rappaport the modal view of economic models

7/29/2019 Rappaport the Modal View of Economic Models

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THE MODAL VIEW OF ECONOMIC MODELS

Steven Rappaport

rvluch economic theorizing consis t s of elaborating and us ingeconomic models. Familiar examples are Keynesian income-expenditure models, the model or theory of the firm in perfect competition, and the model of the rational consumer. Different views ofeconomic models have been proposed by philosophers of economics, one of which is the modal view.! The following passage fromDaniel Hausman, a critic of the modal view, provides a roughaccount of the view:

Instead they [economists] wish to interpret their models asmaking unreal ist ic claims s( 4) ... about how things VIlouldbe, were various complications absent. I shall call this viewof economic models the "modal model" view, since i t in te r -pre ts models as making modal claims about how th ingsv.rould be. According to the modal view, sentences lih:e"Entrepreneurs attempt to maximize profits" do not merelydefine predicates in models and make inexact claims intheories . Rather they state t ru ths about certain possibleeconomies. (1981, pp. 146-147)

One al ternat ive to the modal view is an application to economicmodels of the s t ructura l is t view - or, as i t is sometimes called,"the semantic view" - of scientific theories. A second alternativeto the modal view takes economists ' models to be collections oflawlike generalizations, ,-"hich is an application to economic models of a popular view of scientif ic theories . My aim here istwofold. I ",,,rant to explain in a sat isfactory manner what themodal view affirms. Also, I will sugges t that the modal view hassome dist inct advantages over the two alternatives jus t alludedto.


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62 STEVEN RAPPAPORTI

On the modal view, an economic model consists of a se t K ofdefinitions and non-definitional assumptions plus a set of objectsL whose behavior is described by K and K's logical and mathematical consequences. (Some models are developed without re -lying on definitions; in such cases se t K includes only nondefinitional assumptions.) The objects in L are hypothetical inthat they would exist i f the conditions conveyed by K were metin the real world. For example, the model of the shor t runbehavior of a business firm in perfect competition is typicallydeveloped by presenting the definition of a perfectly competitivemarket, as well as set t ing out a number of assumptions ora..doms. The axioms include such statements as that firm managers select an output level which maximizes firm profi ts , andassumptions about the shapes of various cost curves of the firm.Using logic and mathematics, theorems a re generated from theaxioms and the definition of a competitive market. 2 The modeldescribes the behavior of hypothetical objects, i.e. objects thatwould exist if certain conditions were met. The model includes ase t of firms, firm managers, etc. - this is the model's se t L -whose behavior is described by the sentences of the model.These firms, firm managers, etc. are hypothetical. They wouldexist i f the conditions conveyed l?y the sentences in the set K ofthe model obtained in the real world.What has been said so far about economic models holds fortheoretical models. The modal view in the form I am prepared todefend it also recognizes applied models. An applied model is amodel which has been applied to a real world situation. To applya model 1\1 to a real world situation S is to interpret the variablesand general terms in M in terms of S. To interpret a variable in1\1 in terms of S is to replace the variable with the correspondingvariable whose values are restr ic ted to magnitudes in S. Forexample, consider a Keynesian income-expenditure model whoseaxioms include the following consumption function:

(1) C=a + bDY a>O, O


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THE MODAL VIEW OF ECONOMIC MODELS 63denoting only items in S. For example, to in te rpre t the term"firm" in the model of perfect competition in terms of the wheatmarket in the United s ta tes , is to replace "firm" in the modelwith a term like "American wheat farm."3

On the modal view only theoretical models are about hypothetical objects. Various sentences in an applied model are t rueor false statements about the real world situation to which themode] is being applied. 4 For example, suppose He apply the modelof perfect competition to the wheat market in the United States.The axiom of the model "firm managers select an output levelwhich maximizes firm profits" becomes a t ru th or falsehood aboutjus t the firms in the American Hheat market. I t will be a t ru thprovided tha t managers of wheat farms se t their outpu t levelwhere marginal revenue equals marginal cost (and the secondorder condition for a maximum is also met). But theoret icalmodels do not contain t rue or false statements about real worldsituations. They include true statements about h:vpotheticalobjects. I am not saying non-definitional sentences of a t heoretical model would be t rue if certain circumstances obtained.The sentences of a theoretical model are true. The point is worthemphasizing. A theoretical model includes in effect a domain oruniverse of discourse consisting of hypothetical objects - this isthe se t L mentioned a t the s tar t of this section. The sentences ofthe theoretical model are in terpreted in terms of the domain ofhypothetical objects. For example, a term like "firm" in thetheoretical model of perfect competition is in terpreted as applying to the firms among the hypothetical objects in the model'sdomain. I t is st ipulated or postulated that the non-definitionalsentences of a theoretical model afford a true description of thehypothetical objects in the model's domain. s Thus the t ru th ofthe non-definitional sentences of a theoretical model is quiteactual; i t is only the objects which these sentences are aboutwhich are hypothetical .

