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Pospelov I. G.;

Russia, Moscow, Computing Center of RAS,;

Pospelova L. Ya.;

Russia, Moscow, Computing Center of RAS,;


The ECOMOD system supports the proper structure of an agent-based macroeconomic model taking into account the natural ambiguity of economic concepts. The system is based on the classification of model relationships and variables which expresses their meaning and supports a) editing relationships; b) syntax control; c) semantic control; d) control of balances of assets; e) dimensionality control (existence of consistent system of measurement units);


Поспелов И.Г.;

Россия, Москва, Вычислительный центр РАН,;

Поспелова Л.Я.;

Россия, Москва, Вычислительный центр РАН,;


Система ЭКОМОД контролирует правильность построения макроэкономической модели, учитывая естественную неоднозначность экономических понятий. Система основана на разработанной классификации уравнений и переменных и позволяет редактировать уравнения, проверяя их синтаксис и семантику, а также следит за соблюдением балансов и размерности (существования системы единиц измерения).

  1. Purposes of the System ECOMOD

Our working group in the Computing Center of the Russian academy of Sciences for more than 20 years has been developing the methods of mathematical description of economy. There have been built models of market, planned and mixed economies. Now we are working on modeling of transition economy of Russia. The models displayed and explained the main features of evolution of different economies. They allowed us to analyze problems of energy and ecological problems. The recent models could properly describe the unusual phenomena in the modern Russian economy [1].

The building of each model consists of some certain stages:

  1. to point out economic processes and phenomena of interest (inflation, growth, ecology, money circulation, etc.);
  2. to select essential economic agent whose interactions are responsible for the phenomena of interest (for example producers, consumers, banks, exporters);
  3. to find a set of variables sufficient for description of behavior of the selected agents (flows and stocks of goods and money, prices, rates, etc. );
  4. to seek for corresponding statistical data and analyze them empirically;
  5. to formulate mathematically specific hypothesis on agents' behavior and interactions within economy under consideration and form of these relations a closed system of equation i.e. mathematical model (the main and the hardest part of work);
  6. to investigate analytically, identify and verify the model;
  7. to carry out computer experiments with the model.

Failure that might occur at any stage forced to step back, reconsidered hypothesis and language of description. In case of success we obtained a model that was published and discussed. Then new problems raised, working group changed, new tools and equipment came and in a year no one could repeat computer experiments and even remember what variant of model was actually analyzed. We have gained positive and negative experience of modeling but have lost specific algorithms, equations and data. We have lost opportunity to compare correctly different models and find out influence of certain hypothesis and modifications.

The situation became intolerable when we start modeling the modern Russian economy. Economic relations in modern Russia are changing very rapidly and we have to change our models rapidly as well. It is always pity to know that you already have implemented some idea in the previous model but cannot use it because of differences in language, interpretation and implementation. That is why we put forward the project of ECOMOD system. It must collect and store models ready to use and must give opportunity to pick up appropriate parts of old models for using in new ones.

  1. Knowledge Representation in the Field of Mathematical Modeling of Economy

To collect and store experience of successful solutions in a certain field is the main task of artificial intelligence. The usual approach of knowledge engineering is

  1. to point out the language of basic concepts and terms used in the field;
  2. to explicate and formulate key rules which experts follow in making their conclusions;
  3. to connect rules and concepts into a certain logical model;
  4. to implement the model as a computer dialog system.

When we have tried this approach for our field we have failed. The field of economic modeling has some specific features that make traditional approach inadequate.

The first difficulty is that ECOMOD system must help to solve new problems unknown to expert. So it should be similar to universal tool like "Mathematika" but not to usual applied expert system.

The main difficulty caused by the specific features of economic modeling. In fundamental sciences reliable models are derived from general theory. In computer aided design reliable models are assembled of independent modules. In some applied fields like justice or engineering where we have reliable prescriptions we may formulate a good model as a set of expert rules.

In economy the general theory is absent and experts disagree with each other and make too many mistakes. There are known numerous attempts to assemble a large complex model of economy of modules developed by independent groups of specialists in demography, ecology, industry, finance, etc. They seem not to be very successful. Economy is essentially holistic system and each good interesting economic presents some new point of view on this system. So the main concepts of economy like goods, prices, money, labor, and capital treated in each new model something different. For example there are no standard mathematical implementation of economic theories of J. Keynes or A. Marshall or K. Marx but a number of Keynesian, neoclassical or Marxists’ models.

Economic concept does not describe a set of samples but points out analogy of economic situations or suggestions. That is why we have refused to put in the base of our system usual economic concepts. Instead of it we develop canonical form of the model that reflects the way of model construction but not its interpretation.

  1. Canonical form of the Model
  2. Canonical form of a model is the classification of model equations and variables. The main taxons are economic agent, interaction of agents (classes of equations), asset, message and plan (classes of variables).

    Economic agent (EA) is a set of equations which describes some decision making process in economic system. For example it may be planning of production by firm under given prices and capacities. These equations define plans (of outputs and inputs) as a function (supply and demand ones) of prices. Price serves as messages. Implementation of plans depends on agreement of other agents.

    InterAction (IA) is a set of equations which describes the process of mutual agreement of agents' plans. For example that may be conditions of market equilibrium. Equations of IA define a) messages (e.g., prices) and b) actual values of planned variables depending on agents' plans.

    Important planned variables are flows of assets (labor, capital, goods, securities, etc.). Stocks of assets show the state of agent. Dynamics of stocks is described by balance equations, which serves as constrains in agent's decision making. In our models we describe all way of transformations and transactions for each asset under consideration.

  3. Relations of Similarity of Models
  4. Canonical form includes many conditions of correctness of classification but all of them are necessary and not sufficient. It means that we are free to assign an arbitrary (to some extent) economic meaning to a formal element of a model. That is why canonical form can serve as a tool of knowledge representation. The same system of equation may be presented in canonical form in different ways. These mean that the system has many economic interpretations. Conversely, different systems of equations may have the same structure of canonical form. This means that they give different description of the same aspects of economy.

    Except for total coincidence we strictly defined four types of similarity of canonical forms. These relations may help to modify and compare models automatically by 'interbreeding' of different models. Canonical form guarantees that formal 'interbreeding' will not be economically senseless.

  5. Functions and Architecture of ECOMOD.
  6. ECOMOD [2] must support all stages developing of a new economic model: construction, identification, computer experiments, and interpretation of results.

    On the stage of construction ECOMOD will check the correctness of input flow of model equations in canonical form. It verifies syntax of equations and their interrelations. In particular system looks for conservation of all assets, so that no quantities of an asset arise from nowhere or be lost. System also controls that an agent in its decision-making use only information actually accessible to it. To provide this function we wrote rules of canonical form as a system of axioms. ECOMOD will also visualize model by automatically designed flow charts of different types.

    Model under construction always exists in many versions. ECOMOD will collect all versions and will be able to compare them and build new correct ones. ECOMOD will help to adopt data from models already built to identify new model. We hope that ECOMOD can find automatically appropriate method of numerical solution of the system of equations of the model and so carry out series of computer experiments. ECOMOD also will store results of experiments together with text commentaries and illustrations.

  7. References

1. Петров А.А., Поспелов И.Г., Шананин А.А. От Госплана к неэффективному рынку: Математический анализ эволюции российских экономических структур. The Edwin Mellen Press, Lewiston - Queenston-Lampeter, NY, USA, 1999 393p..

2. Петров А.А., Поспелов И.Г.; Поспелова Л.Я. Представление знаний, содержащихся в математических моделях экономики. Теория и системы управления, 1995, № 5.

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