Valuation and Evaluation:
               Measuring the Quality of Life and Evaluating Policy*




                                           by




                                   Partha Dasgupta

                               University of Cambridge
                                          and
          Beijer International Institute of Ecological Economics, Stockholm




                                    November 1999




       This is a background paper prepared for the World Bank's annual World
Development Report, 2000. In preparing it I have benefited from discussions with
Gretchen Daily, Carol Dasgupta, Paul Ehrlich, Frank Hahn, Sean Holly, Simon Levin,
Jane Lubchenco, William Peterson, Detlev Puetz, Peter Raven, Robert Rowthorn,
Georgina Santos, and Paul Seabright. My greatest debt is to Karl-Göran Mäler, joint
work with whom (Dasgupta and Mäler, 1999) is reported in the technical Appendix of
this paper.

                                         Contents

                      Part I: Reasons for Valuing and Evaluating

1. Means and Ends

2. Whose Well-Being?

3. Why Measure Well-Being?

                             Part II: Measuring Well-Being

4. Constituents versus Determinants of Well-Being

5. Measuring Current Well-Being

6. Estimating Current Well-Being in Poor Countries

7. Wealth as Sustainable Well-Being

                               Part III: Evaluating Policy

8. Valuing Goods and Evaluating Projects

9. The Environmental-Resource Base

10. Institutional Responses to Policy Change

11. Conclusions

       Appendix

       References

                                           Summary

        This paper is about measuring social well-being and evaluating policy. Part I is

concerned with the links between the two, while Parts II and III, respectively, are

devoted to the development of appropriate methods of measuring and evaluating.

        In Part II (Sections 4-7) I identify a minimal set of indices for spanning a general

conception of social well-being. The analysis is motivated by the frequent need to make

welfare comparisons across time and communities. A distinction is drawn between

current well-being and sustainable well-being. Measuring current well-being is the

subject of discussion in Sections 5-6. It is argued that a set of five indices, consisting of

private consumption per head, life expectancy at birth, literacy, and indices of civil and

political liberties, taken together, are a reasonable approximation for the purpose in

hand.

        Indices of the quality of life currently in use, such as UNDP's Human

Development Index, are cardinal measures. Since indices of civil and political liberties

are only ordinal, aggregate measures of social well-being should be required to be

ordinal. In this connection, the Borda index suggests itself. In Section 6 the Borda index

is put to work on data on what were 46 of the poorest countries in the early 1980s.

Interestingly, of the component indices, the ranking of countries in the sample in terms

of life expectancy at birth is found to be the most highly correlated with the countries'

Borda ranking. Even more interestingly, the ranking of countries in terms of gross

nationalproduct(GNP)perheadisalmostashighlycorrelated.Therecanbelittledoubt

that this finding is an empirical happenstance. But it may not be an uncommon

happenstance. If this were so, GNP per head could reasonably continue to be used as

a summary measure of social well-being, even though it has no theoretical claims to be

one.

        It is widely thought that net national product (NNP) per head measures the

economic component of sustainable well-being. In Section 7 and the Appendix it is

shown that this belief is false. It is shown that NNP, suitably defined, can be used to

evaluate economic policies, but that it should not be used in making intertemporal and

cross-country comparisons of the standard of living. In particular, it is shown that

comparisons of sustainable welfare should involve comparisons of wealth. For the

purposes of comparing social well-being in an economy over time, this reduces to

checking if net investment is positive or negative or nil. Writings on the welfare

economics of NNP have mostly addressed economies pursuing optimal policies, and

are thus of limited use. The analysis in Section 7 and the Appendix generalizes this

substantially by studying environments where governments are capable of engaging

only in policy reforms, in economies characterized by substantial non-convexities. The

analysis pertinent for optimizing governments and convex economies are special

limiting cases of the one reported here.

        Part III (Sections 8-10) is about policy evaluation. Policy evaluation techniques

developed in the 1970s, while formally correct, neglected to consider (1) resource

allocation in the wide variety of non-market institutions that prevail throughout the

world, and (2) the role the environmental-resource base plays in our lives. In Part III it

is argued that the evaluation of policy changes can be done effectively only if there is

a fair understanding of the way socio-economic and ecological systems would respond

to the changes. The observation is no doubt banal, but all too often decision-makers

have neglected to model the combined socio-economic and ecological system before

embarking upon new policies or keeping faith in prevailing ones. Examples are

provided to show that such neglect has probably meant even greater hardship for

precisely those groups of people who are commonly regarded as being particularly

deserving of consideration. The examples are also designed to demonstrate how recent

advances in our understanding of general resource allocation mechanisms and of

environmental and resource economics can be incorporated in a systematic way into

what are currently the best-practice policy evaluation techniques.


JEL Classification: O2, P5, Q2

              Part I




Reasons for Valuing and Evaluating

1. Means and Ends

       In common parlance we use the term "valuation" when comparing objects, and

"evaluation" when comparing the relative merits of actions. Of course, the objects

needn't be concrete, they can be abstract (e.g. ideas). Nor is evaluation restricted to a

narrowly construed notion of action. For example, we evaluate "strategies", which are

conditional actions that can be personal or collective ("do this if that happens", "do that

if he does this", and so forth). We also evaluate "policies", which too can be personal or

collective. In this sense "valuation" is passive, while "evaluation" signifies more of an

active engagement. We frequently "value" in order to be able to "evaluate"; but not

always: we sometimes value simply because we wish to understand a state of affairs.

       This article is about measuring the quality of life and evaluating policies. When

discussing the latter, I shall be thinking of public policies, the sort of policies

governments are expected to ponder over. They involve such matters as the character

ofpublicinvestment,the structureoftaxesand transfers,environmentallegislation,and

so forth. To be sure, in speaking of the evaluation of public policies, I mean the

evaluation of changes in public policies. Both valuation and evaluation involve

comparisons. For example, when we ask if the standard of living in some country is

currently higher than in some other, we are asking for a comparison. When we wish to

evaluate a public policy, we have to compare it to some other policy, which typically

would be the status quo; that is, the outcome which would prevail if existing policies

were kept in place. Evaluation involves the consideration of counter-factuals.

       The qualification "public" means two, often related, things. First, choice of one

public policy, rather than another, implies one background environment, rather than

another, within which the various parties in society can act. The choice influences the

constraints to which the various parties are subject. So, evaluating a public policy

requires that the likely responses of the economic system to the policy be assessed.

Secondly, the evaluation needs to be conducted on behalf of a large, possibly disparate

group of people, possessing different preferences, values, and needs. This calls for an

acceptable procedure for aggregating the often conficting claims of members of the

polity. It also requires that we identify those features of the consequences of the choice

that are to be used to conduct the evaluation. In short, to be able to evaluate public

policies we need measures of the quality of life.


                                             1

        But as we have already noted, the need for quality-of-life indices arises not only

becausepolicieshavetobeevaluated,thereareanumberofotherreasons.Forexample,

we often wish to know if a group (e.g. women in a country) are doing as well today as

they did in the past, or if one group (e.g. a country) enjoys a higher standard of living

than another. In what follows, I am much concerned with such questions as these. One

of my aims is to develop suitable indices for answering them. I also develop indices,

based on quality-of-life measures, that would be appropriate for evaluating public

policies. As we will see, the most suitable criteria for policy evaluation are not

necessarily quality-of-life indices, even though, of course, the criteria are based on such

indices.

        The construction of quality-of-life indices has received considerable attention in

recent years in such publications as the annual Human Development Report of the

United Nations Development Programme (UNDP). But assessing the likely response

of the economic system to policy choice is inherently the harder task. So, even although

this article is about quality-of-life indices and policy-evaluation techniques, later in this

essay (Part III, Section 10) I touch upon "institutional" responses to policy choice so as

to highlight the fact that such responses affect the way policy evaluation should be

conducted. In fact, it can be argued that, at the level of international discourse on

development policies, disagreements stem largely from our common lack of

understanding of the ways socio-economic and ecological systems respond to policy

changes, they stem less from disagreements over what one might call "ethical values",

in particular, they stem less from disagreements over what ought to be the ingredients

of quality-of-life indices.

        This last observation may appear odd. Economists continue to stress that people

differ in their judgement on what are appropriate rates of trade-off among competing

social goals. Political differences among people are to be traced to this, or so the

assertion goes.1 My own understanding is otherwise. Differences in people's opinions

about how the world "works" assume importance in political debates long before




  1 Among the most prominent expositions of this view are Robbins (1932), Samuelson (1947), Graaff
(1962), and Joan Robinson (1964).




                                               2

differences in ethical views manifest themselves. I have yet to meet someone who does

notwishtoseeunemploymentreducedordestitutionathingofthepastorcurrentrates

of disappearance of the rain forests stemmed. I have also heard many disagreements on

what are the most effective means of bringing them about. As the philosopher Hilary

Putnam has put it (Putnam, 1989, p. 7): "It is all well and good to describe hypothetical

cases in which two people "agree on the facts and disagree about values", but ... (w)hen

and where did a Nazi and an anti-Nazi, a communist and a social democrat, a

fundamentalist and a liberal ... agree on the facts?"

       It can also be argued that if development policies espoused by international

bodies have not infrequently failed, they have failed because of our vastly imperfect

knowledge and understanding of the way economic systems respond to policies, by

which I mean, of course, the way people respond to policies and the way ecosystems

respond to the treatment meted out to them. I don't know of much evidence that the

failureswereduetoawrongviewofwhatconstituteseconomicprogress.Inshort,even

thoughwearegenerallyinagreementaboutcollectiveends,wetypicallydisagreeabout

the right means to farther those ends. Later, in Part III (Sections 9-10), I provide

examples of this. Nevertheless, even if there is wide-spread agreement on what counts

as social well-being, there is need for an account of what this agreement amounts to. In

the remaining sections of Part I and in Part II, I provide an account.

2. Whose Well-Being?

       In what follows, I use the terms "well-being", "welfare", the "standard of living",

and the "quality of life" interchangeably. I am interested here in measures of social well-

being. I take it as understood that we are to build the measure from the ground up.

Since the locus of sensation, perception, and feeling is at the individual level, it is

appropriate to start there and to then build up. It is the individual who matters. I am

setting aside here arguments that have been offered for treating all animals equally

(Singer, 1976). Their acceptance would have far-reaching implications for many of our

institutions. I am limiting myself to measures of human well-being.

       A not infrequent criticism of the practice of founding measures of social well-

being on individual well-beings is based on the thought that "the whole is greater than

the sum of the parts". Taken literally, this viewpoint is an acknowledgement that the

processes which shape the way individual values and opportunities get translated into


                                             3

social outcomes are non-linear, with positive feedback. Usually, though, the thought is

nottakenliterally,butisregardedmoreasofferingametaphorforthe"bodycollective".

Now those who espouse collectivist goals (e.g. national prestige) ought to be required

to offer reasons why such goals are desirable. I don't know of any convincing reason

which does not reduce to a concern over the individual members of the body collective

(e.g. securing pride among members of the collective, thus enabling them to flourish

cooperatively).

        Disagreements between religious and secular people (and among religious

people themselves) would also appear, ultimately, to be over facts (viz. over the

existence, character and the will of God). Ethical differences stem from such

disagreements. Religious tolerance encourages people to live their lives in the light of

their own religious sensibilities, so long, that is, they do not infringe on the liberties of

others. These are subtle and complex matters and have been much discussed over the

centuries.2 Their wide recognition today, which is perhaps the most far-reaching

influenceoftheEnlightenment,isareasonwhyquality-of-lifeindicesmustincludecivil

and political liberties.

        Thesebriefobservationswillbe seentohaveinfluencedthenotionof socialwell-

being I offer in Part II (Sections 4-8) of this essay. But the notion has also been informed

by the overarching conception of citizenship, which is taken to cover three arenas: the

civil, the political, and the socio-economic.3 Recall that civil society is the sphere of

autonomous institutions, protected by the rule of law, in which people may conduct

their business freely and independently of the State. The civil element of citizenship

consists of the right to justice.

        Recall too that by the political element one means the right of a person to

participate in the exercise of political power, as a member of a body invested with

political authority, or as an elector of the members of such a body. And, recall finally,

that the socio-economic element is a range that encompasses the right to a certain share



   2Russell (1946) is a concise reference.

   3See T. H. Marshall (1964, pp. 71-2). Marshall's classic statement on the nature of social democracies
is further advanced in Marshall (1981). Rawls' two principles of justice (Rawls, 1972) pertain to the
productionanddistributionofthreebasic typesoffreedom:civil,politicalandsocio-economic. Rawlsian
justice concerns the fair distribution of what he calls "social primary goods", namely, liberty and
opportunity, income and wealth, and the bases of self-respect (see especially, Rawls, 1972, p. 303).

                                                    4

of resources, the right to share to the full in the social heritage, and to live the life of a

civilized being commensurate with the standards prevailing in the society in question.

        Quality-of-life indices in use today are based exclusively on the socio-economic

sphere of citizenship (e.g. UNDP's Human Development Index; see UNDP, 1998). This

is so limiting as to be potentially misleading. However, in Section 6, where I study data

pertaining to the world's poorest countries, we will discover that an exclusive concern

with the socio-economic sphere is not wildly misleading for the study of contemporary

societies. To me this suggests that, in the world as we know it, the three elements of

citizenship do not pull against one another, but rather that, generally speaking,

strengthening onehelps strengthenthe others. If thiswere more widely true,and I have

no reason to think otherwise, it would be an encouraging finding.

        Thus, even although, in developing measures of social well-being, I will

necessarily be thinking in aggregate terms, it bears stressing that the aggregate I

consider is composed of aspects of the lives of individual people. To the extent people

differ in their access to positions and opportunities owing to differences in their ethnic

or religious background, certain consequences would seem to follow, such as the

prevalence of communal strife. Since communal strife (in the extreme, civil war) is

frequentlybothacauseandconsequenceofauthoritarianismandcorruptionatthelevel

of government, the inequalities can be seen manifested in a restriction of civil and

political liberties. In other words, indices of civil and political liberties reflect inequities

along ethnic or religious lines.

        To the extent people differ in their access to basic goods and services owing to

systematicinequalitiesinthesocio-economicsphere(e.g.ownershipofland),wewould

wish to place greater weight on those who lack ready access to them. So there is an

explicit weighting system in any reasoned measure of social well-being.

        In recent years much has been written on such weighting systems, for example,

those which are embodied in such measures of inequality as the Gini coefficient (see,

for example, Sen 1992; UNDP, 1998; World Bank, 1998). In what follows, I build on this

literature. So I take the literature for granted here. What I want to do, first of all, is to

concentrate on the objects we would wish to study if we were to assess an individual's

livingstandard.Aggregatewell-beingforagivencohortofpeoplewillthenberegarded

to be the average well-being of the cohort. The thought-experiment I invoke to do this


                                              5

is the now-familiar conception due to Harsanyi (1955), in which the standard of living

in a society is deduced to be the expected living standard of someone who had equi-

probability of finding themselves in the place of each member of society.4 This is, of

course, what practical measures frequently amount to (e.g. national income per head,

and UNDP's Human Development Index (UNDP, 1991)). Inequality among a given

cohort (e.g. between men and women, and between the poor and non-poor) can then

be studied separately and additionally.

