This chapter uses a range of quotes and findings from the internet and the literature. The key premises of this chapter, which is illustrated with examples, are as follows. First, Big Data requires the use of algorithms. Second, algorithms can create misleading information. Third, algorithms can lead to destructive outcomes. But we should not forget that humans program algorithms. With Big Data come algorithms to run many and involved computations. We cannot oversee all these data ourselves, so we need the help of algorithms to make computations for us. We might label these algorithms as Artificial Intelligence, but this might suggest that they can do things on their own. They can run massive computations, but they need to be fed with data. And this feeding is usually done by us, by humans, and we also choose the algorithms to be used.

In practice we do not always have clear guidance from economic theory about specifying an econometric model. At one extreme, it may be said that we should “let the data speak.” It is good to know that when they “speak” that what they say makes sense. We must be aware of a particularly important phenomenon in empirical econometrics: the spurious relationship. If you encounter a spurious relationship but do not recognize it as such, you may inadequately consider such a relationship for hypothesis testing or for the creation of forecasts. A spurious relationship appears when the model is not well specified. In this chapter, we see from a case study that people can draw strong but inappropriate conclusions if the econometric model is not well specified. We see that if you a priori hypothesize a structural break at a particular moment in time, and based on that very assumption analyze the data, then it is easy to draw inaccurate conclusions. As with influential observations, the lesson here is that one should first create an econometric model, and, given that model, investigate whether there could have been a structural break.

This chapter deals with missing data and a few approaches to managing such. There are several reasons why data can be missing. For example, people can throw away older data, which can sometimes be sensible. It may also be the case that you want to analyze a phenomenon that occurs at an hourly level but only have data at the daily level; thus, the hourly data are missing. It may also be that a survey is simply too long, so people get tired and do not answer all questions. In this chapter we review various situations where data are missing and how we can recognize them. Sometimes we know how to manage the situation of missing data. Often there is no need to panic and modifications of models and/or estimation methods can be used. We encounter a case in which data can be made missing on purpose, by selective sampling, to subsequently facilitate empirical analysis. Such analysis explicitly takes account of the missingness, and the impact of missing data can become minor.

Currently we may have access to large databases, sometimes coined as Big Data, and for those large datasets simple econometric models will not do. When you have a million people in your database, such as insurance firms or telephone providers or charities, and you have collected information on these individuals for many years, you simply cannot summarize these data using a small-sized econometric model with just a few regressors. In this chapter we address diverse options for how to handle Big Data. We kick off with a discussion about what Big Data is and why it is special. Next, we discuss a few options such as selective sampling, aggregation, nonlinear models, and variable reduction. Methods such as ridge regression, lasso, elastic net, and artificial neural networks are also addressed; these latter concepts are nowadays described as so-called machine learning methods. We see that with these methods the number of choices rapidly increases, and that reproducibility can reduce. The analysis of Big Data therefore comes at a cost of more analysis and of more choices to make and to report.

INTRODUCTION

For someone always seeming to doubt his own originality, Lionel Robbins had a considerable effect on economists’ professional self-image (Backhouse & Medema 2009b: 810). The very first paragraph of his autobiography asks his reader to think of him merely as someone who repeatedly found himself in the right place at the right time to comment on what others were doing to reshape economic thought (Robbins 1971: 11). The Preface to the first edition of his most famous work, An Essay on the Nature and Significance of Economic Science, strikes the same tone. It positions him as simply rendering increasingly legible analytical themes that were the creation of other, more visionary economists (Robbins 1932: xlii). This chapter focuses primarily on Robbins's definition of economics as the study of choice under conditions of scarcity, because it provides another important turning point in the prehistory of economics imperialism. Even in relation to his most celebrated achievement, though, Robbins said that he was merely doing other people's intellectual bidding for them, in particular that of the English marginalist pathfinders, Stanley Jevons and Philip Wicksteed (Robbins 1984 [1935]: 22). At most, he allowed himself credit for seeing more clearly than anyone else what united the otherwise disparate advances of those he considered to have reworked Jevonian and Wicksteedian insights most effectively. He always held the promise of scientific unification in exceptionally high regard.

Robbins has been taken at his word by other economists, as he is today best remembered as the foremost theoretical synthesizer of his day. More attention was being paid in the 1930s than previously to trying to bridge the gap in Anglophone economics between the English marginalists and Carl Menger's Austrian followers (Vaughn 1994: 14). Robbins was well placed to succeed in this venture, being fluent in German and therefore able to read for himself countless works that were yet to be translated into English (O’Brien 1990: 162). He also used his position as Head of the Department of Economics to bring to the London School of Economics Austrian economists he had previously befriended during his visits to Vienna (Robbins 1971: 91).

