Adaptive economic growth. Camb J Econ

Abstract

This paper develops an evolutionary theory of adaptive growth, understood as a product of structural change and economic self-transformation,
based upon processes that are closely connected with but not reducible to the growth of knowledge. The dominant connecting
theme is enterprise, the innovative variations it generates and the multiple connections between investment, innovation, demand
and structural transformation in the market process. The paper explores the dependence of macroeconomic productivity growth
on the diversity of technical progress functions and income elasticities of demand at the industry level, and the resolution
of this diversity into patterns of economic change through market processes. It is shown how industry growth rates are constrained
by higher-order processes of emergence that convert an ensemble of industry growth rates into an aggregate rate of growth.
The growth of productivity, output and employment are determined mutually and endogenously, and their values depend on the
variation in the primary causal influences in the system.

Full text

Adaptive economic growth
J. Stan Metcalfe, John Foster and Ronnie Ramlogan*
This paper develops an evolutionary theory of adaptive growth, understood as
a product of structural change and economic self-transformation, based upon
processes that are closely connected with but not reducible to the growth of
knowledge. The dominant connecting theme is enterprise, the innovative variations
it generates and the multiple connections between investment, innovation, demand
and structural transformation in the market process. The paper explores the
dependence of macroeconomic productivity growth on the diversity of technical
progress functions and income elasticities of demand at the industry level, and the
resolution of this diversity into patterns of economic change through market
processes. It is shown how industry growth rates are constrained by higher-order
processes of emergence that convert an ensemble of industry growth rates into an
aggregate rate of growth. The growth of productivity, output and employment are
determined mutually and endogenously, and their values depend on the variation in
the primary causal influences in the system.
Key words: Evolution and growth, Technical progress, Structural change, Increasing
returns
JEL classifications: 03, 04
1. Introduction
This paper provides an evolutionary account of technical progress and economic growth in
which the central phenomena to be explained are self-transformation, the emergence of
macrostructure from microdiversity, and coordination through market processes. Like
Nelson and Winter (1974), we argue that macroeconomic explanations of economic growth
based on technical progress should be compatible with the vast diversity of micro and meso
level evidence concerning the events and processes that constitute the notion of ‘innovation’.
Manuscript received 25 April 2003; final version received 15 April 2005.
Address for correspondence: Stan Metcalfe, ESRC Centre for Research on Innovation and Competition,
University of Manchester, Harold Hankins Building, University Precinct Centre, Oxford Road, Manchester
M13 9QH, UK; email: stan.metcalfe@man.ac.uk
* University of Manchester, University of Queensland and University of Manchester, respectively.
We thank Ian Steedman, Malcolm Treadgold, Peter Hall, Clem Tisdell, Franco Malerba, Fabio Montobbio,
Francesco Lissoni, Dick Lipsey and colleagues at the Brisbane Club workshop in Manchester, July 2002, for
stimulating discussion in relation to previous drafts. We are particularly appreciative of the constructive and
challenging comments of two anonymous referees, and we also thank Sharon Dalton, who helped greatly in
producing the many final drafts. This paper is a development of Metcalfe (1999), which was read to the
EAEPE Conference in Lisbon, November 1998, at the kind invitation of Geoff Hodgson, Ash Amin and
Francisco Loucxa
˜
. This work was carried out with the support of the ESRC Centre for Innovation and
Competition, and this version has been developed in the context of the ESRC financed NEXSUS project. The
usual disclaimer applies.
Cambridge Journal of Economics 2006, 30, 7–32
doi:10.1093/cje/bei055
Advance Access publication 4 July, 2005
Ó The Author 2005. Published by Oxford University Press on behalf of the Cambridge Political Economy Society.
All rights reserved.

Modern theories of endogenous growth, even in their most sophisticated forms,
1
do not do
this in any comprehensive manner. We argue that this is a fundamental shortcoming,
because it is the generation and resolution of economic diversity that is the principal source
of growth. How we assemble the macro from the micro is a central theme of this paper, as is
the related issue of the audit trail along which we track the emergent consequences of
individual innovations. Like endogenous growth theory, however, we do place considerable
emphasis on dynamic increasing returns as a key element in the understanding of
the connections between innovation, enterprise and adaptive growth. However, the
perspective we take is that pioneered by Allyn Young and Nicholas Kaldor, an approach
that draws attention to the creative functions of markets, as well as their allocative functions,
in respect of the generation of economic change (Kaldor, 1972, 1985, 1996; Nell, 1998).
Expanding economic systems self-transform their patterns of self-organisation, and so the
problem of growth is a problem of adaptation; of changing the allocation of resources and
the composition of demand in response to the opportunities opened up by the growth of
knowledge. Since much knowledge is practical and, thus, defined in relation to technique,
organisation and consumption practice, it follows that the growth and application of
knowledge are embedded unavoidably in the economic process. As Schumpeter insisted,
transformation arises from within the socio-economic system and enterprise-driven,
adaptive development is the primary process, while aggregate growth is a secondary
outcome. Although enterprise is the conduit through which both the acquisition and
application of knowledge flow, it is markets that facilitate the transmission and coordination
of knowledge both prior to, and during, the occurrence of trade and contracting. Knowledge
is not something that is detachable from the economic process, in the manner of an
exogenous ‘factor of production’. If we make enterprise and the market the twin pillars of
economic growth, it is the internal development of knowledge that renders the underlying
process of economic evolution both adaptive and transformative in character (Fine, 2000).
Two broad questions arise: ‘How does enterpr ise connect with economic growth?’ and
‘How can we construct a growth theory that captures the creative and adaptive features
that characterise all economic change?’ Our answers lead to a theory of growth premised on
the view that market processes are essential to the coordination of microdiversity (Eliasson,
1998; Silverberg and Verspagen, 1998; Fagerberg and Verspagen, 1999). It differs from
many accounts of growth in a number of important ways. First, the analytical framework
that we present is quite different from those that treat growth as a macroeconomic
phenomenon simpliciter. All the aggregates that we deal with are emergent consequences of
the interaction between different industries in relation to the g rowth of productivity and the
distribution of the ensuing increments in demand. The macroeconomic dimension of our
analysis relates to the connections that exist between the ensembles of activities that define
an economic system. It deals with the interdependence between economic sectors, because
productivity growth in one sector spreads to others via income and expenditure flows
through markets. Growth rates are emergent system properties, they are premised on
interdependence, and these system properties are inseparable from the manner in which
activities are coordinated and ordered.
Second, it is emphasised in the following exposition that enter prise economies are
inherently restless and that they experience continual change in relation to the relative
importance of different economic activities. The qualitative nature of these activities
changes over time and they are never in a steady state of growth, as this is usually
1
Aghion and Howitt (1992), Kurz and Salvadori (1998).
8 J. S. Metcalfe et al.