I t is Horth deflecting a misunderstanding of the modal view,a misunderstanding which has led to a negative appraisal of theview by some. Consider the following passage from one ofHausman's discussions of the modal view:

Many economists have regarded their theories as makingclaims about how things would be were various com plicati


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64 STEVEN RAPPAPORTpossible economies, so much the bet ter . (1981, p. 147)

This passage implies that the modal view of economic models iscommitted to an ontology of possible or hypothetical objects. Butthe modal view carries no such commitment. The modal view saystheoretical economic models afford t rue descriptions of the be-havior of hypothetical objects. This does not mean the modalview is committed to the existence of hypothetical objects of anykind. To say a model provides a t rue account of hypotheticalobjects of some sort, is to say the model describes the behaviorof objects that would exist i f certain conditions were met. Thishardly implies that objects of the sort in question do exist. I cangive a t rue description of a forest fire that would occur in theSanta Cruz mountains if certain conditions were met. But thisdoes not mean that the fire exists or is occurring.

Even though the modal view of economic models is notcommitted to the existence of hypothetical or possible objects, itmight still be thought that the modal view relies on or presup-poses the possible worlds framework which some philosophers -David Lewis, Kripke, e t al. - have tried to develop to interpretordinary modal discourse and provide semantics for modal logic.(Of course, many who adopt the possible worlds framework donot think that there are possible worlds, possible objects, etc.;only modal realists like David Lewis think this.) The modal viewdoes say theoretical economic models afford true descriptions ofhypothetical objects. And, it might be said, what else is ahypothetical object but an object that exists in, or is an inhabi-tant of, a possible world? The conclusion that would be drawn isthat the modal view is unattractive given i ts involvement withthe problematic possible worlds framework. However, the line ofthought jus t set out is not persuasive. To be sure, the modalview of economists' models uses the concept of a hypotheticalobject. As indicated above, this notion is explainable as follows:

(2) X is a hypothetical object iff if certain conditions weremet in the real world, then X would exist .The subjunctive conditional on the r ight side of "iff" in (2)obviously does not contain a term expressing the concept of a(logically) possible world or kindred notions such as an inhabi-tant of a possible world. Of course, there is an analysis ofsubjunct ive conditionals, developed by David Lewis, Stalnaker,et a1., which uses the possible worlds framework. A rough,informal version of this analysis applied to what follows "iff" in(2) above is as follows (Lewis, 1973, p. I):


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THE MODAL VIEW OF ECONOMIC MODELS 65(3) " I f certain condition were met in the real world, then Xwould exist" means that X exists in that possible world mostlike the actual world in which the certain conditions aremet.

I f (3) reflects how we are to understand subjunctive conditionalslike the r igh t side' of (2), then the notion of a hypotheticalobject , and so the modal view, does presuppose the possibleworlds framework. But the modal view's involvement \vith theframework would simply be a resul t of the correct analysis ofsubjunct ive conditionals, which happens to use the possibleworlds framework. And this involvement could hardly be seen asa defect in the modal view. On the other hand, there is nogeneral agreement among philosophers that the possible worldsapproach does rep re sen t the correc t analysis of subjunct iveconditionals. And if i t should tu rn out tha t a possible worldsanalysis of subjunct ive conditionals is not correc t , then themodal view's notion of a hypothetical object defined by (2) wouldnot presuppose the possible worlds framework. In sum, ei therthe modal view presupposes the possible worlds frame\\rork, butthis implies no defect in the modal view. Or the modal view doesnot involve the possible worlds framework at all in which case itcannot be seen as unattractive because of a commitment to tha tframework.

I I

I t should be reasonably clear what the modal view of economicmodels amounts to. I now want to sketch the two alternatives tothe modal view referred to a t the outset. Let us s tar t with whatI will call "the law ike generalization view of economic models."This is an applicat ion of a view of scientific theories which issuccinctly se t out in the following passage from Hausman: 6

Few contemporary philosophers still accept the posit ivistview of scientific theories. Theories cannot be formalized inthe way in which the logical positivists wished, and to viewscientific theories as primarily formal or syntactic objectsdoes not do jus t ice to the way in which theories areconstructed or used. Furthermore, the problems of relatingtheory to observat ion, in the form in which posit ivistspm:ied them, are intractable. Many philosophers now sett lefor an informal cons t rual of theories as collections of law-like statements (not uninterpreted, purely syntact ic sen-


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66 STEVEN RAPPAPORTtences) systematically related to one another. (1984, p. 12)

Applying the view of scientific theories presented here to economic models gives us the lawlike generalization view. Accordingto this, an economic model is a se t of lawlike general statements(t rue or false sentences) systematically related to one another.Presumably the sort of systematization in question is deductive.So, on the lawlike generalization view, an economic model is a se tof lawlike generalit ies which can be organized into a deductivesystem. This does not mean the la\.,rlike generalization viewreflects acceptance of the logical empiricist view that a formal-ized deductive system underlies a scientific theory, including aneconomic model. On the lawlike generalization view, an economicmodel can be seen as a nonformal deductive system, and noformalized deductive system need be associated with the model.One feature of the lawlike generalization view which bearsemphasizing is that statements comprising an economic model areabout real world objects. For example, the model of the rationalconsumer familiar from microeconomic textbooks includes thesentence

(4 ) consumers have preferences that are t ransi t ive.The term "consumers" in (4) denotes ot' applies to real worldconsumers such as you and me. A distinction between theoreticaland applied models such as the modal view makes is not recognized by the lawlike generalization view. All economic models areapplied in the sense that their terms are interpreted as denotingreal world economic phenomena, and their variables are regardedas expressing real world economic magnitudes. 7

