“Once we attend to the miniature world, the outside world stops and is lost to us,” Susan Stewart notes in her account of miniatures in the arts and literature. Using the example of a toy, she describes miniatures as worlds of “arrested life.”¹ One way of looking at models is to understand them as manifestations of a desire for control or reflections of human anxiety compensating for a chaotic world. Solow’s model presented an orderly world on an equilibrium growth path. Everything beyond that world – from natural resources to distribution to power – was relegated to the realm of the unknown, at least for the time being. In this sense, the model offered a retreat; it was a small-scale space protected from contamination by an outside world that could not be scaled down. Critics of mathematical economics have frequently written about its fictional abstractions in these terms. One such critic, Sidney Schoeffler, whom we encountered in Chapter 5, wondered whether the reason that economists stuck with models that were, to him, so obviously inadequate from a scientific and logical point of view was that they satisfied specific psychological needs. “Unbearable facts are eliminated and desires are satisfied by imagery so that man can live in harmony with himself and with his environment,” he quoted from the psychology literature.² Like Stewart’s miniatures, mathematical models might compensate for the order and calm that a real world lacks. Historians of economics have inquired into how general equilibrium analysis fulfilled a need for protection for the mathematical economist Gerard Debreu, a retreat from the complications and frictions of his lived experience.³ “Finding equilibrium,” in Till Düppe’s and E. Roy Weintraub’s account, was not simply a matter of devising the most depersonalized and aloof axiomatic system. It was also an expression of the lives of their protagonists.⁴

In contrast to general equilibrium theorists, the modelers in this book were not in the first place concerned with the formulation of abstract axiomatic worlds. Their epistemic values were different. They focused on “practicability,” on a model being “useful” and “realistic enough.” Still, concepts of economic equilibrium, the harmony of interests, and perfect rationality also informed their reasoning. Solow’s model was indeed a prime visualization of such a well-running world, as Schoeffler would have it, a “wish-fulfilling intellectual imagery.”⁵ The model supported the belief that capitalism was not a series of erratic and arbitrary fluctuations and crises. Yet the protagonists of this book did not suppose an automatic harmony of market mechanisms. Rather than a flight from the world, they thought that their models provided them with an opportunity to, as a maker of different kinds of miniatures has put it, “confront, question, critique, or consider it.”⁶ Their epistemic virtues, I have argued, were tightly interlinked with their stance toward economic management. These modelers not only believed in the manageability of the economy, but they actually wanted to help manage it themselves. It is in this way that models prompted economists to emphasize the irregular, nonsystematic element of economic phenomena, the “cacophony of the marketplace,” as Solow once put it.⁷ Such an epistemological stance came along with several tensions linked to the ambiguity and openness of their models rather than the closure they provided.

My approach in this book was to take seriously the many ways in which economists treated models as artifacts. In the context of specific practices, models were not fixed, closed-off realities. They were made, used, adapted, and repurposed; they prompted questions, raised problems, and motivated action; they excluded issues, made some things invisible, and drew their “builders” and “users,” as the historical actors put it, into their highly specific worlds. At the same time, they were not as clean-cut as one would want to believe; they allowed for different and sometimes contradictory interpretations. Their ultimate indeterminacy raised a variety of model talk concerning both their economic contents and their meanings in research and policy-making (Chapter 5). The past chapters led through different encounters with Solow’s model. My central question was what this “simple” model was and did (Chapter 1). Due to its small scale and particular form, the model was able to interact with various other forms of economic knowledge and take on several roles. When Solow aimed to create a simple model for his students, the by-product of his more complex modeling work turned out to be a contribution to growth theory (Chapter 4). In effect, it introduced a specific way of theorizing and, in the eyes and hands of growth modelers, came to provide a more general case that confined other approaches to special cases. It also equipped economists with what they appreciated as an easy-to-use and more efficient technique of measuring growth and its factors than existing gauges (Chapter 2). And it figured as a simpler version of more complex, quantitative models, interpreted as providing “qualitative” knowledge (Chapter 3). Modelers compared the work it did with literary miniatures such as “parables” or “fables,” for it enabled them to tell clean-cut stories about how modern growth worked. In this way, the different trajectories in this book showed how the model shifted gears, changed purposes, appearances, and meanings depending on its specific engagements.

