ECONOMIC MODELS AS MINI-THEORIES. Steven Rappaport. John Maynard Keynes once noted, Economics is a science of

Transcription

1 ECONOMIC MODELS AS MINI-THEORIES Steven Rappaport John Maynard Keynes once noted, Economics is a science of thinking in terms of models joined to the art of choosing which models are relevant to the contemporary world. 1 Keynes remark can be roughly paraphrased by saying that economic thinking is (at least largely) the construction of models and their employment in various cognitive activities, such as explaining real world economic phenomena. In light of this fact, under-standing economic inquiry requires understanding models and their uses. I want to shed some light on economists models by using Larry Laudan s distinction between mini-theories and global theories. Specifically, I will bring out that economic models are mini-theories, as well as say something about the relationship between models and the broader network of beliefs which constitute global theories in economics. It is worth emphasizing that the claim that economic models are mini-theories, is intended as an initial and only partial account of models. Viewing models as minitheories leaves room for adopting some further, more penetrating account of the nature of models, and underdetermines the choice as to which more profound account 1

2 is selected. The mini-theory/global theory distinction came into prominence as part of the emergence of the so-called globalist perspective in the philosophy of science in the early 1960s. Globalists include Thomas Kuhn, Paul Feyerabend, Imre Lakatos and Larry Laudan. Here is Laudan s own useful preliminary account of the two kinds of theories: In the standard literature on scientific inference, as well as in common scientific practice, the term theory refers to (at least) two very [sic] types of things. We often use the term theory to denote a very specific set of related doctrines (commonly called hypotheses or axioms or principles which can be utilized for making specific experimental predictions and for giving detailed explanations of natural phenomena.... By contrast, the term theory is also used to refer to much more general, much less easily testable, sets of doctrines or assumptions. For instance, one speaks about the atomic theory, or the theory of evolution, or the kinetic theory of gases. In each of these cases, we are referring not to a single theory, but to a whole spectrum of individual theories. The term evolutionary theory for instance, does not refer to any single theory but to an entire family of doctrines, historically and conceptually related, all of which work from the assumption that organic species have common lines of descent. (Laudan, 1977, PP. 71-2) In the first use of theory Laudan identifies, the term denotes what I am calling mini-theories ( mini-theories is 2

3 actually Laudan s own term). A mini-theory may be described as a specific set of assumptions or axioms together with their logical and mathematical consequences. In short, a mini-theory is a well-defined deductive system. 2 (A mini-theory may also include one or more definitions, although these may not be sharply distinguished from the theory s assumptions.) Global theories are harder to characterize, and different globalists offer divergent accounts of them. In the passage quoted previously, Laudan suggests that a global theory is a spectrum of mini-theories which are historically and conceptually related. It is a key feature of global theories that they are associated with a set of distinct mini-theories. For example, the theory of evolution or Darwinism is a global theory. In The Origin of Species, Darwin himself states a mini-theory which is a version of the theory of evolution, though what the assumptions and derived statements of Darwin s own theory are has been a matter of controversy. Subsequent to Darwin, there have been versions of the theory which differ from Darwin s, an important example being the synthetic theory of evolution which incorporates Mendelian genetics. These other versions, as well as Darwin s own version, are minitheories associated with the global theory of evolution. Are there other features of global theories which might 3

4 serve to identify them? Laudan believes that global theories typically include an ontology, as well as methodological rules (criteria for evaluating a theory as acceptable, worth further development, and so on). The global theory behaviorism belonging to psychology includes an ontology according to which the only basic entities in the domain of psychology are publicly observable behaviors of organisms. And the global theory Newtonianism includes the official methodological rule that only mini-theories or hypotheses inductively inferred from the empirical evidence are to be accepted. Yet, Laudan acknowledges that not all global theories incorporate an ontology and methodological rules, an acknowledgment he backs up with historical examples (Laudan, 1977, pp ). One additional feature of global theories deserves attention. As the examples of global theories Laudan supplies suggest, a global theory is usually associated with a set of general statements that are not comfortably regarded either as methodological rules or part of an ontology. Examples include f=ma, which is associated with the global theory Newtonianism, and the claim that all organic life is related, which is associated with the theory of evolution. Let us use the term global statements to refer to such general statements. Global statements are in some sense accepted by 4

