At the beginning of 1970, Amartya Sen prepared an anthology of selected readings in Growth Economics. What qualified the collection for publication with Penguin Books, known for inexpensive paperbacks, was its promise of a larger audience. While the field of growth economics did not even exist ten years earlier, it was now so central to the study of economics that Sen could note that “an undergraduate can no longer go through his economic theory course without meeting ‘the rate of growth’ face to face and without noticing its well-cultivated, if somewhat wayward, charm.”¹ Straining to finish his survey-like introduction, he wrote a letter to Robert Solow, a former colleague at the Massachusetts Institute of Technology (MIT). Solow was well known for a model he had published in 1956. This model had been essential in stabilizing the specific, “technical” notion of a “rate of growth” that Sen talked about. In his message, Sen thanked Solow for clarifying in previous correspondence that the motivation of the model “was to trace full employment paths.”² This clarification concerned the very status of the mathematical model as a “model.” It could be read both as representing the actual workings of capitalist economies and as sketching some imaginary world that was purely hypothetical or could possibly be established in the future. In his reply, Solow conceded that “my general discussion in the 1956 article was ambiguous, for the simple reason that it wasn’t clear to me at the time exactly what I was doing.”³ While Solow viewed his fifteen years younger self as somewhat confused, I read this anecdote differently. It attests, in a refreshingly honest manner, to the essential ambiguity of models. It is widely held that mathematical models made economists formulate their theories in a determinate and precise way. But their mathematical forms needed to be given “economic” meaning. At the same time, these forms essentially framed what “economic” meant. As for Solow, it took him some time to settle on what his model was all about.

The exchange points our attention to the tricky connection between models and a world outside their narrow confines – not only in economics but in many other fields in the arts, sciences, and engineering that involve languages and practices of “modeling.” In principle, as the philosopher and historian of science Marx W. Wartofsky has noted, “anything may be taken as a model of anything else.” The essential feature of what he has called a “modeling relationship” is that “it is being taken as a model which makes an actual out of a potential model.”⁴ In this book, I want to find out what made Solow’s model a “model” and what that meant. I do so from a historian’s perspective: Attending to other forms of economic knowledge-making and their settings between the 1930s and 1960s helps me think of modeling as a concrete practice and investigate the model’s specific material and medial characteristics. At the same time, this approach allows me to tell episodes from the history of “growth” as an economists’ problem. Overall, this book seeks to contribute to scholarship puzzling over the character, relevance, and effects of economic abstractions. My central argument is that models were more than figures of thought, expressions of social imaginaries, or rhetorical strategies. Due to their specific mathematical forms and to economists’ way of treating them as tools, they exhibited certain practical qualities that made them rather efficient carriers of a specific way of reasoning. The central ambiguity and openness that characterized their status as models decisively contributed to their dissemination. As did Solow in correspondence with Sen, economists throughout this book emphasized that their models were merely models – stylized constructs, heuristic devices, tools for investigation. And yet, it was precisely such framing that allowed Solow’s model to be employed in a variety of ways and unfold its suggestive power, irrespective of the modeler’s intentions. Ultimately, it turned into a model of what it means to think like an economist.⁵ The ambiguity it already featured on Solow’s desk remained. “At any rate,” Sen replied, “others have read much more into your 1956 model.”⁶ Perhaps in an attempt to control the model’s openness, he added a footnote in the published anthology, quoting the modeler’s own motivation that “the idea is to trace full employment paths, no more.”⁷

A Simple Model of Growth

As one of several formulations of a “neoclassical growth model,” Solow’s model is most commonly credited with “explaining economic growth and the long-term effects of economic policy” and with “illuminating the importance of innovation and technological progress to society’s increasing wealth.”⁸ In “A Contribution to the Theory of Economic Growth,” published in the Quarterly Journal of Economics in 1956, specific notions of “explanation” were at play. In a nutshell, the “simple model” featured the relation between the growth rates of the variables “output,” “capital,” and “labor.”⁹ While labor was given outside and independently of the model, capital could vary and adapted flexibly to the given amount of labor in order to ensure the most efficient output. The result was a self-sustaining equilibrium expressed in the form of a linear differential equation: A state of growth determined only by output and saving, in which both capital and labor were fully employed. Consequently, population growth or capital investment were not enough to increase this optimal growth rate. Instead, it could only be changed through additional factors that were not part of the model, such as “technological change.” The model’s simple appearance provided a rather efficient view of economic growth, drawing a line between a clean, well-ordered inside and a messy outside of all kinds of things that were excluded from analysis. A year later, in 1957, the model figured as an instrument for measuring economic growth and its sources. It estimated that technical change was responsible for almost 90 per cent of growth since the turn of the century.¹⁰

