Adjusting the model to adjust the world

布拉格之春

Abstract

Economic methodologists most often study the relations between models and reality while focusing on the issues of the model's epistemic relevance in terms of its relation to the ‘real world’ and representing the real world in a model. We complement the discussion by bringing the model's constructive mechanisms or self-implementing technologies in play. By this, we mean the elements of the economic model that are aimed at ‘implementing’ it by envisaging the ways to change the reality in order to bring it more in line with the model. We are thus concerned mainly not with the ways to change the model to ‘fit’ the reality, but rather with the model's own armature that is supposed to transform the world along theoretical lines. The case we study is Arrow–Debreu–McKenzie general equilibrium model. In particular, we show the following: gradient methods and stability could be regarded as constructive mechanisms of general equilibrium modeling in the context of market socialism debates; the obsession of general equilibrium theorists with these concepts can be partly explained by the fact that they hoped not to be faithful to reality, but rather to adjust it to fit the theoretical model; mechanism design theory initiated by the stability theorist Leonid Hurwicz could be seen as a successor of this position. We conclude by showing the relevance of this analysis for epistemic culture of much of contemporary economics and hence, claim that it is an important complement to the traditional philosophy of economic modeling.

Keywords: models, general equilibrium, stability of equilibrium, mechanism design, implementation

布拉格之春

An economic model is purported to explain what happens in the real world. However, there is a continued dissatisfaction with economic models that are often characterized as unrealistic and useless in explaining real-world phenomena. Thus, the aim of many economic methodologists has been to understand how overtly unrealistic models may still contribute to our knowledge about the real world. In this paper, we develop another account of modeling practices that complements the existing frameworks. We focus on constructive mechanisms of the models, i.e., on the built-in elements that are designed to ‘implement’ the model by adjusting the reality so that the model's propositions become true.

We consider general equilibrium model in its relations to market socialism and mechanism design as a case in point. Since its creation Arrow-Debreu-McKenzie (ADM) general equilibrium model has been a cornerstone of rigorous theoretical modeling in economics. General equilibrium theory, for which the ADM model plays a constitutive role, has been for a long time one of the most general and most significant intellectual constructions of neoclassical economics and in that sense got a paradigmatic standing, hence the particular attention we pay to it.1 1. This does not mean that we only analyze the model as it was advanced by Arrow and Debreu (1954 Arrow, K. J., & Debreu, G. (1954). Existence of an equilibrium for a competitive economy. Econometrica, 22, 265–290. 10.2307/1907353.
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, 1959 McKenzie, L. W. (1959). On the existence of general equilibrium for a competitive market. Econometrica, 27, 54–71. 10.2307/1907777.
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), further formalized by Debreu (1959 Debreu, G. (1959). Theory of value: An axiomatic analysis of economic equilibrium. New York, NY: Wiley.
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), and canonically presented by Arrow and Hahn (1971 Arrow, K. J., & Hahn, F. (1971). General competitive analysis. San Francisco, CA: Holden-Day.
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). Rather, we consider the complex of ideas related, in various ways, to this model as the general framework of analysis.
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Clarifying various aspects of the ADM model may thus help in addressing wider questions on the nature and various functions of theoretical models in economics.

This case is also particularly interesting because no one among the progenitors of the postwar general equilibrium theory ever thought of the Walrasian model as a faithful description of a real world and this attitude can hardly be accounted for on purely ‘representational’ terms. We identify the constructive mechanisms of the ADM modeling framework and argue that at some point they were in fact conceived as enabling one to implement the model.

布拉格之春

Building models, stabilizing reality

There could be several purposes for building a model in economics: ‘to explore the world, explain events, isolate causal capacities, test theories, predict outcomes, analyze policy choices, describe processes, and so forth’ (Morgan & Knuuttila, 2012 Morgan, M. S., & Knuuttila, T. (2012). Models and modelling in economics. In U. Mäki (volume ed.), D. Gabbay, P. Thagard, & J. Woods (general eds.), Philosophy of economics. 1st ed. One volume of the handbook of the philosophy of science (pp. 49–87). Amsterdam: North-Holland.
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, p. 70). In the philosophy of economics, models are usually considered as representations or as epistemic tools; in both cases, the modeler is expected to acquire knowledge about the real world (or ‘target system’) by working with or manipulating the model.

Knuuttila (2010 Knuuttila, T. (2010). Not just underlying structures: Towards a semiotic approach to scientific representation and modeling. In M.Bergman, S.Paavola, A.-V.Pietarinen, & H.Rydenfelt (Eds.), Ideas in action: Proceedings of the applying Peirce conference (pp. 163–172). Nordic Studies in Pragmatism 1. Helsinki: Nordic Pragmatism Network.
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) points out that the issue of representation was not in the center of discussion in the philosophy of science until 1980s when the shift occurred due to the rise of interest in modeling. Until recently representation was considered as a twofold concept aiming to explain how the model and its real-world target are connected. For example, semantic approach implies that by reproducing the structure of a real-world target and relations between the target's elements, a model represents the real world. Another approach suggests introducing a pragmatic context as a third part of the model by highlighting the specific intentions of agent and her activity of representing (Suárez, 2004 Suárez, M. (2004). An inferential conception of scientific representation. Philosophy of Science, 71, 767–779.
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, 2010 Suárez, M. (2010). Scientific representation. Blackwell's Philosophy Compass, 5, 91–101.
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).

