ECOLOGICAL ECONOMICS

Ecological Economics 17 (1996) 147-156

Commentary

The concept of weak sustainability

Maite Cabeza Gut& Departament d ‘Economia i Histhria Econbmica, Universitut Autbnoma de Barcelona, Barcelona, Spain

Received 7 March 1995; accepted 6 December 1995

Abstract

This paper surveys the links between growth theory with exhaustible resources and the concept of weak sustainability. It examines the underlying assumptions behind this concept, and questions the usefulness of the weak sustainability index as an indicator of sustainable development.

Keywords: Production functions; Sustainability; Growth theory; Exhaustible resources; Natural capital

1. Introduction

The need to develop sustainability indicators is central if we are interested in assessing whether an economy is sustainable. Within the field of eco- nomics, this search for an operational definition of

sustainable development has led, among many other contributions, to the concepts of strong and weak sustainability.

Strong sustainability regards natural capital as providing some functions that are not substitutable by man-made capital. These functions, labeled ‘criti- cal natural capital’, are stressed by defining sustain- ability as leaving the future generations a stock of natural capital not smaller than the one enjoyed by the present generation. That is, sustainability is viewed in terms of non-decreasing natural capital. Counter to this concept, is the concept of weak

sustainability. Following the definition proposed in Pearce and Atkinson (19931, an economy is consid- ered sustainable if its savings rate is greater than the combined depreciation rate on natural and man-made capital. Under this notion, sustainability is equivalent

to non-decreasing total capital stock. This is referred to as ‘weak’ sustainability since no restrictions on

the degree of substitutability between natural and man-made capital are introduced, and thus natural capital receives no special treatment. Consistent with this interpretation, Pearce and Atkinson (1993) pre-

sent a weak sustainability index as an economic indicator of sustainable development. The weak sus- tainability index proposed is defined as the differ- ence between the savings rate and the sum of the depreciation rate of natural and man-made capital. That is, an economy is considered to be ‘weakly’ sustainable if and only if the weak sustainability index is greater than zero.

The strong and weak concepts just outlined can be considered to represent two opposing ends in the quest to give a workable dimension to sustainability. ’ This article focuses on the second of these views, with the purpose of emphasizing the key role that the

I For a more complete classification of views of sustainability,

see Turner et al. (1994). Chapter 2.

0921-8009/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved.

SSDI 0921-8009(95)00112-3

148 M. Cabeza Gut&/ Ecological Economics I7 (1996) 147-156

assumption on the degree of substitution between natural and man-made capital plays in building the concept of weak sustainability. The presentation that follows is organized in five sections. Section 2 sum- marizes the key points from growth theory with exhaustible resources relevant for our discussion. In Section 3 the link between this theory and the con- cept of weak sustainability is examined. Section 4 stresses some of the assumptions behind the concept of weak sustainability and Section 5 questions the

usefulness of the weak sustainability index as a tool for assessing sustainability. Finally, Section 6 con- tains the concluding remarks.

2. Growth theory with limited resources

The concept of weak sustainability can be pre- sented as a direct application of the savings-invest- ment rule from growth theory with exhaustible re- sources. This area in economic theory grew mainly from the concern with “the implications of a finite earth for the growth possibilities open to an econ-

omy.” 2 The work done was largely directed to- wards studying the conditions under which the exis-

tence of a finite pool of exhaustible resources would allow a non-decreasing stream of consumption per capita. Our specific concern in this section is with

summarizing the conclusions reached in this body of literature, which are most relevant for our discussion on weak sustainability.

One of the objectives of Solow (1974) was to look at the conditions that would allow an economy to grow forever under the presence of limited natural resources. According to his model, considering that some resource could be available only in limited amount did not necessarily change the possibility for output to grow indefinitely. Furthermore, he stated that the earlier generations could always draw on the finite pool of resources as long as they added to the stock of reproducible capital. But, as Solow himself underlined, these conclusions only held if the elastic- ity of substitution between natural capital and man- made capital was not less than unity. That is, the introduction of exhaustible resources into intertem-

’ Dasgupta and Heal (1979, p. 194).

poral optimization did not imply any great reversal of basic principles if certain conditions, in this case in terms of substitutability between forms of capital, were met.

