Tyndall˚Centre
for Climate Change Research
Long run technical change in an energy-
environment-economy (E3) model for an
IA system: a model of Kondratiev waves
Jonathan Koehler
April 2002
Tyndall Centre for Climate Change Research Working Paper 15
Long run technical change in an
energy-environment-economy (E3)
model for an IA system: A model of
Kondratiev waves
Jonathan Köhler
Tyndall Centre for Climate Change Research
School of Environmental Sciences
University of East Anglia
and
Department of Applied Economics,
University of Cambridge
Email: j.koehler@econ.cam.ac.uk, tel. +44 1223 335289
Tyndall Centre Working Paper No. 15
April 2002
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Abstract
A world macroeconomic model is being developed to investigate policies for climate change
and sustainable development, as a module of an IAM structure for the UK Tyndall Centre.
This requires an economic model for the next 50-100 years, to show how changes in industrial
structure and technology change GHG emissions. There is no suitable and generally accepted
theory of long term technical change for incorporation in a macroeconomic modelling
structure. However, there is now a good descriptive theory, which is intended to provide an
economic history perspective of long term change. This is Freeman and Louçã (2001). The
objective of our model is to interpret this descriptive theory in quantitative terms, in the
context of the macroeconomic analysis. It will model the dynamics of Input-Output
coefficients and the implied industrial structure, incorporating endogenous technical change
from R&D and investment, with learning-by-doing.
Keywords
Macroeconomics, endogenous technical change, Kondratiev waves
1. Introduction
A world macroeconomic model is being developed to investigate policies for climate change
and sustainable development, as a module of an IAM. To ‘couple’ with climate change
models, a timescale of 100 years is necessary, because changes in CO2 concentrations, which
are now strongly influencing the atmosphere, become significant over a time period of 50-100
years or more.
This raises particular difficulties for economic modelling. Looking back over the last 200
years, the socio-economic system seems to be characterised by ongoing fundamental change,
rather than convergence to an equilibrium state. Our opinion is that over such a long time, a
neo-classical economic model incorporating a long term equilibrium for the world economy is
inappropriate. It is necessary instead to consider the dynamic processes of socio-economic
development. These processes have been called ‘Kondratiev waves’ in the literature on long
term economic development.
Thus, in order to build an appropriate module for an Integrated Assessment of climate change,
we consider that an economic model should have the following characteristics:
• It should model the relevant anthropogenic emissions.
• A world model is necessary, since CO2 and the other GHGs are a global phenomenon.
• It should provide simulations out to 2100, to allow the analysis of policy impacts over the
timescales in which changes in CO2 and the climate are significant.
• The model should be dynamic, not necessarily converging to an equilibrium.
• Differentiated geographical regions and industrial sectors should be part of the model
structure. Although highly aggregated, this model must be able to distinguish between the
world regions with different time paths of development and of emissions and pollution.
The same argument holds for different industrial sectors, since e.g. the transport sector has
very different characteristics to e.g. food. Also, the study of long term socio-economic
change requires a specific model of R&D and investment, which is also very different in
different industrial sectors. An Input-Output (IO) structure accounting for sectoral activity
is a convenient way to consider the interrelationships between the different sectors.
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• The model should be checked against historical data as far as possible, with validation
using time series data based methodology . Over the long term, there is inadequate
detailed data against which to parameterise the model. Econometric methods can be used
to a certain extent, to ensure that the model recreates recent data, but for the longer term
elements, a statistically based analysis will not be feasible, however, the results can be
checked against historical patterns of prices and production.
This paper suggests a quantitative theory of long term technical change. It will be part of a
global macroeconometric model. Dewick, Green and Miozzo (2002) describe the process of
assessing the future technologies to which this theory will be applied. A (descriptive) theory
of long term economic change is discussed and an interpretation suitable for incorporation in
a macroeconomic modelling framework introduced. The conclusions will relate this work to
environmental modelling.
2. A theory of industrial revolutions
These considerations lead us to the conclusion that there is a requirement for a detailed
analysis of the macroeconomics of long term changes.