Soon, the “Contribution” found its professional readership. In contrast to other economists’ works in the 1950s, it was not likely to be read by lay readers. It was, as a commentator noted, one of the more “technical papers, not suitable for leisurely general reading.”¹¹ Heavily discussed within the realm of economic theory, it was singled out as the “most important paper” that contributed to a “major revision” of contemporary growth theory.¹² It became a constitutive pillar of American mainstream economics that dominated the profession until the 1970s and frames economic knowledge, in academe as well as policy-related realms, to the present day. In 1987, it earned its constructor the highest accolade of the profession, the Swedish national bank’s Prize in Economic Sciences in Memory of Alfred Nobel. Established proponents of economics enthusiastically celebrated “the Solow model” as being “at the back of all economists’ minds in approaching growth theory.” It was said to have provided not only “an engine of analysis” but nothing less than “the organizing structure” of a variety of disciplinary fields – from development economics to international trade and public finance.¹³ At the same time that Solow’s model experienced a striking success, it was confronted with the most fundamental criticism. In fact, if success means that it was received and discussed widely, it had an equally successful life in the eyes and hands of its critics. The model attracted criticism for the utter unrealism of its assumptions, the provision of tautological knowledge, and the ideological veiling of capitalist destruction. It was dismissed for failing to explain growth and to provide an understanding of why economic development was uneven. In this way, Solow’s model also became a symbol for economists’ disinterestedness in the economic world, and an exemplar for the discipline’s shaky scientific foundations.

Indeed, what a curious world this model presented. It depicted the relation between capital and labor, yet it excluded questions of power between social formations. It spoke of a community, its production, and growth. Yet there were no workers on factory floors, no investment decisions by managers, no material transformations. There were no nonaugmentable things such as energy or land, no environmental depletion. There were no unpaid activities like the rearing of children. And there was no money. To interpret the mathematical equations in terms of a physical economy required a series of assumptions regarding its space and time. Most importantly, it presented a world of “perfect competition,” in which the fully flexible working of a market ensured equilibrium. There were no failures to coordinate, no overproduction, no underproduction. At each moment in time, everything that was produced was immediately either consumed or saved and invested. The assumption of “perfect foresight” established that future developments of prices and interest rates were known in the present. There was no uncertainty, no risk. In this frictionless cosmos, nothing essential evolved. The mathematical economy changed only in scale, not in composition – a ceaseless cycle taking place at one point in time. Historical dynamics and contingency were excluded. This list of absences can of course be continued.¹⁴

What was it that made this utterly frictionless world so appealing to economists and soon to other academics, policy-makers, and professionals? In the eyes of its contemporary theorists, what set the model apart was not some novel idea. That growth was not entirely dependent on capital accumulation had already been theorized in different ways. What made this model so attractive was precisely its specific format. Sen’s introduction lauded Solow’s model for its “beautiful simplicity,” adding to a long line of appraisals that denoted it “an ingeniously simple yet extremely useful model for the examination of various aspects of the problem of growth,” which is how one of the early readers described it.¹⁵ The trouble with statements like this is that the qualities of being “simple” and “useful” depended on their relation to other forms of growth knowledge that were around. How was the problem of growth formulated such that, both in the eyes of contemporaries and in retrospect, Solow’s model could provide a simple and useful means to investigate it?

Problematizing Growth at Midcentury

Solow’s model equipped the postwar vocabulary of growth, development, and productivity with an efficient image of a manageable mechanism that led toward an ever more prosperous future. By 1956, growth had already become the center of American political economy, guiding both domestic policies and Cold War geopolitical strategy. The “eschatology of peaceful prosperity,” as Charles Maier has framed it, formed the core of American identity as a liberal capitalist nation.¹⁶ Transgressing party lines, private enterprise was seen as the very foundation for rising national output; government was assigned the status of a neutral arbiter deciding in the interest of growth. The politics of growth and productivity built on the rising importance of economic language and knowledge within government institutions since the beginning of the century. In the United States and elsewhere, it subjected policy-making to a primarily economic evaluation; public expenditures were mainly legitimized by their contribution to growth – a synonym of progress.¹⁷ The expansion of the economy became the primary goal of national economic management, achievable through increasing efficiency and rising consumption and decoupled, for instance, from any limitations through natural resources.¹⁸ The career of Solow’s model went hand-in-hand with the “economic miracle” of the postwar golden age of growth that saw rising production and decreasing unemployment as well as a rise in carbon emissions and decreasing biodiversity. Much of the research surrounding it was financed by the notorious Cold War knowledge institutions. It fit a postwar climate of anti-communism as well as the forms and procedures of high modern bureaucracy. In the most straightforward “biographical” sense, it may have had its beginnings in Cold War culture. But it decisively related to earlier forms of economic knowledge as much as it contained various potentialities for future engagements with growth.