An influential account of idealization and representation in economic modeling is summarized in the so-called models-as-isolations-and-surrogate-systems (MISS) framework (Mäki, 2009 Mäki, U. (2009). MISSing the world. Models as isolations and credible surrogate systems. Erkenntnis, 70, 29–43.
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). This approach implies that models are representations of some real systems constructed by isolating some important features of the target system. Representation could be a surrogate or substitute system. The surrogate model allows one to get information about target system indirectly by manipulating the model. Substitute systems fail to provide inferences about reality. Rather, they can help acquire knowledge only about the model's imagined world, and thus are supposed to offer much less in terms of epistemic content. The cause of this failure is lack of connections between the model and the reality. MISS account highlights this problem and suggests a concept of resemblance to build relations between model and reality.

Resemblance means that a model and a target system are in some sense similar. MISS assumes only partial resemblance, i.e., similarity between some key elements or parts of model and reality.2 2. For example, if the model explains a certain mechanism of the real world then the modeled and real mechanisms should resemble each other in sufficient degrees.
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This notion implies that there is no need for full resemblance to obtain information about the real system and thus for a surrogate model to be a good representation. However, one should clarify what are the important parts of the model that need to resemble reality. On Mäki's account, it is determined by a set of both ontological and pragmatic constraints. The purpose of modeling plays the key role in implicitly indicating what elements of the model should resemble the target.3 3. As Reiss (2013 Reiss, J. (2013). Models, representation, and economic practice. In J.-H.Wolf & U.Gähde (Eds.), Models, simulations and the reduction of complexity (pp. 107–116). Hamburg: DeGruyter.
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) noted, once the purpose of model is stated, it is only facts that will judge whether the model is good representation or not.
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MISS expands the pragmatic context of a model by including modeler's purposes, audiences addressed, and commentary as parts of representation:

Agent A uses object M as a representative of some target system R for purpose P, addressing audience E, prompting genuine issues of resemblance to arise; and applies commentary C to identify and align these components. (Mäki, 2009 Mäki, U. (2009). MISSing the world. Models as isolations and credible surrogate systems. Erkenntnis, 70, 29–43.
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, p. 32)

This framework should help appraise a model as surrogate or substitute given the model's representational success or failure. However, the pragmatic context outlined by Mäki (purpose, audience, and commentary) is only of secondary importance in this account. Emphasized is, rather, whether there are similarities between a model and its target. Although Mäki does note that purposes of modeling may be different (both epistemic and non-epistemic), i.e. MISS should deal with all the alternatives, the issues of resemblance seem to prevail. If a model succeeds in meeting its purpose but has no similarities with the correspondent real target MISS account would consider it as a substitute system and, ultimately, a failure of representation.
Now, could a model be non-representative and still useful? Necessity of at least partial resemblance between a model and real world may seem obvious and common and is shared by many accounts. However, in some models, this type of reference to the real world is not an issue. Friedman's (1953 Friedman, M. (1953). The methodology of positive economics. In Essays in positive economics (pp. 3–43). Chicago, IL: University of Chicago Press.
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) famous essay is the most salient example. More recently, Grüne-Yanoff (2013 Grüne-Yanoff, T. (2013). Appraising models nonrepresentationally. Philosophy of Science, 80, 850–861.
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) considered the models that claim to explain the real target without being similar to it. He argues that one can still learn from non-representational models that are merely focused on possible effects and are not concerned with realism of properties or processes. Instead, these models may affect one's confidence in hypotheses about the world by changing the perspective, affecting one's beliefs in necessary or background conditions of some processes.4 4. This approach emerges from the discussion of ‘how-possible’/‘how-actual’ explanations in the philosophy of science (Dray, 1957 Dray, W. (1957). Laws and explanations in history. Oxford: Oxford University Press.
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; Resnik, 1991 Resnik, D. B. (1991). How-possibly explanations in biology. Acta Biotheoretica, 39, 141–149. 10.1007/BF00046596.
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). How-possible usually refers to an explanation for an event, which is deemed impossible but could happen under particular, “not so real” or unexpected, conditions. How-actual explanations, on the contrary, deal with actual events and their real causes (Dray and Reiner). On another interpretation, how-possible explanations are the candidates for how-actual, they do not capture something unexpected or considered impossible, they just lack the empirical base to be verified (Resnik). On the latter account, how-possible explanations are assumed to be consistent and credible enough because they could potentially capture the (sufficient parts of) real-world causes. This is not the case for Drey–Reiner's interpretation maintaining that a new explanation changes one's perspective by expanding the variety of explanations. In both analyses of how-possible explanations, the models are non-representative and they do not need to be similar even in parts to the real target because (in Dray–Reiner's case) model is challenging one's confidence in something that is not (or even was not) present in reality, whereas on Resnik's account an explanation simply cannot be justified by empirical tests.
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However, one can still learn from these models. The controversial point here is the very distinction between representational/non-representational models because a model may start with some possible conditions and lead to an actual mechanism and concrete result (Mäki, 2009 Mäki, U. (2009). MISSing the world. Models as isolations and credible surrogate systems. Erkenntnis, 70, 29–43.
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); hence, further assumptions are needed to consider a given model as representational or not. Grüne-Yanoff argues that these issues should be settled by the context and modeler's purpose of building the model.