It is important to make explicit here the particular way in which exhaustible resources are introduced in the model. Solow’s model (Solow, 1974), as in all macroeconomic growth models, uses an aggregate production function to characterize the technology. A single aggregate output Q is produced using three inputs-labor (L), man-made capital (K) and flow of natural resources (N), according to the production function Q = Q(L, K,N). With respect to the precise functional form, Solow considers it important for the production function to have two key properties. First, the natural resource (N) should be essential in the production of Q. That is, if N = 0, then Q = 0. The second property he requires is for the average prod- uct of natural capital not to have an upper bound. The specific functional form that Solow (1974) se- lects for the production function in order to develop his model is the Cobb-Douglas. 3 The Cobb-Douglas production function is used since, as it is easy to show, the two desirable properties described above hold. 4 Solow justifies the need for the first property on the basis that, if it was not introduced, it would imply that production would be possible without natural resources and thus, the introduction of these types of resources would not bring anything new to the analysis. The second property is justified by stating that if the average product of the flow of natural resources was bounded, then only a finite amount of output could ever be produced with the

3 The Cobb-Douglas production function takes the form of

Q = AL” KbNC, where A is the efficiency parameter, and a, b

and c are the elasticities of production with respect to labor,

man-made capital and natural capital, respectively. Solow remarks

in his paper that a function of the type: Q = Q&K) NC, could

also be used.

4 The Cobb-Douglas is a special case of the Constant Elasticity

of Substitution (CES) function with an elasticity of substitution

equal to 1. A more general CES function would not do, since for a

CES with an elasticity of substitution greater than 1, even though

the average product of each input has no upper bound, inputs are

not essential in the sense described above. In the case of a CES

with an elasticity smaller than 1, all inputs are essential, but their

average product has an upper bound. (For proof, see Arrow et al.

(1961)).

M. Cabeza Gut&/Ecological Economics 17 (1996) 147-156 149

finite pool of resources, hence, the only level of

consumption per capita maintainable for an infinite amount of time would be zero. At this point, it is important to stress that the need to introduce this second property is directly linked to the initial pur- pose of Solow’s (1974) paper, which is to find conditions under which a positive level of consump- tion per capita can be maintained for an infinite amount of time. This is equivalent to saying, if

natural resources are limited, and substitution among resources is limited, then consumption per capita might not remain constant forever.

Stiglitz’s concern (Stiglitz, 1974) was also about how the existence of a finite amount of natural capital could limit economic and population growth. His contribution emphasized the role of the substitu- tion between natural and man-made capital, and the role of technological change and returns to scale as offsetting forces to the limits to growth imposed by exhaustible resources. The conclusions included a set of relations between rate of technical change, popula- tion growth, and input shares which represent the different conditions that guarantee the possibility of having a sustainable level of per capita consumption. As in the case of Solow’s model, these results were

derived from the particular case of a Cobb-Douglas technology where the man-made capital cost share is greater than the natural capital share. Nevertheless, Stiglitz shows how the same results could be ob- tained from a separable production function of the

sort Q = Q(F(K,N),L), as long as the elasticity of

substitution between man-made capital (K) and nat- ural capital (N) is greater than 1. 5 In this case, no

restrictions are placed on the elasticity of substitution between any form of capital (K or N) and the input labor (0

The substitution assumption plays once more a key part in the work by Dasgupta and Heal (1979). In their model, natural resources are also essential

inputs, but they allow for an unconstrained possibil- ity of substituting natural capital for man-made capi- tal. Taking this unlimited substitution into account, they are able to derive the result that exhaustible resources do not pose limits to growth, even in the

5 F(K,N) acts as a nested function within the production function.

absence of technological change. With the presence of technological change the possibilities of unlimited growth become even greater.