That Solow’s system of mathematical equations was plausible as a “model of growth” depended on its fit with existing economic knowledge. First and foremost, its variables related to the statistical entity of the economy, a scientific-administrative object that already exhibited historical depth. Shaped by the rise of the nation state, the associated military planning, and early twentieth-century managerialism, governmental statistics gave new form to older visions of the economy. Since the seventeenth century, it had been presented as a closed and self-regulating system. Whether in encyclopedic, organic, mechanic, hydraulic, or bookkeeping form, portrayals of the economy not only made it intellectually manageable but also prompted action to realize that order.¹⁹ Actualizing earlier displays of the economy, the postwar era established an intricate knowledge infrastructure based on metaphors of flows and cycles in which goods, capital, and work circulated.²⁰ While long-standing ideas about the flourishing of the whole (such as the growth of the wealth of nations or the improvement of productive techniques) remained central parts of governmental thought, the very objects of inquiry and intervention differed considerably.²¹ It was still about the performance of a system as a whole, but now that system had the money-based form of an aggregated macroeconomy. The most prominent numbers in this regard were the national income and its reformulations, the gross national product (GNP), and the gross domestic product (GDP). These metrics featured the national economy as a closed entity of interdependent statistical parameters that was amenable to administrative action.²² Drawing on longer-standing forms of economic knowledge, Solow’s model bolstered the belief that stable growth could be created and sustained. Merging with other midcentury tools of governance, it gave the relations between the growth rates of national product, capital, and labor statistics.

When working on this book, I wanted to gain a better understanding of the knowledge that provided “growth” with its specific form. Genealogies of the economy have often focused on the broader problematizations of that entity as a central administrative–quantitative category. In a Foucauldian vein, they investigated the historical processes of how and why something previously unproblematic turned into a problem and became the object of social regulation – scientifically, ethically, and politically.²³ While these approaches emphasized the crucial role of economic knowledge tools for a liberal governmentality, the specifics of these instruments have rarely come to the fore. This book focuses on the characteristics of models and measurements of growth. It does so by investigating the problematization of the growing economy in economic research. This does not need to imply the perspective that economists’ problems are autonomous from those outside their field’s boundaries. There is no doubt, certainly not for the historical actors themselves, that their work intensively interacted with governmental interest. It was prompted and funded by governmental institutions; in turn, their renditions of the growing economy made the very phenomenon to be governed appear visible and amenable.²⁴ Looking at how different tools of modeling and measuring shaped the scientific problematic of growth, this book takes inspiration from a branch of history of science that has focused on how things (as diverse as dreams, the self, or atoms) gained scientific interest, how they turned into objects of scientific inquiry, and how they lost scientific attention. In the process, this literature has argued, phenomena became more or less real, depending on how “densely they are woven into scientific thought and practice.”²⁵

The measurers and modelers of the following pages were aware that their research was not in the first place dealing with some world out there but rather a matter of “phenomenotechnique.”²⁶ Framed by Gaston Bachelard, the concept emphasizes the notorious difficulty to clearly differentiate between tools and phenomena when they are transformed into scientific problematics.²⁷ The growing economy that was assembled and scrutinized in the offices of national accountants, the mainframe computers of input–output researchers, and the notebooks of MIT’s modelers was not a phenomenon of the life world. What economists denoted their “instruments” embodied theoretical ideas, conventions, normative judgments, beliefs, and imaginations, which all contributed to realizing the phenomenotechnical growing economy.²⁸ The problematics of growth research consisted of mathematical variables, correlation coefficients, and statistical parameters. In this sense, the growing economy that Solow’s model depicted was already a scientific object that constituted a mesh of earlier and new threads, disregarding some and actualizing other elements of previous research objects.²⁹ Most importantly, it spoke to the variables in time series data of national product, capital, and labor. Built on similar assumptions, the model neatly fit the dominant empirical problematization of economic growth. It inscribed itself into an infrastructure of knowledge, in which models and data mutually stabilized each other.

In her review of works historicizing economic growth, historian Venus Bivar wondered whether the difficulty of merging the history of statistics with newer approaches to the history of capitalism came from a difficulty “to marry the material and the abstract.”³⁰ While this book will not provide such warranted synthesis, it does seek to concretize the abstract in treating models and measurements of growth as deeply entrenched in research practices that were both discursive and material. The shaping and reshaping of the growing economy involved not only intellectual considerations but also practical requirements, institutional backing, and public financing. Paying attention to the nitty-gritty of the tedious phenomenotechnical work that went into the numbers of national accounts, productivity measurements, and input–output analysis allows me to feature Solow’s model as part of a process of giving form to the problem of growth and thereby reframing that problem in a specific way. From this perspective, Solow’s model contributed a further leap in both abstraction and concretization. Presenting growth as a simple mechanism, it carried the objectification of the economy to extremes. The model was used as a highly efficient gauge, detached from previous attempts to get closer to the material realities of production, separated from the intricate work of making numbers, and ignoring the contexts and weaknesses of the underlying empirical material. It fortified the idea of the economy as a separate sphere that was independent of all things social, cultural, political, and temporal. Doing so, it eased the perception of growth numbers as a glimpse into a world out there. This somewhat paradoxical effect was not simply a matter of continuities and breaks from earlier instantiations of the growing economy. Rather, it derived from a decisive transformation: The reformulation of economic growth in terms of a model and its embedding into a practice of modeling.