3. Why Measure Well-Being?

        We need measures of social well-being for at least five purposes. First, there is

need for an aggregate index of economic activity, of a kind which would help one to

summariseamacroeconomy.Grossnationalproduct(GNP)hasbeenfoundtobeuseful

in this role. Secondly, we may wish to compare the states of affairs in different places

(e.g. countries),or betweendifferentgroups ofpeople (e.g.thepoor incomparisonwith

the rich, or men in comparison with women), at a given point in time.

        It is the case that in international publications the indices which are typically

usedforthesecondpurposereflectonlythecurrentlivingstandard.Forexample,when

the World Bank, in its annual World Development Report (e.g. World Bank, 1995),

compares life expectancy at birth, infant survival rate, and public and private

consumption per head across countries in a given year, one of the points of the exercise

is to compare the current quality of life across countries (see the Appendix below,

Proposition 3). However, in the same publication, countries are ranked in accordance

with their GNP per head. The question is, why? Now it may be that the intention is to

includeinasummarymeasureacountry'sfutureprospects.Beingthesumofaggregate

consumption and investment, GNP may appear to be adequate for the task. The

problem is that, as it doesn't include the depreciation of capital assets, GNP is incapable

of reflecting future prospects (Section 9). GNP is not the flow equivalent of wealth (see

Appendix below, Propositions 4-5). So it doesn't quite do to regard a country to be poor

on grounds that its GNP perhead is low. As awelfare measure, GNP per head isneither




   4It will be recalled that Rawls' thought experiment was so constructed that average living standard
was replaced by max-min living standard (Rawls, 1971). It will be noticed that the indices I work with
below do not capture this thought-experiment exactly, but it does so with reasonably good
approximation.

                                                  6

here nor there and no amount of finessing can rescue it. GNP is a measure of current

economic activity and the prospects such activity brings with it, nothing more.

       The third reason we need quality-of-life indices is that we frequently wish to

makewelfarecomparisonsovertimeofpeopleinthesameplace(e.g.thesamecountry)

ormembersofaparticulargroup(e.g.thepoororrich,suitablydefined,orwomen).For

example, we may ask if a country is doing better today than it did a decade ago, and so

forth. This too is something the World Bank does in its annual World Development

Report, when estimating changes over time in such indicators in a country as life

expectancy at birth, infant survival rate, and public and private consumption per head

(see, for example, World Bank, 1995). The idea there is to compare the current standard

of living of a group of people at different dates (see Appendix below, Proposition 3).

       The previous two reasons for the need for welfare indices focussed on measures

which would reflect the current living standard. In contrast, the fourth reason stems

from a desire to estimate the economic component of the standard of living an economy

is capable of sustaining along alternative programmes. Early definitions of national

income (Lindahl, 1934; Hicks, 1940; Samuelson, 1961; Weitzman, 1976) were designed

to address this latter problem, and the bulk of recent theoretical explorations in green

net national product ("green NNP") have returned to it.5 It has been the claim of this

literature that NNP per head (that is, GNP per head minus the per capita accounting

value of the depreciation of all capital assets), is the measure we seek (see the references

inthepreviousfootnote).IntheAppendixbelow,Ishow(Proposition2andtheremarks

following it) that the claim is mistaken: NNP per head is inadequate for the task. I also

show that per capita wealth, suitably defined, is the appropriate index. More

particularly, it is demonstrated in the Appendix (Proposition 4) that if net investment

perheadispositive(negative),sustainablelivingstandardincreases(decreases).Itmay

not be a coincidence that Adam Smith's classic was an inquiry into the wealth of

nations, not the income of nations.

       The thought then arises that per capita wealth can perhaps also be used in

making cross-country comparison of sustainable living standards. In the Appendix

(Proposition 6) I show that it can be so used, but only under what should be regarded


   5See, for example, Solow (1986, 1992), Hartwick (1990, 1994), Asheim (1994, 1997), Aronsson,
Johansson, and Löfgren (1997), Aronsson and Löfgren (1998), and Weitzman (1998).

                                               7

as very strong assumptions. If the assumptions don't hold, there is no simple index

adequate for the task. In Section 7 I present a non-technical account of these findings.

       Finally, the fifth reason we seek a quality-of-life index is that we need ways to

evaluate alternative economic policies. Criterion functions for social cost-benefit

analysis of investment projects, such as the present discounted value of the flow of

accounting profits (e.g. Dasgupta, Marglin and Sen, 1972; Little and Mirrlees, 1974;

Squire and Van der Taak, 1975) are examples of such indicators (Section 8).

       Since economic activity, the current quality of life, evaluation criteria for policy

choice, and sustainable living standard are not the same object, their numerical

measures are not necessarily the same. For example, in a market economy the wage bill

for labour ought obviously to be included if the required index is to measure aggregate

economic activity, as in GNP. But it is by no means obvious that the item ought to be

included if the index is to measure social well-being (Nordhaus and Tobin, 1972;

Dasgupta and Mäler, 1999; see the Appendix below). The moral is banal: the way an

index ought to be defined, let alone estimated, is not independent of the purpose to

which it is put.

       But before all else, we should make clear to ourselves the purpose of the

evaluation before undertaking it, and we should be prepared to conduct the evaluation

as dispassionately as possible. Making good points with bad arguments may disguise

the fact that there exist good arguments which would have served the purpose. Here

is an example of the kind of mistake one makes when attempting an over-kill:

       In drawing attention to the enormous inequality in today's world, UNDP (1998,

p. 30) writes: "New estimates show that the world's 225 richest people have a combined

wealth of over 1 trillion US dollars, equal to the annual income of the poorest 47 percent

of the world's people (2.5 billion)."

       It should be known that wealth is a stock and income a flow. Consequently, one

should be converted into the other before the figures can be compared. The standard

practice would be to convert wealth into a figure for permanent income by using a 5

percent annual interest rate, that is, to divide wealth by a factor of 20. When this

conversion is performed on the data, my calculations, albeit they are very crude, tell me

that the world's richest 225 people, having a combined annual income of over 50 billion

US dollars, earn more than the combined annual incomes of people in the world's 12


                                             8

poorest countries, or about 7 percent of the world'spopulation (385 million). This is still

a sobering piece of statistic.

        It can be argued, of course, that if we seek a welfare indicator, we should

measure well-being directly and not look for a surrogate and give it a different name,

present discounted value of the flow of accounting profits, net national product (NNP),

wealth, or whatever. There is something in this. On the other hand, as there are several

reasons for seeking a welfare measure, for many purposes the most convenient index

could be something other than the thing itself. For example, we could be interested in

some object X, but X may prove especially hard to measure (e.g. because it involves

estimating non-linear functions of observable quantities). Suppose now that for some

purposes X is known to correlate perfectly with Y and that Y is easier to measure than

X (e.g. because Y is a linear function of observable quantities). Then we would wish to

rely on Y for those purposes. As is well known, wealth is linear in quantities, with the

weights being at least in part revealed by observable market prices. This is the case also

with the present discounted value of the flow of accounting profits. There lies the

attraction of these indices.




                                             9

      Part II




Measuring Well-Being




        10

4. Constituents and Determinants of Social Well-Being

       Thepreceedingobservationsuggeststhattherearetwowaysofmeasuringsocial

well-being. One is to study the constituents of well-being (e.g. health, happiness,

freedomtobeanddo;morebroadly,basicliberties);theotheristovaluethecommodity

determinants of well-being (goods and services which are inputs in the production of

well-being; for example, food, clothing, potable water, shelter, and resources devoted

to national security). The former procedure measures "output", for example, indices of

health,andcivilandpoliticalliberties,whereasthelattervaluesandthenaggregatesthe

required "inputs", for example, expenditure on health, and resources deployed for the

protection and promotion of civil and political liberties.6 If undertaken with sufficient

precision and care, either on its own would do the job (Dasgupta, 1993, Ch. 7*): changes

in a suitable aggregate measure of either the constituents, or the determinants, can be

made to serve as a measure of changes in the quality of life in a society. Along the

former route we would measure the constituents directly and aggregate them in a

suitable way, using social weights to reflect the relative worth of the various

constituents (Dasgupta, Marglin and Sen, 1972). Along the latter route we would need

to estimate accounting prices (see below) of the determinants of well-being in order to

arrive at a suitable index for the purpose in hand, for example, wealth (see the

Appendix, Proposition 4). As we have already observed, wealth is a linear function of

the stocks of goods and services. This is why we frequently measure social well-being

indirectly in terms of its determinants, rather than measure it directly in terms of its

constituents.

       In practice, neither the constituents nor the determinants, on their own, reflect

what we wish to see captured in any reasoned conception of the quality of life. The

problem is that there would be far too many person-specific accounting prices to

contend with (e.g. those based on income distributional weights) if we were to estimate

anoverarchingmeasureusingonly thedeterminantsofsocialwelfare.At thesametime,

a person's disposable income, as is customarily measured, does reflect aspects of



   6To be sure, there are goods, such as education and skills, which perform both functions: they are at
once constituents and determinants of well-being. They do not pose problems if we are able to track the
two functions and their contributions to well-being.




                                                  11

welfare and the extent of certain patterns of freedom (viz. the freedom to choose over

commodity bundles), matters which are hard to come to grips with directly. For this

reason, governments and international agencies pursue both avenues at once, and it is

today a commonplace to assess the quality of life by studying a heterodox collection of

socio-economic indicators (see, for example, the World Bank's annual World

Development Report, for example, World Bank, 1996; and the United Nations

Development Programmes' annual Human Development Report, for example, UNDP,

1998). Earlier, we noted several weaknesses in the indices currently in use. So, in the

following section I develop an index which overcomes some of their limitations.

       Well-being isn't the same as happiness. One could be in a happy frame of mind

under the influence of drugs and yet be in a state which could only be regarded as

reflecting a low quality of life. This and other such examples have been much discussed

in moral philosophy (see, for example, Sidgwick, 1907). Moreover, it is especially hard

to get a quantitative feel for the experiential state associated with the sense of well-

being. The nub is that states of mind are involved. Admittedly, other minds are not as

inscrutible to one as they are commonly made out to be; one's own experiences provide

the right source of information. Placing ourselves sympathetically in various possible

situations is a way of obtaining the sort of information we seek.

       We could, of course, study such objective indices as a country's divorce or

suicide rate, so as to measure experiential states. This too has been suggested. But such

indicators are seriously deficient. Divorce rates in a society may be low not because

marriages are happy, but because the cost of divorce is, for women, prohibitively high.

Similarly, the rate of suicide picks out features of the lower tail of the distribution of

mental states. We would wish to know something about the entire distribution. A

related approach would be to ask people if, on some specified scale (say, from 1 to 10),

they were happy (see, for example, Frey and Stutzer, 1999). States of mind are not

unmeasurable. In any event, whether we should include indices of the state of mind

when evaluating a person's well-being depends on the point of the exercise. For

example, contractarian theories of the State (e.g. Rawls, 1972; Nozick, 1974) typically

would not allow the State to be concerned with whether citizens were happy. Such

theories would see the business of the State as being restricted to making sure that basic

liberties are enjoyed.


                                             12

       This said, happiness is far too important a component of well-being to be

bypassed. So it is a puzzle that the contemporary literature on social well-being simply

ignores it. A prior question would be to ask what, in a normal state of mind, is

conducive to happiness? Interestingly, at reasonably high levels of income, income

would appear not to contribute much to happiness. Surveys in a number of western

countries have revealed that substantial growth in per capita income has not translated

into any significant increase in reported happiness (Easterlin, 1974; Scitovsky, 1976;

Oswald, 1997). A natural conclusion to draw from this would be that, at relatively high

levels of income, personal happiness depends on one's income or expenditure relative

to the mean income or expenditure of some reference group (e.g., per capita national

income; Easterlin, 1974). But I know of no comparable finding among the poor in poor

countries and would be surprised if there were such findings to be found. It is hard to

believe that at really low levels of income happiness isn't associated with income.

       Studies suggest that health contributes significantly to happiness: other things

being the same, healthy people are happier than those who suffer from ill health (see,

forexample,Frey andStutzer,1999).Studies inEuropealsosuggest thatunemployment

contributes significantly to unhappiness. Interestingly, in their study of a large sample

from the various cantons of Switzerland, Frey and Stutzer (1999) have found that

associational life plays a role too: people who are more engaged in civic activities are

happier. Assuming that these findings are robust, indices of health, and civic and

political liberties could serve as surrogates for happiness. In poor countries,

consumption too would be presumed to be a surrogate. So if we were to include these

indices in our measure of well-being, we would not need to introduce measures of

happiness directly. This is the route I follow in the next section.

5. Measuring Current Well-Being

       Theproblem,then,istoidentifyaminimalsetofindiceswhichwouldspanone's

conception of social well-being, be it current well-being or sustainable well-being. We

havenotedalreadythatitisimportanttoavoiddouble-counting.Forexample,statistics

ontheproportionsinpopulationsnothavingaccesstopotablewaterareinfrequentuse

when depicting the quality of life, as are statistics on infant mortality rates. But the two

would be expected to be highly correlated, indeed one is an important cause of the

other. If one has the former (latter) piece of information, one doesn't need the latter


                                            13

(former) in constructing a quality-of-life index.

        It has become customary to make cross-country and intertemporal comparisons

of the quality of life in terms of current well-being. In this section we look at the issues

that are involved in making such comparisons.

        Begin with a person. In choosing an index of her standard of living, a balance has

to be struck between the claims of completeness and costs. Leaving aside for the

moment the extent of civil and political liberties she enjoys, there would seem to be at

least three broad kinds of indices one can use in constructing a measure of her current

well-being: her disposable income, her health status, and her educational attainments.7

Now, these are different categories of goods. Health and education would seem to

embody aspects of what are called "positive freedoms" (moreover, they are both ends

and means), whereas disposable income contributes to the enjoyment of freedoms. So

then why do we wish to mix them up here?

        The reason is that someone's real disposable income measures the extent to

which consumption goods like food and clothing, shelter, legal aid and general

amenities are obtainable by that someone in the market. But primary health-care and

education aren't this sort of goods. As improvements in primary health care and

primary education give rise to wide-ranging "externalities" when they were privately

supplied, private markets don't provide an ideal resource allocation mechanism for

their supply. Markets for these goods need to be allied to an explicit support by the

State,inamannerwhichassurescitizensoftheirsupply.Nowgovernmentinvolvement

in the provision of primary health-care and education varies enormously across poor

countries. For this reason it is possible for people on average to enjoy a higher

disposable income in one country, and yet suffer from worse health-care and education

facilities than in another. Stating matters in the reverse way, it is possible for people in

one country on average to be better educated and to enjoy better health than in another

even while their access to other material goods is more restricted (see Table 1, below).

Disposable income, health and education indices reflect in their various ways the

current socio-economic status of a person.