conceived. Ultimately, the idea of steady-state growth in a capitalist economy is untenable
simply because the idea of the steady growth of knowledge is untenable. This, of itself,
poses a deep challenge for growth theorists. The steady state frameworks applied to semi-
stationary growth (Bliss, 1975) or to proportional dynamics (Pasinetti, 1993) are seductive
devices to reduce the economy to a single sector in the sense that the relative proportions of
different activities are frozen in time. However, there is neither structural change in these
contrived macro worlds nor development, only uniform expansion or, just as readily,
uniform contraction. So we effectively rule out any meaningful connection between the
growth of knowledge and economic growth.
1
This is not simply because aggregation
obscures the significance of diversity and economic structure, as if the latter were
a tiresome statistical complication in the analysis of growth. Rather, it is because
transfor mation, or adaptation, is the way the economy responds to emergent novelty in
the form of innovation. To hide this is to remove from view the very process that explains
the growth of productivity and output. We call this the ‘ensemble approach’ to economic
growth, in which the dynamics of an economic system depend on its structural
configuration and how this changes. Macro phenomena are necessarily constructed
statistics, and they have no independent existence beyond their reflection of the underlying
structure of the ensemble. As we shall see, the way we aggregate is dependent on the precise
theory of coordination and change that we invoke.
Third, from a macro perspective, it is not possible to confront two of the most important
stylised facts of modern economic growth; namely, the wide micro diversity of productivity
across different industries and the ever-present element of structural change over time
(Kuznets, 1954, 1971, 1977; Harberger, 1998). Nor is it possible to incorporate the role of
demand in shaping growth patterns between industries; indeed, it is remarkable that the
modern growth story, as told in the endogenous growth literature, is predominantly
a supply-side account of the expansion of productivity and inputs. Changes in demand are
largely ignored, and the coordinating role of emerging markets in the growth process is lost
from view. How market coordination works is central to any understanding of growth, but
coordination is not equilibrium, it is order and, in knowledge-driven economies, order is
forever changing (Loasby, 1999).
Fourth, the origins of restless capitalism lie in its unlimited capacity to generate new
knowledge and new behaviour from within, and it is this propensity for endogenous
variation that makes it so dynamic and versatile, sufficiently so that economies may be
completely transformed in str ucture over relatively short periods of historical time. Growth
is not simply a result of calculation within known circumstances but of human imagination
and the search for novelty and competitive advantage. Moreover, every advance in
knowledge creates the conditions for further advances; in the language of systems theory,
economic growth is an autocatalytic process in which change begets change. As Nell has so
neatly expressed the point, ‘scarcity is incompatible with equilibrium’, and we might add,
because scarcity poses a problem and problems demand solutions, even if they are not
always achieved.
2
Yet variety and innovation are only part of the picture. Equally important
1
This is the force of Richardson’s penetrating analysis of Smith’s theory of an economy that ‘is in a state of
constant and internally generated change’ (1975, p. 351). Harcourt (1993), too, emphasises the uneven and
cumulative development of capitalist, market economies.
2
Nell (1998, p. 7). We are grateful to a referee for drawing our attention to Nell’s important work on
transformational growth. It is clear to us that further integration of post-Keynesian and evolutionary ideas
would be of considerable importance, but it is beyond the scope of this paper. Related ideas can be found in
the work of Bensusan-Butt (1960), in the more recent work by Amendola and Gaffard (1998), and in the
work of Becker et al. (2004).
Adaptive economic growth 9

is the coordination of variety by market institutions to resolve differences in behaviour into
evolving patterns of economic activity. The g rowth consequences of novel behaviour are
deeply dependent on the way in which economic activities are coordinated within market
processes; and these processes of coordination require a demand-side as well as the more
familiar supply-side perspective on the innovation process. Thus, market processes are not
only about the immediate order that arises from reconciliation of capacity and demand,
activity by activity, firm by firm and industry by industry, they are also the means to
transfor m that order to adapt as the circumstances of innovation and investment dictate.
Hence, and fifth, the theoretical and empirical challenge is to place structural change and
the adaptive reallocation of productive resources through market processes at the core of
theory. We argue that this requires evolutionary analysis, and the associated evolutionary
methods are inherently statistical in nature. Therefore, we deal below with the central
problem of how to combine lower-level variables into higher-level averages, and how to
relate statistical moments around these averages to the pattern of economic change. We find
it helpful to distinguish secondary moments between endogenous variables from primary
moments defined over the given data of the economy, and then to explain those secondary
moments and their changes in terms of the more fundamental primary equivalents.
1
Finally, in developing this evolutionary approach to adaptive economic growth, we
achieve two main objectives. The first is to develop evolutionary theory further, beyond the
partial frameworks of firm and industry, which have so far characterised its development;
and the second is to connect evolutionary growth theory to the immensely rich literatures
concerned with innovation and its management, the history of technology, and the
capabilities of firms and other institutions that jointly shape the growth and application of
knowledge. These literatures are natural complements to an evolutionary theory of
economic growth; they frame our understanding of the processes generating and limiting
innovation, and they provide countless empirical examples to shape our thinking on the
knowledge–growth connection. Equilibrium, macro-oriented growth theory, cannot make
these connections, an evolutionary theory can (Montgomery, 1995; Foss and Knudson,
1996, Moran and Ghoshal, 1999).
2
To make headway, we have had to limit the domain of our discussion and the device we
have used to achieve this is ‘the industry’, which becomes the primary unit of our analysis
in relation to technical progress and demand. Yet the processes we seek to capture apply
just as much within industries as they do between industries. Consequently, the economic
properties of each industr y are emergent consequences of evolutionary processes within
and between firms and would be given more attention in a fuller analysis of the problem.
Variation and selection within industries are the evolutionary foundation of variation and
selection between industries. Thus, our argument here is meso and macro rather than
micro and macro.
3
However, we must not lose sight of the underlying argument that
economic evolution is multilayered and that the dynamism of industries is premised on
enterprise investment and innovation in firms. That we keep these within-industry issues in
the black box reflects our judgment that the evolutionary analysis of firms in industries is
1
The idea that economic change is determined as to rate and direction by the variety contained within an
economic system is an application of one of the central principles of evolutionary analysis, Fisher’s principle.
See Metcalfe (1998) for a detailed elaboration of this point. See also Montobbio (2002) on the Fisher
theorem and industrial dynamics.
2
Evolutionary approaches may also contribute towards meeting the considerable challenge of writing
a reasoned history of capitalism (Freeman and Loucxa
˜
, 2001).
3
See Dopfer et al. (2004) for an extended discussion of how the ‘meso’ level of analysis relates to the more
familiar ‘micro’ and the ‘macro’ levels of inquiry.
10 J. S. Metcalfe et al.