Models as Multifarious Artifacts

“Modeling is an age-old business,” an operations researcher noted, thinking of the “clay models of the great pyramids at Giza or a wooden model of Noah’s ark.”³¹ Indeed, practices of modeling, designing, blueprinting, planning, and sketching have a long history. But the history of mathematical modeling as an epistemic practice is decisively shorter, the history of mathematical modeling in the social sciences even shorter, and the history of talking about mathematical economic models in terms of material objects shorter still. Only in the middle of the twentieth century were mathematical models rather than mechanical analogies widely seen as the stuff of modern science. Only then did it become customary in fields of applied mathematics to use the term “model” and speak of “modeling” as the prime scientific activity.³² In the aftermath of wartime planning, a larger movement of social scientists, among them economists, also adopted the language of modeling. Their use of the term “model” was characterized by a diversity in practices stretching from cybernetics to information theory, from systems analysis to game theory, from operations research to systems engineering.³³ The 1960s saw a veritable boom of the use of the term for a whole variety of things: Mechanical models, theoretical constructs, pictures, diagrams, computational models, hypothetical models, copies, prototypes, mental constructs, material models in museums and for teaching as well as logical models that had no reference outside language. What the contemporary observer Wartofsky called a “model muddle” was not only semantic but also ontological. It related to both the status of whatever was labeled a model and the status of the things it was said to represent – encapsulating the exchange between Sen and Solow above.³⁴

Scholarship in the history of science has shown how larger postwar developments made it easy and attractive for social scientists to problematize their objects in terms of mathematical systems and dispense with other approaches. As part of these shifts, one instantiation of “the economy” was a perfectly efficient, optimizable system of simultaneous equations, which provided postwar economics with one of its major research objects. Historians have given particular attention to to game theory, general equilibrium theory, operations research, Cold-War interdisciplinary rationalities, mathematical economists’ flashy cybernetic imaginaries, and the puzzling emphasis they put on the epistemic virtues of mathematical beauty and elegance.³⁵ This book also relates to the analytical frameworks of formalist economics and the impact of the digital computer, involves a partly similar personnel, and sometimes sets the storyline at overlapping institutions. At the center, however, is a specific practice and language of modeling that aimed to draw on quantitative knowledge, related more strongly to prewar economics, adapted a more antiquated kind of mathematics, and connected “simplicity” with empirical and political “usefulness” rather than formal “elegance.” Distancing their projects from the abstract aesthetics and intricate makeup of axiomatic systems of general equilibrium theory, the mathematical economists in this book thought that their models promised to make economic theory more realistic and closer to empirical relevance. And in contrast to some of their contemporaries, whose enthusiasm for the computer fed into a matching penchant for complexity, they wanted to keep the complexity of their models to a minimum. Their views testified to a multiplicity of model understandings in the sciences, in particular when it came to the varying status of mathematical models between concrete objects and abstract entities.³⁶

The modelers in the following pages adhered to the view that mathematics was the “language of modern science,” which only made it natural for them to turn to the archive of mathematical formalisms. In the first place, to put it very bluntly, making economics “scientific” to them meant something like reframing ill-defined problems by using the abstract and precise language of mathematics and making the underlying presumptions explicit. The clear-eyed scientific economist explicitly stated assumptions and definitions. These set up a logically consistent mathematical formulation. Conclusions were clear-cut. Utterings in this vein, however, made up only one layer of economists’ model talk. When they went into what they were doing in their research, it often came across as a concrete activity of working toward and with some kind of artifacts. In this vein, historian of science Mary S. Morgan has described economic modeling as a “style of reasoning” that consists in constructing and manipulating “small mathematical, statistical, graphical, diagrammatic, and even physical objects.” Models, in this sense, are not abstract structures but concrete artifacts that are deliberately made in a process that involves articulated as well as craft-based knowledge.³⁷ In the following chapters, economists, especially Solow, will indeed refer to their modeling work as an art and handicraft. Such statements, often made in a fairly casual way and rarely part of a formalized methodology, make up a second layer of model talk. Here, modeling appears as a concrete activity of making something new and artificial and of tinkering and toying with it. The relation of the resulting knowledge to a world outside the confines of models was rather informal. Model knowledge was not supposed to be true or lead to exact forecasts or precise statements about probabilities. The two layers of model talk did not necessarily agree with one another. But they both belonged to a practice of modeling that is understood here as involving the work as well as the performance of economics as a modeling science.

Taking seriously economists’ model talk as a part (and not simply as a description) of their modeling work opens the possibility to investigate how the power of economic abstractions derived from the way they were built and used as artifacts. For one, it highlights models’ difficult relation to a reality outside their confines. Solow’s “Contribution” did not present any empirical study – its results merely derived from the constructed model, and neither the model nor its assumptions were “tested.” The growth rate it presented was derived from a mathematical equilibrium system, rather than calculated from numbers of the past. When the model was used as an instrument of measurement, it served as a means to interpret given data as if the numbers resulted from a world that looked like the model. Whatever was not part of the clean cosmos (the ever-extendable list of absences I sketched in the first section) was stashed away in a “residual,” which now captured the messy outside of the model in a separate error-term. From a methodologist’s standpoint, Marcel Boumans has noted that it is through the process of creating new objects from already existing bits and pieces of knowledge (metaphors, analogies, mathematical concepts and techniques, data, and policy views) that the “justification” for models is “built in.” They do not have to satisfy some disconnected, external criteria but have to be adequate for their very specific purpose.³⁸ Seen in this way, the model was a successive form, picking up on what was there, integrating justification from the start.

