Models And Modeling
Models And Modeling
Social sciences rely increasingly on modeling as a result of their mathematization, the overall computerization of science, and the increase of available data. Once dubbed the “hermeneutic sciences,” the social sciences now resemble more than before the natural sciences, in which model building, testing, and comparison occupy a central role. In this development, economists have undoubtedly been pioneers among the social scientists: Since World War II, model building has become the main practice of economists. What is more, the various modeling methods adopted and developed by economists have disseminated to other social sciences. Especially, political scientists have been inspired by the rational-choice style of modeling and the associated mathematical techniques used by economists (see Morton 1999). Sociologists have, however, preferred statistical modeling, being rather skeptical about modeling social phenomena in abstract mathematical terms (Edling 2002).
Interestingly, although social scientists use in their modeling activities the same kinds of mathematical and statistical tools that natural scientists use, they often see models in a different light than do natural scientists. Whereas for social scientists models tend to be highly abstract and even unrealistic depictions of their target systems, both natural scientists and philosophers have tended to appreciate the concreteness of models as opposed to the theory. This contrast between the attitudes of social and natural scientists is partly explained by the fact that with models, social scientists often refer to what they call “formal” or “mathematical models,” which seem hopelessly plain and simple in comparison to the social phenomena they aim to explain. Although by “formal models” social scientists usually mean “mathematical models,” a model need not be mathematical to be formal. Any model that is presented symbolically or diagrammatically, allowing one to manipulate the model in order to obtain different results or predictions, can be regarded as formal. A good example of formal but not mathematical models is provided by chemical formulas (such as H2O for water). Several philosophers, especially adherents to the semantic conception of theories (see below), distinguish between “abstract models” and the mathematical means used to express them. From their point of view, a set of mathematical equations, that is, what frequently is called a “mathematical model” by social scientists, actually should not be regarded as a model, but rather the abstract entity to which these equations refer.
Generally speaking, the most conspicuous feature of scientific models is perhaps the variety of the forms and functions they may take in scientific endeavors. The things called “models” in science make up a truly heterogeneous group: They can be diagrams, physical three-dimensional things, mathematical equations, computer simulations, model organisms, or even laboratory populations. Apart from explanation and prediction, models are used for heuristic purposes and as a tool for theory construction. Moreover, it is typical of modeling that models are often employed to explore the implications, dynamics, or internal consistency of multiple theoretical assumptions. Models can also be used as “proofs” of various theoretical possibilities.
Examples of well-known theoretical models in economics and political science include the Heckscher-Ohlin-Samuelson model, which is a general equilibrium mathematical model of international trade; the Hicks-Hansen IS-LM model, which summarizes some major features of Keynesian macroeconomics with the help of two curves; the Edgeworth-Bowley diagram, which is a geometric device defining efficient allocations in exchange situations; and the Hotelling-Downs model of two-party competition, which predicts that candidates converge to the policy preferred by the median voter. What is remarkable about these models (and is reflected, in fact, by their names) are the long histories during which they have been developed and extended by several authors. These examples exemplify also other typical features of models: their didactic value, for which the IS-LM model is especially famous, and the applicability of models as general templates to very different kinds of problems. For instance, the Edgeworth-Bowley diagram has been used for analyzing various kinds of situations in economics: consumers in exchange, production decisions of firms, welfare questions, and so on. The Hotelling-Downs model has in turn traveled from economics to political science, in which instance the original geographical dimension of the model has become merely metaphoric.
Theoretical models in the social sciences are tested either through experimentation or by estimating them by statistical methods. Often, though, the empirical models in the social sciences are based on informal theoretical reasoning, not having a formal model as a starting point. Apart from testing, integrating data, and guiding further observation and theory construction, empirical quantitative models are also constructed for predictive purposes. The statistical techniques used for predictive analysis can be grouped into different regression techniques widely used by econometrics and machine-learning approaches that originate from the research on artificial intelligence. Sharing characteristics of both theory and experiment, computer simulation offers an alternative to traditional mathematical modeling in that it allows theoreticians to experiment with more complex theoretical models than what is possible if the models are required to be analytically solvable. Moreover, the possibility provided by multiagent simulation models of exploring the emergence of macro-level behaviors from the interactions of micro-level entities in some environmental contexts seems attractive from the social science point of view.
Given the multiplicity of models and their uses in science, it has been difficult to explicate what kind of entities models are and how they give us knowledge. Two different philosophical approaches to models can be discerned in the literature. On one hand, there have been attempts to establish, within a formal framework, what scientific models are: The earlier, syntactic view of theories and the prevailing semantic approach to models are both attempts of this kind. According to the syntactic view, the task of a model was to provide an interpretation to a skeletal axiomatized theory “in terms of more or less familiar conceptual or visualizable materials” (Nagel 1961, p. 90). The syntactic view was contested by the semantic conception of theories, which replaced the syntactic formulation of a theory with a theory's models. According to the semantic conception, theories are not assemblages of propositions or statements, but rather assemblages of models, which are taken to be structures that are defined by the use of suitable logico-mathematical language.