far better understood than the evolutionary analysis of industries in economies (Downie,
1958; Nelson and Winter, 1982; Anderson, 1994; Dosi, 2000; Metcalfe, 1998). The trial
and error, fallible nature of the discover y of, and investment in, new knowledge apply
between industries just as they do within industries and firms.
A summary of the argument may help here. This theory of self-transformation relies on
the interaction between three processes acting across an ensemble of interconnected
industries that constitute the ‘economy’. These are the dynamics of investment and
induced productivity growth, the dynamics of demand growth, and the aggregate
constraint imposed by the coordination that takes place in the capital market. On this
interconnected ensemble, we can define whatever aggregate measures we wish, but we do
not require these aggregates to mimic the behaviour of any micro representative agent.
That would be a most counter-evolutionary requirement to impose on the aggregation
process, for we are concerned with the emergence of patterns at higher levels that are not
present at lower levels of aggregation. In turn, these higher levels of emergence act as
constraints on lower levels of emergence. The chief example of an evolutionary constraint
is provided below by the idea that injections equal leakages in the aggregate flow of income.
In each industr y, we have dynamic increasing returns, where output growth induces
productivity growth through innovation along the Smithian lines developed by Young and
Kaldor and, taking the ensemble of industries together, we establish the average rate of
productivity growth. This is necessarily equal to the rate of growth of per capita income,
which, in turn, induces growth in the per capita level of demand for the output of each
industry. In this way, growth feeds on itself, it is autocatalytic, and feedback effects from the
growth in demand make the rates of industry productivity growth interdependent. The
uneven distribution of growth across industries produces structural change in the economy
automatically, and the consequent changes in the relative importance of the different
industries redefine the dynamic complementarities between them. Thus, aggregate growth
rates are emergent phenomena, they arise because of the economic interaction between the
industries, but they are not independent of the aggregate requirement that leakages equal
injections. This is not a new story to anyone who has thought through the implications of the
famous dictum that the division of labour determines and is determined by the extent of the
market. However, it is a story that allows the weaving together of diversity in technical
progress with diversity in demand dynamics to generate endogenous, evolutionary growth
and adaptation.
2. Some evidence for structural transformation
It should not be necessary to belabour the evidence in favour of the ongoing structural
transfor mation of economies as they develop and grow; the support for this most important
of stylised facts is conclusive (Pasinetti, 1993; Freeman and Loucxa
˜
, 2001; Cornwall and
Cornwall, 2002).
1
To an earlier pre-macro generation of growth economists, nothing was
more natural than to point to the changing composition of economic activity both
qualitatively and quantitatively in the course of economic development. Fabricant (1940)
can be permitted to speak for the many others of this generation of economists:
When we turn from the averages and concentrate upon the movements of manufacturing
production in individual industries, we find sharp differences in the secular rates of change in the
physical output of these industries. In every period, some decline, some forge ahead, and only
1
To which list one might add a distinguished group of economic historians, including Landes (1969) and
Mokyr (2002).
Adaptive economic growth 11

a few industries follow the general trend of manufacturing output. These disparate rates of
growth affect, and are affected by changes in the structure of industry, in technical processes, in
the kind of goods produced and in the distribution of employment. (our emphasis, p. 9)
No better statement could encapsulate the themes of this paper. The aggregate growth rate
is a statistical construction in relation to which there may be no industry that grows at the
average rate for the ensemble. Because growth rates differ across activities, the economic
system evolves and, with it, the relations between averages and their components. Induced
changes in structure continually redefine the economy-wide relations between productivity
growth, employment growth and output growth and the contributions that each industry
makes to these aggregates.
A short digression may help at this point to drive home the empirical significance of
adaptive processes, for the evidence can tell different stories according to the level of
economic aggregation that is employed. The picture within industries is of a different kind
from that between industries, which, in turn, differ s from broad comparisons in terms of
the grand sectors, ag riculture, manufacturing and services, defined by Colin Clark, among
others. In this section we use the NBER–CES Manufacturing Productivity dataset
covering 459 four-digit SIC industries over the period 1958–96. Relative to most macro
datasets, this provides highly disaggregated information; although it can be argued that it is
still highly aggregated relative to the level of individual markets, products and firms. Thus,
while it can be still be used to identify some features of structural transformation, much
remains hidd en. This data allow computation of the shares of each industry in total
employment and total output together with the levels and rates of change of labour
productivity. If structure is changing, the first place to look is at the patterns of the
employment and output shares and the changes they evince over time. In semi-stationary,
proportional growth, these shares are constant, which is only possible if all industries grow
at the same rate and if all rates of productivity growth are the same.
This is a hypothesis that we can reject with confidence. In the absence of any structural
change, the employment share structure in the base year will exactly predict the employment
share structure in all subsequent years, and similarly for the output shares. Figure 1(a) and
(b) shows the consequences of using the output and employment shares in the base period to
predict the corresponding shares in the years up to 1996. Each graph shows the correlation
coefficient between the shares in each successive year t and the base year shares for
employment and output, respectively. With proportional growth, these correlation coef-
ficients would remain constant at unity but, as we see, they decline in a monotonic manner
and become weaker as time passes. Also shown in Figure 1(c) are the results of a different
test carried out, namely the correlation between employment and output shares over time
and, as shown, this also weakens but less dramatically. That it does so reflects the f act that
the industry productivity levels in successive years are correlated more weakly.
An alternative way of measuring the rate of structural change is to compute the variation
over time for the Herfindahl indices of employment and output. With proportional growth,
these indices would be constant. Figure 2 shows the variation over time in the Herfindahl
index for employment shares, H ¼ +e
2
j
: This index measures the average employment
share at each date. From Figure 2, we see persistent evidence of structural change in the
economy’s employment pattern. The rate of change of the Herfindahl is readily seen to be
proportional to the covariance between employment shares and employment growth rates
dH
dt
¼ 2+e
j
ðn
j
 nÞe
j
¼ 2C
e
ðenÞ
12 J. S. Metcalfe et al.

where, n
j
is the growth rate of industry j’s employment and n ¼ +e
j
n
j
is the aggregate
employment growth rate across all the industries. Consequently, the Herfindahl rises or
falls as employment shares are positively or negatively correlated with the growth rates of
employment in each sector. The rather dramatic fall and rise of the index provide clear
evidence against the hypothesis of proportional growth.
Although this evidence raises interesting questions in its own right, these cannot be
answered without an appropr iate analytical framework. If structural transformation is
pervasive and ongoing, it can only be because the forces shaping the evolution of demand
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96
0.6
0.7
0.8
0.9
1.0
Corr e
t
e
t+n
Corr z
t
z
t+n
0.4
0.6
0.8
1.0
A
B
Fig. 1. (a) Correlation of employment shares e
t
e
tþn
; (b) Correlation of output shares z
t
z
tþn
;
(c) Correlation between employment and output shares e
t
z
t
e
tþn
z
tþn
(base year¼58).
Adaptive economic growth 13

and the development of technology in the various industries are operating unevenly and
cumulatively. Any theory of structural transformation must be capable of connecting
together the uneven incidence of ‘demand and supply’ forces to show how the evolution of
individual industries is connected to the evolution of the economy as a whole. This is the
task addressed in the remainder of this paper. In any growth model, the phenomena that
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96
Corr e
t
z
t
e
t+n
z
t+n
0.5
0.6
0.7
0.8
C
Fig. 1. (continued )
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96
Year
0.0034
0.0036
0.0038
0.0040
0.0042
0.0044
0.0046
0.0048
H
Fig. 2. Adjusted Herfindahl Index, 1958–96.
14 J. S. Metcalfe et al.

must be explained are the growth rates of output, employment and productivity, and it is on
these relations alone that our framework is focused.
3. The basic framework
Imagine an economy to be describable in ter ms of an ensemble of distinct activities, or
industries, each one producing a single product.
1
Each industry is distinguished by the
unique knowledge base that is embodied in its production methods. In relation to
technology, the chief simplification we allow is that the capital coefficient, ‘b
j
’ is given for
each industry but varies across industries, and that all innovations are Harrod neutral
improvements in processes of production; progress is purely labour augmenting. Let a
j
be
unit labour requirements, then labour productivity for the industry is, of course, q
j
¼ 1=a
j
.
In each industry the values of these coefficients are determined as averages of the
coefficients in the constituent firms and reflect the variety in production methods across
firms as well as the relative contribution each firm makes to the output of its industry.
2
At
levels of aggregation above the industry, input proportions will change in response to the
different growth rates of the various industries, but this is not f actor substitution in the
traditional sense it is, instead, factor reallocation or adaptation.
3
At each moment in time, the structure of the ensemble is captured in the shares of
aggregate employment and output of each industry. Let z
j
be the share of industry j in the
output of all the industries and e
j
be the corresponding share of total employment. The
measures of output shares are contingent on the particular set of price weights used to
construct the aggregate measure of output. We take these prices as given.
4
Average unit
labour requirements across the ensemble are