Theoretical model, instrument of measurement, a means of storytelling, a didactic device – all this happened at and around Solow’s desk. From there, and simultaneously from the desks where other versions of the neoclassical growth model were constructed, it circulated widely. It was adapted, extended, and applied in a variety of projects, in different fields over many decades. In the realm of economic theory, “the Solow model” became one of the dominant workhorse models that defined what was accepted as economic knowledge. Economists replaced parameters and equations with different formulations, clarified the model’s interrelationships, searched for more solid foundations for its results, and generalized its outcomes. Such work could, for instance, use the “elegant” curve of the neoclassical growth model as a graphic device to show that it became “unmanageable” when land was included.⁸ In the form of the model, the notion of economic growth made its way as a useable concept into other areas of economists’ study such as development economics, cycles, and public finance. In 1987, when Solow was awarded the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, the model was said to have sparked “hundreds of theoretical and empirical articles.” It had become, as the press release from the Royal Swedish Academy of Sciences announced, a “framework for structuring modern macroeconomic theory.”⁹ On the occasion of his Nobel lecture, Solow noted in an ironic tone that “‘the neoclassical model of economic growth’ started a small industry.”¹⁰ If we take these utterings at face value, how can we account for the model’s tenacity?

Given that I have emphasized the many roles the model played in the 1950s and the 1960s, it probably will not come as a surprise that economists of later decades praised its versatility. It is telling that they compared the Solow model to the Feynman diagrams in theoretical physics, taking “abstract concepts of equilibrium over time” and “shaping them into tools for ordinary economists.”¹¹ Introduced as a bookkeeping device for simplifying calculations in quantum electrodynamics in the late 1940s, the Feynman diagrams were adopted in a variety of fields. The historian David Kaiser has argued that these now routine diagrammatic applications “helped to transform the way physicists saw the world, and their place within it.”¹² Similarly, the Solow model – in concert with a whole collection of small- and larger-scale models – acted as an agent of disciplinary change that transformed both economists’ reasoning practices as well as the domain of economic expertise. That economists draw the comparison with the Feynman diagrams is telling in yet another way. It supports the argument that economists themselves understood a model as a specific kind of concrete artifact. The economists who adopted and continued work on Solow’s model spoke of a “machinery,” an “apparatus,” a “tool,” and an “instrument.”¹³ They considered it the right tool for a job. In fact, it turned into different tools for many jobs.

Throughout this book I have argued that Solow’s model, and the forms of knowledge it built upon, already framed the jobs it was supposed to do and prefigured the very problems it should solve. This was not entirely obscure to practitioners. After all, the model was not appreciated for any specific realism, empirical correctness, or explanatory power. In the first place, this practice of mathematical modeling was not about forging an agreement between theory and a reality but, akin to a technological practice, about fixing together various bits of knowledge, making things work, and thereby creating an artifactual reality in its own right.¹⁴ The Feynman diagrams, as many other examples from the history of science, had been introduced as “convenient ways to talk about the world,” but already in the next generation of practitioners they acquired an “added sense of realism.”¹⁵ Similarly, as the following two examples will illustrate, the consolidation of Solow’s model had implications for “economic growth” as an economist-made technophenomenon.¹⁶ Here, the passing of time is essential. “The Solow model” was implemented in long-lasting constellations used by successive groups of economists who had learned economic modeling as a craft and were trained in treating mathematical models as concrete artifacts. In the following section I will sketch two trajectories that indicate the uses of the model in the 1970s and 1980s, namely in a field of economic measurement called “growth accounting” and in the establishment of epistemic infrastructures for policy-making. These trajectories point at the different chronologies that unfold when focusing on the level of the artifacts and infrastructures of economic knowledge rather than the rise and fall of theoretical and political ideas.

