Economic models and their flexible interpretations: a philosophy of science perspective

ABSTRACT

We mobilise contemporary philosophy of science to further clarify observations on economic modelling made by Gilboa et al. (2023). We adopt a normative stance towards these modelling practices to identify the extent to which they are epistemically justified. Our message is simple: many of the distinctions proposed by Gilboa et al. (2023) are useful, but without the proper qualifications, too much flexibility in choosing the right interpretation risks downplaying the crucial role that empirical evidence should play in any modelling endeavour.

KEYWORDS:

• Economic modelling
• scientific explanation
• normative economics

1. Introduction

Most of what Gilboa, Postlewaite, Samuelson and Schmeidler (2023) say about economics is clearly correct and also easily recognisable from the perspective of the philosophy of economics. Economics is a predominantly model-driven science – especially compared to other social sciences – kept together by an overarching foundational ‘theory’.¹ At the same time, the central assumptions of this theory are repeatedly questioned on empirical grounds, and developments such as behavioural economics have not resulted in more consistently predictive models – at least to the extent that one would expect if they really provided general corrections to the universally applicable empirical theory. Gilboa et al. (2023) argue that these features of economics would be puzzling if economists indeed only valued prediction as an epistemic goal. Instead, they propose, economists also value their models on other grounds and for other reasons, including explanation, conceptual exploration, analogical inference, and critique.

Gilboa et al. (2023) explicitly state that their observations are sociological and, as such, purely descriptive of the practice and self-understanding of economists. Nevertheless, these observations are clearly, if not outright normative, at least largely rationalising. As philosophers of science, our aim is to further clarify these observations about modelling practices and to provide an unabashedly normative epistemic justification for some of them, while drawing attention to more problematic ones. In particular, we mobilise the philosophy of science literature on the nature of model-based representation, inference, and explanation. This literature offers systematic explication of the why and the how of many of the autoethnographic observations made by Gilboa et al. In addition, an explicitly normative stance is useful not only for defending economists from various outside criticisms, some of which may in fact be well taken, but also for providing a baseline for constructive critique. Critique will always remain somewhat unsatisfactory without a clear understanding of what ought to be done, and without some conception of alternative means of attaining the same ends. It is in this spirit that we marshal recent (and some not so recent) philosophy of science in what follows, thereby further sharpening some of the observations in Gilboa et al. (2023)’s original contribution. Our message is simple: many of the distinctions put forward by Gilboa et al. (2023) are useful, but without the proper qualification they risk downplaying the crucial role that empirical evidence should play in any modelling endeavour.

2. Economic theory as a tool-box

Much of the confusion concerning the empirical content of economic ‘theory’ is an exceptionally salient instance of the Davidsonian point that there is no categorical and immovable distinction between a conceptual scheme and the empirical content that it is used to structure. In the case of Expected Utility Theory (EUT), depending on how it (or its variants) is used and applied, it can be more a conceptual scheme with little empirical content (e.g. decision theory), an empirical theory of the psychology of decision-making (as in judgement and decision-making research), or something in between (consumer theory).

We (and many others) agree with the authors that standard microeconomic theory is closer to being a common language for model-building than an empirically substantial and nearly universal predictive theory of human decision-making. This is neither a novel methodological stance in economics nor a new philosophical explication of it, as this view of economic theory was quite clearly formulated in the nineteenth century by Alfred Marshall (1885).

This view in turn implies a tool-box approach to the science of economics: economics does not offer a grand unifying empirical theory with direct predictive and explanatory power – something possibly akin to foundational theories in physics – but an impressive set of tools for reasoning, to be creatively applied to empirical phenomena involving exchange, incentives and price signals (or anything that can be made to fit this conceptual framework). Thus there is always room for interpreting how a particular tool is, or ought to be, used in a particular context – and therefore how a particular model or model template is or ought to be interpreted. In addition, even if economics is best seen as a set of tools, this does not mean it is a random collection of unrelated tools. As Gilboa et al. (2023) correctly point out, the models of economics are held together by a unifying theory. But if the role of the theory, and the sense of unity implied, is not the same as in physics (or at least in lay imageries of physics), i.e. of uncovering universal and fundamentally simple properties that explain the observed phenomena, what is it?