a
z
¼ +z
i
a
i
and average ensemble labour
productivity is

q
e
¼ +e
j
q
j
, from which it follows that

a
z

q
e
¼ 1, while e
j
q
j
¼ z
j

q
e
: Conse-
quently, across industries, output structure and employment structure differ to exactly the
degree that productivity levels differ from average productivity.
As with all evolutionary arguments, what are to be explained are the differential growth
rates of output, employment and productivity across the ensemble. Without differential
growth, we cannot have structural change and, unless these growth rate differences are
endogenously determined, we cannot have self-transformation. In elaborating this point, it
is useful to remember the following relations. First, that
g
j
¼ g
z
þ
ˆ
z
j
and n
j
¼ n þ
ˆ
e
j
Each growth rate, of output (g
j
), in the fir st case, of employment (n
j
) in the second, is equal
to the average growth rate (g
z
or n) plus the appropriate rate of growth of the share of that
industry in the aggregate (
ˆ
z
j
or
ˆ
e
j
). Obviously, when the industry and aggregate growth
rates are equal, structure is frozen, the case of proportional growth. Moreover, when the
structures change, so necessarily do the average growth rates, even when the individual
growth rates are given.
1
Strictly speaking, we could allow for joint production and tie the same activities to competition in multiple
markets. It would take us too far to do this here.
2
Consequently, the industry coefficients have their own evolutionary history depending on the dynamics of
selection within industries.
3
It is a considerable simplification that product innovations are ruled out of this account, particularly in the
light of the arguments below about the evolution of demand. See Saviotti (1996) and Saviotti and Pyka
(2004) on this point.
4
Our micro interpretation of these prices would be that they are set to meet the investment requirements of
firms in the industry and that, as a consequence, the average price depends on the industry growth rate.
Adaptive economic growth 15

Second, that
ˆ
e
j
þ
ˆ
q
j
¼
ˆ
z
j
þ
ˆ
q
This relates the two measures of structural change in an industry to the deviation of that
industry’s productivity growth (
ˆ
q
j
) from the population average rate of productivity growth
(
ˆ
q). Consequently, in an industry in which productivity increases at the average rate, the
output share will change at the same rate as the employment share. We can see immediately
that proportional growth necessarily implies that all sectors have a common rate of
productivity growth, a position that is not conformable to the facts.
In the analysis below, we reject the idea of a production function that offers smooth
substitution possibilities at either industry or economy levels of analysis, and we abandon the
possibility of analysing the growth process in terms of ‘shifts in’ and ‘movements around’
a production function. This is for two reasons. First, in general, there is no specification of
the technologies of the different industries that can eliminate capital reversing price effects,
and these effects destroy the hypothesis of normal substitution between capital and labour
in response to changes in the relative cost of labour and ‘capital’ (Harcourt, 1972; Bliss,
1975; Kurz and Salvadori, 1995; Kaldor 1996). Second, and more fundamentally, we
maintain that all changes in technique require a change in practical knowledge, so that
the fundamental phenomenon is innovation qua adaptation, not factor substitution in a
‘given’ state of knowledge. Evidence concerning the localised nature of progress provides
a powerful underpinning for this view (Antonelli, 2001; Atkinson and Stiglitz, 1969).
This is not as drastic a step as it might seem. A theory of adaptive growth must
necessarily focus on changes in technology rather than the state of technology and, as Usher
(1980) put it, ‘no progress’ means ‘no growth’. By the same token, we reject the idea of an
aggregate stock of knowledge that is matched to an aggregate production function
(Steedman, 2003).
4. Produ ctivity growth and the Fabricant Laws
If we reject any reference to the production function and aggregate knowledge in the
growth process, how can we build up an account of the self-transfor mation of industries
and, ultimately, economies? Such an account should make the transfor mation process
endogenous, it should conne ct with the sector specific growth of knowledge, and it should
emphasise the fundamental features of enterpr ise in relation to investment and innovation.
It should involve markets in the process of translating creativity into patterns of growth and
decline and be able to aggregate out a macro level account of economic change. If we are to
choose any principle that draws together these desiderata, it is that the division of labour is
limited by, and in turn limits, the extent of the market. Changes in the division of labour
require changes in technology in the broad, and extension of the market requires the
growth of per capita income. No other principle would seem to have the ability to unify the
transfor mation of produ ction methods and the extension of demand to create an
endogenous theory of enterprise and economic transformation.
In a remarkable empirical investigation into the growth of manufacturing in the USA
over the period 1899–1939, Solomon Fabricant (1942) set out the basis of the view that we
espouse. He drew attention to the fact that rapidly growing output in an industry is usually
associated with rising employment and increasing labour productivity and that, when
output is in decline, so is productivity. Across industries, there are wide variations both in
levels of productivity and in growth rates of productivity, so Fabricant saw that the way
16 J. S. Metcalfe et al.

was open to explain these differences in ter ms of the differential growth of the markets
for different groups of products. Moreover, growth of output is usually associated with
net investment, and conversely, such that output growth usually implies the growth
of measured capital per worker. The significance of this was not only that investment
creates the capacity to serve a growing market, but that this is the major channel through
which technical advances ‘cut into unit labour requirements’ (p. 96). The great
significance of Fabricant’s work lay in the fact that it could provide analytical foundations
for a non-aggregative theory of endogenous growth and self-transformation on ‘Smithian’
principles.
1
The starting point is a general definition of investment as any use of productive resources
that improves the capacity of productive assets of any kind, assets being defined in the
conventional way, by the ability to yield future income streams. Investment is the activity
that enhances productive economic capabilities and, in this sense, it is much broader than
the laying down of new plant and capital infrastructure. Investments in human capital, in
research and development, in improvements in the organisation of firms are all of
importance in this view (Scott, 1989). Investment can then be interpreted as the cost of
making the arrangements to improve capabilities and thus the cost of generating improve-
ments in productivity. Of course, any change in capabilities will require the g rowth of
knowledge somewhere in the economy, but the kinds of knowledge require d tend to vary
enormously and cannot be reduced to any common denominator. When we broaden the
conception of knowledge in this way, it becomes obvious that the growth of the market also
requires the growth of knowledge. Thus, we can distinguish those improvements in
productivity that are directly related to investment in current productive capacity, and all
other residual improvements in productivity that are investment related but where those
investments leave current capacity unaffected.
This approach requires a representation that makes it operational in an analytical sense.
Although there are different ways of doing this, we have chosen the familiar technical
progress function as the way of linking the improvement in productivity to the economic
conditions in each ind ustry (Eltis, 1973). These functions are averages of the correspond-
ing firm-level functions which, in turn, are a necessarily imperfect reflection of the micro
tendencies to enterprise, investment and innovation within firms. They are not natural
phenomena but are the reflection of human motivation and imagination. We let each
technical progress function be of the following form
ˆ
q
j
¼ a
j
þ v
j
I
Q

j
where I=Q is the rate of investment in physical capacity expansion, v
j
is the coefficient that
translates that investment into productivity growth, and a
j
is the residual rate of
productivity growth, which reflects all the remaining kinds of non-capacity expanding
investment. The investment ratio is b
j
g
j
and, in a growth context, we can reasonably
assume that the growth rate of capacity is the same as the growth rate of actual output.
2
If
this is accepted, it follows that the progress function becomes
ˆ
q
j
¼ a
j
þ b
j
g
j
ð1Þ
1
Part II of Salter’s (1960) justly famous analysis of productivity, investment and delay in the use of new
techniques is in fact an application of Fabricant’s method to UK data.
2
This is not crucial, but to allow for variable utilisation would be impossible without opening the black box
of the individual industries. We leave this as unfinished business.
Adaptive economic growth 17