The second alternative to the modal view I want to discuss isthe structuralist position. The structural ist view I \.,rill describeis an application to economic models of a fairly simple compositeof versions of the structuralist vie\v of scientific theories pre-sented by several different authors.s On the s t ructura l is t vie\.,ran economic model is associated with a definition of a predicate.For example, a Keynesian income-expenditure model is associatedwith the definition: X is a Keynesian economic system iff Xsatisfies the following axioms. A l ist of the axioms would follow,which would include sentences like the consumption function (1)set out in section 1. As the example indicates, a list of the axiomsof a model is included in the definiens of the definition of thepredicate which the model gives. A realization for an economicmodel is an item which is denoted by the predicate defined bythe mode1. 9 For example, suppose the American economy in 1929-


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THE MODAL VIEW OF ECONOMIC MODELS 671933 satisfies the axioms of a Keynesian income-expendituremodel. In th is case, the American economy in 1929-1933 is de-noted by the predicate "is a Keynesian economic system," and sois a realization for the model. In addition, an economic model hasa se t of in tended applications, which comprise the real Vo,,rorldi tems which are intended to be (or which proponents of lhemodel want to be) realizations for the model. For example, theAmerican economy in 1929-1933 might be among the in tendedapplications of a Keynesian income-expenditure model. Letting Pbe the predica te defined by an economic model and X a realworld item, "X is a P" is an empirical hypothesis. lo The sentencesin the list of axioms included in the definiens of the definition ofthe predicate an economic model gives are without t ru th-value .In other words, apar t from a realization for a model, the axioms -and therefore the theorems which follow from them - are lackinga t ruth-value (Hausman, 1981, p. 46; Hands, 1985, p. 306, p.322).Thus the axioms l is ted in the definiens invite comparison \-liththe axioms of a deductive system whose non-logical terms areuninterpreted. The axioms of such a system are open sentences,and so truth-valueless. But the empirical hypotheses associatedwith an economic model are true or false. An empirical hypothesis"X is a P" is t rue j us t in case the real world item which "X"denotes is a realization for the model \vhich gives the definitionof "P."

The distinction between the modal and lawlike generalizationviews of economic models should be fairly clear. On the latter, alleconomic models are about real world objects , whereas on themodal view only applied models concern real world phenomena.Theoretical models are about hypothetical objects . But the relat ionship between the modal and s t ruc tura l is t views of economicmodels is less clear cut. A key difference between the two is thatthe s t ruc tura l i s t view associates a defini t ion of a predicate -which includes a l ist of t ru th-valueless axioms - with an economic model, whereas the modal view does no such thing. Butthere are some similarities between the s t ructural is t and modalviews. The empirical hypotheses associated with an economicmodel on the s t ruc tura l i s t view are ra ther analogous to theapplied models corresponding to a theoretical model on the modalview. Both the empirical hypotheses and the correspondingapplied models say something, whether t rue or false, about realworld economic phenomena; though an empirical hypothesis is asingle statement, whereas applied models of the modal view arewhole groups of statements. 11 Does the structural is t view recognize anything analogous to the theoretical models of the modalvie\v? The se t of axioms included in the definition of the predi-


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68 STEVEN RAPPAPORTcate associated with a model does not fill the bill. For, on themodal view the axioms of a theoretical model - which are includedin the model's se t K - are tru ths p albeit about hypotheticalobjects. But the axioms included in the definition of a predicateassociated with a model on the structuralist view lack a t ru th-value, unless a realization for the model is supplied. However,the structuralist view does recognize something which is similarto the theoretical models of the modal view. Suppose we have aset of hypothetical objects which constitute a realization for aneconomic model, and so the axioms listed in the definition of thepredicate the model gives become truths when interpreted interms of the hypothetical objects in question. Obviously this setof t ruths plus the realization for the model in question are quitesimilar to a theoretical model as conceived by the modal view.

IIII now turn to indicating some advantages of the modal view ofeconomic models over the two rival positions set out in sectionII. Let us f i rs t compare the merits of the modal view and thelawlike generalization view. There is a feature of economic theorizing which the modal view accounts for much better than doesthe lawlike generalization view. The feature I have in mind isthat some economic models do not purpor t to describe any realworld phenomena. I will call such models "nondescriptive models."12 A clear example of a nondescriptive model is the Tieboutmodel in public finance. The following are assumptions or axiomsof the Tiebout model (Tiebout, 1972, pp. 516-518):

(AI) Consumer-voters living under local governments arefully mobile and move to the community whose tax andexpenditure package best satisfies the i r preference forlocal public g o o d s ~ (A2) Consumer-voters have full kno\vledge of the tax and expenditure packages of the differentlocal governments. (A3) There are a large number of communities in which consumer-voters can choose to live. (A4)The source of consumer-voter incomes provides no obstacleto their full mobility - for example, they might derive alltheir income from dividends on common stock they own.(A5) There a re no external benefits or costs from theprovision of public goods by the communities from whichthe consumer-voters can choose. (A6) A local communityreaches its optimum size when its expenditure package forexisting residents is provided at lowest average cost. (A 7)


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THE MODAL VIEW OF ECONOMIC MODELS 69Communities below optimum size try to get new residents tolower costs , and communities a t optimum size t ry to keeppopulation constant .

