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CIAO DATE: 03/02
Critical Review
Winter–Spring 1998 (Vol.12 Nos.1–2)
The Faults of Formalism and the Magic of Markets
By Daniel M. Hausman *
Abstract
Contrary to Peter J. Boettke’s essay, “What Went Wrong with Economics?”, there is no connection between “formalism” and the alleged inability of mainstream economists to regard theoretical models as anything other than either depictions of real market economies or bases for criticizing market economies and justifying government intervention. Although Boettke’s criticisms of the excesses of formalism are justified, Austrian economists such as Boettke need to justify their view that government interventions into economic affairs are inevitably harmful.
In his essay, “What Went Wrong with Economics? Equilibrium as a Flight from Reality” (Critical Review 11, no. 1), Peter Boettke offers the reader a historical diagnosis of the ills of economics. The root problem is methodological. Instead of treating the notion of an equilibrium as an ideal type, to be used as a point of contrast for the study of economic institutions and processes, economists have either pretended (incredibly) that real economies are in equilibrium, or they have maintained that departures from equilibrium represent economic failures to be rectified by government intervention. Boettke maintains that this central methodological mistake is tied to two others. First, economists have become so enchanted with their mathematical tools that they have become unable to make use of any claims about economics, no matter how insightful, unless they can be formulated within a mathematical model. Second (and largely as a consequence), economists have had almost nothing to say about disequilibrium and dynamics. So instead of developing the sort of rigorous “realistic” theorizing exemplified in Hayek’s work—which concerns the contrasts between static equilibrium and real, dynamic disequilibrium dynamic processes—economists have lost themselves in their formal models, rarely looking out at the real world and then only to pretend that their model is the real world; or, alternatively, in preaching government intervention to make the real world conform to the model. The result is just the disastrous interventionism that Hayek feared, though he thought that it would come from the anti-theoretic stance of historicists rather than from the excesses of “formalism.”
Although Boettke diagnoses some of the deficiencies of contemporary economic theorizing, the details of his criticisms are hard to pin down and to substantiate. In particular, Boettke’s critique of the misuse of the notion of competitive equilibrium is puzzling, and its connection to his condemnation of formalism is hard to understand. The alternative to formalism supposedly exemplified in Hayek’s economics is never spelled out, and when one looks at the contrasts Boettke draws between Hayek’s work and the work of a contemporary “formalist” such as Stiglitz, the puzzle only grows.
Adam Smith suggested that agents pursuing their own interests in market economies will (as if directed by an invisible hand) serve the common good more effectively than if they aimed directly at the common good. Smith could make no rigorous argument for this conjecture, but the notion that a decentralized economy might promote overall welfare seemed to conform to the experience of Smith’s successors, and his conjecture captured their imagination. In this century economists have apparently proven a version of Smith’s claims about an invisible hand. If individuals are perfectly informed and in a specific sense rational and self-interested, if production possibilities are well-behaved, if there are many buyers and sellers in every market and markets for every (perfectly divisible) commodity at every date and place, and if there are no externalities or public goods, then at least one Pareto-optimal economic equilibrium obtains. The thought that decentralized markets “work” is captured in the conclusion that there exists an economic equilibrium—that is, is a state of affairs in which there are no excess demands in any market and no excess supplies of any good that is not free. The thought that people are brought to serve the common good is translated into the conclusion that this equilibrium is Pareto optimal—that is, that there is no alternative that is unanimously preferred to it.
One might well wonder why economists are so excited about the notion of a Pareto optimum, since it is not very high praise for a social state S that for any alternative S’, somebody prefers S to S’. Moreover, even if one supposes that it is a good thing to satisfy people’s preferences and denies that interpersonal comparisons of the extent to which preferences are satisfied can be made, one cannot infer that R is better than Q from the fact that R is Pareto optimal and that Q is not. The proof that competitive equilibria are Pareto optimal is better interpreted as showing that competitive equilibria do not show a particular vice—that they do not pass up unanimously favored improvements—rather than that they possess any particular virtue. Yet at least this much can be proven, and the proof has played an important role in arguments concerning the welfare properties of markets. Together with the so-called second welfare theorem (that any optimal outcome can be achieved as a competitive equilibrium given the right initial distribution of endowments), this result lies at the foundation of modern welfare economics.