Our central argument is that, since 1750, socio-economic activity has been characterised by a
series of fundamental changes in technology, institutions and society. This follows the earlier
thinking of Kondratiev, Schumpeter and more recently evolutionary economists (Nelson and
Winter (1982), Brian W. Arthur (1994), Silverberg, Richard Day, Dosi) and economic
historians (Paul David, Chris Freeman, Carlota Perez).
Freeman and Louçã (2001) include a history of economic thought in this area, starting from a
critique of cliometrics, the use of econometric methods in economic historical analysis. They
cover the ideas of Kondratiev and Schumpeter in particular, who were the leading early
figures in economic analysis of long term economic changes. Kondratiev formulated the
hypothesis that there were long waves in capitalist development, now called ‘Kondratiev
Waves’. He undertook one of the first quantified statistical analyses of long term economic
data and identified an approximate dating of the long term upswings and downswings with
distinctive characteristics in capitalist economies. Schumpeter applied economic theoretical
ideas to the study of long term economic change, in a search for an economic theory of the
processes of economic change in economic history.
The current (numerical) models of long term technical change have often been developed in
the tradition of evolutionary economics, often using the mathematics developed for dynamic
processes in biology. e.g. Brian W. Arthur (1994) applied a random process to the cost
reduction in a competition between two technologies to demonstrate that one technology
would eventually dominate the market with 100% probability and this would not necessarily
be the most effective technology, the phenomenon of ‘lock-in’.
The problem with the models in this field is that they are theoretical and conceptual, rather
than dependent upon empirical analysis. They are not based on the assumption of economic
rationality or a Walrasian economic structure, so there is no consensus about what a
reasonable theoretical structure might be. Also, this field has concentrated on industrial
structure, studying competition between firms, often with different technologies. This is vital
for an understanding of the processes of change, but there has been very little work in this
tradition on macroeconomic models; Robert Boyer is the main macro modeller in this area.
Empirical analysis in the normal sense (for economists) of econometrics has some serious
limitations for this analysis. Indeed, the econometric approach initiated by Kondratiev is
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specifically rejected by Freeman and Louçã. Econometric models depend on looking
backwards to develop the model and then can only extrapolate from past trends into the
future. The data for long term economic change is necessarily sketchy and econometric
methods are therefore ill suited to such broad analyses, particularly when a view of the long
term future is needed and fundamental changes in the socio-economic system are postulated.
To summarise, there is no suitable and generally accepted theory of long term technical
change for incorporation in a macroeconomic modelling structure.
However, there is now a good descriptive theory, which is intended to provide an economic
history perspective of long term change. This is Freeman and Louçã (2001).
They argue that Kondratiev waves involve a process of dynamic interaction between 5
subsystems: science, technology, economy, politics and culture. For our purpose of
developing a quantitative model, it is only realistic to try and model technology and economy.
The impacts and feedbacks through the other subsystems will be reflected qualitatively in the
macroeconomic model structure and through scenarios. The objective of our model is to
interpret this descriptive theory in quantitative terms, as far as is plausible, in the context of
the macroeconomic analysis outlined in the introduction.
3. A summary of the theory of Freeman and Louçã
They identify 5 waves of technology and socio-economic activity since the industrial
revolution in the UK:
1. Water powered mechanisation of industry.
2. Steam powered mechanisation of industry and transport, based on iron and coal.
3. Electrification of industry, transport and the home, with steel as a core input.
4. Motorisation of transport, civil and war economies, with industrial chemicals and oil as
core inputs
5. Computerisation of the economy.
The features of these waves are summarised in Table 1, taken from their table p141.
Following Perez (1983), they characterise Kondratiev waves as a succession of new
technology systems (Freeman and Louçã pp 147-8).
1. For each long wave, there are ‘core inputs’ e.g. iron for the railway wave, that becomes
very cheap and universally available. This opens up new possibilities of production factor
combinations. The sector producing these inputs is the ‘motive branch’.