        The move from the individual to the aggregate is frought with well-known



  7 For a detailed discussion, see Dasgupta (1993, chs. 2-5).

                                                 14

difficulties. As I am focussing on (current) well-being, averaged over a population, I

bypass inequality measures here.8 A problem frequently overlooked concerns the

legitimacy of moving from a person's disposable income, when thinking of a person's

well-being, to a country's aggregate output per head, when reflecting upon social well-

being. Thus, GNP per head continues to be regarded as the quintessential indicator of

a country's living standard. The gigantic literature on the determinants of economic

growthtestifiestothis,asdoannualpublicationsfrominternationalorganizations.Even

the Human Development Index of the United Nations Development Programme takes

one of the components of the quality of life to be GNP per head.9

       Personal income is the return on a person's wealth. But GNP is not the return on

a nation's wealth. This will make for complications when, in Section 7, we come to

develop the concept of sustainable living standard (see also the Appendix, below). As

I am now interested in developing an index of the current standard of living, I have to

ignoresavingforthefuture.Thisleavesmewithaggregateconsumption,whichconsists

of private and government consumption. But note that the latter is composed mainly

of expenditures on health, education, and defense. We will measure the quality of

health and education directly (by life expectancy at birth and literacy). This means that

we would be counting health and education twice if we were to include government

expenditure on them in our summary index. So we ignore such components of

government expenditure.

       This leaves us with defense, a central responsibility of government. But in poor

countries, which is what I am in the main concerned with here, the machinary for

warfareisalltoofrequentlyusedbygovernmentsagainsttheirowncitizens.Moreover,

what counts for citizens is their freedom to be and to do, a freedom which is generally

compromised if national security is threatened. As civil and political liberties are prime

components of the quality of life, we must include them explicitly. But this in turn

means that we can ignore defense expenditure when constructing an index of the socio-

economic component of social well-being.



  8The literature on distributional issues is vast (see Sen, 1992). Their consideration can be included in
what follows by imputing person-specific weights to individual well-beings.

  9The others are life expectancy at birth and literacy. See UNDP (1998). The Human Development
Index has been finessed over the years so as to be, for example, sensitive to gender inequalities.

                                                    15

       Let me sum up: a minimal set of indices which would span one's conception of

average well-being in a society would include private consumption per head, life

expectancy a birth, literacy, and civil and political liberties.10

       There remains the question of aggregating the five indices. Here we run into an

interesting problem, one which has been greatly neglected in the literature on living

standards. Indices which reflect the economic component of well-being are strongly

cardinal, that is, they are scale invariant. For example, whether one measures private

consumption in dollars or cents doesn't matter, so long as we remember that the latter

is one-hundredth of the former. This enables us to say, for example, that someone's

consumptionrateistwicethatofanotherperson,orthatsomeonetodayconsumesthree

times as much as he did ten years ago, and so forth. But indices of civil and political

liberties aren't like that, and cannot be like that. They are ordinal. It can make sense to

say that the average citizen of some country enjoys greater civil liberties than the

average citizen of some other country, or that civil liberties have increased in a country,

but it makes no sense to say that civil liberties in one country are four times those in

another, and so on. So we need an ordinal aggregator.

       Of the many we could devise, the one best known and most studied is the Borda

Rule. This rule provides a method of rank-order scoring, the procedure being to award

eachalternative (say,a country) apoint equal toits rankin each criterionof ranking (the

criteriabeing(i)percapitaprivateconsumption,(ii)lifeexpectancyatbirth,(iii)literacy,

(iv) political liberties, and (v) civil liberties), adding each alternative's scores to obtain

its aggregate score, and then ranking alternatives on the basis of their aggregate scores.

To illustrate, suppose a country has the ranks i, j, k, l, and m, respectively, for the five

criteria. Then its Borda score is i + j + k + l + m. The rule invariably yields a complete

ordering of alternatives. It can be viewed as a "social welfare function", since the criteria

can be thought of as "voters". Of Arrow's classic axioms on social choice, the Borda Rule

violates the one concerning the independence of irrelevant alternatives (Arrow, 1963).

The strengths and limitations of the Borda Rule have been investigated by Goodman

and Markowitz (1952) and Fine and Fine (1974). There is now a good intuitive

understanding of it. So I use it for illustrating how one could make cross-country



   10For a more thorough justification of the choice of these indices, see Dasgupta (1993, chs. 2-5).

                                                  16

comparisons of the current quality of life if we are restricted to the use of ordinal

indices, as we ought to be.11

6. Estimating Current Well-Being in Poor Countries

         Our laboratory consists of countries which were in the early 1970s among the

world's poorest in terms of income per head. The hope is to gain a preliminary

understanding of the way the various components of well-being are related in today's

world. Given the context in which such discussions have recently been undertaken, the

restriction to the world's poorest countries is both deliberate and right.

         We consider countries where in 1970 GNP per head was less than $1,500 at 1980

international dollars.12 The idea is to look at a snap-shot of the quality of life in each

country. The year in question is 1979-1980. I was able to obtain data on all five

components of social well-being for only 46 out of the more than 55 countries which

should be on our list. Table 1 summarizes the data. Since GNP per head is probably the

most familiar international statistic, figures for this are provided in the first column of

figures (but in parentheses, so as to remind ourselves that the country ranking on the

basis of GNP per head is not being used in the construction of the Borda index).

         The second column in Table 1 consists of estimates of private consumption per

head in 1980. The third and fourth columns of figures present life expectancy at birth

and literacy, respectively, again, for the year 1980.

         Thefifthandsixth columnsoffiguresin Table1represent indicesofpolitical and

civil liberties in our sample, for the year 1979. They are taken from the valuable

compendium of Taylor and Jodice (1983). Rights to political liberty are taken to be the

right on the part of citizens to play a part in determining who governs their country,

and what the laws are and will be. Countries are coded with scores ranging from 1




   11 Of course, we could create a cardinal aggregator for the socio-economic indices (private
consumption per head, life expectancy at birth, and literacy) and then construct the Borda ranking out
of the three resulting rankings, namely, the rankings based on civil and political liberties and the socio-
economic aggregate. In what follows in the text, I avoid creating complications by working directly with
the five rankings.

   12As the exercize that follows is purely illustrative, I have relied on data collated in Dasgupta and
Weale (1992) and Dasgupta (1993). There per capita GNP was taken to be one of the socio-economic
components of the quality of life. As I have just argued in the text (Sections 4-5), this was a mistake. So
I have re-done the calculations by replacing per capita GNP by private consumption per head. This
makes for some difference in the ranking of poor nations.

                                                    17

(highest degree of liberty) to 7 (lowest degree of liberty). Values for this index are given

in the fifth column of figures in Table 1.

        Civil rights are different. They are rights the individual has vis-a-vis the State.

Of particular importance in the construction of the index in Taylor and Jodice (1983) are

freedomofthePressandothermediaconcernedwiththedisseminationofinformation,

and the independence of the judiciary. The index measures the extent to which people,

becausethey areprotectedby anindependentjudiciary, areopenlyableto expresstheir

opinions without fear of reprisals. Countries are coded with scores ranging from 1

(highest degree of liberty) to 7 (lowest degree of liberty). Values of the index are given

in the sixth column of figures.

        Even a glance at the last two columns tells us that for the most part political and

civil liberties were scarce goods in poor countries in the late 1970s. Citizens of 32

countries in our sample of 46 suffered from systems that score 5 or more for political

rights, and those of no fewer than 39 countries from systems that score 5 or more for

civil rights. Theis suggests that civil rights can be, and are frequently, curtailed in

countries where elections are held. The scores reflect severe deprivation of basic

liberties.Therewereexceptionsofcourse,mostnotablyBotswana,India,Mauritiusand

Sri Lanka. But for the most part the columns make for dismal reading. And when they

are combined with the columns which reflect the socio-economic sphere of life, the

picture which emerges is chilling. There was nothing to commend the state of affairs in

a large number of the countries in our sample.

        The first column in Table 2 presents the Borda ranking of nations, based on the

rankings in the five columns that follow. Countries are listed in accordance with their

Borda ranks. The ranking is from the worst (score of 1; Mali and Ethiopia being the joint

losers) to the best (score of 46; Mauritious being the winner). For completeness, country

rankings on the basis of GNP per head are provided in the final column, in parentheses.

        It is a useful exercize first to look at the best- and worst-off sets of countries.

From the first column of figures, we note that in ascending order of aggregate well-

being, the 10 lowest-ranked countries in 1980 were: Mali, Ethiopia, Niger, Mauritania,

Chad, Malawi, Uganda, Burundi, Somalia, and Benin. How does this list compare with

the ranking of nations based exclusively on GNP per head? To see this, we note from

the final column that, in ascending order, the 10 poorest countries in terms of GNP per


                                             18

head were: Zaire, Uganda, Ethiopia, Burundi, Tanzania, Chad, Mali, Rwanda, Somalia,

and Malawi. The lists aren't the same, but they are strikingly similar. All are in sub-

Saharan Africa, and the lists contain seven countries in common.

        Turning next to the ten highest-ranked countries, we note first that in terms of

social well-being they are, in descending order: Mauritius, Sri Lanka, Ecuador, Korea,

Paraguay, Thailand, Botswana, Bolivia and Morocco (tied), and the Philippines.

        The relative positions of China on the Borda ranking (coming in at 17 from the

top) and India (coming in five places ahead, at 12) deserves a brief comment. For a long

while China and India have provided commentators with a classic tension:

achievements in the economic sphere against those in the arena of political and civil

liberties. As can be seen from Table 1, China beat India handsomely in each of the 3

socio-economicindicesonourlist(forexample,privateconsumptionperheadinChina

in 1980 was more than twice that in India), while India beat China in political and civil

liberties. All this is consistent with general knowledge. However, the fact that the two

finishsocloseinarankingof46countriesmeansthattheordinaldistancebetweenthem

in political and civil liberties is large relative to their distance in terms of the socio-

economic indicators. Other things remaining the same, had more countries managed

tosqueezethemselvesinbetweenChinaandIndiainthesocio-economicindicators,the

overall ranking of these two countries would have been reversed (recall that the Borda

Rule violates the "independence of irrelevant alternatives" axiom in Arrow, 1963). On

the other hand, had more countries squeezed themselves in between China and India

in the sphere of political and civil liberties, the Borda gap between the two countries

would have been greater. Clearly then, the relative placings of China and India are

sensitive to the aggregator being used. To me this is instructive.13

        How does the list of the 10 top countries compare with the list of the 10 least poor

countries.Asithappens,theyareverysimilar.The10leastpoorcountriesinoursample

were,indescendingorder:Ecuador,Korea,Paraguay,Jordan,Tunisia,Thailand,China,




  13InDasguptaand Weale(1992)and Dasgupta(1993),wheresuch computationswerefirstundertaken,
the socio-economic indices that were included were GNP per head, life expectancy at birth, infant
survival rate, and literacy. Since life expectancy at birth is strongly influenced by infant survival, this
amounted to counting similar health indices twice. It explains why, using what was essentially the same
data set as Table 1, the two earlier studies found China to have a higher Borda score than India, the
reverse of the present finding.

                                                   19

the Philippines, Bolivia, and Mauritius. There are 7 countries in common. We conclude

tentatively that, among the poorest of poor nations, rankings in terms of our index of

aggregate well-being are not too different from their rankings based on income per

head.

        But this is a qualitative claim, and it will be informative to get a quantitative feel

for the relationship between the Borda ranking and each of the rankings based on the

five components of social well-being. Statistically, how close then is the Borda ranking

to the other five? In order to examine this we look at rank correlations.

        Table 3 provides the (Spearman) correlation coefficient for each pair of rankings

from the seven rankings of nations in Table 2. It transpires that the correlation

coefficientbetweentheBordarankingandtheothersare:0.84withprivateconsumption

per head; 0.88 with life expectancy at birth; 0.72 with literacy; 0.76 with political rights;

and 0.75 with civil rights. I had not expected this. I had no reason to think that life

expectancy at birth would be the closest to our measure of the quality of life.

        At the same time, it is interesting that the Borda ranking of countries is highly

correlated (0.87) with the ranking of countries based on GNP per head. The present

findings imply that if we had to choose a single, ordinal indicator of aggregate well-

being, either life expectancy at birth or GNP per head would do! There must be a moral

to this.

        In this paper I have argued that GNP per head should not be considered to be a

component of social well-being, that rather, private consumption per head should be.

Notsurprisinglythough,thelinkbetweenGNPandprivateconsumptionisclose:inour

sample, the correlation coefficient is 0.91. It is customary in studies of economic

development to regress GNP per head against other socio-economic indicators, to see

how closely they are related. The last row of figures in Table 3 presents Spearman rank

correlation coefficients between GNP per head and each of the chosen five components

of well-being. Ignoring private consumption per head, the highest correlation (0.83) is

with life expectancy at birth. Again, I did not expect this. I also had no prior notion that

correlation with literacy (0.61) would be considerably less.

        Richer countries seemed to have enjoyed greater political and civil liberties. But

the correlation is not overly high (the correlation coefficient between private

consumption per head and political rights is 0.51 and with civil rights is 0.50). But


                                              20

neither private consumption per head nor political and civil liberties should be thought

of as being exogenously given. Any such link between them as we observe in

international data should only be seen as a link, nothing more. No causal relationship

can be presumed from the data. However, correlation coefficients of 0.51 and 0.50 do

meanthattheclaimthatthecircumstanceswhichmakeforpovertyarealsothosewhich

make it necessary for governments to deny citizens their civil and political liberties is

simply false. There are countries in the sample which are very poor in terms of private

consumption and which enjoy relatively high civil and political liberties.

       Literacy is a rogue index: it stands somewhat apart from the other socio-

economic indices. The correlation coefficient between literacy and political and civil

liberties are 0.28 and 0.30 respectively. These are relatively low figures, far and away

the lowest figures in Table 3.

7. Wealth as Sustainable Well-Being

       One may wonder where, if anywhere, net national product (NNP), suitably

defined with all relevant accounting prices, comes in. Recall that GNP is an index of

economic activity, including as it does "gross" capital formation, not "net". NNP is

superior precisely on this count (Section 3). It reflects not only one of the economic

components of current well-being (viz. consumption), it is sensitive also to the

provisions currently made for the economic component of future well-being. In the

previous two sections we studied indices of current well-being. Here we study

sustainable well-being (a formal definition of which is provided in the Appendix,

Sections A.5-A.6). This requires of us to peer into future possibilities. For tractibility, I

restrict our discussion to the socio-economic component of well-being, the implicit

hypothesis being that civil and political liberties are a given. This isn't a good

hypothesis, but there isn't anything I can do about it. We still lack an adequate

overarching theory which relates "economics" to "political science". In particular, there

is no workable model in which both future production possibilities and civil and

political liberties are endogenous. So with hands tied behind the proverbial back, I

consider intertemporal output and consumption possibilities, but notcivil and political

liberties.IntheAppendixacanonicalmodelofproductionandaccumulation,involving

labour, physical, knowledge, and environmental capital is presented. It enables us to

draw a number of conclusions. The discussion here is based on findings arrived at in


                                           21

the Appendix.

        What does NNP reflect? Following Weitzman (1976), NNP at any given date is

widely thought to measure the sustainable standard of living made possible by an

economy's assets at that date. Why might we be interested in such a result? We would

be interested in it if it enabled us to make NNP comparisons, say between two dates,

so as to infer how sustainable living standards compared between those same two

dates. For example, if the Weitzman result were correct, we would conclude that

sustainable living standard in a country had grown over a period if we were to observe

that its NNP per head had grown over that same period.

