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Adjusting the model to adjust theworld: constructive mechanisms inpostwar general equilibrium theoryIvan Boldyreva & Alexey Ushakovb

a Department of Economics, Witten/Herdecke University, Witten,Germanyb International College of Economics and Finance, NationalResearch University Higher School of Economics, Moscow, RussianFederationPublished online: 26 Feb 2015.

To cite this article: Ivan Boldyrev & Alexey Ushakov (2015): Adjusting the model to adjust theworld: constructive mechanisms in postwar general equilibrium theory, Journal of EconomicMethodology, DOI: 10.1080/1350178X.2014.1003581

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

Ivan Boldyreva* and Alexey Ushakovb

aDepartment of Economics, Witten/Herdecke University, Witten, Germany; bInternational Collegeof Economics and Finance, National Research University Higher School of Economics, Moscow,

Russian Federation

(Received 30 September 2014; accepted 9 October 2014)

Economic methodologists most often study the relations between models and realitywhile focusing on the issues of the model’s epistemic relevance in terms of its relationto the ‘real world’ and representing the real world in a model. We complement thediscussion by bringing the model’s constructive mechanisms or self-implementingtechnologies in play. By this, we mean the elements of the economic model that areaimed at ‘implementing’ it by envisaging the ways to change the reality in order tobring it more in line with the model. We are thus concerned mainly not with the ways tochange the model to ‘fit’ the reality, but rather with the model’s own armature that issupposed 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 ofgeneral equilibrium modeling in the context of market socialism debates; the obsessionof general equilibrium theorists with these concepts can be partly explained by the factthat they hoped not to be faithful to reality, but rather to adjust it to fit the theoreticalmodel; mechanism design theory initiated by the stability theorist Leonid Hurwiczcould be seen as a successor of this position. We conclude by showing the relevance ofthis analysis for epistemic culture of much of contemporary economics and hence,claim that it is an important complement to the traditional philosophy of economicmodeling.

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

Jel Classification: A11; B21; B24; B41

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)

q 2015 Taylor & Francis

*Corresponding author. Current address: Department of Economics, National Research UniversityHigher School of Economics, Moscow, Russian Federation. Email: ivan.boldyrev@uni-wh.de

Journal of Economic Methodology, 2015

http://dx.doi.org/10.1080/1350178X.2014.1003581

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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 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.

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, 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) 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 (Suarez, 2004, 2010).

An influential account of idealization and representation in economic modeling is

summarized in the so-called models-as-isolations-and-surrogate-systems (MISS) frame-

work (Maki, 2009). 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 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 Maki’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 MISS expands the

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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, addressingaudience E, prompting genuine issues of resemblance to arise; and applies commentary C toidentify and align these components. (Maki, 2009, 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 Maki

(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 Maki 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) famous essay is the most salient example. More

recently, Grune-Yanoff (2013) 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 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 (Maki, 2009); hence, further assumptions are

needed to consider a given model as representational or not. Grune-Yanoff argues that

these issues should be settled by the context and modeler’s purpose of building the model.

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 Grune-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 representsome external target systems accurately. Apart from being representative things, models aretypically also productive things whose workability and experimentability are crucial for theirepistemic value. Models can function not only as tools and inference generators, but also asresearch objects in their own right. In the capacity of inference generators models can be usedas representations. In scientific practice, however, they also function as exemplifications,proofs of existence, demonstrations, and test-beds. Thus, conceiving of models asrepresentations loses the sight of many of their distinctive properties. What is more, it gets

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the cognitive challenge of modeling the wrong way, as it assumes that we already knew whatour relevant target systems were and had the appropriate means at hand to represent them.(Knuuttila, 2005, p. 69)

Thus, Hacking (1983) 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) 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) and MacKenzie (2006),

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, 2013; Svetlova, 2012).5 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.

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 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),

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), namely Walrasian general equilibrium

model in the rigorous interpretation given to it by Kenneth Arrow, Gerard Debreu and

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Lionel McKenzie – clearly Maki’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.

