Nội dung

ACCOUNTING FOR GROWTH: THE ROLE OF PHYSICAL WORK Robert U Ayres & Benjamin Warr1 Center for the Management of Environmental Resources INSEAD Fontainebleau, France Email: robert.ayres@insead.edu Abstract This paper tests several related hypothesis for explaining US economic growth since 1900. It begins from the belief that consumption of natural resources – especially energy (or, more precisely, exergy) — has been, and still is, an important factor of production and driver of economic growth. However the major result of the paper is that it is not `raw’ energy (exergy) as an input, but exergy converted to useful (physical) work that – along with capital and (human) labor – really explains output and drives long-term economic growth. We develop a formal model (Resource-EXergy Service or REXS) based on these ideas. Using this model we demonstrate first that, if raw energy inputs are included with capital and labor in a CobbDouglas or any other production function satisfying the Euler (constant returns) condition, the 100-year growth history of the US cannot be explained without introducing an exogenous `technical progress’ multiplier (the Solow residual) to explain most of the growth. However, if we replace raw energy as an input by `useful work’ (the sum total of all types of physical work by animals, prime movers and heat transfer systems) as a factor of production, the historical growth path of the US is reproduced with high accuracy from 1900 until the mid 1970s, without any residual except during brief periods of economic dislocation, and with fairly high accuracy since then. (There are indications that an additional factor, possibly information technology, needs to be taken into account as a fourth input factor since the 1970s.) Various hypotheses for explaining the latest period are discussed briefly, along with future implications. R. U. Ayres & B. Warr Accounting for growth: the role of physical work Page 1 1. Introduction The primary motivation of this paper is to revisit the neoclassical theory of growth from the physical (thermodynamic) perspective. The `standard’ growth theory, which was formulated in its current production function form (independently) by Robert Solow and Trevor Swan [Solow 1956; Swan 1956; Solow 1957]. The standard theory assumes that production of goods and services (in monetary terms) can be expressed as a function of capital and labor, yet the major contribution to growth had to be attributed to an unexplained exogenous driver called `technological progress’. Both casual observation and physical intuition have convinced many investigators since Georgescu-Roegen first expounded on the subject, that production in the real world cannot be understood without taking into account the role of materials and energy [Georgescu-Roegen 1971]. Our primary objective in this paper is to elaborate and quantify this intuition – which we share – and to simultaneously endogenize `technological progress’, insofar as possible. A further, though secondary, objective is to clarify the differences between our current approach and the several earlier attempts to incorporate resource flows explicitly into growth models [Jorgenson and Houthakker 1973; Allen et al 1976; Hannon and Joyce 1981; Jorgenson 1983; Jorgenson 1984]. We attempt to explain, hereafter, why the several earlier attempts did not succeed and how – and why – the present approach differs from earlier ones. Before passing on, we also emphasize that several features of our work follow (albeit indirectly) from our concept of growth dynamics as a positive feedback cycle. This may not seem immediately relevant to our main results. But it is relevant to some of the choices we make later in formalizing the growth model. The generic positive feedback cycle, in economics, operates as follows: cheaper resource inputs, due to discoveries, economies of scale and experience (or learning-by-doing) enable tangible goods and intangible services to be produced and delivered at ever lower cost. This is another way of saying that resource flows are productive, which is our point of departure. Lower cost, in competitive markets, translates into lower prices for all products and services. Thanks to non-zero price elasticity, lower prices encourage higher demand. Since demand for final goods and services necessarily corresponds to the sum of factor payments, most of which go back to labor as wages and salaries, it follows that wages of labor tend to increase as output rises.2 This, in turn, stimulates the further substitution of natural resources, especially fossil fuels, and mechanical power produced from resource inputs, for human (and animal) labor. This continuing substitution drives further increases in scale, experience, learning and still lower costs. Based on both qualitative and quantitative evidence, the existence of the positive feedback cycle sketched briefly above implies that physical resource flows must