The final steps in deriving the savings-investment rule that is needed to define the weak sustainability indicator are found in Hartwick (1977) and Solow (1986). Hartwick’s article presents the result, later known as the Hartwick or Hartwick-Solow Rule, that in order to have a stream of constant level of con- sumption per capita to infinity, society should invest all the current returns obtained from the utilization of the stock of exhaustible resources. Hartwick calls this the savings-investment rule which, according to him, was already implicit in the model of Solow (1974). This is again an outcome derived using a

Cobb-Douglas technology, even though in Hartwick (1978) we find the extension to this rule for the case of the Constant elasticity of substitution (CES) tech-

nology, with an elasticity of substitution greater than 1. More than a decade later, the article by Solow (1986) includes the final step in showing how the savings-investment rule can be interpreted as stating that the stock of capital-including the initial en- dowment of resources-is being maintained intact. This is obtained by Solow using a Cobb-Douglas technology under constant returns to scale, with no technological change and no population growth. He states that the conclusions are not easily extended when we have the presence of technological change and/or population growth, and that even if the rate of technological change is as large as the rate of population growth, the savings-investment rule still might not guarantee a constant level of consumption

per capita. ’ In this section, we have summarized some of the

key elements of the analysis of growth theory with exhaustible resources. The direct relation between this theory and the concept of weak sustainability is presented in the next section.

3. The links between growth theory and weak sustainability

If we define sustainable development solely in terms of intergenerational equity, and this intergener-

6(1986, p. 145).

150 hf. Cabeza Gut&s/Ecological Economics 17 (19%) 147-156

ational equity is expressed as a constant stream of consumption per capita for an infinite amount of time, the link between weak sustainability and growth theory is straightforward. In fact, weak sustainability becomes nothing but a different name for Hartwick- Solow’s rule expressed in the form of maintaining total capital stock. As Pearce (1994) himself states, the precise expression of the weak sustainability index presented in Pearce and Atkinson (1993) can be viewed in terms of a ‘savings rule’, where con- stant or non-declining total capital stock is achieved by having the country’s savings for each period to be greater or equal to the sum of the depreciation on all forms of capital. ’

Hence, one could conclude that the concept of weak sustainability is just a by-product of growth theory with exhaustible resources when: 1. The definition of sustainability is restricted to

non-declining consumption per capita. 2. The environment-economy relationship is re-

stricted to introducing an aggregate input called ‘natural capital’ into the production function, with no special treatment for such input except for its existence in limited quantity. With respect to assertion (0, it is worth noting

that even though Pearce and Atkinson (1993) do not explicitly mention it as the definition of sustainabil- ity that they are using, their straight application of the Hartwick-Solow rule into the arena of sustain- ability seems to necessarily imply it. Assertion (2), on the other hand, emphasizes another important limitation implicit in the concept of weak sustainabil- ity. This limitation arises from the fact that other important links between the environment and the economy, like the need for natural capital to produce man-made capital or, even more crucially, the role of the former as life support services, are excluded from the concept. The role of the environment as a waste

7 The one difference worth noticing is that the weak sustainabil-

ity indicator includes the possibility of depreciation of all forms of

capital. Growth models with exhaustible resources consider in

general that man-made capital does not depreciate over time.

Stiglitz (1974) makes explicit this assumption by considering that

we can either think of output as net output, or assume that there is

no depreciation of man-made capital.

site could still be considered to be included in the analysis in the form of a limited resource, where an increase in pollution caused by the production pro- cess is recorded as an increase in use of input N. Here N would include not only natural resources such as oil or coal, but also waste sites, the absorb- ing capacity of air or water, for example. If that is the case, however, justifying a high degree of substi- tutability between natural capital and man-made cap- ital would seem even harder.

The limitations of these apparent restrictions im- plicit in weak sustainability as a tool for analyzing sustainability could definitely constitute a basis for a critical assessment of the concept. That would not necessarily extend to the growth theory counterpart. As stated earlier in the paper, the objective of this latter body of literature grew from the interest in studying the conditions under which a constant stream of consumption per capita into the future could be guaranteed. That was their key focus, which yields the already mentioned conclusion that the inclusion of exhaustible resources implied no limitation if technology was represented by either a Cobb-Doug- las production function with a man-made capital share greater than the natural capital share, or by a CES production function with elasticity of substitu- tion greater than 1. 8 The case of a small degree of substitution was eliminated earlier on in the analysis after it was pointed out that if natural resources were only substitutable on a small scale by man-made capital, no positive stream of consumption per capita could be enjoyed forever under the presence of exhaustible resources.