Yet the proof of the existence and optimality of competitive equilibrium does not establish Smith’s conjecture. His conjecture concerned the outcome in real societies of real self-interested behavior, while the theorem concerns the hypothetical outcome of perfectly rational self-interested behavior in circumstances that are strikingly unlike any actual circumstances. What possible point could there be in theorizing about a Never-Never Land of perfect knowledge, complete futures markets, infinite divisibility, non-increasing returns to scale, and so forth? One answer is that reality approximates this Never-Never Land in its economically relevant respects. Like Boettke, I do not think this response is tenable, and I shall say nothing more about it. A second answer is that one might wonder whether a Pareto-optimal competitive equilibrium could be reached even if we were free of all those complexities that distinguish our world from Never-Never Land. Obviously not everyone would or should be interested in this purely theoretical question, but given the prevalence of economic theorizing employing such models, one can argue that there is some value in asking this odd “What if” question.
Be that as it may, Smith’s conjecture has not been proven. Historical experience has established that market economies that have been subjected to relatively little government interference have grown more rapidly and persistently than other kinds of economies that have been tried thus far. That experience does not, however, establish that market economies are better than untried alternatives; and only in exceptional circumstances does the historical record warrant any view of what the consequences would be of any particular proposal for reforming market economies. To address such questions, one needs economic theory. Boettke complains that contemporary “formalist” economic theory is unable to answer such questions. Because of their insistence on mathematical modeling, formalist economists can only deal with unrealistic non-existent circumstances, and they are consequently forced either to pretend that reality approximates their simplistic models or that reality could be made to approximate the models with the help of judicious government intervention. But we are not in perfectly competitive equilibrium, and government intervention could not possibly overcome all the barriers that forever separate us from perfectly competitive equilibrium.
In that case, what possible use could models of perfectly competitive equilibrium have? One answer is that these models are of no use at all. For example, Joseph Stiglitz (1994, 267) writes,
| Imperfect and costly information, imperfect capital markets, imperfect competition: These are the realities of market economies—aspects that must be taken into account by those countries embarking on the choice of an economic system. The fact that competition is imperfect or capital markets are imperfect does not mean that the market system should not be adopted. What it does mean is that in their choices, they should not be confused by theorems and ideologies based on an irrelevant model of the market economy. Most important, it means that in deciding on what form of market economy they might adopt, including what role the government ought to play, they need to have in mind how actual market economies function, not the quite irrelevant paradigm of perfect competition. |
This radical answer is not Boettke’s or Hayek’s. Boettke (1997, 23) argues that models of perfectly competitive equilibrium should be regarded as ideal types.
| An ideal type is neither intended to describe reality nor to indict it. It is instead a theoretical construct intended to illuminate certain things that might occur in reality; empirical investigation determines whether these phenomena are actually present and how they came to be there. Deployed as an ideal type, equilibrium analysis allowed economists to describe what the world would be like in the absence of imperfections such as uncertainty and change. The descriptive value of the model lay precisely in its departure from observed reality, for this underscored the function of real-world institutions in dealing with imperfect knowledge, uncertainty, and so forth. |
Although there are some obscurities in Boettke’s account (in what sense “might” there be complete futures markets?), the basic idea seems clear enough. The point of an ideal type is to provide a perspective or a point of comparison. By studying how reality differs from the ideal type, economists can learn things about actual markets that they might otherwise have overlooked. Ideal types appear to have an entirely heuristic role. A “good” ideal type is one that helps economists to learn about economies, while a bad one does not. The extent to which the ideal type approximates reality is not itself of any particular importance.
If this interpretation of Boettke’s view is correct, then it is puzzling why the model of competitive equilibrium should be so prominent. The reason would have to be that comparing actual economies with an ideal type of a perfectly competitive equilibrium is in fact more informative than comparing actual economies with an ideal type of a command economy, a Keynesian economy, or any of a dozen different institutionalist ideal types. This seems dubious. For heuristic purposes, one would have thought eclecticism desirable. Many different perspectives should be more informative than just one.
Boettke himself (1997, 44) seems ambivalent about whether ideal types are only of heuristic value:
| The main task of any science is to investigate the degree of correspondence between various ideal types and empirical reality; but this means that science is primarily a matter of experimentation or, in social science, historical research—not model-building but model-testing (i. e., testing of the applicability of intelligible models to given situations). Still, the “falsification” of an ideal type in a given instance does not require that it be discarded as useless. It may aid the scientist in constructing ever more realistic models of the circumstances of that particular time and place. . . . Treating models as ideal types allows one, or one’s colleagues, to root out one’s ideological prejudices by subjecting one’s models to the empirical test of applicability as well as the philosophical test of intelligibility. |
When Boettke boldly asserts that “the main task of science is to investigate the degree of correspondence between various ideal types and empirical reality,” presumably he does not mean that scientific theories have only a heuristic significance. It would be odd to speak, as Boettke does, of “testing” theories or models, if the role of theories and models were only to guide the study of reality. In addition to their heuristic role, it seems that ideal types also aim to represent reality. The heuristic role only becomes central when the representational effort fails.