布拉格之春

What follows from the discussion so far is that to enrich the philosophy of modeling by tackling the non-representational issues, one may abandon similarity or resemblance. ‘How-possible’ explanation is one example of such accounts which successfully captured epistemic functions of various models. It turned out that a model may contribute to changing the beliefs of the agent who uses it, without claiming resemblance. Non-representational accounts studied by Grüne-Yanoff suggest that a pragmatic context of a model may be more significant for appraising its contribution then a detected similarity between a model and its target. But this pragmatic context was mainly captured by the changes the modeling provoked in the agent of inquiry, i.e., in the head of a scientist. However, it might be helpful to go further and to abandon the implicit assumption that the target system is something fixed and given. This idea is common for general account of representation and is expressed by Knuuttila:

Our understanding of modeling should not be restricted to the view that models represent some external target systems accurately. Apart from being representative things, models are typically also productive things whose workability and experimentability are crucial for their epistemic value. Models can function not only as tools and inference generators, but also as research objects in their own right. In the capacity of inference generators models can be used as representations. In scientific practice, however, they also function as exemplifications, proofs of existence, demonstrations, and test-beds. Thus, conceiving of models as representations loses the sight of many of their distinctive properties. What is more, it gets the cognitive challenge of modeling the wrong way, as it assumes that we already knew what our relevant target systems were and had the appropriate means at hand to represent them. (Knuuttila, 2005 Knuuttila, T. (2005). Models as epistemic artefacts: Toward a non-represenationalist account of scientific representation. PhD Thesis. University of Helsinki, Helsinki, Finland.
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, p. 69)

Thus, Hacking (1983 Hacking, I. (1983). Representing and intervening. Cambridge: Cambridge University Press.
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) proposed to turn attention from representing to intervening, i.e. to focus on the aspect of manipulating reality governed by theoretical considerations. The case studied by Knuuttila and Boon (2011 Knuuttila, T., & Boon, M. (2011). How do models give us knowledge? The case of Carnot's ideal heat engine. European Journal for Philosophy of Science, 1, 309–334. 10.1007/s13194-011-0029-3.
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) suggests that the process of manipulation is based on the co-construction of both model and target system.
We would propose to complement representational and non-representational accounts by looking at the ways economic modeling is aimed at transforming its own target. More precisely, we would like to show that some economic models include certain constructive mechanisms that are implicitly or explicitly built in order to transform economic reality in a way that would make it closer to the model and thus would ‘make’ the model true.

This emphasis on the normative adjustment of reality in such a way that it could correspond to the model at hand is reminiscent of a recently revived idea of performativity. Introduced in economic literature by sociologists Callon (1998 Callon, M. (Ed.). (1998). The laws of the markets. Malden, MA: Blackwell.
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) and MacKenzie (2006 MacKenzie, D. (2006). An engine, not a camera. How financial models shape markets. Cambridge, MA: MIT Press.
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), this idea referred to the situations in which a model becomes a part of reality it pretends to describe and this embeddedness makes a difference (see recent illuminating analyses in Herrmann-Pillath, 2010 Herrmann-Pillath, C. (2010). A neurolinguistic approach to performativity in economics. Journal of Economic Methodology, 17, 241–260. 10.1080/1350178X.2010.500739.
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, 2013 Herrmann-Pillath, C. (2013). Performativity of economic systems: Approach and implications for taxonomy. Journal of Economic Methodology, 20, 139–163. 10.1080/1350178X.2013.801559.
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).5 5. Callon is particularly clear on this point. In suggesting that we abandon the ‘representational idiom’ (Pickering, 1995 Pickering, A. (1995). The mangle of practice: Time, agency, and science. Chicago, IL: University of Chicago Press.
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) he makes a strong claim: ‘Economics does not have to describe reality; its mission is to say what the economy is supposed to be and to propose solutions and devices to make it that way’ (Callon, 2007 Callon, M. (2007). What does it mean to say that economics is performative? In D.MacKenzie, F.Muniesa, & L.Siu (Eds.), Do economists make markets? On the performativity of economics (pp. 311–357). Princeton, NJ: Princeton University Press.
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, p. 325).
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The second condition is crucial since the first is trivially true. In fact, what Callon and MacKenzie studied was an old and venerable problem of linkages between ‘model’ and ‘reality’ and their mutual influences. Their contribution consisted mainly in putting it in a language of contemporary sociology and providing a rather compelling analysis of concrete examples. In particular, MacKenzie studied option pricing models that were literally used by traders and apparently did matter for their decisions. This straightforward connection is, however, quite rare. What we see in economics is, rather, a plethora of indirect links that have to be studied in detail.

