Model estimation and data issues

P. Soderholm r Energy Economics 23 2001 77]97 ¨ 87

4. Model estimation and data issues

In this paper the translog cost share model is estimated by pooling time-series data across six west European countries, Belgium, Ireland, Italy, Netherlands, Spain and the United Kingdom. For these countries annual time-series data between 1984 and 1994 have been collected. This gives us a total sample of 66 observations. The data needed to estimate the model include fossil fueled electricity produc- tion, installed thermal power capacity, fossil fuel use for electricity production, estimates of the system load factors and the relevant prices for the three fossil fuels. How these variables have been calculated, where they have been collected and other related data issues are reviewed in Appendix A. Apart from the variables Ž . mentioned above, a dummy variable D and the corresponding coefficients i ST Ž . g have been included in the share equations to capture the effects of the UK i ST coal strike in 1984r1985, during which the British electricity sector had to substi- tute oil for coal. In order to implement the translog fuel demand system empirically we need to specify the stochastic framework. We desire a specification, which recognizes that variables not observed by the econometrician still enter the different countries’ Ž . cost minimizing behavior. Specifically, here an additive disturbance term « is i t n Ž appended to each of the three cost share equations where t and n represent an . index over the country-time observations . Furthermore, we assume that each error term can be decomposed into three elements so that; Ž . « s a q m q w 11 i t n i n i t i t n where a is a country-specific error, m , represents intra-equation inter-temporal i n i t Ž effects by following a first-order autoregressive process but it exhibits no error . autocorrelation across equations , and finally w , which is a term that may be i t n contemporaneously correlated across equations. The country-specific errors may be interpreted as unobserved fundamental differences among the electricity systems in Ž . the six countries that still influence the countries’ fuel choices . We assume that these differences are fixed over time for a given country, and consequently we are able to eliminate the country-specific disturbance component by introducing dummy variables for each country. Thus, the following terms are appended to each cost share equation; 5 Ž . g D where D s 1 for country n and O otherwise 12 Ý i n n n ns 1 This approach is normally referred to as the fixed-effects model, and it over- comes the bias of the estimation results that can occur in the presence of Ž unobserved country’s effects that are correlated with the regressors e.g. Friedlan- . der et al., 1993 . In addition, since cross-country data tend to reflect long-run Ž responses, the removal of all cross-country variance and the reliance on within- P. Soderholm r Energy Economics 23 2001 77]97 ¨ 88 . country variance fits well with our purpose of only estimating short-run responses. Since cross-equation contemporaneous correlation of the w terms is expected we i t n assume that the resulting disturbance vector is multivariate normally distributed Ž . with mean vector zero and constant non-singular covariance matrix V . t n Ž . The system of share equations in Eq. 6 provide two seemingly unrelated regression models that can be used to estimate the parameters of the model. The restrictions suggested by economic theory must also be imposed to obtain efficient estimates of parameters and elasticities. Furthermore, the estimation of a full model, all three fuel share equations, would result in the disturbance covariance matrix to be singular, thereby violating a necessary condition in the theory of econometrics. To avoid this problem one of the fuel share equations can be dropped without loss of generality. Since the system of equations was estimated by Ž Ž . the method of maximum likelihood using the Time Series Processor TSP . computer program the results are invariant to the choice of equation to be Ž . dropped Berndt, 1991 .

5. Empirical results and discussion