ANALYSIS
Natural capital and the theory of economic growth
Richard W. England *
Center for Business and Economic Research,Uni6ersity of New Hampshire,Durham,NH 03824-3593, USA Received 27 August 1999; received in revised form 7 April 2000; accepted 10 April 2000
Abstract
During the past half century, theorizing about economic growth has forced economists to reconsider and revise the capital concept a number of times. This paper explores the analytical relationship between capital accumulation and economic growth, on the one hand, and the natural world, on the other. Section 1 sketches modern growth theory with an emphasis on whether or not the economy is seen as facing biophysical ‘limits to growth.’ Section 2 argues that analysis of the role that ‘natural capital’ plays in the production process must occur before one can assess the prospects for economic growth. Section 3 inserts natural capital into a simple growth model and discusses the implications that (1) depletion of natural capital, (2) complementarity in production of natural and social forms of capital and (3) accumulation of technical knowledge have for the growth process. © 2000 Elsevier Science B.V. All rights reserved.
Keywords:Complementarity; Economic growth; Natural capital; Social capital; Technological innovation
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1. Nature and modern growth theory
The modern theory of economic growth was launched by Domar (1946) and Harrod (1939) over half a century ago. Both authors observed that net investment spending boosts aggregate income immediately while simultaneously expand-ing potential output of future periods. Their ele-mentary growth models also suggested that one should expect the capitalist growth process to be highly unstable and marked by periodic crises.
In his neoclassical response to Domar and Har-rod, Solow (1956) argued that opportunities to substitute capital for labor in the production pro-cess might permit steady-state growth instead of periodic crises of the macroeconomy. Further-more, Solow’s growth model envisioned the possi-bility of rising material living standards fueled by technological progress.
One of the striking features of these early mod-ern growth models is their silence about the natu-ral foundation of production. Capital goods and human labor combine to produce commodity out-put, but no land is required as a site, no materials are needed from which to form commodities, and
* Corresponding author. Tel.: +1-603-8623335. E-mail address:rwe@christa.unh.edu (R.W. England).
no energy is required to drive the process of commodity production and exchange. As Solow himself (1956, p. 67) remarked, ‘The production function is homogeneous of first degree. This amounts to assuming… no scarce nonaug-mentable resource like land.’
By the 1970s, the debate over the prospects for economic growth shifted terrain. Meadows et al. (1972) did not ask whether the historical process of economic growth was stable or not. Rather, these authors posited the existence of biophysical ‘limits to growth’ which would eventually bring economic growth to an end. In reaction to the ‘limits to growth’ thesis, the emergence of the environmental movement, and global energy price shocks, modern growth theorists did begin to incorporate natural resources and pollution into their models during the 1970s. Stiglitz (1974), for example, proposed an aggregate production func-tion with labor, capital goods and natural re-sources as substitutes in production. His model implied that worsening natural resource scarcity could be offset by technical progress: ‘With tech-nical change, at any positive rate, we can easily find paths along which aggregate output does not decline… To sustain a constant level of per capita consumption requires a more stringent condition on the rate of technical change.’ (pp. 130 – 1) Hence, insurmountable limits to growth seemed to be far from inevitable.
By the 1980s, technological optimism had come to dominate macroeconomic theorizing about the links between economic growth and the natural world. Baumol (1986), for example, claimed that the economic inventories of natural resources could increase monotonically and perpetually even if their physical stocks declined incessantly. That is, resources whose physical quantities are finite and declining may nevertheless be increased by technological advance in terms of their prospective economic contribution, and may do so for the indefinite future.’ (p. 178)
Theoretical analyses such as those of Stiglitz (1974) and Baumol (1986) have apparently left their imprint on the economic growth theory re-vival of the past decade. Aghion and Howitt (1998) do acknowledge that pollution and natural resources are issues worth considering. However,
their Schumpeterian model implies that accumula-tion of ‘intellectual capital’ can deflect biophysical constraints on economic activity, thereby permit-ting growth into the indefinite future. Barro and Sala-i-Martin (1995), on the other hand, do not even mention land, energy, raw materials or pol-lution in their influential survey of contemporary growth models. For them, produced capital goods and human skills constitute the entire aggregate stock of capital. Macroeconomic activity appar-ently draws upon boundless sources of natural resources and bottomless sinks for waste prod-ucts, thereby eliminating the need for an explicit discussion of economic growth within a natural world.