布拉格之春

However, we would need to make two reservations here. First, radical as it may seem, performativity literature, in fact, does not claim that economics ‘performs’ reality in a strong sense, ‘from scratch.’ Studied, rather, are particular interactions and ‘back-and-forth’ movements happening between theoretical ideas, their practical implications, sociotechnical arrangements necessary to implement them, institutional contexts relevant to this implementation, and the elements resisting it. Second, our approach, as well as that of performativity theorists, does not imply that any economic theory should be or is actually ‘performed’ in the sense of ‘strong’ or ‘Barnesian’ performativity. Unlike this literature, however, we look at the internal logic of modeling in the historical perspective and do not analyze the concrete cases of ‘performation’ (be it successful or not). The possible influence a model exerts on reality is not only a matter of applicability, practical relevance and similar traditional issues. It is, obviously, an important factor in the development of modeling itself. Economic models serve as instruments of studying (and transforming) the real world, but they are also designed in view of this (possible) ‘performation’.

The performative dimension of economics is surely recognized in philosophy of economic modeling,6 6. For example, Morgan and Knuuttila (2012 Morgan, M. S., & Knuuttila, T. (2012). Models and modelling in economics. In U. Mäki (volume ed.), D. Gabbay, P. Thagard, & J. Woods (general eds.), Philosophy of economics. 1st ed. One volume of the handbook of the philosophy of science (pp. 49–87). Amsterdam: North-Holland.
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) refer to the work of MacKenzie (2006 MacKenzie, D. (2006). An engine, not a camera. How financial models shape markets. Cambridge, MA: MIT Press.
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).
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which means that it is acknowledged that economics can sometimes make difference for its own epistemic validity. However, although models are now more and more regarded as autonomous entities or devices (Morgan & Knuuttila, 2012 Morgan, M. S., & Knuuttila, T. (2012). Models and modelling in economics. In U. Mäki (volume ed.), D. Gabbay, P. Thagard, & J. Woods (general eds.), Philosophy of economics. 1st ed. One volume of the handbook of the philosophy of science (pp. 49–87). Amsterdam: North-Holland.
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), relatively little has been done to single out the elements of models that could be instrumental for implementing them, and this is precisely what we set out to do.

We would like to focus on the model that is particularly problematic as far as representation is concerned (Hausman, 1992 Hausman, D. (1992). The inexact and separate science of economics. Cambridge: Cambridge University Press.
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), namely Walrasian general equilibrium model in the rigorous interpretation given to it by Kenneth Arrow, Gérard Debreu and Lionel McKenzie – clearly Mäki's ‘substitute system’. We claim that in the general equilibrium modeling the element of adjustment, or implementation, played a prominent role. We also point out the specific constructive mechanisms, or self-implementing technologies inherent in (some of) the general equilibrium models and aimed at ‘making’ it true. In this, we will have to trace connections between general equilibrium theory, market socialism, and mechanism design literatures. To be sure, our analysis does not claim to match all of general equilibrium theory. Rather, we would emphasize the particular set of ideas associated mainly, but not exclusively, with the contributions of Leonid Hurwicz as a pioneer of modern mechanism design.