When it came to the making of his model, Solow hinted at its being a side-product of a different modeling endeavor in the context of teaching. It then, however, turned out to have a different purpose as a contribution to economic theory and, in the ensuing years, created several new purposes, revealing a stimulative character. As an artifact, Solow’s model was not simply a transparent representation of some facets of the economic world. Its specific material and medial characteristics both restricted what could be thought, seen, and done with its help and afforded various uses and interpretations. Depending on the specific engagements with the model, it was able to actualize different capacities. In this sense, it was not simply a passive instrument.³⁹ The reader of the “Contribution” above who enthused over the model’s ingenious simplicity highlighted that it was also “extremely useful.” In various ways, Solow’s model prompted its use as a practical “tool,” realizing several of its instrumental and pedagogical functions. As a working object, it offered the opportunity to learn something about the (ever so parsimoniously defined) problem of growth. As an instrument of measurement, it formatted data in a way that economists deemed productive for further inquiry. Understood as a “prototype,” it laid a foundation for both building larger-scale models and for integrating more factors into its small world. As a miniature, it provided the minimally efficient scale to investigate the growth dynamics of bigger models. As a teaching device, it served as an entry point to the practice of modeling and becoming an economist. In all these engagements, the simple artifact provided a first step. It was seen as tentative because its makeup was too sketchy, in need of further work. At the same time, it provided the rules for subsequent models. Being adaptable and extendable, the simple model, for instance, allowed for the accommodation of various other factors, but only if they were first formatted in a suitable way. Its clean-cut form did not allow for contaminations. In this sense, the model was something preliminary and provocative, realizing its active potential.⁴⁰

The introduction of models in economics, as the mentioned scholarship emphasized, did not merely translate verbal study into the more precise and efficient language of mathematics. Models are not simply texts to be read; they not only repackage but format theoretical ideas. Modeling transformed the very objects of investigation and thereby changed the problems economists deemed relevant and, not least, the ways they thought were appropriate to approach these questions.⁴¹ As in any other science, economists distanced their knowledge from mere opinion. From midcentury onwards, they did so primarily through reference to mathematical models. While the practice of modeling was indeed personal and drew on the skills and qualities of the modeler, it was still seen as providing privileged, depersonalized knowledge – not necessarily in the sense of scientificity relating to some specific rules and criteria (for instance, Popperian ones) but in the sense of a counterpart to subjective, irrational opinion that distinguished itself through asking the “right” questions. In effect, modeling provided economists with scientific appeal and public authority on a diverse range of questions. After all, the discipline was stylized as the most scientific of the social sciences – a status that has been claimed and challenged ever since. This book focuses on one model in particular, which makes it possible to not only think about modeling as a way of reasoning more generally but to investigate a specific instantiation of a modeling practice within American postwar economics. The practice came with a situated meaning of “technical economics” that related to both the work of modeling and the application of the knowledge thereby gained within the realm of economic expertise.⁴²

The Politics of a Model

“The basic neoliberal model of growth is the Solow model. Like all neoliberal thinking, the Solow model is based on the assumption of pervasiveness and efficiency of markets.”⁴³ The ambiguity broached by Sen on the eve of his publication continued to accompany the model. In this case, it was almost sixty years later in 2012 that the Ethiopian Prime Minister (and former President) excoriated “development” policies and their phantasmatic belief in the power of markets. That Solow’s model, developed in relation to national statistics and postwar interventionism, could turn into a symbol of market fundamentalism was due to its specific ambivalence and openness as a “model.” Was it an image of the world as it was, an imaginary of what it should look like, or a vision of a world yet to come? The model carried these possibilities into its different engagements, to an extent that makes it hard to speak of the same model.⁴⁴ From the perspective taken here, its specific politics pertained not only to the (necessarily political, value-laden) imagery of the growing economy and what it turned (in)visible. It also consisted in its efficient format, which made it easy to repurpose and to tell clean-cut stories about growth and its sources.⁴⁵ The historical actors in this book related the epistemic and the political in a more confined way, above all, with regard to the sphere of economic expertise and policy-making. It was especially in these situations that the model could unfold its suggestive power – the world it portrayed was to be established. And since it did not provide any hints at how to do so, it was adaptable to a variety of political strategies. In this sense, the story of Solow’s model provides a further angle on a history of market thinking that is not restricted to the circulation of neoliberal ideas. Instead, it points to the persistence of knowledge artifacts and infrastructures that are intended to manage the macroeconomy across the twentieth century.⁴⁶