Although this view makes better sense of Boettke’s text, we still have not explained why variations on one particular ideal type should possess such a hegemony in economics. When one turns to Hayek’s own work for an answer, one finds the following remark:
| While in the field of the Pure Logic of Choice our analysis can be made exhaustive, that is, while we can here develop a formal apparatus which covers all conceivable situations, the supplementary hypotheses must of necessity be selective, that is, we must select from the infinite variety of possible situations such ideal types as for some reason we regard as specially relevant to conditions in the real world. (1949, 47) |
Hayek is here distinguishing between two components of economic models. One part consists of what Hayek calls “the Pure Logic of Choice,” by which he means some formulation of (at least some subset of) the fundamental principles of contemporary economics. The model of individuals as rationally pursuing their own interests is not, in Hayek’s view, an ideal type, because this “formal apparatus” “covers all conceivable situations.” Economists only generate ideal types when they add simplifying assumptions concerning, for example, knowledge or the absence of externalities. Hayek believes that his own concern with an ideal type of competitive equilibrium is justified by the tendency of real economies toward equilibrium (1949, 44–45, 49). It is hard to say exactly what this means and exactly how the equilibrium he is thinking of relates to perfectly competitive equilibrium, because the factors that prevent an economy from reaching equilibrium are so deep and pervasive. But the importance of equilibrium for Hayek is not mainly heuristic. What explains and justifies the ubiquity of equilibrium models in “formalist” economics (most of which are not models of perfect competition) seems to be that these are the only mathematically tractable models that embed the “Pure Logic of Choice.” One finds not just one ideal type, but a whole range that share a common core that is not itself (in Hayek’s view) an ideal type.
Boettke is right to complain that the contemporary range of these ideal types is limited by the insistence on formalization, but his charge that formalist economists in general misunderstand the nature of their constructions is hard to substantiate. Of course there are individual formalist economists (like individual Austrian economists or individual stamp collectors) who have said some very silly things. The question is whether formalists in general overlook the heuristic uses of ideal types. Notice that there is no methodological mistake—though there may be empirical error—in arguing that a particular ideal type approximates reality or that with appropriate government intervention, such an ideal type would approximate reality. The methodological mistake Boettke identifies is supposed to lie in an inability to understand how an ideal type could otherwise be of value.
| Absent from both types of formalism was recognition of any possibility other than all or nothing. Either the real world exemplified static equilibrium, or it could not approach that state without a push from the state. The intermediate possibilities represented by real-world institutions of adjustment to disequilibrium became invisible because the model contained only equilibrium. (1997, 19) |
The earlier quotation from Stiglitz might be taken as exemplifying this mistake. Since Stiglitz is acutely aware that economies are not in perfectly competitive equilibrium and cannot be brought into it via government intervention, he asserts that “the paradigm of perfect competition” is “quite irrelevant.”
Without undertaking an extensive literature review, I cannot determine whether “formalist” economists in general commit this sin, but it seems fair to focus on Stiglitz’s work, since Boettke singles Stiglitz out as exemplifying the blunders of formalist economics. If Stiglitz does not make the mistakes that Boettke alleges, it might be that Boettke is wrong merely about Stiglitz, who turns out to be an exception to the erroneous rule. But if Boettke’s own evidence conflicts with his claim, one can conclude that his claim is at least unproven.
In the extracted quotation, Stiglitz says that the model of perfect competition is “irrelevant” for policy makers. He does not say that it is irrelevant for theorists. Unless Stiglitz is prepared to condemn most of his own life’s work, which has been devoted to studying ways in which economic reality differs from perfect competition, he could not possibly believe that the model of perfect competition is of no importance for economic theorists. He asks, for example, whether imperfect knowledge is consistent with the absence of externalities (1994, 29–30)—which would not be worth asking if one did not “take seriously” a model in which externalities are absent. He argues that a complete set of markets is inconsistent with perfect information and indeed is itself a conceptual impossibility (1994, 37–9), and the reason he thinks about the possibility of complete markets is that perfectly competitive equilibrium requires them. So Stiglitz does not believe that the model of perfectly competitive equilibrium is worthless.
