ذخیره انرژی در پیشرفت فنی و مطلوب سرمایه سهام: نقش تجسم

We study optimal capital accumulation at the firm level when technical progress is energy saving. Energy and capital are complementary. First we solve a benchmark case with disembodied technical progress. Then, we turn to the model with embodiment. We characterize the optimal replacement of obsolete capital, and the optimal capital stock. The latter is shown to be lower under embodiment compared to the benchmark case. Moreover, we demonstrate that a rising energy price has two opposite effects on the optimal capital stock under embodiment: the traditional direct negative effects, but also an indirect positive effect via the optimal scrapping rule. Nevertheless, the optimal capital stock is shown to remain a decreasing function of the energy cost.

It is widely admitted that rising oil prices have a negative impact on economic activity. Indeed, eight of the nine recessions experienced by the US economy after the World War II (until the early 1990s) were preceded by an increase in the oil price (see Brown and Yucel, 2001, for a survey, and Hamilton, 1983, for a seminal inspection into how the energy cost affected the US economy over this period). Obviously, this argument is not correct in the opposite direction, as the declining oil prices in the mid-1980s did not induce any expansion for example. However, the inverse relationship between the oil price and economic activity when the former is rising sounds as a robust empirical regularity. It suggested a number of theoretical contributions, especially after the first oil shock in 1973, which caused a dramatic slowdown in the economic activity of the major industrialized countries. There are several explanations of the inverse relationship between oil prices and economic activity (see again Brown and Yucel, 2001, for a survey). Some invoke income transfers from oil importing countries to oil exporting countries; others are based on the monetary policy implemented after the oil shocks, etc. The most known (and accepted) explanation relies on a classic supply side effect: rising oil prices are indicative of the reduced availability of basic inputs to production. This concerns the energy input itself but also and specially, the capital input as advocated by Baily (1981). In particular, Baily argued that the productivity slowdown experienced by the US economy and the other industrialized countries after the first oil shock might well be due to a reduction in the utilization rate of capital, namely in the decrease of the effective stock of capital. The keywords, said Baily, are embodied technological change, obsolescence of capital goods and the energy cost. Technical advances are typically embodied in the capital goods, implying that investment is the unique channel through which these innovations could be incorporated into the productive sectors. As a corollary, the old capital goods get less and less efficient over time, which might well induce the firms to scrap them (obsolescence). Therefore, the implications of embodied technical change are extremely different from those of the typical neutral and disembodied technological progress specifications adopted in the neoclassical theory. According to Baily, embodiment is behind the productivity slowdown. The rising energy cost following the first oil shock caused a massive capital obsolescence and a subsequent decline in capital services: ‘...Energy-inefficient vintages of capital will be utilized less intensively and scrapped earlier following a rise in energy prices’. Robert Gordon (1981), after recognizing that Baily's hypothesis is indeed highly attractive, pointed at the difficulty of its empirical validation in the macroeconomy (as measuring the utilization rate is rather hard for certain sectors, like the non-farm non-manufacturing sectors) and reported that in any case, it does not seem to be supported systematically by the evidence available from certain energy-consuming industries like the airline industry. Our paper is devoted to the study of the supply side effect depicted above in the presence of energy saving technological progress. Indeed, there are two major departures with respect to Baily's setting. In the latter, obsolescence is simply modelled through a decreasing effective output (at a given constant rate) as capital ages, and there is no explicit scrapping decision (of the oldest capital goods). In our model, the scrapping decision is endogenous, and since we assume complementarity between capital and energy inputs, finite scrapping time is indeed optimal. Secondly, in Baily's set-up, embodied technological progress makes capital goods less productive over time while in our model, technological progress is energy saving. Obviously, embodied technological progress may work in both directions, but as far as the energy-saving characteristic is accounted for, the implications of a more costly energy on optimal capital accumulation are naturally more complex. We will carefully investigate how the presence of an energy saving embodied technical change affects the optimal capital accumulation decisions at the firm level. There is a growing evidence that energy-saving technological progress has been significant in the last two decades. In a recent contribution, Newell et al. (1999) studied whether the increase in the energy cost in the recent years induces energy saving innovations in the USA. Their conclusion is neat: the induced innovation hypothesis is more than plausible. More recently, Kuper and Soest (2002) found in a panel of sectors of the Dutch economy that energy saving technical progress is particularly significant in periods preceded by high and rising energy prices, while the pace of this form of technical change is definitely much slower in periods of low energy prices. Overall, the energy saving nature of technical progress is increasingly becoming a key descriptive feature of many innovations that have been taking place in the manufacturing and transport sectors in the recent years. Naturally, a more rigorous specification of this induced innovation mechanism would require endogenizing technical progress in terms of the energy price. Since we focus on capital accumulation at the firm level, technological progress is exogenous in our model. Nonetheless, we do model its energy saving characteristic through the embodiment assumption. The embodiment of technological progress in capital goods is introduced via a vintage capital technology in line with the specifications adopted by Solow et al. (1966), and more recently by Malcomson, 1975, Van Hilten, 1991, Boucekkine et al., 1996, Boucekkine et al., 1997 and Boucekkine et al., 1998. In addition to capital and labor, production involves energy expenditures. Vintage capital models with energy as an input have been intensively used in the late 1970s by some well-known US economists confronted with the productivity slowdown puzzle. Indeed, Baily (1981) himself (see also Shoven and Slepian, 1978) uses a vintage capital model with exogenous obsolescence rules. As argued above, we allow instead for an endogenous determination of the scrapping time of old capital goods, and this is likely to produce some very different economic mechanisms. Indeed, we show that an increase in the energy price level decreases the scrapping age, and the resulting lower scrapping time induces a rising, and not a falling, optimal effective capital stock for our optimal scrapping condition to hold even if the direct effect of the energy price level prevails: we show that in our model with complementary capital and energy and a rise in energy price generates a decrease in the effective capital stock. In order to clearly show the implications of the embodiment of technological progress, we first analyze the optimal capital accumulation decision in the presence of a disembodied energy saving technical progress, i.e. when technical progress affects the whole capital stock independently of its age distribution. Explicitly comparative exercises between the embodiment case and the disembodiment benchmark will be conducted along the way. The paper is organized as follows. The next section analyzes the properties of the benchmark model with disembodied energy saving technical progress. The third section is devoted to study the counter-part model with energy saving embodied technical progress. The optimal scrapping rule is first derived; then, the determinants of the optimal effective capital stock are studied in detail with reference to Baily's work and a thorough comparison with the benchmark case. Section 4 concludes.