On the other hand, issues such as scientific reasoning, scientific discovery, and theory change have prompted philosophers to focus on the role and place of models in scientific practice (see Hesse 1966). Continuing this line of work, Margaret Morrison and Mary Morgan (1999) have suggested that models should be understood as investigative instruments that mediate between theory and data because of their autonomous nature. The autonomousness of models is due to their heterogeneous construction: Apart from theoretical notions and empirical data, they may contain also analogies, mathematical techniques, stylized facts, and policy views (Boumans 1999). As Morrison and Morgan stress that through the work of constructing and manipulating models we learn from them, their approach provides a starting point for treating models also as productive things, instead of attributing their cognitive value only to representation (Knuuttila 2005).
Indeed, the epistemic value of models has traditionally been assigned to representation. It has been claimed that models give us knowledge to the extent that they represent accurately their target phenomena. This has proven problematical, especially for the social sciences, because we usually already have some kind of preunderstanding of the social reality—which may not match with the theoretical representations of it. Of all the social sciences, economics, whose mathematization started already in the nineteenth century, has been most ridden with this problem. The most persistent philosophical problem of economics has concerned the “realisticness” of economic theories and their basic assumptions. The issue has been whether such assumptions as utility maximization, perfect information, and perfectly competitive markets “are (‘too’) unrealistic or (‘sufficiently’) realistic,” or whether that should matter at all (Mäki 1994, p. 236). Famously, the 1974 Nobel prize winner in economics, Milton Friedman, has claimed that the “unrealism” of the assumptions of economics does not matter because the goal of science is the development of hypotheses that give “valid and meaningful” predictions about phenomena (Friedman 1953). To economists themselves, however, the basic assumptions do seem to matter—being a subject of continued discussion—and thus the question is how to defend them.
Uskali Mäki has suggested that economists practice a “method of isolation,” in which a set of elements is theoretically removed from the influence of other elements in a given situation with the help of idealizing assumptions (Mäki 1992). Consequently, a theory may be true even if it is partial and involves idealizations, if it has succeeded in representing the workings of the isolated causal factors in a right way. Robert Sugden (2002) denies that economic models are made by abstracting key features of the real world. He treats economic models as (more or less) “credible worlds” whose relation to the real world is established by inferential reasoning. Moreover, he claims that we compare model systems to real systems in much the same way as we compare two real systems to each other. What the two approaches have in common is that they both conceive of economic modeling as devising plausible causal mechanisms that might produce the observable phenomena.
SEE ALSO Economics; Friedman, Milton; Game Theory; Heckscher-Ohlin-Samuelson Model; Ideal Type; IS-LM Model; Mathematics in the Social Sciences; Mundell-Fleming Model; Philosophy of Science; Positivism; Realism; Samuelson, Paul A.; Social Science
BIBLIOGRAPHY
Boumans, Marcel. 1999. Built-In Justification. In Models as Mediators: Perspectives on Natural and Social Science, ed. Mary S. Morgan and Margaret Morrison, 66–96. Cambridge, U.K.: Cambridge University Press.
Edling, Cristofer R. 2002. Mathematics in Sociology. Annual Review of Sociology 28: 197–220.
Friedman, Milton. 1953. Essays in Positive Economics. Chicago: University of Chicago Press.
Hesse, Mary. 1966. Models and Analogies in Science. Notre Dame, IN: University of Notre Dame Press.
Knuuttila, Tarja. 2005. Models, Representation, and Mediation. Philosophy of Science 72: 1260–1271.
Mäki, Uskali. 1992. On the Method of Isolation in Economics. Poznań Studies in the Philosophy of Science and Humanities 26: 316–351.
Mäki, Uskali. 1994. Reorienting the Assumptions Issue. In New Directions in Economic Methodology, ed. Roger Backhouse, 236–256. London: Routledge.
Morrison, Margaret, and Mary S. Morgan. 1999. Models as Mediating Instruments. In Models as Mediators: Perspectives on Natural and Social Science, ed. Mary S. Morgan and Margaret Morrison, 10–37. Cambridge, U.K.: Cambridge University Press.
Morton, Rebecca M. 1999. Methods and Models: A Guide to the Empirical Analysis of Formal Models in Political Science. Cambridge, U.K.: Cambridge University Press.
Nagel, Ernest. 1961. The Structure of Science. New York: Harcourt, Brace.
Sugden, Robert. 2002. Credible Worlds: The Status of the Theoretical Models in Economics. In Fact and Fiction in Economics: Models, Realism, and Social Construction, ed. Uskali Mäki, 107–136. Cambridge, U.K.: Cambridge University Press.
Tarja Knuuttila