1. SUMMARY The role of energy in economic growth
(Stern) presents a review of literature with respect of energy and economic development,
from there, it modifies the Solow model to include an energy component. Its results show that
when energy is considered abundant it neither constitutes a limit nor a causal factor of
economic growth.
(Stern) pretends to evaluate the significance of energy in economic growth and try to
understand the factors that affects (positively or negatively) the links between them. Theories
that have explained growth without taking into account the energy parameter are limited, so
the theories that explain growth entirely by energy supply without considering knowledge,
information and institutions are.
The first step is to understand the role of energy in production. Based on the laws of
thermodynamics it is impossible to leave aside energy as a essential factor of production. In
addition there is a limit to substitution due to the generation of entropy between processes.
Moreover mass and energy are irreproducible, however theoretically the vector of energy and
raw material are reproducible as factors of production though are caused by natural processes
(i.e. in human scale are non-reproducible). Anyway energy and materials need to be extracted,
which represents a disruption of the natural environment. Information, features of organized
matter and energy, is not reproducible but it is necessary to support productive processes. In
this respect, capital and labor are easier to measure than information and knowledge so they
can be used to estimate the latter, but capital and labor are less easy to be measure than
energy.
THE MAINSTREA GROWTH THEORY
Growth theory
The Solow is the most know model, it present economic growth as a function of capital
accumulation, labor and other economic variables such as population growth rate, savings rate
and depreciation. However the long-run growth stagnates as the economy approaches its
equilibrium state without any technological progress. This model is exogenous since the main
long run growth variable is created outside the economic system (technology progress).
Endogenous models AK
Schumpeteriam models
Growth models and no technical change
These models depend ultimately on technological progress since resource extraction depend
on it. Capital accumulation must account for the loss of natural resources. Institutions
intervene for the growth sake and technological deployment. Some models attempt to
maximize social welfare or reach sustainability (nondeclining social welfare)
Solow show that sustainability is possible if nonrenewable resources are substitutable for
capital. However if there is exhaustion of resources and the economic growth rate falls to zero,

2. which it is also shown by Dasgrupta-Heal that with a constant discount rate there is depletion
and economic stagnation.
The main point of these models is that it is understood that decoupling of the economy and
resources is possible through technology. However That might be a misinterpretation since
sustainability can be achieved through renewable resources and the absence of population
growth.
Growth models with resources and technical growth
The technical feasibility of sustainability does not imply real sustainability. Most of these
models are aimed to show how technological progress can support sustained consumption.
THE ECOLOGICAL ECONOMICS APPROACH
In the ecological economics view, energy is the most important factor of the economy. It is
based on the biophysical foundations of any human activity. Substitution plays a limited role
on compensating scarcity of natural resources. “Increased energy use is the main or only cause
of economic growth”. The whole economic system is assumed as a group of energy fluxes
which defines an creates intermediate productions factors. Other flows such as capital and
labor are maintain and supported by the energy fluxes. Commodities prices are defined by
their embodied energy within them or correlated to the price of energy.
Energy return on investment and economic output
EROI is the energy produced by the energy used for extraction, the higher the better. Fossil
fuels and renewable EROI´s are different in benefit of fossil fuels. “Declining EROI would
threaten not just growth but also the level of output of the economy and, therefore,
sustainability”.
Limits to substitution
Depend on which type of substitution 1) within category of similar production inputs or 2)
between categories. Solow explained that WITHIN substitution is feasible in different energy
sources. However transition in the micro-level is easier, as well as transition after exhaustion.
While for BETWEEN substitution, there are difficulties to measure the elasticities. By empirical
analysis has been found that the elasticity between capital and energy is less than unity.
The thermodynamic limits for substitution can be analyzed easily for individual processes. For
complex system, the these limits are found for elasticities less than unity.
In this respect the Georgescu-Roegen´s fund flows model recognizes three flows of materials
energy and information, transformed by two agents (human labor and manufactured capital).
It implies a low limit for substitution and lack for opportunities to increase substitution.

3. After all, from a macroeconomic view, every activity needs materials and energy. The
elasticities of substitution are higher when there is a less aggregated sector , more difficult at a
macro level1.
Limits to technological change
Knowledge is embodied in the capital accumulated, both manufactured and human. However
“there are still thermodynamic restrictions on the extent to which energy and material flows
can be reduced in this way”
Knowledge is non-rival in use. This implies constant returns to knowledge while other inputs
are under diminishing returns. However knowledge cannot compensate infinitively for the
diminishing returns of the others. In addition, knowledge cannot participate without the other
inputs as well.
SYNTHESIS
(Stern) presents a modified Solow model that tries to explain the long run history of economy.
Based on economic transition therories 1) endogenous technical change approach by Galor
and Weil, and Lucas 2) slow transition by Hansen and Prescott (transition starts when
technological progress its own use profitable)
The difference between England and Netherlands to lead the industrial revolution was the
availability of coal in the UK. First coal decrease its price with respct to the other conventional
fuels. Then innovation was required and industrial revolution came.
The model adds an energy variable that has poor substitutability with K and L, while keeping K-
L substitutability at unity. Then energy can be either a constraint or enabler of economic
growth based on its availability by resources and technological change.
Two augmenting indexes are applied “to labor” and “to energy” which reflect technological
progress, effective supply and quality in both parameters. Materials are ignored so they are
assumed that they can be put together with the energy factor2
RESULTS. At abundant energy, economic growth depends on Solow´s considerations, however
when it is scarce it depends on the energy supply and the energy augmenting index. Another
factor is the price of energy if decreasing economic growth can be boosted, this is also
supported by Ayres an Warr as a major driver.
The low substitutability between energy and the other inputs is explained since if energy
supply were constant it would represent a constraint. Reasons. 1) experiences in Sweden show
how infrastructure act greatly to decrease the effect of energy. 2) it is difficult to differentiate
the energy and labor augmenting factors. 3) ecological economics equilibrium requires a
microeconomic limit of energy for any activity and a macroeconomic limit to compensate for
depreciation.
1
IMPORTANT for small scale economies
2
How, why?