MULTIPLE MEANINGS OF RIGOUR AND PRECISION

At heart, the debate about economics imperialism might not have moved on very far from when Ralph Souter (1993b: 94) first introduced the notion into social science (see Chapter 1). This was in the 1930s. He argued that rigour and precision looked very different from beyond a mathematical mindset than from within it. They remain prized assets in economics imperialists’ rhetorical armoury but in the absence of Souter's reflections on the many meanings they might acquire. Explanation through mathematical analogy within the model will certainly bring additional rigour and precision to understandings of that world, but this should not be confused with saying that the world beyond the model is now fully understood. The system of equations will reveal mathematical solutions to what, in essence, are merely mathematical problems. Inductive inference to the world beyond the model involves a leap of faith that even the most aggressive selling of economics imperialism does nothing to overcome. The colonists purport to operate somewhere between the world within substitute models and actual day-to-day experiences, connecting the two in a causal explanation. Yet these are distinct ontological realms that respond to different standards of rigour and precision. Souter recognized this 90 years ago, but the long-forgotten nature of his work shows that his warnings went unheeded.

Souter (1933a: 377–8) had shown that the economists of his day were left with a choice of entering one of two strictly parallel domains: Lionel Robbins's new one or Alfred Marshall's old one. Robbins's is where economics imperialists continue to be positioned today, with rigour and precision being defined in relation to the logically sound specification of the world within the model. Marshall's attracts the critics of economics imperialism, because its definitions of rigour and precision are linked to how well the world within the model captures the characteristics of the empirical realities it is asked to imitate. In modern-day philosophical terms, two different representational relationships between model and target are being invoked: “standing for” the real world in the former, “making present” the real world in the latter, or representing versus re-presenting (Prendergast 2000: 5). Mathematical analogy can replace observational content in Robbins's model worlds and still be epistemically reasonable, but not in Marshall’s.

INTRODUCTION

Sitting in a refreshment room at Berlin railway station in 1891, the 29-year-old David Hilbert uttered one of the most memorable lines in the whole history of mathematics. He had been attending the annual meeting of the German Mathematical Society in Halle, and he was waiting with some fellow conference attendees for his connecting train back to Konigsberg. The friends were reflecting on what they believed to have been the most important talk they had heard at the conference. Hermann Wiener had delivered a provocative lecture in which he outlined the need for more rigorous underpinnings to the theory of geometry. Very few people still took Euclid's Elements, written in the third century BCE, as a repository of literal truths, but the primitive elements of geometry had remained largely unchanged since that time (Henderson 2013: 101). “Man mu. jederzeit an Stelle von ‘Punkte, Geraden, Ebenen’ ‘Tische, Stuhle, Bierseidel’ sagen konnen”, Hilbert suddenly interjected into the conversation (Blumenthal 1935: 402–03). This starkly revealing sentence is usually translated into English as: “You can say at any time ‘tables, chairs, beer mugs’ instead of ‘points, straight lines, planes’”.

Such is the retrospective power that has been loaded onto Hilbert's comment that it sounds as though it belongs to an apocryphal story. However, the biographer in question, Otto Blumenthal, was one of Hilbert's closest collaborators. His account was seen by Hilbert before it was despatched for publication, presumably therefore with his blessing. There is still the chance he did not use these exact words and the standard English translation might add a more dramatic gloss to what was actually said. At this stage of his career, though, Hilbert certainly thought it should be possible to substitute any words drawn from a random letter generator for the well-known geometrical concepts of “points”, “lines” and “planes”, yet still leave intact the underlying logical structure through which he would henceforth seek to describe the relationship between points, lines and planes. I know of no contemporary economics imperialist who cites Hilbert's 1891 challenge to the need for confirmed empirical content within mathematical objects as direct inspiration for their activities.