Neoclassical Growth in Action

The perhaps most enduring way in which the neoclassical growth model has left its imprint on economic knowledge is its use as a device for measurement. In Chapter 2, I showed how economists appreciated it as a more efficient procedure for measuring the factors of growth than existing indices. The superior economy of this instrument of measurement, however, came at great costs. For one, it cast the economy as a whole, its growth, and the role of productivity in neoclassical terms. Whatever did not fit into this rendition of the economy – the ever-extendable list of things that were excluded from the model – was neatly tucked away in a “residual.” Such a device created a strict boundary between what was known (meaning that it was part of the model), and what was unknown (the “rest”). The first category involved conventional measures of capital and labor. The residual contained not only measurement errors but all kinds of things that played a role in the world of economic practices but were not specifically measured: From inequality to various types of capital to all kinds of cultural, social, and temporal factors that affected measures of GNP. In this sense, the numbers that the neoclassical model created could just as well be read as measures of the enormous distance between the model and the world it was intended to gauge. But, while others spoke of a “measure of our ignorance,” Solow strikingly framed the residual as “technical progress.” He was aware of and outspoken about the stakes of his interpretative maneuver. The procedure required, he noted with a seeming shrug of the shoulders, more than a deliberate suspension of disbelief.¹⁷ Once others applied the model as a measuring device, such qualifications were easily waived.

Soon, the model came to set the terms of debate over “technical change.” It was employed to measure growth and productivity of national economies, industries, and individual firms. While Solow had qualified his use of “technical change” as “a shorthand expression for any kind of shift in the production function,” for the most part the literature using the model simply carried on with the label.¹⁸ A 1963 study of growth and productivity of the Australian economy, for example, employed “the method … developed by R. M. Solow.”¹⁹ The lower table in Figure E.1 shows the relevant development of the index of “technical progress,” here still put in quotes. Similarly, a paper measuring the rate of technical change in the Indian Tata Iron and Steel Company (TISCO) noted that “the method of estimation chosen is that of Professor Solow.”²⁰ Another example was a paper on “technological change” in US agriculture, which featured a table visualizing the application of “the Solow model” (Figure E.2).²¹

Figure E.1 The “index of ‘technical proress’”

(Edwards and Drane, “Australian Economy,” 268)

Figure E.2 The “Application of the Solow model to agriculture”

(Lave, “Empirical Estimates of Technological Change,” 944)

In these early instances, the model was applied as it was, leaving its form intact and keeping Solow’s label for the rest. It was used as a simple tool to measure productivity in datasets that, with a couple of reformulations, fit its format. Critics maintained that the residual captured all kinds of things and was not actually to be taken as “technical change.” Even Solow himself asked economists not to equate technical change in common speech (“inventions… like the electric light or the automobile or the electronic computer”) with the statistical constructs of econometric research. “Economists, who give the impression of having invented the idea of technological progress in the past 6 or 7 years,” he mused, “have something much more pedestrian in mind.” Rather than talking about technological progress, they should use “the pedestrian label of ‘increase in output per unit of input’. It is a statistical artifact.”²² This came at a point in Solow’s career when he started to more frequently urge his colleagues not to mistake the categories of econometric analysis for real-world entities. Irrespective of the intentions of its constructor, the model gained a life of its own as an easy-to-use measuring device.