        IntheAppendixbelow,Ishowthat,alas,thiscannotbedone:unlessaneconomy

is in a steady state, NNP per head does not measure the sustainable standard of living

(Proposition 2) in the sense that comparisons of NNP per head across time and

communities do not amount to comparisons of the standard of living across time and

communities (Propositions 4-7). This in turn means that NNP per head should not be

used in making intertemporal or cross-country comparisons of well-being. I show that

in order to make intertemporal comparisons of a community's sustainable living

standard, the appropriate index is wealth (Propositions 4 and 6), which is another way

of saying that, in making intertemporal comparisons of a community's sustainable

welfare, we should estimate if net investment has been positive, negative, or nil.

Unfortunately, I am unable to conduct the kind of numerical investigation I was able

to offer in Section 6: There are as yet only a few reliable country-estimates of the value

of changes in natural capital over time. Nevertheless, there are reasons for thinking that

many of the countries in sub-Saharan Africa have seen their assets decline during the

past four decades or so. The development of international statistics on changes in the

wealth of nations should now be a matter of urgency.14

        The findings derived in the Appendix reflect the fact that NNP is not the flow

equivalent of wealth. However, NNP, properly defined, can be used to evaluate short-

term changes in economic policy. This is proved in Proposition 1 in the Appendix. To

be sure, if NNP is to be used for the purposes of policy evaluation, accounting prices

should be used. Recall that the accounting price of a resource is the increase in social


   14Serageldin (1995) has reported empirical work conducted at the World Bank on measuring changes
in wealth (see also World Bank, 1996).

                                                 22

well-being if a unit more of the resource were made available costlessly. Assume for

simplicitythatlabourissuppliedinelastically(intheAppendixIdropthisassumption).

In this case, NNP in a closed economy, when correctly measured, reads as:

        NNP = Consumption + net investment in physical capital + the value of the net

change in the stock of natural capital - the value of current environmental damages.15

        Notice that the value of net changes in human capital and knowledge are

included implictly in the first two terms in the formula for NNP. It is useful also to note

that the convention of regarding expenditures on public health and education as part

of final demand implicitly equates the cost of their provision with the contribution they

make to social well-being. This in all probability results in an underestimate in poor

countries. If education were a constituent of the standard of living, and not merely a

determinant through being instrumental in raising productivity, then its accounting

price would be that much higher. We should note as well that current defensive

expenditure against damages to the flow of environmental amenities ought to be

included in the estimation of final demand. Similarly, investment in the stock of

environmental defensive capital should be included in NNP. These, and a number of

other rules for constructing national accounts are proved in the Appendix. In the

remainder of this essay I explore methods appropriate for evaluating policy change.




  15 In an open economy the value of net exports ought to be deducted from the equation. See Sefton and
Weale (1996).

                                                  23

    Part III




Evaluating Policy




       24

8. Valuing Goods and Evaluating Projects

        Policy changes are perturbations to a prevailing state of affairs. Investment

projects can therefore be interpreted as policy changes. A project consisting of a dam

would be a perturbation to an economy without the dam. The economic forecast

without the project can be thought of as the status-quo. We could, of course, analyse the

consequences of a policy change in terms of their impact on the constituents of social

well-being. But as I argued earlier, there are advantages in analysing them in terms of

their impact on the determinants of social well-being. The linear indices I have been

alluding to, such as the present discounted value of the flow of accounting profits from

a project, work most effectively if the perturbation being evaluated is "small".16 What

constitutes "smallness" is a delicate matter and the project evaluator has to be sensitive

to it. An investment project can be small in terms of a country's NNP and yet have a big

impact on the lives of some very poor people; in which case it wouldn't be small for

them. The way to proceed would be to estimate the net benefits the people in question

would experience if the project were undertaken. The net benefits would typically be

non-linear functions of quantities.

        In evaluating an investment project, the need for labour, intermediate products,

and raw materials is estimated, and the project's output and its impact on the ecological

system are predicted, quantitatively, for each period. Most often, though, one does not

have sufficient knowledgeto make precise estimatesof the consequences.One therefore

needs quantitative estimates of the uncertainties, preferably in terms of probabilities.

This means that, in general, one has to model the integrated ecological and economic

system.17 The evaluation procedure involves estimating the impact of projects on

human well-being - now and in the future. In order to arrive at an estimate, each and

every commodity of the project has to be valued in terms of some numeraire (e.g.

consumption, as in the formula for NNP in Section 7). The accounting price of a

commodity or service is measured by its social opportunity cost in terms of the

numeraire. These steps are common to all methods of evaluation.

        If we wish to assess the impact on social well-being of a brief policy change (e.g.



   16Formally, we are then able to limit ourselves to the first-order approximations of the perturbations.

   17See Daily et al. (1999) for an elaboration of this step.

                                                     25

a short-term investment project), then, as we noted in Section 7, the effect of the change

on NNP (suitably defined) could be used for evaluating the worthwhileness of the

change (Appendix, Proposition 1). For long-lasting projects the most useful criterion is

the presentdiscounted valueof theflow ofaccounting profits.To estimatethis, onefirst

computes the net social profit of a project in each period of its life. The net social prifit,

in turn, is obtained by multiplying the project's inputs and outputs in the period in

question by their corresponding accounting prices and adding them (outputs are taken

to be positive, inputs are taken to be negative). Using a suitable discount rate, often

called the "social rate of discount", the per period net social profits yielded by a project

are added.18 Projects which yield a positive present discounted value of net social

profits are then recommended, those which yield a negative present discounted value

of net social profits are rejected.

        Proceduresforestimatingtheaccountingpricesofgoodsandservicesweremuch

discussed at the World Bank in the 1970s (see, for example, Squire and Van der Taak,

1975).Thetheoryofaccountingpricesthatexistedatthattimeassumedineffectthatthe

economy in which social cost-benefit analysis is conducted has an optimal economic

policy in place -, perhaps a second-best policy, but an optimal policy nonetheless. This

wasassumedexplicitlyinLittleandMirrlees(1974).Incontrast,Dasgupta,Marglinand

Sen (1972) developed prescriptions for project evaluation in economies where projects

could be thought of as policy reforms, that is, perturbations to economic forecasts that

may be riddled with inefficiencies and inequities. However, they offered no formal

theory to justify their prescriptions for an economy moving through time.19 Theoretical

foundations of social cost-benefit analysis when investment projects are policy reforms

have since been developed by Dasgupta and Mäler (1999). The theory is presented in

the Appendix below. It is important to stress that the theory does not presume

economies to possess a convex structure: production non-convexities arising from

economies of scale and scope and from ecological thresholds can be accomodated. This




  18The social rate of discount in any period is the percentage rate of decrease over that period and the
next in the accounting price of the numeraire.

  19 Projects as policy reform have been studied also by Meade (1955), Mäler (1975), Starrett (1988),
Ahmad and Stern (1990) and Dreze and Stern (1990). But their analysis was limited to what were
esentially timeless economies.

                                                   26

isasignificantimprovementonearliertheories,whichreliedheavilyontheassumption

that economies possess a convex structure.

        What would those valuation techniques developed in the 1970s and extended

recently instruct us if they were put to work on current concerns? In a recent lecture, the

President of the World Bank has correctly observed that, "... the success of most projects

is dependent on many assumptions extraneous to the project itself. Building new

schools is of no use without roads to get the children to the schools and without trained

teachers, books and equipment... Initiatives to make progress creating equal

opportunities for women make no sense if women have to spend many hours each day

carrying clean water, or finding and gathering fuel for cooking. Seeking universal

primary education without prenatal and postnatal health care means that children get

to school mentally and physically damaged. Establishing a health system but doing

nothing about clean water and sewerage diminishes enormously the impact of any

effort." (Wolfensohn, 1999, p. 8.)

        The author is pointing at the need to understand an economic system's response

to projectselection. Hisexamples areabout complementarities. Justas a shoefor theleft

foot is useless without the corresponding shoe for the right foot, establishing a health

system, but doing nothing about clean water, would not amount to much. The

accounting price of an object whose complements are unavailable is low, in the extreme

itisnil.Projectswhichproduced onewithoutitscomplementswouldregister anegative

present discounted value of social profits. In short, an integrated project could pass the

test even when its components, each on its own, would not.

9. The Environmental-Resource Base20

        Asignificantweaknessoftheseveralmanualsonsocialcost-benefitanalysisthat

were written during the 1970s was their total neglect of the natural world around us.

The environment simply didn't get a look in.21 Since market failure abounds in our



   20Some of the material of this section is taken from Dasgupta (1993) and Dasgupta, Levin and
Lubchenco (1999).




   21Dasgupta (1982) was an attempt to put that right.




                                                 27

dealingswiththeenvironment,marketscannotbereliedupontoprovideuswithprices

whichwouldevenapproximatelysignalthesocialscarcitiesofenvironmentalresources.

A great deal of work in environmental and resource economics since the 1970s has been

directed at discovering methods for estimating the accounting prices of various types

of environmental resources. But in considerable measure practical methods have been

developedforestimatingtheaccountingpricesof"amenities"(see,forexample,Mitchell

and Carson, 1989; Freeman, 1992), much less so for the multitude of ecosystem services

which constitute our life-support system, such as pollination, recycling of biomass,

nitrogen fixation, and water purification. We also lack a systematic body of work on

valuation techniques appropriate for the many non-market institutional settings in

which environmental resources are known to be transacted.

       However, the following is even now abundantly clear. Indicators of social well-

being in frequent use (e.g. GNP per head, life expectancy at birth, and the infant

survival rate) do not reflect the impact of economic activities on the environment and

the latter's response to the treatment meted out to it. Since such indices as GNP per

head pertain to commodity production, they don't fully take into account the use of

natural capital in the production process. So, statistics on past movements of GNP tell

us nothing about the resource stocks that remain. They don't make clear, for example,

whether increases in GNP per head are being realized by means of a depletion of the

resource base (for example, if increases in agricultural production are not being

achieved by means that adversely affect the services ecosystems are capable of

providingus).Overtheyearsenvironmentalandresourceeconomistshaveshownhow

national accounting systems need to be revised so as to include the value of the changes

in the environmental resource-base that occur each year due to human activities (see,

for example, Mäler 1974; Dasgupta and Heal 1979; Dasgupta and Mäler, 1999). We

should be in a position to determine whether resource degradation in the various

locations of the world has yet to reach the stage from which their current economic

activities are unsustainable. But the practice of national-income accounting has lagged

so far behind its theory, that we have little idea of what the facts have been. It is entirely

possiblethattimetrendsinsuchcommonlyusedsocio-economicindicatorsasGNPper

head, life expectancy at birth, and the infant survival rate give us a singularly

misleading picture of movements over time of the true standard of living.


                                              28

       To state the matter in another way, current-day estimates of socio-economic

indicators are biased because the accounting value of changes in the stocks of natural

capital are not taken into account. Because their accounting prices are not available,

environmental resources on site are frequently regarded as having no value. This

amounts to regarding the depreciation of natural capital as of no consequence. But as

theseresourcesarescarce goods,theiraccounting pricesare positive.Ifthey depreciate,

there is a social loss. This means that profits attributed to projects which degrade the

environment are frequently greater than the social profits they generate. Estimates of

theirratesofreturnarehigherthantheirsocialratesofreturn.Wrongsetsofinvestment

projectsthereforegetselected,inboththeprivateandpublicsectors:resource-intensive

projects look better than they actually are. It should be no surprise, therefore, that

installed technologies are often unfriendly towards the environment. This is likely to

be especially true in poor countries, where environmental legislations are usually

neither strong nor effectively enforced.

       The extent of such bias in investment activities will obviously vary from case to

case, and from country to country. But it can be substantial. In their work on the

depreciation of natural resources in Costa Rica, Solorzano et al. (1991) estimated that in

1989 the depreciation of three resources -- forests, soil, and fisheries -- amounted to

about 10 percent of gross domestic product and over a third of gross capital

accumulation.

       One can go further: the bias extends to the prior stage of research and

development. When environmental resources are underpriced (in the extreme, when

they are not priced at all), there is little incentive on anyone's part to develop

technologies which would economize their use. So the direction of technological

researchandtechnologicalchangearesystematicallydirectedagainsttheenvironment.

Consequently, environmental "cures" are sought once it is perceived that past choices

have been damaging to the environment, whereas "prevention", or input reduction,

would have been the better choice. To give an example, Chichilnisky and Heal (1998)

compared the costs of restoring the ecological functioning of the Catskill Watershed

ecosystem in New York State, to the costs of replacing the natural water purification

and filtration services the ecosystem has provided in the past by building a water-

purification plant costing 8 billion US dollars. They showed the overwhelming


                                           29

economic advantages of preservation over construction: independent of the other

services the Catskill watershed provides, and ignoring the annual running costs of 300

million US dollars for a filtration plant, the capital costs alone showed a more than 6-

fold advantage for investing in the natural-capital base.

        But bad habits are hard to overcome. Even today the environment has not

entered the common lexicon of economic discourse. Accounting for the environment,

if at all it comes into the calculus, is an after-thought to the real business of "doing

economics". Thus, for example, a recent issue of The Economist (25 September 1999)

carries a 38-page Survey of the World Economy in which the environmental-resource

base makes no appearance in the authors' assessment of what lies ahead. But we are all

so ingrained in our habits that I rather doubt if many readers will have noticed this fact.

        Itisworthemphasizingthatthepurposeofestimatingenvironmentalaccounting

prices is not to value the entire environment; rather, it is to evaluate the benefits and

costs associated with changes made to the environment due to human activities. Prices,

whetheractualoraccounting,havesignificanceonlywhentherearepotentialexchanges

from which choices have to be made (for example, when one has to choose among

alternative investment projects). Thus, the statement that a particular act of investment

can be expected to degrade the environment by, say, 1 million dollars annually has

meaning, because it says, among other things, that if the investment were not to be

undertaken, humanity would enjoy an additional 1 million dollars of benefits in the

form of environmental services. The statement also has operational significance: the

estimate could (and should) be used for calculating the present discounted value of the

flow of social profits attributable to the investment in question.

        Contrast such an estimate of the value of an incremental change in the

environmental-resource base with the one which says that, world-wide, the flow of

environmental services is currently worth, in total, 33 trillion US dollars annually

(Costanzaetal.,1997).Theformerismeaningfulbecauseitpresumesthathumanitywill

survive the incremental change and be there to experience and assess the change. The

reason the latter should cause us to balk is that if environmental services were to cease,

life would not exist. But then who would be there to receive 33 trillion US dollars of

annual benefits if humanity were to exchange its very existence for them? This is a case

where, paradoxically, the value of an entire something has no meaning and, therefore,


                                            30

is of no use, even though the value of incremental changes to that same something not

only has meaning, it also has use.