Nor does Stiglitz maintain that reality is approximately in perfectly competitive equilibrium or that government intervention could bring this about. Having argued at great length that markets are necessarily imperfect, the question cannot be how to make them perfect. The question instead is what set of institutions will bring about the best results—and there is absolutely no presumption that government intervention will improve matters. To the contrary, Stiglitz addresses section after section of his 1994 book to a painstaking account of the risks and difficulties to which government engagement in economic life is subject. In his own words:
| This pervasiveness of failures [as compared to competitive equilibrium], while it reduces our confidence in the efficiency of market solutions, also reduces our confidence in the ability of the government to correct them. (1994, 44). |
Boettke’s accusation cannot, therefore, be sustained. Stiglitz does not regard perfectly competitive equilibrium as an ideal that can be realized with the help of government intervention. On the contrary, Stiglitz employs the model of perfectly competitive equilibrium precisely as an ideal type: He uses the comparison between reality and the model to identify institutions and practices that are important because of the divergence between reality and the model.
| The advocates of market socialism made, however, a critical mistake, in not paying sufficient attention to the institutions (e.g., banks) which have arisen under capitalism to solve the problems created by absent markets. They are not a perfect substitute. But they may result in an allocation of investment that is better than it otherwise would be—and better than it is under market socialism. (Ibid., 92) |
What is it, then, that bothers Boettke so much about Stiglitz’s work? Why does he place Stiglitz in the camp of those who reject “empirically meaningful and rigorous theorizing” (Boettke 1997, 46) rather than welcoming him to the side of the angels? One reason is that Stiglitz is a formalist: He values mathematical modeling, and he probably believes that if an idea “could not be translated into an appropriate model, there was not much that could be done with it” (ibid., 22). But as Stiglitz’s work demonstrates, such a commitment to “formalism” is fully consistent with regarding economic models as ideal types. The commitment to mathematical modeling does not imply (and indeed has little connection to) the view that models must be regarded as approximating reality or as ideals to be achieved by means of government intervention.
Is formalism of the sort exemplified by Stiglitz’s work a mistake? The question is ambiguous. It might be interpreted as: “Is it sometimes a mistake to address economic questions with mathematical tools?” or as “Is it a mistake to address them only with mathematical tools?” Boettke would, I believe, answer yes to both of these questions, but let us address them separately. Consider the first question first. Boettke holds that it is sometimes a mistake to attempt to address economic questions with mathematical models, because economists do not possess the mathematical tools needed to model complicated dynamic relations. Attempting to employ mathematical models despite these inadequacies distorts inquiries concerning the consequences of ignorance or concerning processes of discovery, and it creates misunderstandings.
This is a serious and important criticism, but there are two reasons to hesitate before accepting it. First, mathematical techniques are constantly changing and improving. Explicitly dynamic problems are hard to model mathematically, but I know of no proof that the job cannot be done. The second reason to hesitate before accepting Boettke’s condemnation of mathematical modeling is that one needs to consider how serious the distortion and misunderstanding will be and how gravely they will compromise the results. Even if formalist treatments of problems concerning knowledge will necessarily be imperfect, they will not necessarily be worthless. A wrench is the wrong tool for driving a nail, but if one does not have a hammer, it may be the best tool to use all the same. Stiglitz himself is well aware that a great deal is left out of his models. “No simple model can capture the processes by which institutions adapt to changing circumstances,” he writes (1994, 25; see also 65).
Whether or not there is any mistake in addressing questions concerning ignorance, innovation, and discovery by means of mathematical models, one might agree with Boettke that it is a mistake to insist that there is no other way to address these questions. As Boettke sensibly points out (1997, 50), the syntactic clarity and precision of mathematical models do not insure their semantic clarity or precision; and indeed confusion concerning the interpretation of theorems is very common in economics. I am personally quite sympathetic to Boettke’s point here. Many economists have become so enchanted with mathematical techniques that they are unable to appreciate important observations and valid arguments when these are made in ordinary prose.
But there is a deeper issue. At one point Hayek observes that even when competition is imperfect “this does not mean the competition does not also bring about as effective a use of resources as can be brought about by any known means where in the nature of the case it must be imperfect” (1949, 104). Quite so, but does competition in fact accomplish this? Does it “bring about as effective a use of resources as can be brought about by any known means?” Boettke writes (1997, 27), “Of course, in this process of perceiving the future, entrepreneurs may (and do) make errors, but these errors can, by creating further discovery opportunities, generate further activity aimed at allocating or reallocating resources in a more effective manner to obtains the ends sought after.” This seems possible. But is it? What, in fact, are the consequences when entrepreneurs seize the opportunities created by the errors of others? Does their activity improve or diminish economic performance?