The history of science has emphasized that the circulation of knowledge consists of practices of transformation, adaptation, and reinterpretation. The central point is that these processes are productive and not merely applications by passive recipients. This is also true for an area of research between economics and economic history called “growth accounting,” for which Solow’s model is said to have “laid the foundation.”²³ The field, picking up pace in the 1960s and active until the present day, built on both aggregate production functions and index number constructions as its major instruments. What came to be called the “Solow residual” had a major role to play, not only as a common tool but also as a frequent contrasting foil for approaches that did not use a neoclassical production function.²⁴ The overarching aim of growth accounting was to include ever more additional factors of production. This was an attempt to curtail the list of absences that came with the model. But, in order to make the model measure more things, these had first to be brought into a form that fit the model-guided measurement procedure. In the decades to come, intangible factors of production such as “knowledge” or “education,” for instance, were recast as quantitative entities so that they could enter the growth accounting framework. Approaches that used the neoclassical growth model as a measuring device added ever more items as parameters in the production function: Organizational characteristics, human capital in the forms of education and health, population changes, or government policies. Once researchers committed to using that tool, they had to turn the things they wanted to know into inputs that fit the model. This is not only about the affordances and the limitations that come with an instrument’s use. As the model framed ways of thinking, seeing, and acting, it guided perception. Once it became the standard of the field, it essentially prefigured the object it was supposed to measure.

As an instrument of measurement, the Solow model’s rendition of the economy not only affected economists’ ideas and theories. The quantitative kind of knowledge it provided was explicitly thought to be useful in economic expertise and policy-making. In this way, its restrictive imaginary power extended directly to economic governance, where the Solow residual was widely treated as a straightforward yardstick to allocate resources “in the interests of economic growth.”²⁵ Chapter 2 showed how national accounts captured the economic benefits of public expenditure, thus providing quantitative arguments for state investments. At the same time, this meant subjecting policy to an economic evaluation. The neoclassical growth model took part in this broader trend as it became one crucial instrument to measure how all kinds of factors contributed to the increase of national income and thus, so the argument commonly went, to progress. Of the various factors for cutting down the Solow residual, it was especially aggregate statistics of “research and development” that policy-makers picked as a parameter to fine-tune the growth of the national economy.²⁶ Policies directed at growth and focusing on the economic value of scientific knowledge were simpler to advance than policies that aimed at other results (such as, for instance, pushing for more effective pharmaceuticals). The promotion of policies for stimulating technological innovation relied to a great extent on aggregate time series production function regressions. Here, Solow’s model presented processes of knowledge-making in the form of a production function, measured in terms of inputs and outputs. It thus contributed to a development that reduced the realm of the economic to efficiency calculations and subordinated public policies to that realm.²⁷

With the “Solow Residual,” the model had a scintillating career in the world of economic expertise. Yet there was another, less visible way in which it contributed so-called technical knowledge for economic governance. From the 1960s onward, when economic planning rose to new prominence, Solow’s model was integrated in the epistemic infrastructure of policy-making. Large-scale macroeconometric forecasting and planning models figured as decision support systems in a variety of institutions from planning offices and institutions in public administration to central banks and businesses.²⁸ Economists argued that these models provided a more systematic character to the knowledge used in governance as it was able to lay out the assumed consequences of various possible policies and added a long-term purview. Providing such an overhead perspective, models were intended to enable planners to figure out ways to better order the whole. Most planning and forecasting models worked as evaluation tools measuring potential effects of policies on national economic growth. Examples stretch from the Federal Republic of Germany (putting the macroeconomic goals of growth and stability into its constitution in 1967), to Colombia’s Plan Decenal (which was essential for the collaboration between the National Front, the US, and international lenders), to Belgium’s planning model MARIBEL (which was only introduced in 1970 to promote “democratic” decision-making).²⁹ While the concrete purposes, the institutional embedding of planning, and its effects on policy-making differed widely, macroeconometric models commonly included projections of the long-run and established specific growth targets. Here, the neoclassical growth model had a special role to play.

