration systems”. In this case, expenditures on filters can be viewed as a perfect substitute for purity of drinking water and, therefore, such expenditures can be used to approximate the value of quality improvements. In general, the correlation between defensive expenditures and willingness to pay for environmental improvements is not necessarily positive. Thus, caution must be exercised when using defensive expenditures as a way to approximate shadow prices. For additional discussion, see Bockstaehl and Freeman’s paper. A related class of approaches to the estimation of shadow prices focuses on the least expensive way to reach a predefined target. This is in the spirit of the “politically determined willingness to pay” approach discussed above, but the targets need not be current political goals. For example, Hultkrantz (1991) used the opportunity cost of protecting 15% of Swedish old-growth forests to value biodiversity loss. According to Hultkrantz (1991), scientific evidence provided by ecologists suggested that 15% of the current Swedish stock of old-growth forest must be set aside in order to guarantee a sufficient level of biodiversity. A basic weakness of this approach is of course that it is not based

28 For more on taxes in this connection, see Aronsson and Löfgren (1999).

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on preference information, so that we do not know how much society is willing to pay to reach this goal. Finally, the “maintenance costs” approach is sometimes used. It is defined as “the costs of using the natural environment which would have been incurred if the environment had been used in such a way that its future use would not have been affected” [Bartelmus and van Tongeren (1994, p. 16)]. Again, there seems to be no clear theoretical basis for this approach. See Section 14.1.1 for further discussion of this approach. Bergman (2002) applies ideas on defensive expenditures within a computable general equilibrium model of Sweden, in which sulphur emissions and their accumulation interact with the economy. Sulphur emissions affect welfare in his model by absorbing capital and labor into removal activities and by affecting total factor productivity. There is also a direct link between welfare and environmental quality in the model. Defensive expenditures are used as indicators of the value of neutralizing sulphur emissions in some of the experiments. For example, the SEEA-version of green NNP in Bergman’s model includes (i) the hypothetical expenditure needed to keep environmental quality constant and (ii) actual expenditures (such as liming of lakes) on “removal activities”. He finds that the difference between three versions of green NNP and conventional NNP is rather small in simulations, concluding that “The results, . . . , indicate that a significant share of the total economic impact of sulphur deposition is in fact reflected in the conventional NNP measure,” Bergman (2002, p. 58). From a theoretical perspective it is clear that welfare measures should always be based on preference information. Shortcuts such as defensive expenditures and similar approaches allow must always be seen in this light: they are valid if we can safely assume that marginal valuations are adjusted to them. 11.2. Valuation of stocks In the early to mid-1980s, several studies examined issues related to natural resource depletion [Ward (1982), Landefeld and Hines (1985)]. Triggered by these and other developments, the SNA now treats forests and certain other natural resources more like man-made assets in the accounts.29 There are a number of different proposals as to how depreciation charges should be calculated for natural resources. Several empirical methods have been suggested in the literature, e.g., market prices, present values, net rents, Ricardian rents, contingent valuation, hedonic methods, replacement cost methods, opportunity costs and a method suggested by El Serafy (1989). We discuss here the net rent method and El Serafy’s approach.

29 SNA is limited to economic assets, from which economic benefits accrues to the owner. The SEEA allows

for a broader natural asset boundary, where a natural resource does not have to be an economic asset.

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11.2.1. Economic depreciation Harold Hotelling (1925) gave a rigorous analysis of economic depreciation as early as 1925, although his study of was limited to the depreciation of machines. We will use his basic insights here and develop depreciation formulae for more general cases. We begin with a simple model discrete time model to set out the basic intuition and then use the Hamilton–Jacobi equation in continuous time to derive the key results in a compact way. Let V (t) be the value of a capital stock s at time t. Thus, V (t) is the capitalized value of future services, valued at q(t) at each moment of time from t, t + 1, . . . , T : V (t) =

T 

q(τ )R(τ ),

τ =t

where R(τ ) = (1 + δ)t−τ is a discount factor. At t + 1, the value of the stock will be V (t + 1) =

T 

q(τ )R(τ ),

τ =t+1

so by substitution we can express V (t) as V (t) = q(t) +

V (t + 1) . 1+δ

Economic depreciation is given by the value of the asset at the beginning of the period less the value of the asset at the end of the period, or D(t) = V (t) − V (t + 1). In the case of a nonrenewable resource, we define the net value of services (current resource rent) as q(t) = pc(t) − h(c(t)), where p is the price of the nonrenewable resource and h(c(t)) denotes the total costs of extraction. Consequently,
 δV (t + 1) . D(t) = pc(t) − h c(t) − 1+δ Hence, economic depreciation of the exhaustible resource has a value smaller than the current resource rents. It appears difficult to estimate the last term in this expression, but as shown by, e.g., Vincent and Hartwick (1997) this is not necessary if a number of idealized conditions hold. We will derive this result by using the Hamilton–Jacobi equation, beginning with the simplest case of an exhaustible resource. ∞ As before, let Vt = sup t u(cτ , sτ ) exp(−δ(τ − t)) dτ be the value function, where the supremum is understood to be taken over a feasible set defined by a set of constraints. Hotelling (1925) defines depreciation as the decrease in value of a particular machine, where value is defined as the annual rental value plus a scrap value. The depreciation

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amount can be interpreted as the sum of money that must be “put back” in order to hold “wealth” (or the present value of profits in the case of a firm) constant. Following Hotelling, we define depreciation as Dt = −

dVt . dt

(19)

We then note that, for the general problem stated in (2) and (1) above, the following apply:  ∞ u(cτ , sτ )e−δ(τ −t) dτ, Vt = sup (20) t

dVt = δVt − u(ct , st ), dt Dt = u(ct , st ) − δVt .

(21) (22)

P ROPOSITION 10 [Kriström (2002)]. In an economy described by  ∞ u(cτ , sτ )e−δ(τ −t) dτ max t

s.t.

. si,t = di (ct , st ),

i = 1, . . . , n,

the total depreciation charge for the stocks of the economy is given by the shadow price of the stock at time t multiplied by the net change of the stock:  . . λi,t si,t , Di,t = −λi,t si,t . Dt = − P ROOF. Dt = u(ct , st )−δVt = u(ct , st )−u(ct , st )− equation (8).



. λi,t si,t by the Hamilton–Jacobi


Total depreciation in this economy is the shadow value of the resources needed to keep wealth constant. Consequently, this way of defining depreciation clearly has close links with sustainability concepts. It should also be noted that SNA 93 uses a very similar “Hicks–Hotelling” concept of depreciation, see Hulten (1995, p. 158, Eq. (5.15)). We saw in Proposition 1 that the same quantity indicates whether the present value of welfare is increasing or decreasing along an optimal path. ∞ 11.2.1.1. Exhaustible resources. Suppose that an oil-well of size s0 = t c(τ ) dτ is subject to extraction by a competitive firm. The revenues are given by pc and the total costs of extraction are h(c), with MC ≡ dh dc > 0. The profits and the Hamiltonian are, respectively, πt = pc − h(c),

H = pc − h(c) − λc

(23)

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and we immediately find that Dt = λc = (p − MC)c,

(24)

where the last line follow from the first-order conditions. This is often called the net rent method and it has been studied in detail by Hartwick (1990) and others. The interpretation of the amount λc is, as suggested above, the amount of money that must be “put back” into the firm to hold the value of the firm constant.30 Lozada (1995) pointed out that the value of a mine is not independent of the market structure. In current value terms, the value of the remaining stock can be higher in t + 1 compared to t in the competitive case; i.e., there are capital gains. Capital gains are certainly a gain at the level of the firm, but not for the (closed) economy as a whole. Lozada (1995) therefore argues that capital gains should not enter the depreciation formulas used for the national accounts. Because marginal costs are difficult to estimate, one is often left with approximations of average costs; as pointed out by Hultkrantz (1991) and Vincent and Hartwick (1997) average costs may be very crude approximations to marginal costs in applications. Kriström (2002) makes the following observation to get around the problem of estimating marginal costs. Let ε ATC denote the elasticity of average total cost (ATC), and observe that (1 + ε ATC )ATC = MC. Then,

 MC λc = (p − MC)c = pc − h(c) 1 + εATC = pc − h(c) , ATC where ε ATC =

d(h(c)/c) c dc (h(c)/c)

and ATC = h(c)/c.

On certain arguments, ε ATC is more amendable to empirical work than marginal costs, because average costs are directly observable In his survey of nonrenewable resource theory, Krautkraemer (1998) provides a detailed discussion of current treatments of nonrenewable resources in national accounts. He points out, among other things, that “the current treatment of nonrenewable resource also excludes from national income the value of reserve additions resulting from exploration and development activities.” This issue has been treated in Dasgupta, Kriström and Mäler (1997a, 1997b) and Hartwick (2000). The former conclude that NNP should not include both the value of new discoveries and current exploration costs, because this would involve double counting (this result assumes that the cost of discoveries depends on current rather than cumulative expenditures).

30 The Hotelling Valuation Principle implies that V /s = p − MC: average reserve value is equal to current 0

net price and independent of future prices and costs. This principle of valuing the stock is extensively discussed in Krautkraemer (1998). If MC is approximately zero, then V = pQ, which agrees with our intuition. Compare the discussion of the wealth measure for the Hotelling model, where we found that NW = λ0 s0 .

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11.2.1.2. Renewable resources. To calculate economic depreciation in the case of a renewable resource we use the dynamics stated above for the unidimensional case: πt = pc − h(c),




 H = pc − h(c) + λ d(s) − c , . s = d(s) − c, . . Dt = λs = (p − MC)s.