Elsewhere (Kuorikoski & Marchionni, 2014), we have found it useful to resort to physicist Richard Feynman’s distinction between Euclidean and Babylonian science, in the way elaborated by philosopher William Wimsatt (1981). In the Euclidean ideal, science is based on a set of fundamental axioms from which empirical results are logically derived for the purposes of prediction or explanation. The best way to improve science so conceived is to make the fundamental axioms as precise and error-free as possible, as this would automatically result in better predictions. The Euclidean ideal is a poor fit for a science like economics that deals with open, complex, and constantly evolving systems without universal and constant foundational building blocks. In contrast, the Babylonian ideal of science is one that aims to increase the reliability of knowledge by means of controlling for the effects of inevitable errors in assumptions. As there are no universal, eternal, and precise empirical parameters that underlie all decision-making, all modelling assumptions are bound to be false in some respects. In contrast to an Euclidean image, no axiom or assumption is therefore treated as an inviolable truth, and the economic theorist is free to relax or alter any assumption, as long as this is done so that the consequences of this alteration remain tractable with respect to existing alternative models.

Conceiving of economics according to the Babylonian image offers a unifying way of thinking about some of the sociological features that Gilboa et al. (2023) highlight while simultaneously giving us a handle to make more normative claims about epistemological justification. That there are different potential uses for economic models does not imply that any conceivable model is a good model just because it can be used for something or other. For example, the kind of analytical modelling that Gilboa et al. (2023) emphasise makes perfect sense in a Babylonian image of science: it is part of the attempt to locate potential sources of error in the theoretical framework, i.e. results that depend on a very specific set of assumptions and hence are unlikely to be realised in any concrete economic system, or outright inconsistencies between individually plausible assumptions. Gilboa et al. (2023) also single out the critical role of purely theoretical modelling, what they call critiquing reasoning. Analogously, using a suite of models that share a common core rather than applying a single correct model is a way of increasing the reliability of the inferences by relying on the more robust components of the theoretical edifice (see Kuorikoski et al., 2010; Wimsatt, 2007).

A key role for the unifying theory, the ‘standard’ microeconomic assumptions, is to provide the baseline models, common points of reference that alternative models can be meaningfully compared to. These models need not be realistic or predictive of any particular economic phenomena as such. Instead, they serve two interrelated functions. First, they help to define what phenomena are interesting targets for explanation: observed deviations from what the standard assumptions would predict are singled out as being in need of explanation. Second, since not all standard assumptions are relaxed at the same time, baseline models allow the researcher to keep track of the relations between dependencies demonstrated in different theoretical models.

3. Kinds of models

According to Gilboa et al.(2023), there are three kinds of models in economics, or rather three ways in which a model can be interpreted: positive, normative, and analytical.

They introduce the distinction by means of an analogy with an architect’s maquette.

It may be useful to first think of physical models such as maquettes constructed by an architect. Assume, for concreteness, that we examine a maquette of a town square. Such a maquette can (i) describe a square that exists, or that existed in the past; (ii) describe the architect’s proposed design for a square; or (iii) test the feasibility of a possible square. (Gilboa et al., 2023, p. 4)

The first one corresponds to the positive interpretation, the second to the normative, and the third to the analytical. We will talk more about positive models and their functions in Section 3.3, but first we comment on the normative and analytical categories (3.1 and 3.2, respectively).

3.1. Normative models

Gilboa et al. (2023) distinguish between the positive and normative interpretation as follows: ‘[a] theory demonstrating that increased educational attainment on the part of women and increased assortativeness in marriages will lead to increased inequality in family incomes is positive [emphasis added].’ On the other hand, ‘[a] paper arguing that we should subsidize the cost of higher education in order to flatten the profile of education attainment and hence, family income, is normative [emphasis added].’ According to this characterisation, the normative models of the economists are like the models of the architects or of the geologists and experts in hydrodynamics, which are meant to guide the construction of good buildings or dams. But is this really all that normativity amounts to in economics²?

Normative economics is more than the provision of technical norms and purely instrumental normativity. It is, in other words, much more than just prescription. The normative branch of economics is often more robustly normative in that (a) the conceptual framework is itself a normative theory of instrumental rationality and (b) often, the objective function or the empirically estimated ‘welfare’ is understood as being intrinsically good for the objects of research. A good dam is good by virtue of fulfilling a specific function, but there is nothing intrinsically good in its ability to withstand water pressure.