How are such questions to be addressed without mathematical modeling? The theory of the second best (Lipsey and Lancaster 1956–57) removes any presumption that corrections of errors necessarily improve outcomes. Without such a presumption, and without mathematical modelling, how could Hayek’s or Boettke’s claims be established or refuted? Stiglitz asks, “If markets do not work efficiently under these idealized circumstances, how can we be confident that they would work efficiently under more complicated circumstances? Only by an act of (and indeed a leap of) faith!” (1994, 26).
Boettke never responds to this critique. He is acutely aware of the need for evidence only when he is considering the views of those he disagrees with. The notion of an efficiency wage is, he maintains, “an ad hoc, empirically ungrounded dogma” (1997, 42). Boettke complains that Bardhan and Roemer’s attribution of the political failures of contemporary governments to inequalities of influence owing to inequalities of wealth “is more assumed than proved” (ibid., 36). But Boettke has no such doubts about the benefits of unimpeded markets: “To find such an error is to produce economic information that is useful in a world that does not approximate equilibrium; to use this information to make a profit is to move that world a little closer to the normative ideal” (ibid., 33). He is not worried about the fact that this view appears to be “more assumed than proved.” Boettke maintains that “the divergence between ideal and reality can highlight the ways reality may have institutionalized error-correcting properties that can, in fact, be seen as propelling the world in a direction reminiscent of general equilibrium” (ibid., 43–4). How does he know that the divergence will not highlight deficiencies in real markets? Might not his optimistic view be “empirically ungrounded dogma”?
Boettke’s apparent presumption that any respectable economic theory must demonstrate the superiority of unimpeded markets to any feasible alternative may explain his dissatisfaction with Stiglitz’s work and “formalism” in general much better than any of the methodological points canvassed above. Boettke (1997, 35) writes:
| Still missing from the [Stiglitz’s] analysis is an examination of how imperfect human beings attempt to cope in a real world of ignorance and uncertainty. As a result, we get the bifurcation of the world into a private sector that [is] unable to do anything to cope with the slightest departure from general equilibrium, and a public sector that, being the creation of the normative equilibrium theorists’ imagination, is able to rectify the resulting problem “as if by an invisible hand.” As in the earlier Neo-Keynesian synthesis of Paul Samuelson, the gap between norm and reality is closed by the omniscient state. |
As demonstrated by the passages quoted before, which were taken from a work of Stiglitz’s that Boettke cites, this accusation is off the mark. So is Boettke’s view that the majority of economists regard the market as “a dystopia, devoid of dynamic adjustment properties” (1997, 19). Although he is concerned to study the institutions that “solve the problems created by absent markets,” and although he notes that they “may result in an allocation of investment that is better . . . than it is under market socialism,” Stiglitz (1994, 92), like most economists, does not rule out the possibility that specific government interventions may improve economic performance. Is that perhaps his cardinal sin and indeed the fatal flaw in the discipline as a whole? Despite his insights concerning the limitations of mathematical modeling, it seems that Boettke’s central concern is that economists return to their true calling as uncompromising defenders of laissez-faire.
References
Boettke, Peter J. 1997. “What Went Wrong with Economics? Equilibrium as a Flight from Reality.” Critical Review 11 (1): 11–64.
Hayek, Friedrich A. 1949a. “Economics and Knowledge.” In Hayek 1949b.
Hayek, Friedrich A. 1949b. Individualism and Economic Order. London: Routledge & Kegan Paul.
Hayek, Friedrich A. 1949c. “The Meaning of Competition.” In Hayek, 1949b.
Lipsey, R., and K. Lancaster. 1956–57. “The General Theory of the Second Best.” Review of Economic Studies 24: 11–31.
Stiglitz, Joseph. 1994. Whither Socialism?. Cambridge, Mass.: MIT Press.
Endotes
*: Daniel M. Hausman, Department of Philosophy, University of Wisconsin-Madison, Madison, WI 53706, is the author of Capital Profits and Prices: An Essay in the Philosophy of Economics (Columbia, 1981), The Inexact and Separate Science of Economics (Cambridge, 1992), Essays in Philosophy and Economic Methodology (Cambridge, 1992), Economic Analysis and Moral Philosophy (with Michael McPherson, Cambridge, 1996), and Causal Asymmetries (Cambridge, 1998). Back.