On the other hand, the concept of sustainability arose from a much broader concern about the con- flicts between economic activity and the environ- ment, with special emphasis on inter- and intra-gen- erational equity. That is, the study of sustainability

8 The CES production function for a two-input case would take

the form of:

Y=[p,K-P+PNN-P]-“pforpZ-l

where the elasticity of substitution, a(K,N), between the two

inputs K and N can be defined in terms of the substitution

parameter, p. as:

1 u(K,N)=-.

1-p

M. Cabeza Gut&s/Ecological Economics I7 (I 996) 147-156 151

includes a strong emphasis on distributional issues. 9 Thus, even though both growth theory with ex- haustible resources, and the analysis of sustainable development share some common ground, the focus of the latter goes far beyond analyzing the conditions that can guarantee constant consumption per capita into the future. At this point one might wonder about the implications of taking the concept of weak sus- tainability, an outcome from the literature on the Hartwick-Solow rule, and try to apply it in a differ- ent arena. In other words, how far can the incursion of the concept of weak sustainability go into analyz- ing sustainability? The next section concentrates on showing that it does not go too far, by exposing the restrictive nature of the assumptions upon which the concept of weak sustainability relies.

4. The assumptions behind weak sustainability

The study of the degree of robustness of any model includes, among other things, the spelling out of the assumptions that are involved in it, including those implied by the specific functional form(s) se- lected. This sets the basis for questioning, at both the theoretical and empirical level, the degree of applica- bility of the model. This section focuses mainly on highlighting some of the assumptions relating to the degree of substitutability between natural and man- made capital, implicit in the concept of weak sustain- ability.

A first assumption in deriving the concept weak sustainability that has been underlined is that of the high degree of subsfitution between natural and man-made capital. As stated, the Hartwick-Solow rule only guarantees constant consumption per capita, if elasticity of substitution between both forms of capital is greater or equal to one. As explained earlier, the Cobb-Douglas is the preferred functional form to derive this result.

Basing most of the analysis on growth theory with exhaustible resources on the extremely restrictive case of a Cobb-Douglas technology appears ex-

9 For a discussion on the importance of the distributional issues

in discussing sustainability, see, for example, Martinez-Alier

(1994).

tremely dubious. In the case of weak sustainability this weakness just seems to get worse. It will be argued later on in this paper that, by assuming a high degree of substitutability between natural and man- made capital, and applying it to the analysis of sustainability, we are in fact diminishing the concern by which it was originally created-namely, the potential conflicts between viable economic develop- ment and preservation of the environment. As estab- lished by Victor (19911, “the easier it is to substitute manufactured capital for depleting resources or a degraded environment, the less concern there need to be about the ca acity of the environment to sustain development.” PO

Intimately related to the subject of substitution between natural and man-made capital is that of input aggregation. The questioning of such aggrega- tion has already been argued with respect to the difficulty of adding flows and stocks, by Georgescu- Roegen (19791, and with respect to the difficulty of finding an appropriate numeraire, by Victor et al. (1995). A third aggregation problem can be intro- duced using the concept of separability from produc- tion theory, revised later on in this section. The concept of weak sustainability treats natural capital as a homogenous category of capital, distinct from man-made capital. Substitutions are then studied on the basis of setting degrees of substitutability be- tween these two categories. But, in learning about sustainable development, it is clear that even on the assumption that a numeraire was found to aggregate oil and coal the different categories of natural capital could hardly be compounded into a unique category. Natural resources play radically different functions within the economy. One important first gross disag- gregation of natural capital found in the literature is between critical natural capital, capturing those envi- ronmental resources directly related to functions of support of life systems, and non-critical natural capi- tal, even though, as has been clearly pointed out, the task of identifying each of them is not easy. ”

=X&991, p. 194).

