"Factor 4", a term coined in France, corresponds to the commitment undertaken in 2003 to reduce by at least 75% French greenhouse gas (GHG) emissions by 2050, compared to the 1990 level. The European Council and the European Parliament have also endorsed this objective, and asserted on numerous occasions and in various documents the need to develop long-term strategies to encourage the transition to a low carbon economy. These unilateral commitments are not sufficient per se to efficiently tackle climate change, but if they prove to be successful, they could prompt other countries to act in turn and unlock international negotiations. However, major uncertainties exist at this stage about the cost and even the feasibility of this objective. The debate on the adequate mix of instruments (market instruments, standards, public investments, R&D efforts, etc.) that should be implemented in order to attain such reductions at a reasonable cost is still ongoing.
Market instruments, based on the increase in the price of fossil fuels, are often presented as promising tools to achieve ambitious GHG reductions, because they are economically efficient. Whatever mix of instruments is chosen, these market instruments nevertheless appear inevitable: a situation with low fossil fuel prices indeed seems incompatible with a significant decrease in their utilization. It may be posited that the necessary price increase will occur naturally due to supply-demand factors and that no additional policy is necessary. Even if this happens to be true, which is very unlikely, the question remains: what should the consumer price of fossil fuels be for their consumption to be reduced by a factor of four in the long run?
This question has of course been already addressed. In France, an official commission chaired by Alain Quinet was set up in 2008, with the aim of determining the social value of carbon that should be used by the French government in the cost-benefit analysis for public investments (see Quinet (2009)). The approach adopted was to determine the carbon value that should be applied to the whole economy, so as to achieve a 75% reduction in emissions, i.e. the question addressed above. The commission used the results of simulations performed by three French integrated assessment models, GEMINI-E3 (Vielle & Bernard (1998)), POLES (Criqui et al. (2006)) and IM-ACLIM-R (Sassi et al. (2010)), which computed the initial level and the time path of the carbon value that would allow European economies to reduce their carbon emissions by a factor of four at a forty-year horizon. GEMINI-E3 is a sectoral Computable General Equilibrium model, POLES an extremely detailed bottom-up model, and IMACLIM-R, a hybrid model. Their level of disaggregation and detail allows them to provide an accurate description of sectoral and even sometimes microeconomic effects. Nevertheless, due to their complexity, it is difficult to understand the precise origin of their results, which vary greatly across the three models. As regards the questions we wish to address here, the three models include assumptions on the substitution possibilities in the different sectors of the economy and on the magnitude of sectoral energy-saving technical progress, which is either exogenous or driven by learning-by-doing effects. These assumptions have a major influence on the results obtained, but the complexity of the models, their large size and in particular their sectoral disaggregation are such that it is impossible to deduce, from these assumptions, information such as the implicit average rate of energy-saving technical progress. However, for given substitution possibilities, energy-saving technical progress naturally decreases the carbon value necessary to achieve the emission-reduction objective. It is therefore very important to start with an accurate estimate of the substitution possibilities, and then to disentangle clearly the role of the instrument from that of technical progress to achieve this objective.
We build here a stylized macroeconomic model, sufficiently aggregated so as to ensure that assumptions about technical progress are explicit and their influence can be easily analyzed. We model an open economy producing a generic good, which can be consumed or invested, and importing fossil fuel as its sole source of energy. (1) Whereas, usually, energy is only considered to be an input in the production process, we also introduce here households' consumption of fossil fuels, and the fact that fossil fuels are used together with durable goods. This consumption includes residential energy and fuel for transport. Transport and, to a lesser extent, housing sectors are indeed the larger emitters and have been until now unable to reduce their GHG emissions in France (see Table 1). Both rely heavily on fossil fuel and it seems important to take them properly into account.
Final or intermediate fossil energy consumption can be reduced either by substitutions triggered by an increase in the consumer energy price or by technical progress. Substitution possibilities exist between energy, durable goods and non-durable goods on the households' side, and between energy, capital and labor on the production side. However, these substitution possibilities are limited. The other option is to rely on fossil energy-saving technological progress. Therefore, we introduce two forms of technical progress, respectively labor-saving and energy-saving. The energy-saving technical progress we consider consists of both improvements in energy efficiency and the replacement of fossil fuels by renewables. Thus, we do not explicitly introduce renewables in the model.
We present two versions of the model.
In Section 2, we develop the first version, with exogenous technical progress. The rates of labor-saving and energy-saving technical progress are estimated using French annual historical data. We address the following question: considering that the rates of technical progress remain those observed in the (recent) past, what carbon price path will enable C[O.sub.2] emissions to be reduced by a factor of four within 40 years? (2) The implicit assumption is that the policies put in place in our simulations, namely the increase in fossil fuel consumer prices, have no impact on the rate of fossil energy-saving technical progress, and that no specific policy aimed at increasing this rate is implemented.
We perform three simulations. In the first, the rate of energy saving technical progress equals the average historical value obtained in the estimate, and we introduce the carbon tax proposed in the Quinet report. It shows that this tax path is far from sufficient to reduce C[O.sub.2] emissions by a factor of four at a forty-year horizon. It only yields a 25% reduction in emissions. Hence, we conclude that in large applied models there are more substitution possibilities and/or more energy-saving technical progress than in our model. In the second simulation, we determine what the magnitude of an oil shock would have to be in order to reach the same level of reductions as with the tax, and compare the consequences of this oil shock to those of the carbon tax. In the last simulation, we increase exogenously the rate of fossil energy-saving technical progress sufficiently to reduce emissions by a factor of four with the carbon tax recommended in the Quinet report. The rate of fossil energy-saving technical progress must be greatly (unreasonably) increased to reach Factor 4. This exercise remains unsatisfactory since this increase in the technical progress rate is costless, and does not occur at the expense of the other rate of technical progress in the model, the labor-saving technical progress.
In Section 3, we incorporate an endogenous mechanism into the model, so that the rate of technical progress on fossil energy can be stimulated by a price effect and by a size effect of the research effort directed at saving fossil energy. The rate of technical progress associated with energy use is indeed likely to be closely correlated with the level of the energy price. Technical progress is not fully endogenized: the total amount of resources devoted to research is exogenous. We analyze the extent to which the endogenization of the direction of technical change affects the results obtained in the first exercise.
We perform similar simulations as in the previous section. The results are as follows. When the direction of technical progress is endogenous, the introduction of the carbon tax induces a re-direction of the research effort towards energy-saving technical progress. Its rate immediately increases greatly, and stabilizes in the medium run above its baseline value. It comes at a small cost in terms of overall growth. Nevertheless, the re-direction of technical progress is not sufficient to reach the Factor 4 objective. A supplementary measure is needed, namely a subsidy to fossil energy-saving technical progress.
THE MODEL WITH EXOGENOUS TECHNICAL PROGRESS
The first version of the model consists in a standard exogenous growth model integrating fossil fuel use both on the households and firms' side, rigidities in the adjustment of the housing and the productive sectors, and two types of technical progress, respectively labor and energysaving. We describe successively households' and firms' behaviour and the closure of the model, the calibration method and results, and the simulations performed.
Several macroeconomists have emphasized that distinguishing non-durable and durable goods is important to obtain an accurate representation, both on a theoretical and an empirical point of view, of households' consumption and savings decisions along their life cycle. Ogaki & Reinhart (1998) for instance show that introducing separately non-durable and durable goods modifies very significantly the estimation of the intertemporal elasticity of substitution of...
A Stylized Applied Energy-Economy Model for France.
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