Adjusting the model to adjust the world: constructive mechanisms in postwar general equilibrium theory

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

Jel Classification:

• A11
• B21
• B24
• B41

Notes

^1. This does not mean that we only analyze the model as it was advanced by Arrow and Debreu (1954), and McKenzie (1954, 1959), further formalized by Debreu (1959), and canonically presented by Arrow and Hahn (1971). Rather, we consider the complex of ideas related, in various ways, to this model as the general framework of analysis.

^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.

^3. As Reiss (2013) noted, once the purpose of model is stated, it is only facts that will judge whether the model is good representation or not.

^4. This approach emerges from the discussion of ‘how-possible’/‘how-actual’ explanations in the philosophy of science (Dray, 1957; Reiner, 1993; Resnik, 1991). 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.

^5. Callon is particularly clear on this point. In suggesting that we abandon the ‘representational idiom’ (Pickering, 1995) 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, p. 325).

^6. For example, Morgan and Knuuttila (2012) refer to the work of MacKenzie (2006).

^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).

^8. Mathematical programming was institutionalized in the postwar American economics mainly as operations research implying multiple applications beyond the domain of economics proper.

^9. Interestingly, Callon (2007, p. 320f.) talks about adjustment – the term very frequently invoked by stability theorists and mechanism design scholars.

^10. Dantzig (1951, p. 339), in turn, acknowledges that ‘the general nature of the “simplex” approach… was stimulated by discussions with Leonid Hurwicz’.

^11. 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). They also make the case for the rules being relevant both as description and prescription, thus rendering the very idea of rationality inherently normative.

^12. Arrow's (1974) 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).

^13. Lange was at Cowles in 1939–1944.

^14. As Robert Dorfman (1984, p. 294, cited in Backhouse, 2012, p. 24) recollects, Koopmans perceived clearly that an entire economy could be thought of as solving a vast linear programming problem in which the prices that emerged from competitive markets played the same role as the dual variables in Dantzig's theory of linear programming. This implied that the theory of linear programming could serve as a basis for rigorous formulation of the theory of general economic equilibrium.

^15. The paper documented Koopmans' talk at the famous conference on the activity analysis held in 1949. On this conference, see Backhouse (2012), its importance for the development of general equilibrium theory is acknowledged both by Debreu (1959) and by Arrow and Hahn (1971) and elucidated in detail by Düppe and Weintraub (2014a, 2014b).

^16. The general consensus unifying Koopmans, Lange, Lerner, Samuelson, and others was thus the particular understanding of market (demand) mechanisms as a key to the problems of resource allocation and the importance of technical calculative procedures for arriving at concrete solutions to these problems. However, important as this complex back-and-forth movement between the study of market mechanisms and normative planning ideas might seem, the very idea of what ‘the market’ is was, for the most GE theorists at that time, rather abstract and meager, hardly moving beyond the adjustment ideas developed in stability literature we referred to. On the lack of more sophisticated accounts of market mechanisms, see Mirowski (2002).

^17. Arrow, another major progenitor of contemporary general equilibrium theory, was also an adherent of planning. In one of the latest autobiographical texts (Arrow, 2009), he concedes that the idea of planning was important for him at that time, albeit making certain reservations and claiming that, in fact, despite an enormous influence of Lange and Lerner (and – we would add – Arrow's advisor Harold Hotelling) along with equally enormous amount of intellectual energy spent, socialist ideas and models of planning had little influence on real economic situation. In an unpublished interview taken by our research group in April 2012, Arrow added to the skepticism toward his own socialist past the idea that in the general equilibrium theory he was just developing Hicks who had nothing to do with socialist concerns. However, he also recalled Frederick Taylor's (1929) presidential address to the American economic association dealing with the optimal running of socialist economy. Moreover, Hicks was the main reference in stability theory. The ambiguity thus remains, and we could still argue that in 1940–1960s Arrow not only knew about socialist and constructivist interpretations of the general equilibrium model, but also actively participated in its development along these lines. More on that in Mirowski (2002, p. 298f.) and Klein (2013).

^18. Interestingly, the notorious normative problem of Walrasian tâtonnement – the question of who changes the prices – is circumvented here. The issue is, rather, whether the process as such, guided by the social planner or market forces, is stable.

^19. Albeit not without tension due to the differences in their epistemic cultures, on which we cannot elaborate further here, see Mirowski & Nik-Khah, 2008. However, historical studies do suggest that the two communities shared a common research agenda and maintained strong ties – both conceptual and institutional (Lee, 2013).