布拉格之春

Enacting general equilibrium

General equilibrium model was first advanced by Walras (1874 Walras, L. (1874). éléments d'économie politique pure, ou théorie de la richesse sociale [Elements of pure economics, or the theory of social wealth]. Lausanne: Corbaz et Co.
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) who is often considered to be one of the key pure theorists in economics (Schumpeter, 1954 Schumpeter, J. A. (1954). History of economic analysis. New York, NY: Oxford University Press.
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). The model was an attempt to describe economic system as a whole, but also to make it in a rigorous and consistent way. After Walras, relatively little had been done in the formal development of the model, until ADM who in the 1950s (upon rediscovering the mathematical formulations made by Wald (1951 Wald, A. (1951). On some systems of equations of mathematical economics. Econometrica, 19, 368–403. 10.2307/1907464.
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) and using mathematical apparatus that was first applied by von von Neumann (1945 von Neumann, J. (1945). A model of general economic equilibrium. Review of Economic Studies, 13, 1–9. 10.2307/2296111.
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) and Nash (1950 Nash, J. F.Jr. (1950). Equilibrium points in n-person games. PNAS, 36, 48–49. 10.1073/pnas.36.1.48.
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)) managed to prove the existence of market equilibrium in a rather general model and derived its welfare properties (the prehistory of this achievement was first systematized in Weintraub, 1983 Weintraub, E. R. (1983). The existence of a competitive equilibrium: 1930–1954. Journal of Economic Literature, 21, 1–39.
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). The existence of competitive equilibrium demonstrated by Arrow and Debreu guaranteed that the markets may in principle coordinate on the aggregate level, and that was also a normative result relevant for the underlying conceptual motivations of the founders and further practitioners of the general equilibrium theory. After that, efforts of many mathematical economists were directed at the proof of stability and uniqueness of equilibrium (see Ingrao & Israel, 1990 Ingrao, B., & Israel, G. (1990). Invisible hand.: Economic equilibrium in the history of science. Cambridge, MA: The MIT Press.
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There was an important ambiguity in interpreting general equilibrium model. Prior to this successful formalization and axiomatization the ideas of Walrasian theory were used as an analytical tool by market socialists (Lange & Taylor, 1938 Lange, O., & Taylor, F. M. (1938). On the economic theory of socialism. Minneapolis: University of Minnesota Press.
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; Lerner, 1944 Lerner, A. P. (1944). The economics of control. New York, NY: Macmillan.
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) who tried to reconcile the centralized socialist planning with the efficiency properties of general equilibrium. They were, in fact, the first to rigorously formulate the principles of welfare economics and establish a certain form of equivalence between Walrasian equilibrium and a Pareto-efficient state (Lange, 1942 Lange, O. (1942). The foundations of welfare economics. Econometrica, 10, 215–228. 10.2307/1905465.
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). These normative propositions imply that equilibrium and the competitive market mechanism associated with it are in some sense desirable and optimal. But market socialists took Walrasian construct not just as a general model of market, but also as a guide to action, a normative ideal one needed to achieve. It turned out that the same mathematical object (equilibrium) could be interpreted both as an outcome of spontaneous decentralized market process and as a result of centralized socialist planning duly organized and implemented.

The implementation envisaged by market socialists involved the idea that central planning should in some ways mimic the decentralized market mechanism, the main mediator being the price system that took advantage of local knowledge and information transmission – features of the competitive market emphasized by the Austrian school. This was a key to linking Walrasian tradition with socialist planning.

Thus, the idea of social engineering that constitutes the technological, or constructive dimension of the ADM model, did not emerge from nowhere. The founders of the rigorous general equilibrium theorizing (and of contemporary mathematical economics in general) associated with the Cowles Commission in the 1940–1960s had strong socialist concerns (Mirowski, 2002 Mirowski, Ph. (2002). Machine dreams: Economics becomes cyborg science. New York, NY: Cambridge University Press.
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). Mirowski showed that the Second World War created a complex of disciplines (of which the main was operations research) that focused on various problems of optimal planning. In particular, Jacob Marshak and Tjalling Koopmans (the heads of Cowles Commission between 1943 and 1955) were engaged in planning problems, as well as their younger colleagues such as Kenneth Arrow, Leonid Hurwicz, and Roy Radner. These individuals became the main contributors to the development of both general equilibrium modeling and its constrictive mechanisms.

The ADM model regarded ‘as the “mother structure” for all of rigorous economics’ (Mirowski, 2002 Mirowski, Ph. (2002). Machine dreams: Economics becomes cyborg science. New York, NY: Cambridge University Press.
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, p. 394) was expected to provide the most general framework for global planning and control that eventually would help to resolve the enormous computational problems associated with the operation of the economy and with economic policy. ‘Cowles believed that the Walrasian model demonstrated that ideal centralized planning and decentralized market operation were really identical’ (Mirowski, 2002 Mirowski, Ph. (2002). Machine dreams: Economics becomes cyborg science. New York, NY: Cambridge University Press.
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, 285; for the straightforward interpretation of the ADM model as a planning device in the spirit of market socialism, see Shubik, 1977 Shubik, M. (1977). Competitive and controlled price economies: The Arrow–Debreu model revisited. In G.Schwödiauer (Ed.), Equilibrium and disequilibrium in economic theory (pp. 211–224). Dordrecht: Reidel.
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).

布拉格之春

On Mirowski's interpretation, Koopmans saw the future of economics in engineering and programming (the very term revealing an affinity to computing problems, but also to planning and control) and saw theoretical economists as those who should provide the most fundamental principles of planning further elaborated by some applied analysts.7 7. Koopmans' normative orientation in research priorities was also quite salient in the rational choice theory that shifted during his directorship at Cowles (1948–1955) from the empirical studies of actual behavior to the normative ‘logic of choice’ and formulating prescriptions that, it was hoped, could be used by economic agents willing to learn to be rational (see the detailed historical account in Herfeld, 2014 Herfeld, C. (2014). Defining the rules of rationality: Marschak, Koopmans, and the normative shift in economics, 1943–1954. Unpublished.
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).
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This vision was in various ways supported by Arrow, Hurwicz and Radner. This development is understandable given the fact that no one among the founders of the general equilibrium theory ever thought it could be an accurate description of real economies (see, in particular, Düppe, 2010 Düppe, T. (2010). Debreu's apologies for mathematical economics after 1983. Erasmus Journal for Philosophy and Economics, 3, 1–32.
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for the case of Debreu and the preface to Arrow & Hahn, 1971 Arrow, K. J., & Hahn, F. (1971). General competitive analysis. San Francisco, CA: Holden-Day.
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). The prohibitively high level of mathematical sophistication paired with the overtly unrealistic assumptions did not encourage one to think otherwise. The issues of representation or resemblance were of secondary importance – rather, the ADM model was considered to be a powerful device for conceptual exploration. Moreover, at the times of inception of the ADM framework the prevailing idea was, instead, to devise an economy that would function in a way that is closer to equilibrium.

