The Economic Growth Enigma: Capital, Labour & Useful Energy*

elsevier energy policy coverABSTRACT: In this article we show that the application of flexible semi-parametric statistical techniques enables significant improvements in model fitting of macroeconomic models. As applied to the explanation of the past economic growth (since 1900) in US, UK and Japan, the new results demonstrate quite conclusively the non-linear relationships between capital, labour and useful energy with economic growth. They also indicate that output elasticities of capital, labour and useful energy are extremely variable over time. We suggest that these results confirm the economic intuition that growth since the industrial revolution has been driven largely by declining energy costs due to the discovery and exploitation of relatively inexpensive fossil fuel resources. Implications for the 21st century, which are also discussed briefly by exploring the implications of an ACEGES-based scenario of oil production, are as follows: (a) the provision of adequate and affordable quantities of useful energy as a pre-condition for economic growth and (b) the design of energy systems as `technology incubators’ for a prosperous 21st century.

* From Energy Policy, Elsevier. 13 July 2013.  Vlasios Voudouris, Robert Ayres

 1. Introduction

The standard (Solow) model and the neoclassical theory of economic growth assume that there are only two important `factors of production’ and that energy and other natural resource inputs contribute very little to the economy, because of their negligible role in the national accounts. This contradicts economic intuition. Economic history suggests that increasing natural resource flows have always been a major factor of production, at least since the large scale exploitation of coal resources in the 18th century. Declining costs of energy — in relation to the rising wages of labour —have induced ever-increasing substitution of machine-work (activated by fossil fuels) for human labour (activated by consumption of grains or fruit). This long-term substitution has evidently been a key driver of economic growth [see also Allen, 2009; Wrigley, 2010, for broadly similar discussions].

The `real’ economy can be thought of as an evolving materials-processing system. The system consists of processing stages, starting with extraction, conversion of energy into useful energy, production of finished goods and services, final consumption and disposal of wastes. An adequate description of the economic system must include materials and energy flows as well as money flows.

These flows and conversion processes are governed by the laws of thermodynamics. At each stage, until the last (consumption), mass-exergy (maximum work performed by energy) flows are split into (i) useful energy and (ii) waste energy categories. Value is added to the useful energy flows, reducing their entropy content and increasing their exergy content per unit mass (thanks to exogenous inputs of exergy), while the high entropy (low exergy) wastes are returned to the environment. The important point here is that to properly explore the importance of energy in terms of powering economic growth one should use measures of useful energy rather than measures of energy flows or energy carriers such as barrels of oil.

In view of the assumption by most economists that energy is not a factor of production, the association between primary energy consumption and gross domestic product (GDP) suggests that global energy production is driven by global energy demand, which is driven by global GDP (see Fig. 1). In other words, it is assumed that there are no supply constraints. For purposes of forecasting future energy needs, it follows that a GDP growth forecast, together with a forecast of price and income elasticities, should be sufficient. This is exactly the methodology normally employed in the computable general equilibrium (CGE) models used by the Paris-based IEA (International Energy Agency), the US EIA (Energy Information Administration) and the IMF (Interna­tional Monetary Fund).

The simplest Cobb–Douglas production function (of capital and labour) takes the following mathematical form  . . . . . .

–> Click HERE for full text and graphics. 2013 Elsevier Ltd. All rights reserved


  1. Policy implications for the 21st century

Unlike the argument of neoclassical economists who consider energy as a production factor of only marginal importance, the work presented here provides strong empirical evidences of the importance of energy (more specifically useful energy) to support economic growth. Given the challenging outlook of fossil fuels, the implications of unsustainable or over-realistic energy policies are profound.

By way of an example, Fig. 16 shows one plausible scenario of the world crude oil production (excluding oil shale, heavy oil, extra-heavy oil, deep-water oil and polar oil). The dotted line represents the equilibrium (supply equals demand), while the ‘points’ represent the simulated conventional oil production esti­mated using the ACEGES model. It is clear from the 2-D density that when the demand for crude oil (not total petroleum demand) is below 88 million barrels per day, the market is well supplied (there is spare capacity). However, as the demand for crude oil becomes more than about 95 million barrels per day, crude oil production from conventional resources will not meet the demand.

This means that enhanced production of unconventional oil or a major sift in the transport sector (most of the demand for oil is coming from the transport sector) is required in order to fill the gap between supply and demand – assuming that we want to avoid an unprecedented economic and social crisis during the 21st century. Policies for investment decisions on oil exploration and development are important because oil fuels are a vital part of the economic activities, particularly long-distance transportation of physical commodities and human capital.

Some might argue that gas will be a good substitute for oil to fuel economic growth. This might be the case if there is a significant change in the structure of the aggregate energy demand of the transport sector (e.g., electric cars and gas-fuelled cars). Clearly, gas can be an important energy carrier for industrial processes and electricity generation. Thus, gas is likely to provide useful energy to power (but not necessarily to fuel) economic growth until at least the first half of the 21st century.

