Principle, Practice, and Paradox.

Principle, Practice, and Paradox: an unrecognized consensus in the philosophy of economic modeling.

Lewis Osterweis Kopman

**Draft, comments welcome, please no citations**


Introduction
Over the past few decades there has been much criticism of the practice of modeling in economics. This criticism has centered around the notion that because of modeling's unrealistic assumptions it cannot be explanatory. Such criticism reached an apex recently with a paper by Julian Reiss, the 'Explanation Paradox' (EP) (2012), in which he emphasizes the apparent disagreements between philosophers of economics regarding modeling's explanatory-ness. He concludes that, so long as philosophers consider economic models explanatory, they exhibit a logical fallacy. I argue, however, that there are two broad yet unrecognized consensuses within the philosophy of economics regarding the explanatory potential of economic models. Consensus 1 suggests that unrealistic and abstract assumptions in models do not hinder their ability to explain. Consensus 2, however, suggests that the domain of economics is so complex as to render such explanations extremely difficult to achieve. Reiss' paradox, I assert, depends on Consensus 1 and 2 being ignored. Consequentially, once Consensus 1 and 2 are taken into account, the EP becomes benign, and, perhaps, a broad agreement about modeling in economics can be used to found further research in alternative epistemic techniques.
This paper shall proceed as follows. I will first set out to qualify the claims of the consensuses I perceive within the philosophy of economics regarding models: Consensus 1, that economic models can in principle be explanatory, and Consensus 2, that for all practical purposes explanation is very difficult to achieve. I will then delve into the EP, arguing that Reiss fails to break the consensus argued for above.

Consensus 1: models can in principle be explanatory
In order to model a phenomenon, one typically makes assumptions about it or surrounding relevant phenomena which are strictly false. Cartwright calls this the problem of unrealistic assumptions, which asks, how can results which are contingent on different circumstances than those occurring in the real world help explain the real world? Largely, however, philosophy of economics is in consensus that such falsehoods do not prohibit that model's ability to explain, given that the model is false in particularly innocuous ways. Such an account is given in simple language in Cartwright (2005), in which she discusses the difference between Galilean and non-Galilean assumptions. She bases these concepts roughly on the structure of Galileo's famed thought experiments regarding falling bodies. She explains,

Galileo's experiments aimed to establish what I have been calling a tendency
claim. They were not designed to tell us how any particular falling body will
move in the vicinity of the earth; nor to establish a regularity about how bodies
of a certain kind will move. Rather, the experiments were designed to find
out what contribution the motion due to the pull of the earth will make, with
the assumption that that contribution is stable across all the different kinds of
situations falling bodies will get into. How did Galileo find out what the
stable contribution from the pull of the earth is? He eliminated (as far as possible)
all other causes of motion on the bodies in his experiment so that he could see
how they move when only the earth affects them. That is, the contribution that
the earth's pull makes to their motion. (2005:10)

Cartwright emphasizes that by eliminating all other potential explanatory factors, Galileo was not only able to understand how bodies fall in general, but that doing so allowed him to learn something about the force which caused bodies to behave that way. Galilean assumptions, Cartwright argues, are thus attempts to mimic an experimental set up which limits other causal factors, but instead in the context of a model. And just like Galilean experiments, Galilean assumptions need not hinder explanation. On the contrary, they allow us to understand phenomena in such a way that enables us to generalize their effects to systems beyond the model in question.
Other philosophers of economics give similar accounts, most notably Mäki in his engagement with Milton Friedman and what he calls (2008: 131) "the experimental moment in theoretical modeling," where idealizations in theoretical models serve a similar purpose as that which physical manipulation serves in the laboratory, which is to render extraneous as many causal factors as possible apart from the one you are attempting to measure. Such an insight, Mäki argues (2008: 132), allows one to "ignore simple criticisms of falsehood in assumptions. We should not focus on individual assumptions and their realisticness without a good grasp of the function they serve in a larger context." The question then becomes exactly how one ensures that the assumptions one is making are Galilean, and that the results of one's model are thus generalizable and not contingent on the specific assumptions made. Such a process is known as robustness testing, and it involves measuring the extent to which the factors one attempted to make extraneous still bear on the conclusions of a model. The more that they have affected the conclusion, the less such a model can be said to have demonstrated a distinctive causal (or statistical) relationship between any given phenomenon and its supposed effects.
So, if economic models can succeed in making robust Galilean, or isolating, idealizations, then they can overcome the problem of false assumptions, but that does not necessarily mean that their explanations bear on the target of the model. Much of the criticism regarding modeling in economics has been that such assumptions, regardless of their robustness, are so abstracted that they lose all relevance to the 'real world.' The model, critics argue, and not the world, becomes the real object of enquiry, designed for mathematical elegance rather than explanatory power. The response by philosophers of economics has been similar to that regarding false assumptions: not all models. Rather, one must examine the operation and context of each abstraction to see exactly how it functions. Largely, philosophers agree that models need to be accompanied by a series of inductive inferences that tie them to the world. To explain:

