# The importance of using realistic assumptions in economic modeling

## Abstract

In the present paper it is argued that differences among economic models are basically differences in their selected part of the real world these models try to account for. Therefore, their range of applicability to a target system turns out to be important for their selection for particular purposes. In this respect, an approach based on the similarity of models to a target system and to the modelers' purposes is provided. It is also argued that models vary in their values of similarity. These values will help agents to select the model that best meets the role of examining some phenomenon of interest.

Keywords: similarity; economic models; mechanisms; possibility tree; substantive assumptions; domain of applicability.

## Introduction

In mainstream economics, the use of unrealistic assumptions is usually defended not only for pragmatic reasons, but also due to the intrinsic difficulties in determining such degree of realism.<fnref n="1" /> Because of that, the criterion used for evaluating economic models is often associated with their ability to provide accurate predictions or explanations relevant to the modelers' purposes. At this juncture, mainstream economists have found a strong epistemological support in Milton Friedman's approach (Friedman, 1953; hereafter referred to as F53). According to F53, all assumptions are unrealistic, since they involve idealizations and abstractions. Therefore, asking the right question is not about the realism of assumptions (for they never are), but about their approximation to reality. To such controversy, F53 responds that the only way to know whether approximations are good or not is by testing the predictive accuracy of model implications.

The present paper undertakes a critique to F53's approach in particular and to the indiscriminated use of unrealistic assumptions in economic modeling in general. On the one hand, it is asserted that F53's defense of unrealisticness only makes sense as long as economic models account for invariant regularities. However, this is not the case. In economic phenomena, causal links between variables are not *singular* but *plural*. People's activities and unstable background conditions play a central role here. In this sense, it is argued that economic phenomena do not respond to a logic of stable causal factors or invariant regularities, but to a logic of possibility trees or open-ended results.

In addition to this, there is an epistemological problem that arises from the very use of invariant regularities: even when they are identified in the economic realm, there is no guarantee that such stability will prevail in the future. It is shown that predictions based on knowledge from the past involve not only external validity problems but also negative exposures to "black swans". An alternative approach is proposed here, where models are evaluated, not by their degree of invariance or accuracy of their (past) predictions, but by their *similarity* to the selected part of

<footnote n="1">¹ In order to clarify the distinction between the features of the model assumptions and the philosophical stance which defends the objectivity of the perceived objects, Mäki (1989) proposes to call "realisticness" to the former and "realism" to the latter. For this reason, the terms "realisticness" and "realism of assumptions" will be used interchangeably throughout the present paper.</footnote>
the world (or target system) about which predictions are made. Since the core structure of models depends on their substantive assumptions, and since this approach aims to find structural resemblance between a model and a target system, it is argued that the realism of substantive assumptions is crucial for the assessment and subsequent choice of economic models for explaining, predicting or representing some phenomenon of interest.

## The problem of unrealisticness

In economics there is a certain consensus in understanding the real world as a complex system endowed with a myriad of interacting causes. Heterodox scholars have proposed to analyze economics from its own complexity, paying attention to the political and economic institutions of societies, their history, the non-ergodicity of economic processes, the non-intended emergent phenomena from people's interactions at the meso level, etc.

Mainstream economists, on the other hand, have advocated simplifying reality to the extreme, separating economics from its interdisciplinary character, endowing agents with a transmundane rationality, and introducing excessive mathematics to economic models in order to make them more “sophisticated”. Such is the emphasis on the construction and formalization of economic models, that it has been said that "to do economics is to do modeling" (Mäki, 2002, p. 10).

Nevertheless, the problem of making models the basic unit of economic analysis is their departure from what was originally intended to be investigated: *the real world*. The introduction of numerous distorted model assumptions has generated an endless debate regarding whether they tell us something about the world of genuine people, markets or production, or whether they are just intellectual games about imaginary worlds without any utility for pragmatic purposes, such as explaining financial crises or applying economic policies.