2. New products based on the new factor combinations give rise to new industries whose
growth drives the whole economy e.g. railways; associated production of rails,
locomotives, railway equipment.
3. There are new forms of organisation of production brought about by the new industries
and products, a new ‘techno-economic paradigm’.
4. Such a fundamental change will lead to a period of turbulent adjustment from the old
paradigm to the new.
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Table 1 Condensed summary of Kondratiev Waves source: Freeman and Louçã (2001) p141.
Wave Decisive Carrier Core input(s) Infrastructure Management; Upswing (boom)
innovations Branches Organisation
Downswing
(crisis of
adjustment)
1. Water powered Arkwright’s Cotton spinning, Iron, Cotton, Canals Factory systems 1780s-1815
mechanisation of mill 1771 Iron Coal Turnpike roads Entrepreneurs
industry Sailing ships Partnerships 1815-1848
2. Steam powered Liverpool and Railways, Iron, Railways Joint stock companies 1848-1873
mechanisation of Manchester Steam engines, Coal Telegraph Sub-contracting to
industry and transport railway 1830 Machine tools, Steamships craft workers 1873-1895
Alkali industry
3. Electrification of Bessemer steel Electrical equipment Steel, Steel railways Specialised, professional 1895-1918
industry, transport process 1875 Heavy engineering Copper, Steel ships management systems
and the home Edison’s electric Chemicals Metal alloys Telephone ‘Taylorism’ 1918-1940
power plant Steel products giant firms
1882
4. Motorisation Ford’s assembly Cars Oil, Radio Mass production and 1941-1973
line 1914 Aircraft Gas Motorways consumption
Burton process Internal combustion Synthetic Airports ‘Fordism’ 1973-?
for cracking engines materials Airlines Hierarchies
oil 1913 Oil refining
5. Computerisation of IBM computers Computers Silicon ‘Chips’ Internet Networks: internal, approx. 1980-?
the economy 1960s Software (integrated local, global
Intel processor Telecommunications circuits)
1972 equipment
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Freeman and Louçã identify the following 6 phases in the life cycle of a technology system:
1. Laboratory/invention
2. Decisive demonstration(s) of technical and commercial feasibility. Continuing with the
railways example, the opening of the Liverpool and Manchester railway in the UK in 1830
is an outstanding example.
3. Explosive, turbulent growth, characterised by heavy investment and many business
startups and failures. There is a period of structural crisis in the economy as society
changes to the new organisational methods, employment and skills and regime of
regulation, brought about in response to the new technology.
4. Continued high growth, as the new technology system becomes the defining characteristic
of the economy.
5. Slowdown, as the technology is challenged by new technologies, leading to the next crisis
of structural adjustment.
6. Maturity, leading to a (smaller) continuing role of the technology in the economy or slow
disappearance.
As can be seen in figure 1, phases 2-5 take roughly 50 years. In phase 1, which is of
indeterminate length, there is a negligible macroeconomic effect. The timing of the invention
leading to a breakthrough in the technology and the application in a ‘decisive demonstration’
is more or less random, viewed from a economic perspective. It is phases 2-5 that lead to the
Kondratiev waves.
Output
1 2 3 4 5 6
Phase
0 years 50 years
Time
Figure 1 Phases in the life cycle of a technology system
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This view of Kondratiev waves leads Freeman and Louçã to the following
conclusions/hypotheses:
1. There is a period in which there are technological and/or organisational innovations
offering very high profits in a period of general decline in the rate of profit (Phases 2 and
3).
2. There are recurring structural crises of adjustment, structural unemployment, social unrest
as society switches from one technology system to the next (phases 3 and 5).
3. The new technological system is associated with a change of regulatory and institutional
regime.
4. Each wave generates a new cohort of very large firms, compared to the industrial
organisation of the previous wave, in the new sector(s).
