# How are scientific models used

## model

A model is a (simplified) image of a real system or problem (= archetype). If the mapping is done in such a way that every element or every relationship between elements of the original is opposed to an element or a relationship in the model and vice versa, one speaks of an isomorphic or structurally identical model. Due to the complexity of many real systems, however, homomorphic (structurally similar) models are generally used, which contain simplifications and which result from abstraction by combining or neglecting insignificant elements.

a) Replica of a real object with the same or a different scale; in production e.g. press or cast models.

b) Thought structure that separates out demarcated and manageable sub-contexts from the total mutual dependence on empirical facts and depicts a section of reality. With the help of the underlying principle of isolating abstraction, it is possible to highlight characteristic facts and thus to simplify the complex causal relationships. Model types:

1. Verbal models formulated in normal language.

2. Through the transition to mathematical terminology and the use of mathematical operations, one obtains logic calculi or calculus models. Mathematical models represent a special form of calculus models (quantifiable facts, system of equations). (Simple) determination models are used to determine certain variables, decision models, alternative, optimization models to determine one or more variables from a range of variation.

3. With the mathematical calculus models, a further differentiation is made between deterministic models (single-valued quantities) and stochastic models (multi-valued quantities). If time is included, static or state models (timing not taken into account), comparative-static models (different points in time) and dynamic or progression models (changes over time) are obtained.

A model is intended to depict the complex interrelationships of economic reality in a simplified manner in order to obtain certain statements. Since no model can reproduce the variety of processes taking place in economic reality, every model must work with abstractions. In order to obtain logically complete statements about economic reality, the model must also be formulated in a logically complete manner, i.e. it must be syntactically closed and semantically complete. The results of the model analysis, which is usually a partial analysis and not a total analysis, are based on hypotheses. Since verification is usually not possible, they are considered true until they have been refuted (falsification). According to the criterion of the type of statement, a distinction is made between description models, explanatory models and decision models.

In economic sociology:  as a scientific means of knowledge, symbolic, graphic representation of the structure, the behavior of facts, systems under certain points of view. The construction of an M. is based on simplifying assumptions that isolate certain aspects and thus make them more accessible for analysis. The model abstracts from the individual case, it should generally reflect the similarities in the relationship structures and processes of a larger class of issues. The results that are obtained through various operations in the model - depending on the type of model, for example simulation, use of mathematical calculi - are transferred to the realm of reality depicted in the model by inference by analogy. They have a hypothetical and often purely heuristic character. The accusation of M. piatonism has been raised against a number of M.s whose assumptions are not based on an empirical factual situation, but on certain M. properties (representability, cohesion, elegance).

 In imitation learning, the model is the model that is imitated.

As an aid to the scientific knowledge process in the field of economics, it represents a simplified image of a section of economic reality, constructed with a view to a specific question, characterized by the connections between the observed phenomena. Since the question functions as a selection principle, many aspects of reality are abstracted (Reduction of complexity, abstraction). Models serve different purposes. Certain model-like ideas are already needed to describe and classify economic phenomena. They play a central role, especially in explaining economic relationships and conditions. Here they have to replace the usual experiment in natural science as models of thought, since the latter is only possible to a limited extent in the social sciences for various reasons. However, models only become an aid to explanation in the sense of empirical science if the variables used in them can be operationalized (operationalization) and can therefore be identified with empirical values. In addition, at least one requirement of the model must be interpretable as a behavioral hypothesis (nomological hypothesis), while other requirements as boundary conditions must have correspondences in economic reality. However, many, if not most, of the models used in economics have not yet reached this "stage of maturity" in the sense of empirical science. Due to its logical structure, an explanatory model can in principle also be used to forecast economic events, although this may require knowledge of certain data that the model itself cannot provide. It is only one step from the forecast model to the planning model and the decision model as the basis for optimization and control processes. For this purpose, certain boundary conditions are not simply to be accepted, but rather to be manipulated with regard to an objective function in such a way that it is maximized. Regardless of whether models are presented verbally, graphically or mathematically-analytically, it is first necessary to determine which parameters should be included in the model. Variables that remain outside are assumed to be either insignificant, compensating for one another, or constant under the chosen question; in the latter case there is the frequently used ceteris parbus clause. It is used especially for partial models. A distinction is made between exogenous and endogenous variables for the variables appearing in the model. Exogenous variables that are not "explained" in the model, but assumed as given, are used to determine the endogenous variables. In mathematical-analytical models, this is done through functional links between endogenous and exogenous variables. Take the consumption function C = F (Y) = Ci + c as an example2 Y, in which the endogenous variable C (consumption) is "explained" by the exogenous variable Y (national income). As in the example, the functional relationship is often linear, but this does not have to be the case. The sizes Ci and c2 are called parameters. In more complicated models, the endogenous variables are determined not only by exogenous variables, but also by other endogenous variables, some of which are delayed in time. When it comes to the links between the variables used in the model, a distinction has to be made between definition equations, behavioral equations and equilibrium conditions. In addition, restrictions must be taken into account, which also represent relationships between variables and limit their value ranges. If one has its "solution" from the equations (or inequalities) and the other assumptions of the model - depending on whether it is a static, dynamic or evolutionary analysis, it consists of a state or path of equilibrium (equilibrium theory) or describes it the behavior of the observed variables over time - deduced and at the same time recognized the "mode of operation" of the model, is to be assessed on the basis of the respective objective whether the model purpose is sufficiently fulfilled so that the model can be used theoretically and for economic or corporate policy purposes , or whether the model approach, possibly with modification of the question, still needs to be refined or modified. Literature: Kleinewefers, H./Jans, A., Introduction to economic and economic-political modeling, Munich 1983. Stobbe, A., Volkswirtschaftslehre II (Microeconomics), 2nd edition, Berlin 1991.

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