Although the notion of biophysical limits to growth has not yet taken root in modern macroe-conomics, it has recently enjoyed a resurgence of popularity among those biologists, economists and other scholars who identify with ‘ecological economics.’ Daly (1996), for example, has argued that biophysical and ethical factors will eventually require a ‘‘steady-state economy’’ with constant populations of humans and their artifacts and a restrained physical throughput of materials and energy to reproduce those populations.
Daly’s claim has been resisted by the main-stream of economists, however, in part because his thesis of a steady state has not been derived from a conventional growth model. In the follow-ing sections, the capital concept will expand to include ‘natural capital’ and then that broader notion of capital will be inserted into an elemen-tary model of economic growth. Some tentative conclusions about the transition from an era of exponential economic growth to an era of steady-state economics will conclude this paper.
2. Natural capital and production
Ecological economists have recently proposed that we recognize explicitly the essential role of ‘natural capital’ in commodity production. Daly (1994, p. 181) points to climate and mineral de-posits. Ayres (1996, p. 241), in turn, refers to aquifers and stratospheric ozone as specific forms of natural capital. In addition to examples such as these, we also need a formal definition of what we mean by ‘natural capital.’ Drawing upon earlier work by Boulding (1978, ch. 4) and Georgescu-Roegen (1972, ch. 9), England (1998) has offered such a definition.
In his discussion of production theory, Georgescu-Roegen distinguished between two very different elements of the production process: ‘fund elements, which represent the agents of the process, and the flow elements, which are used or acted upon by the agents’ (p. 230). These fund elements include:
(B1, …,Bm), the populations of nonproduced
organisms, each population representing a par-ticular biological species;
(K1, …,Kn), the populations of produced
means of production, whether biological or mechanical, commonly described as ‘‘capital goods’’;
L, the population of human producers and
their dependents; and
S, the earth’s surface area, which serves as a
site for other funds’ activity and as a solar energy collector.
The transformative activity of these funds re-quires input flows of energy and materials in appropriate amounts and at appropriate moments of time. As Georgescu-Roegen (1972, p. 303) in-sisted, there are two and only two sources of these input flows: (i) a constant annual flow of solar radiation beyond our control, and (ii) finite terres-trial stocks of minerals which we can decumulate into input flows at highly variable rates. Let us denote the solar energy flow byf and the nonliv-ing stocks from which input flows are extracted and into which waste products get discharged as
Mk, k=1, …,p.
What, then, are the components of natural capital? This discussion suggests a diverse list of elements:
the earth’s nondepreciating surface (S);
the solar flux (f), or perhaps its capitalized
value;
the set of nonproduced populations
(B1, …,Bm), organized into various
ecosystems;1
the set of material stocks in the earth’s crust
and atmosphere (M1, …,Mp), which yield raw
materials and receive waste products.
Without this natural ensemble of assets, hu-mans (L) and their produced servants (K1, …,Kn)
would be unable to function, develop and repro-duce. Thus, natural capital, denoted hereafter by
N, yields a variety of services and materials essen-tial to the human economy.
Two hypotheses about the natural capital stock are central to the ecological economics literature. Let us call them the depletion and the comple-mentarity hypotheses. The first claims that the value of the natural capital stock has declined significantly during the past century or more be-cause of humanity’s economic practices. Bebe-cause we do not have time-series estimates for N, this hypothesis cannot yet be empirically confirmed or denied, at least not in a rigorous fashion. How-ever, we do have physical measures of fossil fuel consumption, soil erosion, deforestation and loss of wetlands, thinning of stratospheric ozone, groundwater pollution, etc., which strongly sug-gest natural capital depletion.2
The second, and perhaps more controversial, hypothesis about natural capital is that it comple-ments — and cannot easily substitute for — hu-mans and their produced capital goods as commodities are produced. Once again, available empirical evidence can neither confirm nor dismiss this hypothesis. Thompson and Taylor (1995), for instance, report that more than 50 studies of capital-energy substitutability since 1973 have re-sulted in estimated elasticities of substitution which are ‘highly variable between sectors and countries, and across time.’ Some econometric studies have even employed production function
specifications which preclude complementarity among factor inputs, a priori.
