یک مدل رشد درونزا با تجسم تغییرات فنی صرفه جویی در انرژی

In this paper, we extend the Romer [Journal of Political Economy 98 (Part 2) (1990) S271] model in two ways. First we include energy consumption of intermediates. Second, intermediates become heterogeneous due to endogenous energy-saving technical change. We show that the resulting model can still generate steady state growth, but the growth rate depends negatively on the growth of real energy prices. The reason is that real energy price rises will lower the profitability of using new intermediate goods, and hence, the profitability of doing research, and therefore have a negative impact on growth. We also show that the introduction of an energy tax that is recycled in the form of an R&D subsidy may increase growth. We conclude that in order to have energy efficiency growth and output growth under rising real energy prices, a combination of R&D and energy policy is called for.

Steady state economic growth requires a corresponding growth of energy consumption, unless the energy efficiency of production grows faster than output itself.1 The last 30 years or so have indeed shown a significant growth of the energy efficiency of production. A striking example in this respect is Japan.2 During the period 1955–1973, Japan’s manufacturing industry enjoyed an average annual growth rate of 13.3%, which was supported by a stable supply of cheap energy, growing at 12.9% per year (the annual increase in rate of energy efficiency was only 0.4% in that period). In the Seventies, however, the world economy experienced two big energy-price shocks, and policy makers in Japan had to take strict measures to increase energy efficiency. They were very successful indeed, since Japan’s manufacturing industry grew at 3% per year on average during the years 1974–1994, while its energy consumption declined by 0.4% (hence, energy efficiency increased by 3.4%). The key to this miracle was energy-saving technological change through the development and production of more energy-efficient products. Although the influence of energy on growth has been a popular topic in ‘old’ growth theory, mainly in the context of exhaustible resources,3 in ‘new’ growth theory energy consumption has so far not been a serious issue, although there are some exceptions (Aghion and Howitt, 1998 and Smulders and de Nooij, 2001). Energy-economy modellers, on the other hand, have shown a renewed interest in the relationship between energy use and technology, mainly in the form of induced technological change (henceforth, ITC).4 Their main research question has been whether price shocks and policy changes induce the development of energy-saving technologies. For example, Newell et al. (1999) have empirically tested the induced innovation hypothesis at the product level, using a dataset on consumer durables. They did indeed find evidence that the energy efficiency of these durables had increased in response to rising energy prices and government regulations, besides autonomous overall technological change. Popp (2001) has addressed the ITC question at the aggregate level by relating U.S. patent data from 1970 to 1994 to changes in energy-prices. He finds that there is a strong positive impact of energy prices on technological change. The ITC idea has been quickly assimilated in environment-economy models.5 Not only because induced innovations are a reality to be taken into account, and certainly so in the long term, but also because induced energy-saving technical change makes for less gloomy growth prospects from an energy consumption perspective. The reason for the latter is that if price changes induce energy-saving technological change, then policies that raise the user price of energy (e.g. environmental taxes and regulations) may help pollution abatement, while the negative impacts of higher energy prices on the growth of an economy may in part be overcome through induced energy-saving technological change. Recent studies nonetheless showed that that ‘wish’ is hard to realise. Two recent examples are Goulder and Schneider (1999) and Nordhaus (2002). The numerical model of Goulder and Schneider (1999) show that a carbon-tax may stimulate research in alternative energy industries. Such a tax however may discourage R&D by non-energy industries and by carbon-based energy industries. The reduction in the latter industries may even slow down their output growth, and hence, the overall growth of economy. Nordhaus (2002) compares the implications of policy changes in two different set-ups: in the basic model increases in the price of carbon energy relative to other inputs induce users to purchase more fuel-efficient equipment or employ less-energy-intensive products and services. In the modified model a rise in the price of carbon energy induces firms to develop new processes and products that are less carbon intensive than existing products. Nordhaus (2002) concludes that substitution (of other factors for energy) is a powerful factor that may even surpass ITC in implementing climate-change policies. Nordhaus (2002) also stresses the main shortcoming of a purely ITC oriented analysis: “the investments in inventive activity are too small to make a major difference (…). R&D is about 2% of output in the energy sector, while conventional investment is close to 30% of output. Even with supernormal returns, the small fraction devoted to research is unlikely to outweigh other investment” (Nordhaus, 2002, p. 284). But it is not only R&D in the energy sector itself that will be influenced by profit incentives arising from rising