        An approach similar to Costanza et al. (1997) appears in a Focus article in The

Economist (26 June 1999). In observing the disturbing tendency of compound interest

to make large figures in the distant future look very small today, it is remarked (p. 128):

"Suppose a long-term discount rate of 7 percent (after inflation) is used ... Suppose also

that the project's benefits arrive 200 years from now ... If global GDP grows by 3 percent

a year during those two centuries, the value of the world's output in 2200 will be 8

quadrillion US dollars (a 16-figure number). But in present-value terms, that

stupendous sum would be worth just 10 billion US dollars. In other words, it would not

make sense for the world to spend any more than 10 billion US dollars (under 2 US

dollars a person) today on a measure that would prevent the loss of the planet's entire

output 200 years from now."

        We have already seen one problem with this reasoning. Another is its

presumption that social rates of discount are independent of the income forecast whose

perturbation is being discounted. The underlying assumption in the passage is a

massive perturbation (zero world output in year 2200). This would involve a secular

declineinoutput,atleastfromsomepointintimeinthefuture.Butsocialdiscountrates

associated with declining consumption streams would be expected to be negative.22

When viewed from the present, negative discount rates amplify incomes in the distant

future, they don't shrink them. Discounting future incomes produces paradoxes only

when it isn't recognised that, as discount rates are themselves accounting prices, they

should be endogenous to the analyses, the rates cannot be plucked out of the air.

10. Institutional Responses to Policy Change

        It is easy enough to define policy change (for example, an investment project) as

aperturbationtoaneconomicforecast.Itisaltogetheramoredifficultmattertoidentify

what the perturbation actually consists of. Any system, human or otherwise, should be

expected to respond when subjected to a perturbation. In an economy that is not

pursuing an optimum policy, a policy change can create all sorts of effects that ripple

through without being noticed by the public offices, for the reason that there may be no



   22See Dasgupta and Mäler (1995, pp. 2,400-1) for why this would be so.

                                                 31

public "signals" accompanying them. Tracing the ripples requires an understanding of

the way markets and non-market institutions interact.

        Very many transactions take place in non-market institutions. A prime set of

examples are transactions involving environmental services. In poor countries further

examples abound. In recent years long-term relationships have been studied by

economistsandpoliticalscientistswiththesamecareandrigourthattheyusedtoinvest

in the study of markets and the State. There is now a large and illuminating theoretical

andempiricalliteratureonthewidevarietyofwaysinwhichpeoplecopewithresource

scarcity when there are no formal markets for exchanging goods and services across

time, space, and circumstances.23 The literature offers us a lever with which to predict,

in broad terms, the way people, both individually and communally, would respond to

policy changes. Unfortunately, the literature hasn't filtered through sufficiently to

decision-makers. I want to illustrate what I mean by providing two examples, one a

local miniature, the other altogether grander and near-global.

        For manyyears now, thepolitical scientist, ElinorOstrom, has beenstudying the

management of common-property resources in various parts of the world. In her work

on collectively-managed irrigation systems in Nepal (Ostrom, 1996), she has accounted

for differences in rights and responsibilities among users (who gets how much water

and when, who is responsible for which maintenance task of the canal system, and so

forth) in terms of such facts as that some farmers are head-enders, while others are tail-

enders.Head-endershaveabuilt-inadvantage,inthattheycanpreventtail-endersfrom

receiving water. On the other hand, head-enders need the tail-enders' labour for repair

andmaintenanceoftraditionalcanalsystems,whicharecomposedoftemporary,stone-

trees-and-mud headworks. This means that both sets of parties can in principle gain

from cooperation. However, in the absence of cooperation their fortunes would differ

greatly. So, cooperative arrangements would be expected to display asymmetries, and

they do so display.24



  23 I have gone into this literature in detail in Dasgupta (1999).




  24 In fact, a general finding from studies on the management of common property systems is that
entitlements to products of the commons is, and was, almost always based on private holdings. See
McKean (1992) and Ostrom and Gardner (1993).

                                                    32

        In Ostrom (1996), the author reported that a number of communities in her

sample had been given well-meaning aid by donors, in that the canals had been

improved by the construction of permanent headworks. But she observed that those

canal systems that had been improved were frequently in worse repair and were

delivering less water to tail-enders than previously. Ostrom also reported that water

allocationwasmoreequitableintraditionalfarm-managementsystemsthaninmodern

systems managed by external agencies, such as government and foreign donors. She

estimated from her sample that agricultural productivity is higher in traditional

systems.

        Ostrom has an explanation for this. She argues that unless it is accompanied by

counter-measures, the construction of permanent headworks alters the relative

bargaining positions of the head- and tail-enders. Head-enders now don't need the

labour of tail-enders to maintain the canal system. So the new sharing scheme involves

even less water for tail-enders. Head-enders gain from the permanent structures, but

tail-enders lose disproportionately. This is an example of how well-meaning aid can go

wrong if the institution receiving the aid is not understood by the donor.

        Resource allocation rules practised at the local level are not infrequently

overturnedbycentralfiat.Anumber ofStatesintheSahelimposedruleswhichineffect

destroyed communitarian management practices in the forests. Villages ceased to have

authoritytoenforcesanctionsonthosewhoviolatedlocally-institutedrulesofuse.State

authority turned the local commons into free-access resources.

        My second example is altogether more grand and fiercely debated. So, of course,

I will be a lot more tentative in what I say. It has to do with the experience people in

poor countries have had with structural adjustment programmes, which involved

reductions in the plethora of economic distortions that had been introduced by

governments over decades.

        Many have criticised the way structural adjustment programmes have been

carried out. They have pointed to the additional hardship many of the poor have

experienced in their wake. But it is possible to argue that structural adjustments,

facilitating as they did, the growth of markets, were necessary. And it has been so




                                           33

argued by proponents of the programmes. What I want to suggest is that both

proponentsandopponentsoftheprogrammesmayberight.Growthofmarketsbenefit

many, but they can simultaneously make vulnerable people face additional economic

hardship and thereby increase the incidence and intensity of poverty and destitution in

an economy.

       How and why might this happen? There are a number of pathways by which it

can happen. Here I will sketch one that I have developed in previous writings (e.g.

Dasgupta, 1993, 1999).

       Long-term relationships in rural communities in poor countries are typically

sustained by the practice of social norms, for example, norms of reciprocity. This isn't

the place to elaborate upon the way social norms should technically be viewed (as self-

enforcing behavioural strategies). The point about social norms which bears stressing,

however, is that they can be practised only among people who expect to encounter one

another repeatedly in similar situations.

       Consider then a group of "far-sighted" people who know one another and who

prepare to interact indefinitely with one another. By a far-sighted person I mean now

someone who applies a low rate to discount future costs and benefits of alternative

courses of action. Assume as well that the parties in question are not separately mobile

(although they could be collectively mobile, as in the case of nomadic societies);

otherwise the chance of future encounters with one another would be low and people

(being far-sighted!) would discount heavily the future benefits of current cooperation.

       The basic idea is this: if people are far-sighted and are not separately mobile, a

credible threat by all that they would impose sufficiently stiff sanctions on anyone who

broke the agreement would deter everyone from breaking it. But the threat of sanctions

would cease to have potency if opportunistic behaviour were to become personally

more enticing. This can happen during a process in which formal markets grow nearby

and uncorrelated migration accompanies the process. As opportunities outside the

village improve, those with lesser ties (e.g. young men) are more likely to take

advantage of them and make a break with those customary obligations that are

enshrined in prevailing social norms. Those with greater attachments would perceive

this, and so infer that the expected benefits from complying with agreements are now

lower. Either way, norms of reciprocity could be expected to break down, making


                                            34

certain groups of people (e.g. women, the old, and the very young) worse off. This is a

case where improved institutional performance elsewhere (e.g. growth of markets in

the economy at large) has an adverse effect on the functioning of a local, non-market

institution.Totheextentlocalcommon-propertynaturalresourcesaremadevulnerable

by the breakdown of communitarian control mechanisms, structural adjustment

programmes would have been expected to be unfriendly also to the environment and,

therefore, to those who are directly dependent on them for their livelihood. This is

because whenthe marketvalue ofa resource-baseincreases, thereis especialadditional

pressure on the base if people have relatively free access to it.25 Structural adjustment

programmes devoid of safety-nets for those who are vulnerable to the erosion of

communitarian practices are defective. They can also be damaging to the environment

unless the structure of property rights, be they private or communitarian, is

simultaneously made more secure. We should not have expected matters to have been

otherwise.26

11. Conclusions

        This paper has been about measuring social well-being and evaluating policy.

Part I was concerned with the links between the two, while Parts II and III were

devoted, respectively, to the development of appropriate methods of measuring and

evaluating.

        InPartII(Sections4-7)Iidentifiedaminimalsetofindicesforspanningageneral

conception of social well-being. The analysis was motivated by our frequent need to

make welfare comparisons across time and communities. A distinction was drawn

between current well-being and sustainable well-being. Measuring current well-being

was the subject of discussion in Sections 4-6. It was argued that a set of five indices,

consisting of private consumption per head, life expectancy at birth, literacy, and

indicesofcivilandpoliticalliberties,takentogether,areareasonableapproximationfor


   25SeeDasgupta(1990)foratheoreticalanalysis;andReed(1992)foranempiricalinvestigation,inthree
poor countries, of some of the effects of structural adjustment programmes on resource bases.

   26As I am wholly inexpert on the matter, I am not offering even a sketch of the kinds of argument that
can be advanced to show that the reforms that were urged upon Russia in the early 1990s suffered from
a lack of acknowledgement of the role that governance plays in the operation of markets. In an
illuminating body of work, Richard Rose (see, for example, Rose, 1999) has been investigating the way
social networks there have entered spheres of activity they would not have if citizens were to have
enjoyed reliable governance.

                                                    35

the purpose in hand.

        Indices of the quality of life currently in use, such as UNDP's Human

Development Index, are cardinal measures. Since indices of civil and political liberties

are only ordinal, aggregate measures of social well-being should be required to be

ordinal.Inthisconnection,theBordaindexsuggesteditself.InSection6theBordaindex

was put to work on data on what were 46 of the poorest countries in about 1980.

Interestingly, of the component indices, the ranking of countries in the sample in terms

of lifeexpectancyatbirthwas foundtobethe mosthighlycorrelated withthecountries'

Borda ranking. Even more interestingly, the ranking of countries in terms of their GNP

per head was found to be almost as highly correlated. There can be little doubt that this

finding is an empirical happenstance. But it may not be an uncommon happenstance.

If this were so, GNP per head could reasonably continue to be used as a summary

measure of social well-being even though it has no theoretical claims to be one.

        It is widely thought that NNP per head measures the economic component of

sustainble well-being. In Section 7 it was argued that this belief is false. (In the

Appendixtheargumentissubstantiated.)ItwasshownthatNNP,suitablydefined,can

be used to evaluate economic policies, but that it should not be used in making

intertemporal and cross-country comparisons of sustainable well-being. In particular,

it was shown that comparisons of sustainable welfare should involve comparisons of

wealth. For comparing social well-being in an economy over time, this reduces to

checking if net investment is positive or negative or nil. Writings on the welfare

economics of NNP have mostly addressed economies pursuing optimal policies, and

are thus of limited use. The analysis in Section 7 (and the Appendix below) generalize

this substantially by studying environments where governments are capable of

engaging only in policy reforms in economies characterized by substantial non-

convexities. The analysis pertinent for optimizing governments and convex economies

are special limiting cases of the one reported here.

        PartIII(Sections8-10)wasaboutpolicyevaluation.Policyevaluationtechniques

developed in the 1970s, while formally correct, neglected to consider (1) resource

allocation in the wide variety of non-market institutions that prevail throughout the

world,and(2)theroletheenvironmental-resourcebaseplaysinourlives.Itwasargued

that the evaluation of policy changes can be done effectively only if there is a fair


                                           36

understanding of the way the socio-economic and ecological systems would respond

to the changes. The observation is no doubt banal, but all too often decision-makers

have neglected to model the combined socio-economic and ecological system before

embarking upon new policies or keeping faith in prevailing ones. Examples were

provided to show that such neglect has probably meant even greater hardship for

precisely those groups of people who are commonly regarded as being particularly

deserving of consideration. The examples were also designed to demonstrate how

recent advances in our understanding of general resource allocation mechanisms and

of environmental and resource economics can be incorporated in a systematic way into

what are currently the best-practice policy evaluation techniques.




                                          37

                                          Appendix27

A.1 The Model

       Consideramodeleconomywheretheproductionofgoodsandservicesrequires

labour, manufactured capital, and natural resources. The economy is deterministic.
Time is continuous and is denoted by t ( 0). Assume that there is an all-purpose, non-
deteriorating durable good, whose stock at t is Kt ( 0). The good can be either

consumed, or spent in increasing the stock of natural resources, or reinvested for its

own accumulation. For reasons to be identified in Section A.9, I assume that both

population size and the stock of human capital are constant, which means that we may

ignore them. The all-purpose good can be produced with its own stock (K), labour (L)

and the flow of natural resources (R) as inputs. I write the production function as F(K,

L, R). Production of the all-purpose durable good at date t is then F(Kt, Lt, Rt). I take it

that F is an increasing and continuously differentiable function of each of its variables.

But I do not assume F to be concave. It transpires that we do not need to, given that our

interest is in the welfare economics of policy reform.
       Let Ct ( 0) denote aggregate consumption at t, and Et ( 0) the expenditure on

increasing the natural-resource base. Net accumulation of physical capital satisfies the

condition:

       dKt/dt = F(Kt, Lt, Rt) - Ct - Et.                                                (1)

       It helps to interpret natural resources in broad terms. It enables us to consider a

number of issues. We should certainly include in the natural-resource base the

multitude of capital assets that provide the many and varied ecosystem services upon

which life is based. But we should add to this minerals and fossil fuels. Note too that

environmental pollution can be viewed as the reverse side of environmental resources.

In some cases the emission of pollutants amounts directly to a degradation of

ecosystems (e.g. loss of biomass); in others it amounts to a reduction in environmental

quality (e.g. deterioration of air and water quality), which also amounts to degradation

of ecosystems. This means that for analytical purposes there is no reason to distinguish

resource economics from environmental economics, nor resource management



  27This Appendix is based very closely on Dasgupta and Mäler (1999).




                                               38

problems from pollution management problems (Dasgupta, 1982). To put it crudely,

"resources" are a "good", while "pollution" (the degrader of resources) is a "bad". So we
work with an aggregate stock of natural resources, whose size at t is denoted by St (

0). For simplicity of exposition we assume that resource extraction is costless.

         Let the natural rate of regeneration of the resource base be M(St), where M(S) is

a continuously differentiable function.28 We suppose that the base can also be

augmented by expenditure Et (exploration costs in the case of minerals and fossil fuels,

clean-up costs in the case of polluted water, and so forth). Define

         Zt =    t
               -  Ed.29                                                                                (2)

In certain applications of the model, Zt would be a measure of the stock of knowledge

at t. This interpretation enables us to connect our model with one where there is

endogenous technical progress. Let us now re-express equation (2) in the more useable

form,

         dZt/dt = Et.                                                                                  (3)

         There are a number of ways in which one can model the process by which the

resource base is deliberately augmented. Let N(Et, Zt, St) denote the rate at which this

augmentation occurs, where N is taken to be a continuously differentiable function. It

is natural to assume that N is non-decreasing in both E and Z. We therefore assume it

to be so.