(25) (26) (27) (28)

Thus, rents are multiplied by (net) growth less consumption. If the cost function is linear, h(t) = bc(t), then D(t) = (p − b) ∗ (r(s) − c(t)), where b is average (and marginal) cost. This approach is often used in applications, although the involved approximation can be very crude. Vincent (1999) illustrates this in the case of slowly regenerating forest stocks [Equation (27) implies immediate regeneration]. 11.2.2. El Serafy’s approach El Serafy (1999) has proposed the use of the so-called user cost method, which goes back to Hicks (1939), who argued that (p. 187) “If a person’s receipts are derived from the exploitation of a wasting asset, liable to give out at some future date, we should say that his receipts are in excess of his income, the difference between them being reckoned as an allowance for depreciation. In this case, if he is to consume no more than his income, he must re-lend some parts of his receipts . . . ” El Serafy (1999) proposed that true income (x) from an exhaustible resource with expected life n years at current extraction rate, yielding net revenues pc − h(c), should be defined as x = pc − h(c) −

pc − h(c) (1 + δ)n+1

for a given choice of discount rate δ. Hence, the true income from the exhaustible resource is less than the revenues, the extent of the difference depending on the parameters n and δ. For further discussion, see Kriström (2002). 11.3. Transboundary pollution Next we consider two extensions of the basic model that relate to international trade, the case of transboundary pollution and the case of trade in assets. The case of transboundary pollution is relatively straightforward to handle, while the treatment of trade in assets is a bit more complex. Many of the most pressing environmental problems are transboundary, as exemplified by upstream–downstream problems, global warming, acid rain and the many other environmental problems that do not respect national borders. When attempting to take those issues into account, it is clear that there is more than one way to define a consistent welfare index. To analyze the issue at hand, consider the simplest setup.

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Let there be n countries each of which emits ej , j = 1, . . . , n. Environmental quality in country j is given by  ei aij , zj = where aij is an element of the transportation matrix, giving the amount of depositions in country j per unit of emission in country i. Let welfare in country j be given by uj (cj , zj ). Assume that the only interaction among countries is by way of transboundary pollution, so that there is no trade in goods. Further, let production in each country take the simple form, cj = f (ej ), j = 1, . . . , n. Consider a small change in ej . To a first-order approximation, uj = uj,c (cj , zj ) × cj + uj,z (cj , zj )zj . This small change may affect all other countries, depending on the structure of the transportation matrix. If aij = 1 for all i, j then the transboundary problem reduces to a global issue and the location of emission is unimportant for the welfare in country i = 1, . . . , n. Upstream-downstream problems and regional problems, like acid-rain, can be represented by changing the structure of transportation matrix. As defined, welfare in the country is only affected by cj and zj , which means that as long as we keep track of total deposition in the country, we may construct a welfare index accordingly. If we want to construct a globally consistent accounting system, then we could either have all countries in the world deducting the imported damage caused by the emissions in country j , or we could take the view that country j should deduct the total damage caused to others in its accounts. This corresponds to the difference between gross national product and gross national income, as noted in Dasgupta, Kriström and Mäler (1995, p. 145). If we take the first view, then country j should not deduct the damage caused by its exports of pollution, because this is already accounted for by other countries. If we take the second view, then we should only deduct the damages caused by exports of pollution, not the imports, since this is already taken care of by the emitting country. 11.4. A small open economy To consider the effect of trade in assets, we begin by looking at a small open economy, so that import and export prices are given. There are no extraction costs nor costs for exploration. The economy extracts an exhaustible resource, which it sells abroad in order to purchase a consumption good on the world market. The resource market is assumed to be in equilibrium at all times. The country is assumed to maximize the stream of utility subject to a budget constraint. The objective function is:  ∞ u(cm ) exp(−δt) dt, 0

where cm is the imported good. The relevant constraints for this maximization problem are written as: . st = −R, 0  pR R − qm cm , s(0) = s0 > 0, R, cm  0,

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where pR is the export-price in foreign currency of the extracted amount of the stock, R, and qm is the price of the imported good (in foreign currency). The second constraint is the balance-of-payment in foreign currency, assuming for now that no capital market exists. In this simple model, the country cannot save by selling the resource on the world-market and investing the proceeds. The maximization problem is solved by setting up the corresponding Lagrangian: L = u(cm ) − λ1 R + λ2 (pR R − qm cm ) = H (•) + λ2 (pR R − qm cm ), where H (•) denotes the Hamiltonian. Linearizing the Hamiltonian, as in, e.g., Mäler (1991), using consumption as the numeraire and the first-order conditions, a linear welfare index (NNP) for this economy can be written as NNP = cm − (pR /qm )R = 0, where NNP can be interpreted as the net national product of this economy. As before, we should think of this index as portraying the change in welfare. This result is exactly the same as in Dasgupta and Heal (1979, p. 245), the only difference here is the explicit account of the trade possibility. Thus, (change in) NNP for the “cake-eating” island with trading possibility is zero, provided that prices are constant. We now allow the country to invest the proceeds from selling the natural resource abroad, thereby adding one relevant aspect to the model. Our linear welfare-index will no longer be zero. We may note that the balance of trade surplus of the OPEC countries was 372.6 billion USD in the period 1974–1982, with a substantial fraction being invested in short/long-term assets abroad, as is shown in Siebert (1985, Table IV:1, p. 67). With this possibility available the revenues from the exhaustible resource can, for example, be invested in a renewable resource in another country. The budget constraint now needs to be modified to reflect the opportunity of generating a capital stock abroad. We define the current account surplus as follows: dB/dt = δB + pR R − qm cm , where B denotes the country’s foreign assets and δ is now interpreted as the worldmarket interest rate. In the long run, the present value of the net trade surplus must go to zero, or limt→∞ B exp(−δt) = 0. Using this fact and proceeding as above, one finds that (with constant prices) NNP = cm − λ1 R + λ2 dB/dt, where λi (i = 1, 2) denote the shadow prices. In this case, there is no reason why the linear welfare index should be zero. Asheim (1996a, 1996b) and Vincent, Panayouto and Hartwick (1997) provide detailed analysis of the question of capital gains in the open economy. See also Sefton and Weale (1996). In a nonautonomous model, capital gains should be included, because they would act in much the same way as an exogenous change of technology.

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12. Expanded social accounting matrices The standard national accounts can be viewed as a particular sub-matrix of a SAM developed for green accounting, since green accounting essentially entails expanding the stock/flow notions used in standard accounting. It is natural to ask how the Hamiltonian formalism can be usefully coupled with the organizing discipline that follows from a SAM. The literature is still developing on this issue. Mäler (1991), using the Hamiltonian formalism, provides a detailed SAM for a model that includes many pertinent issues, including the handling of flow and stock externalities, defensive expenditures and stock accounts. Such a SAM could be extended to include transboundary pollution and other extensions we have considered. To appreciate the potential usefulness of a SAM, consider a simple example. Let there be two production sectors, pulp factories and fisheries. Assume that pulp production affects the production of fish negatively. For example, the cost of fishing might increase, because the fisherman must search larger areas, due to the negative externality. Consequently, when we sum value-added in the two sectors, the negative externality will be included in conventionally estimated NNP. In an extended SAM, this will be immediate. In addition, one obtains information about the environmental damages in the SAM, which could be of separate interest. Applications based on these kinds of ideas can be found in Ahlroth (2001), Hultkrantz (1991) and Vincent (1999). See Bergman’s (2005) chapter in this handbook for more detailed discussion. We return to the risks for double counting in our discussion of the SEEA in Section 14.1. In a recent contribution, Hartwick (2000) has explored the link between Hamiltonians and SAMs in detail. To illustrate the steps in his methodology, consider the simplest Ramsey-type model with technology f (s, l) and utility function for the representative household: u = u(c). Total production y is allocated between investment and consumption, so that y = c + ds/dt = f (s, l). Following Hartwick (2000), assume that production technology has constant returns to scale, so that y = fs s + fl l. The price of output can be set to one, and when input factors are paid their marginal products r and w, we have y = rs + wl. Thus, y is net national product = net national income = value of factor payments. By linearizing the utility function around zero and dividing through by the marginal utility of consumption, the Hamiltonian is interpreted as NNP. A SAM can now easily be constructed, showing the flows between production activity, factor inputs and the household. Hartwick (2000) proceeds to show how this methodology can be consistently applied to a series of models involving exhaustible and renewable resources. Observe that Hartwick’s interpretation of NNP is not as an index of welfare change. This concludes our review of conceptual issues in green accounting. We turn now to the practical import of these ideas. As we noted at the outset, there is a gap between theory and practice. Furthermore, there is no lack of ideas on how to paint the national accounts “greener”. In the sequel, we paint our own picture of the practical developments of green accounting, reminding the reader that we do not provide a complete survey of the relevant empirical issues.

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13. Developments in applied green accounting The development of “applied” green accounting has a long and distinguished history. This section contains a capsule summary of the developments. The next section has a brief review of selected studies. 13.1. The Nordhaus–Tobin measure of economic welfare (MEW) One of the best known studies in the literature on green accounting is James Tobin and William Nordhaus’ (1972) attempt to provide a “Measure of Economic Welfare” (MEW). In some ways, their contribution came as an input to the debates circling around the net benefits of the “consumption society”, a debate that surfaced in the 1960s. Using a number of innovative ideas, including regression analysis to shed light on the costs of urbanization, they were able to calculate a MEW that foreshadows many later developments in the green accounting literature. In particular, they were among the first to point out clearly that they were trying to estimate a measure of sustainable income. Nordhaus and Tobin adjusted GNP in three ways: they reclassified certain items of expenditure; imputed for services of consumer capital and leisure and household work; and finally corrected for the “disamenities of urbanization”. In the first category, they make the appealing reclassification of education expenditures as capital investments, an idea later picked up, e.g., by the World Bank in their measure of genuine savings, to be discussed in Section 14.6. Including human capital in the productive resource base of the economy and proceeding as in the theoretical models outlined above provides a rigorous motivation for including the net change of human capital in the welfare measure. Nordhaus and Tobin (1972, p. 7) also reclassified military costs, police protection and public health expenditures and other “regrettably necessary inputs to activities that may yield utility” as intermediate consumption. In the second category, they imputed a value for leisure, arguing that voluntary choices to work less increases individual welfare, but could decrease NNP. Dasgupta, Kriström and Mäler (1995, p. 142), conclude that the net change in human capital stock should be included in NNP, and that the part of the wage bill that corresponds to returns on “raw labor” should be deducted. See also Hartwick (2000). Because the wage bill is a significant part of national income, such a procedure has significant implications for the level of an adjusted income. The basic argument is, yet again, a reminder of the purpose of measurement: we are not looking for an index to be used for macroeconomic purposes. If we are interested in an index that can be interpreted as a small change welfare measure, the implication for the measurement of the wage bill follows. Finally, arguing that “higher earnings of urban residents may simply be compensation for the disamenities of urban life and work”, Nordhaus and Tobin used an innovative cross-sectional regression technique to calculate the income needed to hold people in areas with greater population densities. This “disamenity premium” was calculated to be about 5% of GNP.