INTRODUCTION

It is possible to think in a manner that has a clearly mathematical underlying rationale but without surrendering to overtly mathematical expression. However, this is not a path that economists, in general, chose to take. The previous chapter reviewed key developments in the process of argument through mathematical postulation, where mathematical relationships only have to be findable in principle. Mathematical truths could henceforth be asserted through proof-making without the need for external validation of the conditions under which such truths were likely to manifest themselves in practice. Even though this never became consensus metamathematical opinion in the manner of a Kuhnian paradigm, enough mathematical economists were convinced by this core ontological claim for it to have left a lasting mark on economic theory from the 1950s onwards. This chapter focuses on the parallel turn towards hypothetical mathematical modelling as a second means of translating mathematical instincts into direct mathematical expression, where this time we are more likely to be told that the relevant mathematical relationships have actually been found. The key factor here is the similarity between what is causing equilibrium in the model world and the closest corresponding causal mechanisms in the real world. What might be demonstrated as being true in the model is also on many occasions treated as being true of the world beyond, even if the explanation of why such resemblance holds is often somewhat sketchy. We are returned to the fundamental ontological difference between a model world that might be thought into existence in its own terms and what lies beyond these hypothetical relations in real-world economic experiences. The distinction between defined and described mathematical functions simmers away just below the surface.

The broader discussion about how realistic model-world relationships have to be receives precious little attention from economists, and the distinction between defined and described mathematical functions none at all. It is therefore unsurprising that the dividing line between mathematical postulation and hypothetical mathematical modelling has become increasingly fuzzy over time. Léon Walras's 1874 classic, Éléments d’Économie Politique Pure (usually translated into English as Elements of Pure Economics), was very clearly a theoretical exercise in mathematical postulation (Walras 1984/1954 [1874]).

THE REVOLUTIONARY INTENT IN ECONOMICS IMPERIALISM

This book is about methodological revolutionaries. It discusses a first group of people who changed fundamentally what economists accepted as good theoretical practice. I show how these intellectual pioneers reduced the most essential elements of economic theory to working through the logical implications of beginning with a market model and subjecting it to modes of mathematical reasoning. I also discuss a second group of people who changed equally fundamentally economists’ willingness to position their mathematical market models as the one true means of generating valid social explanations. I show how these later trailblazers made the case for an economics imperialism that displays little respect for the established domains of the individual social sciences. The earlier reconstitution of economic theory in ever more noticeably mathematical form can be thought of as the prehistory of today's increasingly prominent boundary-hopping activities. None of the former group ever made the case explicitly for economics imperialism, but without their theoretical innovations the scope for subsequent disciplinary transgressions would have been far more circumscribed. More than a century of deep methodological reflection within economics about how best to mathematize market models ultimately created the context for a debate about how far the resulting mathematical objects could be taken beyond economics.

These revolutionary activities have led to a situation in which all manner of non-market aspects of everyday life come to be treated for analytical purposes as if they are market phenomena. However, this requires not only a change of explanatory focus but also a reconceptualization of the social realities being studied (Kuorikoski & Lehtinen 2010: 357). The latter shift is clearly the more controversial, because it involves accepting that something is not as it is experienced in real life for the sake of methodological convenience. The use of market models to explain various aspects of social life amounts to more than mere deference to the most up-to-date techniques. It tells us how we must view what is of interest in the world, even if we struggle to be convinced that every element of our daily lives can be reduced to simple market calculations. Of the many resulting ironies, perhaps one stands out above all others.

INTRODUCTION

The case for economics imperialism is a specific example of the broader argument for scientific unification. But it is not a matter of using similar means of observation and measurement to adjudicate on the similarity between the causal processes in operation. The explanation does not follow careful empirical investigation of the causes at work; rather, it comes first. Every social situation is reduced to an instrumentally rational individual ignoring conflicting social stimuli to always maximize their market gains, and an explanatory narrative is then built around those actions. Explanatory notions are thus allowed to overpower causal notions, and scientific unification very quickly becomes the search for new social situations to submit to a single structure of explanation (Kitcher 1989: 495). The boundary-hopping activities in which economics imperialists engage are one-way transgressions enacted via the imposition of mathematical market models (Nik-Khah & Van Horn 2015: 72).

These are circumstances in which no invitation to appropriate new subject matter is ever sought, and what might otherwise be a negotiated coming together instead gives way to the law of the jungle. Economics imperialists are easy to convince that their side will be the last one standing in any ensuing battle for supremacy (Van Bouwel 2011: 47). Listening only to them, the sense of an imminent takeover is never far away (Fine 2004: 121). Looking at the practice in social science journals, the same feeling can also quite easily take hold. It is one of the curiosities of economics imperialism that very few members of its club make the case explicitly for it. But for every economist who has spoken loudly in support of transgressive mathematical market models, there are many more who have followed their prescriptions but without the fanfare. Even if they are concerned not to openly ruffle feathers, they are equally intent on pushing the parameters of insisting on strict obedience to an abstract market logic.