         The dynamics of the resource base can be expressed as:

         dSt/dt = M(St) - Rt + N(Et, Zt, St).                                                          (4)

         We formulate the idea of social welfare in a conventional manner and ignore

those many matters which arise when households are heterogeneous. We do this so as

to keep the notation tidy. Following the classic articles of Koopmans (1960, 1972), we
assume that social well-being at t ( 0) is of the "utilitarian" form,                 
                                                                                     tU(C, L)e-   (-t)d,

where U is strictly concave, increasing in C, decreasing in L (at least at large enough
values of L), and continuously differentiable in both C and L.  (> 0), a constant, is the

"utility" discount rate. Our analysis does not require that U be concave. We assume it




   28If the resource in question were minerals or fossil fuels, St would denote known reserves at t and we
would have M(S) = 0 for all S.

   29Z0 is part of the data of the economy. Like K0 and S0, it is an "initial condition".

                                                    39

nonetheless to be concave for ethical reasons.

A.2 The Analytics of Policy Reform

       Let (Ct, Lt, Rt, Et, Kt, Zt, St)0 denote an economic programme, from the present (t
                                        


= 0) to the indefinite future. A theory of economic policy capable of speaking only to

optimizing governments would be of very limited interest. For it to be of practical use,

a theory should be able to cover economies where governments not only do not

optimize, but perhaps cannot even ensure that economic programmes resulting from

its policies are intertemporally efficient. Consider then such an economy. To have a

problem to discuss, imagine that even though the government does not optimize, it can

bring about small changes to the economy by altering its existing, sub-optimal policies

in minor ways. The perturbation in question may, for example, consist of small

adjustments to the prevailing structure of taxes, or it could be minor alterations to the

existing set of property rights, or it could be a public investment, or whatever. We call

any such perturbation a policy reform. We proceed to develop the mathematics of

policy reforms.

       For concreteness, consider an economy facing the technological constraints in

equations (1), (3) and (4). In addition, it faces institutional constraints (sometime called

transaction and information constraints) which we will formalize presently. The initial

capital stocks (K0, Z0, S0) are given and known. By the institutional structure of the

economywewillmeanmarketstructures,thestructureofproperty-rights,taxrates,and

so forth. We take it that the institutional structure is given and known. If in addition we

knew the behavioural characteristics of the various agencies in the economy (i.e. those

ofhouseholds,firms,thegovernment,andsoon)itwouldbepossibletomakeaforecast

of the economy, by which we mean a forecast of the economic programme (Ct, Lt, Rt, Et,

Kt, Zt, St)0 that would be expected to unfold. We call this relationship a resource
            


allocation mechanism. So, a resource allocation mechanism is a mapping from initial

capital stocks (K0, Z0, S0) into the set of economic programmes (Ct, Lt, Rt, Et, Kt, Zt, St)0


satisfying equations (1), (3)-(4).

       We now formalise this. Write
       t  (Kt, Zt, St), and                                                               (5)
       ()t  (C, L, R, E, K, Z, S)t , for t  0.
                                                                                          (6)
Next let {t, t} denote the set of possible t and t pairs, and {()t } the set of economic
                                                                      




                                                40

programmes from t to the indefinite future. A resource allocation mechanism, , can

then be expressed as a mapping
         : {t, t} {()t }.                                                                             (7)
 would depend on calender time if knowledge, or population, or terms of trade were

to change autonomously over time.30 If they were not to display any exogenous shift,
 would be independent of t. For reasons to be discussed in Section A.8, we will pay
particular attention to the case where is autonomous. So let us assume that does not

depend on calendar time (i.e. it is time-consistent).
         It bears re-emphasis that we do not assume  to sustain an optimum economic

programme, nor even do we assume that it sustains an efficient programme. The
following analysis is valid even if is riddled with economic distortions and inequities.
         To make the dependence of the economic forecast on  explicit, let (Ct(), Lt(),
Rt(), Et(), Kt(), Zt(), St())0 denote the forecast at t = 0. Consider date t ( 0). Use (5)-
                                        


(7) to define
         Vt(, t)         -(-t)
                      t e       U(C(), L())d.                                                         (8)

Theright-hand-side(RHS)ofequation(8)issocialwelfareatt.Inthetheoryofoptimum

programming Vt is called the value function at t (Bellman, 1957).31

         Beforeputtingtheconceptofresourceallocationmechanismtowork,itisaswell

that we discuss examples by way of illustration. Imagine first that all capital assets are

private property and that there is a complete set of competitive forward markets
capable of sustaining a unique equilibrium. In this case  would be defined in terms of

this equilibrium. (If equilibrium were not unique, a selection rule among the multiple

equilibria would need to be specified.) Most studies on green accounting (e.g. Heal,

1998) are implicitly based on this mechanism.

         Of particular interest are situations where some of the assets are not private

property. Consider, for example, the class of cases where K and Z are private property,



   30Thereareexceptionstothisstatementinextremecases,namely,closedeconomieswhereproduction
is subject to constant-returns-to-scale, population changes exponentially, technical change is Harrod-
neutral, there are no environmental resources, and social well-being is based on classical utilitarianism
(Mirrlees, 1967). In such an economy  would be a mapping from the set of capital assets per efficiency
unit of labour into the set of economic programmes, where the programmes are expressed in efficiency
units of labour.

   31In all this, we take it that Vt is well defined. The assumption that  > 0 is crucial for this.

                                                      41

but S is not. It may be that S is a local common-property resource, not open to outsiders.

If S is managed efficiently, we are back to the case of a competitive equilibrium

allocation, albeit one not entirely supported by market prices, but in part by, say, social

norms.

       On the other hand, it may be that local institutions are not functioning well (e.g.

because social norms are breaking down), in that the marginal private benefits from the

use of S exceed the corresponding marginal social benefits. Suppose in addition that

decisions bearing on the net accumulation of K and Z are guided by the profit motive.
Then these behavioural rules together help determine . In a similar manner, we could
characterize  for the case where S is open-access.

       These observations imply that institutional assumptions underlie our notion of

resourceallocationmechanism.Aspectsoftheconceptof"socialcapital"(Putnam,1993)
would appear in our framework as part of the defining characteristics of , as would

ideas relating to "social capability" (Adelman and Morris, 1965; Abramovitz, 1986), and

"social infrastructure" (Halland Jones, 1999); otheraspects would be reflected asfactors

in the production functions F and N.32

       The crucial assumption we now make is that Vt is differentiable in each of the
three components of . We apologise for imposing a technical condition on something

which is endogenous, but space forbids we explore here the various conditions on an

economy's fundamentals (behavioural characteristics of the various agencies and

properties of the various production functions and ecological processes; initial set of

property rights; and so forth) which would guarantee a differentiable value function.

       It is not easy to judge if differentiability of Vt is a strong assumption. What is
certainly true is that if is a differentiable mapping, then Vt is differentiable. We should
therefore ask if is differentiable. This is not easy to answer. An economy's underlying
institutional structure is incorporated in , and there are no obvious limits to the kinds

of institutions one can envision. So one looks at what might be termed "canonical"

institutions. Analytically, the most well understood are those which support optimum

economic programmes. What do we know of the mathematical properties of the
corresponding ?



  32The analytics underlying the idea of social capital are explored in Dasgupta (1999).

                                                 42

        We know that if the production functions are concave and differentiable

everywhere, then for optimum economic programmes Vt is differentiable in each of the
components of . Interest therefore lies in cases where the production functions are not

concave. Now, we know that even if such production functions are differentiable, not

only could optimum economic programmes be discontinuous in each of the
components of , so could Vt be discontinuous (Skiba, 1978). But at points where Vt is

discontinuous,socialcost-benefitanalysisofpolicyreformscannotbeconductedsolely

with the aid of accounting prices: the relevant "consumer surpluses" need to be

estimated.33

        Having noted this, it should be stressed that such discontinuities as we are

alluding to are non-generic. So, unless the optimising economy were by fluke at one of

the points of discontinuity (they are called "bifurcation points"), Vt would be

differentiablewithinasufficientlysmallneighbourhoodoftheinitialcapitalstocks.The

same could be expected to be true for other "canonical" institutions, such as market

economies subject to fixed distortions. It would seem, therefore, that the demand that

Vt be differentiable would not appear to rule out much of practical significance. The

theory we offer here about the role of NNP in social cost-benefit analysis of policy

reforms is valid for a considerably more general set of environments than is usual in

writings on NNP.

A.3 Local Accounting Prices and their Dynamics

        Define,
        pt()  Vt(, t)/Kt; qt()  Vt(, t)/Zt; and rt()  Vt(, t)/St.                           (9)

We refer to them as local accounting prices. They measure social scarcities of the

economy's capital assets along the economic forecast.

        How might local accounting prices be estimated? If households are not rationed

in any market and externalities are negligible, market prices would be the reasonable

estimates. However, when households are rationed or externalities are rampant,

estimatinglocalaccountingpricesinvolvesmorecomplicatedwork.Forexample,inthe

presence of environmental externalities market prices need to be augmented by the

external effects (see, for example, Freeman, 1992, for an excellent account of current


  33The analysis that follows can be extended to cover cases where Vt possesses right- and left-
derivatives everywhere, but is not differentiable everywhere.

                                                  43

evaluation techniques). If households are rationed, one has to estimate "willingness-to-

pay". And so on. We will presently show that NNP, computed on the basis of local

accounting prices, can be used to evaluate short-term policy reform.

       What are the dynamics of local accounting prices? To study this, note that the
current-value Hamiltonian associated with  can be expressed as

       Ht = U(Ct, Lt) + pt(F(Kt, Lt, Rt) - Ct - Et) + qtEt + rt(M(St) - Rt + N(Et, Zt, St)). (10)

Recall equation (8), which we re-write here as:
       Vt(, t)       -(-t)
                  t  e    U(C, L)d.                                                          (11)

Vt is social well-being at t. Differentiating Vt with respect to t we obtain
       dVt/dt = Vt - U(Ct, Lt).                                                              (12)
But Vt = Vt(, t). Using (9), we conclude also that
       dVt/dt = ptdKt/dt + qtdZt/dt + rtdSt/dt + Vt/t.                                       (13)

Now combine equations (10), (12)-(13) to obtain
       Ht = Vt - Vt/t.                                                                       (14)

We can use equations (9) and (14) to conclude that
       dpt/dt = - Ht/Kt + pt; dqt/dt = - Ht/Zt + qt; and drt/dt = - Ht/St +
rt.                                                                                          (15)

The equations embodied in (15) define the dynamics of local accounting prices. It will

be noticed that they are formally the same as the Pontryagin conditions for the

evolution of accounting prices in an optimizing economy. Note also that all future

effects on the economy of changes in the structure of assets are reflected in local

accounting prices. That is why they are useful objects.
       As  has been assumed not to depend on calendar time, Vt does not depend on

it either. So equation (14) reduces to
       Ht = Vt.                                                                              (16)

Equation (16) is fundamental in intertemporal welfare economics. It says that the

Hamiltonian equals the return on social well-being even in a non-optimizing economy.

A.4 Using NNP to Evaluate Short-Term Policy Reforms
       Recall that  is being assumed not to depend on calendar time. Let us now think
of a short-term policy reform as a perturbation to  over the short interval [0, ]. The
perturbation is expressed as . During [0, ] the resource allocation mechanism is
denoted as ( + ). From  onward the economy is assumed to be governed by 


                                               44

again. Note now that if the reform were undertaken, the economic variables during [0,
] would be slightly perturbed ((Ct + Ct) rather than Ct, and so forth). Note too that at
 stocks of capital assets would be slightly different from what they would have been

had the reform not been undertaken.34
         Let the stocks at  be ( + ) as a consequence of the short-term reform. The

change in V0 arising from the reform can then be expressed as
V0 = V0(+, 0) - V0(, 0)

   =    -t
     0  e [U(C(+), L(+)) - U(C(), L())]dt + e- [V(, +) - V(, )] (17)


         On using equation (9) and the accumulation equations (1), (3) and (4), equation

(17) can be expressed as:
         V0 = e- (UCC + ULL) + e- (VKK + VZZ + VSS) + (),
                                                                                                         (18)
where () is an error term with the property that [()/] 0 as  0.35
         Equation(18)issimpletointerpret.Apolicyreformundertakenduring[0,]has

two effects on V0. First, the reform affects consumption and leisure during the period
of the reform. Second, it affects the asset structure of the economy at , when the reform

ends.Theright-hand-side(RHS)ofequation(A.18)measuresthecombinedeffectofthe

two sets of changes on V0.
         Consider now the perturbation to the asset structure at  as a consequence of the

short-term reform. Observe that
         K =      
                 0 (dKt/dt)dt = (dKt/dt)t=0 +  (),
where  () is an error term with the property that [ ()/] 0 as  0. Perturbations

to Z and S can be estimated in a similar manner. Therefore, equation (18) can be re-

written as
         V0/ = e- (UCC + ULL + p0(dKt/dt)t=0 + q0(dZt/dt)t=0 + r0(dSt/dt)t=0) +
                     


(),                                                                                                      (19)
where () is an error term with the property that () 0 as  0. The left-hand-side
(LHS) of (19) is the change in social well-being per unit of time during [0, ]. As we are
interested in small perturbations, we let  0. The LHS of equation (19) then becomes



   34It is here that we are invoking the assumption that  is a differentiable mapping. Seierstad and
Sydsaeter (1987) offers a rigorous account of the reasoning involved here.

   35UC and UL are evaluated at t=0. VK is the partial derivative of V with respect to K at t=0, and so forth.
I have now dropped writing the dependence of the economic forecast on . This saves on notation.

                                                    45

the change in social welfare occasioned by the short-term reform, and the RHS tends in

the limit to:
         UCC0 + ULL0 + p0(dKt/dt)t=0 + q0(dZt/dt)t=0 + r0(dSt/dt)t=0.                              (20)

         Choose consumption as numeraire and write

         n0 = -UL/UC; m0 = p0/UC; u0 = q0/UC; and v0 = r0/UC.36

On dividing expression (20) by UC, we obtain
         C0 - n0L0 + m0(dKt/dt)t=0 + u0(dZt/dt)t=0 + v0(dSt/dt)t=0.                                (21)

Now use equations (1), (3) and (4) to convert expression (21) into:
C0 - n0L0 + m0(F(Kt,Lt,Rt)-Ct-Et)t=0 + u0(Et)t=0 + v0(M(St)-Rt + N(Et,Zt,St))t=0.                  (22)

Ifexpression(21),orequivalently(22),ispositive,theshort-termreformincreasessocial

welfare, so it is desirable; if it is negative, the reform decreases social welfare, so it is

undesirable. Define

         ^
          t  UCCt + ULLt + ptdKt/dt + qtdZt/dt + rtdSt/dt,                                       (23a)

and thereby

          t  Ct - ntLt + mtdKt/dt + utdZt/dt + vtdSt/dt.                                         (23b)

If the right-hand-sides of equations (23a,b) have a familiar ring to them, it is because

they represent NNP at t (in utility and consumption numeraires, respectively),

measured in local accounting prices. Observe now that expression (21) is the change in

NNP at t = 0 occasioned by the short-term policy reform at t = 0. So we have

         Proposition 1: A short-term policy reform increases social well-being if and only

if it registers an increase in net national product measured in local accounting prices.