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The study is a hallmark in the literature on adjusted income measures, combining economic theory with innovative empirical approaches. Samuelson’s Economics textbook may have been important in popularizing MEW. Other studies followed Nordhaus and Tobin’s lead. For example, Uno, in 1973, proposed a measure of economic welfare by adjusting the Japanese national product in a number of ways, see Uno (1998). Daly and Cobb (1989) developed a Index of Sustainable Economic Welfare (ISEW) based on MEW. ISEW has been computed in several countries, e.g., Austria, Germany, Netherlands, Sweden, UK and USA. A distinguishing feature of ISEW is that it includes distributional issues, although this (and other adjustments) are not placed within a formal model. It remains to be shown that ISEW is a sign-preserving index of underlying welfare change, let alone a consistent index of sustainable development. 13.2. Norwegian resource accounts A second important early development in green accounting took place in Norway in the beginning of the 1970s.31 A set of resource accounts in physical terms were used to shed light on questions regarding the future use of hydropower, the management of the recently-discovered oil and natural gas sources and concerns about over-fishing in the North Sea. In addition, the proper degree of agricultural self-sufficiency was also subject to analysis via the new accounts. A principal advantage of resource accounts in physical terms is that they avoid the complexity of transforming resource use into monetary terms. According to Lone (1987), the work of Ayres and Kneese (1969) on the mass balance principle provided an important intellectual starting point for developing physical (rather than monetary) resource accounts. In selecting the scope of the accounts, a number of criteria were used: (i) political and economic importance; (ii) costs of acquiring the data; and (iii) sector and commodity definitions that were consistent with the SNA system. After several years of internal work within the governmental departments, a detailed resource accounting system in physical terms was introduced in 1978. In this system, resources are classified as being either material or environmental, where the material resources are subdivided into mineral, biotic, and inflowing resources (hydropower). A material account typically includes three pieces of information: the inand out-going resource base including adjustments other than gross extraction (discoveries, reappraisals, new technology etc.); an extraction and trade part, where extraction, import, and export are recorded by sector; finally, a part of the system which describes domestic use in a systematic fashion. The environmental accounts include emissions of pollutants such as sulphur dioxide, nitrogen oxides, carbon monoxide and lead. They

31 This section is based on Kriström (1995).

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also include land use accounts, whose primary purpose is to detail availability of land and its changes in various classes. One of the purposes, initially, was to develop resource budgets that would detail planned use of each resource. The budgets were considered to foster a better, and more farsighted, resource use. Alfsen, Bye and Lorentsen (1987) find the closest resemblance of resource budgets in a 1985 governmental quadrennial Long Term Program compiled by the ministry of finance, but they point out that the only nonhistorical numbers contained in the report were not budgets, in terms of planned, or optimal use. The system has been used to determine catch quotas in the North Sea and to fix the proper exploitation rate of the oil reserves. In addition, cost efficiency studies (nitrogen leaching) in agriculture and models for projection of emissions have utilized data from the system. An important lesson that emerges from the Norwegian system is the importance of making an early identification of the user side of the information provided in resource accounts. Today, the Norwegian program is much smaller than originally planned, focussing mainly oil and natural gas issues. 13.3. Other developments In 1982, the United Nations Environment Program (UNEP) began work on environmental accounting. A series of state-of-the-art workshops in 1983 focussed on the shortcomings of income measurement within the national accounts, particularly with respect to natural resources. Further developments of the SNA were stimulated by the Brundtland report, because it pinpointed the need for an analysis of economy-environment interactions and measures that would address the sustainability issue empirically. The consensus was, however, that such concerns did not justify a complete overhaul of SNA fundamentals, and that a satellite system of accounts was therefore to preferred. The UNSO prepared the SEEA handbook and released an interim report in 1993. Meanwhile, several countries undertook official commissions to review the needs to supplement and extend the current systems of accounts. For example, Denmark and Sweden completed two commissions on green accounting in the beginning of the 1990s, each reaching widely different conclusions [see Danish Commission on Resource Accounting (1990) and Swedish Commission on Resource Accounting (1991)]. The Danish position came out to be strongly negative towards monetary accounts, while the Swedish commission expressed cautious optimism. A recent compilation of progress in different countries by the “London Group” [SCB (1996)] details the progress of green accounting in Australia, Austria, Canada, Denmark, Finland, France, Germany, Italy, Netherlands, Norway, Sweden, UK and the U.S. Aspiration levels vary considerably, although the surveyed countries all conduct some kind of natural green accounting, and with a few exceptions, in both monetary and physical terms. Energy accounts and emission data are generally available, but environmental damages are seldom expressed in monetary terms.

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Perhaps the most ambitious project is carried out in the Netherlands, where a National Accounting Matrix including Environmental Accounts (NAMEA) has been developed. This matrix has also been adopted elsewhere, e.g., in Sweden. Substantial efforts have been undertaken at the Netherlands Statistical Office to calculate a sustainable national income, using an extension of methodology attributed to Hueting, see, e.g., Hueting (1992). He describes his approach as follows [Hueting (1992, p. 36)] “Define physical standards for environmental functions, based on their sustainable use. Formulate the measures necessary to meet these standards. Finally, estimate the amounts of money involved in putting the measures into practice.” Hueting (1992, p. 40) exemplifies this methodology by an application to erosion (in Indonesia). The sustainable standard for erosion is set equal to the natural rate of increment of the top soil and the cost of reaching this goal is calculated. Hueting (1992) notes that he works in a partial equilibrium framework, so that price repercussions are not included. A computable general equilibrium model has been developed to extend the original idea: the cost of reaching the sustainability standards is computed and deducted from national product, see Verbruggen et al. (undated). The theoretical underpinnings of this approach will have to be developed before one can see a clear link between welfare and the suggested index. In the U.S., a recent National Research Council report edited by Nordhaus and Kokkelenberg (1999) strongly endorses green accounting in physical and monetary terms: “The panel concludes that extending the U.S. national income and product accounts (NIPA) to include assets and production activities associated with natural resources and environment is an important goal. Environmental and natural-resource accounts would provide useful data on resource trends and help governments, business, and individuals better plan their economic activities and investments.” Furthermore, the panel concludes that such work would be an “essential investment for the nation” provided that such activities “. . . [do] not come at the expense of maintaining and improving the current core national accounts. . . ” (p. 5).

14. Selected applications To illustrate further applications of green accounting, we discuss in some detail a small number of studies. These have been selected either because they have been given wide publicity or because they present applications that have gone a long way towards implementing the theoretical ideas discussed earlier. The reader interested in further applications is referred to the detailed progress reports for a number of countries that appear in the London group report of 1996. Vincent and Hartwick (1997) survey progress on forest resource accounting. The special issue of Environment and Development Economics (2000) contains additional empirical applications. We choose here to focus on the SEEA, because it is intended to be used by all member in the UN. We include a discussion of the well-known Repetto et al. study and selected country applications, as well as the genuine savings concept developed by the World Bank.

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14.1. The SEEA The United Nations (Integrated) System of Environmental and Economic Accounting (SEEA) was published in December 1993, following a long process of discussions and refinements. The system is closely linked to the SNA and therefore has objectives that are rather different from the ones that we have explored in the context of theoretical models. El Serafy (1996, p. 87) notes that “The objective has been to reflect environmental deterioration in the SNA to the extent that the SNA framework will allow.” Hence, the SEEA is a satellite system that is built upon the principles of the SNA. The upshot of this is that we cannot expect to find that the proposed measures of income are consistent with theoretical measures like FLH-income. Even so, it is important to disentangle just what the system is supposed to measure, and specifically whether the revised income measures can be given welfare interpretations. Incidentally, a new version of the SEEA is under way. Software for testing the revised system is available at the United Nations (Statistics Division) homepage. The SEEA integrates use/value-added tables, balance sheets for environmental and economic assets, and tables for intermediate, final consumption and capital accumulation. In summary, the basic SEEA matrix structure is as follows: (1) opening stocks (produced and nonproduced); (2) use/value-added tables (GDP, NDP, EDP); (3) supply tables (goods and services, imports of residuals); (4) revaluation and other changes; (5) closing stocks. The system expands on the SNA, by way of separating out expenditures related to environmental issues, and providing detailed accounts of how environmental assets interact with the economy. This entails using a wider definition of the asset boundary, and accounting for the economy’s impacts on natural assets in terms of environmental costs of production and consumption activities.32 There is a link between changes in nonproduced natural resource stock and the production account, so that NNP is affected by degradation of stocks. Thus, depletion and degradation are treated as production costs in the SEEA, while SNA-93 treats such changes in nonproduced assets as “other volume changes” that are presented in the asset accounts. The SEEA treatment leads to different income and production concepts, as well as (environmentally) adjusted measures of capital formation. Focussing on a widely interpreted measure of the economy’s stocks has theoretical appeal, as we have seen above, even though the empirical problems that such an approach imposes on the user are significant. In particular, certain crucial life-supporting stocks such as the stock of air or water cannot be given a meaningful value.

32 The asset-boundary includes, in principle, all assets [United Nations (1993, p. 8)], referred to as “the

Handbook” in the sequel.

