• Our Expertise
• Structural Equations
• Estimation of invariant coëfficients
• Solutions of simultaneous equations and optimizations
• Other examples
• Academic references of G.d'Alcantara
Our Expertise
We have always worked on the basis of a double principle: policy oriented projects need to be based on rigorous methodologies; scientific research has to be applied to real life decision problems. The methodologies of our expertise fit in a three step model construction process. In view of answering the policy question asked, we conceive a model which can answer the question: we specify structural equations, we make econometric estimations of invariant coefficients and we find model solutions.
Economic theory and mathematics allow translating economic reality into behavioural, institutional and technological relations in the form of stable structural equations . Structural equations represent the different players and their behaviour derived from the theoretical formulation of the way they implicitly optimize their objectives. Make estimations of the coefficients is done using econometric methods to find values for these invariant parameters of the structural equations compatible with the observed values of the variables. Find model solutions means find the simultaneous solutions of sets of structural equations and optimisation problems for succeeding points in time: it produces "a simulation" or "a projection". The impact of decisions, events or rules can then be interpreted from the difference between various simulations.
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Structural equations
An example of this approach is given in the article written with Prof. Dr. A.P. Barten, Factor demand explanation in the COMET model and published in Economic Modelling , London, 1984. Click here. Fa ctor demand equations are derived from a cost minimizing behaviour of the companies under the constraint of the technologies. The optimal demand for each production factor is then derived with a cost minimization calculus. It results to be a function of the relative factor utilization prices and of all output categories. The coefficients representing the technologies are defined following a multioutput/multiinput production function. The coefficients determining the output mix has been derived from input/output analysis and taken from official macroeconomic input/output data. Other coefficients represent the specific dynamics of an incomplete adjustment process of variables towards the levels of their theoretically derived optimum decisions.
Thanks to the structural equations the values of the coefficients can be interpreted . The structural approach has a considerable advantage to answer the questions of the decision maker. It allows to explain him the solution of the model in terms of the structure of the world he knows and to tune these results in function of the interpretation of the discussions with him. The Hermes model is described in Chapter 3 "The HERMES model for the member States of the EC" by A. Italianer, G. d'Alcantara and P. Zagame, published in "HERMES" by the Commission of the European Communities with North Holland in 1993, click here, I based the conception of this multinational sectoral macroeconomic model on the SERENA model, developed in the late seventies for the Belgian Planning Bureau. It uses the PuttyClay type of production function. The factor demand functions are derived from these functions. This approach allows to clearly identifying the coefficients of technologies of old vintages which may have to be scrapped when dramatic relative factor price changes occur. It explains the need to invest in new technologies, from a given point in time on. The investments made in energy utilization have been a clear example starting from the oil price shock.
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Estimation of invariant coëfficients
The estimation of the coefficients corresponds to finding an empirical version of the stable relation between the explained variables and the explanatory variables, corresponding both to the law derived from the theory and the observed values of the variables. In some cases the observed data of the variables used are not sufficiently informative or the sample too small. Then other non sample sources of information are used about the value of the coefficients, such as the result of existing empirical studies, values related to the understanding of the theory used. The estimation method including such a priori knowledge is the Bayesian approach, which uses distributions about the a priori values of the coefficients. An example is the Export equation Luc Bauwens and me estimated in An export model for the Belgian industry published in the European economic review 22 , 1983, p. 265276. Click here. In practice many coefficients are estimated conditionally with respect to values of another coefficient, fixed as part of the specification of the equations, taking into account the variancecovariance matrix of the coefficients.
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Solutions of simultaneous equations and optimizations
"Simulate of a model" means solving the complete set of equations over a period of time, for a given set of values of the exogenous variables. Simulations over the past and projections into the future of such models are normally made using the GaussSeidl method, improved to accelerate the time needed to reach the solution. An example of a model solved using this approach is given in the article written with A.P. Barten and G. Carrin , COMET. A medium term macroeconomic model for the European Economic Community. In « European economic review », 7, 1976, p. 63115. Click here. The final result of simulations of such models are not «forecasts» but mainly «sensitivity analysis» of various policy objectives when policy instruments are used or external events happen. An example of this can be found in the Chapter " Simulating economic policy with the COMET model " by A. P. Barten and G. d'Alcantara, published by P. Artus and O. Guvenen in International Macroeconomic Modelling for Policy Decisions, Martinus Nijhof, 1986. Click here
When there is an explicit optimisation in the model, specialised optimisation software's are used. It is possible to combine simulation and optimization in one run, for example having the demand model solved using an econometrically estimated demand system and the choice of optimal localization and technology of the corresponding production plant using a Linear Programming method. This is the method used in our "Petrochemical, refinery and energy world model" used for the "Oil for Economic Development" negotiation within the EuroArab Dialogue (OAPEC and EC) industry question. The software used was Minos.
Solving models, particularly big models which have many sets of variables belonging to categories such as of goods and services consumed production sectors (volumes of production, employment, investment, wage rates, prices.) categories of financial assets and interest rates, countries of origin or destination of imports and exports. require flexible software's. LABOMS i s such software, able to use the particular properties of many similar structural specifications of the equations and matrix notations for variables. LABOMS is a model solution software I used around 1973 and Yvan Pomes further developed. LABOMS means LArge Block wise Oriented Model solution Software. It is now distributed by ECOMETRIC SARL, Consulting and Decision Making Software, 118, Route de Trêves, L6960 SENNINGEN Grand Duché du Luxembourg (Email yvan.pomes@pi.be ). Click here.
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Other examples
• Demand systems for consumption, production factor demand, imports from different countries, portfolio allocation.
• Production possibility frontiers and dual cost functions
• Market price determination with perfect competition, market power, monopoly, .
• Game theory and bargaining processes determining wages, oil prices.
• World trade organizations regulating international trade flows and prices.
• Capital markets determining asset/liability matrix, interest rates, exchange rates.
• Public finance with budgetary norms, taxation rules, social security systems for social risks, public debt management.
• Regulatory setups for network industries : universal obligation, reserved activity, licences, price caps, access rules for infrastructures, access price rules, information duties and sanctions.
• Optimal localization, Business Plan models, Cost Benefit analysis .
• Productivity in the services: a European seminar for the FAST programme at the KUleuven with R. Petrella Political, economic and cultural subsidiary and the growth of the service economy (published by the College of Europe);
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Academic references of G.d'Alcantara
