(untitled) (MAUSAM, 1985)
The paper describes the Moduleco system which is designed to facilitate the construction and the use of large scale (1000 equations or more) dynamic and non-linear macroecenomic models. The Moduleco system will include a software for the management of the time-series data base, a special modeling language for the model equations Input, a special common language to active the tasks, several tools of formal computation and an interactive language for easy data input-output and for easy scenario generation. The paper describes also the mathematical algorithms which are to be included in the Moduleco system. Indeed, we have noticed that most of the macroeconomic models can be put in a quasi triangular form: possibly after renumbering of the variables and equations, there exist a small set of variables, called loop variables, such as for given values of them, the remaining model is triangular and can be solved directly. As we have shown that quasi-triangular models can be simulated and optimized. much faster than general ones, the Moduleco system will include methods for automatic renumbering of variables and equations in order to minimize the number of loop variables. The simulation and optimization algorithms will then be adapted to take into account this quasi triangularity. Experiments made on 4 concrete macroeconomic models have shown the efficiency of the proposed methods. Moreover, the adjoint variable technique, well known in optimal control theory, has been adapted to the structure of macroeconomic models. On the example of the French STAR model (139 equations), it is shown that this technique is 106 times faster to compute the gradient than the finite difference technique generally used by economists.