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The SEEA includes four different versions, or stages, that describes linkages between the economy and the environment in increasing detail and complexity. The first stage basically presents available information within the SNA on environmentally related expenditures. Such expenditures are those that households, industries and government organizations have actually incurred to avoid damage or eliminate the damage once it has occurred. It is important to note that those expenditures are, quite correctly, not separately deducted from national product in the accounts. The second stage provides accounts in physical terms, including a linkage to the monetary accounts, where the treatment of the physical resources is inspired by the Norwegian resource accounting system and the Dutch NAMEA. Opening and closing stocks are recorded, as well as an account of changes during the period (extraction, natural regeneration, etc.). Flow accounts, notably wastes and residuals, as well as material flows, are included. Non-produced economic assets include land/soil, sub-soil assets, forests, fishery resources and water resources, each of which may be disaggregated for further detail. For example, land may be disaggregated into agricultural land, forest land and other land, while the economic uses of forest land can be shown by forest type. The physical information is used to create monetary asset accounts, on which we write more below (see, e.g., Section 14.1.1). The third version is an attempt at “full” green accounting, by including estimates of environmental damages into the accounts, using several of the valuation techniques that we have discussed above. More precisely, it includes “different approaches for estimating the value of natural assets and the imputed costs of their uses” [Draft Operational Manual, United Nations (1998, p. 29)]. Three different valuation methods of increasing complexity and controversy are considered. The first uses market values and follows SNA principles for valuing nonfinancial assets. The second approach seeks to obtain an estimate of the cost for sustaining the current level of the stock. Finally, the third “module” proposes the use of contingent valuation and related techniques. An important difference between the SEEA and the SNA is that environmental costs in the SEEA, in the form of degradation or depletion of natural resources, affect national product, as noted above. The final stage is essentially left to further research and will include household production and the use of recreational and other unpriced environmental services in household production. The accounts can be used to analyze the links between environmental and economic policy in a relatively straightforward manner, since SNA conventions are used. Simple applications already exist, e.g., the general equilibrium analysis of carbon tax policy carried out by Harrison and Kriström (1998), where a pollution module was easy to attach to the make/use tables. A number of SEEA pilot studies have been carried out (including Colombia, Ghana, Indonesia, Japan, Mexico, the Philippines, Papua New Guinea, The Republic of Korea, Thailand and the USA) and a number of studies are under construction or partially published (Italy, China and Sweden).

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14.1.1. The SEEA and valuation Regarding valuation of nonfinancial assets, the SEEA discusses three main approaches: (i) market prices of natural assets, (ii) the present value of expected net proceeds, and (iii) the net-price method. El Serafy’s approach is considered for depletion of (exhaustible) mineral resources. The Handbook suggests using different approaches for different assets. For changes in land quality, market prices should be used, as far as possible. For depletion of natural assets such as wild biota, subsoil assets or water, the net price method (cf. the section on valuation of stocks above) “could be used” (p. 61). For forests, stumpage values are considered appropriate. With regard to environmental damage, the Handbook discusses three different approaches: (i) market valuation, (ii) direct methods (e.g., contingent valuation), and (iii) indirect methods (e.g., “environmental protection costs”). The most important of these in the SEEA are the indirect methods, in particular the “maintenance cost concept”. According to the Handbook: “The (hypothetical) maintenance costs are – mainly prevention costs that would have been necessary to prevent negative impacts of economic activities on the environment and/or to meet given sustainability standards –” [Handbook (p. 19)]. Such costs seem difficult to estimate and the question of whether or not they can be viewed as approximations to welfare changes remains open. In general, as we have stated previously, valuation should be based on preference information. Furthermore, we need to be careful in distinguishing between marginal and nonmarginal changes. Contingent valuation methods typically provide information about nonmarginal changes, because one targets compensated surplus measures. The upshot of this is that it is not obvious how we should add consumer surpluses measures to a linear index like (adjusted versions of) NNP. 14.1.2. Environmentally adjusted domestic product (EDP) The fundamental accounting identities that define environmentally adjusted domestic product (EDP) in the SEEA are as follows [United Nations (1998, pp. 41–42)]: Y + M = IC + C + I G + X,

(29a)

EVAi = Yi − ICi − Di − ECi = NVAi − ECi ,   ECh = NDP − EC = C + I G − D − EC, EDP = EVAi −

(29b) (29c)

where the notation is as follows: Y : output; M: imports; IC: intermediate consumption; C: final consumption; I G : gross investment; X: exports; EVAi : environmentally adjusted value-added for sector i; Di : depreciation industry i; NVAi : net value-added

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industry i; ECi : degradation industry i; ECh : environmental costs generated by household h. Disentangling the EDP concept and relating it to the theoretical developments above is complicated by the fact that the SEEA provides three different versions of EDP, depending on which of the valuation methods is used. In addition, net exports of residuals can be incorporated in the definition of EDP, but will not be discussed further here. There seems to be no clear statement about the exact interpretation of EDP in the Handbook. Possibly it could be interpreted as a version of sustainable income, although this interpretation is not independent of which valuation method is used. The second approach of estimating maintenance cost for valuation purposes might perhaps provide a basis for this interpretation (barring the problem of using costs to measure welfare changes). The Draft manual [United Nations (1998)] provides the following discussion about the maintenance cost concept: “The maintenance costs, applied to emissions, reflect the most efficient (least-cost) practices and technologies applicable in maintaining the waste/pollution absorption capacity of environmental assets. In practice, best available technologies applied to current production and consumption processes would in some cases be capable of abating only part of the emissions generated during the accounting period. Remaining emissions would have to be “endured” as their removal should be considered sub-optimal (owing to marginal costs exceeding social standards) in simulated markets. Alternatively, the cost of avoiding the polluting activity altogether, in order to meet an explicitly set standard, would have to be estimated.” [Draft Manual, United Nations (1998, p. 84)] Hence, given estimates of the maintenance cost per unit of pollution in different sectors of the economy, EDP is calculated as described in the equations and definitions above. To appreciate the possibility of double counting in this framework, write total net profits π(z) as a function of an environmental quality parameter z and assume, which seems natural (but not necessarily true), that dπ /dz < 0. Next, define net value-added as NVA(z) = π(z) + wagebill. This means that net value-added is not independent of environmental quality, which the maintenance cost concept appears to imply. In other words, some parts of environmental damages are already reflected in π(z), so that there is a certain risk that a fraction of environmental damages are already accounted for. Recall the results from Bergman’s (2002) CGE model discussed above: he found that NNP (in his model) reflected a lot of information about environmental costs. Furthermore, Mäler (1989, p. 22) argues in his discussion of a consistent green accounting system: “. . . it is quite important to separate changes in environmental flows – y1 – that is the changes which do not have any long-term consequences, from changes in stock resources y2 . The former should only be included as far as they affect consumers directly. Their effects on production will be captured by profits.”

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In conclusion, there is a risk that environmental damages are doubly counted if some part of value-added already reflects environmental costs. The extent to which this is true in the SEEA is difficult to assess. More importantly, we take the view that the SEEA, in the version under review, has yet to provide a clear answer about what the system is supposed to measure. It is not a Keynesian style set of accounts for macro-economic purposes, neither does it provide welfare-change indices and, as far as we can tell, it does not necessarily produce a measure of sustainable income. Along certain dimensions, the SEEA is a step in the right direction. For example, it helps modelers to obtain information collected within an SNA framework. Ahlroth’s (2001) thesis, to be discussed in Section 14.2 below, presents a rigorous application of ideas that are very close to those presented in the SEEA. Thus it may be possible to translate the SEEA ideas into the Hamiltonian formalism discussed in the theoretical literature. Again, we believe this formalism is very useful, because double-counting issues are easier to resolve. The forthcoming version of the SEEA may elucidate this point further. We now turn to applications of the SEEA, beginning with the proposed forest accounting schedule and proceeding to country studies. 14.1.3. The SEEA and forest accounting The draft manual [United Nations (1998)] contains detailed example of how forest accounts should be compiled within the SEEA framework. However, their proposed approach is not necessarily consistent with the theoretical constructs we have discussed in this paper. The manual proposes that conventional NDP in forestry should be reduced by [United Nations (1998, p. 108)]: “The value of depletion, i.e., that part of the value of removals or losses of noncultivated standing timber (and other of the forest’s noncultivated biological assets) due to logging, harvesting, hunting and clearance of forests, which exceeds the sustainable use”33 and “the value of decrease in the market value of land due to degradation resulting from forestry, logging or other forest-related activities and deforestation (clearance of forest land).” Clearly, there is a substantial risk of double counting if this approach is followed, a risk that is duly noted in the Draft Manual [United Nations (1998, p. 114)]: “Economic land is recorded in the SNA monetary balance sheets at market prices. As regards forest issues, the main problem is whether the value of land in the national accounts is or is not separated from the value of standing” and (p. 117) “When assessing maintenance costs associated with a sustainable use of forests, one has thus to ensure that double counting is avoided. When, for instance, sustainable use is to be achieved through a reduction of

33 Essentially, this means that the total cut exceeds the growth of the forests.

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fellings, maintenance costs may be roughly estimated by the corresponding reduction of the value-added of logging. The value of the depletion allowance calculated in step 5 has therefore to be reduced accordingly.” Vincent and Hartwick (1997) have proposed a framework which deals with forest accounting in a lucid way. In particular, they are able to show that conventionally measured NDP includes a significant amount of information. Intuitively, this is due to the fact that profits in forestry depends on environmental services provided by other sectors and vice versa. 14.1.4. Applying the SEEA in Mexico van Tongeren et al. (1992) present an integrated environmental and economic accounting system for Mexico. The study followed the guidelines set forth in UNSO’s draft handbook on environmental accounting. Oil depletion, deforestation, land use and environmental asset depletion (air and water pollution, soil erosion, ground water and solid waste) were the main concerns. Two environmentally adjusted domestic products (EDP) are calculated. EDP1 is based on market transactions, while EDP2 includes calculations involving less generally agreed upon principles (such as the avoidance cost method). These are found to comprise 94 and 87% of conventional NDP, respectively. Valuation of changes in oil and timber stocks was carried out by using both the net rent method and El Serafy’s approach. In the second case, one needs to calculate the discounted sum of depletion allowances necessary in keeping income constant. The study year (1985) gives different results for the two approaches: net rent is 1162 pesos/barrel, the depletion allowance is 160 pesos/barrel. Average stumpage values for forests were computed to be 21.5 and 1.6 pesos/m3 , respectively. The van Tongeren et al. study also includes environmental quality changes. Besides valuing soil erosion and solid waste generation (by households), the authors also include sulfur dioxide, nitrogen oxide, carbon monoxide and emissions of suspended particulates. Land erosion was valued at the cost of fertilizer to maintain the productivity of the land. Ground water loss was valued at the cost of re-injecting water back into underground water reservoirs. Finally, water and air pollution were valued at the cost of reducing such pollution “to acceptable levels” (p. 7). As we have noted several times, such methods do not take account of information about consumers’ preferences. The authors select not to include new finds of oil in the net change of the oil stock, a treatment we discussed above. Changes of the stock of forests are only accounted for if the harvests are larger than the maximum sustainable yield, which is at odds with the general ideas presented in welfare green accounting. Much the same is true for the treatment of sanitation services produced by the government, which was deducted from GDP. Similar applications of the SEEA have been carried out for Papua New Guinea, Namibia and a few other countries.