Enacting general equilibrium

General equilibriummodel was first advanced byWalras (1874) who is often considered to

be one of the key pure theorists in economics (Schumpeter, 1954). 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 byWald (1951) and using mathematical apparatus that was first applied

by von von Neumann (1945) and Nash (1950)) 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). 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).

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; Lerner, 1944) 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). 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 ADMmodel, 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 showed that the Second World War created a complex of

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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, 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, 285; for the

straightforward interpretation of the ADM model as a planning device in the spirit of

market socialism, see Shubik, 1977).

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

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, Duppe, 2010 for the case of Debreu and the preface to Arrow

& Hahn, 1971). 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.

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) 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).

Indeed, general equilibrium models could be regarded as dealing with combinations of

optimization problems and with coordinating individual consumption and production

plans.

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Along with formulating the models that defined the solutions of optimization problems

economists and operations researchers8 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; Mirowski,

2002). 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) labeled as ‘sociotechnical arrangements’ – a socially organized techniques

of implementation.9

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, p. 15, see also Kjeldsen, 2000).

This algorithmic vision was tightly connected to the idea of adjusting reality toward a

normatively given objective.

Hurwicz (1973) provides a helpful classification of these calculative procedures. For

the linear case, the simplex method – introduced in 1947 by the mathematician Dantzig

(1951),10 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).

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, 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.11 Thus,

Arrow and Hurwicz (1957) 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) 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, p. 272).12

But since Samuelson (1947) a constrained optimization technique has also gained

significance as a tool for economic analysis. Again, Hurwicz (1973) notes that the Kuhn–

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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.

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.

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) 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) and Samuelson (1941).

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

_p ¼ zðpÞ (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 for intellectual history describing the stabilization

of these beliefs).

Ingrao and Israel (1990, 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

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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, 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) Cowles Commission

monograph.13 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 decisionof the managers of production and of the productive resources in public ownership and also alldecisions of individuals as consumers and as suppliers of labour are made on the basis of theseprices. As a result of these decisions the quantity demanded and supplied of each commodityis determined. If the quantity demanded of a commodity is not equal to the quantity suppliedthe price of that commodity has to be changed. It has to be raised if demand exceeds supplyand lowered if the reverse is the case. Thus the Central Planning Board fixes a new set ofprices which serves as a basis for new decisions, and which results in a new set of quantitiesdemanded and supplied. Through this process of trial and error equilibrium prices are finallydetermined. (Lange, 1936, 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.

And it was Lange who took up the notion of the so-called ‘gradient system’ and re-

interpreted it along the lines of the socialist planning. Gradient systems are a special type

of the stability framework introduced by Samuelson in which the dynamics of a variable

(in the case of general equilibrium stability theory – the price vector) can be interpreted as

a gradient of a specific function (the ‘potential function’). Hands (1994) showed that one

of the reasons for Samuelson to abstain from using Liapunov-type dynamics in his earlier

contributions to stability theory was that he was afraid of the normative implications

inherent in such (otherwise technically very promising) enterprise:

Samuelson realized that if a Walrasian system is a gradient system . . . then the generalequilibrium price vector p* must maximize some (potential) function. If this (potential)function is interpreted as social welfare or social utility, then the door is left open for a type ofwelfare economics with much stronger claims about the Pareto optimality of perfectcompetition than Samuelson wished to endorse. (Hands, 1994, p. 263f.)

The logic of a gradient system is linked to the counter-intuitive and restrictive formalism

of the symmetry of Jacobian matrix generated by the excess demand functions of the

economy modeled. Such a symmetry ‘implies that the economy reduces to one big

gradient system which maximizes something like an aggregate price potential’ (Hands,

1994, p. 267). But although Samuelson, with all his inclinations toward social engineering,

was nevertheless unwilling to follow this path, Lange quickly recognized the implications

of this assumption and touched upon it in his 1944 book. Economy as a gradient system is

amenable to manipulation on behalf of planning authorities because, roughly speaking, the

effects of interaction between individual agents that could yield unexpected results (i.e.,

income effects in general equilibrium framework) vanish in such a system. As we have

seen from the discussion of gradient methods, seeing economy as one big agent was a good

opportunity to apply the gradient methods known from optimization theory to the general

equilibrium model as a model of coordination. In some way, it amounted to assuming the

coordination away.