a model demonstrates that A causes B in the model
A operates in the real world (Inductive)
B occurs in the real world (Inductive)
Therefore, (inference) there is reason to believe that in the real world, A causes B.

The strength of such an inference depends on the confidence we have in our inductive claims that A and B both occur in the real world roughly as they do in the model. The model then, employs such an inference in its claim that A causes B.
Mäki (2013) offers a useful typology for assessing assumptions in such a way. He argues that there are two types of models: substitute models are those where there is either minimal inductive confidence or no inference takes place, whereas surrogate models consciously contextualize their assumptions in such a way as to make the work of a model relevant to corresponding phenomena. Sugden (2000) makes a similar claim, although instead of identifying models as a series of abstractions he claims that they function as counterfactual worlds. The function of counterfactual worlds, though, is essentially the same: to isolate tendencies that we perceive or posit about the real world. The 'gap' between counterfactual world and the real one, he argues, is similarly filled by inductive inference. The more confidence we have in such an inference, the more "credible" the model is. Hausman has also made similar arguments in the context of his investigations of the economic philosophy of John Stuart Mill. Hausman,(2011a:72-73) claims that Mill was wrong to be so dogmatically opposed to gathering inductive evidence to bolster claims of phenomenal regularity. Indeed "It seems that if someone is going to be serious about learning about the economy… it has to be the case that they have empirical tools to gather useful aggregate economic data that provide serious direct evidence about regularities." The discipline seems to largely agree that such "bridge" principles, as Mäki calls them, are theoretically available to model builders, and it is by no means inevitable that isolating idealizations necessarily isolate the model as well. Critics of abstraction, Mäki (2012) claims, are mistaking methodology for ontology; models employ isolations to facilitate explanation, not to isolate economists from the world.
So the philosophy of economics seems to agree that modeling can be explanatory, given "false" assumptions are shown to be robust and that they are contextualized in credible inductive inference so as to "bridge" them to the real world. The problem, however, is that there is still much contestation as to exactly how to test robustness, or how to objectively judge the "credibility" of the contextualizing inferences specifically in the domain of economics. Indeed, while many of the philosophers mentioned above agree that if such tests were adequately performed then economic models could be explanatory, they also seem to agree, that for all practical purposes such tests are extraordinarily difficult, and that the credibility of the current web of inductive inferences which commonly grounds such models is highly contestable. Thus, while most philosophers of economics agree that there is nothing methodologically flawed regarding modeling in economics, most also agree that, practically, any explanations which models may offer economics will almost certainly be extremely limited, and far below the expectations that most seem to have of the discipline. Thus, in the typical fashion of the philosopher, much ink has been spilt defending models, only to concede that many critics are essentially right, albeit for the wrong reasons.

Consensus 2: models in economics are unlikely to be explanatory
While Cartwright, Hausman, Sugden, and Mäki all defend the practice of modeling in principle, they all have expressed serious doubt that the practice of modeling in economics will be able to explain actual economic phenomena. They all, in some regard, believe that the domain of economics is too complex. Hausman (1981:119) provides a useful analogy for starting such a discussion.

Consider what happens when natural scientists attempt to deal with
complicated everyday phenomena. Take the trite example of the path of
a leaf's fall. In what sense can it be explained by physicists? Precise
deductive-nomological explanation seems out of the question.