Grüne-Yanoff et al. (2014) contrast two ways of evaluating economic models: one in terms of descriptive validity and one in terms of normative validity. Normative validity also requires justification (see also Hands, 2014). Even instrumental rationality can be understood differently from how it is understood in economics and standard decision theory. For example, it has been argued that it is unclear that, were we to behave in the way dictated by EUT, we would perform better on certain relevant performance metrics such as cumulative or average earnings or wellbeing (see for example Berg, 2014). Similarly, money pump and Dutch book arguments in favour of EUT can be challenged by the observation that people who violate the theory’s tenets in their decision-making (and there are many) still remain in the ranks of successful decision makers (Hands, 2014). Finally, the old argument that ‘ought implies can’ has sometimes been advanced against the normative interpretation of RCT insofar as some of the decision-making procedures that EUT dictates are not feasible (Hands, 2014; Mongin, 2009). Whether or not these arguments generally undermine the normative validity of RCT remains under debate, but the important point for us is that the normative validity of specific normative economic models is not to be taken for granted.

But even if we agree that standard decision theory is the best or a good normative account of instrumental rationality in the sense of dictating what a rational agent ought to do given her preferences and beliefs, this does not mean that any model based on the theory is automatically normative in a more substantial sense, that is, in the sense of telling us what a real agent ought to do, what kind of institutions ought to be built, or what is good for real people. For example, there is no reason to assume without further argument that individual welfare maximisation should be pursued vis-á-vis other intrinsic goods such as substantive freedom á la Sen (Cartwright & Davis, 2016; Herfeld, 2022). More generally, the move from a positive to a normative interpretation of a given also implies a move from an empirical to a normative justification – a justification that cannot simply be taken for granted. The road from abstract principles of instrumental rationality to prescriptions in real decision-making contexts may not always be straightforward.

3.2. Analytical models

For Gilboa et al. (2023), analytical models are proofs of concept, and their role is methodological: they serve to probe the theory and its consistency or scope. They claim that such models play an important epistemic role and are not always guided by empirical observations.

While we have already briefly outlined how such purely within-theory activity can be epistemically important, it is one thing to recognise that analytical modelling is an important and legitimate component of economic practice, and another to give pride of place to analytical models vis-a-vis positive models. We do not want to claim that this is the case in current economics; it could be argued that, if anything, theory is being unduly disregarded these days. Rather, as philosophers of economics have asked us to do (Alexandrova et al., 2021; Northcott, 2018), we should ask whether economics displays the mix of modelling strategies that best achieves a science’s epistemic and practical goals. Claiming that models may have different purposes does not entail that any purpose is as good as any other, or should be pursued to the same extent, especially when we are facing a science with perceived or actual relevance to society.

3.3. Explanatory models

Gilboa et al. (2023) are right that many of the models of economics are not meant to provide maximally accurate predictions but rather understanding of the observed phenomena. Recent philosophy of science has offered much-needed clarity on the question of how unrealistic and non-predictive economic models are nevertheless necessary for understanding economic phenomena (Ylikoski & Aydinonat, 2014).

Most importantly, even though there may be some truth to their claim that economists often take ‘a warm feeling’ to be an indicator of understanding (Gilboa et al., 2023), since Hempel (1965), philosophers analysing explanation have consistently pointed out that the feeling of understanding should not be equated with understanding itself. Furthermore, we may want to distinguish, on the one hand, the norms prevalent in economics regarding what counts as explanatory (the sociological question) and, on the other hand, the justification for those norms (the normative question). To do so, an independently motivated account of explanation and understanding is required.

One of the most popular accounts of causal explanation currently on offer in the philosophy of science is the manipulationist-counterfactual one (Woodward, 2003). According to this account, successful explanations track objective relations of dependence which enable, in principle, the manipulation and control of the phenomenon to be explained. To explain is to cite a cause, and a cause is something that, had it been different, the effect would have been different as well. Good explanations reveal (counterfactual) dependencies that imply precisely in which respects the phenomenon would have been different if the explanatory factor had been different in some specific way. At the heart of the question of whether an explanation is correct, there is thus always a relatively objective empirical question – a question of whether such a dependency really obtains in the system under investigation – which is not a matter of anyone’s subjective feelings, opinions, or perspectives.