The discussion about whether economics should be an abstract science intended to solve highly theoretical problems, or if, on the contrary, should pay attention to the causal processes that take place in the real world, is as old as the discipline itself. Sismondi, for example, in his *Nouveaux Principes d'Économie Politique* (1819) has seen political economy adopting a more sententious language, enveloped in calculations increasingly difficult to follow, losing itself in abstractions and becoming, in every way, an “occult science”. Leontief (1971) has considered that, within orthodox economics, there has always been a continuous interest in the imaginary and the hypothetical, rather than the real and observable. Frisch (1970), Worswick (1972) or even Coase (1993) have argued that the core assumptions of mainstream economics could be associated more with the purpose of gaining mathematical manipulation rather than with looking for some degree of similarity with concrete reality. Blaug (1997) laments the excessive formalism within mainstream economics, a school where the interest in real-world issues has been completely lost:

> "Modern economics is sick. Economics has increasingly become an intellectual game played for its own sake and not for its practical consequences for understanding the economic world. Economists have converted the subject into a sort of social mathematics in which analytical rigor is everything and practical relevance is nothing". (Blaug, 1997, p.3)

Mainstream economists have generally not entered this debate, and have continued doing models as if there was nothing wrong with their underlying methodology. However, one of their first (and most controversial) responses came from the hand of Milton Friedman, who in 1953 published his essay entitled "The Methodology of Positive Economics." In it, F53 argued that the
realism of the assumptions is irrelevant in the evaluation of a theory or model. All the assumptions are unrealistic, since they involve omissions, abstractions, idealizations, etc. None of them will give a true description of reality. As a positive science, F53 advocates a narrow notion of the goals of economics. According to F53, what is really valuable of a model or hypothesis is its ability to provide "a system of generalizations that can be used to make correct predictions about the consequences of any change in circumstances" (p. 4). In this sense, he proposes to pay attention only to the model implications:

(...) the relevant question to ask about the "assumptions" of a theory is not whether they are descriptively "realistic," for they never are, but whether they are sufficiently good approximations for the purpose in hand. And this question can be answered only by seeing whether the theory works, which means whether it yields sufficiently accurate predictions. (p. 15)

F53 uses the law of falling bodies as an example of his stance. That law claims that the acceleration of a body dropped in a vacuum is a constant *g*, and is independent of the shape of the body, the manner of dropping it, etcetera. The distance traveled by a falling body is given by the formula $s = \frac{1}{2} gt^2$, where *s* is the distance and *t* is the time. At sea level the air pressure is about 15 pounds per square inch. It is obvious that the assumption of "vacuum" is not realistic, since 15 is different from zero. However, it is not relevant to demonstrate that there exists a difference between the assumed value and the real value, but rather to know if such a difference is significant or not, that is, if the assumption of vacuum is (or not) a good approximation to reality. In this sense, F53 argues that the only way to know this is through the accuracy of the predictions of the law.

If the above argument is true, then the testing of assumptions and the testing of predictions cannot be separated. There is only one test: the empirical test of the model implications. In other words, it is not possible to *directly* estimate the discrepancy between what is asserted in the model assumptions and what is observed in the real world. Such a discrepancy is estimated *indirectly* through the model implications. This is something that should not be overlooked. If the two tests are reduced to one test only, then defending the realism of assumptions is unsustainable, as there is no empirical way to know if an assumption is realistic or unrealistic.

"(...) a theory cannot be tested by comparing its "assumptions" directly with "reality." Indeed, there is no meaningful way in which this can be done. Complete "realism" is clearly unattainable, and the question whether a theory is realistic "enough" can be settled only by seeing whether it yields predictions that are good enough for the purpose in hand or that are better than predictions from alternative theories. Yet the belief that a theory can be tested by the realism of its assumptions independently of the accuracy of its predictions is widespread and the source of much of the perennial criticism of economic theory as unrealistic. Such criticism is largely irrelevant, and, in consequence, most attempts to reform economic theory that it has stimulated have been unsuccessful." (F53, p. 41)

Critiques of Friedman's approach soon appeared.<fnref n="2" /> Nagel (1963), for instance, proposed a distinction between three types of assumptions: as *non-exhaustive descriptions*, as *abstractions* and as *falsehoods*. Nagel considered that the first two kinds are not problematic, yet this was not true of the last one. Likewise, Musgrave (1981) criticized Friedman's approach for not being able to distinguish between three different types of assumptions: *negligibility*, *heuristic* and *domain* assumptions. Each of these makes a different type of assertion and therefore plays a different role in economic models. While he accepted the unrealism of the first two kinds of