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Lange (1936) provided the simplest version of the decentralization procedure. But

there was another, linear version available that became the starting point for the

economists who tried to reconcile the planning vision of market socialists with the theory

of economic equilibrium that required decentralization and coordination of heterogeneous

interests. This updated version of planning and implementation was provided by

Koopmans (1951).14

In the end of his classical paper on a linear model of production15 Koopmans (1951,

p. 93) elaborates on ‘the institutional arrangements under which decisions about the

components of activity vector x are arrived at’. The ‘centralized decision-making agency’

could use the information of the matrix of production coefficients and choose a

corresponding activity vector that could yield optimal results. But Koopmans also considers

an opposite case where the decentralized decision-making takes place, i.e., where the activity

levels are determined locally by those who are aware of a corresponding matrix column only.

Koopmans concretizes this institutional logic by distributing the managing responsibilities

among the helmsman (a curious name for the Lange’s Central Planning Board, inadvertently

reminding of Mao, especially in 1949) who chooses and announces the prices of final

commodities; custodians for primary, intermediary, and final commodities who mimic the

market by adjusting the prices in the direction of the excess demand; and managers of

productive activities who command the production process by neglecting the activities of

negative profitability, keeping those with zero profitability unchanged and enlarging those

with positive profitability by issuing respective orders to the custodians. As Koopmans

himself admits, these intricate rules (yielding, quite tautologically, in the manner of result-

generating proposition, the necessary optimality in a static sense) just redescribe the working

of a competitive system. The simple rules formulated for helmsman (actually representing a

single ‘consumer’), custodians, and managers ‘suggest methods whereby a planned economy

can strive for efficient allocation of resources in production’ or, in a decentralized economy,

‘help in the appraisal of alternative forms of economic organization or of market behavior

from the point of view of efficiency’ (Koopmans, 1951, p. 95). The firm as such may also be

regarded as a small planned economy and governed accordingly.

Koopmans consciously abstracted from the dynamic properties of these rules. In other

words, he abstained from the studies of adjustment processes and, in particular, from

investigating the stability of tatonnement. It was Samuelson (1949) who reformulated them

(again, referring to the familiar idea of prices moving in the direction of excess demand) in

the language of differential equations and derived non-convergence – the system was

oscillating as a frictionless pendulum (Hurwicz, 1973). Interestingly, Samuelson’s idea was

to use economic intuition of how markets work in order to derive solutions of dynamic

resource allocation problems (Backhouse, 2012).16 Arrow and Hurwicz (1960b) modify

Koopmans’s rules and finally derive convergence for the strictly concave economy.

However, Arrow and Hurwicz are mostly referred to in the context of their joint papers

on stability theory. Along with trying to improve the working of a linear planning system

suggested by Koopmans they did the same with the respect to the general equilibrium

model looking for the constructive mechanisms to implement the results of the perfect

competition.

Hurwicz, stability, and mechanism design

Ingrao and Israel (1990) claim that historically the same group of ‘utopically’ oriented

economists also considered the questions of stability to be redundant, which is only partly

true. The most important economist who, one the one hand, was strongly influenced by the

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‘utopian-normative’ approach (both relating to the issue of stability and with respect to

economic theory in general) and, on the other, made a significant contribution to the theory

of stability, was Leonid Hurwicz.

Born in Moscow in the year of the Russian revolution, Hurwicz was always intimately

connected to the culture of socialism, be it in half-authoritarian Poland of the 1930s where

he studied law, in London and Geneva where he got acquainted to the major critics of

market socialism Hayek and Mises, or in the USA, where he was assistant to Lange.

A member of the Cowles commission, Hurwicz, was fully initiated into the problems

discussed there.

From the standpoint of our discussion Hurwicz is quite a remarkable figure.