In developing his model, Charles Tiebout was not t ry ing todescribe any real world phenomena of in teres t to economists.And this was fortunate. Axioms of the model such as (A2) areobvious falsehoods const rued as being about consumer-votersliving under real world local governments in the United Statesor anywhere else. Thus the Tiebout model would afford a verypoor description of real world phenomena were i t to be regardedtha t way.13

I f the Tiebout model does not purport to describe real worldphenomena, what is i t supposed to do? Public goods, in theeconomist's sense of the term, have the nonexcludability feature,i.e. i t is not feasible to charge a price for them and excludethose who do not pay from consuming the goods. National de-fense is a frequent ly cited example. Hany economists have be-l ieved that neither" the national government nor a system ofprivate markets is likely to provide the quant i t ies of publicgoods people really want . Essentially this is because of theproblem of preference 'revelation. Each person has a motive toconceal his preference for a public good hoping i t will beprovided anyway. Due to the nonexcludability feature, the pe r -son will then be able to consume the good without having to payfor it. Tiebout developed his model for the purpose of establishing the follo\.ring claim: 14(TC) The prOVISIon of public goods by local government canapproach the quanti t ies people want.

Given axioms (AI )-(A4) of the Tiebout model, ci t izen-voters willreveal their preferences for public goods by moving to anothercommunity or staying put. Voting with one's feet provides thesolu tion to the problem of preference revelation a t the locallevel. The equil ibrium state of the model obtains when no consumer-voter can bet ter satisfy his preference for public goodsprovided by local government by moving to another communityof less than optimum size. That is, once no consumer-voter canbetLer satisfy his preference for public goods by moving toanother community, no motive exists for fu r the r adjustment .Thus, when the Tiebout model is in equilibrium, consumer-votershave come a t least fairly close to gett ing the quantit ies of publicgoodf:> they wanL insofar as local government can provide these.Given tha t the Tiebout model generates th is conclusion, claim


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70 STEVEN RAPPAPORT(TC) would seem to be clearly warranted.

On the lawlike generalization view of economic models, wewould have ~ o regard the Tiebout model as being about realworld phenomena. A term such as "consumer-voter" in the axiomsof the model would have to be interpreted as denoting orapplying to inhabitants of real world local communities such asSanta Cruz, California and Ghent, Belgium. Now this way oflooking a t the Tiebout model would make sense provided that themodel is to be regarded as an attempt to describe real worldphenomena. For, i f the model is to be seen as attempting to tellus something about what happens in real world local communities, then of course- we should construe terms such as "consumer-voter" as denoting inhabitants of real world local communities. But i f the Tiebout model is not to be viewed as describinghow real world local communities work, what point is there ininterpret ing the terms in i t as denoting real world objects? Ithink it is safe to say that the Tiebout model should not beregarded as an attempt to describe what happens in real worldlocal communities. The model does not purpor t to give such adescription. Instead, it is designed to establish a certain possi-bili ty, viz. the one conveyed by claim (TC) above. Moreover,viewed as an effort to describe the real world, the Tiebout modelwould have to be judged quite deficient. Again, axioms such as(AI) and (A2) are evident falsehoods when interpreted as beingabout the inhabitants of real world local communities. Is Thus,interpret ing the terms in the Tiebout model as the la\vlikegeneralization view would have us do, would make 'little sense. I twould dis tor t the character of the model and the role i t isdesigned to play.

However, the way the modal view of economic models regardsthe Tiebout model resul ts in no such distortion. On the modalview, Tiebout's model is a theoretical model whose se t K containsthe axioms (Al)-(A7), and whose se t L is a set of hypotheticalobjects including consumer-voters and local communities havingdifferent tax systems and mixes of public goods. A term like"consumer-voter" in the axioms of the model does not denoteinhabitants of real world local communities, but ra ther thehypothetical consumer-voters in the model's se t L. Thus theTiebout model is not seen by the modal view as attempting todescribe what happens in real world local communities. Instead,the axioms of the model afford a t rue descript ion of what happens in the model's domain of hypothetical objects . Obviously,the account the modal view gives of the Tiebout model is entirelyfaithful to the fact that the model does not purpor t to describeany rp5l world phenomena. I6 Moreover, the role Tiebout's model is


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THE MODAL VIEW OF ECONOMIC MODELS 71designed to play can be easily understood in terms of the modalview. Again, Tiebout developed his model in order to show that i tis possible for local governments to provide the quantit ies ofpublic goods which approximates what consumer-voters , ..rant. Onthe modal view, Tiebout tried to establish such a possibility bydeveloping a set of assumptions which afford a t rue descriptionof a hypothetical domain. He reasoned from his assumptions tothe theorem or conclusion tha t the consumer-voters of thehypothet ical domain do come a t least close to satisfying the i rpreferences for public goods. Surely this is a very sensibleapproach to t ry ing to establ ish the possibility in ques t ion.

Judging from our discussion of the Tiebout model, i t seemstha t the lawlike generalization view of economic models does notfit a t all well the fact tha t economics includes nondescript ivemodels. But the modal view is entirely consonant with this fact.And this is a significant advantage of the modal view over thelawlike general izat ion view.