However, the plausible existence of adequate gas resources is not enough. Timely investment plans need to be placed in order to adequately supply the market. Thus, there is uncertainty with respect to the upstream investment plans to extract gas at a rate needed to meet the expected increased demand for gas. In our view, investment plans that aim to increase the production capacity of gas by about 5–15% per annum (not dissimilar with the historic growth rates for oil production) is likely to be sufficient to comfortably supply the gas market over the period 2015—2035. Following Stern (2012), this will imply a significantly revised gas pricing `regime’ because the economic and market fundamentals of the gas market of the 21st century will be different compared with the economic and market fundamentals of the gas market of the 20th century (where gas was treated as a `free’ commodity).

Despite the relative inattention to the problems of fossil fuel resource depletion (particularly the relatively inexpensive oil), we argue that it is important to continuously evaluate any foreseeable collision between increasing consumption of useful energy and the finite energy resources of the planet. Although technology and market economics are likely to find solution to difficult problems (with significant social cost when rapid adjustments are required), the idea of the limits to growth because of declining `useful energy return’ on `useful energy investment’ should be given proper attention in policy agendas, assuming that energy policies aim is to design energy systems capable of fuelling and powering a prosperous 21st century.

  1. Conclusions

As a way of addressing the economic growth enigma, we re­examined the argument of the importance of useful energy by employing the power of modern statistical techniques and meth­ods. By examining the economic growth of UK, Japan and US during the 20th century, we demonstrate quite conclusively non­linear relationships between capital, labour and useful energy with economic growth.

Without calling on sophisticated theorems of aggregation, we postulate a generalised production function with three factors of production, namely capital, labour and useful energy. Furthermore, the proposed generalised production function also introduces the modification that the coefficients of the three production factors need not be constant over time. The use of flexible distributions to capture the `unexplained rest’ of economic growth is also proposed.

We argue that the empirical results presented in Section 4.2 confirm the economic intuition that growth since the industrial revolution has been driven largely by the increased stock of capital and the adequate supply of useful energy due to the discovery and exploitation of relatively inexpensive fossil fuels. Thus energy policies need to continuously explore the existence of plausible signs of collision between increasing consumption of useful energy and the finite energy resources of the planet.

We have also noted the relative association between capital development and increased use of useful energy. Clearly, the empirical evidence reported here needs to be `validated’ with respect to additional countries and/or time periods. Having said that Allen (2009) and Wrigley (2010) present broadly similar conclusions with respect to the English industrial revolution. Thus, history might provide a degree of policy recommendations for the 21st century given primarily the challenging outlook of `inexpen­sive’ crude oil production. As we move forward, it is important to look at the smooth transition of the energy system (plausibly with gas and renewables as key energy carriers to power economies) in order to:

  • Provide adequate and affordable quantities of useful energy.
  • Act as `technology incubators’ for a prosperous 21st century.

To conclude, the generalised production function of Eq. (3) is more flexible compared with the conventional (parametric) pro­duction function in several ways, but mainly in that it does not assume a specific parametric functional form for the factors of production, while providing better fits to the data than the standard parametric production function. The ability to take into account flexible parametric distributions with long tails — reflect­ing the fact that improbable events can have large impacts — is especially valuable, given that fluctuations from a central trend are not really Gaussian random processes. Having said that the practical significance of our results starts with the fact that useful energy is an important factor of production.

This means that future economic growth presupposes the availability of increasing quan­tities of useful energy. Hence, traditional computable general equilibrium models make unwarranted assumptions e.g. that the economy grows in equilibrium, and that growth is driven only by the accumulation of capital per worker. If the latter were true, the economy would continue to grow regardless of the cost of energy or (more precisely) the declining `useful energy return’ on `useful energy investment’. We also note that the proposed generalised production function of Eq. (3) reduces to the Cobb—Douglas form — additive in the logarithms — in the limit, whereas other forms, such as the LINEX function of ratios of the variables, are possible. It remains for future research to determine whether other (non-additive) forms are preferable.

From a policy perspective, the major conclusion is quite simple that an increasing supply of affordable useful energy is a precondition for continued growth. Taking the climate change problem seriously, it means that extra­ordinary efforts will be needed to increase the efficiency (e.g., strengthened automobile fuel-efficiency standards), and to increase the output of renewables and nuclear power safely, while sustainably phasing out fossil fuels (particularly coal).

—> Click HERE for full text and graphics. 2013 Elsevier Ltd. All rights reserved

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About the authors:

Vlasios VoudourisDr. Vlasios Voudouris is CEO of ABM Analytics Ltd. He is Affiliate Professor (energy & commodities) at ESCP Europe’s London campus, where he contributes to the Research Centre for Energy Management (RCEM), teaches on the Master in Energy Management and various Executive programmes. He is European Academic Director of the Executive Master in Energy Management. He is best known for his work on agent-based, fundamentally driven models that focus on energy & commodities market dynamics to support risk-adjusted investments decisions.


robert-ayresRobert Ayres’s career has focused on the application of physical ideas, especially the laws of thermodynamics, to economics; a long-standing pioneering interest in material flows and transformations (Industrial Ecology or Industrial Metabolism); and most recently to challenging long-held ideas on the economic theory of growth.


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