When it came to integrating growth, most macroeconometric models included a neoclassical framework. In the short-run, they afforded an analysis of policy effects, in which the role of demand was crucial. In their portrayal of the long-run, however, demand had no role to play. In these long-run scenarios, markets were assumed to work smoothly. This was the “land of the margin” that Solow had invoked in his 1956 paper, the cosmos of the neoclassical growth model (Chapter 1). This is not to say that it was precisely Solow’s model that circulated. As I have mentioned several times, Solow’s was not the only formulation of a neoclassical growth model. In particular, when it came to policy modeling, Tinbergen’s version was probably closer to the minds of planners. One example for the employment of the small-scale model, however, is a project that directly linked to Solow’s paper – the Norwegian planning model. Illustrating the porousness of the boundaries between governmental expertise and academic work, Norwegian planner Leif Johansen both extended the neoclassical growth model as a contribution to economic theory and made Solow’s model an essential part of the architecture of a quantitative multi-sector growth model for planning purposes.³⁰ This model, in turn, was implemented as part of a computerized infrastructure for administrative decision-making in the Norwegian ministry of finance in the late 1960s.³¹

In the Norwegian planning system, the neoclassical growth model contributed to calculating both a balanced growth path in the remote future and the factors that would increase that growth. Johansen’s “Multi-Sectoral Study of Economic Growth” (1960) presented a model economy that consisted of several sectors and was supposed to show the effects of changes (for example, technological progress) on various sectors of the economy and their relationship to one another (such as the redistribution of labor and capital between the sectors). Using data from Norwegian national accounts, the model was implemented numerically to provide a guide to macroeconomic planning. In all of this, the (adapted) neoclassical growth model served as a kind of design for establishing and checking the behavior of the larger-scale model. Since Johansen thought it would be difficult “to see the macroeconomic implications of a multi-sector model,” he used the small-scale model as a benchmark for judging the larger model’s behavior. Only if it corresponded to the behavior of the smaller one was it to be considered reasonable.³² Like many others who used and extended Solow’s model, Johansen stressed its operational practicability and functional simplicity. Here, the model became part of a larger-scale construction that carried most of its phenomenotechnical characteristics: The economy created was a system of efficient production, which, in the neoclassical long-run, grew without frictions on a balanced growth path. Based on the assumptions of the efficient utilization of resources and consumer sovereignty, questions of distribution or any other kind of concerns that went beyond efficiency were excluded from the start.

As a part of planning models, Solow’s model fit perfectly in the environments of interventionism and the mixed economy from where it came. Similar to the way Solow made sense of his modeling practice, Johansen emphasized that equilibrium was not achieved automatically by the forces of the market: It had to be maintained by active policy. His model provided “a background and a framework for the continuous flow of decisions” within the realm of policy-making.³³ In the technical framework of 1960s macroeconomic planning, a variety of political strategies were viable. In each case, however, the major point of reference was growth. In that vein, Johansen stressed the possibility of creating the appropriate institutions for implementing “a continuous and balanced growth process with full employment of both labor and capital equipment.”³⁴ Being a life-long card-carrying member of the Norwegian Communist Party, he himself did so with an eye on Soviet planning.

The concrete architectures of macroeconomic planning models differed, and their institutional embedding framed the way in which the knowledge they provided wielded influence on policy-making. At their core, however, all these modeling projects adhered to a similar epistemology and ontology: It was not about an “as if,” a hypothetical on whose ground government should act. Recall the often-cited methodological stance associated with Milton Friedman that one should proceed working with a model as if its assumptions were true – as long as its predictions were accurate. In Chapter 1 I have compared that perspective with Solow’s 1956 preamble that the crucial assumptions needed to be “realistic enough.” As vague as that formulation might be, it put a prime on the concrete modeling situation, the problem at hand, and the role of the modeler’s skills in judging the adequacy of an assumption. Similarly, in the eyes of their constructors, large-scale planning models did not provide a glance into the future “as if” their assumptions were true. The projects discussed in these pages were embedded in a discourse that was all about “what happens if.” Planners designed a menu of possible actions that in turn generated a set of different outcomes. Here, economic expertise was neither predictive nor probabilistic. Instead, planning models were tools for imagining possible future worlds that might very well be realized.³⁵