When it came to the economy Solow’s model portrayed, it was indeed a world of fully competitive markets that constituted what most of its critics saw as its ideological content. This was a world that certainly did not exist in the 1950s. But it could be understood as a nostalgic reference to an imagined nineteenth-century in which a large number of entrepreneurs competed rationally in order to maximize profit. After all, it was called “neoclassical,” a label that, in the postwar United States, denoted approaches loosely affiliated with a heritage of the previous century in the form of marginal productivity theory. Marginal productivity theory provided an explanation of how returns of national wealth were allocated to the various “factors” involved in its production. While economists had previously cast this question in terms of rivalling social groups who participated in creating wealth (capital and labor in particular), neoclassical theory at the turbulent turn of the century answered it through the workings of competitive markets.⁴⁷ Value accrued from utility rather than, for instance, labor cost. In this way, production and distribution became analytically separated; within that analytical frame, no statement relating to justice of distribution was viable. Everyone was assumed to gain exactly the fair share of what they had contributed to production. Mathematical renditions of neoclassical theory formulated systems of supply and demand equations; their solution provided equilibrium prices. In such a framing, income distribution appeared independent of institutions, social relations, and history – which would also become one of the main arguments against neoclassical theory in the second half of the twentieth century, the Solow model in particular.⁴⁸

Already in the nineteenth century, neoclassicism was not easily mapped onto political preferences. Some marginalist thinkers (such as Carl Menger) actively pursued anti-socialist campaigns and offered forceful apologias of the status quo against the booming workers’ movement. Others (such as Léon Walras) focused on the compatibilities of marginalist theory with models of a moneyless planned economy and socialist politics.⁴⁹ This political indeterminacy carried into post–Second World War economics as it picked up on optimization techniques from the context of war planning and the computer metaphors that came with the mainframe. Equilibrium systems presented mechanisms that ensured the efficient “allocation” of resources. Akin to other kinds of postwar structuralist reasoning, these systems were interpreted as fitting different kinds of institutional setups, ranging from “centrally planned” to “free market” economies. In any case, such models were intended to transform economic theory in order to make it more useful for governmental purposes.

Conceptualizing models as interventionist tools was also not specific to the postwar era. The creation of macroeconomics as a separate field in the 1930s, for instance, had been intrinsically related to the ideas and practices of interwar economic governance. In the view of early econometric modelers such as the Dutch economist Jan Tinbergen and the Norwegian Ragnar Frisch, economics was a means to fight unemployment and inequality. Because of the existence of crises, frictions, and depressions, they argued for a decidedly scientific approach to policy-making, which essentially meant that models should provide the basis for economic planning, for monetary as well as fiscal policies.⁵⁰ These early econometricians provided new analytical tools that distinguished between the economics of individual action (the micro-level of economic analysis) and the large-number-phenomena of economic statistics (the macro-level).⁵¹ Tinbergen pushed the notion of a mathematical “model” as a representation of an economic mechanism. As early as 1942, he constructed and implemented a neoclassical growth model.⁵² Other early models that explored long-term growth possibilities were built in the context of the design of five-year-plans: The Soviet economist G. A. Fel’dman developed, among several others in the 1920s, mathematical formulations of Marxian schemes of expanded reproduction, and the Indian planner Prasanta C. Mahalanobis sought to maximize long-run growth by calculating the optimal allocation of investment among sectors in the early 1950s.⁵³

MIT’s Department of Economics and Social Science took a particular place in American postwar economics in that it linked the “usability” of mathematical forms to their fit with “economic” meaning and their practicality for intervention. Solow’s model was not intended to directly provide knowledge for policy-making. However, MIT’s “neoclassical synthesis,” the theoretical label to which the model is usually subsumed, did have a distinctly governmental character. It was based on the notion that integrating neoclassical ideas of a self-regulating market in a Keynesian framework allowed for more effective policy designs. In the midcentury US, interventionist policies under the label of “Keynesianism” directed attention at what has been called “the mixed economy,” a shifting mixture of private and public ownership, free enterprise, and planning.⁵⁴ The new economics held that national economic management required a scientific apparatus and propped up the idea of macroeconomic stabilization by using markets.⁵⁵ The government’s job was to establish high employment, set up an equitable distribution of income, control the business cycle, and enhance growth whenever wages and prices did not adjust quickly enough to bring markets into equilibrium.⁵⁶ MIT’s mathematical economics came with an overtly self-conscious “middle of the road” political positioning between libertarian and radical economists, both of whom, to MIT’s protagonists, lacked intellectual rigor and mathematical competency.⁵⁷ They reconciled “left-liberal statist impulses with imperatives to repudiate socialism,” as the historian Philip Mirowski has put it. “Keynesian macroeconomics was seen as the epitome of the ‘middle way’.”⁵⁸

The essential “moral” of the model, as Solow and other neoclassical modelers in the 1950s and 1960s agreed, was that if government took the right steps, the model, in the long-run, would come into its own. In this imagined world of manageable growth, the product of (industrial) economies would grow at approximately the same rate as capital accumulation. The possibility came from an intervening government; judicious fine-tuning would balance saving and investment so that everything saved was invested. Or, as Trevor Swan, who constructed a neoclassical growth model the same year as Solow, put it, either “the Authorities have read the General Theory or … they are socialists who don’t need to.”⁵⁹ Seen as one element in a toolkit of governmental technologies of postwar liberalism, Solow’s model visualized the bright promises of a messianism of affluence, based on the possibilities of balancing the whole and establishing full employment to link an expanding mass-consumption society with increasing wealth and welfare. For Solow and his colleagues, the fact that the model portrayed a world of free markets did not imply that what they saw as real-world markets worked best without government regulations or organized labor. The model itself, however, left open how the world it portrayed could be achieved, for it excluded any interaction between the micro- and macro-level (through the assumption of perfect competition) and between the short- and long-run (through the assumption of perfect foresight). This was one of the facets of the model’s ambiguity that opened it up to various political uses and made it compatible with different political ideologies.