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14.2. Sweden Following an official commission report in 1991, the development of green accounting in Sweden has followed three distinct paths. Statistics Sweden is responsible for resource accounting in physical terms while the EPA heads efforts towards compiling environmental indices.34 Finally, the National Bureau of Economic Research began an extensive program of monetary resource accounts in 1992, which is based on the SEEA tables. The monetary accounts includes valuation studies of environmental effects from emissions of sulphur and nitrogen oxides, as well as accounts for the forest ecosystems. The assessment of sulphur and nitrogen emissions includes effects on forests, agricultural land, fishing, ground water, freshwater, the Baltic sea, health effects, recreation and corrosion of real capital. The related environmental issues studied are acidification, eutrophication, damages from tropospheric ozone, and air and water pollution from nitrogen oxides and nitrates. The forest accounts include values of timber, berries, fungi, game, lichen, the costs for preserving biodiversity, the value of CO2 -assimilation and the costs of acidification. For details about the forest accounting study, see Hultkrantz (1991), Kriström (2001) and KI (2000). Based on the data collected within the National Bureau of Economic Research project, Ahlroth (2001) combines an optimal control theory model with empirical information to adjust NDP for the effects of sulphur and nitrogen emissions. Her accounting matrix is based on the SEEA. Thus, the study is one of the few attempts that now exists to bridge a gap between two traditions in the green accounting literature. In her model, the utility function includes a composite good and a vector of stocks and flows of the pollutants. Production is a function of labor, capital, and flows of natural resources and energy. There are linkages between flow and stock pollutants and the productive stocks in the model. For example, timber growth is affected by the stock of acidifying substances in the soil and real capital is affected by corrosion via acidification.35 Labor supply in future periods is also effected by pollution. Incidentally, the model is quite similar to the model used by Hamilton and Clemens (1999), which is a basis for the World Bank’s genuine savings approach (see further below). Using the Hartwick–Mäler approach, Ahlroth (2001) obtains a modified national product as the sum of consumption, stock/flow utility impacts of pollution (converted into monetary terms) and the sum of the net change of all stocks, valued at the appropriate shadow prices. 34 The physical accounts includes emissions from 16 economic sectors plus the public sector and the house-

holds, integrated in the framework of the national accounts. Emissions to air: sulphur dioxide (SO2 ), nitrogen oxides (NOx ), carbon dioxide (CO2 ), organochlorine compounds (measured as AOX), laughing gas (N2 O) and volatile organic compounds (VOC). Emissions to water: nitrogen (N) and phosphorus (P). Environmental profiles for 16 economic sectors. Input–output analyses for emissions of SO2 , NOx and CO2 for all sectors including households. (Extracted from http://www.konj.se.) 35 Whether or not there exists a productivity loss from acidification in the case of forests (“waldsterben”), is hotly contested. A recent assessment suggest that the correlation is small, or zero. See Binkley and Högberg (1997).

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Production losses were estimated with dose-response functions. Recreational and several other values were estimated by the contingent valuation (CV) method. Abatement costs and environmental protection expenditures for reducing sulfur and nitrogen emissions were estimated to allow comparison. In summary, the study finds that the environmental costs of sulfur and nitrogen (in 1991) in Sweden is, as a percentage of NNP, around 2%.36 In the Swedish Medium Term Survey, the Ministry of Finance (1999), presents an assessment of whether or not Sweden is on a sustainable development path. Data are based on the collected efforts of the government authorities mentioned above. Computations were carried out at the National Bureau of Economic Research. The Ministry takes the view that development is sustainable if green NNP is not reduced over time. To this end, the Ministry computes a green NNP measure for the years 1993 and 1997, based on the linearization (Hartwick–Mäler type) approach. No adjustments are made for the value of leisure time, although this possibility is mentioned. Furthermore, the study does not include a number of environmental damages, including global environmental threats such as global warming, ozone layer depletion and biodiversity loss. Finally, the Ministry also points to the importance of including human capital in future calculations. Results are presented in Table 3. The value of the net change of timber is calculated as stumpage price times estimated increase of cubic meters of standing timber. This figure is already included in the SNA93 version of NDP, so no particular addition is needed under that framework. The value of mine depletion is calculated via an application of Hartwick’s rule [Hartwick (1977)]. Net operating surplus in the mining sector is subtracted from NDP as depletion and a 3.5% return on capital invested is imputed for the sector, on the basis that Table 3 Environmentally adjusted NNP for Sweden 1993, 1997 Year

1993

1997

Consumption Net trade Investment Depreciation

1,314,601 78,011 209,854 −222,529

1,372,220 161,823 244,700 −212,600

Conv. NNP ForestStock Mine depletion Natural capital Env. damage

1,379,937 6230 −1250 −5780 −3400

1,566,143 5670 −1250 −5420 −3300

Adj. NNP

1,375,737

1,561,843

SEK billion, 1997 prices.

36 1991 NNP was 1246 billion SEK and the adjusted measure 1220 billion SEK, Ahlroth (2001, p. 56).

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this is the return on an investment equal to the net value of the extracted resources. The item “natural capital” is calculated as the loss of production incurred by environmental degradation. For example, cadmium and other forms of contamination are estimated to incur a loss of soils of about 1000 ha/year. The market value of foregone income from these soils is then calculated (which turns out to be roughly of the same magnitude as the cost of liming). Finally, the item representing environmental damage includes noise and health impacts of pollution. The adjustments of conventional NNP amount to about 1.3% in total. Since adjusted NNP does not decrease, the results are taken to indicate that Sweden’s development is sustainable. 14.3. Indonesia The study of Indonesia by Repetto and his co-workers is the best-known application of green accounting.37 A key motivation for this work is the observation that in the SNA (before 1993) depreciation of man-made capital is treated differently from depreciation of natural assets. Repetto et al. (1989) set out to treat all assets symmetrically in the national accounts. They study Indonesia during 1971–1984, a period of rapid Indonesian economic growth; GDP increased 7.1% per year on average. This growth was, to a large extent, based on intensive exploitation of oil, gas, minerals, forest products and other natural resources. As a first step, the authors construct physical resource accounts for forests, oil, and soil. For each asset, a physical and monetary account is constructed. They select the net rent method to calculate depreciation allowance, i.e., the depreciation allowance is (p − MC)c, although MC was assumed to be equal to ATC in this study. Forests are divided into ‘primary’ and ‘secondary’. The stumpage value of timber in ‘primary’ forests is obtained by subtracting the costs of extraction and transportation from export value. The stumpage values for ‘secondary’ forests are calculated to be roughly half the value of primary forests. Finally, plantation forests are provisionally assigned a value of zero, since they constitute a minor fraction of the total stock. The petroleum resources are valued by subtracting by the average extraction and transportation costs from the market price of oil (fob export price) (cf. the net rent method). Estimates of erosion are based on erosion models that relate data on topography, climate, soil characteristics and land use to erosion. The models predict, among other things, that a shift from forest to agriculture implies a soil loss of 133 tonnes per hectare. The authors also estimate that the depreciation of soil fertility is roughly the size of the annual production increase, or 4% of the value of crop production. Repetto et al. propose a measure of income, defined as EDP = GDP − depreciation of natural assets, which shows an average growth of about 4% during the period studied, see Figure 5. 37 A similar application is made for Costa Rica, see World Resources Institute (1991).

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Figure 5. EDP and GDP for Indonesia.

Critiques of the study have focused on, among other things, valuation procedures and the choice of income measure. Clarke and Dragun (1989) argue that the net rent method is not an appropriate valuation method (in the case of a renewable resource), as decreasing the stock may be part of a program to increase future growth of the forests; compare the use of clearings and thinnings. One approach would be to separate final fellings from the investment-like cleanings and thinnings in the accounts. It is difficult to assess how such reclassifications affect the final results. For further discussion about the approximation properties of the Repetto et al. approach, see Vincent (1999). El Serafy (1999) argues that the method of adding new discoveries of petroleum to output in the year of discovery is debatable. Similarly, Vincent (1993, p. 8) argues that discoveries should not be included in measures of net depletion of a nonrenewable resource. The effect of this approach is apparent in Figure 5, when adjusted output is actually higher than conventional GDP, due to the treatment of discoveries. If capital gains (from oil) are included this makes a huge difference, according to the computations by Vincent, Panayouto and Hartwick (1997). Repetto et al.’s EDP concept is not a welfare index in the sense of the theoretical models presented above. For instance, they use gross rather than net investments in physical capital, do not include loss of ecological services through pollution damages, and limit the role of forests to the value of timber. While these are relevant concerns, they are relatively easy to handle with better data. The Repetto et al. effort has been instrumental in encouraging the practical use of green accounting.