5 adherents of the global theory to which they belong. Lakatos and perhaps Kuhn hold that a global theory includes a single set of global statements which do not change over the entire history of the theory, and a change in any of these statements would result in a different global theory. Lakatos, for instance, would include these unalterable global statements in the hard core of the global theory, or, in Lakatos preferred terminology, the scientific research program. Laudan takes global theories to be more protean entities than do Kuhn and Lakatos. Laudan believes that at a given time, a global theory has a set of global statements that partly define its identity at that time. To give up any of these statements at the time in question is to repudiate the global theory (Laudan, 1977, p. 99). Yet, over the entire history of a global theory, its global statements may change and it still remains the same global theory (Laudan, 1977, pp ). Laudan persuasively argues for this claim relying on historical examples. I think it wise to follow Laudan here. The global statements belonging to a particular global theory do not constitute, or are not part of, anything like a Lakatosian hard core. A particular global statement might be modified or dropped from a global theory, and it could still remain the same global theory. 5

6 To sum up, a mini-theory is a well-defined deductive system. On the other hand, a global theory is associated with a set of mini-theories which partly constitute it. These minitheories may be adopted by adherents of the global theory contemporaneously, or they may be adopted successively as the reigning mini-theory is replaced by another deemed better by the fans of the global theory. Often, but not always, a global theory incorporates methodological rules and an ontology. Finally, global theories regularly include global statements as explained previously. How is a global theory related to a mini-theory which it includes? Laudan talks of a global theory inspiring or generating constituent mini-theories. He cashes out these metaphors in terms of particular kinds of conceptual and historical connections between mini-theories and their parent global theories (Laudan, 1977, pp ). Below I will use an economic example to partially illuminate the relation between a mini-theory and its parent global theory. The chief claim I wish to make here is that economic models are mini-theories in the sense just described. And it seems to me that this claim ought to be seen as pretty obviously true. As a matter of fact, when an economist 6

7 constructs a particular model, he sets out a number of assumptions like Firm managers seek to maximize profits, or The MPC is greater than zero but less than one, and perhaps states one or more definitions, such as the definition of a perfectly competitive market. The economist then derives further statements of interest using logic and mathematics. The product of these activities is a set of statements organized into a deductive system, in other words, it is a mini-theory. I want to provide some confirmation for this general description of economists models by examining one particular model. The model I want to treat is the Tiebout model in public finance. Economists typically believe that neither the national government nor a system of private markets is likely to provide the quantities of pure public goods that people want. This is because of the problem of preference revelation. Each person has a motive to conceal his preference for a pure public good hoping that it will be provided anyway. Due to the nonexcludability feature of pure public goods, the person will then be able to consume the good without paying for it. Charles Tiebout developed the model bearing his name to address the following problem: is it possible for there to be a set of social 7

8 institutions in which people reveal their true preferences for pure public goods, and, as a result, get the approximate quantities of these goods they want? To deal with this issue, Tiebout constructed a model. He (Tiebout, 1972, pp ) sets out the following assumptions or axioms of the model: fully (A1) Consumer-voters living under local governments are mobile and move to the community whose tax and expenditure package best satisfies their preferences for local pure public goods. (A2) Consumer-voters have full knowledge of the tax and expenditure packages of the different local governments. (A3) There are a large number of communities in which consumer-voters can choose to live. (A4) The source of consumer-voter income provides no obstacle to their mobility- - for example, they might derive all their income from dividends on common stock. (A5) There are no external benefits or costs from the provision of pure public goods by the communities from which the consumer-voters can choose. (A6) A local community reaches its optimum size when its expenditure package for existing residents is provided at the lowest average cost. (A7) Communities below optimum size try to get new residents to lower costs, and communities at optimum size try to keep population constant. After stating the axioms of his model, Tiebout develops their implications to address the problem at hand. Given axioms (A1) through (A4), consumer-voters will 8

9 reveal their preferences for pure public goods by moving to another local community or staying put. Voting with one s feet is the solution to the problem of preference revelation at the local level. The equilibrium state of the model obtains when no consumer-voter can better satisfy his preference for locally provided pure public goods by moving to another community below optimum size. Thus, when the Tiebout model is in equilibrium, consumer-voters have come at least fairly close to getting the quantities of pure public goods they want, insofar as local government is able to supply these. And this implies (TH1) the provision of pure public goods by local government can approach the quantities people want. This theorem of the Tiebout model brings out that a set of local governments offering diverse packages of pure public goods affords a solution to the problem the model addresses. The Tiebout model certainly appears to fit the definition of a mini-theory. The model includes seven assumptions or axioms. Additional statements of interest, such as (TH1), are derived from the assumptions. That is all it takes to be a mini-theory. And so the Tiebout model affords some confirmation of the generalization that economic models are 9