<footnote n="2">² F53 has generated an enormous critical literature. For reasons of space, I will only focus on what I consider are some of the most salient critiques to F53. See Hands (2001) for a more complete analysis.</footnote>
assumptions, it was not the case for the domain assumptions: "if a domain assumption is always
false, then the theory containing it can be applied to no actual situation and is in fact
untestable" (Musgrave, 1981, p. 381). Similarly, Kuorikoski and Lehtinen (2009) asseverated that
theoretical modeling usually involves two types of assumptions: "auxiliary" and "substantive".
Substantive assumptions concern aspects of the model's central causal mechanism about which
one makes important assertions. On the other hand, auxiliary assumptions are required for
making inferences from substantive assumptions to conclusions feasible. Since the latter play
the heuristic role of making the model more tractable, their unrealisticness is not significant.
Nevertheless, it is required that substantive assumptions be realistic, so that they may carry
their epistemic weight into the results. More recently, Rodrik (2015) have argued that we
always need to apply a realism filter to "critical assumptions" before a model can be considered
useful. An assumption is critical "if its modification in an arguably more realistic direction would
produce a substantive difference in the conclusion produced by the model" (Rodrik 2015, 27). As
a consequence, the realism filter should be focused not on the whole set of the model
assumptions, but only on those that make a difference in its results.

However, these critiques take for granted the feasibility of testing the model assumptions. And
this is precisely what F53 put into question. How do we know if a substantive assumption is
credible? How do we know if a domain assumption is false? The answer is: *Through the
accuracy of the model predictions*. This is the only way to know if an assumption is a good
approximation to reality.

To make things worse, the use of unrealistic assumptions can be defended by considering that
model assumptions are never tested in isolation, but in groups or collections. This is the so-
called Duhem-Quine's thesis. According to this thesis, when we derive predictions from models,
we are implicitly accepting a bunch of other hypotheses about the phenomena in question and
the empirical methods we use to measure them. This thesis has been—and continues being
today— the workhorse of many mainstream economists since, to a large extent, it protects the
central model assumptions from possible falsifications. Starting from the fact that a model's
empirical test involves not only the test of its core assumptions but also of its auxiliary ones, any
attempt of falsification can be rejected by arguing that the problem does not lie in the core
assumptions but in the auxiliary ones. An interesting historical example is the various attempts
to test the neoclassical theory of demand. Over the last eighty years, repeated attempts have
been made in order to test the empirical implications of this theory, including the symmetry of
Slutsky matrix, the homogeneity (of degree zero) of individual (and aggregate) demand
functions, the Walras's Law, etc. Almost always, empirical results falsified the theory
implications (see, for example Schultz (1938), and Deaton and Muelbauer, 1980). However, far
from rejecting the neoclassical demand theory, mainstream economists put into question the
very features of the empirical tests. In Duhem-Quine terms, this means problematizing the
auxiliary assumptions rather than the core ones.

## Invariant regularities. Two meta-theoretical assumptions

F53 asseverates that the task of positive economics is to provide a system of generalizations
that can be used for making accurate predictions. This accuracy is the basis for accepting or
rejecting models: those that provide more accurate predictions will be always preferred over
others not that accurate.

However, we should have in mind that, when we talk about “predictive accuracy”, we are
relying on the success of a model in previous circumstances. We know nothing about the future,
but we use models that were successful in the past for having clues about what might happen in
the future. Therefore, F53 seems to be advocating an approach in which scientific progress goes
hand in hand with the discovery of tendencies or invariant regularities. Such investigative practice can be illustrated as follows: Let us suppose three models $M_1$, $M_2$ and $M_3$, each of them appealing to different mechanisms or background conditions, so that different results R can be inferred: $R_1$ for $M_1$, $R_2$ for $M_2$ and $R_3$ for $M_3$. Let us suppose that the empirical evidence has been up to now in favor of $R_1$. $M_1$ would be, therefore, the model that provides the most accurate predictions. According to F53, this evidence would enable us to use said model for future situations.

However, the requirement of invariant knowledge for predictive purposes involves two types of assumptions: an *ontological assumption* about the existence of stable factors, and an *epistemological assumption* by which invariant generalizations can be used in different situations. Either of these assumptions must be met so that the use of invariant knowledge is fruitful. On the one hand, we may assume an ontology of stable causal factors in which, if a cause C were properly isolated from perturbing factors, it would be possible to predict what will happen once C is triggered (see for example Cartwright, 1999; Maki, 1992). On the other hand, we might not stick to an ontological commitment, but rather to a weaker approach where the only requirement is observing invariant regularities at the level of events. Both assumptions are *independent*, in the sense that any of them may occur without the other. There is the chance that a stable causal factor C can be found in isolation, but at the level of events other factors end up disturbing such stability. Similarly, it is possible to find regularities which are not the manifest results of a stable causal factor but of a bunch of factors that, in their interaction, produce a regular tendency. What it really matters is that at least one of these assumptions is met so that an invariant-based prediction approach makes sense.