He received 2007 Nobel prize ‘for having laid the foundations of mechanism design

theory,’ in particular for developing a concept of incentive compatibility in the 1970s.

Mechanism design theory, as Hurwicz (1973, p. 1) himself put it, ‘refuses to accept the

institutional status quo of a particular time and place as the only legitimate object of

interest and yet recognizes constraints that disqualify naıve utopias’. The program

formulated by Hurwicz in the 1970s thus included both the constructivist idea of going

beyond the existing institutional framework by devising new institutions and an attempt to

overcome an abstract utopian (socialist!) ideal of creating a perfect society.

Hurwicz gained reputation in general equilibrium theory after publishing his results on

equilibrium stability together with Arrow and with the collaboration of a mathematician

H. D. Block (Arrow, Block, & Hurwicz, 1959; Arrow & Hurwicz, 1958).17 The two

papers Arrow and Hurwicz produced were overtly inconclusive and positively biased:

they admitted taking notice only of some cases, but in all of them equilibrium

achieved by the tatonnement process was proved to be globally stable (meaning that the

system converges to it from any point, and not just from its neighborhood). Even more

important in our context is the idea of the system stability different from the equilibrium

stability dealt with before. This generalization is justified on purely conceptual terms:

‘When there are two or more equilibria, it cannot be the case that all equilibrium

points are globally stable’ (Arrow & Hurwicz, 1958, p. 524, cf. Feiwel, 1987, p. 263).

But even if some equilibria are unstable, the cases considered suggested global stability of

the whole edifice that gave hope for its relevance and even a certain degree of

realisticness.

However, that was not the case. As Hurwicz’ colleague Scarf’s (1960) and Gale’s

(1963) examples showed, no general result on the stability of the tatonnement can be

established. In general, it turned out that for the tatonnement to be globally stable market

excess demand functions should conform to the weak axiom of revealed preferences –

‘a property that is very special indeed’ (Fisher, 2011, p. 37). However, at least it gave an

idea of how a stable economy, representational issues put aside, should look like – or, we

would add, should be made to look like.

The latter was precisely the response of Hurwicz! His idea was to experiment with

various models in order to construct, design an economic system that would be on the

whole stable (cf. Feiwel, 1987, p. 262).18 He concedes that Scarf’s and Gale’s examples

somehow discouraged him:

[O]nce it was noted that there can be instabilities, this opened the question whether one couldthink of alternative stable mechanisms that one could consider either from a normative,descriptive, or computational point of view. (Feiwel, 1987, p. 268)

What is given here is a particularly instructive classification. A descriptive point of view

invoked by Hurwicz implies the process of finding a model that would adequately capture

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the functioning of a real economy. A computational point of view is characteristic for

some mathematical economists that were mostly interested in constructing a viable

algorithm for computing equilibrium prices. The best example of such research is the work

of Scarf (1973). It is of particular interest for our story that even Scarf’s negative results on

stability were a part of this computational programme: as Scarf (1991) himself noted, his

interest in finding counter-examples of tatonnement stability were guided by a conjecture

that this Walrasian idea is in fact algorithmically viable and hence, can be computationally

effective. If a general equilibrium model together with tatonnement were globally stable

one could hope for a constructive solution of an equilibrium problem, i.e., of computing

equilibria referring simply to the respective excess demands. But this hope was not

realized.

Hurwicz explicitly states that the problem of stability attracted him not only on

theoretical grounds:

Imagine that you have centralized economy that operates by collecting information,computing what should be done, and then issuing commands. (This is an idealized version of aplanned economy.) . . . How do you solve the problem of optimization centrally, supposingthat you even have all the data? . . . [M]ost problems . . . can only be solved by some iterativemethod . . . But an iterative process of computation would be of no interest unless it has atendency to converge to the correct answer. But what is a convergence if not stability of theiterative process? (Feiwel, 1987, pp. 260–261)

In the interview, Hurwicz claims that while designing a stable system converging to

equilibrium is a normative and often a computational task, ‘the study of stability of the

competitive system may be viewed as a first step in understanding the working of actual

economies’ (Feiwel, 1987, p. 262). We posit that historically this was not true. The whole

program of studying the tatonnement stability was normativelymotivated, and it was not a

coincidence that such a normatively oriented scholar as Hurwicz contributed most to

stability theory.