To be sure, it would be false to believe that all of general equilibrium theory was about planning – as it would be wrong to claim that any economic model is performative in the strong sense (or built in view of its own ‘performation’). Neither is it the case that any form of social engineering is necessarily inspired by socialist ideas. But at this particular historical juncture, the market socialist controversy clearly formed an important intellectual background for the development of the general equilibrium model. This context, as will be shown below, was related to the model's self-implementing technologies both on the level of particular scholars and on the conceptual plane. In what follows, we will also indicate more precisely the elements of the Walrasian model that could be regarded as making it true – beyond the particular motives of general equilibrium theorists. In other words, we will unearth its constructive mechanisms.

布拉格之春

Bridging concepts: gradient methods

Importantly, parallel to the general equilibrium theorizing neoclassical economists paid much attention to the development of mathematical programming. It was primarily Samuelson (1947 Samuelson, P. A. (1947). Foundations of economic analysis. Cambridge, MA: Harvard University Press.
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) who has to be given credit for formulating the economic problem in the spirit of Robbins by formalizing it as a constrained optimization problem (Rizvi, 2003 Rizvi, S. A. T. (2003). Postwar neoclassical microeconomics. In W. J.Samuels, J. E.Biddle, & J. B.Davis (Eds.), Blackwell companion to the history of economic thought (pp. 377–394). Oxford: Blackwell.
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). Indeed, general equilibrium models could be regarded as dealing with combinations of optimization problems and with coordinating individual consumption and production plans.

Along with formulating the models that defined the solutions of optimization problems economists and operations researchers8 8. Mathematical programming was institutionalized in the postwar American economics mainly as operations research implying multiple applications beyond the domain of economics proper.
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started to look for implementation mechanisms that could help achieve these solutions. In fact, what was proposed were calculative devices supporting theoretical solutions. This was quite clear in the frequently drawn analogy between the working of a price system and a computer (Lee, 2006 Lee, K. S. (2006). Mechanism design theory embodying an algorithm-centered vision of markets/organizations/institutions. History of Political Economy, 38(Suppl. 1), 283–304. 10.1215/00182702-2005-026.
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; Mirowski, 2002 Mirowski, Ph. (2002). Machine dreams: Economics becomes cyborg science. New York, NY: Cambridge University Press.
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). What we would like to claim is that in case of economics these calculative devices were, in fact, institutionally interpreted and transformed into something similar to what Callon (2007 Callon, M. (2007). What does it mean to say that economics is performative? In D.MacKenzie, F.Muniesa, & L.Siu (Eds.), Do economists make markets? On the performativity of economics (pp. 311–357). Princeton, NJ: Princeton University Press.
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) labeled as ‘sociotechnical arrangements’ – a socially organized techniques of implementation.9 9. Interestingly, Callon (2007 Callon, M. (2007). What does it mean to say that economics is performative? In D.MacKenzie, F.Muniesa, & L.Siu (Eds.), Do economists make markets? On the performativity of economics (pp. 311–357). Princeton, NJ: Princeton University Press.
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, p. 320f.) talks about adjustment – the term very frequently invoked by stability theorists and mechanism design scholars.
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This logic was quite well discernible in how the discipline of mathematical programming defined itself. In one important source, it was referred to as ‘the construction of a schedule of actions by means of which an economy, organization, or other complex of activities may move from one defined state to another, or from a defined state toward some specifically defined objective’ (Dantzig & Wood, 1951 Dantzig, G. B., & Wood, M. K. (1951). The programming of interdependent activities: general discussion. In T. C.Koopmans (Ed.), Activity analysis of production and allocation (pp. 15–18). New York, NY: Wiley.
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, p. 15, see also Kjeldsen, 2000 Kjeldsen, T. H. (2000). A contextualized historical analysis of the Kuhn–Tucker theorem in nonlinear programming: The impact of World War II. Historia Mathematica, 27, 331–361. 10.1006/hmat.2000.2289.
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). This algorithmic vision was tightly connected to the idea of adjusting reality toward a normatively given objective.