be a major factor of production. Indeed, including a fossil energy flow proxy in the neoclassical production function, without any constraint on factor share, seems to account for economic growth quite accurately, at least for limited time periods, without any exogenous time-dependent term [Hannon and Joyce 1981; Kümmel 1982b; Cleveland et al 1984; Kümmel et al 1985; Kümmel 1989; Kaufmann 1992; Beaudreau 1998; Cleveland et al 1998; Kümmel et al 2000]. It is important to note, however, that including energy or exergy as a factor of production does not explain economic growth for periods longer than two or three decades, without recalibration or R. U. Ayres & B. Warr Accounting for growth: the role of physical work Page 2 without a time dependent multiplier.3 The reason for this (negative) empirical result becomes clear hereafter. The fact that economic growth tends to be very closely correlated with energy consumption, at least for short periods does not a priori mean that energy consumption is the cause of the growth. Indeed, many economic growth models still assume exactly the opposite: that economic growth (due to accumulation of capital, and labor, plus technical progress) is responsible for increasing energy and natural resource consumption. This automatically explains (indeed, guarantees) high correlation. We argue, on the contrary, that declining resource prices can have a direct impact on growth, via the positive feedback loop. The direction of causality must evidently be determined empirically by other means, either theory based or empirical. 4 The major new feature of our approach is that, in contrast to earlier treatments that introduced (commercial) energy(exergy), or energy(exergy) and materials separately, as factors of production, we consider physical work (or `exergy services’) as the appropriate independent variable for the production function. The term exergy is introduced and explained in section 2 which follows. It is important to emphasize here that physical work is a well-defined concept from thermodynamics and physics; it must be distinguished from the term as it is used in ordinary language, where `work’ is generally what people do to earn a living. The relationship between potential work (exergy) and actual work – or exergy services – performed in the economy is explained in Section 3. In brief, the ratio of actual work to potential work can be interpreted as the thermodynamic efficiency with which the economy converts resource inputs into finished materials and services. To avoid confusion, it is important to note that term `thermodynamic efficiency’, introduced above, is not related to economic efficiency. Thermodynamic efficiency is a straightforward ratio between (physical work) output and resource input. As will be seen, both numerator and denominator are measured in the same physical units (e.g. gigajoules or GJ). Moreover, we are able to estimate both inputs and outputs, and the resulting ratio, with reasonable accuracy, from published empirical data. (See Sections 2 and 3). Introducing an additional factor creates certain conceptual problems that we must acknowledge from the outset. Suppose we had opted (as some modelers have) to choose exergy inputs as a factor of production, measured in monetary terms. Payments for fossil fuels, minerals, ores, farm products and other forms of `raw’ exergy inputs are actually payments for `produced’ outputs of the extractive industries, agriculture and forest products sectors. By convention, all of these are intermediates, accounting for a very small percentage of GDP, – perhaps 4% without agriculture and less than 10% even if agriculture is included. Evidently, electric power, motive power, space heat and industrial heat are also produced outputs. Of course, some capital and labor are required to produce these intermediate products. However, among these exergy services only electric power is regarded as a commodity produced and sold by a well-defined industrial sector for which financial accounts are kept. Motive power is produced and consumed (mostly) within the agriculture, transportation and construction sectors, while heat is produced and consumed within many other sectors, including households. They are not regarded as (or, accounted for) commodities, and they do not have explicit market prices. If shadow prices for these kinds of exergy services (useful work) were available, it is likely that the corresponding payments would account – in toto – for a considerably greater share of the US GDP. But, needless to say, capital and labor, as well as R. U. Ayres & B. Warr Accounting for growth: the role of physical work Page 3 inputs from the extractive and farming sectors, are also required to produce these intermediates, just as they, in turn, are required to produce other goods and services. In short, to introduce either `raw’exergy or exergy services as a third factor of production also forces us to think in