         Note that NNP as defined here is not NNP as it is usually defined. Conventional

NNP is the sum of aggregate consumption and net investment in physical capital, with

both measured at market prices. Expressions (23a,b) tell us that all components of NNP

should be valued at the local accounting prices given in equation (9), and that the

accounting value of net investment in the stocks of all durable capital goods

(manufactured, natural, human, and knowledge capital) should be included in NNP.

The NNP we are studying here is "green NNP".37




   36 Since the economic programme sustained by  is not a first-best, m0 is typically not equal to 1.

   37Dasgupta and Mäler (1991), Mäler (1991), and Dasgupta, Kriström and Mäler (1999) contain a more
detailed account of the various components of NNP.

                                                46

       Notethatautonomouschangesinwouldnotaffectourresult.Beingexogenous,

such changes would be unaffected by elementary policy reforms, so they are irrelevant

for social cost-benefit analysis of policy reform.

       The policy reforms we have envisaged here are confined to a short interval. But

what if a reform were small but irreversible (e.g. a small permanent change in fuel tax)?

In Section A.9 (Proposition 8) we show how accounting prices can be used to construct

indices with which one may evaluate the desirability of such a reform. The indices

developed there are linear in quantities. If those indices were not put to use (Johansson

and Löfgren, 1996), future changes in consumer surpluses would need to be estimated

for the purposes of social cost-benefit analysis. This is because a permanent reform, no

matter how small, would have cumulative effects on the size of capital stocks.

       How are short-term policy reforms related to optimum planning? Consider an

indefinite sequence of such reforms at every t, each of which increases NNP at t, where

NNP is computed at the prevailing local accounting prices. We take it that the entire

sequence is conducted in a counter-factual manner; that is, as a tatonnement. Such an
                                                                      ^

adjustment process is called a "gradient process" (it is also called the "hill-climbing

method"). So far we have not needed to assume convexity of the production possibility

set. Now we do. In a well-known paper, Arrow and Hurwicz (1958) proved in the

context of a finite-dimensional economy that, provided the set of production

possibilities has a sufficiently convex structure, the gradient process converges to the

optimum. A corresponding result for our model economy would be harder to prove,

given that we are considering infinite-dimensional consumption streams. Our

conjecture is that, despite this, a sequence of short-term policy reforms in the form of

a suitably defined gradient process would converge to the optimum economic

programme if the economy had a strong convex structure.

A.5 The Hamiltonian as Constant-Equivalent Utility

       In the previous section we showed that NNP can be used as an index for

conducting social cost-benefit analysis of short-term policy reforms. But the theoretical

literature on green NNP has been directed toward a quite different end (see especially

Weitzman, 1998). It has arguedthat NNP measures"constant-equivalent consumption".

We now look into this interpretation. In order to do that we have to assume that Vt is

differentiable everywhere. So we do so.


                                            47

         Continue to assume that Vt/t = 0. Since
[t e -(-t)  d] = 1, equation (15) can be written as
         Ht = Ht{[t e    -(-t) d]} = [t e     -(-t) Htd] = Vt,

from which we have

         Ht[t e
               -(-t)  d] =      -(-t)
                              t e     Htd = Vt            -(-t)
                                                      t   e     U(C, L)d.                               (24)

Equation (24) can be summarized as:

         Proposition 2: Along any economic programme the Hamiltonian at each date

equals the constant-equivalent flow of utility starting from that date.

         This resultwasprovedfor optimumeconomic programmesby Weitzman(1976),

who restricted his analysis to linear utility functions (specifically that U(C,L) = C). Since

in this case the Hamiltonian is NNP, Weitzman interpreted NNP as the constant-

equivalent consumption. The interpretation is today in wide usage.

A.6 Social Well-Being and the Concept of Sustainability

         World Commission (1987) defined "sustainable development" as an economic

programme in which, loosely speaking, the well-being of future generations is not

jeopardized. There are a number of possible interpretations of this.38 Consider the

following:
         (a) An economic development is sustainable if dUt/dt  0, where U0  lim Ut as
t -0.
         (b) An economic development is sustainable if dUt/dt  0.
         (c) An economic development is sustainable if dVt/dt  0,
where Vt(, t)            -(-t)
                       t e     U(C, L)d.

         It is clear that (a) lacks ethical foundation. For example, it may be desirable to

reduce U in the short run in order to accumulate assets in order that the flow of U is still

higher in the future. In this sense (b) offers greater flexibility in ethical reasoning: it

permits initial sacrifices in the current standard of living, U (a burden assumed by the

generation engaged in the reasoning), but requires that no future generation should

have to experience a decline in their standard of living.
         Consider the resource allocation mechanism . The mechanism allows one to



   38See Pezzey (1992) for a thorough treatment. It should be noted that to ask if economic development
is sustainable is different from asking if a given level of consumption is sustainable. See below in the text.



                                                      48

make an economic forecast. Suppose (b) were to be adopted as the definition of

sustainable development. Now

        dUt/dt = UCdCt/dt + ULdLt/dt.                                                                  (25)

From equation (25) we may conclude with:

        Proposition 3: If sustainable development is taken to mean that, starting from

now, utility must never decline, then an economic programme corresponds to

sustainabledevelopmentif,andonlyif,thevalueofchangesintheflowofconsumption

services is always non-negative.

A.7 Comparisons of Social Welfare Across Time

        In contrast to (b), the focus of (c) as a notion of sustainable development is social

well-being, V. The criterion permits the first generation to make initial sacrifices in V

(relative to the past), but requires that social well-being should never decline in the

future. Note that, while (b) implies (c), (c) does not imply (b).39 In short, (c) is more

general. In what follows, we adopt (c) as our notion of sustainable development and

develop criteria for judging if a given economic programme represents sustainable

development.
        Continue to assume that Vt/t = 0. Differentiating both sides of equation (15)

with respect to time, we have
        dHt/dt = dVt/dt.                                                                               (26)

Use (23b) to define
        It  ptdKt/dt; It  qtdZt/dt; and It  rtdSt/dt,
          K                Z                         S                                                 (27)

which are net investments in the three types of capital assets, respectively, expressed

in utility numeraire. We may then define aggregate net investment as,

        It = It + It + It .
               K    Z    S 40                                                                          (28)

It follows from equations (10), (13) and (26)-(28) that
        UCdC/dt + ULdL/dt + dIt/dt = It.                                                               (29)



   39For an arbitrary this is a trivial matter to confirm. Interestingly, Asheim (1994) has identified cases
where even an optimum economic programme may satisfy (c), while violating (b).

   40Note that the summation in equation (28) does not imply any assumptions regarding substitution
possibilities among the three kinds of capital assets. Whatever substitution possibilities there may be
would be reflected in the local accounting prices.




                                                     49

        Equation (29) enables us to obtain two alternative indicators of sustainable

development. The first can be obtained from the RHS of equation (29). For it implies

        Proposition 4: An economic programme increases social well-being over time if,

and only if, along the programme net investment in the economy's capital assets is

always positive.41

        The result has intuitive appeal. It says that social welfare is higher today than it

was yesterday if the economy is wealthier today. Here, an economy's "wealth" is

interpreted as the accounting value of all its capital assets, and wealth comparisons are

madeatconstantprices.InafamousarticleSamuelson(1961)arguedinconnectionwith

national income accounting that welfare comparisons should deal with "wealth-like"

entities. Proposition 4 formalizes that insight.

        Note,however,thatwhatwehaveobtainedisanequivalenceresult:Proposition

4 cannot on its own tell us if sustainable development is feasible. Whether the economy

is capableofgrowingwealthier indefinitelydepends,amongotherthings, ontheextent

to which different assets are substitutable in production.42

        An equivalent way of characterising sustainable development is to use the LHS

of equation (29). We state the result as:

        Proposition 5: Social welfare increases (decreases) over a short interval of time

if, and only if, during the interval the value of net changes in the flow of consumption

services plus the change in the value of net aggregate investment is positive (negative).

        For making intertemporal welfare comparisons it is customary to compare NNP

over time at constant prices. Proposition 5 says that this is not a correct procedure

unless the economy is stationary (i.e. dpt/dt = dqt/dt = drt/dt = 0). We conclude that




   41This result, shown to be a property of optimum economic programmes, originated in Solow (1974,
1992) and Hartwick (1977), who determined the investment rule that would sustain the maximum
constant utility stream, and in Dasgupta and Heal (1979, ch. 10), who showed in the context of a model
economy consisting of manufactured capital and an exhaustible resource that, along an optimum
economic programme social well-being is an increasing function of time if  = 0 and that this requires
net savings to be positive. Pearce, Hamilton and Atkinson (1996) suggested the use of the rule we have
obtained in the text for practical purposes, but offered no proof that the suggestion is valid. Serageldin
(1995) has reported empirical work done at the World Bank on the use of the rule. See also World Bank
(1996).

   42For an account of this, see Dasgupta and Heal (1979, ch. 7). The problem is deeper than was
recognizedinthatwork,sincesubstitutabilityinvolvessubstitutabilitynotmerelyinproduction,butalso
in consumption. On this see Dasgupta, Levin, Lubchenco and Mäler (1999).

                                                    50

intertemporalNNPcomparisonsarefarlessinformativeaboutchangesinsocialwelfare

over time than is commonly believed. Indeed, they would be highly misleading

indicatorsifrelativepriceswerechangingsignificantly.Notethatthisisconsistentwith

Proposition 1, which says that NNP provides a valid measure of the impact on social

well-being of short-term policy reforms.

A.8 Comparisons of Social Welfare Across Space

       In both popular and academic writings cross-country comparisons of GNP per

head are today a commonplace method for comparing well-being across countries. The

analysis in the previous section suggests not only that this practice is wrong, but also

that replacing GNP by NNP would not rescue matters. So the question is what index

should be used instead? We look into this.

       It is simplest to consider a continuum of closed economies, parametrized by x (a

scalar).43 We may interpret differences among economies in terms of differences in

initial endowments, or behavioural characteristics, or the resource allocation

mechanismsguidingthem. Butinorderto makemeaningfulcomparisonsof socialwell-

being, we must be able to ascribe the same value-function to all countries, that is, the
same utility function U(.) and the same .

       Consideradatewhenthecross-countrycomparisonsaretobemade.Tokeepthe

notation simple,wedropthetime subscript.LetHxbethe Hamiltonianincountryxand
Vx the value function there. Recall equation (15). In the present case it reads as Hx = Vx.

An argument identical to the one establishing equation (29) then yields
       [pxdKx/dx+qxdZx/dx+rxdSx/dx+Vx/x]=UCdCx/dx+ULdLx/dx+dIx/dx
+ Hx/x,                                                                                          (30)

where Ix is net aggregate investment in country x.
       For tractability, the interesting special case to consider is Vx/x = Hx/x =

0.44 From the LHS of equation (30) we conclude:

       Proposition 6: Social well-being in a country is higher (lower) than in any of its




   43I assume a continuum of economies in order to make use of the calculus. It simplifies the
computations. The analysis that follows can be easily adapted for the case where there is a discrete
number of economies.

   44The condition requires that the same resource allocation mechanism prevails in all countries. The
condition is strong.

                                                 51

immediate neighbours if in the aggregate it is wealthier (less wealthy).

        Proposition 6 formalizes the insight in Samuelson (1961) that in making welfare

comparisons across countries, one should compare their wealths. It corresponds to

Proposition 4.

        An equivalent indicator for making welfare comparisons can be obtained from

the RHS of equation (30):

        Proposition 7: Social well-being in a country is higher (lower) than in any of its

immediate neighbours if the value of the difference in the flow of consumption services

between them plus the difference in the value of aggregate net investment between

them is positive (negative).

        Notice that the recommendation in Proposition 7 (which corresponds to

Proposition 5) would not amount to NNP comparisons across countries unless local

accounting prices were the same (i.e. dpx/dx = dqx/dx = drx/dx = 0). I conclude that

cross-countrycomparisonsofNNPtellusnothingaboutdifferencesinsocialwell-being

excepting under empirically uninteresting circumstances.

        Equation (30) is exact, but the pair of (linear) indicators we have obtained in
Propositions 6 and 7 serve their purpose accurately only when Vx/x = 0. I believe this
to be a strong condition. If, as we suspect is the case, Vx/x is not even approximately

zero, there are no linear indices to be had for making cross-country welfare

comparisons.

A.9 Evaluation of Permanent Policy Change

        The technique we have developed for making cross-country comparisons of

social well-being can also be used for evaluating the desirability of a permanent policy

reform, or of a permanent change in some parameter of the economy. In keeping with
the notation introduced in section 4, let  be this parameter (e.g. the given resource

allocationmechanism).Then,retracingtheargumentsthere,wemaywriteequation(16)

as
        Ht() = Vt().                                                                  (31)

Using equations (27)-(29), we obtain
        dVt()/d = dHt()/d = UCdCt()/d + ULdLt()/d + dIt()/d.                         (32)

From equation (32) we have

Proposition 8:If the value of the changes in consumption services plus the change in the


                                             52

value of net investment occasioned by a permanent change in a parameter

characterisinganeconomyispositive(negative),socialwell-beingincreases(decreases).

A.10 Technological Change and Growth Accounting

       How should NNP be computed in the presence of technical change? Note first

that resource augmentation, N, in equation (4) could itself be regarded as a form of

technical progress. This said, it must also be granted that the growth and decay of

knowledge involve wider considerations. For example, it has been customary in the

economics literature to regard technical progress as shifts in production functions. In

what follows I explore this route by introducing technical progress in the production

of the final good in the model of Section A.3.

       We need to extend our notation. Denote by E1t and E2t expenditures on resource

augmentationandongeneralizedresearchanddevelopment(R&D),respectively.Now

define Z1t and Z2t by the equations

       dZ1t/dt = E1t,                                                               (33)

and    dZ2t/dt = E2t.                                                               (34)

Z1 and Z2 can be thought of as two types of knowledge. Denote the resource

augmentation function as N(E1, Z1, S) and imagine that output of the produced

consumption good at t can be expressed as
       Yt = etQ(Z2t)F(Kt, Lt, Rt),                                                  (35)
where   0 and Q (Z2)  0. Technical progress in the production of the final good
appears here as the term etQ(Z2t). It combines exogenous factors () with endogenous

ones (Z2).

       Letconsumptionbethenumeraire,u1andu2thelocalaccountingpricesofZ1and

Z2, respectively, and let the remaining local accounting prices be denoted as in Section

A.5. Retracing the arguments leading to (23b), it is a simple matter to conclude that

NNP reads as:

         t= Ct - ntLt + mtdKt/dt + u1tdZ1t/dt + u2tdZ2t/dt + vtdSt/dt.              (36)

       Similarly one can confirm that the discussion in Section A.5 on the evaluation of

short-term policy reform remains unchanged in the presence of technical change.