Hurwicz (1973 Hurwicz, L. (1973). The design of mechanisms for resource allocation. American Economic Review, 63, 1–30.
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) provides a helpful classification of these calculative procedures. For the linear case, the simplex method – introduced in 1947 by the mathematician Dantzig (1951 Dantzig, G. B. (1951). Maximization of a linear function of variables subject to linear inequalities. In T. C.Koopmans (Ed.), Activity analysis of production and allocation (pp. 339–347). New York, NY: Wiley.
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),1010. Dantzig (1951 Dantzig, G. B. (1951). Maximization of a linear function of variables subject to linear inequalities. In T. C.Koopmans (Ed.), Activity analysis of production and allocation (pp. 339–347). New York, NY: Wiley.
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, p. 339), in turn, acknowledges that ‘the general nature of the “simplex” approach… was stimulated by discussions with Leonid Hurwicz’.
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an advisor of US Air Force and consultant of the Research and Development (RAND) corporation, – is the most important technique. It redefines a solution of a linear programming problem as a search of extreme points on a polytope and involves moving along its edges in the direction determined by the function to be optimized. Dantzig's method was enthusiastically received in the Cowles commission as a technique that would finally allow to circumvent the non-computability issue that had been haunting the whole business of solving concrete allocation problems in the 1940s (Erickson et al., 2013 Erickson, P., KleinJ. L., Daston, L., Lemov, R., Sturm, Th., Gordin, M. D. (2013). How reason almost lost its mind. The strange career of Cold War rationality. Chicago, IL: University of Chicago Press.
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).

Nonlinear unconstrained optimization required similar implementation technologies, and it was Arrow and Hurwicz who were fulfilling the task. Note that it is not that common in the histories of general equilibrium theory to refer to the other work of Arrow and Hurwicz, done before their joint papers on stability and somehow underlying it. This earlier technical work was devoted to the so-called gradient methods in mathematical programming. According to Hurwicz's recollection, ‘it was natural to interpret the dynamics of programming as a certain kind of mechanism for resource allocation’ (Feiwel, 1987 Feiwel, G. (Ed.). (1987). Arrow and the ascent of modern economic theory. Houndmills: Macmillan.
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, p. 259).

Gradient method refers to the way of finding a solution of an optimization problem, or, in other words, the technology of implementing an optimum. In the simplest formulation, it involves moving toward the optimum in the steepest way, which means to move along the gradient of the function optimized.

What is striking in the whole business of applying gradient methods is its affinity to the socialist way of issuing commands and providing concrete algorithms for action.1111. To be sure, the pervasiveness of simple rules and algorithms can be also seen as a basic element of the Cold War rationality, as it is shown by Erickson et al. (2013 Erickson, P., KleinJ. L., Daston, L., Lemov, R., Sturm, Th., Gordin, M. D. (2013). How reason almost lost its mind. The strange career of Cold War rationality. Chicago, IL: University of Chicago Press.
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). They also make the case for the rules being relevant both as description and prescription, thus rendering the very idea of rationality inherently normative.
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Thus, Arrow and Hurwicz (1957 Arrow, K. J., & Hurwicz, L. (1957). Gradient methods for constrained maxima. Operations Research, 5, 258–265. 10.1287/opre.5.2.258.
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) provide economic interpretations of the gradient systems by invoking a firm, which changes the scale of one of its activities and manipulates various parameters in order to achieve the optimal state. Usual analysis of the conditions of convergence is also given. At that time, Arrow and Hurwicz (1960a Arrow, K. J., & Hurwicz, L. (1960a). Stability of the gradient process in n-person games. Journal of the Society for Industrial and Applied Mathematics, 8, 280–294. 10.1137/0108016.
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) still believed that gradient method could also become a simple and universal computational technique. In general, ‘the focus was… on the parallelism between market processes and their stability on one hand, and the convergence of iterative computational procedures on the other’ (Feiwel, 1987 Feiwel, G. (Ed.). (1987). Arrow and the ascent of modern economic theory. Houndmills: Macmillan.
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, p. 272).1212. Arrow's (1974 Arrow, K. J. (1974). Limited knowledge and economic analysis. American Economic Review, 64, 1–10.
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) enthusiasm persisted in the 1970s as well: ‘[W]ith the development of mathematical programming and high-speed computers, the centralized alternative no longer appears preposterous. After all, it would appear that one could mimic the workings of a decentralized system by an appropriately chosen centralized algorithm’ (p. 5).
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But since Samuelson (1947 Samuelson, P. A. (1947). Foundations of economic analysis. Cambridge, MA: Harvard University Press.
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) a constrained optimization technique has also gained significance as a tool for economic analysis. Again, Hurwicz (1973 Hurwicz, L. (1973). The design of mechanisms for resource allocation. American Economic Review, 63, 1–30.
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) notes that the Kuhn–Tucker theorem that associated a constrained maximum with a saddle point of the corresponding Lagrangian can be seen as a result inviting to apply gradient methods to finding this solution as well.

布拉格之春

Hence, we see that on the elementary level of optimization theory (that could be regarded as a technical basis for neoclassical microeconomics) the founding fathers, along with their colleagues in operations research, were preoccupied not only with defining and describing the optimal solutions but also with the implementation technologies, primarily in the form of gradient methods – calculative devices easily translating itself into algorithms of finding the desired optimal states.