These comments about the messiness of the existing econometric literature miss the main point, however. Even if there is convincing empir-ical evidence that coal can substitute for petroleum, that steel can substitute for aluminum, or even that telecommunications can substitute for transport services, these substitution measures cannot demonstrate that natural capital, as defined here, is a general substitute for humans and their produced artifacts. Technical opportuni-ties to substitute among specific forms of natural capital do not imply that natural capital in the general sense can be replaced by humans and their constructions.3
There are two reasons to accept the comple-mentarity hypothesis, at least provisionally. The first is that human labor and produced capital goods are transformers of energy and materials flows into finished products and that the stock of natural capital is the source of these essential input flows. Funds can substitute for one another as transformative agents, but each fund requires complementary input flows in order to perform its assigned tasks.4
A second argument for complementarity is rooted in ecological research. Recall that ecosys-tems provide a wide array of services to humanity (deGroot, 1994). If we denote these ecosystem services as Ei, i=1, …,s then (B1, …,Bm) [
(E1, …,Es). That is, the ecological interaction of
many nonproduced funds generates a rich ensem-ble of services enjoyed by humanity. Many ecolo-gists believe that there is a critical minimum level of natural capital in the form of ecosystems below which humanity will not enjoy the ecosystem ser-vices necessary for human survival. If they are correct, preservation of ecosystems is essential if humans and their artifacts are to remain productive.
In sum, existing measures of the aggregate cap-ital stock neglect the productive contribution of nonproduced assets provided by nature. Hence, the conception and measurement of capital should be broadened to include these natural assets. As we shall see, this expanded view of capital has important implications if the natural capital de-pletion and complementarity theses are correct.
3. Natural capital and growth
Let us proceed by inserting natural capital into an elementary growth model. Suppose that hu-mans and their produced capital goods substitute readily for one another. Then one can aggregate the human population (L) and the value of hu-man artifacts (K) to obtain the stock of human-made, or social, capital (H):
H=K+sL, s\0, (1)
whereHcan be loosely interpreted as the value of machines and human machine-equivalents avail-able to the economy. If one accepts the hypothesis that human-made and natural capital are comple-mentary in production, then, in general,
Y=min[AH,CN], (2)
whereYis aggregate output of commodities,Nis the value of natural capital available for human enjoyment and use, and both coefficients are positive.
During the past 10 000 years, humanity has invented both agriculture and industry. These de-velopments have been linked historically to growth of human population (L: \0),
accumula-tion of produced capital goods (K: \0), and
labor-saving innovation (s;\0). All three of those
historic trends have contributed to growth of the stock of human-made capital (H: \0). Until
re-cent times, the extent of human settlement and economic development was modest compared to the entire planet so that H-capital was relatively scarce compared to N-capital on a global scale. That is,
(H/N)B(C/A). (3) 3This logical error can be found in the influential essay by
Goeller and Weinberg (1978).
It follows that, during the agro-industrial period of the distant and recent past, the aggregate pro-duction function assumed a historically-specific form:5
Y=AH. (4)
Assume that society accumulates a constant proportion (s) of its aggregate income as addi-tional produced means of production. Assume, also, that human population grows at a constant percentage rate (n) and that labor-saving innova-tion proceeds at a constant rate (s; /s\0). It
follows that aggregate output and the H-stock will grow at the common percentage rate:
gH=gY=
sA+(s; /s+n)
(r/s+1)
n
(5)where r=(K/L)
If population growth and technical innovation proceed sufficiently rapidly, that is, if sABn+
(s; /s), then there exists a steady-state growth path along which (r;/r)=(s; /s)\0. Along this path,
exponential growth of aggregate income (Y) and per capita income (y) occurs:
(Y: /Y)=n+(s; /s)\0, (6)
and
(y;/y)=(s; /s)\0, (7)
results which will be familiar to any student of modern growth theory.
Often missed by contemporary growth theo-rists, however, are the detrimental effects of eco-nomic activity and exponential growth on the
N-stock. Consider an index number for the natu-ral capital stock such that
N=N(B1, …,Bm,M), (8)
where M is the terrestrial stock of low-entropy energy and materials available for human use.6
Because of the thermodynamic dissipation of en-ergy which accompanies economic activity, we can expect that
M: =mY, mB0 (9)
Innovations that conserve energy and materials might lowermand reduce the absolute magnitude of M: at any moment, but M: remains negative nonetheless.
On the ecological front, most undomesticated species have relatively rigid space, or habitat, requirements:
Bi=Bi(SB), (10)
with population sizes varying directly with the surface area of ecosystems (SB). Because human
settlements tend to displace ecosystem habitats,
(S:B/SB)=(d:/d)−N=0, (11)
where d=(L/(S−SB)) is the density of human
settlement. Hence, if human population is grow-ing, habitat for humanity competes with habitat for ecosystems unless settlement density grows rapidly enough.7
Economic growth and development during the agro-industrial period has tended, therefore, to deplete the stock of natural capital for several reasons. Exponential growth of human popula-tion tends to reduce the land area available to ecosystems, thereby threatening the availability of valuable ecosystem services. Industrialization and urbanization relieve this spatial competition be-tween human settlements and ecosystems for land, but tend to intensify the rate at which earthly sources of low-entropy energy and materials are dissipated. Either way, N: B0.