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14.4. Malaysia Vincent (1993, 1997) has examined resource use in Malaysia. Like Indonesia, Malaysia is rich in natural resources and Vincent’s study can be viewed as an attempt to check whether different parts of Malaysia satisfies Hartwick’s rule. He focuses on minerals and timber, the two most important natural resources in Malaysia. A geographical breakdown of resource use shows that net investments have been positive in Peninsular Malaysia in the 1970s and 1980s, while net investments have been negative in Eastern Malaysia during the same period. While the Peninsula has depleted its natural resources, it has used the proceeds to invest in human-made capital. The total capital stock appears to be larger than in the beginning of the 1970s. The evidence on the net change of the total (measured) capital stock in the other parts of the country is somewhat mixed, although the evidence points to a future economic decline in these areas – the current level of consumption is not sustainable. For various reasons, human capital is not included in the calculations, but substantial decreases in the illiteracy rate and significant expansions of the education system since 1970 suggests that the human capital stock has increased. This increase possibly outweighs the negative net investments in the Eastern parts. 14.5. The Philippines The Philippine Environmental and Natural Resources Accounting Project (ENRAP) attempts to cover several extensions of the conventional accounts [Angeles and Peskin (1996, p. 1)]: • nonmarket household production; • unpaid use of waste disposal services into air and water resources; • direct use of environmental assets for recreation; • natural resource depreciation; • damages arising from pollution. The accounting exercise is based on a double-entry system that expands on conventional accounts by way of extending them with additional items (hence, the standard accounts are not changed). A substantial number of nonmarket goods are added into the accounts, leading to a comprehensive “Modified Net Product”. Nonmarket household production in forest land was assessed by way of targeted surveys (unmonitored fuelwood production). The value of waste services was estimated by examining least cost techniques for reducing “uncontrolled residuals”. Environmental damages converted into monetary terms include health damages (work days lost, medication and foregone earnings due to premature death from PM10 and lead exposure) and off-site damages, including: coral reefs (foregone fish production via erosion and pollution from mine tailings), reservoirs (reduced life-span of dams), agricultural production (water pollution and irrigated land) and inland fisheries. Natural resource depreciation was calculated for (dipterocarp) forests, mineral resources (El Serafy method), small surface fisheries and upland soils (asset value

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changes). Substantial effort has been expended to obtain depreciation measures on each natural resource stock. The authors conclude that “. . . the numbers generated (depreciation charges) are much lower than what would be derived through the application of replacement cost concepts, such as the net rent method and the nutrient replacement values which were generated earlier by the World Resources Institute (cf. the Indonesia study above)”. The ENRAP project has generated data that has been used to shed light on a number of policy-relevant issues, such as • exploring the impacts of reaching “high growth targets”; • buttressing the effects of trade liberalization; • addressing the benefits and costs of switching to nonleaded gasoline (which includes the health impacts of producing unleaded gasoline); • assessing the environmental impacts of achieving rice self-sufficiency. Overall the ENRAP program seems to be one of the most comprehensive applications of green accounting currently available. It provides a useful illustration of how resource accounts can serve as an information base for policy analysis. 14.6. Genuine savings We have discussed a number of advantages of focussing on wealth rather than income, given the typical objectives of green accounting. In recent years, there has been considerable interest in empirical assessment of measures of wealth that go beyond wealth measures traditionally offered in the national accounts. The World Bank has, since 1997, promoted a comprehensive measure of additions to national wealth, called genuine savings.38 Hamilton and Clemens (1999, p. 333) argue that: “Augmented measures of savings and wealth in the national accounts are critical to conceptualizing and achieving sustainable development, which was a prime motivation for publishing Expanding the Measure of Wealth [World Bank (1997)].” Genuine savings are defined as net savings plus the value of investment in human capital minus value of resource depletion minus the value of environmental degradation. As conceptualized in Hamilton and Clemens (1999), genuine savings can rigorously be defined as the change of wealth over time along the optimal path (see above). Thus, genuine savings and economic depreciation are the opposite sides of the same coin (±dV /dt in our notation). If genuine savings are negative in some period t, this indicates that the economy is living off its assets, rather than creating new wealth. For empirical purposes, genuine savings are calculated by first deducting consumption and depreciation of man-made capital from GDP to obtain standard net savings. Next, the value of net change of the stocks of productive natural resources is deducted

38 Pearce and Atkinson (1993) presents an assessment of an expanded notion of savings for 20 countries.

Using the national accounts standard definition of savings and estimates of resource depletion, they find that gross savings is less than resource depletion (including depreciation of man made capital).

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from net savings, given that extraction exceeds natural generation. If the net change of a renewable resource is positive, this is not considered to increase genuine savings. The reason for this asymmetrical treatment is empirical. “Empirical investigations of regions where growth exceeds harvest reveals a number of heavily forested countries (including Bolivia, Central African Republic, Republic of Congo, and Guyana), where valuing net growth at unit rents would equal 20–50 percent of GDP . . . . It is likely that mechanically adding net forest growth to GNP and savings would implicitly include the growth of many uneconomic trees (those with zero rental value)” [Hamilton and Clemens (1999, p. 337)]. As noted by Hamilton and Clemens (1999), forests provide many nonmarket goods, but data limitations forces a less comprehensive measurement of how forests add to wealth. When and if a comprehensive global permit market for carbon is in place, a revision will be almost automatic, since carbon sequestration services will pass through the market. The availability and usefulness of data on the value of nonmarket forest goods is discussed in Kriström (2001). Current data limitations also mean that only forests are included among renewable natural resources. The fundamental “nonmarket” adjustment is made for environmental degradation, by way of subtracting the value of the net change of the stock of pollution. This is calculated by multiplying the net change in pollution by the associated social marginal cost. As of now, carbon dioxide emissions net of atmospheric assimilation are included in the calculations. The marginal social cost is set to USD 20, following Fankhauser’s study. Finally, investment in human capital is valued by current education expenditures and added to genuine savings. In the Hamilton and Clemens model, education expenditures are a lower bound on the value of investment in human capital. Whether or not all kinds of education are investment rather than consumption could be argued at length. Some types of education do not necessarily increase output in the future, but rather increase individual welfare in ways not recognized by the market. The difference between net and gross additions to human capital seems also to be a very difficult empirical issue. Nevertheless, human capital should clearly play a part in any expanded notion of savings. Note that this genuine savings measure does not take into account population growth. This could be important in certain countries where the growth has been fast.39 Recent revisions, including a name change: genuine savings are now called adjusted net savings, are available at the World Banks homepage. Hamilton and Clemens (1999) make a number of interesting observations, based on their calculations of genuine savings for a large number of countries during the period 1970–1993. For example, they report that the genuine savings rate in sub-Saharan Africa was marginally positive in the 1970s, after which the rates have been negative. This, indeed, suggests a bleak outlook for future well-being. The authors comment that “not

39 For more on this, see Dasgupta (2002).

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only has sub-Saharan Africa performed badly by conventional measures, it is clear that the wealth inherent in the resource stocks of these countries is being liquidated and dissipated” [Hamilton and Clemens (1999, p. 344)]. At the other end of the spectrum lie the East Asia and Pacific regions, with very high savings rates throughout the period. Of course, bleak macroeconomic performance is not inconsistent with very high rates of genuine savings (cf. the Asian crisis of 1997). The calculations by Dasgupta (2002) suggest an even gloomier outcome in certain developing countries if the savings numbers are put on a per capita basis. According to his calculations, the average Pakistani is today less than half as wealthy as he was in 1970. The average Bangladeshi is a bit over half as wealthy today as she was in 1970.

15. Conclusions In 1664 William Petty published the first embryo of national accounts, arguing that “just accounts might be kept of the People, with their Increases and Decreases of them, the Wealth and Foreign Trade.”40 In some ways, our survey does try to present ways of discerning exactly what “just accounts” are supposed to contain. Indeed, one of our basic arguments has been that green accounting must rest on the twin pillars of clearly defined objectives and a sound theoretical base. Much progress has been made in the last few years in this regard, at least in the sense that empirical studies now have a firmer theoretical foundation. A useful way forward is to find an even happier marriage between theorists and empiricists in green accounting. The combination of theory and empirical work in the studies by, e.g., Ahlroth (2001), Bergman (2002), Hultkrantz (1991) and Vincent (1999) are useful starting points. These studies provide a fairly representative sample of studies which have clearly defined objectives and provide a useful theoretical base for their measurements. We have discussed a number of different approaches to dynamic welfare measurement. Needless to say, society’s welfare measure must reflect the extent to which it is forward-looking. This means, of course, that societies with different preferences may rank the same physical changes differently. Clearly this is not surprising, but bears restatement to emphasize that there is no universal measure of social welfare. In spite of the extent of the literature and the occasional debates between contributors, there is substantial agreement on many major issues and there is a gradual process of convergence under way. It seems to us likely that the convergence will eventually lead to the following consensus. There are a number of weakness with green NNP, specifically the strong assumptions needed to justify an interpretation of this as sustainable income or welfare. The standard interpretation of NPP as a welfare measure used in cost benefit analysis is more robust, yet one has to carefully treat price changes. What also seems to be very robust is the conclusion that changes in the values of stocks are ”sufficient statistics” for welfare changes, and these are of course a measure of the change in wealth. 40 As quoted in Stone (1985, p. 117).

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They are also sufficient to measure changes in the linearized Hamiltonian. So via a circuitous route we seem to be agreeing with Samuelson and others who have argued for wealth-based measures in a dynamic context. It may useful to end with one of our starting points, namely the fact that green accounting provides a consistent information system, useful for understanding links between the economy and the environment. Thus, while much of our discussion has come to circle around the properties of certain indices like NNP, it is as an information system that green accounting probably will be most useful for the analyst. There is still some way to go before the literature has converged on the most useful shaping of such an information system; the richness of current proposals on accounting systems reflects the fact that we are still probing useful extensions of the conventional accounting system. The challenges that lie ahead are likely to be more on the empirical side, given the relatively large amount of work that has been carried out on the foundations. While our discussion has come to focus on the links between the economy and the natural environment, the framework presented here should prove useful in other extensions of accounting systems. The development of social accounting has come to be influenced very clearly by social problems that nations have been grappling with, ever since Petty introduced his political arithmetic centuries ago. This is not the place to speculate about what those problems are likely to be, although inquiries into time use, accumulation of knowledge and human capital and further scrutiny of the output of the health sector are likely focal points.

Acknowledgements Special thanks to Jeffrey Vincent for detailed comments. Thanks also to Sofia Ahlroth, Geir Asheim, Anni Huhtala and Kristian Skånberg for their most useful comments on various parts of the manuscript. We also acknowledge useful discussions with Graciela Chichilnisky, Partha Dasgupta, Karl-Göran Mäler and Martin Weitzman. The usual disclaimer applies.