Nevertheless, what follows shows that these two assumptions are problematic to tackle the issue of prediction in economics.

Let us start with the ontological assumption. Some approaches in philosophy of science have proposed monistic ontologies of entities with properties (e.g., Cartwright, 1989; Glennan, 2002). Machamer, Darden and Craver (2000) and Machamer (2004), on the other hand, have proposed a dualistic ontology of entities and activities. Activities are “the producers of change”, while entities are “the things that engage in activities” (Machamer, Darden and Craver, 2000, p. 3).

In this latter approach, *activity* turns out to be a "singular" notion, in the sense that whenever a causal factor C is triggered, only one activity A is involved in the production of a result R. On some occasions, R may not follow from C, yet this does not depend necessarily on A but maybe on some perturbing factors. For instance, if we have a headache and the aspirin we take does not produce relief, it does not necessarily depend on the very activity the aspirin produces in our body. Acetylsalicylic acid inhibits the production of prostaglandins. This is the activity of aspirin. Every time we take an aspirin, such inhibition activity starts to work. There are no other activities that replace it. The fact that an aspirin fails to relieve headache does not necessarily mean that the activity of inhibition does not take place. In a general tendency, it does, although it is very likely that it is countered by some perturbing factors. The issue is not the activity A, but its manifest results (see, for instance, Cartwright, 2009).

Although Machamer *et al.*'s approach has been especially addressed for explaining biological mechanisms, it can also be useful to understand the working of economic phenomena, because it highlights the notion of activity and its relationship with entities and/or variables. In this regard, economic activities are plainly the decisions of individuals or groups of individuals. When we say that the demand for a good goes down, what we are saying is that people carry out the activity of buying less of that good. If the interest rate increases, it is usually due to the central bank's decision or because people have increased their demand for money or credit; in both cases, people's activities are crucial.
People's activities are influenced by a myriad of factors: socio-cultural sphere, the information they receive from the world, the expectations they form about the evolution of certain variables, etc. Depending on what types of activities people carry out, different results will be observed in the economy. Therefore, we could say that economic activities are not singular but "plural": once a causal factor C is triggered, a set of potential activities ($A_1, A_2, ..., A_n$) may start to work. Each of these activities are involved in the production of a different result ($R_1, R_2, ..., R_n$). The prevailing result will depend on how people form their expectations, how they interpret information from the political world, the socio-cultural framework, the changes in the economic structures, etc.

If we had to outline the previous situation, we would hardly appeal to a mechanistic diagram, since what we observe is a path that, depending on what conditions prevail, branches out to different sides. Therefore, a better way of schematizing this situation could be through the use of possibility-tree diagrams.

Usually, a possibility tree is a diagram that shows possible alternatives with their respective probabilities once some initial factor is triggered. In our case, the notion of "possibility tree" is not (necessarily) associated with probabilities or some probability theory. Instead, it only means that there exists a multiplicity of courses of action or alternative paths that can be followed —in terms of possibility— after activating a particular causal factor. For example, by increasing money supply, the possible effects are an increase in the demand for bonds, or an increase in the price level, or a greater hoarding. When running after an animal, there is the chance that it runs, although it is also possible that it decides to attack us or stay paralyzed. By leaving the state of autarky, a nation can be benefited or damaged. It all depends on what factors come into play at a particular moment and how they end up interacting.

In economics, a good example of this is the "Keynes effect". Keynes effect has been usually conceived as a mechanism in which an increase in the real quantity of money leads to a decrease in the interest rate, stimulating investment and consequently employment and output level. However, it would be wrong to think that a positive change in the real quantity of money will invariably lead to higher levels of output. It is even implausible to think that changes in real quantity of money will invariably lead to a decrease in the interest rate. On the contrary, depending on the contextual framework and on people's expectations, the causal path of an economy may be different. Keynes was explicit on this matter:

"(...) whilst an increase in the quantity of money may be expected, *cet. par.*, to reduce the rate of interest, this will not happen if the liquidity-preferences of the public are increasing more than the quantity of money; and whilst a decline in the rate of interest may be expected, *cet. par.*, to increase the volume of investment, this will not happen if the schedule of the marginal efficiency of capital is falling more rapidly than the rate of interest; and whilst an increase in the volume of investment may be expected, *cet. par.*, to increase employment, this may not happen if the propensity to consume is falling off. Finally, if employment increases, prices will rise in a degree partly governed by the shapes of the physical supply functions, and partly by the liability of the wage-unit to rise in terms of money. And when output has increased and prices have risen, the effect of this on liquidity-preference will be to increase the quantity of money necessary to maintain a given rate of interest." (Keynes, 2012, p. 173).