       The question remains: what factors contribute to changes in GNP over time? To

see what the answer could be, consider that GNP in our model economy is given by

(35).Differentiatingbothsidesofequation(35)withrespecttot,re-arrangingterms,and


                                           53

dropping the time subscript from variables for the sake of notational simplicity, we

obtain the growth accounting identity as
        (dY/dt)/Y   + (Q (Z2)dZ2/dt)/Q(Z2) + (FKdK/dt)/F + (FLdL/dt)/F +

(FRdR/dt)]/F.                                                                         (37)

        The sum of the first two terms on the RHS of equation (37) measures the

percentage rate of change in "total factor productivity", while the remaining terms

together represent the contributions of changes in the "factors of production" to the
percentage rate of change in GNP. Since  is an exogenous factor, it is unexplained
within the model. For this reason it is called the "residual". When it is not zero,  could
well be the most important determinant of Vt/t.

        Inafamousarticle,Solow(1957)usedareduced-formoftheproductionfunction

in (35) to estimate the contribution of changes in the factors of production to growth of

non-farm GNP per "man-hour" in the US economy over the period 1909-1949, and

discovered that it was a mere 12 percent of the average annual rate of growth.45 In

otherwords,88percentofthegrowthwasattributabletotheresidual.(Solow'sestimate
of  was 1.5 percent per year.) A significant empirical literature since then has shown

that when K is better measured (e.g. by accounting for changes in the utilization of

capacity and changes in what is embodied in capital; see footnote 28 below) and when

account is taken of human-capital formation, the residual is small for the non-farm

sector in the US economy.46

        This is congenial to intuition. We should doubt if it is prudent to postulate

everlasting increases in total factor productivity, let alone in per capita output. To do

so would be to place an enormous burden of proof on an experience which is not much

more than a few hundred years old. Extrapolation into the past is a sobering exercise:

over the long haul of time (say, a few thousand years), the residual has been not much

more than zero.

        It is in any case hard to believe that serendipity, unbacked by R&D effort and

investment in physical capital (learning by doing), can be a continual source of
productivitygrowth.Apositivevalueof wouldimplythattheeconomyisguaranteed



  45Solow assumed in particular that Q (Z2) = 0.

  46Jorgenson (1995) contains a masterly account of this complex literature.

                                                54

a "free lunch" forever. To be sure, such an assumption would guarantee that growth in

aggregate consumption was sustainable. In fact, that would be its attraction: it would

enable us to assume away problems of environmental and resource scarcities. But there

arenotheoreticalor empiricalgroundsforpresumingthat itisa reasonableassumption.

At this point in our understanding of the process by which discoveries are made, it
makes greater sense to set  = 0 in (35), (which would imply that Vt/t = 0).47 This

thought is reinforced by the observation that most environmental resources go

unrecorded in growth accounting. The implication is obvious: when we regress growth

in GNP on growth in inputs which exclude the use of environmental resources, we
obtain too high an estimate of  if in fact the use of such resources has been growing.

In adopting this position, I am not suggesting that there is no such thing as technical

change; what I am suggesting is that of the first two terms on the right-hand-side of

equation (37), it is the second term which is significant. It denotes the contribution of

technical change to productivity growth.

         Productivity growth in equation (37) is productivity growth in GNP. It has often

been suggested that we should instead be interested in productivity growth in NNP, as

defined in equation (36). For example, in their important early work on Indonesia,

Repetto et al. (1989) showed that if one were to include deforestation, soil erosion, and

the depreciation of oil reserves in the country's national accounts, Indonesia's rate of

growth in NNP during the 1980s would be half the estimated growth rate of her GNP.

And there are other environmental and natural resources that Repetto et al. did not

consider.

         In Section A.6 it was shown that NNP comparisons across time tell us nothing

about changes in social well-being unless an economy is in a steady state. It was also




   47Lau (1996) reports on a series of studies that have specified the aggregate production function to be
of the form Yt = F(AtKt Ht
                       a  (1-a), Lt), where K is physical capital, H is human capital, A is the augmentation
factor of the composite capital, L is the number of labour-hours, and 0 < a < 1. The studies have
uncovered that, since the end of the Second World-War, the contribution of technical progress (i.e. the
percentage rate of change in At) to growth in Yt in today's newly industrialized countries has been
negligible. He also reports that, if new knowledge is taken to be embodied in new capital-equipment, the
contribution of growth in the value of At to growth in Yt among western industrialized economies has
been a mere 10 percent, that of growth in physical capital some 75 percent, while the contributions of
growthinhumancapitalandlabour-hourshaveeachbeensome7percent.Laualsonotesthatthestudies
are silent on whether technical progress in Western industrialized economies has been exogenous or the
fruit of expenditures on research and development.

                                                      55

shown that we should ask instead if, in the aggregate, net investment is positive. It is

possible for an economy's GNP (per head) to increase over a period of time even while,

in the aggregate, net investment (per head) is negative. I know of no evidence that in

recent years this has not been experienced in a number of countries.48

A.11 Commentary

        GreenNNPhaswidelybeeninterpretedasconstant-equivalentconsumption.In

Section A.5 it was shown that, excepting for the uninteresting case where U is linear in

consumption (or else homogeneous of degree less than one), this interpretation is

simply false. What is true is that the Hamiltonian which equals constant-equivalent

utility(Proposition2).However,sincetheHamiltonianistypicallyanon-linearfunction

of consumption and leisure, it is of little practical use.

        In developing the concept of NNP I have made use of a series of models of

increasing generality. However, of necessity even the most general of the models had

important features missing. I comment on a few of them. Readers can easily fill in the

details.

        (1) Problems associated with intragenerational distribution have been ignored.

However, it is theoretically a simple matter to include them. The way to do it would be

to enlarge the set of commodities so as to distinguish a good consumed or supplied by

one person from that same good consumed or supplied by another person. This means,

for example, that a piece of clothing worn by a poor person should be regarded as a

different commodity from that same type of clothing worn by a rich person. Such

commoditiesarecalled"namedgoods"(Hahn,1971).Accountingpricesofnamedgoods

would typically depend on the names attached to them. With this re-interpretation of

goods and services, the results we have obtained continue to hold.49

        (2) Environmental externalities can be incorporated by a device identical to (1)

above.To describewhois affected,inwhich manner,andby whoseactionsinvolves the

use of named goods and services. It follows that accounting prices would be "named",




  48Serageldin (1995) contains a report on the beginnings of this research programme.

  49 I am assuming in this example that income or wealth mal-distribution is the cause of concern.
Dasgupta, Marglin and Sen (1972) suggested the use of income distributional weights as a rough-and-
ready way to capture such concern. The Bergson social welfare function was designed precisely to
incorporate these considerations.

                                                 56

so as to distinguish private costs from social costs and private benefits from social

benefits.Indeed,Pigouviantaxesandsubsidiesonexternalitiescanbecomputedonthe

basisofnamedaccountingprices(DasguptaandHeal,1979,ch.3;Mäler,1991;Freeman,

1992).

        (3)Uncertaintyhasbeenavoidedhere.Assumethenthatsocialwell-beingatdate

t=0 is the expected value of the present discounted flow of utility. The natural move

would be to make use of the idea of contingent goods, and therefore of contingent

accounting prices. Our analysis would then go through.

        (4)Thediscussionhasbeenrestrictedtoclosedeconomies.However,theanalysis

can be extended to an economy that trades with the rest of the world. Dasgupta,

Kriström and Mäler (1995) and Sefton and Weale (1996) contain an account of this.

        (5) Human capital has been absent from the discussion. Analytically it is not

difficult to include it. Human capital can be thought of as another form of capital. So net

investment in it would be included in NNP (see Dasgupta, Kriström and Mäler, 1995,

foraformulation).However,unlikephysicalcapital,humancapitalisnon-transferable.

So they should be regarded as named goods.

        (6) The models studied here have not included demographic change. It is

customary in growth accounting to regard changes in population over time as

exogenously given. However, in many societies parents regard children as both an end

in themselves and a means to other things (e.g. income security). So population needs

toberegardedasastockwhosemovementsovertimeare,atleastinpart,endogenously

determined. The problem is that our current understanding of the determinants of

fertility behaviour is weak. Moreover, serious problems arise when one comes to

construct intergenerational welfare economics in such a world. There is no received

theory. Population ethics is an underdeveloped field of inquiry. For the moment it

would seem reasonable to conduct such analyses as we have conducted conditional on

specified demographic movements. This has been our approach here.50

        Finally,itisaswelltore-stressthatthisAppendixbeenaboutconceptualmatters

only. The findings here imply that the estimation of accounting prices should now be

a priority. This said, it must be acknowledged that estimating the accounting prices of


   50See Dasgupta (1998) for a discussion of some of the more transparent problems that arise when one
thinks about the concept of optimum population.

                                                  57

certain categories of resources will prove to be impossible. So no single index could

suffice. But this means that tradeoffs would have to be made explicitly (e.g. how much

biodiversity should be permitted to be destroyed for the sake of so many dollars of

aggregate income?). These are hard choices, even tragic choices. But I believe they are

unavoidable.




                                          58

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                                         65

                                    Table 1
                        Living Standards' Indicators in 1980

                    ( Y)        C           E         L       R1    R2

Bangl ade s h        ( 540)     491        48         26      4     4
Be ni n              ( 534)     427        47         28      7     7
Bol i v i a        ( 1529)     1147        50         63      3     5
Bot s wana         ( 1477)      827        55         35      3     2
Bur undi             ( 333)     393        46         25      6     7
C. A. R.             ( 487)     536        47         33      7     7
Chad                 ( 353)     339        42         15      6     6
Chi na             ( 1619)      955        67         69      6     6
Ec uador           ( 2607)     1642        63         81      3     5
Egy pt               ( 995)     657        58         44      5     5
Et hi opi a          ( 325)     260        44         15      7     7
Hai t i              ( 696)     633        52         23      6     7
Hondur as          ( 1075)      720        60         60      3     6
I ndi a              ( 614)     423        54         36      3     2
I ndone s i a      ( 1063)      606        53         62      5     5
J or dan           ( 1885)     1372        62         70      6     6
Ke ny a              ( 662)     430        55         47      5     5
Kor e a            ( 2369)     1486        67         93      5     5
Le s ot ho           ( 694)    1106        52         52      4     5
Li be r i a          ( 680)     374        52         25      4     6
Madagas c ar         ( 589)     437        51         50      5     5
Mal awi              ( 417)     334        44         25      6     6
Mal i                ( 356)     288        44         10      7     7
Maur i t ani a       ( 576)     271        43         17      6     6
Maur i t i us      ( 1484)     1042        65         85      2     4
Mor oc c o         ( 1200)      803        57         28      4     3
Ne pal               ( 490)     456        45         19      6     5
Ni ge r              ( 441)     309        42         10      6     7
Ni ge r i a          ( 824)     511        48         34      3     5
Pak i s t an         ( 990)     821        49         24      5     6
Par aguay          ( 1979)     1464        66         84      5     5
Phi l i ppi ne s   ( 1551)     1039        61         75      5     5
Rwanda               ( 379)     322        45         50      5     6
Se ne gal            ( 744)     655        45         10      3     4
Si e r r a L.        ( 512)     394        38         15      5     6
Somal i a            ( 415)     324        44         60      7     7
Sr i Lank a        ( 1200)      509        68         85      3     2
Sudan                ( 652)     554        46         32      5     5
Swaz i l and       ( 1079)      550        51         65      6     5
Tanz ani a           ( 353)     275        50         79      6     6
Thai l and         ( 1694)     1117        62         86      4     6
Tuni s i a         ( 1845)     1107        60         62      6     5
Uganda               ( 257)     252        46         52      7     7
Zai r e              ( 224)     168        49         55      6     7
Zambi a              ( 716)     387        50         44      5     5
Zi mbabwe            ( 930)     586        55         69      5     5


                                       66

67

Ke y :                 Y - per capita GNP (international dollars)
                       C - per capita private consumption (international dollars)
                       E - life expectancy at birth (years)
                       L - adult literacy rate (%)

                       R1 index of political rights
                         -
                       R2- index of civil rights

Abbreviations: C.A.R. (Central African Republic) and Sierra L. (Sierra Leone).

Source: World Bank (1982) and Dasgupta and Weale (1992)




                                                    68

                                       Table 2
                      Rankings of Living Standards Data for 1980


                 BORDA   C          E        L       R1         R2    ( Y)
                 RANK


Mal i             1      6           5        1         1        1      7
Et hi opi a       1      3           5        4         1        1      3
Ni ge r           3      7           2        1         7        1    11
Maur i t ani a    4      4           4        7         7       11    17
Chad              5     11           2        4         7       11      6
Mal awi           6     10           5       10         7       11    10
Uganda            6      2          12       27         1        1      2
Bur undi          8     14          12       11         7        1      4
Somal i a         9      9           5       30         1        1      9
Be ni n          10     17          15       15         1        1    15
Si e r r a L.    11     15           1        4       20        11    14
Zai r e          12      1          19       29         7        1      1
C. A. R.         13     24          15       18         1        1    12
Ne pal           14     20           9        8         7       23    13
Hai t i          15     29          26        9         7        1    24
Rwanda           16      8           9       25       20        11      8
Tanz ani a       17      5          21       40         7       11      5
Li be r i a      18     12          26       11       33        11    22
Pak i s t an     19     34          19       10       20        11    29
Sudan            20     26          12       17       20        23    20
Zambi a          21     13          21       22       20        23    25
Madagas c ar     22     19          24       25       20        23    18
Swaz i l and     23     25          24       35         7       23    33
Ke ny a          24     18          31       24       20        23    21
Se ne gal        25     30           9        1       38        40    26
Ni ge r i a      26     23          17       19       38        23    27
Bangl ade s h    27     21          17       14       33        40    16
Egy pt           28     31          35       22       20        23    30
I ndone s i a    29     28          29       32       20        23    31
Chi na           30     36          44       36         7       11    40
Zi mbabwe        31     27          31       36       20        23    28
J or dan         32     43          39       38         7       11    43
Tuni s i a       32     40          36       32         7       23    42
Hondur as        34     32          36       30       38        11    32
I ndi a          35     16          29       21       38        44    19
Le s ot ho       35     39          26       27       33        23    23
Phi l i ppi ne s 37     37          38       39       20        23    39
Bol i v i a      38     42          21       34       38        23    38
Mor oc c o       38     33          34       15       33        43    35
Bot s wana       40     35          31       20       38        44    36
Thai l and       41     41          39       45       33        11    41
Par aguay        42     44          43       42       20        23    43
Kor e a          43     45          44       46       20        23    45
Ec uador         44     46          41       41       38        23    46
Sr i Lank a      45     22          46       43       38        44    34
Maur i t i us    46     38          42       43       46        40    36




                                         69

Key:                   BORDA RANK - ranking using Borda Rule
                       C - per capita private consumption (international dollars)
                       E - life expectancy at birth (years)
                       L - adult literacy rate (%)

                       R1- index   of political rights
                       R2- index of civil rights
                       Y - per capita GNP (international dollars)



Abbreviations: C.A.R. (Central African Republic), and Sierra L. (Sierra Leone).




                                                     70

                              Table 3

      (Spearman) Correlation Matrix of Living Standard Rankings




C          0.84

E          0.88         0.75

L          0.72         0.54        0.79

R1         0.76         0.51        0.48         0.28

R2         0.75         0.50        0.50         0.30      0.76

Y          0.87         0.91        0.83         0.61      0.55   0.57




           Borda          C         E            L         R1     R2




                                71