As a design for econometric planning, the Solow model contributed to the quantitative generation of possible future worlds that could be achieved through macroeconomic management. The rationale was the following: Since prices and wages did not adjust quickly enough to bring markets into equilibrium in the short-run, the main task of economic expertise was to manage aggregate demand. Once a certain rate of employment was reached, market competition would establish an efficient allocation of resources. Whatever issues specific markets might exhibit, economic expertise was able to provide appropriate knowledge for intervening to foster competitive markets.³⁶ In this sense, planning models were part of a program that they themselves shaped. It was about making the economy that they depicted resemble the model ever more closely, making it akin to a determinate and predictable system.

I have argued that the ambiguity of mathematical models was conducive to their application to policy design. Several political programs could be supported by the same models, but on the flipside a model came with a variety of closures, which tended to become invisible when models turned into standards. Over and over, modelers in the previous chapters spoke of their models as tools but did not, contrary to what we might expect, argue for their neutrality. For the philosopher Alain Badiou, probably taking a swipe at contemporary French planning at the end of the 1960s, these models figured as a “technical image of the interests of the bourgeois class,” readily “objectify[ing] class objectives.”³⁷ Johansen, in contrast, stressed a certain ideological flexibility of models: Planning techniques could be used to achieve the “goals of a central power complex,” and be employed “in the interest of one particular class.”³⁸ This, however, did not mean that he thought of models as neutral. Clearly, they promoted a kind of policy-making that gave priority to “total efficiency and the development of consumption.”³⁹ Once the model system for macroeconomic planning was established, implicit assumptions were consolidated, and the values and goals embodied by the model were not questioned further.

The model infrastructure of policy-making that evolved from the interventionism of the 1950s and 1960s remained rather stable. Despite the collapse of the Bretton–Woods system and debt crises, the vision of a future world of perfect efficiency and balanced growth seems to have translated well into the 1970s and beyond, as did the role of growth as the benchmark par excellence. The Norwegian system of planning models is indeed active until the present day, for forecasting as well as in the design of policy programs.⁴⁰ This is similar in the US, at least according to Gregory Mankiw, who in the 2000s bemoaned that the infrastructure of policy-making relied on the same old models. To him, developments in macroeconomic theory since the 1970s “had only minor impact on the practical analysis of monetary or fiscal policy.”⁴¹ A glance at the scarce literature on the practices of providing economic knowledge for governance suggests that, alongside the establishment of DSGE (dynamic stochastic general equilibrium) models in the early 2000s, existing models were adapted and became more detailed with new, more fine-grained variables. The very foundational architecture of these models, in particular a specific kind of “Keynesian” structural equation model, remained relatively stable, both in Treasury Departments and at the FED, for instance.⁴²

The examples of growth accounting and planning models illustrate how a small-scale model, a clean zone of domesticated experience, could take on a life independently of the model constructors and have effects in policy-making – not simply through its aesthetic appeal but, more concretely, as a suitable component for the epistemic infrastructures of economic expertise. That it fit existing governmental technologies (national income accounts, productivity measurements, input–output models) was no accident but built in. It neatly blended in and provided an efficient mechanism that calculated the effects of various factors on “long-term growth,” which was not only limitless through the power of technological progress but also worked entirely without paying attention to the distribution of income. The two examples I provided highlighted the ability of the model to be extended, put together with other models, and adapted to new data sets and new computing capacities. The work of modeling is rarely finished: Both the work on and of the model go on. In a way, the neoclassical growth model became a representation of the preferred form of accepted economic analysis and of what economists considered worth investigating. It was not only about the acceptance of a specific technique but the hegemony of a specific kind of problematization. Due to its inherent ambiguity and suggestive power, however, its consolidation came with ironic twists – which brings us back to where this book started.