The key relevant distinction that Hausman is drawing is that of "everyday phenomena" which he is implicitly contrasting with laboratory phenomena. The natural sciences whose domains largely exist outside of the laboratory often have a large tolerance for error and vagueness. Think, for instance, of meteorology or plate-tectonics. Hausman argues that economics is essentially more like meteorology than like physics. The problem, however, is that it seems society has far less tolerance for error and vagueness when it comes to explaining the complex progressions of the economy than of the weather. Mäki and Sugden also make such complexity concessions in their defenses of modeling. Mäki (2008:137) even goes so far as to suggest that a model's explanatory success should not bear on the "realisticness" or falsity of its assumptions, "given the massive epistemic uncertainty when dealing with an immensely complex and effectively uncontrollable subject matter like society." Cartwright, however, has given the most systematic account of exactly what constitutes such complexity.
Cartwright's argument can be simply put in an analogy she (1991) makes: models are like fables, insofar as they are only generally true and only of very contrived situations. To explain why, she posits that the world is very rarely causally modular (2001), meaning that causes can rarely be separated and manipulated independently, and that probabilities, rather than arising out of necessary associations instead consist of complex matrixes of stable (enough) capacities (1999), meaning that they are often altered by exogenous factors that are hard to formally anticipate. Modeling, however, largely consists of isolating causes and establishing necessary associations between causes and their effects. Another way of phrasing Cartwright's general argument is that in economics, it is almost impossible to ensure that one's assumptions are Galilean. The lack of modularity and the finicky nature of probabilities, then, are a good start in an important effort to describe the microscopic qualities of the "complexity" to which Hausman, Mäki, and many others who defend models in principle refer.
But just how complex does a system need to be before modeling becomes impractical and less useful in explanation? An article by Alexandrova and Northcott (2009) has rather disparaging implications. Alexandrova & Northcott give an account of a model that supposedly helped to design more efficient spectrum auctions. Or did it? Alexandrova and Northcott, by comparing various "stories" of how models may have helped design the spectrum auctions, including Hausman's emphasis on de-idealization and Cartwright's on capacities, found that models of auction design had been nothing more than "useful heuristics, generating categories in terms of which to start the design process," rather than key explanatory road maps (2009: 322). Alexandrova and Northcott go on to take a firmer stance against modeling than those noted above so far, suggesting that even the "contrived situations" highlighted by Cartwright seem so unlikely to occur in the domain of economics that for all practical purposes attempting to model them towards a goal of explanation seems ill-advised. It is hard to imagine, after all, a more contrived situation within the domain of economic modeling than that of being tasked with designing a relatively closed system where one gets to constrain the actors almost at will. As noted above, however, they concede that models may have useful heuristic properties to act as starting points towards further experimental work.
While this seems to be a divergence from the consensus described above, I would assert that the downgrade of economic modeling from explanatory tool to heuristic tool is only a slight transition. As I have noted, those above remained skeptical of modeling's explanatory potential in economics while also arguing for its possibility in principle. Alexandrova and Northcott are, in a sense, merely bringing further evidence to bear and further qualifying the same argument: one is right to be skeptical of explanation via economic modeling, as even a model which had widely been considered explanatorily successful could not be rigorously defended as such. Indeed, in a recent interview, Hausman (Gutting and Hausman, 2015) seems to be making a similar heuristic concession, in which he struggles to claim that economic models can do any more than to "identify the relevant factors and to set the terms of intelligent debate." Mäki is, I believe, ultimately arguing for a similar claim. Given that he remains committed to the notion that models can evoke the 'real' world, but, as just noted, does not think that such an account should be judged based on a model's ability to explain, surely then rests the value of his account on modelings' ability to at least identify relevant phenomena. Alexandrova and Northcott thus do not stray notably far from the consensus, and indeed provide a useful framework with which to better describe it.
Even if we do change our expectations of models in economics from providing explanation to merely setting "the terms of intelligent debate," there are still issues. Namely, those resulting, as Cartwright (2009) argues, out of the current paucity of credible inductive inference with which we currently guide models. Such principles in this argument are analogous to the bridge principles necessary described in Consensus 1. Recent work is attempting to remedy this. Such work, however, will not necessarily lead to a greater explanatory potential in economic modeling. In fact, it may only reinforce the aforementioned trepidation.
The recent work of David Soros (2013), has sought to challenge the conventional principle that economic actors can, without hindering robustness, be assumed to have perfect information and thus always act in the most efficient way to increase their benefit based on the criteria of the model. Soros, however, argues that actors must be assumed to have fallible information, in the sense that it is bound to be "biased or inconsistent or both" (2013:310), and that acting on such fallible information will reflect back onto, and thus change the outcome of, any given market operation, a process which he labels reflexivity. Because it is hard to measure to what extent and in what ways the information and theories of actors are fallible, market operations will inevitably develop with a level of indeterminacy. While Soros' appeal to the "commonsensical" nature of reflexivity to ground his argument is dubious, Rosenberg (2013), has recently argued that very similar processes are common in ecology and evolutionary biology, and that such commonality provides substantial inductive evidence for Soros' argument.
Moreover, there have already been attempts to incorporate this inductive inference into an economic model, albeit with interesting implications. Frydman and Goldberg's (2013) attempt to design "imperfect knowledge economies" as an operable assumption upon which models can be built is essentially a formalization of Soros and Rosenberg's discussion. Interestingly, Frydman and Goldberg claim (2013: 133), "…when revisions of forecasting strategies (or more broadly, change on the individual and aggregate levels) cannot be adequately characterized with qualitative and contingent conditions, empirically relevant mathematical models of how market outcomes unfold over time may be beyond the reach of economic analysis. In this sense, IKE explores the frontier of what formal macroeconomic and finance theory can deliver. How far, and in which contexts, this boundary can be extended is the crucial open question." Frydman and Goldberg seem to be suggesting that economic models can begin to account for their own explanatory limitations.
So, just as philosophers of economics seem to agree that in principle models can be explanatory, they also seem to agree that economic models are unlikely to be so. Economic systems seem too complex to create simple causal stories from which Galilean assumptions can be isolated. Additionally, there seems to be no guarantee that increasing our inductive web of understanding around those systems will make them appear simpler. But, why is recognizing this consensus important? Recently, Julian Reiss published the EP, which has received a substantial amount of attention, much of it positive. In light of the consensus, however, I will argue that its impact is greatly diminished.