We see that the theoretical problem of stability was reformulated and along with

studying the properties of equilibrium came to be regarded as a problem of its

implementation. The very word ‘mechanism’ suggests this technological meaning:

a mechanism is intentional, it involves not only a description of a problem, but also (as ‘a

mechanism of’) an indication of the ways to realize some goals. Hurwicz, in particular,

was concerned with the mechanisms of resource allocation that, following Robbins’

definition, could be characterized as economic mechanism par excellence. Stability

analysis can thus be regarded as the major self-implementing technology of the ADM

model.

Why bother? Constructive mechanisms at work

The preceding discussion was framed along some particular historical narrative. It showed

that constructive mechanisms were, in fact, always present and accompanied economic

model-building in the postwar neoclassical theory. Almost all of the general equilibrium

(GE) theorists we referred to did not claim to be descriptively accurate and thus to build

their models as representations. Rather, they sought to endow them with additional

calculative techniques that would be instrumental in finding/arriving at an optimal solution

or equilibrium. One is left wondering whether this story is still relevant today. Although

we are not able to give a conclusive answer, we can reasonably conjecture that for

contemporary economists these issues are no less vital than they were for the members of

the postwar Cowles commission.

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Mechanism design, a field initiated by our major protagonist, Hurwicz, has become a

theoretical foothold for many important developments in the postwar economics. Indeed,

at its inception, it was deeply connected to the studies of adjustment processes by Hurwicz,

Arrow, and their collaborators and further, after the disappointing results in general

equilibrium theory, became a refuge for many its adherents (although not without the

related difficulties that make the picture not so rosy as it might seem, cf. Lee, 2006). After

realizing further limitations of the adjustment processes linked mainly to the information

asymmetries (Makowski & Ostroy, 1993, 2001), mechanism design theorists, armed with

Hurwicz’s notion of incentive compatibility, started to work on the ways to redesign the

incentive structures so that to motivate economic agents to reveal their private information

to the social planner/market regulator in order to establish optimal mechanisms. Planning

became more local, but the principles of mechanism design – to construct social

institutions with some desired properties, be it new markets or auction rules (Roth,

2002) – remained the same. Mechanism design theorists joined their efforts with

experimental economists19 who, on their part, are moving from the mere explanatory work

of testing the principles of rational choice and game-theoretic propositions in the

laboratory to actively creating the rules for the new markets and auctions as ‘economic

machines’ (Guala, 2001, 2007). Behavioral economists in their attempts to ‘nudge’

(Thaler & Sunstein 2008) human decisions in order to make economic agents more

rational are also, in fact, indirectly trying to provide certain implementation technologies

for various well-known economic models and to produce homo oeconomicus apart from

merely registering the deviations from the model of rational choice. In other words, the

theory of rational choice becomes normative (Hands, 2011) and as such in need of

implementation. A recent paper summarizing a growing body of literature on social

preferences invokes a ‘sophisticated social planner’ who pays attention not only to the

egoistic motivations in providing an incentive structure, but also takes account of the

other-regarding preferences and other value issues (Bowles & Polanıa-Reyes, 2012).

On the other part of theoretical spectrum, in the new institutional economics,

development economics, and economic history, the similar tendencies are discernible.

A nice example would be the recent work of Douglass North and his collaborators (North,

Wallis, & Webb, 2009, 2012) on violence and ‘limited access orders’. An important

argument emerging in this literature considers the limitation of violence as an institutional

key to achieving the desired rates of economic growth and the path of the successful

economic development. To limit the violence one needs, in fact, to find an incentive

structure that could make execution of violence disadvantageous for the most of the

interest groups and powers in a given country. Although their analysis is, admittedly,

descriptive, what they try to arrive at are lessons from history and proposal for institutional

design governed by the same intellectual patterns as those we discussed above, i.e., quite

germane to what mechanism design theory proposed on the micro-level.