The s t ruc tura l i s t view is the other account of economicmodels whose merits I want to compare with those of the modalview. An advantage which has been claimed for the structural is tview is tha t i t explains what D. Wade Hands has called " theempirical immunity" of economic theory. Hands describes this asfollows:

Despite the fact tha t most economists openly advocate thesevere empirical test ing of economic theories, they in factalmost never practice what they preach. Negative evidence,if acknowledged at all, is never quite sufficient to dislodge(or cause the rejection of) a professionally popular theory.(1985, p. 322)

There is no genera l agreement on the extent of the evidence1,.,rhich apparent ly disconfirms models or theories economistspersevere in accepting. 17 But let us grant the claim that economists continue to hold onto models in the face of what seems tobe adverse empirical evidence. The s t ruc tura l i s t view is s up -posed to make sense of this practice in the fonoY..ring way (Hands,1985, pp. 322-323). On the s t ruc tura l i s t account of economicmodels, there may be empirical evidence which disconf i rms aparticular empirical hypothes is such as "the American economyin the 1970s is a Keynesian economic system." But an economicmodel i tself is not disconfirmed by such empirical evidence.Indeed, an economic model is not the sort of thing that could bedisconfirmed by any empirical evidence,18 It is no wonder, then,tha t economists hold onto models in the face of apparen t ly


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72 STEVEN RAPPAPORTadverse evidence; i t is not really evidence against the modelsthemselves. Now the modal view can make sense of the empiricalimmunity of economics as easily as the structuralist account can.On the modal view, empirical evidence can disconfirm an appliedmodel corresponding to some theoretical model. But such evi-dence does noti"mpugn the theoretical model at all. Empiricalev"idence of whatever sort is powerless to disconfirm a theoreti-cal model. 19 For empirical evidence is formulated by statementscharacterizing real world economic phenomena, while a theoreti-cal model includes t ruths about hypothetical economic phe-nomena. Since on the modal view apparent ly adverse empiricalevidence does not tell against theoretical models, i t is notsurprising economists persevere in accepting theoretical modelsin the face of evidence which some have taken to disconfirmeconomic theories. In sum, the ability to explain the empiricalimmunity of economics does not dist inguish the st ructural is tview of economic models from the modal view.

Another advantage which has been claimed for the s t ruc tur -alist view of economic models is expressed in the followingpassage from Hausman:

This kind of endeavor is particularly prominent in econom-ics, where theorists devote a great deal of effor t to ex-ploring the impli'cations of perfect rationality, perfect in -formation, and perfect competition. These explorations,which are separate from questions of application and as-sessment , are, I believe, what economists (but not eco-nometricians) call "models." One can thus make good use ofthe semantic view to help understand theoretical models ineconomics. (Hausman, 1984, p. 13)

Given the reference to perfect competition ahd the like, Hausmanseems to claim here that the st ructural is t view of models (hecalls it "the semantic view") has the advantage of enabling us tounders tand nondescriptive models in economics such as theTiebout model and the model of perfect competition. This claimimplies that nondescriptive models can be viewed along s t ruc-turalist lines without distorting their nature or role in economictheorizing. This implication seems plausible enough. We mightreconstruct the Tiebout model along structural is t lines by re -casting the model as defining a predicate like "is a Tieboutsystem of local governments." The definition would be this: X isa Tiebout system of local governments iff X satisfies the follow-ing axioms. The definiens would be completed by listing axioms(A1)-(A7) of the Tiebout model set out above. A set or system of


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THE MODAL VIEW OF ECONOMIC MODELS 73hypothetical consumer-voLers and local governments could bespecified as a realization for the model. This set of hypotheticalobjects would be denoted by "is a Tiebout system of localgo'vernments." Theorems of the model can be in te rpre ted inte rms of the seL of hypothet ical objects in question, includingthe Lheorem that \d1en the TiebouL model is in equilibrium,consumer-voters a t least come fairl:-. close to g-etting the quantities of public goods they want. The fact that this theorem sointerpreted can be deduced establishes the possibility that localgovernments can provide a t least close to the quanti t ies ofpublic goods people want. This structural ist presentation of theTiebouL model seems compatible 'with the fact that it is a nondescript ive model, as well as the fact that its role is to establishthe p o s s i b i 1 i t ~ y jus t mentioned. 20 Yet the apparen t fact tha tviewing nondescriptive models along structuralis t lines does notdistort their nature or role, gives us no reason for preferr ingthe s t ructural is t view of economic models over the modal view.As indigated above, the modal view is entirely consonant with thepresence in economics, and the functioning, of nondescript ivemodels.

The last two paragraphs may give the impression that thes t ruc tura l i s t and modal views of economic models are pre t tymuch bed as far as their worth or merits go. But this is not so.The modal view enjoys a significant advantage over the s t ruc-tural ist view. The modal view is a much better description thanthe structuralis t v"iew of the way economisLs in fact present andapply their models. As a matter of fact, in presenting or developing a model, economists do not give a definition of a predicateof the sort described by the structuralis t position. For example,in developing his model, Tiebout simply did not state a s tructur-alist style definition of a predicate such as "is a Tiebout systemof local governments ." Economists do set out assumptions oraxioms when they develop a model. And sometimes present ing amodel includes giving one or more definitions. But the definitionsare not a t all like a s t ructura l is t definition of a predicate. Forexample, the usual development of the model of the beha'i.rior of afirm in per fec t competition includes a definition of a perfect lycompetitive market. The definition specifies conditions individually necessary and jointly sufficient for a market being perfectlycompetitive, conditions such as the firms on the sellers' side ofthe market produce a homogeneous good. But the definition doesnot say a market is perfect ly competi t ive iff i t satisf ies theaxioms of the model such as "firm managers select an ou tpu tlevel which maximizes firm profi ts ." So the s t ruc tura l i s t viewjus t does not fit the way economists actually presen t the i r