The explanation paradox
The 'paradox' of the EP reads as such,

economic models are false
economic models are nevertheless explanatory
only true accounts can explain

In the following section, I am going to argue that if Consensus 1 and 2 are taken to be genuine, the EP falls apart. This is for two reasons. First, Consensus 1 demonstrates that there are acceptable ways of qualifying the contrast between (1) and (3). Indeed, these are qualifications that Reiss quietly accepts. Second, the qualified (1) and (3) can only sustain a paradox if (2) holds; essentially, Reiss must argue that despite the qualified (1) and (3) failing in the case of most economic models, they are still considered explanatory. Consensus 2 demonstrates that, at least among philosophers of economics, this seems unjustified. If informed by Consensus 1 and 2, the EP essentially becomes another iteration of the same argument: if economic models can be shown to be false in a specifically Galilean way, then they could be explanatory, but they consistently prove false in non-Galilean ways.
As an example to demonstrate the EP, Reiss formulates an old model that inspired Hotellings Law, which states that (2012:44) "…. If one seller of a good increases his price ever so slightly, he will not immediately lose all his business to competitors." Reiss then goes on to explain that this is a relaxation of another law, that of one price, which holds that in "one market the same goods must sell at the same price- if they did not, customers would flock to the cheapest seller, forcing more expensive sellers to lower their prices or driving them out of the market." Hostelling built a model that factors in spatial distance. In order to simplify the model, Hostelling measures spatial differences along a one-dimensional straight line, and equally distributed consumers along that line. Hostelling found that in order to maximize profits, firms would move as close together as possible, without becoming identical, in order to maximize the amount of customers for whom their firm was closest.
This model of course contains many assumptions which are strictly false, which Reiss notes (ibid:46): "we move in three- and not one dimensional space; goods differ with respect to many aspects other than distance from the point of consumption; customers are not uniformly distributed along a line and demand is seldom completely inelastic; sellers act on numerous motives of which profit maximization is at best one." Despite these false assumptions (1), he claims it is considered explanatory (2). But, how can this be so, argues Reiss, if (ibid:43) "causal explanations cannot be successful unless they are true" (3). It is at this point that Reiss feels that he has reached an impasse, and the above paradox is declared.
Reiss notes that one way to resolve the paradox is to argue that models (ibid:50)

…are true in the abstract: they do not represent what is true but rather
would be true in the absence of interferences…. The core idea is that
models can be thought of as Galilean thought experiments…. This line of
defense is perfectly legitimate for a variety of false modeling assumptions
in science. In many domains, especially in mechanics has the method of
analysis and synthesis been used with great success. Natural systems often
do not obey to neat scientific laws because they are too complex and too
changing. So we experimentally create-in the lab or in the head- situations
that are simpler, more manageable and free to predict what happens in more
complex, more natural situations.