real energy prices. Indeed, a macro perspective regarding the consumption of energy as part of the macro-economic production process and its relation with R&D efforts that are driven by economic incentives may be a far better starting point for the analysis of the effects of incentive driven technological change in environment-economy models. And if one is interested in the effectiveness of energy policy measures and their impact on long term growth, then new growth theory seems to be the logical point of departure. The preoccupation of new growth theorists with steady state growth situations actually takes the sustainability of the steady state for granted, even though this has been a hotly debated issue from the Seventies until now (Meadows et al., 1972 started this debate, while Lomborg, 2001 is the latest contribution, but many others have contributed too). And although new growth theorists have successfully addressed the problem of endogenising growth by linking growth performance to (Schumpeterian) profit incentives, they have also continued to neglect the fact that equally endogenous energy-saving technical change will be necessary to make these growth paths sustainable in practice. Our contribution to the discussion on endogenous growth then lies in the incorporation of energy as an explicit factor of production in an endogenous growth model based on Romer (1990). There are other influential studies in endogenous growth literature than Romer (1990), though. Lucas (1988), Grossman and Helpman (1991) and Aghion and Howitt (1992) are the most important contributors. But we ‘borrow’ the Romer (1990) model, because it allows us to use the idea of embodiment of technical change as in traditional (putty–putty) vintage modelling. For, technical change pertaining to the energy efficiency of production must largely be embodied in new machinery and equipment. This implies that the rate of investment in physical capital is instrumental in realising the potential energy efficiency improvements based on the accumulation of new knowledge: the macro-economic budget constraint is not only constraining the accumulation of capital in volume terms, but also the rate at which the energy efficiency of production at the aggregate level changes. In the context of the Romer (1990) model, this implies that we will allow firms to use intermediate factors of production that incorporate the latest technological developments with respect to the energy consumption characteristics of these intermediates. By doing so, we break the symmetry between intermediates present in Romer’s original model.6 Because of this symmetry, technical change in the original Romer model merely increases the number of all intermediate goods used in producing output. But by doing so, technical change also provides opportunities for the division of production tasks between intermediates, thus, raising the productivity of all factors as a whole. This idea is comparable to the notion of Smithsonian labour division. In Romer (1990), therefore, technical change is of an organisational nature, ‘embodied’ in the whole rather than in individual machines/intermediates, and it takes the form of horizontal product differentiation.7 The Aghion and Howitt (1992) model, by contrast, starts from the assumption that technical change is completely embodied in new equipment that uses only the latest technology. Already existing technologies are driven out of the market by the arrival of superior technologies. This is the so-called creative destruction effect first labelled as such by Schumpeter. One of the most interesting features of the Aghion and Howitt model is that the current rate of technological progress is negatively influenced by an increase in the expected future rate of technological change because of the profit erosion on existing technologies caused by the entry of superior technologies in the future. Their model may be regarded as an improvement over the Romer model at least with respect to the asymmetries between intermediates. However, their model is frequently used to explain vertical (quality) product differentiation as it allows for just one technology to be used at a certain point in time in some sector of industry. The latter feature makes this model less suitable for our purposes. Our model then takes up an intermediate position between the Romer (1990) model and the Aghion and Howitt (1992) model. For as in Romer (1990) we have infinitely many technologies being used at the same time, while we also allow for qualitative differences between individual intermediate goods, as in the Aghion and Howitt (1992) model. In our model, therefore, productivity growth at the aggregate level is the result of both love of variety and quality improvements. Further details of our model are as follows. A representative firm in the final-goods sector produces output by using human capital and a continuum of varieties, in the way defined by Ethier (1982). Each intermediate good in turn is produced by a monopolist. The operation of an intermediate good requires the services of raw capital and energy in proportions described by a Cobb–Douglas technology. Hence, we allow for substitution between energy and capital, although we should state here that the Cobb–Douglas form may overestimate substitution possibilities as they exist in practice.8 However, we stick to the Cobb–Douglas specification because it perfectly fits the purpose of building a model that is able to generate balanced growth. We capture the rise in the productivity of new intermediates by incorporating a Hicks-neutral