10 indeed mini-theories. Moreover, Tiebout s model is a neoclassical microeconomic model. More fully, I submit that neoclassical microeconomics is a global theory, and the Tiebout model is one of the numerous mini-theories partly constituting neoclassical microeconomics. I want to follow up this claim by saying something about the relationship between the Tiebout model and neoclassical microeconomics. The following pair of statements are global statements of neoclassical microtheory: (GS1) Individuals are optimizers, i.e., they act to as to maximize or minimize something (utility, profit, etc.), perhaps subject to constraints. (GS2) Individuals are able to rank alternatives from the most to the least desirable. These global statements are reflected in the axioms of the Tiebout model. Specifically, axiom (A1) says that consumervoters move to the community whose tax and expenditure package best satisfies their preferences for locally provided pure public goods. This presupposes that consumer-voters are able to rank tax and expenditure packages of different local governments from most to least desirable. Of course, this reflects (GS2). By saying that consumer-voters actually move to the community best satisfying their preferences for locally provided pure public goods, axiom (A1) implies that consumervoters optimize. This reflects (GS1). In short, a key axiom of 10

11 the Tiebout model is an application to the model s subject matter of two global statements belonging to the model s parent global theory. It is such facts that Laudan has in mind in speaking of global theories inspiring their component minitheories. I want to conclude by returning to a point made at the outset of this paper. The claim that economic models are minitheories is intended as but a partial account of models. A philosophically more penetrating account of models is needed to supplement this claim. The literature contains a number of more profound views about economic models. One such view is the lawlike generalization view. This holds that an economic model is a set of statements organized into a deductive system, which includes some lawlike generalizations making claims about real world economic phenomena. Should these lawlike generalizations be true, the model would contain scientific laws. 3 Another theory about the nature of economic models is the modal view. According to this, theoretical economic models are truths about hypothetical firms, consumers, etc. But applied models include statements that are true of false of the real world situation to which the model is being applied. Both theoretical and applied models are deductive 11

12 systems. They differ in the subject matter of their constituent statements, with theoretical models being about hypothetical objects and applied models being about the real world. 4 Either of the two accounts of models just described is consistent with the claim that models are mini-theories. 5 But then viewing economic models as mini-theories does not logically commit one to adopt either of the two more profound accounts of models. The claim that models are mini-theories is a starting point in the process of understanding economists models, not the terminus of this process. 12

13 NOTES 1. This passage is from a letter by Keynes to Roy Harrod. The letter is partially excerpted in Hausman, 1994, pp A mini-theory can be expressed by means of different kinds of representations--sentences of a natural language, graphs, equations, and so on. But, a mini-theory s assumptions and derived statements or theorems cannot be identified with a set of sentences of a particular language which formulate the mini-theory in some context. For instance, the English sentence Consumers seek to maximize their utility expresses an assumption of the neoclassical model of the rational 13

14 consumer. It is the proposition or content expressed by the sentence, not the sentence itself, that is an assumption of the model of the rational consumer. 3. The lawlike generalization view of economic models is the position that typically would be favored by philosophers in the positivist tradition. For instance, the twentieth century positivist May Brodbeck (1968, p. 10) says, A theory is such a deductively connected set of laws. 4. The modal view is defended in Rappaport, 1998, Chapter The structuralist view of economic models claims that a model is a definition of a predicate or kind or system. For instance, a Keynesian income-expenditure model would be Keynesian identified with the following definition: X is a economic system iff X satisfies the following axioms. A list including such sentences as of axioms would follow, Consumption is a positive function of disposable income. Hausman and others have defended the structuralist view. (See Hausman, 1992, Chapter 5.) It is not altogether obvious how the structuralist view of models can be made consistent 14

15 with the claim that economic models are mini-theories. REFERENCES 15

16 Brodbeck, May (ed.). (1968), Readings in the Philosophy of the Social Sciences, New York, NY: Macmillan Co. Hausman, Daniel. (1992), The Inexact and Separate Science of Economics, New York, NY: Cambridge University Press. Hausman, Daniel (ed.). (1994), The Philosophy of Economics Second Edition, New York, NY: Cambridge University Press. Laudan, Larry. (1977), Progress and Its Problems, Berkeley, CA: University of California Press. Rappaport, Steven. (1998), Models and Reality in Economics, Cheltenham, UK: Edward Elgar Publishing Ltd. Tiebout, Charles. (1972), A pure theory of local expenditure, (eds), Readings in in Matthew Edel and Jerome Rothenberg Urban Economics, New York, NY: Macmillan Co. 16