Already, one sees a hole in the EP. Reiss had claimed that "only true accounts can explain," but he seems to be willing to concede that assumptions that are false in precisely Galilean ways can still provide the basis for explanation. Reiss' argument then must rest on the fact that economic models are false in precisely non-Galilean ways, i.e. that they do not assist in identifying what a causal factor does in isolation from disturbing factors. Reiss does mention that robustness tests could be done to test to what extent a model's assumptions are Galilean, but quickly points out that such tests are usually not done and those that are consistently fail (ibid:52).
So the EP as originally formulated is actually quite misleading if we are to be faithful to the argument he puts forth. It should really read something like,

all models contain falsehoods
economic models are nevertheless explanatory
only accounts that are false along Galilean lines can still be explanatory.

The only way a paradox can be sustained is if he can argue that models are never-the-less considered explanatory in economics, despite the fact that they routinely fail robustness testing. Working economists may or may not hold this position. As I have argued in Consensus 2, however, philosophers of economics are very weary of actually making this claim. And it is precisely the work of philosophers of economics, and not working economists, which Reiss cites in his argument.
Indeed, in his section on (2), Reiss mentions Alexandrova and Northcott's skepticism that models in economics are likely to be explanatory. But, instead of engaging seriously with their alternative of allowing economic models to continue as heuristic devices, he simply repeats that models in fact (ibid:54) "are regarded as explanatory by themselves. One may of course deny that they are but then arguments have to be given, and it must be explained why a large part of the economics profession thinks otherwise." But regarded as explanatory by whom? Not, I would assert, by the authors whom he cites or by philosophers of economics in general. And why, exactly, must arguments be given to explain otherwise? This seems like a demand outside of the terms his argument, upon which many non-philosophical factors surely bear, and which do nothing to prove the explanatory potential of models in principle or in practice. Indeed, in claiming that Alexandrova and Northcott ignore the problem- despite the fact that they give a compelling account of why economic models are by and large not explanatory- because economic models are considered explanatory 'more broadly,' Reiss is merely offering his own distraction. Reiss bases his argument by contrasting the views, not of thinkers more broadly, but by precisely the philosophers of economics whom I mention above. This distraction hides the fact that, when (2) is undermined, the EP turns into a largely unoriginal argument, a reformulation of Consensus 1 and 2. To give one final iteration of Reiss' principles,

all models contain falsehoods
economic models are rarely, if ever, considered explanatory
This is because only accounts that are false along Galilean lines can be explanatory, and economic models have consistently failed to demonstrate that they are as such.

There is no explanation paradox. There are dilemmas that economic model builders face in chasing explanation. These dilemmas, for the foreseeable future, seem largely insurmountable. The world is a very complex place, after all. But such dilemmas do not amount to an inherent logical fallacy. To claim so is misleading and does little to help modelers overcome their challenges or encourage philosophers of economics to seek novel epistemological techniques.
Funnily enough, Alexandrova and Northcott (2013) actually do attempt to answer Reiss' rather distracting call to explain why economics continues to be inundated with modeling and its corresponding claims of explanation. They give the amusing response of citing Alison Gopnik's (2000) description of "the 'aha' feeling shared by children and scientists alike." The feeling, Alexandrova and Northcott suggest, is the explanatory equivalent of an orgasm: intense, euphoric, but by no means an indication of conception (Alexandrova and Northcott, 2013: 266). Philosophers, I would add, are just as susceptible to such 'aha' moments.