terms of a multi-sector input-output structure with inter-industry feedbacks. The two choices (exergy or exergy services) differ only in the magnitudes of the feedbacks from downstream products and services back to extraction and primary processing. At first glance this might argue against introducing either of them as a third factor. Note that capital goods are also produced intermediates. The inputs to capital goods production are – again – capital, labor and other intermediates (including exergy and/or exergy services.) The key conceptual difference is that capital goods and labor are not consumed in the production process5 (although depreciation is almost a form of consumption), whence they are cumulable, and capital and labor services are proportional to the corresponding stocks. On the other hand, resource (exergy) flows, or exergy service flows, are not cumulable; they are consumed immediately in the production process. Furthermore, thanks to cumulability, capital services and labor services can be – within limits – regarded as independent variables in the sense of being independent of current economic conditions (i.e. demand vis a vis potential supply). Of course, the true relationship between capital and output is one of mutual dependence, but with a time lag between the output level and the stock levels. It takes a few years for capital stocks to respond to current economic conditions via the price mechanism. The potential labor supply responds through demographic feedbacks over an even longer time frame, whence adjustment of current labor supply occurs mainly through the political process (i.e. laws regarding minimum schooling requirements, retirement ages, work-weeks, immigration, and so on). On the other hand, both resource (exergy) consumption, and exergy service (useful work) consumption levels respond rather quickly to economic conditions (via prices), whereas the forward impact of changes in prices on demand – up or down – driven by technological improvements and/or resource scarcity lags by several years.. Having acknowledged these points, the question arises: do they, taken together, preclude the use of exergy flows or exergy service flows as inputs to a formal production function? We think that the answer is `no’. We argue (Section 4) that the economic system should be understood as a sequential materials processing system, converting raw materials (and fuels) by stages into final products and services. The existence of (possibly lagged) feedbacks from downstream sectors to upstream sectors is understood. Capital services constitute one such lagged feedback. Exergy services can be regarded as a generic intermediate with both feedback and feed-forward. Whether it has explanatory power is then an empirical question. Section 5 presents the formal Resource-EXergy Service (REXS) model, which is mainly defined by a choice of variables and production function. Section 6 presents the main results and Section 7 summarizes and discusses further implications. R. U. Ayres & B. Warr Accounting for growth: the role of physical work Page 4 2. The role of natural resources and energy (exergy) An obvious implication of economic history – and one that is consistent with our view of growth dynamics as a feedback cycle – it that important `engine of growth’ since the first industrial revolution has been the continuously declining real price of physical resources, especially energy (and power) delivered at a point of use. The tendency of virtually all raw material and fuel costs to decline over time (lumber was the main exception) has been thoroughly documented, especially by economists at Resources For the Future (RFF) [Barnett and Morse 1962; Potter and Christy 1968; Smith and Krutilla 1979]. The increasing availability of energy from fossil fuels, and power from steam engines and internal combustion engines (ICEs), has clearly played a fundamental role in past economic growth. Machines powered by fossil energy have gradually displaced animals, wind power, water power and human muscles and thus made human workers vastly more productive than they would otherwise have been. There is no dispute among economists on this point. The term energy as used above, and in most discussions (including the economics literature) is actually technically incorrect. The reason is that energy is conserved in every activity or process and therefore cannot be `used up’ – as most common usages of the term imply. But energy is not necessarily available to do useful work. The standard textbook example is the heat energy in the ocean water, virtually none of which can be utilized fordoing useful work. As was discovered nearly two centuries ago by the French engineer Sadi Carnot, heat can only be converted into useful work if there is a temperature gradient. Absolute temperature does not matter. It is the temperature difference between two reservoirs that determines the amount of work that can be extracted