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74 STEVEN RAPPAPORTmodels apart from applications to the real world. The modal viewaffords a better fit here. On the modal view a theoretical modelmay include one or more definitions like the definition of aperfectly competitive market, and i t definitely includes a sepa-rate list of axioms or assumptions. And, as jus t indicated, this infact is how economists presen t their models. Nor in applyingtheir models to the real world, do economists affirm empiricalhypotheses of the sort the structuralist view talks of . Instead,economists apply models to real world situations in the mannerdescribed by the modal vie\',' in the second paragraph of section1.2l This could be readily confirmed by looking at applications ofmodels to real world situations given in textbooks on micro-economic and macroeconomic theory.

I t might be admitted that the s tructura l is t view does notafford as faithful a description of the way economic models areactually presented as does the modal view. But, it might be said,the structuralist view should not be seen as a description of howeconomists actually presen t and apply their models. Instead itshould be seen as characterizing a way in which economic modelscan be reconstructed which is illuminating.22 And we shouldcompare the structural ist and modal views as illuminating recon-struct ions of economic models, ra ther than descript ions of theactual manner in which models are handled in economics. Inresponse to this, the modal view itself involves a certain amountof reconstruct ion of economists' models. On the modal view, atheoretical model includes a se t of hypothetical objects whosebehavior is described by the axioms of the model. But in pre -senting their models, economists usually do not specify a set ofobjects explicitly identified as hypothetical whose behavior isdescribed by assumptions of the models. Furthermore, I amwilling to gran t tha t economic models can be reconstructed orrestated along structural is t lines. For a given economic model,philosophers of economics can invent a predicate and recast themodel so that i t gives a structural is t style definition of thepredicate - this was done above for the Tiebout model. But whatgain in illumination would flow from restat ing economic modelsalong s tructura l is t lines which we do not ge t from the modalview? As we have seen, vie\ ...ing economic models from the s t ruc-turalist perspective can make sense of the empirical immunity ofeconomic theory. But recall that the modal view can do this jus tas well. I t has been claimed the structural ist view enables us tounderstand nondescript ive models in economics such as theTiebout Model. But, as indicated above, the modal view alsoaffords us this unders tanding. In short , I do not see tha tanything illuminating resul ts from structuralist reconstruct ions


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THE MODAL VIEW OF ECONOMIC MODELS 75of economic models which the modal view does not also give us.But since the modal view is a much better descript ion of howeconomists actually present and apply models, the modal view isthe beUer of the two accounts of economic models. 23

The modal view has been compared to the structural is t andlmvlih.e g e n e n : : l . l i ~ a t i o n v i ( ~ \ , ' s of economic models. On the basis ofthe discussion here, the modal view is preferable to either of itstwo rivals.

De Anza Colle?,"e

NOTES1. On Neil DeMarchi's recent interpretat ion of J. S. Mill'sphilosophy of economics, Mill adopts a somewhat crude ver -

sion of the modal view. (DeMarchi himself seriously underestimates the relevance of the modal view to unders tandingpost-classical economic theory.) See DeMarchi, 1986. I havetr ied to show (Rappaport, 1986) that the modal view can beused to defend neoclassical microeconomics from the chargeof incorporat ing falsehoods.

2. A look at any standard presenta t ion of neoclassical microeconomics will verify this descript ion of the elaborat ion ofthe model. For example, see Nicholson, 1978, p. 286, pp.3. A useful distinction can be made between casualapplications of economic models and applications employingthe techniques of econometrics (Gibbard and Varian, 1978, p.672). I am describing here only casual applications of economic models.

4. Economic models seldom, if ever , fit the real world exactly.So i t would be be t te r to say tha t sentences in an appliedmodel are approximately t rue concerning' the rea l worldsituation to which the model is being applied. And to say thisis to affirm that the real world situation in question closelyresembles the way the \.,rorld \vould be i f the sentences in theapplied model were t rue.

5. Gibbard and Varian claim (1978, p. 667) that the sentencesof a model that is not applied to a real world si tuat ion are\vithout t ru th-value . This contradicts the account of theoretical models supplied by the modal view. But I do not findacceptable this claim Gibbard and Varian make abou t thesentences of non-applied models. See Rappaport, 1986, p. 292,pp. 295-296 note 6. The way the non-definitional sentences ofa theoretical model acquire the i r t ru th is a case of what


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76 STEVEN RAPPAPORTQuine calls "legislative postulation," which he regards as away in which sentences in set theory have their truth fixed.See Quine, 1966, pp. 110-113.