This example clearly shows the lack of a "singular" invariant connection between economic variables. There is no causal force that induces people to demand more bonds whenever the quantity of money is increased. Depending on the context they may buy goods, hoard the extra money, etc. In economics, the dualistic ontology of entities and activities should take into
account the fact that the latter are to be understood in a *potential* sense, since any of them may
take place.

The second assumption refers to the chance of finding regularities at the level of events, even if an ontology of possible causal paths underlies them. If the price of beef rises 500%, people could keep consuming the same amount of beef, or they could substitute it (partially or totally) for other meals, like pork, poultry or even vegan meat. However, it is very likely to expect an important decline in the consumption of beef. Similarly, when one sees a dog chasing pigeons in the park, there is the chance that they will stay put, escape or attack. But pigeons (almost) always end up escaping. This means that, in many situations, even if there are several alternatives or courses of action available, there can be a "dominant" course that prevails. The reasons can be attributed to different factors: the stability in the expectations' formation process, institutional factors that do not change over time, behavioral predispositions, etc. When this happens, it is likely to observe a tendency or regular behavior of some economic entity/variable.

However, there are certain problems that this epistemic assumption entails. On the one hand, the fact that an invariant regularity continues to hold in the future. One is about the prevalence of such invariance over time. The other is about what we can do with that knowledge. This is not new. Cartwright and Efstathiou (2011), for example, have asserted that there exists no bridge that connects the discovery of causal factors with their respective use. And without this bridge, there is no guarantee that a causal factor will work in different circumstances or scenarios, regardless of its level of invariance. More specifically, this account mentions two problems: *unstable enablers* and *external validity*. The problem with unstable enablers refers to the fact that the effect of a particular cause depends on a set of other causal factors operating simultaneously. In this juncture, any change in a causal factor's background conditions will affect the contribution of such a factor. External validity, on the other hand, is associated with the problem of generalizing from a particular setting or population to the one of interest. There is external validity when the result obtained in some target system holds outside of that target. However, even if we establish results very securely in a particular test, the methods used in such situations provide no basis for extending the results to a population or setting different from those in the test. Because of this, the knowledge of invariant regularities turns out to be very narrow in scope and thus very limited in their predictive power.

In relation to the latter thesis, Taleb (2007) considers that invariant knowledge (or, better put, knowledge derived from past data) is not only of little help in understanding both the present and the future, but it is also an inductivist stance that expose us to the appearance of "black swans". Statistically speaking, a black swan is an event that lies far away from the mean of a bell curve. Since it is a highly improbable event, it is practically impossible to predict. However, the most important problem of black swans is not necessarily their unpredictability, but especially the huge impact they produce in normal activities, to such a degree that they may end up changing the course of history. Historical cases abound: the great depression of 30', the sinking of the Titanic, the financial crisis of 2008, or even the COVID-19 pandemic are events that, to a greater or lesser extent, have taken place due to our tendency to stick to what we already know, that is, to invariant knowledge.

Invariance cannot then be *the* criterion for choosing among different economic models. A model providing accurate predictions only gives us information about what has happened in the past. However, we have no basis to expect that such stability will continue to hold in the future. On the one hand, economic ontology is not about stable singular causal factors, but about possibility trees or open-ended results. Likewise, even if a tendency is discovered, nothing guarantees that such one will continue to hold in different contexts. And last but not least,
whether we only focus on what we know —so that the unknown is dismissed or considered a rarity—we are exposing ourselves to black swans.

## Revising Unrealisticness

The fact that the economic models' predictive accuracy is not an effective tool for choosing which of them using for predicting, explaining or representing some phenomenon of interest, not only calls into question the F53's approach, but also places economists in a dead-end loop: if we choose models for their predictive accuracy, we expose to the perennial problem of induction (and eventually to black swans). And if we take into account the realism of assumptions, then, according to F53, we should test the implications of that model by which these assumptions take part which, in other words, means not paying attention to such realism.