” See, for example, Pearce and Atkinson (1995). These authors

suggest three criteria for indentifying critical natural capita-

namely, irreversibility, uncertainty and loss aversion-even though

they are well aware of the difficulties of applying these criteria in

practice in order to classify natural capital.

152 M. Cabeza Gut&/ Ecological Economics 17 (1996) 147-156

It appears that a simplification of the degree of substitution for modeling purposes, or for the pure quest of indicators, should come from a bit more flexible production function that at least allowed different degrees of substitutability between the dif-

ferent sub-categories of natural capital and man-made capital. ‘* Allowing for such possibilities to be intro- duced into the analysis should definitely be a re- quirement if we want a model that captures rather more closely the very complex links between the

economy and the environment. Pearce (1994) recog- nized that it is the receiving capacity of natural environments and the supply of biological diversity for which there are no real substitutes, rather than the issue of metals or even energy, that gives the greatest cause for concern. If that is the case, it seems clearly contradictory to work with models that have as a starting point a large substitutability between the different forms of natural resources and between natural recources and other forms of capital.

What does it imply, in terms of assumptions about the production function, the aggregation into a unique category of the different sub-categories of natural capital? In other words, what are the implicit as- sumptions about the degree of separability of the different input categories implied by this grouping? In trying to answer this question we have to consider

I2 An example of such production function could be a two-level

CES like:

level1 Q= ( o,NmP1 + Q~Z-“~)- l/(1 - PI)

1 witha(N,Z)=-

t-PI

level2 Z=(~RR-P*+~KK-p~)-““-Pz’

1 with u( R,K) = -

1 - P2

where K = man-made capital, R = non-critical natural capital,

N = critical natural capital, and Z is an aggregate input that

enters the production function defined at level 2. Such a function would still restrict us to the class of constant elasticity of substitu-

tion functions, but it would allow us to set two different degrees

of substitutability between the three inputs. That is, it would allow

for the substitution between K and R, u(K,R), to be greater and

equal to one, but for the substitution between N and the other

inputs to be as small as we wanted. Furthermore, a function like

this would allow for the critical natural resource to be essential for production without having to impose an elasticity equal to one

between man-made capital and the natural resource.

two possibilities. First, that the input natural re- sources that enters the production model includes only the non-critical natural capital component. In this case, the environment-economy link is reduced to the function of the former as supplier of inputs to the latter. A second possibility is that the input

natural capital is an aggregation of the critical and non-critical sub-categories. That is, that the produc- tion function has three inputs-namely, man-made capital, critical natural capital and non-critical natu- ral capital, but that the latter two have been merged into one. Production theory provides a useful insight

into what are the strong implications of aggregation of input categories. In particular, we know that by grouping these two sub-categories of inputs and in- troducing them into the production function as one, we are implicitly imposing the assumption that the production function is separable with respect to these inputs. That is to say: (i) the marginal rate of substitution between critical and non-critical natural capital is independent of the changes of the level of man-made capital, and (ii) the elasticity of substitu- tion between critical and non-critical natural capital is much higher than between any of these two inputs with respect to man-made capital. l3 This is defi- nitely a very restrictive assumption that needs to be kept in mind when questioning the robustness of the model.

In the discussion above we have tried to docu- ment the restrictive nature of the assumption of substitutability between man-made and natural capi- tal. Unless substantial empirical support exists for such a limiting assumption, the usefulness of the concept would definitely be restricted. This conclu- sion would not necessarily apply to growth theory, where one could argue that the different conditions about the degree of substitutability could be inter- preted more as an ‘outcome’ of the analysis rather than as an assumption. In order to support, although

by no means prove, the above statement, we can compare the writings of Solow (1974) with that of

I3 A production function is by definition separable with respect

to a partition of inputs into two groups, if the marginal rate of substitution between a pair of inputs of one group is independent of the changes of one input on the other.