Afterlife

The Introduction opened with Amartya Sen’s 1970 letter to Solow pointing to a certain ambiguity of the model’s status as a “model.” Was it a mimetic portrayal of the world or was it a fictional world that could be established? In the chapters of this book, I traced some of the model’s trajectories as an artifact with its various transformations and interpretations as a “model.” The previous section already indicated that such an approach blurs the idea of contained schools or paradigms. This is the case even if we stick with the realm of economic theory. The exchange between Sen and Solow took place at a time when growth theory was the epitome of the field of economics, not least through MIT’s modelers who were on the top of the profession. Together with their students, they worked extensively on the neoclassical growth model, including, for instance, multiple sectors and the depreciation on capital. In 1964, Samuelson’s Economics, the dominant textbook then in its sixth edition, received a chapter on growth – not merely in the sense of rising GDP or measurements of growth and productivity but in the model-sense of an equilibrium growth path. By the end of the decade, the first anthologies collecting the essential contribution to the field came out, among them Sen’s, and the first textbook on growth theory offered a consolidated introduction for graduate students in 1970.⁴³ Already in the course of the 1970s neoclassical growth theory and its specific style of modeling stopped being the exemplar of what was considered high theory. And yet, this was not the end of Solow’s model.

In 1974, Evsey Domar bemoaned that “simple models [were] not popular anymore.”⁴⁴ The ebbing of growth theory as a field resulted, in part, from the dissolution of the bipartisan consensus on New Deal liberalism, which was linked with the stagflation crisis and the rising cultural critique of growth, abundance, and consumerism. At the same time, growth modeling stopped being a separate field and became part of general economics. This was related to a new vogue in economic theory, new classical macroeconomics, which pushed the concepts of “microfoundations” and “rational expectations,” challenging “Keynesian” economics. The crux of what has come down as “the Lucas critique” was that Keynesian models did not account for agents’ expectations and behavior in reaction to policy changes such as a tax increase.⁴⁵ The new classicals’ idea was to bring together microeconomics (as the study of utility-maximizing rational actors) with the macroeconomic realm of growth, inflation, and unemployment. In the previous chapters we encountered several attempts to relate the whole with the parts, depictions of the macroeconomy with portrayals of firms, sectors, or industries. By the beginning of the 1970s, new classicals did so by modeling “representative agents” (one “representative” profit-maximizing firm and one “representative” utility-maximizing household). In a way, the new classical critique proceeded with the familiar argument that proper scientific economics had to be rigorous. But how different was this desire for an overarching mathematical framework from the approach followed by the modelers discussed in this book. Though Solow’s model was also based on the assumption of perfect competition, it had not provided an explicit formulation. Again, it was this openness that made it adaptable to the new fashion in economic theory. At the same time, engaged in different modeling practices, it changed its very status as a model.⁴⁶

When, from the late 1970s onward, modeling practices in economic theory diversified and a whole variety of models emerged and spread, Solow’s was readily integrated. Focusing on its persistence highlights the model’s ability to transgress the boundaries of different theoretical “schools.” This holds in particular when it comes to the theoretical debates around a new major research object, the so-called real business cycle. The basic idea was to merge long-run growth with short-run business cycles in an overarching mathematical framework. The relevant models adopted, as historians of economics Tiago Mata and Francisco Louçã have demonstrated, a neoclassical production function. The question of how to do so sparked controversy between two schools, “New Classical” and “New Keynesian” macroeconomics. In particular, “the interpretation of the Solow residual became a crucial item of that debate.”⁴⁷ While theoretical outlooks and disciplinary as well as political alignments differed, all the involved parties relied on the residual, “weaponizing” it for their diverging purposes.⁴⁸ Another example for the model changing its status is the revival of neoclassical growth theory from the mid-1980s onward under the label of “endogenous growth theory.” The new models built on the concepts of market clearing and perfect foresight just as before, but they endogenized the previously exogenous factor “technical progress,” which meant it became a part of the model. Technical progress was now treated as just another good produced and purchased on markets. Named “human capital devoted to research” or “stock of knowledge,” a new variable entered the growth model, leaving its basic architecture intact.⁴⁹ In a process of consolidation, Solow’s model, created at a specific time and place and with a specific purpose, had turned into an essentially unchallenged routine. In this sense, the model has had a buoyant, very successful career. Its epistemological and ontological framings, however, were diverse, which makes it in fact worrisome to speak of the same model.

