انیگما رشد اقتصادی: سرمایه، نیروی کار و انرژی مفید؟

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.

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).where Yt is the GDP, Kt is the stock of capital and Lt is the stock of labour, while parameters αα and ββ are constants. Following Solow, 1956 and Solow, 1957, At has been interpreted as the effect of ‘technical progress’ (now called total factor productivity – TFP), which effectively captures the ‘unexplained rest’ (or the total economic output not caused by capital and labour). Eq. (1) may also assume that α+β=1α+β=1 in order to assure constant returns to scale – doubling capital and labour will also double economic output. Eq. (1) has the convenient mathematical property that output elasticities (logarithmic derivatives) of the two factors of production Kt and Lt are just the constants αα and ββ. Therefore, if we assume perfect competition and α+β=1α+β=1, αα and ββ can be shown to be labour and capital's (constant) share of economic output respectively. A theorem taught in macro-economic textbooks postulates a simple economy consisting of many small (price-taking) competing firms producing a single product – such as GDP – from rented capital and rented labour (which are freely substitutable). Then the equilibrium or profit maximising condition requires that total factor requirements must be determined by the marginal productivities of labour and capital. The marginal productivities are the wage rate and the profit rate. Hence, the total payments to labour must be equal to the wage rate times the quantity of labour employed and the total payments to capital must be equal to the profit rate times the quantity of capital employed. In short, the output elasticity of each production factor Kt and Lt must be equal to its cost share in the economic output Yt, which is equal to the sum total of wages and profits, respectively. Using standard data series for labour and capital, as Solow did in his early work, explains only a small fraction (ca. 15%) of economic growth. The usual approach is to assume a convenient exponential form for At, with a constant annual growth rate of around 2% per annum. This implies that economic growth in the future can be assumed to continue, as in the past. This leaves most of the economic growth on the order of 85%, unexplained. A considerable amount of research effort has been expended on trying to reduce the unexplained residual At by introducing quality adjustments to labour and capital. Certainly education and increasing literacy (and numeracy) would be a quality adjustment for labour, while technical performance improvements should also be taken into account for capital goods. Unfortunately none of the proposed adjustments suffice to explain the missing driver. As an alternative to quality adjustments, we replace the exogenous multiplier At by including a third factor of production. Useful energy is not perfectly substitutable for the other two production factors. In effect, we exclude the possibility of producing output from capital alone, or from labour alone, or from useful energy alone. While none of the three factors are a perfect substitute for either of the others, some substitution is possible at the margin. But the range of substitutability is quite limited in reality. The standard Euler–Lagrange optimization procedure, subject to a mathematical constraint on the possible relationships among the factors, introduces the so-called Lagrange multipliers, i.e. ‘shadow prices’ of the constraints. If the constraints are not binding, the shadow prices will be zero, in which case the cost share theorem will still hold as if there were no constraints. But what if substitutability between the factors is much more limited than most economists assume? If this is so then the output elasticity of useful energy must be much larger than its cost share (as normally calculated as revenues of energy companies). If the output elasticity of useful energy is greater than its cost share, it follows that energy is really more productive than its price suggests. In other words, useful energy is under-priced. In that case, the optimum (profit-maximizing) consumption of useful energy in the economy is actually larger than current consumption. Can this possibly be true? Most economists will say ‘no’ because otherwise the traditional cost-share theorem must be discarded. In fact, there is plenty of empirical evidence that firms actually use too much useful energy, rather than too little (this is consistent with under-pricing). Firms consistently neglect cost-saving investments in energy conservation, with very high returns, in favour of investments in marketing, new products or capacity expansion. Governments and consumers behave in roughly the same way, preferring to spend on current consumption rather than investment in future cost savings. However, the fact that many firms use more useful energy than they could does not mean that the national economy could not be more productive (by using more capital and less labour where substitution is possible). Does this mean that useful energy can be neglected as a factor of production? We think not. Instead, we argue below that economic activity – and growth – cannot occur without useful energy Et. Given that the “useful energy return” on “useful energy investment” is declining, policy implications are profound for a sustainable economic growth during the 21st century. Following Ayres and Warr (2009) and Hall and Klitgaard (2012), we explore the importance of the flow of useful energy in supporting the economic growth of US, UK and Japan during the 20th century using modern tools of statistical inference. As explained above, we take useful energy to be an important production factor. Given the importance of fossil fuels to fuel economic activities with useful energy during the 20th century, we use the ACEGES tool, first proposed by Voudouris (2011) and demonstrated by Voudouris et al. (2012), to explore briefly the implications of oil (and gas) production outlook to fuel (and power) economic growth during the 21st century.

As a way of addressing the economic growth enigma, we re-examined 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 non-linear 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 extra-ordinary 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).