technology component in the Cobb–Douglas function. That component is different for each intermediate: the latest intermediates are the most productive, as in ordinary vintage modelling. The fact that the aggregator function is Cobb–Douglas allows us to interpret the growth in this technology component as energy-saving technical change, capital-saving technical change, or a combination of these two. We focus on technology and growth, and assume that total energy supply at any moment in time is exogenous and available at any quantity at real energy prices that are growing at a given rate.9 The intrinsic productivity differences between intermediates provide a combination of a horizontal and vertical product differentiation setting, leading to a gradual and relative obsolescence of older intermediates as technology advances. Hence, our model gives rise to ‘creative wear and tear’ instead of the complete and total ‘creative destruction’ in Aghion and Howitt (1992), since all varieties will live forever although they fade away in time. An R&D sector that creates the knowledge necessary to build a new (more productive) intermediate good completes the supply side of the model. This knowledge is summarised in the form of a blueprint. Because intermediates are imperfect substitutes by assumption, they each have their own market niche. The profits arising from selling intermediates under imperfectly competitive conditions are captured by the R&D sector that sets the price for its blueprints. The model is closed by assuming that the demand for the final good is the result of the intertemporal maximisation of consumer utility. The model enables us to look into the growth implications of rising energy prices and to analyse the growth effects of energy policy in this respect. Increases in real energy prices are likely to occur during the transition that lies ahead of us towards an economy that operates in a relatively ‘renewable fuel intensive’ way. The paper has two important findings. First, it shows that aggregate energy efficiency may be improved through stepping up basic research. Secondly, increasing real energy prices lead to corresponding rises in the user costs of intermediates, and hence, to a fall in profits on those intermediates. This diminishes the incentive to produce newer, more productive intermediates. However, it should be noted that the decrease in this incentive is cushioned to some extent by the ‘ample’ substitution possibilities between raw capital and energy implied by the Cobb–Douglas function.10 If actual substitution possibilities between capital and energy are lower, then the rise in the user costs of intermediates would be higher, ceteris paribus, and the detrimental effects on research incentives would of course be stronger than our model suggests. Nonetheless, the model is clear about what to expect if the growth rate of real energy prices rises. There will be less growth, unless policy measures are taken that counteract the negative effects on research incentives arising from a positive growth rate of real energy prices. The set-up of this paper is as follows. In Section 2 we explain how we have modified the Romer (1990) model. In Section 3, we show what continuously rising real energy prices may mean for growth, and how an energy tax (possibly recycled in the form of a subsidy on research costs) may affect growth. Finally, we provide some concluding remarks in Section 4.

In this paper, we have presented a model that is an extension of the Romer (1990) model. We have introduced endogenous energy-saving technical change into that model by assuming that technological change does not only add new intermediates, but, simultaneously, leads to intrinsic productivity differences between intermediates (due to embodied technical change). We have also assumed that the effective capital services provided by intermediate goods require the consumption of energy. We show that the growth rate now depends positively on the rate of embodied technical change, and that it is higher than the original growth rate in the Romer (1990) model. However, the rate of growth of the system now also depends negatively on the rate of growth of real energy prices, implying that continuously rising real energy prices will tend to slow-down growth. There are two reasons for the negative impact of rising energy prices on growth and technological change. First, growing real energy prices decrease the profitability of using new intermediate goods, and hence, the profitability of doing research. Declining profit opportunities imply lower wages in the R&D sector, which bring on a labour flow from the R&D sector to the final good sector. The ensuing fall in wages in the final output sector induces final output producers to substitute labour for effective capital. Consequently, this internal balancing mechanism lowers the rate of growth of R&D and output. Second, the model allows for substitution between raw capital and energy described by a Cobb–Douglas function. With rising real energy prices, the composition of aggregate effective capital becomes less energy intensive, and therefore, more capital intensive. The combined effect is that the pace of introduction of new intermediaries slows down at a rate that is proportional to the rate of increase in energy prices. In order to have the model show increasing R&D activities due to rising real energy prices, one would have to modify the general framework in such a way that it also allows for applied R&D that improves the productivity characteristics of an intermediate ex post. In this paper, we