Heavy simplifications and idealisations like those that we find in many economic models are often necessary for the formulation of explanations in much the same way as highly unnatural experimental conditions are often necessary for the observation of a specific dependency in a laboratory. Even though the correctness of a particular explanation is an objective, empirical question, explanation as an activity is a cognitive, human enterprise and, as such, it is subject to human limitations. This is why explanatory models need to be suitably simple and tractable for explanatory reasoning for limited beings like us to be possible.

More generally, one of the key take-home messages of philosophical work on explanation is that a single explanation always explains only a limited aspect of a phenomenon (Hempel, 1965). It simply does not make sense to try to explain things such as the financial crisis, the great moderation, or ‘choice’ as a whole. This leaves plenty of room for epistemologically legitimate differences about what kinds of aspects, and hence what kinds of explanations, a particular field finds especially interesting and useful, i.e. field-specific norms for good explanations (Garfinkel, 1981; Miller, 1987; see also Marchionni, 2013).

The manipulationist-counterfactual account of explanation also sheds light on the difference between prediction and understanding. Prediction is, in principle, possible without any theoretical understanding of the phenomenon as long as there is enough data and the phenomenon remains structurally stable. Explanation instead requires information with modal content: information about not only what happens or will happen, but also what would happen if a (structural) change were to occur. These general observations should sound familiar to economists, as these conceptual results have drawn heavily from the macroeconometric debates of the 80’s regarding the relative merits of atheoretical VAR models and structural models.

The manipulationist account also makes sense of the intuition that explanation ‘is likely to be useful in future, yet-unspecified situations’ (p. 8). As explanation is based on knowledge of dependencies and on information with modal content, explanatory models enable inferences to situations characterised by different background conditions than those already observed – on the assumption that the model is correct, of course. Usually, an explanatory model does so by outlining the mechanism responsible for some observed phenomenon (say, an observed correlation) and the mechanism is more invariant to changes in background conditions than the observed correlation, thus making it possible to extrapolate the results to other contexts and populations more reliably than with blind induction (Steel, 2007).

Likewise, this account of explanation also explains why neuroscientific evidence is not directly relevant to economics, as Gilboa et al. point out: although in some sense differences in brain states are causally related to behaviour and thus to economic outcomes, these differences are almost always screened off by psychological or behavioural difference-makers, and such variables provide much more convenient handles for manipulability relations (see, e.g. Kuorikoski & Ylikoski, 2010). On the other hand, it sheds doubt on the rationality of economists’ suspicion of simulation-based models, or their commitment to methodological individualism. Neither of these is justifiable from the point of view of a manipulationist-counterfactual account.

4. Analogical versus deductive inferences

The tool-box view of models and the manipulationist-counterfactual account of explanation shed more light on Gilboa et al. (2023)’s intuitive but ambiguous claim that often the way in which models are applied is not rule-based but case-based (see also Gilboa et al., 2014). They claim that explanation and prediction do not occur by way of deriving the explanandum phenomenon from a general theory plus a set of initial conditions (as the Euclidean view of science would imply), but rather by means of analogical reasoning between a particular model and a target. This view is consistent with the account of model-based explanation outlined in the previous section. That is, learning about the target phenomenon involves manipulating the model to address what-if-things-are-different questions: the function of a theoretical model is to facilitate reasoning concerning how a potential change in a specific assumption (preferences, information, budget constraint etc.) leads to specific changes in other variables. Empirically (nearly empty) general rules are turned into cases by means of operationalisation arguments, namely assumptions about what agents want, know, etc. It is here that analogical inferences become relevant.

The philosophical literature has delved into the conditions for such successful analogical inference, both in general and with regard to model-based inferences in particular, with many competing attempts to explicate what the ultimate grounds for such inferences are (e.g. Hesse, 1966; Norton, 2021; Weisberg, 2012). Some have questioned whether conceptualising the model-to-target ampliative inference in analogical terms is really helpful to begin with (e.g. Kuorikoski & Lehtinen, 2009). For the most part, the intricacies of these disputes need not concern the practitioner. The important point is that simply saying that these inferences are case-based does not get the modeller off the epistemic hook. Analogical inferences require justification, much of which is empirical in nature: the inference relies on establishing that there is indeed a relevant relation (be it isomorphism, homomorphism, similarity, or cognate notions) between the model and the target.