In sum, the self-implementing technologies are still around in various versions of

economic model-building. It does not mean, of course, that they are ubiquitous, but we can

reasonably argue that the practices of doing economics today are shaped in various ways

by the attempts to construct not just a coherent theoretical narrative, but also to ensure its

realization and to implant these constructive mechanisms into the models.

Conclusion

Philosophers of economics are most often preoccupied with the validity of economic

models. In general, this implies finding out what kind of model could be called a successful

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representation and rationalizing the ways unrealistic models with assumptions lacking

empirical support may still be relevant for various practical purposes, be it the explanation

of real-world phenomena or policy considerations. Our approach proposes a different

direction. Once it is recognized that, apart from being a representation, a model may also

be considered as an instrument of social engineering, the plurality of links between model

and reality emerges. Epistemological issues of resemblance should then be supplemented

by the ways economists furnish (often unrealistic) models with various constructive

mechanisms aimed at enacting the optimal solutions described by the model. If a model

contains an explicit proposal to redesign its target, this has important implications for all

sorts of problems tackled in philosophy of economic modeling, ranging from the issues of

the models’ realisticness to assessing the explanatory value of modeling.

It is not that we have to abandon the representational issues altogether. First, even if we

were to realize the proposed transformation of reality along the lines of a given model, the

viability of this enacting process would obviously reveal a representation-based analysis.

Second, we certainly do not claim that any economic model is built in order to be

implemented in reality. Our argument, rather, calls for complementing the problems of

valid explanations and predictions with the consideration of constructive mechanisms, or

self-implementing technologies. In fact, as we have seen, they matter both for the content

of economic theories and for their development. However, throughout the text, we tried to

consciously abstain from dealing with the question of how successful this implementation

might be or was in reality. Rather, our aim is to better understand the internal structure and

functions of existing economic models, as well as the possible motivations of economists

building them.

ADM model, an implausible way of describing the economy, drew its strengths and

virtues not from the idea of a correct representation (its descriptive accuracy was hardly

believed even by its creators), but from the idea of internal coherence and self-adjustment

aimed at performing itself. Hurwicz’ first constructive mechanism used in various models

was a so-called ‘gradient method’ of finding equilibrium. He later used it in his joint work

with Arrow on the stability of general equilibrium. One of the important motivations

behind the stability theory and the parallel work on adjustment in the resource allocation

processes was, in fact, to provide a plausible self-implementing technology for the

Walrasian general equilibrium model (as the one that took most advantage from the

decentralization).

This might also imply that the models should be treated differently because their

pragmatic value for the user might consist not only their representativeness but in

producing the inferences to be easily implemented in reality. In fact, this might become

a more plausible ‘story’ (Morgan, 2001) a model can tell. Hurwicz’s stories of a social

planner or mechanism designer, stories that were told almost parallel to the existence proof

and accompanied the search of stability, became the important element of the ADMmodel

and complemented its blatant lack of realistic descriptions. They show us that a model can

be not just a neutral instrument of description, but may also contain a tool of changing the

reality in order to bring it in line with the model. Hurwicz provided a response to the

Hayek’s challenge claiming that it is possible to design an optimal institutional setting ab

ovo. He thus wanted both to rationalize the system’s stability and to find the ways of

stabilizing it thereby stabilizing the paradoxical beliefs in the harmony of general

equilibrium. A ‘good’, but unrealistic theoretical picture, a normative utopia condensed in

a model, so typical for economics, needs a constructive mechanism that accompanies

model building in economics and gives economists hope to see their visions implemented

in reality.

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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 canonicallypresented by Arrow and Hahn (1971). Rather, we consider the complex of ideas related, invarious 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 andreal 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 judgewhether the model is good representation or not.