This is precisely Fabricant’s Law. Provided that b
j
¼ b
j
v
j
is less than unity, output growth
results in productivity growth and productivity growth is consistent with employment
growth, provided that the industry’s market is growing quickly enough. The coefficient b
j
is
the measure of the degree of dynamic increasing returns in the industry, whereas the
coefficient a
j
is the measure of all those residual influences on technical progress that do
not depend on the immediate expansion of the market for an industry.
1
The same NBER productivity dataset that we used above to explore the rate of
transfor mation within the US manufacturing sector can also be used to investigate
Fabricant’s Law, half a century on. In Figure 3, we show the trend in the growth of labour
productivity for manufacturing as a whole, in which there is some evidence of acceleration
from 1990. Around this average, there is a wide dispersion of rates of productivity growth in
the individual industries, as shown in the frequency distribution in Figure 4. Taking all the
industries together, 65 have negative productivity changes over the period, while the mean
for all the industries is 22.8%.
2
To check the Fabricant relations, we show first in Figure 5(a) the OLS regression
between output growth rates and employment growth rates across all 459 manufacturing
sectors for the period 1958–96. The estimated equation is
n ¼1:55 þ 0:57g
ð0:37Þð0:7Þ R
2
¼ 0:67
from which we infer that, on average, a 10% increase in aggregate output is associated
with a 4.3% increase in labour productivity. If we look within this aggregate, we find
a considerable diver sity of empirical form of the emp loyment, ou tput growth relations.
Fig ure 5(b) gives the scatter plot of the OLS estimates fo r the individual values of a and
b in those 419 sectors where the estimates are significant at a 5% confidence level. With
one exception, all the b coefficients are less than unity, confirming the presence o f
dynamic increasing returns. To a much lesser degree, the a coef ficients are positive, since
there are a substantial number of t he indu str ies where there has b een res idual technical
regress. It will be apparent that, in as much as these regressions support the existence of
technical prog ress functions, there is considerable diversity at the industry level, with no
apparent correlation between the estimated values o f a and b. Thus, Fabricant’s Law
stands up remarkably well as a robust e mpirical descriptor of the relation between
technical progress, investment and the growth of t he market. It is not our purpose to
explore here the origins of the differences in the technical progress functions s ummarised
in Figure 5(b), for that would be a major under taking , drawing on our understanding of
difference s in the condit ions of innovation across indus tries. Rather, we turn our
attention to how the Fabricant relation can be used as the building bloc k for a theory
of self-transformation.
Fabricant was well aware that no industry stands in isolation in relation to the growth of
productivity since
growth in the efficiency of any single industry or group of industries—manufacturing or non-
manufacturing—is thus intimately related to developments elsewhere in the economy. Advance
1
We should note immediately that the same relation has been introduced in other guises, in the work of
Kaldor (1957), in his exposition of Verdoorn’s Law, which, in Verdoorn’s original account, we should note,
has very different foundations from those articulated by Fabricant.
2
The highest percentage change in productivity is 2809% in the computing sector.
18 J. S. Metcalfe et al.

in manufacturing productivity is part of the evolution of the entire industrial system. (p.163, our
emphasis)
This is not an invitation to provide a macroeconomic account of the growth process but
rather, a plea to be sensitive to important relations within the ensemble of manufacturing
activities. Fabricant has in mind two broad kinds of interrelationship. The first is
technological, where a particular development has applications beyond the sector in
which it originated, he gives, among several examples of this phenomena, the diffusion of
electric power and the spread of the linear production line beyond the auto industry.
Modern economists would recognise this as a ‘spillover effect’, although not one that could
be viewed as passive and costless by the recipients of the externally generated knowledge.
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
Year
60
80
100
120
140
160
180
200
Productivity
Fig. 3. Employment share weighted labour productivity.
-1 0
1234
5 6 7 8 9 1011121314151617181920
Productivity Growth
0
10
20
30
40
50
60
70
Frequency
Fig. 4. Distribution of percentage productivity change, 1958–96.
Adaptive economic growth 19

Fabricant’s second argument deserves far more attention than he gave it, and it relates to
demand-side processes and the extension of the market. As he suggests, an industry can
only expand as far as its customers allow, and one of the principal determinants of this
constraint is the rate of growth of per capita income in the economy. However, since every
individual sector makes a contribution to overall productivity growth, it follows immedi-
ately that the productivity growth rates of the various industries are economically
independent. It is through this insight that we can turn Fabricant’s law into a theory of
growth and self-transformation and, in the process, bring to the fore the role of demand
and consumption practices in relation to innovation and produ ctivity growth. This requires
some understanding of the forces determining the rate of growth of demand and the way in
which the growth of each market is connected to the growth of productive capacity and
investment.
Output growth
-10
-5
-0
5
Employment growth
A
B
n = -1.55 + 0.57g
(0.37) (0.7) R
2
= 0.67
24 6810
-3 -1 1 3 5 7
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Fig. 5. (a) The Fabricant relationship; (b) Fabricant coefficients for manufacturing.
20 J. S. Metcalfe et al.

5. Demand and structural change
Demand generally plays a small role in modern growth theory, yet it was at the centre of the
dynamic process that Adam Smith enunciated so long ago. Since structural change is
shaped by differential growth rates of demand and, since differential growth rates of
demand, and thus output, are a cause of differential rates of productivity growth, we have
the basis of a virtuous circle in which demand growth and productivity growth are mutual ly
sustaining.
As soon as we abandon the method of proportional growth there is immediate scope for
giving demand-side forces a key role in the explanation of structural change and for giving
far more attention to the role of demand in the innovation process. Indeed, one of the more
obvious reasons why industry growth rates differ is to be found in hypotheses about the
evolution of demand. As Pasinetti expressed it ‘ ...any investigation into technical progress
must necessarily imply some hypotheses ... on the evolution of consumer preferences as
income increases’. He went further ‘[i]ncreases in productivity and increases in income are
two facets of the same phenomenon. Since the first implies the second, and the composition
of the second determines the relevance of the first, the one cannot be considered if the
other is ignored’ (our emphasis, 1981, p. 69). Pasinetti did not develop further his
treatment of demand in either of his major works on structural change (1981, 1993), yet it
is not difficult to do.
1
We find it convenient to work with per capita income elasticities for each industry, c
j
;
defined as the ratio of the growth in per capita demand for each industry to the growth rate
of per capita income, thus
c
j
¼
g
j
 n
g
z
 n
where n is the rate of growth of total employment, and g
z
¼ +z
j
g
j
is the rate of growth of
aggregate output. These elasticities provide us with the basis for a sorting process across
the set of industries, since they give rise to different growth rates of demand and output.
As we assume, as we are entitled to do in a theory of secular growth, that in each industry
prices are set by firms so as to coordinate the rate of growth of the market with the rate of
growth of capacity, we use the same symbol g
j
to denote both. Then we can write the rate of
growth of that industry as
g
j
¼ n þ c
j
ˆ
q ð2Þ
where
ˆ
q ¼ dlog

q
e
=dt is the yet to be constr ucted aggregate rate of productivity increase. It is
apparent that the rate of growth of each industry cannot be determined before we have
determined the rates of growth of employment and productivity across the ensemble.
Thus, the pattern of growth rates that emerges is simultaneously determined with the
aggregate rate of growth of employment and productivity. Consequently, the variance of
the industry g rowth rates is related to the variance of the income elasticities of demand by
the condition
+z
i
ðg
i
 g
z
Þ
2
¼ V
z
ðgÞ¼
ˆ
q
2
V
z
ðcÞ
1
The effect of relative price changes on demand is suppressed in the following for the same ‘black box’
reason adumbrated earlier. Changes in commodity prices in general relative to the wage are, of course, at the
heart of our argument. The black box also hides the effect of differential wage rates on the process of
adaptation. It turns out that uniform wages are required if economic adjustment is to reflect the true
productivity position in firms and industries. See Salter (1960) and Harcourt (1997) for further discussion.
For further discussion of demand and evolutionary processes, see Bianchi (ed.) (1998).
Adaptive economic growth 21