M. Cabeza Gut&/ Ecological Economics 17 (19%) 147-156 1.53

Pearce and Atkinson (1993). Solow’s concluding

remarks include the following paragraph:

“The second main conclusion is that the introduc- tion of exhaustible resources into this sort of opti- mization model leads to interesting results but to no great reversal of basic principles. This conclusion depends on the presumption that the elasticity of substitution between natural resources and labor- and-capital is no less than unity which would cer- tainly be an educated guess at the moment.” I4

Linking the above paragraph with the initially stated purpose of Solow, of trying to find the condi- tions under which consumption per capita can re- main constant, helps us in ascertaining that the as- sumption of substitutability is one of those condi- tions. If it does not hold, then a constant stream of

consumption is not possible unless some other factor, such as technological change, acts as a counteracting force. In contrast, in the presentation in Pearce and Atkinson (1993) of the weak sustainability index, derived from the concept of weak sustainability, the assumption about the degree of substitutability be-

tween resources is barely spelled out at the begin- ning of the paper and is not mentioned again in the concluding remarks. This, together with the fact that the estimates of the weak sustainability index given in the paper are used as economic indicators of sustainable development seems to indicate a stronger use of the assumption of the possibility of substitut- ing natural capital by man-made capital than that found in growth theory.

Hence, even though mathematically there might not be a substantial difference regarding the treat- ment of the assumption of the degree of substitutabil- ity between growth theory models and the concept of weak sustainability, doubt remains about the differ- ence in the implications of its use. This is definitely something that is open to further discussion and research.

Apart from the assumption about the degree of substitutability, a second important offsetting force to the limits to growth, introduced by the presence of exhaustible resources, is that of technological change. This is exactly the role that it plays in growth theory,

I4 Solow (1974, p, 41).

but it is not explicit in assessing weak sustainability.

Pearce (1994) is aware of the need to modify the analysis to allow for technological change, since “a falling capital stock can sustain a growing per capita consumption level if capital becomes more produc- tive in the future due to technological progress.” l5

However, since the role of technological change is not directly introduced when deriving the weak sustainability index, it is not under review here. Indirectly though, we could still see a link between technological change and weak sustainability. We could consider that the key part played by the as- sumption of a high degree of substitution between natural and man-made capital is mostly in order to allow the average productivity of natural capital to rise as this resource is depleted. In that case, a similar effect could be reached with lower substi- tutability but with natural resource-augmenting tech- nological change. l6 The problem then would shift from one of assuming high substitutability to one of assuming the presence of natural resource-augment- ing technological change. At any rate, three ques- tions arise with respect to the role of technological change in discussing sustainability. First, the prob- lem of empirically distinguishing between the substi- tution among resources within a given technology and technological change. Second, the question of whether technological change will follow the ‘right’ direction. According to the models of endogenous technological change, when relative input prices cor- rectly convey the relative scarcity of resources, the working of market forces solely induces technologi-

15 Pearce (1994, p. 7). In the same paragraph Pearce mentions

that the role of technological change is also important in offsetting

the effect that rising population growth has on the level of

consumption per capita.

I6 Pure factor augmenting technological change would be intro- duced in the production function as:

y= F(EK(K). J%(W) where F is any given functional form, E,(K) is the efficiency

function of input K which is assumed to depend only on the level

of utilization of K and similarly for EN(N). These efficiency

functions change with technological change, in such a way that

the same amount of input used before the technological change would yield to a higher volume of output. Thus, since technologi-

cal change can be interpreted as having ‘augmented’ the amount

of input introduced into the production function, a natural re-

source-augmenting technological change could be considered as a

way of compensating for the depletion of the resource.

1.54 M. Cabeza Gut.&/ Ecological Economics 17 (19%) 147-156

cal change to be biased towards saving the scarce resource. But, if prices fail to do that, because of market failures in signaling such scarcity, for exam- ple, then technology might not follow the uppropri-

are direction. The literature on natural resource price formation seems to point out clearly that in the case of natural resources, prices are far from reflecting true scarcities. If that is the case, then nothing will ensure that economic resources will be invested in developing technologies that are biased into saving natural capital. Finally, a third problem to be consid- ered is the fact that the positive effect that technolog- ical change might have in offsetting the limits to growth by exhaustible resources cannot be analyzed without considering the negative feedback that the new technologies might have on the environment.