4. This approach emerges from the discussion of ‘how-possible’/‘how-actual’ explanations in thephilosophy of science (Dray, 1957; Reiner, 1993; Resnik, 1991). How-possible usually refersto 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 withactual events and their real causes (Dray and Reiner). On another interpretation, how-possibleexplanations are the candidates for how-actual, they do not capture something unexpected orconsidered impossible, they just lack the empirical base to be verified (Resnik). On the latteraccount, how-possible explanations are assumed to be consistent and credible enough becausethey could potentially capture the (sufficient parts of) real-world causes. This is not the case forDrey–Reiner’s interpretation maintaining that a new explanation changes one’s perspective byexpanding the variety of explanations. In both analyses of how-possible explanations, themodels are non-representative and they do not need to be similar even in parts to the real targetbecause (in Dray–Reiner’s case) model is challenging one’s confidence in something that isnot (or even was not) present in reality, whereas on Resnik’s account an explanation simplycannot be justified by empirical tests.

5. Callon is particularly clear on this point. In suggesting that we abandon the ‘representationalidiom’ (Pickering, 1995) he makes a strong claim: ‘Economics does not have to describereality; its mission is to say what the economy is supposed to be and to propose solutions anddevices 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 empiricalstudies 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 detailedhistorical account in Herfeld, 2014).

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

9. Interestingly, Callon (2007, p. 320f.) talks about adjustment – the term very frequentlyinvoked 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 elementof the Cold War rationality, as it is shown by Erickson et al. (2013). They also make the casefor the rules being relevant both as description and prescription, thus rendering the very idea ofrationality inherently normative.

12. Arrow’s (1974) enthusiasm persisted in the 1970s as well: ‘[W]ith the development ofmathematical programming and high-speed computers, the centralized alternative nolonger appears preposterous. After all, it would appear that one could mimic theworkings 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 linearprogramming problem in which the prices that emerged from competitive markets played thesame role as the dual variables in Dantzig’s theory of linear programming. This implied that thetheory of linear programming could serve as a basis for rigorous formulation of the theory ofgeneral economic equilibrium.

15. The paper documented Koopmans’ talk at the famous conference on the activity analysis heldin 1949. On this conference, see Backhouse (2012), its importance for the development of

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general equilibrium theory is acknowledged both by Debreu (1959) and by Arrow and Hahn(1971) and elucidated in detail by Duppe and Weintraub (2014a, 2014b).

16. The general consensus unifying Koopmans, Lange, Lerner, Samuelson, and others was thus theparticular understanding of market (demand) mechanisms as a key to the problems of resourceallocation and the importance of technical calculative procedures for arriving at concretesolutions to these problems. However, important as this complex back-and-forth movementbetween the study of market mechanisms and normative planning ideas might seem, the veryidea of what ‘the market’ is was, for the most GE theorists at that time, rather abstract andmeager, hardly moving beyond the adjustment ideas developed in stability literature wereferred 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 anadherent of planning. In one of the latest autobiographical texts (Arrow, 2009), he concedesthat the idea of planning was important for him at that time, albeit making certain reservationsand claiming that, in fact, despite an enormous influence of Lange and Lerner (and – we wouldadd – Arrow’s advisor Harold Hotelling) along with equally enormous amount of intellectualenergy spent, socialist ideas and models of planning had little influence on real economicsituation. In an unpublished interview taken by our research group in April 2012, Arrow addedto the skepticism toward his own socialist past the idea that in the general equilibrium theory hewas just developing Hicks who had nothing to do with socialist concerns. However, he alsorecalled Frederick Taylor’s (1929) presidential address to the American economic associationdealing with the optimal running of socialist economy. Moreover, Hicks was the mainreference in stability theory. The ambiguity thus remains, and we could still argue that in1940–1960s Arrow not only knew about socialist and constructivist interpretations of thegeneral 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 tatonnement – the question ofwho changes the prices – is circumvented here. The issue is, rather, whether the process assuch, 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 wecannot elaborate further here, see Mirowski & Nik-Khah, 2008. However, historical studies dosuggest that the two communities shared a common research agenda and maintained strongties – both conceptual and institutional (Lee, 2013).

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