In this paper, we have proposed a vintage capital model at the firm level in which energy and capital are complements, the returns to (effective) capital are decreasing, and technological progress is energy saving. We study two versions of the model, with disembodied and with embodied technical progress. Several lessons can be brought out from our analysis. Beside the increase in analytical difficulty, the vintage structure with endogenous scrapping induces some additional worthwhile mechanisms. Compared to the disembodiment case, the firms have one more control (scrapping). As the available capital goods get more and more efficient, they can decide to invest massively in the new vintages and to scrap a significant fraction of the old vintages at the same time. The overall effect on the optimal capital stock is a priori ambiguous. We show that the scrapping effect prevails, so that the optimal capital stock is lower in the embodiment case. Second, we show that the traditional supply side discussion around the inverse relationship between the energy cost and economic activity can be notably enriched if one manages to study properly the vintage effect. In particular, we identify an indirect positive effect of higher energy prices on optimal capital accumulation, which operates via endogenous scrapping. Though the latter effect cannot compensate the direct negative price effect as expected, it may explain why Baily's argument does not work so neatly in certain microeconomic cases (as outlined by Gordon, 1981). Last but not least, this paper can be considered as a contribution to the vintage capital models literature. Indeed, it deals with optimal capital accumulation in a vintage capital partial equilibrium framework with a concave technology while the recent literature has focused on general equilibrium set-ups with linear preferences and technologies. As a consequence, we are able to define an optimal (effective) capital stock, and then to establish the periodicity of the investment paths at the interior solution of the firm's problem, a feature that typically comes from the labor market specifications in the general equilibrium related models. Since non-monotonic investment patterns are primarily observed at the firm level, our mechanism seems more relevant at least at this level.