However, in much of the criticisms to the ubiquitous unrealisticness involved in mainstream economic models, there is not advocacy of some strong philosophical position (such as some sort of scientific realism), but of something much simpler: that there are assumptions that are more "realistic" than others, in the sense that their description is more consistent with what happens in the real world. The earth is neither flat nor round, but it is closer to the second option. The atmospheric pressure in my room is neither 0psi nor 15psi, but it is closer to the latter. And so on.

F53 has not paid attention to the nature of this comparison. For example, F53 does not ask whether assuming an atmospheric pressure of 15psi is more or less realistic than assuming vacuum, but simply examines the assumption of vacuum in relation to the predictive capacity of Galileo's law.

Therefore, a first step consists in examining in greater detail the problem posed by F53 that it is not possible to test the model assumptions regardless of its implications. And for this I will resort to two theses proposed by Karl Hempel: one on the hypothesis-testing procedure, and the other on the credibility of our assertions.

Let's start with the first one. According to Hempel (1966), there are few occasions in which the testing procedure is quite direct (for example, observing that my cat is sleeping on the sofa). However, most of scientific hypotheses require indirect methods of testing (for example, testing that Earth is round through lunar eclipses, as carried out by Aristotle). In cases like these, the test is based on an argument to the effect that *if* the statement were true, *then*, under specified circumstances, certain observable events should occur. What is tested is not what the statement says, but what it implies.

F53 seems to go beyond such discussion. He claims that, in fact, the test of assumptions cannot be carried out without testing the model implications; in other words, the test of the model assumptions *is not independent* from the test of the model implications. In order to explain the difference between what is *indirect* and what is *independent*, let us suppose a model M from which a result R is inferred. Let us also consider a set of assumptions S<sub>1</sub>, S<sub>2</sub> and S<sub>3</sub> that belong to M. We may consider A the "argument" that enables us for testing S<sub>1</sub>, S<sub>2</sub> and S<sub>3</sub>. According to F53, the only way to know if any of these assumptions is a good approximation to reality is by testing the accuracy of R.

Let us then suppose that S<sub>1</sub> is problematic in terms of unrealisticness, and because of that we want to test it. Friedman would say that the only way to do that is by testing the accuracy of R. Hempel, on the other hand, would assert that in case S<sub>1</sub> is not directly testable, we could create an argument for testing it. The argument A that comes from M is a possible argument, yet it is important to point out that *it is not the only one*. This means that we can create a new
argument A* for testing S₁. Let R* be the result inferred from A*. Finally, let us assume that, for testing S₁, A* is a better or more direct argument than A. Thus, if we want to test how (un)realistic is S₁, the accuracy of R* will be for us more important than the accuracy of R.

So as to clarify this distinction, let us take once again the example of Galileo's law and its assumption of vacuum. According to F53, the only way to test the accuracy of such an assumption is by testing the very implications of Galileo's law. But this is not quite correct, as we can create a new argument (perhaps more "direct") for testing the assumption of vacuum (which, in this case, it would mean designing a Torricelli experiment to measure atmospheric pressure).

At sea level the air pressure is approximately 15psi. So we may ask if such an assumption is *realistic*. Clearly it is not, since 15 is different from zero. However, F53 considers that this question has no meaning because, in a strict sense, *all assumptions are unrealistic*. According to F53, what is correct is asking whether the 15psi is close enough to zero for the difference to be judged insignificant, that is, if it is a *good approximation to reality*. The only way to know that is by testing the predictive accuracy of Galileo's law.

As long as we ask the latter kind of question, there will be no independence between the test of the model assumptions and the test of the model predictions. However, this is not true if we ask a third kind of question: *is 15psi more realistic (or more approximate to reality) than 0psi?* Here, Galileo's law –and its respective implications– loses relevance. It does not matter if Galileo was right or wrong in hypothesizing his law of falling bodies. What is being asked now is which of the two values (0 psi or 15 psi) comes closer to reality. That said, a new argument for testing this case arises: the Torricelli's experiment.