In the discussion above we have underlined some of the assumptions implicit in the derivation of the weak sustainability index. Even though at a theoreti- cal level these assumptions seem restrictive enough to strongly question the applicability of the index derived, a case could be made for this indicator if enough empirical support existed for them. There is certainly a long way to go in testing whether there is empirical support for assuming a high degree of substitutabiliy between exhaustible resources and man-made capital. Solow (1974) includes in passing reference to an ‘educated guess’ that this is the case, and Pearce (1994) reproduces the elasticities of sub- stitution between man-made capital and four differ- ent metals, from Brown and Field (1979). Still, this can hardly be considered a documented endorsement for the departing assumption.

There is no doubt that estimating the elasticities of substitution presents many difficulties. Firstly, we face the usual problems of data availability and choice of a reasonably flexible functional form that does not impose too many restrictions and leaves room for some testing on the size of the estimated elasticities. l7 Second, there is the additional prob-

17 This point can be easily illustrated by the extreme case of

considering the limitations in testing the hypothesis of an elastic-

ity of substitution being equal to one, by using in the econometric

model a Cobb-Douglas production function, which has such an

assumption built in. Such testing could be better performed by using a CES specification or a translogarithmic production func-

tion, since both include the Cobb-Douglas as a special case.

lem of estimating elasticities of substitution under technological change. Diamond et al. (1978) showed how the estimation of technological biases is condi- tional upon the estimation of the substitution parame- ters, or how the estimauuu of the substitution param- eters is conditional upon the estimation of technolog- ical biases. That is, in order to estimate elasticities of substitution we have to previously estimate biases or equivalently; in order to estimate technological bi- ases, the substitution parameters have to be estimated first. I8 In any case, not enough estimations of elas- ticities of substitution exist to be able to endorse or, for that matter, to contradict the assumption of a high degree of substitutability between natural and man- made capital. We simply do not know.

If we have reasonable doubts about the restrictive nature of the assumptions on which the concept of weak sustainability is built, and we also lack reason- able empirical support for these assumptions, then what use could be left for such a concept? Could the notion of weak sustainability be saved on the basis of its usefulness in helping the rest of the profession see the need to consider the links between the envi- ronment and the economy? If so, could it help in this respect more than growth theory? These questions are addressed in the next section.

5. Weak sustainability as a rule of thumb?

At the seminar in honor of his retirement, Solow (1986) included the following remarkable paragraph in concluding his lecture:

“The tendency is very great to allow short-run con- siderations to dominate, if only because we can grasp them better. That being so, there is something to be said about rules of thumb, for shorthand ways of taking care of interests that might otherwise be ne- glected. (...I From that point of view, Hartwick’s rule is a better-than-average rule of thumb. (...I We do not know if the rule is robust against such obvious variations as endogenous population growth (and technological progress). The welfare economics of

‘* Diamond et al. (1978) refer to this impossibility of estimating both elasticities and technological biases as the ‘Impossibility theorem’.

M. Cabeza Gut&/Ecological Economics 17 (19%) 147-156 155

an endogenously changing population is altogether murky. But I could see the rule as a rebuttable presumption, as a way of constantly reminding our- selves that there are considerations other than imme- diate utility to be taken into account”. l9

One could argue that the basic message in the above paragraph could be extended to the concept of weak sustainability. In fact, this is exactly the argu- ment given by Pearce (1994) in defending the useful- ness of the concept of weak sustainability. In his article Pearce recognizes as obvious the dependence of the concept on the assumption of high substi- tutability between the different forms of capital, but he defends it on the basis that the ‘savings’ approach to sustainability has in it a good deal of popular persuasiveness. According to him:

“It is, after all, totally familiar to any businessman who knows that his business is not sustainable if assets are continually ‘mined’ to pay dividends or maintain output. This familiarity and appeal is at once a source of power for such measures, and a potential source of a weakness. It is powerful be- cause policy-makers can (and do) understand it. It is risky because it may divert attention away from what some of us would regard as the ‘specialness’ of natural assets (...>. I take a very different view. Such savings rules, I would argue, elevute the status of natural assets over the existing situation in which they are2;till the poor partner in economic develop- ment’ ’ .