The stimulating effects of models often disappointed their own constructors. A recurring theme in this book is the frustration and sometimes even regret that economists uttered when they saw how their artifacts stabilized.⁶⁰ In their own work, phenomenotechnical toolmakers shifted between a language of inquiry (being frank and careful about possible shortcomings and problems with a certain technique, model, or measure) and a language of advocacy that came with the authoritative economic expert.⁶¹ As a corollary of dealing in clean and closed worlds, they seemed, at least at times, uncomfortably aware of the limits of their approach outside of those worlds. This is why this book pays attention to the messiness, the disarrays, and nagging doubts that accompanied models from the very outset. At times, modelers worried about the absences that made their models “deceivingly exact,” conceded that the practice of modeling created “in some cunning way … a substitute for reality itself,” and bemoaned that economists were often “too taken with technique and theory” and did not care enough “about the practical meaning” of what they were doing.⁶² They also admitted disciplinary blind spots: “No doubt we are all too prone to deal in closed systems because they are neat and aesthetically satisfying, and we forget how intimately economic variables are enmeshed in psychological and social and political forces.”⁶³ But such utterings did not change the fact that, as policy experts, for instance as “growthmen,” they did act as the providers of “determinate” and “trustworthy” knowledge. Both types of performance, this book argues, came along with the active potential of models and the muddles they created.

Outline

The book begins with the 1956 publication of Solow’s model, though its storyline does not proceed sequentially from there. Rather than following a chronological narrative, each chapter constructs different trajectories that – moving back and forth in time – embed the model in practices of modeling and measuring the economy and its growth between the 1930s and the 1960s. Most episodes in the following pages relate to the making of phenomenotechnical instruments that visualized the growing economy. I use them to think through the particular features of Solow’s model, the knowledge it generated, and the epistemic virtues and scientific personae that came with this kind of modeling. In historicizing the model from different angles, the trajectories feature different characteristics of the model as they were realized in specific engagements and in relation to other forms of knowledge. Neither of the research episodes that follow were necessary or determinate for Solow’s model achieving its eventual form.⁶⁴ It could very well have come together in different ways. In fact, as indicated, Solow was neither the only one nor the first to publish a neoclassical model of growth. Such simultaneity is a common theme in the history of science that points to the difficulties of when a history of a model starts (and where it ends, for that matter). Priority is not at issue here. What are of issue are the forms of research into the growing economy as well as the stakes, hopes, and disappointments that came with it. To get at these, this book draws on archival material (such as private correspondence, research reports, and lecture notes) as well as on close readings of published sources.

Chapter 1 focuses on the narratological strategies that turned a set of mathematical equations into an economic model in the “Contribution,” the article behind the classic reference “Solow 1956.” In the first place, the “Contribution” was all about the setup and behavior of a smoothly working neoclassical growing economy. The whole paper revolved around this artifact, made (up) by the narrator figure and, at the same time, to be used and experimented with by others, independently of its construction history. While denoting the artifact “a model” throughout, references to a world beyond its narrow boundaries were vague; there was no explicit link to any quantitatively measured entity. Its function as an exemplar for how economic reasoning should look and how the new “art of theorizing” was to be done was straightforward. The text presented its model as improving a so-called precursor, the “Harrod-Domar model.” In this way, it canonized earlier dynamic theory with its focus on instability and crisis by turning it into a special case of steadily growing equilibrium systems. Pulling readers into its realm, the model set the course for an angled historiography of growth theory that downplays the differences in approaches and objects until the present day.

Chapter 2 highlights a further displacement brought about by Solow’s model – the introduction of the so-called “Solow residual” that came with its use as an instrument of measurement. This episode relates the model to the postwar politics of growth and productivity and a line of inquiry that sought to gauge the national whole in terms of monetary units. Existing measurement practices at the National Bureau of Economic Research (NBER) involved the activities of collecting, compiling, and processing data; its researchers complemented and qualified their numbers with descriptive, verbal accounts about how the data had been made and how different measurement procedures led to different results. Here, the model reordered knowledge and nonknowledge about productivity. While commentators were shocked by its utter constructivism and disregard for the ways data were made, it offered a seemingly clean-cut method of measurement that turned statistical inference into a technical procedure. Whatever the model’s neoclassical reading of numbers did not account for was efficiently stashed away in a residual term labeled “technical change.” While Solow explicitly noted that the rest captured all kinds of (relevant) things, both the technique and the label remained.