6. But Hausman himself does not adopt the lawlike general ization view. He seems to accept a st ructural is t construal ofeconomic models. See Hausman, 1981, pp. 44-48; 1984, pp.7. Sometimes the lawlike general izat ion view is putforward as holding for theories in social science generally,and therefore for economic theories or models in particular.See Brodbeck, 1968, pp. 457-458. Alexander Rosenberg hasheld that the general sentences of neoclassical microeconomics are lawlike general s tatements whose subject matteris real world economic phenomena (Rosenberg, 1976, chs. 3, 6,and 8). This reflects acceptance of the lawlike generalizationview. The Rosenberg of 1976 thinks that the lawlike generalizations of microeconomics are qualified by explicit orimplicit ceteris paribus clauses (Ibid., p. 130, pp. 133-138).And this is perfectly compatible with the lawlike generalization view of economic models.

8. Versions of the structural is t (or semantic) view of theoriesare found in Suppes (1957), Stegmiiller (1976), Van Fraassen(1980), and Giere (1984). Hands (1985) and Hausman (1981)present s tructural is t accounts with an emphasis on application to economics ( though Hands' final assessment of thes tructura l is t position is negative).

9. Structural is ts usually speak of models for a theory(Suppes, 1957, p. 253). I have used the term "real izat ion"instead of "model" here to avoid confusion between economicmodels and models as items which satisfy the axioms of adeductively organized theory.

10. Some versions of structuralism would identify an economicmodel with an ordered n- tuple which contains the se t ofrealizations for the model and the se t of intended applicat ions (StegmUller, 1976, p. 118; Hands, 1985, p. 311). Otherversions would identify an economic model or theory with theconjunction of the empirical hypotheses associated with themodel (Giere, 1984, p. 83).

11. In Hausman's version of the structural is t view, an empiricalhypothesis associated with an economic model logically implies what he calls "closures of" the axioms of the model(1981, pp. 47-48). These are the axioms of the model in ter -preted in terms of the real world item or system which theempirical hypothesis is about. In Hausman's version ofstructural ism, a se t of closures of the axioms of a model isthe closest thing to an applied model of the modal view.


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THE MODAL VIEW OF ECONOMIC MODELS 7712. Gibbard and Varian distinguish (1978, p. 665) between ideal

models and descript ive models, though they say little inexplanation of the distinction. What Gibbard and Varian call"ideal models" would seem to be the same as my nondescripLive models. I t should be noted tha t from the fact that amodel is nondescriptive, it does not follow that it can play norole in unders tanding real world economic phenomena. Themodel of perfect competition is nondescriptive. Yet economists standardly use i t as a framework for unders tandingreal world agricultural markets.

13. Economists have made some effort to determine to whatextent the circumstances envisaged by the Tiebout modelresemble what goes on in real world local communities. Theapproach which economists have adopted is to t ry to inferfrom the Tiebout model some statement which can be testedagainst empirical data. An example of such a statement is: acommunity's level of expenditure on public goods is positively correlated with local property values, and the level oflocal taxes is negatively related to property values (Oates,1969, pp. 959-962). The inferred s ta tement is then tes tedwith the aid of multiple regression analysis. Depending onLhe outcome, some conclusion is reached about the resemblance between the world of the Tiebout model and the realwor ld. The fact that economists have tried to determine whatresemblance, i f any, holds between the world of the Tieboutmodel and the real \,"orld, is perfectly consistent with theTHodel not purporting to describe anything in the real world.

14. See Tiebout, 1972, pp. 513-514. Also, Tiebout says (Ibid., p.522) "It is the contention of this article that , for a substantial portion of collective or public goods, this problem doeshave a conceptual solution." (The problem Tiebout is alludingto is specifying a mechanism for getting consumer-voters toreveal their preferences for public goods, and so for thequantities of such goods people want to be provided.) NoteTiebout describes his model as affording a conceptual solution of the problem.

15. Perhaps an advocate of the lawlike generalization view wouldsay (AI) and (A2) are not falsehoods once they are qualified\vith the appropriate ceteris paribus clauses. But in fact, inpresent ing his model Tiebout did not view i ts axioms asqualified by ceteris paribus clauses. Moreover, the ceterisparibus clauses which do qualify some statements in economics exclude each of a number of specif ied circumstanceswhich could explain a breakdown of the s tatement qualified.For example, the law of demand says: ceteris paribus, the


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78 STEVEN RAPPAPORTquantity of a good buyers purchase and the good's ownprice are negatively related. The ceteris paribus clause infront of the law of demand excludes the presence of each ofa number of circumstances - a change in buyers ' income, achange in the price of a subst i tute good, etc. - which, ifpresent, could cause a failure of quanti ty purchased to varynegatively with the good's own price. But what circumstances would be excluded by a ceteris paribus clause infront of, say, axiom (A2) of the Tiebout model? That consumer-voters lack complete knowledge of the tax and expenditure packages of the different local communities? But ifthis is what is excluded, axiom (A2) becomes a mere t au-tology, which would seem inconsistent with at least the spiritof the lawlike general izat ion view of economic models.

16. On the modal view there is an indefinite number of appliedmodels corresponding to the theoretical Tiebout model. TheTiebout model might be applied - in the sense described insection I - to the se t of local communities in the UnitedStates, the set of local communities in France, etc. (But givenwhat we know about people who inhabit real world localcommunities, all these applied models would include s ta te-ments which are false.) The discussion of the Tiebout modelhere does not concern any of these applied models. I t is onlyconcerned with the model Charles Tiebout presented in hisoriginal paper which was designed to establish the possibility conveyed by claim (TC).