Conclusions
Models that employ Galilean assumptions and that are embedded within a rich web of credible inductive inferences can form the basis for explaining real world phenomenon (Consensus 1). What exactly constitutes the real world within specific modeling exercises, however, seems to matter. Domains that are sufficiently complex, seem to contain substantial barriers to the type of causal isolation that even 'good' modeling achieves. Economic markets seem to be such a domain (Consensus 2). There remain important and interesting disagreements on the exact conceptual boundaries of Consensus 1 and 2. What exactly constitutes the complexity of economic markets which makes it so difficult to create robust causal stories about their progression? In what sense can models help us towards such a greater understanding, if not explanation? The consensus that exists, however, does matter, and not only in disproving flawed claims of paradox. Although, in the interest of conceptual clarity, I would re-assert this exercises importance.
Currently, discussions about models occupy a large proportion of the intellectual capital in philosophy of economics. If it is recognized that there is a broad consensus in regards to their possibilities and limitations, then it may spur philosophers into researching alternative epistemic techniques. What can psychological experimentation or sociological survey tell economics about the ways in which actors develop fallible conceptions of markets? Can neuroscience help economists better understand how risk is calculated, fear is spread, and decisions ultimately made? These are a few of the questions that economists are beginning to ask themselves, and they deserve rigorous philosophical consideration. Certainly, given the increasing regularity and severity of economic crises, consideration by philosophers of economics seems warranted.


Work Cited
Alexandrova, A., Northcott, R. (2009) 'Progress in economics: Lessons from the spectrum auctions. In H. Kincaid, D., Ross (Eds.) The Oxford handbook of philosophy of economics (Oxford: Oxford University Press): 306-336.

Alexandrova, A., Northcott, R. (2013) 'It's just a feeling: why economic models do not explain.' Journal of Economic Methodology, 20(3): 262-267.

Cartwright, N. (1991) 'Fables and Models', The Aristotelian Society, Supplementary Volume 65: 55-68.

Cartwright, N. (1999) The Dappled World: A Study of the Boundaries of Science (Cambridge: Cambridge University Press).

Cartwright, N. (2001). 'Modularity: It Can – and Generally Does – Fail,' in D. Costantini, M.C. Galavotti, P. Suppes (eds). Stochastic Dependence and Causality, (CSLI Publications).

Cartwright, N. (2005) 'The Vanity of Rigour in Economics. Theoretical Models and Galilean Experiments', in P. Fontaine, and R. Leonard (eds.), The 'Experiment' in the History of Economics (New York City: Routledge).

Cartwright, N. (2009) 'If No Capacities Then No Credible Worlds. But Can Models Reveal Capacities?' Erkenntnis, 70(1): 45-58.

Colander, D. (2013) 'The systemic failure of economic methodologists' Journal of Economic Methodology, 20(1): 56-68.

Frydman, R., Goldberg, M.D. (2013) 'Change and expectations in macroeconomic models: recognizing the limits to knowability' Journal of Economic Methodology, 20(2): 118-138.

Gutting, G., Hausman D., (2015) 'What Economics Can (and Can't) Do' The New York Times, (14 July).

Hausman, D.M. (1981) Capital, Profits, and Prices: An Essay on the Philosophy of Economics (New York: Columbia University Press).

Hausman, D. (2011a). 'The Inexact and Separate Philosophy of Economics: An Interview with Daniel Hausman' Erasmus Journal for Philosophy and Economics, 4(1): 67-82.

Mäki, U. (2008) 'Realism from the 'lands of Kaleva': an interview with Uskali Mäki' Erasmus Journal for Philosophy and Economics, 1(1): 124-146.

Mäki, U. (2013) 'Mark Blaug's unrealistic crusade for realistic economics' Erasmus Journal for Philosophy and Economics 6(3): 87-103.

Reiss, J. (2012) 'The explanation paradox' Journal of Economic Methodology, 19(1): 43-62.

Rosenberg, A. (2013) 'Reflexivity, uncertainty and the unity of science' Journal of Economic Methodology, 20(4): 429-438.

Soros, G. (2013) 'Fallibility, reflexivity, and the human uncertainty principle' Journal of Economic Methodology, 20(4): 309-329.

Sugden, R. (2000) 'Credible worlds: the status of theoretical models in economics' Journal of Economic Methodology, 7(1): 1-31.

Taleb, N. (2007) The Black Swan: The Impact of the Highly Improbable (New York City: Random House).




PAGE 14