by a so-called heat engine. By the same token, it is the temperature difference between the sun and the earth that drives most natural processes on earth, including the weather and photosynthesis. Exergy is the correct thermodynamic term for `available energy’ or `useful energy’, or energy capable of performing mechanical, chemical or thermal work. The distinction is theoretically important because energy is a conserved quantity: this is the famous first law of thermodynamics. Energy is not `used up’ in physical processes, it is merely degraded from available to less and less available forms. On the other hand, exergy is dissipated (used and destroyed) in all transformation processes. The measure of exergy destruction is the production of a thermodynamic quantity called entropy (second law of thermodynamics). The formal definition of exergy is the maximum work that could theoretically be done by a system as it approaches thermodynamic equilibrium with its surroundings, reversibly. Thus exergy is effectively equivalent to potential work. There is an important distinction between potential work and actual work done by animals or machines. The conversion efficiency between exergy (potential work), as an input, and actual work done, as an output, is also an important concept in thermodynamics. The notion of thermodynamic efficiency plays a key role in this paper. To summarize: the technical definition of exergy is the maximum work that a subsystem can do as it approaches thermodynamic equilibrium (reversibly) with its surroundings. Exergy is also measured in energy units, and exergy values are very nearly the same as enthalpy (heating values) for all ordinary fuels. So, effectively, it is what most people mean when they speak of `energy’,The major exception to this rule is that exergy is a measure that is applicable, and can R. U. Ayres & B. Warr Accounting for growth: the role of physical work Page 5 be estimated with acceptable accuracy, not only for traditional fuels but to all agricultural products and industrial materials, including minerals. This point is important because it enables us to construct an aggregate measure of all resource flows into the economic system, as well as an aggregate measure of all processed intermediate flows. We have tabulated and published exergy values per kg for most common materials and mixtures (such as ores) in [Ayres and Ayres 1999a]. See Appendix A of this paper for more details.. 3. Physical work and thermodynamic conversion efficiency As noted above, exergy is equivalent to maximum potential work. There are several kinds of work, including mechanical work, electrical work and chemical work. For non-engineers, mechanical work can be exemplified in a variety of ways, such as lifting a weight against gravity or compressing a fluid. The term horsepower was introduced in the context of horses pumping water from flooded 18th century British coal and tin mines. A more general definition of work is movement against a potential gradient (or resistance) of some sort. A heat engine is a mechanical device to perform work from heat (though not all work is performed by heat engines.) With this in mind, we can subdivide work into three broad categories, as follows: work done by animal (or human) muscles, work done by heat engines or water or wind turbines and work done in other ways (e.g. thermal or chemical work). Mechanical work can be further subdivided into work done to generate electric power and work done to provide motive power (e.g. to drive motor vehicles.) The power sources in this case are so-called `prime movers’, including all kinds of internal and external combustion engines, from steam turbines to jet engines. So called `renewables, including hydraulic, nuclear, wind and solar power sources for electric power generation are conventionally included. However electric motors are not prime movers, because electricity is generated by some other prime mover, usually a steam or gas turbine. In fact, electricity can be defined (for purposes of this paper) as `pure’ work. Chemical work is exemplified by the reduction of metal ores to obtain the pure metal, or indeed to drive any endothermic chemical synthesis process. (Ammonia synthesis is a good example.) Thermal work is exemplified by the transfer of heat from its point of origin (e.g. a furnace) to its point of use, via one or more heat exchangers and a carrier (such as steam, hot water or hot air.). To measure the useful work U done by the economy, in practice, it is helpful to classify fuels by use. The first category is muscle work, for which the fuel is food or feed.. In the US, human muscle work was quantitatively insignificant by 1900 and can be neglected. Horses and mules, which accounted for most animal work on US farms and urban transport, have not changed significantly since then. Animal work was still significant up to the 1930s but mechanical and electrical work have since become far