17. Alexander Rosenberg claims the empirical failures of neoclassical microeconomics are considerable (1986, p. 129). He affirmed this in response to D. Wade Hands assert ion to thecontrary (1984, p. 497).

18. This claim looks plausible on versions of structuralism whichidentify an economic model with an ordered n-tuple whichincludes the set of realizations of the model, etc. (see note 10above). But the claim would obviously be incorrect on aversion of structuralism identifying a model with the conjunction of empirical hypotheses associated with it.

19. Elsewhere I have developed this point at somewhat greaterlength for neoclassical microeconomic models (Rappaport ,1986, pp. 293-294).

20. Philosophers of economics have applied the st ructural is tview in some detail to Walrasian general equilibrium theory(Handler,- 1980; Hands, 1985). Hands says (1985, p. 329) theset of intended applications of general equilibrium theory ispret ty much empty. The same is t rue of the set of intendedapplications of the st ructural is t r e c o n s t r ~ c t i o n of the


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THE MODAL VIEW OF ECONOMIC MODELS 79Tiebout model. No se t of real world local communities orgovernments is going to satisfy axioms of the Tiebout modellike (A2).

21. Recall from note 3 above that the account of applied modelssupplied by the modal view is restr icted to non-econometricapplicationH of models.

22. Logical empiricis ts made a ra ther similar claim about theirview tha t a scientific theory is associated with a formalizeddeductive system. For example, Richard Rudner says (1966,p. 18) "It would be a serious mistake to construe the foregoing account [of theories as formalized deductive systems] asa description of the actual process by which theories are, orshould be, formulated. I t is not a description of any processof theory construction, actual or proposed; it is, rather , anaccount of the logical or st ructural characterist ics of theories. "

23. Hands makes the sensible suggest ion (1985, p. 304) tha t agood philosophical account of economic models either helpsus bet ter unders tand such models, or accurately describeshow economists actually handle their models, or both. Nycase here for the modal view relies on Hands' criterion. Thest ructural is t view does not enable us to explain anythingabout economic models which the modal view cannot alsoexplain; and the modal view is a more accurate description ofhow economists presen t and apply models. So, on Hands'cri ter ion for a good philosophical account of models, themodal view has the advantage over the s tructura l is t view.

REFERENCESBrodbeck, May. 1968. "Theory Construction." In Readings in the

Pbilosophy o f the Social Sciences, edited by fvlay Brodbeck,New York: Macmillan, pp. 457-463.

DeMarchi, Neil. 1986. "Mill's Unrevised Philosophy of Economics."Philosophy of Science 53: 89-100.Gibbard, A. and Varian, H. 1978. "Economic Models." The Journalof Philosophy 75: 664-683.Giere, R. 1984. Understanding Scientific Reasoning 2nd Edition.

New York: Holt, Rinehart and Winston.Handler, Ernst . 1980. "The Logical Structure of Hodern Neoclas

sical Static Microeconomic General Equilibrium Theory." Er-kenntnis 15: 33-53.

Hands, D. Wade. 1984. "What Economics Is Not: An Economist 'sResponse to Rosenberg." Philosoph.v of Science 51: 495-503.


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80 STEVEN RAPPAPORTHands, D. Wade. 1985. "The Structuralist View of Economic Theo

ries: A Review Essay." Economics and Philosophy 1: 303-335.Hausman, Daniel. 1981. Capital, Profits, and Prices. New York:

Columbia University Press.Hausman, Daniel. 1984. "Introduction." In The Philosophy o f

Economics, edited by Daniel Hausman, New York: CambridgeUniversity Press, pp. 1-50. . .Lewis, David. 1973. Counterfactuals. Cambridge, Massachusetts:

Harvard University Press.Nicholson, W. 1978. Microeconomic Theory. Hinsdale, Illinois: The

Dryden Press.Oates, Wallace. 1969. "The Effects of Property Taxes and Local

Public Spending on Property Values: An Empirical Study ofTax Capitalization and the Tiebout Hypothesis." Journal o fPolitical Economy 77: 957-971.

Quine, W.V.O. 1966. The Ways o f Paradox and Other Essays. NewYork: Random House.

Rappaport, Steven. 1986. "The Modal View and Defending Microeconomics." In PSA 1986 Vol. 1, edited by A. Fine and P.Machamer, East Lansing, Michigan: Philosophy of Science Association, pp. 289-297.

Rosenberg, Alexander. 1976. Microeconomic Laws: A PhilosophicalAnalysis. Pit tsburgh: University of Pit tsburgh Press.

Rosenberg, Alexander. 1986. "What Rosenberg 's Philosophy ofEconomics Is Not." Philosophy o f Science 53: 127-132.

Rudner, Richard. 1966. Philosophy o f Social Science. EnglewoodCliffs, N.J.: Prentice-Hall.

Stegmi.iller, W. 1976. The Structure and Dynamics o f Theories.New York: Springer-Verlag.

Suppes, Patrick. 1957. Introduction to Logic. Princeton, N.J.: D.Van Nostrand Co.

Tiebout, Charles. 1972. "A Pure Theory of Local Expenditures."Reprinted in Readings in Urban Economics, edited by M. Edeland J. Rothenberg, New York: Macmillan, pp. 513-523.

Van Fraassen, Bas. 1980. The Scientific Image. Oxford and NewYork: Oxford University Press.

rappaport the modal view of economic models

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