Thus, the g reater the rate of productivity growth, the greater is the variance of the
industry growth rates for a given variance of income elasticities. This is a good example of
the evolutionary notion that a secondary moment, the variance of g rowth rates, is
functionally dependent on a primary moment, the variance of per capita income elasticities
of demand. It is also a generalisation of Pasinetti’s perspective on the importance of
differences in demand conditions in different sectors in explaining the pattern of economic
growth. It should be noted that, in (2), we have defined the elasticities of demand so as to
allow the distr ibution of demand to be influenced by the growth in per capita income alone.
The assumption that population growth is neutral in its demand composition effects is
a convenient simplification. What matters is that per capita income growth and population
growth have differential demand effects, and this is what we have captured in (2) and its
consequences below. This does not mean that the elasticities are constant over time, and, in
general, they cannot be, a conclusion that is implicit in the idea of Engel’s Law, in which the
elasticities decline with increases in per capital income.
We now have the basis for establishing a relation between aggregate productivity growth
and the individual industry rates of productivity growth. It is obvious that
ˆ
q will be
a weighted average of the individual productivity growth rates but ‘What are the
appropriate weights to construct this average and capture the organic unity of the ensemble
of activities?’ To determine them, note that n
j
is the rate of growth of employment in sector
j so g
j
¼ n
j
þ
ˆ
q
j
, whence n
j
 n ¼ c
j
ˆ
q 
ˆ
q
j
: Now if we weight this last expression by the
employment shares e
j
, we find that
+e
j
ðn
j
 nÞ¼ð+e
j
c
j
Þ
ˆ
q  +e
j
ˆ
q
j
¼ 0
since +e
j
n
j
¼ n by definition. Thus, our weighting scheme is provided by
ˆ
q ¼
1
+e
j
c
j
+e
j
ˆ
q
j
ð3Þ
Unless +e
j
c
j
¼ 1, these weights do not sum to unity. Indeed, it follows immediately that
+e
j
c
j
¼ 1 þ
C
z
ðc
j

a
j
Þ

a
z
where C
z
ðc
j

a
j
Þ is the ‘z’-weighted covariance between industry income elasticities and
average unit labour requirements in each industry. Thus, the employment-weighted
average of the income elasticities has unit value only if this covariance is zero, which in the
absence of any compelling reason to think otherwise, we assume not to be so.
6. The interdependence of rates of productivity growth
Having established the relation between the aggregate and the industry rates of pro-
ductivity growth, let us consider now the consequence that the industry productivity
growth rates are mutually interdependent. In so doing, we are following the line of enquiry
introduced by Allyn Young (1928), who demonstrated how increasing returns generates
reciprocal interdependence of productivity growth between the different industries.
In each industry, there is a technical progress function ((1) above) premised on a stream of
potential innovations that increase labour productivity in a Harrod neutral way. The effects
of this new knowledge are translated into productivity growth through the mechanisms
22 J. S. Metcalfe et al.

embodied in (1) which, in turn, depend on the market coordination of capacity expansion
and growth of demand through the pricing and investment behaviour of firms in each
industry. The significance of this formulation is that it links productivity growth to output
growth, and thus to structural change through the role of the different income elasticities of
demand. Now using (2) and (3), each progress function can be written as
ˆ
q
j
¼ a
j
þ b
j
n þc
j
+e
j
ˆ
q
j
+e
j
c
j

ð4Þ
This expresses Young’s central point, which is that productivity growth in any one sector
increases with productivity growth in all other sectors, provided that its output is a normal
good, and these productivity growth rates are mutually determined through the co-
ordination of demand and capacity in the market process. Such normal goods have
complementary but reciprocal effects on each other’s productivity growth. Equation (4)
constitutes an ensemble of simultaneous productivity growth equations, the solution of
which in the two-industry case is sketched in Figure 6. The schedules Q
1
and Q
2
are the
reciprocal productivity functions for each industry, and they intersect at a to determine the
respective market coordinated rates of productivity growth.
Through point a draw the straight line L–L with slope e
1
=e
2
; the relative employment
shares, to inter sect the 45° line at b. This point measures the rate of aggregate productivity
growth
ˆ
q, and, as drawn,
ˆ
q
1
>
ˆ
q >
ˆ
q
2
: Consider now point c and its related point d, which
jointly depict the patter n of productivity growth if there are no demand feedback effects in
either sector. The proportionate difference between points b and d is a measure of the
importance of reciprocal interdependence in the growth process, it measures what we shall
term the ‘Young effect’, the stimulus to growth generated by the autocatalytic nature of
increasing returns.
0
•
L
L
Q
1
Q
1
Q
2
Q
2
45
o
e
1
e
2
a
c
d
b
q
ˆ
q
∧
∧
q
1
q
1
∧
q
∧
q
2
∧
q
2
∧
Fig. 6. Coordination of increasing returns.
Adaptive economic growth 23

The point about positive feedback, as Young emphasised, is that it augments growth
within and between sectors, amplifying the wellspring of progress, which is provided by the
enterprise grounded relations between processes of innovation and investment in the
broad. In this way, we can comprehend his insistence that changes in one sector induce
changes in other sectors mutually reinforcing the growth of productivity in and within all
the sectors. As he put it, ‘[e]very important advance in the organisation of production ...
alters the conditions of industrial activity and initiates responses elsewhere in the industrial
structure which, in turn, have a further unsettling effect’ (p. 533). The precise form these
changes in organisation take is not the issue in question, rather it is the reciprocal effects on
productivity growth that matter. Could growth be more adaptive than this?
What is the agg regate rate of productivity growth? To establish this, we simply weight
each industry equation (4) by the corresponding employment share weights and sum to
yield the following
ˆ
q ¼
a
e
þ

b
e
n
ð+e
j
c
j
Þð1 

b
u
Þ
ð5Þ
In this expression, a
e
¼ +e
j
a
j
is the average rate of residual progress, as influenced by
investments unrelated to current capacity, and

b
e
¼ +e
j
b
j
is the average progress elasticity
constructed with the employment shares. However,

b
u
¼ +u
j
b
j
is a second average progress
elasticity derived from the weights u
j
¼ e
j
c
j
=+e
j
c
j
, the contribution which that industry
makes to the employment weighted average of the income elasticities. Of course, the u
j
weights are proper weights satisfying +u
j
¼ 1: The conditions for Fabricant’s Law to hold in
the aggregate are