References Aghion, P., Howitt, P. (1997). Endogenous Growth Theory. MIT Press, Cambridge, MA. Ahlroth, S. (2001). “Green accounts for sulphur and nitrogen deposition in Sweden: implementation of a theoretical model in practice”. Licentiate thesis. Department of Forest Economics, SLU-Umeå, Sweden. Alfsen, K.H., Bye, T.A., Lorentsen, L. (1987). “Natural resource accounting and analysis: the Norwegian experience 1978–1986”. Sociale og Okonomiske Studier 65. Central Bureau of Statistics of Norway. Angeles, M.S.D., Peskin, H.M. (1996). “Environmental accounting as instrument of policy: the Philippine experience”. In: International Symposium on Integrated Environmental and Economic Accounting in Theory and Practice, March 5–8, 1996, Tokyo, Japan. Aronsson, T. (1998). “A note on social accounting and unemployment”. Economics Letters 59, 381–384. Aronsson, T., Löfgren, K.-G. (1993). “Welfare consequences of technological and environmental externalities in the Ramsey growth model”. Natural Resource Modelling 7, 1–14.

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Aronsson, T., Löfgren, K.-G. (1998). “Green accounting: what do we know and what do we need to know?” In: Folmer, H., Tietenberg, T. (Eds.), Yearbook of Environment and Resource Economics. Edward Elgar, Cheltenham, UK. Aronsson, T., Löfgren, K.-G. (1999). “Pollution tax design and green national accounting”. European Economic Review 43 (8), 1457–1474. Aronsson, T., Johansson, P.O., Löfgren, K.-G. (1997). Welfare Measurement, Sustainability and Green National Accounting. Edward Elgar, Cheltenham, UK. Asheim, G.B. (1994). “Net national product as an indicator of sustainability”. Scandinavian Journal of Economics 96 (2), 257–265. Asheim, G.B. (1996a). “The Weitzman foundation of NNP with nonconstant interest rates”. June. Also published as Asheim (1997). Asheim, G. (1996b). “Capital gains and ‘net national product’ in open economies”. Journal of Public Economics 59, 419–434. Asheim, G.B. (1997). “Adjusting green NNP to measure sustainability”. Scandinavian Journal of Economics 99 (3), 355–370. Asheim, G.B. (1999). “Green national accounting: why and how?” Working Paper. Department of Economics, University of Oslo. Also published as Asheim (2000). Asheim, G.B. (2000). “Green national accounting: why and how?” Environment and Development Economics 5, 25–48. Asheim, G.B., Weitzman, M.L. (2001). “Does NNP growth indicate welfare improvement?” Working paper. Published in Economics Letters 73, 233–239. Aukrust, O. (1992). “The Scandinavian contribution to national accounting”. Discussion paper 73. Central Bureau of Statistics, Oslo, Norway. Ayres, R.U., Kneese, A.V. (1969). “Production, consumption and externalities”. American Economic Review 59, 282–297. Bartelmus, P., van Tongeren, J. (1994). “Environmental accounting: an operational perspective”. Working paper series 1. Department for Economic and Social Information and Policy Analysis, United Nations, New York. Beltratti, A., Chichilnisky, G., Heal, G.M. (1993). “Sustainable growth and the Green Golden Rule”. In: Goldin, I., Winters, L.A. (Eds.), Approaches to Sustainable Economic Development. Cambridge University Press for the OECD, Paris, pp. 147–172. Beltratti, A., Chichilnisky, G., Heal, G. (1995). “The Green Golden Rule”. Economics Letters 49, 175–179. Bergman, L. (2002). “A CGE analysis of sulphur deposition and Swedens “green” net national product”. In: Kriström, B., Dasgupta, P., Löfgren, K.-G. (Eds.), Essays in Honor of Karl-Göran Mäler. Edward Elgar, Cheltenham, UK. Bergman, L. (2005). “CGE modeling of environmental policy and resource management”. In: Mäler, K.-G., Vincent, J.R. (Eds.), Handbook of Environmental Economics, vol. 3. Elsevier, Amsterdam, pp. 1273– 1306. This volume. Binkley, D., Högberg, P. (1997). “Does atmospheric deposition of nitrogen threaten Swedish forests?” Forest Ecology and Management 92, 119–152. Bockstael, N.E., Freeman, A.M. (2005). “Welfare theory and valuation”. In: Mäler, K.-G., Vincent, J. (Eds.), Handbook of Environmental Economics, vol. 2. Elsevier, Amsterdam, pp. 517–570. Broom, J. (1992). Counting the Cost of Global Warming. White Horse Press, London. Chichilnisky, G. (1993). “What is sustainable development?” Paper presented at Stanford Institute for Theoretical Economics. Published as Chichilnisky (1996). Chichilnisky, G. (1996). “An axiomatic approach to sustainable development”. Social Choice and Welfare 13 (2), 219–248. Chichilnisky, G., Heal, G. (1983). “Community preference and social choice”. Journal of Mathematical Economics 12 (1), 33–62. Chichilnisky, G., Heal, G. (1998). “Economic returns from the biosphere”. Nature 391, 629–630. Cline, W.R. (1992). The Economics of Global Warming. Institute for International Economics, Washington, DC.

1214

G. Heal and B. Kriström

Clarke, H.R., Dragun A.K. (1989). “Natural resource accounting: east gippsland study”. Report to the Australian Environment Council. Crosson, R.P. (1993). “Natural resource and environmental accounting in U.S. agriculture”. In: Workshop on Valuing Natural Capital for Sustainable Development, Woods Hole, MA, July 1–3. Custance, J., Hillier, H. (1998). “Statistical issues in developing indicators of sustainable development”. Journal of the Royal Statistical Society 161 (3), 281–290. Daly, H.E., Cobb, J.B. (1989). For the Common Good. Beacon Press, Boston. Danish Commission on Resource Accounting (1990). “Ökonomi og Miljö i Statistisk Belysning” (“Economy and the Environment in Statistical Light”) (In Danish). Betänkning 1210. Statens Informationstjense, Köpenhavn, Denmark. Dasgupta, P.S. (1993a). “Optimal development and the idea of net national product”. In: Goldin, I., Winters, L.A. (Eds.), Approaches to Sustainable Economic Development. Cambridge University Press for the OECD, Paris, pp. 111–143. Dasgupta, P.S. (1993b). An Inquiry into Well-Being and Destitution. Clarendon Press, Oxford. Dasgupta, P.S. (2002). Human Well-Being and the Natural Environment. Oxford University Press, Oxford, UK. Dasgupta, P.S., Heal, G. (1979). Economic Theory and Exhaustible Resource. Cambridge University Press, Cambridge. Dasgupta, P.S., Mäler, K.-G. (1995). “Poverty, institutions, and the environmental resource-base”. In: Behrman, J., Srinivasan, T.N. (Eds.), Handbook of Development Economics, vol. III. Elsevier, Amsterdam, pp. 2371–2463. Dasgupta, P.S., Mäler, K.-G. (1999). “Net national product and social well-being”. Published as Dasgupta and Mäler (2000). Dasgupta, P.S., Mäler, K.-G. (2000). “Net national product, wealth and social well-being”. Environment and Development Economics 5, 69–93. Dasgupta, P.S., Kriström, B., Mäler, K.-G. (1995). “Current issues in resource accounting”. In: Johansson, P.O., Kriström, B., Mäler, K.-G. (Eds.), Current Issues in Environmental Economics. Manchester University Press, Manchester, UK. Dasgupta, P.S., Kriström, B., Mäler, K.-G. (1997a). “Should search costs and discoveries be included in the national product?” Discussion Paper #104. Beijer Institute of Ecological Economics. Dasgupta, P.S., Kriström, B., Mäler, K.-G. (1997b). “The environment and net national product”. In: Dasgupta, P., Mäler, K.-G. (Eds.), The Environment and Emerging Development Issues. Oxford University Press, Oxford. Ekeland, I., Turnbull, T. (1983). Infinite-Dimensional Optimization and Convexity. University of Chicago Press, Chicago. El Serafy, S. (1989). “The proper calculation of income from natural resources”. In: Ahmad, Y., El Serafy, S., Lutz, E. (Eds.), Environmental Accounting for Sustainable Development. The World Bank, Washington, DC. El Serafy, S. (1996). “Environmental accounting for sustainable development: conceptual and theoretical issues relating to the system of integrated environmental and economic accounting (SEEA)”. Journal of Economic Cooperation Among Islamic Countries 17 (1–2), 87–107. El Serafy, S. (1999). “Natural resource accounting”. In: van den Bergh, J.C.J.M. (Ed.), Handbook of Environmental and Resource Economics. Edward Elgar, Cheltenham, UK. Environment and Development Economics 5 (Special issue) (2000). Fisher, I. (1906). The Nature of Capital and Income. MacMillan, New York. Hamilton, K., Clemens, M. (1999). “Genuine savings rates in developing countries”. The World Bank Economic Review 13 (2), 333–356. Harrison, G.W., Kriström, B. (1998). “General equilibrium effects of increasing carbon taxes in Sweden”. In: Brännlund, R., Mäler, K.-G., Gren, I. (Eds.), Green Taxes: Theory and Practice. Edward Elgar, London. Hartwick, J.M. (1977). “Intergenerational equity and the investing of rents from exhaustible resources”. American Economic Review 66, 972–974.