According to Gilboa et al. (2023), model-based inference being case-based explains why, in economics, the observation of a case that does not fit a model does not and should not lead to its refutation; a case, they say, refutes general rules, not cases. This is correct, and it can be left open what case(s) a given model is similar to. In a similar spirit, Dani Rodrik (2015) points out that economics progresses horizontally rather than vertically, that is, by building new models that may fit some situations rather than by honing a fixed set of models to better fit a given empirical case. This implies that model development can proceed separately from empirical evidence at least to some extent. Nevertheless, we should always ask whether the extent to which theory development is motivated by mathematical possibility vis-a-vis empirical evidence serves the epistemic goal of economics. Even though there is probably some epistemic value in all conceivable analytical modelling, it does not follow that all analytical modelling is worthwhile. For example, Northcott (2018), Alexandrova et al. (2021) have denounced the extent to which, in economics, intellectual resources have traditionally been put into the formulation of models with only tenuous connections to empirical reality. Hence, coming up with new models in an attempt to expand the menu of available cases should be accompanied by efforts to shore up analogical inferences if at least some of our targets belong to the real world.

As a reaction to the credibility revolution, however, economics seems to have reversed its course and the danger is now perhaps that much of economics could become simply applied statistics. Thus, even though more data and evidence-driven science is a welcome, we may have gone too far and again missed the right mix of methods.

5. CODA

Recognising that their models can have multiple different functions does not give economists a free pass. Models ought to be useful in practice, not just in principle, and their intended use ought to be made as clear and transparent as possible. We have shown that philosophical accounts of modelling and explanation provide explicit criteria for evaluating whether an explanatory model does what it is supposed to do. Likewise, philosophical analyses of concepts such as model-based inference, explanation, and rationality highlight the set of constraints and considerations that are relevant to the evaluation of models.

The most important point is that flexibility in interpreting a particular model in terms of possible intended uses and the amount of empirical content does not mean that anything ought to go. In fact, we take some of the cases selected by Gilboa et al. to be symptomatic of too much historical interpretive freedom in economic modelling. For example, although their short narrative of the early reception of Kydland and Prescott’s pioneering RBC precursor model (1982) perhaps over-emphasises its interpretation as a purely methodological contribution questioning a previously unexamined assumption (cf. Hoover, 2012), it is clear that the ambiguities in the way that the model is presented and discussed in the original paper also invites a robustly empirical interpretation with direct policy implications. Similarly, as Gilboa at al. note, the interpretations of Barro’s and Bernheim and Bagwell’s models of intertemporal optimisation and Ricardian equivalence range all the way from analytical critique through a methodological innovation to a serious empirical claim with policy implications – probably depending largely on the political perspective of the interpreter. This interpretive flexibility is not just a failure of some variety of good old Popperian falsificationism, it is also epistemically inefficient in that the proper criteria for appraising a methodological innovation, theory-building (or critiquing reasoning), or explanatory empirical model are obviously quite different. Ideally, it would be better to first decide on the intended use and then build the model best suited for this.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Kulttuurin ja Yhteiskunnan Tutkimuksen Toimikunta [grant number 343010].

Notes on contributors

Jaakko Kuorikoski

Jaakko Kuorikoski is a professor of practical philosophy at the University of Helsinki and a member of The Centre for Philosophy of the Social Sciences TINT. Before this, Kuorikoski worked as an associate professor in a cross-disciplinary New Social Research program at Tampere University and as a lecturer in Theoretical Philosophy at Helsinki. His main areas of specialization are philosophy of economics and philosophy of social sciences. His current research interests include new kinds of data and evidence in the social sciences, philosophy of macroeconomics, scientific understanding, and model-based social epistemology of science.

Caterina Marchionni

Caterina Marchionni is a philosopher of science working in practical philosophy at the University of Helsinki. She is also a member of The Centre for Philosophy of the Social Sciences at the same institution. Caterina specializes in the philosophy of economics and the philosophy of the human and social sciences, in particular on issues of modelling, evidence, and interdisciplinarity. Updated information about Caterina's publications and research projects can be found on her homepage.

Notes

1 Recent developments such as laboratory experiments, agent-based modeling, and data-driven economics have challenged the centrality of theory in the production of economic knowledge. Even so, it is safe to assume that, at least for now, the kind of foundational unifying theory Gilboa et al. talk about still exists. Thanks to a reviewer for recommending that we clarify this point.

2 The distinction between positive and normative is ambiguous and conflates several different distinctions: description vs. prescription, facts vs. values, theory, and application (for discussions see, for example, Hands, 2012; Malecka, 2020).