b
e
< 1 and

b
u
< 1, which are certainly satisfied if the individual progress
elasticities are less than unity, for then we are assured that growth is autocatalytic, with
demand and its distribution, output and productivity growth mutually reinforcing one
another. As Kaldor summed up the point, ‘the process of expansion is self-generating’ (1996,
p.40).
1
Rearranging (5), we can express Fabricant’s Law across the ensemble of industries, as
the averaged relation between productivity growth and output growth, thus
ˆ
q ¼
a
e
þ

b
e
g
z
ð+e
j
c
j
Þð1 

b
u
Þþ

b
e
ð5#Þ
Equations (5) and (5#) combine the reasoning behind the Fabricant technical prog ress
function with the reasoning behind endogenous growth theory, with the very important
proviso that the development of knowledge (productivity) cannot be separated from the
growth of the individual sectors. The growth of applicable knowledge is to this degree
a market-dependent and positive feedback process. What average productivity growth is
cannot be independent of the str ucture of the ensemble of industries, as reflected not only
in the direct employment shares but equally in the various covariances implicit in these
aggregate relations.
The conclusion is that growth amplifies the effects of innovation and links the
productivity dynamics of different industries together in a transparent way, a way that
depends upon demand linkages. Notice carefully, however, that Figure 6 represents
a process of growth coordination at a point in time. It does not represent growth
equilibrium in some more general sense, as a fixed attractor to which productivity patterns
converge and stabilise. Indeed, it is a fundamental assumption of our evolutionary
1
Compare Knight (1956, ch. 8), for a discussion of capitalism as a non-equilibrium self-exciting system.
24 J. S. Metcalfe et al.

perspective that growth is open ended, that there is not any state of dynamic rest in the
presence of innovation driven growth. Thus, points a and b are continually ‘on the move’,
as the relative employment shares and the rates of innovation and output growth vary over
time, even with a given pattern of residual rates of technical progress. The economy is
simultaneously coordinated and restless, as all knowledge-based economies must be. One
way to emphasise this is to recognise that neither of the agg regate progress elasticities

b
e
and

b
u
are constants; they vary with each change in the composition of employment, and,
just as one should expect, the dynamic properties of the economy change as its structure
changes. These are the simple consequences of the importance of increasing returns in the
presence of market coordination.
7. Closing the system: the self-transfor ming nature of
growth and progress
The combination of Fabricant’s Law and differential income elasticities of demand
provides an account of productivity growth differences at the industry level and the
aggregate rate of productivity growth. In each case, the rates of productivity growth are an
emergent consequence of market coordina tion of demand and capacity expansion.
However, we have yet to determine what the aggregate rate of productivity growth will
be. There are limits to the exploitation of increasing returns, and these are naturally set by
limits to the growth of the market in the aggregate. As Kaldor (1972) pointed out, there is
a missing element in the Young approach that can only be dealt with by an explanation of
the relation between capital accumulation and effective demand.
To express it more formally, the sets of relations (5) which lead to Fabricant’s Law,
provide only one relation to determine two unknowns and, without determining both of
them, the industry rates of productivity growth cannot be established. A relation is missing,
and here there are at least two possibilities. The first is to claim that the rate of growth of
employment n is given, by virtue of arguments in relation to the growth of population,
labour migration, changing gender composition of the population, and changes in
institutional rules in relation to the market for labour. Whatever the rationale, the given
value of n determines
ˆ
q through (5) and correspondingly determines the growth rate of
output g
z
. This is the route explicitly followed by Arrow (1962) and Jones (1995A, 1995B)
in their versions of endogenous growth, for they both end up with the claim that
productivity growth is proportional to the growth in employment, albeit for different
reasons. However, in this formulation, even a stationary population is consistent with
unlimited growth, provided the ongoing growth of knowledge is translated into residual
rates of productivity growth.
The alternative closure is to argue that the aggregate growth rate of the economy is
determined by aggregate investment and saving behaviour. On this view, the requirements
for macroeconomic coordination set the aggregate constraints on the relations between
growth rates at industry level. In following this approach, some hypothesis has to be
adopted on the nature of capital markets and saving behaviour. Here, it is sufficient to work
through the argument on Harrodian lines, for Har rod can justifiably be claimed to be the
first of the endogenous growth theorists, in the modern sense.
1
1
Alternative approaches spring readily to mind, including Kaldor’s emphasis on the importance of retained
profits for accumulation. We leave the alternatives as unfinished business.
Adaptive economic growth 25

We start by assuming that all profits are distributed and that the aggregate saving ratio of
households is a constant S
H
. All investment is funded via the capital market and, for this
market to clear, the saving ratio must equal the aggregate investment ratio for the economy.
Now, because I=QðÞ
j
¼ b
j
g
j
; we can also write the aggregate investment ratio as
I
Q
¼ +z
j
b
j
g
j
¼

b
z
g
v
where g
v
¼ +v
j
g
j
is defined using the weights v
j

b
z
¼ z
j
b
j
, so that v
j
measures the
proportionate contribution that each industry makes to the aggregate capital output ratio.
From this, we immediately obtain a version of the familiar Harrod condition
g
v
¼
S
H

b
z
However, g
v
in this formula is not the g rowth rate of aggregate output as normally defined,
which is, of course g
z
, the output share weighted average of the industry growth rates. The
two growth rates would only be equivalent in conditions of proportional growth, i.e., when
growth is not associated with transfor mation, but here they are logically different and are
related by the condition
g
z
¼ g
v

C
z
ðgbÞ

b
z
In this expression C
z
gbðÞis a secondary covariance, since the growth rates are emergent
properties. However, because of the relationship between demand growth and aggregate
productivity growth, it follows that this secondary covariance is proportional to a primary
covariance, namely
ˆ
qC
z
cbðÞ: Thus, the relationship between the aggregate growth rates
becomes
g
z
¼
S
H

b
z

C
z
cb
ðÞ

b
z

ˆ
q ð6Þ
That is to say, the aggregate growth rate is not independent of the forces making for
uneven rates of growth in the individual sectors; the growth rate depends on the variety
within the system. Thus, the two expressions for the growth rate of output are only
equivalent if aggregate productivity is constant or if the covariance between the income
elasticities of demand and the industry capital:output ratios is zero for all possible
structures of the economy. This is only feasible if all the capital:output ratios are the
same or if all the industry income elasticiti es are unity, in which later case the output
structure of the economy does not change over time. As soon as we abandon these
requirements for proportional growth, we find that structure and diversity once again
influence the relation at the macro level between output growth and productivity growth,
and this structure is captured by the primary covariance term in (6).
Now, if we combine together relation (6) with Fabricant’s Law (5#), we can simulta-
neously determine the mutually consistent values for the growth of aggregate output and
the growth of aggregate productivity. This solution is sketched in Figure 7, where we have
assumed for purposes of illustration that C
z
ðc bÞ is negative. The negative association
between the rates of growth of output and productivity reflects the ‘most favourable case’
in that the industries with above average income elasticities of demand are also the
industries with above average capital productivity. Productivity growth consequently has
26 J. S. Metcalfe et al.