abstained from such modifications for reasons of simplicity. However, van Zon (2001) shows that even with such a modification, overall R&D efforts are likely to be negatively affected by rising real marginal costs, although the composition of R&D may change in favour of process R&D at the expense of basic R&D.32 The modified model would imply lower growth in the long run. Nonetheless, our model underestimates the total amount of R&D since it neglects the profit opportunities provided by the possibility of process R&D, or ex post productivity improvements of intermediate goods in the context of our model. By doing so, we probably over-estimate the negative growth effects of rising real energy prices. But by using a Cobb–Douglas function to describe the substitution possibilities between energy and raw capital, we probably under-estimate the negative growth effects of rising real energy prices at the same time. The reason is that certainly in the long run substitution possibilities between raw capital and energy are likely to be more limited than is implied by the use of a Cobb–Douglas function. This is because there are absolute limits to the efficiency of energy conversion that are implied by the laws of nature: physics ‘abhors’ an infinitely high real marginal product of energy. This implies that the asymptotic properties of a Cobb–Douglas production function (or any production function obeying the Inada conditions with respect to energy) exaggerate actual substitution possibilities between capital and energy in the long run. In addition to this, we also exaggerate the negative growth effects of rising real energy prices, because we have neglected the possibility of a decrease in the energy content of final consumer demand, through a switch from material goods to immaterial services. Smulders (1995) has hinted at the possibility that growth would become sustainable if output itself would become more and more immaterial. But that cannot be the solution to the problem of limiting global GHG-emissions as long as people cannot live in virtual houses and live on virtual food. The latter are basic needs and will remain so as long as people themselves are material creatures that transform energy and matter. Assuming that energy will never be created ex nihilo, this also implies that this transformation process will always lead to the consumption of energy that needs to be produced somewhere in the system. Moreover, at present a large part of the world population has difficulties in satisfying their basic needs. Hence, the ‘immaterialisation’ of final output is likely to be a phenomenon that is only relevant in a practical sense in the very long term, when the largest part of the world population has grown rich enough to consider the satisfaction of non-basic needs by immaterial means. In the mean time, the need for material inputs will no doubt continue to grow. Although there are reasons to assume that our model does not capture all the relevant aspects of the world to the best extent possible, the errors introduced in this way are not all biased in the same direction, whereas the general conclusion regarding the reaction of R&D performance towards the growth of real energy prices seems to be fairly robust. Hence, we feel confident that our policy conclusions are valid in principle. The first policy conclusion we have arrived at is that the introduction of an energy tax in the context of the Romer model with basic research is not enough by itself to spur R&D efforts. Rather, these are negatively affected, because either real energy price changes or the introduction of a tax lowers the present value of a blueprint, which in turn reduces the marginal productivity of research labour. The second one is that the recycling of the tax proceeds in the form of subsidies to R&D in order to mitigate the negative growth effects of continuously rising real energy prices may indeed lead to higher growth, but only if R&D activities are not ‘too high’ already. If the latter is the case, then the opportunity costs of doing more R&D in terms of final output lost are simply too high. If R&D activities are low enough then the subsidy can indeed compensate the fall in the marginal product of labour in R&D, and in that case, we can observe even faster growth than before the tax. Finally, we would like to relate our paper to the recent National Energy Policy plan of the Bush administration. The recent policy reversal of the Bush administration regarding a more intensive use of carbon-based energy arises from the fact that continuous economic growth necessitates a higher level of energy consumption, other things, especially technology but also private consumption, remaining the same (i.e. largely material). Given the serious energy shortages recently experienced in the US, and given the generally higher (and therefore politically unattractive) prices of new non-carbon-based energy technologies, there is an immediate incentive to move in the direction of a more intensive use of carbon-based fuels, due to their relatively low prices. However, when restrictions on the use of carbon-based energy are lifted, it is to be expected that R&D activities on new energy technologies will be reduced, since the availability of low priced substitutes depresses the potential profit margins on energy produced using new, less carbon intensive, technologies. This is indeed what our model shows, and the negative impact on R&D activities indicate that active energy and R&D policies are called for in order to secure sustainable growth in the face of rising real energy prices.