4. Basically, mainstream economics could not be wrong in their approach for developed
countries or assuming energy not scarce. At certain point energy should be risen before it
starts being a constraint. Stern´s model proves to be good at macroscale.
(Ayres and Warr)’s model contrast to stern’s model. Inputs are seen as q-substitutes versus q-
complements. In Stern’s, inputs are q-complements and technical change augments both labor
and energy3.
FACTORS AFFECTING THE LINKAGE
Evidence in several developed economies show decreasing in energy intensity with respect to
GDP growth. This evidence can be related to the concept of the Kuznets curve. To identify the
factors, (Stern, 2011) used a general production frontier with separable output and separable
energy and non-energy inputs.
Note: the production frontier hasn’t explored the effect of energy in more labor-intensive and
in the transition to capital-intensive economy.
Substitutability of energy and capital
“Apostolaskis concluded that capital and energy act more as substitutes in the long run and
more as complements in the short run”. “studies that included capital, labor and energy bu
NOT materials as input indicate substitution, while econometric cost functions that also
include materials indicate complementarity.”
“the micro-level Hicks elasticity of substitution between capital and energy is less than unity,
especially in the short run”. In Kehoe’s model, in the short run there is complementarity in the
long run there is substitutability, based on price
Innovation and energy efficiency
It can be accounted by the autonomous energy efficiency index AEEI, or by an energy
augmenting technical change. “When there is endogenous technological change, changes in
prices may induce technological changes”
Energy-saving technology diffusion with decrease in prices can boast energy-using technology
development. If technical change is energy-using the decrease in prices boasts TFP and vice
versa (Jorgenson4). “Diffusion [of energy using technologies] tends to follow logistic curve with
the speed of diffusion depending on among other things how well the innovation fits into the
existing infrastructure.”
Diffusion of energy efficiency tech could be inefficient over places, time and individuals due to
differences, preferences and technological status, and also due to market failures and
behavioral factors.
“Higher fossil fuels reserves are associated with lower energy efficiency. Energy efficiency
converges over time across countries with growing economies and technological change was
3
Doubtedly happening in real life
4
Not sure which article of Jorgenson

5. the most important factor mitigating the global increase in energy use and carbon emissions
due to economic growth”
The rebound effect
There are 3 microeconomic rebound effects and 2 macroeconomic5
Energy quality and shifts in composition of energy input
Through economic development, the energy mix evolves to increase diversity and quality.
“Energy quality is the relative economic usefulness per heat equivalent unit of difference fuels
and electricity.” Fuels have a number of physical attributes that will affect their relative
qualities, including energy density; power density (rate of heat units produced per unit are per
unit time); ease of distribution; the need for a transfer medium; controllability; amenability to
storage; safety; and environmental impacts142–144. Marginal Product of the Fuel depends on the
attributes above and prices.
There are few studies on energy intensity and GDP. Prices-energy quality and GDP (rather
than energy SUPPLY -GDP) showed less decoupling evidence, however other studies have
shown that there is a larger role of technological progress than for energy composition
changes or reduction in energy intensity.
Shifts in the composition of output
Since industries have different energy intensities, shifts in output alter the relationship
between energy and economic growth. Even service-based industries require large energy
supplies. The example of the internet effect but it is not clear in reducing or increasing energy
intensity. Households have presented increases of energy intensity over time whereas the
manufacturing sector, the opposite. Reduction of energy intensity through shifts in output has
not been followed by most developing countries because of the diffusion of pollution-intensive
industries.
EMPIRICAL TESTING OF CAUSAL RELATIONSHIPS
“Two methods for testing for causality among time-series variables are Granger causality tests
165 and co-integration analysis166 Hendry and Juselius 167.”The first method is the most widely
used.
CONCLUSION
“Energy use and output are tightly coupled with energy availability playing a key role in
enabling growth”
“The elasticity of substitution between energy and capital is likely to be low”
“. The current low price of energy reflects a low marginal productivity because of this heavy
use.”
5
Look at the article

6. “Some research indicates that most of the historical reductions in energy intensity in
developed economies and China have been due to technical change, but other research finds a
much larger role for structural change.”
“Technological change tends to be offset to some degree by the rebound effect”
“there is clearly much scope for further research to clarify the prospects for decoupling energy
use and economic growth and for understanding the role of energy in growth.”
Words: TFP, LINEX production function, output elasticity of labor, backstage technology,
boserupiar response to scarcity.
AYRES, R. U. & WARR, B. 2009. The economic growth engine, Cheltenham, Edward Elgar.
STERN, D. I. 2011. The role of energy in economic growth. Annals of the New York Academy of
Sciences, 1219, 26-51.