an accelerating effect on output growth since it concentrates demand in industries with
a relatively greater productivity of invested capital. Since Fabricant’s Law provides
a positive association between the two rates of growth, the solutions for g
z
and
ˆ
q follow,
as shown. The point labelled H is the Harrod solution, with no structural change and
productivity growth independent of output growth. The solution at S is the Smith/Young
solution with mutual interdependence of productivity and output growth. This is the
virtuous circle case in which both forms of growth are mutually reinforcing in terms of
aggregate demand as well in terms of Fabricant’s Law. It will be clear that, ceteris paribus,
a higher saving ratio implies higher values for output growth and productivity growth as
does a higher value for the exogenous progress rate.
If the covariance between the values of b and c is zero, we are back to Harrod’s case, in
which the growth rate of output is independent of the growth rate of productivity, the world
of effective proportional growth. Conversely, if this covariance is positive, ‘the worst case’,
productivity growth and output growth are negatively related from the aggregate demand
side, the solution S# in Figure 7. It is clear that the differences between these three cases are
reflected in the corresponding rate of growth of total employment. If point S lies above the
45° line, employment growth is positive and conversely if the solution lies below this
boundary.
Growth in all its senses, output, employment and productivity, is established within and
depends on the prevailing structure of the economy, which is itself adapting under the forces
of innovation and the distribution of demand. This system evolves, it adapts to the
opportunities created by the exercise of imagination, it is restless. Thus, to claim, as we have,
Fig. 7. Harrod/Young dynamics.
Adaptive economic growth 27

that it is coordinated by market processes in relation to the various industries and in relation
to the market for capital is not to claim that it is in equilibrium. Indeed, capitalism in
equilibrium seems from this view a contradiction in terms. There are always reasons to
change prevailing arrangements and every change opens up new opportunities for further
change, ad infinitum, and this is the powerful message first stated by Smith, refined by Young
and given further theoretical and empirical content by Fabricant, Kaldor and others.
There is an important question remaining in this treatment of growth—how does the
aggregate capital output ratio evolve over time? Although we have treated the capital:
output ratios in each industry as constants, unaffected by the rate of technical progress in
that industry, it does not follow that the agg regate capital:output ratio will be constant. In
general, it will not, precisely because the economy is restless and is adapting to the uneven
growth of knowledge across the industries. The capital output ratio is defined as

b
z
¼ +z
j
b
j
and, since the b
j
are given by assumption, it follows that
d
dt

b
z
¼ +
d
dt
z
j

b
j
¼ +z
j
ðg
j
 g
z
Þb
j
¼ C
z
ðb;gÞ
¼
ˆ
qC
z
ðc;bÞ
The aggregate capital:output ratio is invariant to structural change only when the growth
rates and capital output ratios of the industries are uncorrelated, and this is so either when
productivity growth is zero or when the income elasticities and capital coefficients are
uncorrelated.
This is an example of a more general evolutionary theorem. Namely, that an aggregate is
stationary if its components are uncorrelated with the dynamic ‘causes’ that determine the
changing relative importance of each component in the aggregate. As a general rule, in an
evolving economy, Harrod neutrality at industry level will not produce Harrod neutrality at
the economy level. What is true at the micro level of the members of a population is not
necessarily true at the aggregate level of that population, and the purpose of the
aggregation procedure is to identify how and why the emergent macro properties of the
ensemble do not mimic the corresponding proper ties of the components.
All this tells us that the structure of the economy matters fundamentally for the evolving
relations between capacity growth, productivity growth and employment growth. The
interaction of macroeconomic constraints and Fabricant’s Law generates growth rates for
output and productivity but in no sense do these correspond to any steady state growth
equilibrium. These growth rates are restless and they change from within. Diversity is the
key to adaptive, restless capitalism; and it is the diversity in innovation conditions, that is to
say, in technical progress elasticities, in capital output ratios and in income elasticities of
demand that we have shown to be the basis for the inseparability of growth and self-
transfor mation.
Now it is clear that our awareness of these dynamic processes will be critically sensitive to
the level at which we conduct the analysis. The more we aggregate, the more we hide the
underlying mechanisms of enterprise and economic change, the more we emphasise inertia
rather than flux and adaptation. Thus, as well as working up from the industry level, we
could equally well work down to the evolution of increasing returns in individual firms.
Important though this step is, it risks missing the main point, which is that increasing
returns is not only a matter of what happens in individual firms, rather it is more
fundamentally a matter of the relation between fir ms and thus the relation between
28 J. S. Metcalfe et al.

different industries. As Young put it, large production should not be confused with large-
scale production.
8. Conc luding remarks
Why is capitalism restless and adaptive? The answer provided here is that economic agents
are not passive recipients of messages emanating from the environment, they are not
cybernetic reactors to use Langlois’ perceptive phrase (Langlois, 1983). Rather they are
imaginative and creative interpreters of messages flowing from an environment which itself
is a product of human design. This creativity is deeply intertwined with the processes of
investment and innovation that form the core of our approach to a theory of endogenous
economic transformation. In turn, these same processes are deeply connected with the
growth of knowledge. Consequently, knowledge grows inseparably in the day-to-day
conduct of economic activity. It is inevitable that this new knowledge is unevenly
distributed and that it opens up further opportunities for innovation and investment, that
is, new growth opportunities. Such knowledge-driven systems are not only unpredictable
in detailed consequences; they are necessarily evolutionary in their nature.
1
We have chosen adaptive or restless capitalism as a suitable metaphor for the nature of
economic transformation, precisely because of its link with evolutionary processes. This is
the core of the Smith–Young–Kaldor perspective on which this paper has been built. There
are numerous sources of and kinds of increasing returns, many of which are incompatible
with any competitive equilibrium. In contrast, competition as an evolutionary process
takes all forms of increasing returns in its stride; they speed up and influence the direction
of change and in no way threaten the wreckage of the economic analysis. Hence, g rowth,
technical progress and the competitive process are inseparable; they are genuinely adaptive
evolutionary processes driven by microeconomic diversity and coordinated by market and
other institutions to generate emerging, ever-changing patterns of economic structure.
Space precludes any development here of the implications for growth policy. Suffice it to
say that they would follow from a bottom-up rather than an aggregate economy-down
perspective; that they would depend on the stimulation of enterprise and entrepreneurship;
and that they would depend upon the open, unbiased operation of market institutions.
2
They are properly described as policies for an experimental economy (Foss and Foss,
1999), and the problem for the policy-maker is that they must accommodate the waste and
narrowly conceived inefficiency, which is essential to all evolutionary processes.
Finally, how the pieces fit together as a system is what the economics of growth and self-
transfor mation is about, and this means that one must treat seriously the instituted mar ket
and non-market context in which enterprise paints its picture. Enterprise is as much about
the framing, institutional context as it is about idiosyncratic behaviours. In this regard, for
example, the innovations systems literature has an important contribution to make to our
understanding of economic growth as an evolutionary process at industry as well as at
national levels.
3
History is open ended, so is economic transfor mation at all its levels. The
1
We have not attempted to connect this picture of open-ended growth with the important growth and
development literature, created in the 1950s by, among others, Nurkse (1953) and Hirschman (1958). This
highly original set of ideas linked growth to structural change within a world of disaggregated economic
sectors, demand inter-linkages and increasing returns to create exactly the kind of dynamic, reciprocal
complementarities that are highlighted in this paper.
2
But see Harcourt (1997) for a discussion of the relation between growth policy and flexible labour markets
that draws on the cumulative progress tradition.
3
See Edquist (1996), Carlsson (1995), Nelson (1993), Freeman (1987) and Malerba (2004) for details.
Adaptive economic growth 29

simple point about mod ern, market capitalism is that it has, as it were, the characteristic of
inducing anarchy and translating it into order.
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