5. There is a high level of industrial unrest in 2 phases:
stage 3: structural adjustment, with a mismatch of skills, as workers in ‘old industries
are made redundant while new skills are often only acquired by new entrants to the
workforce.
stage 5: decline in rate of profit with strong unions
4. Implementation of the descriptive theory in a quantitative macroeconomic model
The most difficult challenge in interpreting this descriptive theory of Kondratiev waves is the
very large extent to which each wave has unique features of organisation and sectoral activity,
as can be seen in Table 1. This problem has been addressed using the following approach.
The theory of Kondratiev waves is included in the macroeconomic module for Integrated
Assessment, as outlined in the introduction. Thus the outputs of the theory have to be
compatible with a large scale, dynamic, IO model of a world economy. This implies that it is
the IO structure that has to change over time.
The current and next Kondratiev waves are characterised by the technologies that form the
new technology systems. These technologies are assessed in Dewick, Green and Miozzo
(2002). Also, scenarios have been written to identify the impact of these scenarios on the
world economy and emissions Berkhout (2002). From these possible new technologies, new
economic sectors were identified and used to modify the IO classification as products and
sectors. Then the problem is to write a (simple) model of the dynamics of the new sectors
which will determine how I-O coefficients associated with the new sectors will change over
time.
The necessary features of the technology model are:
• It should generate the output path over time in the 6 phases.
• Following a presentation of Patrick Criqui (Criqui et al., 1999) on how to model endogenous
technical change, it should incorporate or at least take into consideration exogenous
inventions, supply (R&D, technological opportunities) and demand (new products,
markets) inducement factors. It should model path dependency (learning by doing,
increasing returns).
• Have declining production costs in the new sectors, incorporating endogenous technical
change through R&D expenditure, investment and learning by doing i.e. investment
impacts, following e.g. Grübler et al. (1999).
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The key assumptions of the theory are:
• The new technology is taken up by a ‘Carrier branch’ of industry, to use Perez’
terminology.
• The new technology is embodied in a ‘Core input’ , whose price suddenly drops
dramatically, to say 1/10 previous price.
• This leads to ‘super normal’ profits in the carrier branch, which then leads to an
expectation of high profits, resulting in many startups of firms with high R&D
expenditure and investment.
• Output is function of market size and relative prices
• R&D and investment are a function of expected profits
In the longer term, the structure of economic activity changes. There are new products, new
organisations and new institutions. There is a lagged process of diffusion of the new
technology in the following order:
1. industry producing core input
2. carrier branch (new sector)
3. other industries
Thus there is a lagged diffusion process across sectors and countries, including international
spillovers, Foreign Direct Investment, international trade. The initial version of the theory
does not consider these diffusion processes, this will be incorporated in the next stage of
development.
4.1 Theory
The theory will form part of a dynamic macroeconomic model and must therefore link up
with the IO structure of the model. The general macroeconomic model will also provide
information in the form of output quantities and prices for this theory, where not explicitly
modeled here.
For simplicity of exposition, the economy will be divided into only two sectors, a new sector,
dependent on a new general purpose technology and a notional sector, representing the rest of
sectoral activity in the economy. This ignores the idea that the new technology gives rise to a
cluster of associated industries, which form the fast growing part of the economy. The usual
macroeconomic identity for a time period t (and dropping the t subscript) can be written in
matrix notation as:
Yt = [a11 a12 ] [ q1 ] = [ d1 ] + [I1 ] ( + G + X – M) (1)
[a21 a22 ]t[ q2 ]t [ d2 ]t [I2 ]t
where
Yt = output
axx = IO coefficient
qx = total output in sector x
dx = final demand for the products of sector x
Ix = investment in sector x
and G (government spending), X (imports) and M (imports) will be suppressed for this
description.
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There are two sectors, 1 is the current economy, 2 is a new sector that will arise following a
fundamental scientific/engineering advance. Sector 2 represents some new ‘General purpose
technology’, following Perez’ terminology.
At t = 0, q2 << q1
Freeman and Soete (1997) describe the process by which R&D expenditure is chosen as a
complex process of engineers’ beliefs about their new ideas, an expressed desire for new
products from customers and a social/organizational as well as economic process of decision
making within a firm. In particular, there is no strong correlation between what might be
described as ‘rational economic expectations’ of potential markets or prices. So, R&D
expenditure (R&D2t) will not be explained in detail. It could be modeled as a stochastic
fraction of output, or taken as a deterministic proportion of output, calibrated on data for e.g.
the computer hardware industry in the 1950s and ‘60s.