Still, good intentions might be overridden by the independent dynamics of the measure itself. In other words, a measure might be communicating some- thing contrary to what it was created for. That seems to be the case of the weak sustainability index. Initial estimates of this index, like those reported in Pearce and Atkinson (1993), show Japan as the most sus- tainable economy, followed by Costa Rica, The Netherlands, former Czechoslovakia, Poland, Ger- many and the United States. Mexico and The Philip- pines are quoted under the heading of marginally sustainable economies. This is obviously

I9 Solow (1986, pp. 148-149). *O Pearce (1994, p. 11).

surprising. ” Nevertheless, in looking at the esti- mated values of the weak sustainability index, one should keep in mind the two fragile pillars on which the measure is set. Firstly, the restrictive nature of the assumptions behind the concept, such as high substitutability between natural and man-made capi- tal, the aggregation of capital in categories without any formal testing to support this aggregation, valua- tion of natural capital through actual or fictitious market prices, which depend on income and property rights distribution, and the lack of recognition of the use of natural capital in the production of man-made capital. 22 Secondly, the problem of how to properly estimate the depreciation rate of natural capital, nec- essary to compute the weak sustainability index, and which would require the difficult task of deciding how to value in a single numeraire the degradation of the environment. If we take all this into account, then the apparently surprising results reproduced above do not seem so surprising. In fact, they seem to accentuate the weak theoretical and empirical base on which the index is built, rather than generate any practical appeal for the measure. They question, more than support, the usefulness of the weak sus- tainability indicator as a rule of thumb to assess sustainability.

Above in this section, a paragraph from Pearce (1994) was quoted where, in defending the use of the measure, he stated that the concept has a great deal of popular persuasiveness. But what is the use of concluding that the United States or Japan are weakly sustainable economies? As explained earlier in the paper, growth theory with exhaustible resources has shown that there are no limits to growth as long as certain conditions of substitutability between capital categories, technological change and population growth exist-or that there are limits to growth if some of these conditions do not hold. Weak sustain- ability has gone an arguable extra stage that so far seems of doubtful usefulness. It has left aside the strong conditions on which the concept depends, and has provided estimates that work against rather than

*’ See Martinez-Alier (1995) for a critical discussion of Pearce

and Atkinson (1993)‘s results. ‘* For a discussion of the implications of these last two assump-

tions, see Victor et al. (1995).

156 M. Cabeza Gut&/Ecological Economics 17 (1996) 147-156

for promoting any concern about sustainability by

the public.

6. Conclusion

In this paper it has been stressed that the concept of weak sustainability is just a direct application of the Hartwick-Solow rule from growth theory with exhaustible resources. In the literature on weak sus- tainability, this rule is directly translated into analyz- ing sustainability by defining sustainability as non- declining consumption/wealth per capita and by restricting the links between the economy and the environment to considering a resource called ‘natural capital’ in the production process. The problem in

moving from the application of the Hartwick-Solow rule to deriving an indicator of sustainability is that

the restrictive nature on which the rule was based is not given a central role in the analysis of weak sustainability. In fact, it has been suggested in this paper that the key role that the assumption of the degree of substitutability between man-made and natural capital plays is clearer in growth theory with exhaustible resources than in the literature on weak sustainability. In the former, this assumption was underlined as a necessary condition for drawing the

results, whereas in the latter it was only mentioned in passing.

In conclusion, any future work in the field of weak sustainability would appear to be more produc-

tive if it began by working on the foundations of the concept. Focusing on the estimation of elasticities of substitution between different types of capital, such as between renewable and non-renewable resources, would be an example. Analyzing the problems in- volved in calculating the depreciation rate of natural capital would be another. This would seem to do more towards raising awareness in environmental issues than rushing to produce indicators.

Acknowledgements

The author wishes to thank Giuseppe Munda for his very helpful comments on earlier drafts of this paper. Financial help from D.G.XII, European Com-

mission, under contract EV5-CT-92-0084 is ac-

knowledged.

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