Therefore, it would not only be possible to test the assumption of vacuum without testing the implications of Galileo's law, but it is also empirically possible to prove that the assumption of vacuum is less approximate to reality than the assumption of 15psi. It is likely that due to changes in climatic conditions the air pressure is not exactly 15psi. However, what can be said with confidence is that, in the proximity of sea level, the assumption of 15psi will be a lot closer to reality than the assumption of vacuum, and said result is reached without resorting to the implications of Galileo's law. It all depends on the kind of question we are trying to answer. “Is X a good approximation to reality?” leads us to F53's stance. On the contrary, “Is X more realistic than Y?” leads us to new arguments and subsequent implications.

On a more general level, the latter example shows us that the test of S₁ can be *independent* from the test of M. One thing is to say that what is tested are the hypotheses implications (*indirect test*), and quite another thing is to say that the test of the model assumptions is not *independent* of the test of the model predictions. We can take for granted the fact that most of the scientific hypotheses are *indirectly* testable. But –contrary to what F53 claimed– we can also say that the two tests are *independent* from each other (as the Torricelli's experiment is independent of the Galileo's experiment). We do not necessarily need M and its implications to test whether or not S₁ is more or less realistic than some competitor assumption S₁*. On the contrary, we are able to create as many arguments as we want for testing which assumption is more approximate to reality. In such a case, it is the scientific practice that will discuss the relevance and feasibility of different tests and arguments.

To some extent, this approach could also shed some light to the immunizing tactics made by mainstream economists, who have taken Duhem-Quine's thesis as a cornerstone. But Duhem-Quine's thesis is not only about immunizing theories. Quite the contrary; it warns us not to take anything for granted. In this regard, the philosophy of science of the second half of the twentieth century has said a lot about this. And it is that there are modifications that lead to *new implications* –which are considered scientifically worthy– and *ad hoc* modifications –which
are unscientific as they make theories unfalsifiable. It is true that, throughout the history of science, there have been numerous cases where central assumptions have been defended against possible falsifications; a criterion that, on some occasions, has allowed scientists to improve their theories (as the discovery of Neptune when Newton's theory was intended to be rejected for not correctly describing the planetary orbits). But it is also true that, in such practice, there have been *ad hoc* tactics to protect a theory at all costs. For example, when Galileo discovered through his telescope that the moon had mountains and craters, he put into question Aristotelian physics, which claimed that it was a perfectly polished sphere. But the Aristotelian scholars, far from rejecting Aristotle's physics, ended up adding a new *ad hoc* hypothesis: that there was an invisible substance on the moon that filled the craters and covered the mountains, which in turn was impossible to test.

In this juncture, the comparative study between two or more assumptions allows us to get an idea about which of them are good approximations to reality and which are not. Of course, these assertions are nothing more than hypotheses and therefore will be eternally subject to revision. However, the chance of testing the accuracy of different assumptions regardless of the test of some particular model allows us, at least in the first instance, to be well positioned under any *ad hoc* attempt to transfer the weight of the problem to less controversial assumptions. Thus, let M be a model which involves a set of assumptions S<sub>1</sub>, S<sub>2</sub>,..., S<sub>n</sub>. Let us suppose that M is not providing good results, and that its most controversial assumption S<sub>1</sub> is being put into question. To the extent that S<sub>1</sub> is a fundamental assumption of some paradigm or school of thought, it will be defended in the first instance, and consequently another less fundamental assumption will be blamed for the problem (e.g., S<sub>2</sub>). At best, this can lead to new implications. In the worst case, such modification is to be considered as *ad hoc*. Let us now suppose that S<sub>1</sub>* is a competitor of S<sub>1</sub>. The proposal is quite straightforward: use the assumption that is more approximate to reality. Surely their test will be indirect. In such a case, we might test them using the argument that derives from M, or we could create a new argument that comes from a new instance M*. And this new instance would allow us to get an idea of which assumption (S<sub>1</sub> or S<sub>1</sub>*) is closer to reality. It is true that none of these proposals will be completely effective. It is even possible that some assumptions of M* are not true, and that they need to be modified at some moment. However, this should not constitute a counter-argument to the defense of using more realistic assumptions, since conjectural knowledge and trial and error are constituent elements of the very dynamics of scientific research.

Closing the possibility tree. The role of model assumptions

According to F53, model assumptions are not important. As long as a model provides good predictions, we could assume anything about people's behaviors and the background in which they make decisions. However, the logic of possibility trees suggests that, depending on which path we are assuming or taking, we will arrive at different conclusions.