R&D expenditure generates a probability of a major breakthrough, with a step reduction in the
costs of production. Following the work of IIASA in particular (e.g. Grübler et al., 1999)
there is, after this breakthrough, a dynamic cost reduction function of production, dependent
on cumulative R&D expenditure and cumulative investment.
Thus the cost function has two parts, a continuing decrease:
c2t = α1ε exp[-α2Σ0t-1 (R&D2 + I2)] i.e. exponential decay (2)
with constant α1 calibrated on historical data as the initial price level in the sector before a
technological breakthrough.
and a probability of a step decrease, dependent on both cumulative R&D expenditure and
current R&D expenditure:
ε = {1, δ<1}; P[δ|R&D2t, Σ0t-1R&D2] = α3 R&D2t + α4Σ0t-1R&D2 (3)
Investment depends on the depreciation rate ν of the current capital stock, interest rate r,
expected profitability ( (p-q)*c) and Keynes’ ‘animal spirits’ i.e. an exogenous factor.
I2t = α5[ν K2 + p2tq2t - c2tq2t ]/1+r (4)
The macroeconomic model will provide a time path of overall economic activity Y and
historical information for q1. Note, however, that the macroeconomic identity includes
investment as a component of total demand. Thus this theory by determining I2t partly
determines output. Historically, when a new general purpose technology reaches phase 3
(turbulent growth) and then 4 (continued high growth) c.f. section 3, I2 and d2 become the
main drivers of growth in the economy. q2 can be found from the IO relationship and is
therefore dependent on the IO coefficients a12t a22t . The paths of these coefficients over time
will be defined, dependent on relative prices. This is a departure from most IO models, which
assume constant IO coefficients or rely on historical data to track the movements of these
coefficients over time.
By construction, the IO coefficients sum to 1 for each sector:
a11t + a21t = 1 a12t + a22t = 1 (5)
assuming that the new sector will determine the changes in these relationships, it is then
necessary to define the time paths of a21t and a22t.
Given that sector 2 subsumes all the new industries in the cluster for the new general purpose
technology, a22t, the proportion of production of the new sector for its own inputs can be
assumed to be high and constant. The increase in q2 will then come from the assumed rate of
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growth of Y and the change over time of a21. This growth rate must be consistent with both
the very high rate of investment in the new sector and the rapid growth of final demand for
the new sector’s products.
This initial version of the theory will concentrate on supply side issues. A future development
could be the modelling of the changing pattern of final demand. Note, however, that while
final demand does respond to relative prices, the pattern of consumption is also dependent on
many other variables. This will be an output of the general macroeconomic model, but the
change in consumer tastes and associated lifestyles which embed the new technology in a new
pattern off consumption cannot be modelled by economic factors alone. Therefore, writing a
purely economic model of the change in consumption due to say the introduction of cheap
PCs or in the previous Kondratiev wave of cheap motor cars would be misleading. Therefore,
the most productive approach would probably be to use data on consumption patterns from
previous waves.
a12t, is assumed to be dependent on relative prices, as an increasing logistic function, and is a
measure of the diffusion of the new technology into the rest of the economy in this
formulation of the model. There are a series of diffusion processes that take place if more
sectoral detail is included, both between the new sectors that spring up around the new
technology and into the ‘old’ sectors (with a time lag) as they adopt the new technology in
their production processes.
p2/paverage = p2/[(p2tq2t + p1tq1t)/(q1t + q2t)] (6)
∆a12t = α6(a12max - a12t ) p2/paverage (7)
The (exogenous) changes in Y allow the changes in IO coefficients to generate a dynamic
expansion of the market.
p1t can be taken either from historical data or as an output of the macroeconomic model.