more important. The thermodynamic efficiency with which horses and mules convert feed energy to useful work is generally reckoned at about 4% (i.e. one unit of work requires 25 units of feed). The second category is fuel used by prime movers to do mechanical work. This consists of fuel used by electric power generation equipment and fuel used by mobile power sources such as motor vehicles, aircraft and so on. As regards mobile power sources, we define thermodynamic efficiency in terms of useful work performed by the whole vehicle, against air resistance and rolling resistance of the wheels on the road, not just work done by the engine R. U. Ayres & B. Warr Accounting for growth: the role of physical work Page 6 itself. Thus the efficiency of an automobile is the ratio of work done by the vehicle to the total potential work (exergy content) of the fuel. The third broad category is fuel used to generate heat as such, either for industry (process heat to do chemical work) or space heat and domestic uses such as washing and cooking. The efficiency, in this case, refers to the delivery system. Lighting can be thought of as a special case of heating 35% High temperature industrial heat Medium temperature heat Low temperature space heat 30% Electric power generation & distribution Exergy conversion efficiencies Other mechanical work 25% 20% 15% 10% 5% 0% 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 year Figure 1: Energy (exergy) conversion efficiencies, USA 1900-1998 Clearly, the efficiency of muscles as energy convertors has not changed during human history. But the conversion efficiency of heat engines, domestic and commercial heating systems and industrial thermal processes has increased significantly over the past 100 years. We have plotted these increasing conversion efficiencies, from 1900 to 1998 in Figure 1. (Detailed derivations of these curves involve extensive reviews of the engineering literature and technological history. Details, including data sources, can be found in another publication [Ayres and Warr 2003]. Electrical work output is measured directly in kilowatt-hours (kwh) generated. Data are published by the US Federal Power Commission and the US Department of Energy (see Appendix A). Other types of work must be estimated from fuel inputs, multiplied by conversion efficiencies, as shown in Figure 1, over time. Allocations of fossil fuel exergy inputs to the economy by type of work are shown in Figure 2. Electrification has been perhaps the single most important source of useful work for production of goods and services, and (as will be seen R. U. Ayres & B. Warr Accounting for growth: the role of physical work Page 7 later) the most important single driver of economic growth during the twentieth century. The fuel exergy required to generate a kilowatt-hour of electric power has decreased by a factor of ten during the past century. This implies that the thermodynamic efficiency of conversion increased over that period by the same factor, as shown in Figure 2. 90% Percent of total fossil fuel exergy 80% 70% 60% HEAT ELECTRICITY 50% OTHER PRIME MOVERS NON-FUEL 40% 30% 20% 10% 0% 1910 1920 1930 1940 1950 year 1960 1970 1980 1990 2000 Figure 2: Fossil fuel consumption exergy allocation, USA 1900-1998 Electricity prices fell correspondingly, especially during the first half of the century. However, the consumption of electricity in the US has increased over the same period by a factor of more than 1300, as shown in Figure 3. (This exemplifies the positive feedback economic `growth engine’ discussed briefly in the introduction.) R. U. Ayres & B. Warr Accounting for growth: the role of physical work Page 8 1300 LEFT SCALE = electricity prices (cents/kWh) 160 historical non-industrial historical industrial historical all users 1100 1000 120 RIGHT SCALE = index of demand for electricity 900 (1902 = 1) 800 100 700 80 600 500 60 index cents per kWH (constant 1992 $) 140 1200 residential commercial other industrial all users 400 40 300 200 20 100 0 0 1900 1920 1940 Data sources: 1960-1998: Annual Energy Review Table 8.13 year 1960 1980 2000 1907-1970: Historical Statistics: Vol 1, Series S116,118, 119 Figure 3: Electricity prices and electrical demand, USA 1900-1998 4. Towards a new theory of production and growth Before proceeding further, it is important to mention one of the key assumptions of the standard theory, as set forth by Robert Solow, namely that marginal factor productivity can safely be equated with factor share in the national accounts. This simplistic assumption is particularly convenient for models based on Cobb-Douglas production functions. It is built into virtually all textbook discussions of growth theory, since the implications for labor and capital (marginal) productivity are easily derived . Labor gets the lion’s share of payments in the US national accounts, around 70 percent. Capital (defined as interest, dividends, rents and royalties) gets all