The next step we have to make concerns going beyond the simple economy with one agent – something we implicitly assumed throughout when dealing with optimization. And here the key bridging concept pointing toward a constructive mechanism is stability.

布拉格之春

Bridging concepts: stability

The implementation issue involved another difficulty beyond the search for the solution of optimization problems. Postwar mathematical economists were aware of the challenge posed by Hayek concerning the lack of computational abilities to implement optimal solutions and the nature of knowledge that is dispersed among the agents of the economy. According to Hurwicz et al., this called for informational decentralization of decisions. What was at stake implied, of course, the reference to the spontaneous market processes as the most efficient information-processing mechanisms versus the planning solutions that could somehow substitute them.

General equilibrium theory allowed to formulate similar concerns in a more abstract way. The most basic problem solved by the ADM model concerns the existence of equilibrium. However, once described, characterized and proven to exist, competitive equilibrium (as a formalization of a perfectly decentralized system) should be achieved. It is here, we claim, that the major constructive element of the model is situated. The posited equilibrium should be ‘enacted’, and its implementation has to become an inherent element of the model itself. The precise place to search for this implementing technology is the theory of stability.

Stability deals with the dynamics of equilibrium regarding it as an outcome of some process (Hahn, 1982 Hahn, F. (1982). Stability. In K. J.Arrow & M.Intrilligator (Eds.), Handbok of mathematical economics (pp. 744–793). Amsterdam: North-Holland.
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) and studying the properties of this process in order to find the conditions under which economy would converge to equilibrium and stay there. These conditions are, in fact, essential for any conceivable equilibrium model if it is to be useful. Under usefulness we understand that equilibrium is shown to be, first, feasible, second, desirable, and, third, could be implemented (on the former two grounds).

The foundations of stability theory were laid by Hicks (1939 Hicks, J. R. (1939). Value and capital: An inquiry into some fundamental principles of economic theory. Oxford: Clarendon Press.
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) and Samuelson (1941 Samuelson, P. (1941). The stability of equilibrium: Comparative statics and dynamics. Econometrica, 9, 97–120. 10.2307/1906872.
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). Hicks provided the elementary conditions of stability (that price moves in the direction of excess demand), and Samuelson formalized the price dynamics and described the Walrasian tatonnement in the framework of a nonlinear dynamical system of the type  (where p is a price vector and z (p) is an excess demand function). The analysis of similar systems gradually became the most popular way to handle dynamics in mainstream economic theory (see Weintraub, 1991 Weintraub, E. R. (1991). Stabilizing dynamics: Constructing economic knowledge. New York, NY: Cambridge University Press.
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for intellectual history describing the stabilization of these beliefs).

Ingrao and Israel (1990 Ingrao, B., & Israel, G. (1990). Invisible hand.: Economic equilibrium in the history of science. Cambridge, MA: The MIT Press.
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, p. 329) distinguish two aspects in the analysis of equilibrium stability: ‘objective-descriptive’ and ‘utopian-normative’. The former implies that it is the market that somehow demonstrates the stability properties, i.e. market forces drive economic system toward equilibrium or, better to say, economic system itself spontaneously moves to its rest point. The only thing left to theorists within such type of analysis is a coherent and plausible description. The adherents of the second approach, however (such as Lange), are ‘those who believe that the only way to achieve compatibility between contrasting individual interests is to decree… equilibrium – through planning’ (Ingrao & Israel, 1990 Ingrao, B., & Israel, G. (1990). Invisible hand.: Economic equilibrium in the history of science. Cambridge, MA: The MIT Press.
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, p. 332).

Indeed, Lange's interest to the problem of stability was anything but accidental. Stability plays a prominent role in the Appendix to Lange's (1944 Lange, O. (1944). Price flexibility and employment. Bloomington, IN: Principia Press.
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) Cowles Commission monograph.1313. Lange was at Cowles in 1939–1944.
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But before that it was also Lange who explicitly linked Walrasian tatonnement with his planning vision of socialism as soon as 1936, i.e. before Hicks:

Let the Central Planning Board start with a given set of prices chosen at random. All decision of the managers of production and of the productive resources in public ownership and also all decisions of individuals as consumers and as suppliers of labour are made on the basis of these prices. As a result of these decisions the quantity demanded and supplied of each commodity is determined. If the quantity demanded of a commodity is not equal to the quantity supplied the price of that commodity has to be changed. It has to be raised if demand exceeds supply and lowered if the reverse is the case. Thus the Central Planning Board fixes a new set of prices which serves as a basis for new decisions, and which results in a new set of quantities demanded and supplied. Through this process of trial and error equilibrium prices are finally determined. (Lange, 1936 Lange, O. (1936). On the economic theory of socialism: Part one. The Review of Economic Studies, 4, 53–71. 10.2307/2967660.
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, p. 66)

The basic underlying problem of stability theory (the question of who changes the prices) is here solved by introducing the Central Planning Board that, in fact, implements a general equilibrium by moving the system toward it as a stationary state and using the mechanics of tatonnement.