That Solow’s model actually had little to say about productivity growth was a major point of contention and made it a prime example for the intellectual weaknesses and the lack of usefulness of econometric knowledge for policy-making. The disengagement that came with mathematical models is central to Chapter 3. The 1940s saw the reconciliation of a panoply of mathematical wartime techniques with social scientific theorizing. I examine how the economy was depicted as a huge optimization problem that would be solvable by electronic computers. Investigating input–output analysis as it was done at the Harvard Economic Research Project (HERP) under the directorship of Wassily Leontief illustrates the difficulties of making an economic abstraction work in measurement practice. The chapter draws a trajectory from the HERP to the Conference of Activity Analysis of 1949, where mathematical economists combined new techniques of linear programming with what they saw as conventional neoclassical economics. The move from planning tools to devices for theoretical speculation came along with a shift in modeling philosophies and notions of realism. Focusing entirely on mathematical formalisms and abandoning the concern with measurement brought about the main research object of the economics profession in the subsequent years: The economy as a fully flexible and efficient system of production in the form of a system of simultaneous equations. This was the economy that provided the primary point of reference for Solow’s model.

Against the background of mathematical techniques spreading in postwar social science, Chapter 4 situates Solow’s model in the heterogenous landscape of mathematical economics in the early 1950s. Here, Solow enters as a historical actor who got acquainted with different strands of structuralist and mathematical reasoning before he devised the model more or less incidentally in the context of teaching engineering students at MIT. On the trajectory from the linear economy at the Conference on Activity Analysis to Solow and Samuelson’s joint modeling work, I describe Solow’s model as a miniature – not of the world but of other models. Its smaller scale and reduced mathematical form fit older mathematical economics while, at the same time, it related to the more sophisticated systems of proof and proposition characteristic of general equilibrium theory. Rigor and axiomatization also played a role in the construction of the miniature. The related style of modeling, however, did not revolve around the austere beauty of proposition and proof. Rather, it centered on creating simple and manageable artifacts that upheld the promise of being useful tools for economic governance. In the actors’ understanding, this meant finding the minimum efficient scale that allowed for a workable model that could still be provided with economic (here, “neoclassical”) meaning. The efficient shape of Solow’s model made it a particularly talkative artifact. Not least, it provided a starting point for a number of stories, including what economists themselves called “fables” or “parables” about growth.

Throughout the book, we see economic modelers distancing themselves from any explanatory power or realist intentions of their artifacts. Chapter 5 takes a closer look at such utterings as a specific kind of model talk that accompanied modeling as a practice. Economists struggled with both the epistemological status of their small-scale artifacts and the ontological status of the things they were (ever so loosely) supposed to represent. Frequently, such talk related to the power of mathematics as a language, centering on the greater “virility” of their transparent and unambiguous mathematical methods compared to their verbal counterparts and predecessors. In contrast, I focus on instances in which economists grappled with their tricky artifacts and their messy practices. Specifically in the late 1960s, equipping unrealistic assumptions and technical narrowness with political appeal and scientific legitimacy was as much methodological reflection as it was part of struggles for authority in academe and institutions of economic expertise. The talk surrounding Solow’s model presented it as a didactic device, a prototype for larger-scale planning models, an imagery of a world that macroeconomic management was capable of creating, and a part of a toolbox that equipped economists as “little thinkers” with technically sound and rationally appropriate knowledge. While model talk in the first place emphasized the epistemic and political tentativeness of models, Solow’s turned into the epitome of what graduates called the “MIT style of modeling.”

In the course of the 1960s, mathematical modeling gradually stabilized as the primary mode of academic economic research. The Epilogue sketches the fate of “the Solow model” as it consolidated as an epistemic standard for an intellectual practice that focused on refining mathematical artifacts and using them to estimate model-relationships in any given data sets. Building on the idea that it already developed a life of its own at Solow’s desk, the Epilogue inquires into the movements and transformations of the multifarious artifact. It was adapted, extended, and reduced in relation to specific local, institutional, and strategic arrangements in planning offices, universities, and research institutions. Sketching some of its trajectories in the field of growth accounting and macroeconomic management, I wonder how the model sedimented into knowledge infrastructures and how the model’s knowledge, as precarious as it might have been, was equipped with computability, prognostic potential, and policy effectiveness.

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Moving away from a primary focus on people and their ideas and focusing on knowledge artifacts, this book seeks to contribute to a literature that investigates continuities between the 1930s and 1980s. The tenacity of Solow’s model defies all-too clean narratives about the succession of theoretical schools in that it cut across different paradigms over the decades. While broader political dynamics are beyond this book’s purview, the transformations the model underwent – from a personal toy model to an epistemic standard, from model talk to disciplinary language – speak both to the sedimentation of a specific kind of economic reasoning and to the continuities in governmental knowledge.⁶⁵ In what follows, I argue that it was the combination of market imaginaries and the compactness and practical capabilities of economic abstractions that led to their enduring dominance. That models could combine these qualities relied as much on their treatment as artifacts as on their suggestive power – often independently of their modelers’ intentions. Ambiguity was at the core of Solow’s model, even in that one paper in which it was first published. It is here that Chapter 1 begins.