of the rest, because all payments are attributable to one category or the other, by definition. The figures vary slightly from year to year, but they have been relatively stable for the past century or more. It follows that marginal labor productivity should be around 0.7 and marginal capital productivity should be around 0.3 in a Cobb-Douglas framework. Payments to extractive resource owners (excluding farms) are hidden in the capital accounts, and they constitute a very small proportion– perhaps 3-4 percent – of GDP. This implies that resource productivity must be correspondingly small in comparison with labor or capital productivity. This has been a major source of confusion and misdirected effort in the past. We reject this simple assumption (along with most modern modelers) on the basis of two arguments. The first follows from our view of the growth process as a positive feedback cycle, R. U. Ayres & B. Warr Accounting for growth: the role of physical work Page 9 as discussed previously. This implies that resource (exergy) flows – or, more precisely, declining resource prices – are not simply a consequence of growth. They are also (and simultaneously) a cause of growth. This means that the marginal productivity of resource flows should not be quantitatively insignificant compared to the marginal productivities of other factors. Nor should it be constant over a long period of time. There is an apparent inconsistency between very small factor payments directly attributable to physical resources – especially fossil fuels – and the obvious importance of energy (exergy) as a factor of production. The second argument, which is more rigorous, is based on the fact that the identification of marginal factor productivities with factor shares in the national accounts is based on an oversimplification of the neoclassical theory of optimal income allocation. If labor and capital are the only two factors of production, neoclassical theory implies that the productivity of a factor of production must be proportional to the share of that factor in the national income. This proposition is quite easy to prove in a hypothetical single sector economy consisting of a large number of producers manufacturing a single all-purpose good using only labor and capital services.(The textbook example is usually bread, produced by bakeries that produce bread from capital and labor, but without any inputs of flour or fuel [Mankiw 1997].) The supposed link between factor payments and factor productivities gives the national accounts a direct and fundamental (but spurious) role in production theory. In reality, however, (as noted in the introduction) the economy produces final products from a chain of intermediates, not directly from raw materials or, still less, from labor and capital without material inputs. In the simple single sector model used to `prove’ the relationship between factor productivity and factor payments, this crucial fact is neglected. Allowing for the omission of intermediates (by introducing even a two-sector or three-sector production process) the picture changes completely. In effect, downstream value-added stages act as productivity multipliers. This enables a factor receiving a very small share of the national income directly, to contribute a much larger effective share of the value of aggregate production, i.e. to be much more productive than its share of overall labor and capital would seem to imply if the simple theory of income allocation were applicable [Ayres 2001a]. Our rejection of the simplistic identification of marginal productivities with factor shares has two consequences. One is that we are free to depart from the Cobb-Douglas strait-jacket. The other is that we must determine the parameters of the chosen production function by means of statistical fitting procedures. These issues are discussed in the next section. For clarity in further discussion, we use the conventional terminology L for human labor, as indexed to man-hours employed, and K for produced capital (a construct of accumulated investment less depreciation), as compiled and published by the Bureau of Economic Analysis in the US Department of Commerce. We use the symbol E for the energy inputs to the economy, as traditionally defined and compiled by the US Department of Energy. This consists of the heat (actually, enthalpy) content of fossil fuels and fuelwood, plus the nuclear heat used as an input to nuclear electric power generation, and the energy of flowing water harnessed for purposes of hydro-electric power production, plus small contributions from wind and solar heat. This variable has been used many times in the economics literature. We use the symbol B for exergy inputs to the economy, which include the items above –all of which are potential (but not actually performed) work –plus the potential work embodied in non-fuel wood and agricultural products and non-fuel minerals, such as sulfide ores. In