While p2t could be taken from the model, there will be little basis in historical data for this
price. It is more plausibly found from the patterns of growth presented in section 3 above. So,
the cost is found from the above theory and p2t can be calculated as a markup over this cost
c2t. Before the breakthrough, a ‘typical’ or historical level of prices can be assumed. When a
breakthrough occurs and the cost drops, Freeman and Louçã argue that there is no immediate
drop in prices. This presents a (temporary) opportunity to make an exceptional level of
profits. This encourages many new entrants, leading to the 3rd phase of turbulent growth and
in the longer run a reduction in the level of profits as the technology spreads through more
firms. Thus there is a slow and lagged decline in the markup.
The markup m2t = p2t - c2t can be modelled as a declining ( logistic) function in output in
terms of the current model.
m2t/m2min = 1- 1/{1+exp(-(1 -(2q2t)} (8)
5. CONCLUSIONS
This theory formalises assumptions and processes required to generate Kondratiev waves, or
long term structural changes to the world economy in a world of continuing technological
revolutions. This has been undertaken because the modelling of climate change and the
associated policy issues has to consider timescales of 50-100 years at least. Current general
macroeconomic models do not take into account these long term structural changes.
These changes – technological, organisational and eventually cultural - have a fundamental
impact on anthropogenic GHG emissions. The new technologies have very different
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emissions characteristics, and cause the combinations of production processes and hence the
balance of emissions from different economic sectors to change. In order to guide socio-
economic activity, in particular policy to encourage environmentally beneficial technological
development, it is necessary to model these dynamic processes of technological and economic
change. The next step will be to incorporate this theoretical approach into a macroeconomic
model of world emissions, disaggregated into the major world economies and sectors. This
will also enable the processes of international diffusion of technology to be considered.
ACKNOWLEDGEMENTS
This work is funded under the UK Tyndall Centre research theme Integrating Frameworks.
References
Arthur, W. Brian, 1994, Increasing returns and path dependence in the economy, Ann Arbor,
University of Michigan Press.
Berkhout, F., 2002, Scenarios of GHG emissions for the ETech project, Tyndall Centre,
UEA, UK.
Criqui P., Kouvaritakis N., Soria A., Isoard F., (1999) "Technical change and CO2 emission
reduction strategies : from exogenous to endogenous technology in the POLES
model", p.473-488. Colloque européen de l'énergie de l'AEE Le progrès technique
face aux défis énergétiques du futur, Paris.
Dewick, P., K. Green and M. Miozzo (2002), Technological Change, Industry Structure and
the Environment , Tyndall Centre Working Paper No. 13, UMIST.
Freeman C. and F. Louçã, 2001, As Time Goes By, Oxford: OUP.
Freeman C. and L. Soete, 1997, The Economics of Industrial Innovation, 3rd Ed, Pinter,
London.
Grübler, A., Naki enovi , N., and Victor, David G., 1999, Dynamics of Energy Technologies
and Global Change, Energy Policy, 27, pp. 247-80.
Nelson Richard R. and Sidney G. Winter, 1982, An evolutionary theory of economic change,
Cambridge, Mass.; London: Harvard University Press.
Perez C., 1983, Structural change and the Assimilation of New Technologies in the Economic
and Social System, Futures, 15 pp.357-75.
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The inter-disciplinary Tyndall Centre for Climate Change Research undertakes integrated
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Other titles in the Tyndall Working Paper series include:
1. A country-by-country analysis of past and future warming rates, November 2000
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3. Socio-economic futures in climate change impact assessment: using scenarios as
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4. How high are the costs of Kyoto for the US economy?, July 2001
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11. Representing the Integrated Assessment of Climate Change, Adaptation and
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12. The climate regime from The Hague to Marrakech: Saving or sinking the Kyoto
Protocol?, December 2001
13. Technological Change, Industry Structure and the Environment, January 2002
14. The Use of Integrated Assessment: An Institutional Analysis Perspective, April 2002
15. Long run technical change in an energy-environment-economy (E3) model for an IA
system: A model of Kondratiev waves, April 2002
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