Functions approximating total fuel demand behaviour are derived in the CAPRI biofuel model by using a response surface approach which is based on simulation results from the PRIMES energy model. The PRIMES model (E3Mlab, 2011) was identified as an appropriate modelling system as it includes a very detailed representation of European energy markets and thus, permits good correspondence with CAPRI. The input which is provided by the PRIMES team for this analysis is a set of energy scenarios calculated in 2008 and 2009. These results which can be interpreted as simulated observations on total fuel demand behaviour (experimental data) include variations in the variables: total energy demand, economic growth (GDP), fuel price including tax rate and fuel price excluding tax rate, all differentiated by fuel type (diesel, gasoline), European Member State and projection year (2010, 2015, 2020, 2025, 2030). For simplification, it is decided to limit the response surface to the responses of GDP and fuel price including tax rate to fossil fuel demand differentiated for diesel and gasoline. This is done, on the one hand, because it is assumed that these are the
most important fuel demand drivers and, on the other hand, variations for further drivers are not clearly identified in the PRIMES scenario results at hand.57
The core assumption underlying this approach is that the experimental data deliver a realistic picture of the real world fuel demand behaviour. Basically, functions of the type
(1.34)
y
i=
g x
i(
1,...,x x
k,
n)
+ε
are estimated. Thereby, y is the response variable (fuel demand), n is the number of influencing variables X and k is the number of variables which are investigated explicitly in the response surface.
X
denotes the variables which can not be considered as explanatory variables as they show no variance in the underlying dataset. Thus, they will become part of the constant response surface intercept and are assumed to be fixed within a subsequent scenario analysis.ε
is an error term. The number of the variables k is restricted to (1) fuel price and (2) GDP. All other (policy) drivers are consequently covered in the constant response surface intercept or in the error term. The estimation of the response surface is done by a regression analysis. Following Brons (2006) a double log function is chosen to define the regression function (Equation (1.35)) as the estimated regression coefficients can directly be interpreted as elasticities in the demand function.(1.35) log
(
yi, j,s,t)
=δi, j+αi, jlog(
pi, j,s,t)
+βi, jlog(
GDPj,s,t)
+γi, jlog trend +(
t)
εi, j,s,twhere
i = fuel type (diesel, gasoline) trend = trend variable j = region = error term
s = scenario = intercept t = year = pric
ε δ
α e elasticity of demand y = fuel demand = GDP elasticity of demand p = fuel price (incl. tax) = trend elasticity of demand
β γ
For the estimation of the regression coefficients an ordinary least squares criterion is applied. The cross price elasticities of diesel and gasoline are not considered in the regression analysis because simultaneity exist between both explanatory variables which is obvious as both are strongly connected to the crude oil price and thus are significantly correlated. The results of the regression analysis
covering estimates for the regression and are shown in Annex
57
The response surface was limited to the existing PRIMES scenario results as sensitivity runs with additional key-drivers for fuel demand were not possible in the framework of this analysis.
10.16. The coefficient of determination (R2) is used to evaluate the quality of the regression function and the P-value is used to evaluate the significance level of the single regression coefficients which are also displayed in Annex 10.16. As one can observe most of the significant are predominantly positive which is understandable as an increasing GDP supposedly leads to increasing fuel consumption, due to the increase in prosperity. Most of the negative estimates for are not significant. is predominately negative which is also comprehensible as an increase in fuel price might lead to a decrease in fuel consumption. The negative estimates for indicate that apart from the impact of price and GDP a slight decrease of fuel demand might takes place per annum. This trend can be explained taking into account the European ambitions to increase energy efficiency in vehicle engines. is the constant term of the regression function covering further drivers which do not vary within the underlying dataset.
While most of the estimated regressions show a reasonable fit in terms of R2 the P-value for and in some cases DISLindicates less significance. In 50% of all
regions these two coefficients turn out to be not significant. To find approximations for these coefficients which are urgently needed for the response surface, average coefficients are calculated based on the sum of existing significant observations as displayed in Table 4.14. If no significance is observed for a coefficient in a respective country the estimated value is exchanged by the corresponding average value.
Table 4.14: Average regression coefficients
(GDP) for gasoline 0.52 for gasoline -0.36 for diesel 0.54 for diesel -0.68 Source: Own calculation based on Annex 10.16
The resulting matrix of regression coefficients which are finally assumed in the response surface for total fuel demand is shown in Annex 10.17. As the PRIMES data only covers values for the EU27 and estimates for the non-European CAPRI regions are also required, it is assumed that the estimated coefficients for the aggregated EU27 are also applicable for non-European regions.