Following a particular scholarship on modeling, I have maintained throughout this book that a model is embedded in different engagements that decisively frame its character. In the mid-1950s, Solow’s model had been part of an endeavor that celebrated the opportunity to experience the workings of a mathematical world, to test ideas, and to extend the dimensions of economic imagination without having to pay too much attention to empirical reality. Solow and economists of his ilk appreciated a model’s playful character, its exploratory and, above all, its preliminary form. They pleaded for multi-purpose toolboxes to deal flexibly with specific problems at hand. They highlighted the artificiality of their closed worlds and factored in the role of their skills, judgment, and values. And yet, when these economists’ toolboxes stabilized, their models gained a much more steadfast character than their initial framing as exploratory worlds actually allowed for. Between the 1960s and 1980s, mathematical forms and the epistemic norms that accompanied them became increasingly autonomous from their artificers and their specific sites. It is here that the power of models became even more manifest, the power to draw users into their worlds of domesticated experience. By the end of the 1980s, a survey of economic graduate students at elite universities captured a profession that had more appreciation for mathematical technicalities than for dealing with economic problems of whatever they saw as the real world.⁵⁰ Also the essential framing of Solow’s model (and hereby of “growth”) in economic theory changed: In the new endogenous growth theory, the long-term growth rate itself seemed to be malleable. While before, long-term growth was taken as an imaginary trend that could in principle be implemented, it was now something existing in the world.⁵¹ Similarly, in real business cycle theory, “what-if” had turned into “as-if.” Solow himself was highly critical, as real business cycle theory took, he argued, “the construction … as a model of the actual capitalist world.”⁵²

The frustration of the historical actors speaks to the openness of models. In Solow’s own account, there appears to be a break: While he and his colleagues framed growth and technology as state-driven, these were now to be brought about by the workings of the markets. The growthism of the 1980s argued for an automatic trickling-down and thus used growth to legitimize cuts of social measures, decreasing wage rates, and declining employment numbers.⁵³ In contrast to Solow’s view, from the perspective I have taken in this book, however, there was a curious continuity. Thinking back to the early 1950s, the small-scale model came with cautious “qualifications” that highlighted some of its absences and warned the reader of taking it too literally. Such caveats replaced an earlier way of presenting mathematical economic knowledge. In his account of dynamic instability, Harrod, for instance, had emphasized the lack of certainty in an essayistic treatment circling around a mathematical framework (Chapter 1). Solow’s work separated the mathematics and the verbal treatment. Now the model constituted the very object of analysis; it provided secure knowledge. Uncertainty was relegated to the qualifications, a verbal account of how the model was not straightforwardly related to anything beyond its boundaries. It was strikingly easy for subsequent modelers to dispense with such contained paragraphs of doubt. By constructing mathematical models and treating them as some kind of material objects, the economists in this book had created artifactual realities, which developed a life of their own. The list of absences, which had an eerie presence in their writings, vanished when models became increasingly autonomous. Once integrated into different kinds of practice, Solow’s model was not only interpreted differently but – given it consisted of the combination of algebraic equations, diagrammatic visualization, and verbal accounts – indeed became a different “model.” Regardless of initial intentions and of the modeler’s protest, it turned, in some quarters, into a carrier of a market fundamentalist world view and an exemplar for the belief in the omnipotence of markets.