Ch. 22:

National Income and the Environment

1215

Hartwick, J.M. (1990). “Natural resources, national accounting, and economic depreciation”. Journal of Public Economics 43, 291–304. Hartwick, J.M. (1994). “National wealth and net national product”. Scandinavian Journal of Economics 96 (2), 253–256. Hartwick, J.M. (2000). National Accounting and Capital. Edward Elgar, Cheltenham, UK. Heal, G.M. (1998). Valuing the Future: Economic Theory and Sustainability. Columbia University Press, New York. Heal, G.M. (2000). Nature and the Marketplace: Capturing the Value of Ecosystem Services. Island Press, Washington, DC. Heal, G., Kriström B. (2000). “National income and the environment”. Working paper. Columbia University. Hicks, J.R. (1939). Value and Capital, second ed. Oxford University Press, Oxford, UK. Hicks, J.R. (1990). “The unification of macroeconomics”. Economic Journal 100, 528–538. Hotelling, H. (1925). “A general mathematical theory of depreciation”. Journal of the American Statistical Association 20, 340–353. Hueting, R. (1992). “Correcting national income for environmental losses: a practical solution for a theoretical dilemma”. In: Krabbe, J.J., Heijman, W.J.M. (Eds.), National Income and Nature: Externalities, Growth and Steady State. Kluwer Academic, Dordrecht, pp. 23–47. Hulten, C.R. (1995). “Capital and wealth in the revised SNA”. In: Kendrick, J.W. (Ed.), The New System of National Accounts. Kluwer Academic, Boston. Hultkrantz, L. (1991). “National accounts of timber and forest environmental resources in Sweden”. Environmental and Resource Economics 2, 283–305. Kendrick, J.W. (1995). “Introduction and overview”. In: Kendrick, J.W. (Ed.), The New System of National Accounts. Kluwer Academic, Boston. Keynes, J.M. (1940). How to Pay for the War: A Radical Plan for the Chancellor of the Exchequer. Macmillan, London. Krautkraemer, J.A. (1998). “Nonrenewable resource scarcity”. Journal of Economic Literature 36, 2065– 2107. KI (2000). http://www.konj.se. Environmental accounts, Report series. Kriström, B. (1995). “Accounting for the environment in Scandinavia”. In: Milon, W., Shogren, J. (Eds.), Integrating Ecological and Economic Indicators: Practical Methods for Environmental Policy Analysis. Praeger, London. Kriström, B. (2001). “Valuing forests”. In: Chichilnisky, G., Raven, P. (Eds.), Managing Human dominated Eco-Systems. MBO Press. Kriström, B. (2002). “Hotelling on depreciation”. In: Kriström, B., Dasgupta, P., Löfgren, K.-G. (Eds.), Essays in Honor of Karl-Göran Mäler. Edward Elgar, Cheltenham, UK. Landefeld, J.S., Hines, J.R. (1985). “National accounting for nonrenewable natural resources in the mining industries”. Review of Income and Wealth 31 (1), 1–20. Lindahl, E. (1932). “The concept of income”. In: Bagge, G. (Ed.), Essays in Honour of Gustav Cassel. Allen & Unwin, London. Lindahl, E. (1939). Studies in the Theory of Money and Capital. Allen and Unwin, London. Lindahl, E. (1954). “Nationalbokföringens Grundbegrepp” (“Fundamentals of National Accounting”) (In Swedish) Ekonomisk Tidskrift 2, 87–138. Lone, Ö. (1987). Natural Resource Accounting and Budgeting: A Short History and Some Critical Reflections on the Norwegian Experience 1975–1987. OECD, Paris. Lozada, G. (1995). “Resource depletion, national income accounting, and the value of optimal dynamic programs”. Resource and Energy Economics 17 (2), 137–154. Mäler, K.-G. (1989). “Sustainable Development”. Mimeo. Stockholm School of Economics. September. Mäler, K.-G. (1991). “National accounts and environmental resources”. Environmental and Resource Economics 1 (1), 1–15. Mäler, K.-G. (1995). “The arrow lectures”. Mimeo. Stanford University. Ministry of Finance (1999). “Vas är hållbar utveckling?” Bilaga 7 till Långtidsutredningen 1999/2000 (In Swedish). (“What is Sustainable Development” Supplement 7 to the Medium Term Survey).

1216

G. Heal and B. Kriström

National Research Council (NRC) (2000). Watershed Management for Potable Water Supply. Assessing the New York City Strategy. NAP, Washington, DC. 564 p. Nordhaus, W.D. (1995). “How should we measure sustainable income?” Cowles Foundation Discussion Paper 1101. Yale University. Nordhaus, W.D., Tobin, J. (1972). “Is growth obsolete?” In: Economic Growth. National Bureau of Economic Research, New York. Also in: Income and Wealth, vol. 38. National Bureau of Economic Research, New York, 1973. Nordhaus, W.D., Kokkelenberg, E.C. (Eds.) (1999). Nature’s Numbers: Expanding the National Economic Accounts to Include the Environment. National Academy Press, Washington, DC. Ohlsson, I. (1953). On National Accounting. National Institute of Economic Research, Stockholm, Sweden. Pearce, D., Atkinson, G. (1993). “Capital theory and the measurement of sustainable development: an indicator of weak sustainability”. Ecological Economics 8 (2), 103–108. Pemberton, M., Ulph, D.T. (2001). “Measuring income and measuring sustainability”. Scandinavian Journal of Economics 103 (1). Repetto, R., Magrath, W., Wells, M., Beer, C., Rossinni, F. (1989). “Wasting assets: natural resources in the national income accounts”. World Resources Institute, Washington, DC. Also Chapter 25 in: In: Markandya, A., Richardson, J. (Eds.), Environmental Economics: A Reader. St. Martin’s Press, New York, 1992. Ramsey, F.P. (1928). “A mathematical theory of saving”. The Economic Journal 38, 543–559. Samuelson, P.A. (1951). “Some aspects of the pure theory of capital”. Quarterly Journal of Economics 51, 469–496. Samuelson, P.A. (1961). “The evaluation of ‘social income’ capital formation and wealth”. In: Lutz, F.A., Hague, D.C. (Eds.), The Theory of Capital. St. Martins Press, New York. Sefton, J., Weale, M. (1996). “The net national product and exhaustible resources: the effects of foreign trade”. Journal of Public Economics 61 (1), 21–48. Siebert, H. (1985). Economics of the Resource Exporting Country: Intertemporal Theory of Supply and Trade. JAI Press, Greenwich. Solow, R.M. (1994). “Perspectives on growth theory”. Journal of Economic Perspectives 8, 45–54. SCB (1996). “Third meeting of the London group on natural resource and environmental accounting”. Mimeo. Statistics Sweden, Stockholm. Stone, R.T. (1951). “Functions and criteria in a system of social accounts”. In: Income and Wealth, Series I. Bowes and Bowes, Cambridge, pp. 1–74. Stone, R.T. (1985). “The accounts of society”. In: Les Prix Nobel. Almquist and Wicksell International, Stockholm. The page reference is from Nobel lecture repository, http://www.nobel.se/economics/laureates/ 1984/stone-lecture.pdf. Stone, R.T. (1988). “When will the war end?” Cambridge Journal of Economics 12 (2), 193–201. Studentski, P. (1958). The Income of Nations. New York University Press, New York. Swedish Commission on Resource Accounting (1991). Räkna med Miljön: Förslag till Miljö- och Miljöräkenskaper. Allmänna Förlaget, Stockholm (In Swedish with English summary). Available in condensed form as: Taking Nature into Account: Proposed Scheme of Resource And Environmental Accounting. Ministry of Finance, Stockholm, 1991. Tobin, J. (1987). “Fisher, Irving”. In: The New Palgrave Dictionary of Economics. Macmillan, New York. United Nations (1993). “Integrated economic and environmental accounting”. Sales No. E 93.XVII. 12. United Nations Statistics Division, New York. United Nations (1998). “Integrated Economic and Environmental Accounting—An Operation Manual”. Draft. United Nations Statistics Division. Uno, K. (1998). Environmental Options: Accounting for Sustainability. Kluwer Academic, Amsterdam. Usher, D. (1994). “Income and the Hamiltonian”. Review of Income and Wealth Series 40 (2), 123–141. van Tongeren, J., Schweinfest, S., Lutz, E., Gomez-Lunam, M., Guillen-Martin, F. (1992). “Integrated environmental and economic accounting – the case of Mexico”. In: CIDIE Workshop on Environmental Economics and Natural resource Management in Developing Countries. World Bank, Washington, DC. 22–24 January.

Ch. 22:

National Income and the Environment

1217

Varian, H. (1992). Microeconomic Analysis, third ed. Norton, New York. Verbruggen, H., Dellink, R.B., Gerlagh, R., Hofkes, M.W., Huib, M.A. (undated). “Alternative calculations of a sustainable national income according to Hueting”. Mimeo. Vincent, J.R. (1993). “Natural resources and economic growth”. Mimeo. Harvard University. Vincent, J.R. (1997). “Resource depletion and economic sustainability in Malaysia”. Environment and Development Economics 2 (1), 19–37. Vincent, J.R. (1999). “Net accumulation of timber resources”. Review of Income and Wealth 45 (2), 251–262. Vincent, J.R., Hartwick, J.M. (1997). Forest Resources and the National Income Accounts: Concepts and Experience. FAO, Rome. Vincent, J.R., Panayouto, T., Hartwick, J.M. (1997). “Resource depletion and sustainability in small open economies”. Journal of Environmental Economics and Management 33, 274–286. von Weizäcker, C.C. (1967). “Lemmas for a theory of approximatedly optimal growth”. Review of Economic Studies, 143–151. Ward, M. (1982). Accounting for the Depletion of Natural Resources in the National Accounts of Developing Countries. OECD, Paris. Weitzman, M.L. (1976). “On the welfare significance of net national product in a dynamic economy”. Quarterly Journal of Economics 90, 156–162. Weitzman, M.L. (1999). “A contribution to the theory of welfare comparisons”. NBER Working Paper 6988. February. Weitzman, M.L. (2000). “The linearised Hamiltonian as comprehensive NDP”. Environment and Development Economics 5 (1–2), 55–68. Weitzman, M.L. (2003). Income, Wealth and the Maximum Principle. Harvard University Press, Cambridge, MA. World Bank (1997). “Expanding the measure of wealth. indicators of environmentally sustainable development”. Report 17046 In: Environmentally Sustainable Development Studies and Monographs Series, vol. 17. ESSD Environmentally & Socially Sustainable Development. Work in progress. World Commission on Environment and Development (1987). Our Common Future. Oxford University Press, London. The Brundtland Report. World Resources Institute (WRI) (1991). Wasting Assets: Natural Resources in the National Income Accounts and Accounts Overdue: Natural Resource Depreciation in Costa Rica. WRI, Washington, DC.