The Stochastic Functions of the Model
Functions in E3ME
The aim in the specification and estimation of E3ME's equations is for a coherent economic explanation, with consistent long-term properties, robustness in equation behaviour and parsimony in their specification. In general any aggregate European equations will follow their regional (member country) counterparts.
The main endogenous variables in E3ME are determined from functions estimated on historical data on European energy and material use and the economy. There are a relatively small number of variables (for example total energy demand by fuel user by region) for which stochastic functions are estimated; around 28 in all. However these variables may well be disaggregated in two dimensions (eg. there are 19 fuel users and 29 regions) and IDIOM allows up to 10 alternative functional forms to explain each disaggregated category.
The econometric techniques used to specify the functional form of the equations are the concepts of cointegration and error-correction methodology, particularly as promoted by Engle, Granger and Hendry.
In brief, the process involves two stages. The first-stage is a levels relationship, whereby an attempt is made to identify the existence of a cointegrating relationship between the chosen variables, selected on the basis of economic theory and a priori reasoning, eg for employment demand the list of variables contains real output, real wage costs, hours-worked, a composite real energy price and measures of technological progress.
If a cointegrating relationship exists, then the second stage regression is known as the error-correction representation, and involves a dynamic, first-difference, regression of all the variables from the first stage, along with lags of the dependent variable, lagged differences of the exogenous variables, and the error-correction term (the lagged residual from the first stage regression). Due to limitations of data size, however, only one lag of each variable is included in the second-stage.
Stationarity tests on the residual from the levels equation are performed to check whether a cointegrating set is obtained. For both regressions, the estimation technique used is instrumental variables, principally because of the simultaneous nature of many of the relationships, eg wage, employment and price determination.
For more detail about E3ME's stochastic functions, see the relevant
chapter in the E3ME
manual.
E3ME: An Energy-Environment-Economy Model of Europe
For more information contact:
Hector Pollitt
Project Manager - European Modelling
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