To the extent that this theoretical account is accurate, its implications are clear. If H: B0 and
5Note that the Y=AK production relation favored by endogenous growth theorists is therefore a special case and not necessarily applicable to all time periods, past and future. Note also that destruction of ecosystems did makeN-capital relatively scarce on a local scale even before the modern era. On Easter Island, see Brander and Taylor (1998).
6I have argued previously that measurement of this capital index value will be problematic. (England, 1998).
N: B0, then there must arrive a moment in the
world’s history when natural capital is no longer relatively abundant and human-made capital is no longer relatively scarce. At that moment, aggre-gate output is no longer constrained by the popu-lations of humans and their artifacts and by the productivity of human effort. Rather, the scale of economic activity is constrained by the remaining stock of natural capital and by its productivity. Because H-capital has become relatively abun-dant, one suspects that the economic incentive to save and invest in produced capital goods would weaken. When this moment arrives, a new era of history has begun.
After this point, economic growth can con-tinue — but only if economic institutions and practices are dramatically reformed and, even then, perhaps not indefinitely. Because (H/N)\
(C/A), the aggregate production relation has become
Y=CN. (12)
This implies that aggregate output will continue to grow only if (C: /C)+(N: /N)\0. This
inequal-ity can be satisfied only if technological innova-tion shifts from a labor-saving to a N-saving direction and if preservation of the remaining stock of natural capital becomes a social priority. Continued growth of per capita income can also occur if natural capital is preserved and if techno-logical change favors growth of its productivity. Reducing the growth rate of human population is also imperative, in part to protect ecosystems from human settlement, but also because
(y;/y)\0 if and only if (C: /C)\n−(N: /N) (13)
This inequality would seem to provide a simple recipe for rising affluence even if natural capital has become relatively scarce: focus enough human ingenuity on preserving and enhancing the pro-ductivity of natural capital. That conclusion would be too hasty, however. As Ayres and Miller (1980) have pointed out, the relationship between accumulation of technological knowledge and growth of capital productivity is far from obvious.
These authors have argued that knowledge is the ability to copy or reproduce tangible or
intan-gible ‘objects’ given the availability of appropriate energy and materials (p. 358). What if, however, certain physical principles limit our capacity to intelligently transform energy and materials into commodities? As Ayres and Miller (1980, pp. 359 – 60) put the matter,
[T]here is a definite lower limit to the amount of electricity required to produce a horsepower of mechanical work… [and] to the amount of elec-tricity required to produce a given amount of illumination. And, of course, there is a lower limit to the amount of available work derived from fossil fuels… There are upper limits to the strength of materials… Velocity cannot exceed the speed of light. And so on.8
These arguments imply that the productivity of natural capital (C) might increase as the stock of appropriate technological knowledge (T) rose, but that diminishing returns to additional technologi-cal knowledge might eventually set in. Hence, (C: /C)0 even though (T: /T)\0 and constant.
In this eventuality, inequality (13) is no longer satisfied and per capita income can no longer grow.
4. Conclusion
For half a century, modern growth theorists have tried to identify the empirical determinants of economic growth and the theoretical conditions under which steady-state growth can proceed. For three decades, Daly and other scholars have ar-gued that there are biophysical limits to growth and that exponential growth of aggregate output cannot continue indefinitely. The purpose of this paper has been to identify the theoretical condi-tions which would imply Daly’s steady-state econ-omy. These conditions are: (i) relative scarcity of natural capital, (ii) general complementarity of human-made and natural capital in production, and (iii) exhaustion of opportunities to raise N
productivity through accumulation of technical knowledge. Note that these theoretical results do not necessarily imply a sudden end to exponential growth of the global economy. Rather, one might witness a transitional period during which labor productivity and per capita real income continue to grow but at decelerating rates. If conditions (i) – (iii) are realized, however, this transition will ultimately yield to a global steady-state economy.
Acknowledgements
The author would like to thank Robert U. Ayres, Benigno Valde´s, an anonymous referee and Michael Goldberg for their helpful suggestions. Flaws in this paper are the sole responsibility of the author.
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