In order to clarify this point, let us consider once again the Keynes effect example. Once the increase in the quantity of money takes place, Keynes proposes different possible scenarios. The most important one is the relation between quantity of money and production: when the money supply is increased, a decrease in the interest rate will take place, stimulating investment and consequently employment and production. For this to happen, certain conditions have to be met, namely, that there are constant returns to scale (so that prices do not rise or fall as output increases), the liquidity preference is not increasing (or at least such increase is lower than the increase in the quantity of money), the marginal efficiency of capital is not falling more rapidly than the interest rate, the marginal propensity to consume is not decreasing, etcetera.
However, Keynes was aware that other possible scenarios may happen. For instance, we may assume a different scenario where the liquidity preference grows more than the quantity of money. If so, then the monetary policy will have no impact on the interest rate. Likewise, if entrepreneurs do not have good expectations about future sales, then it is likely that the marginal efficiency of capital ends up falling more rapidly than the interest rate, which means that firms will be reluctant to invest, even if credits are cheaper. Keynes also considers a fourth scenario in which the rise of investment brings about an increase in primary employment in the investment industries. Through Kahn's multiplier, the raise in primary employment will produce a higher increase in total employment. However, the latter will increase as long as firms producing consumer goods do not expect a drop in the marginal propensity to consume. If this happens (for instance, as a result of propaganda in favor of restricting individual consumption), then such firms would find no incentive to hire additional workers.

This example shows us that the model assumptions meet an important role in economic modeling, in the sense that each assumption leads us to a different node in a possibility tree. More precisely, under the logic of possibility trees, once X is activated, $Y_a, Y_b, ..., Y_n$ can occur. For a specific phenomenon (e.g., $Y_a$) that follows from X, a set of background conditions "BC" must be met. In contrast, if a different set of conditions BC* is met, then $Y_b$ will be obtained, that is:

$$ (X \cdot BC) \rightarrow Y_a $$

$$ (X \cdot BC^*) \rightarrow Y_b $$

where "." and ">" represent the logical connectors "conjunction" and "conditional", respectively. It is quite important to identify the information contained in the background conditions, since they are the ones which specify the path that an economic process is to follow. It is not the same to assume that prices do not change as output increases than to assume a positive change. It is not the same to assume good expectations on future sales than to assume bad ones. It is not the same to assume a constant marginal propensity to consume than a decreasing one. And so on.

As can be seen, assumptions are a determining factor in economic modeling, since they are responsible for showing us what would happen under different conditions. It is also clear, nevertheless, that not all model assumptions fulfill the same role. For example, it would be absurd for the assumption of indifference curves differentiable at every point to be taken as a condition to be fulfilled in the real world. Since in most of the economic models their results are obtained via a prior chain of deductive reasoning, it is plausible that several model assumptions just fulfill the heuristic role of simplifying or facilitating such reasoning.

At this juncture, let us recall that different scholars (e.g., Kuorikoski and Lehtinen, 2009; Musgrave, 1981; Nagel, 1963) have examined different kinds of assumptions according to the role they play in economic modeling. If we combine these approaches with the concept of possibility tree, we could distinguish, at least, between two kinds of assumptions: substantive and tractability assumptions. Substantive assumptions are assertions about the possible paths in a possibility tree. This means that if they are replaced by other assumptions, then the path in a possibility tree will change. If prices do not change as output increases, a path in all the possible paths of a possibility tree will take place; if prices rise, another path will come about. This is what usually occurs in economic models: as they make use of different substantive
assumptions, they end up referring to different scenarios or different nodes of a possibility tree.
In Musgrave’s terms, they have different ranges of applicability.<fnref n="3" />

Tractability assumptions, on the other hand, play the role of making feasible the inferences
from substantive assumptions to conclusions. Theoretical modeling always involves making
distortions from the real world in order to facilitate inferences deductively. Assuming that there
are only two countries or only two goods play a similar heuristic role to assuming only one
planet rotating around the sun. They are introduced with the sole purpose of gaining
tractability; nobody would expect to find an economy with only two goods or a planetary
system with only one planet and one star.

Authors such as Hans Albert (2012) or Hilary Putnam (2002) have warned about the problem of distinguishing between these different kinds of assumptions, which eventually might serve as a way to immunize certain postulates of mainstream economic models. However, these approaches seem to not take into consideration the role that different assumptions play in theoretical modeling and in the consequent closure of potential paths of a possibility tree. While the demarcation between the two classes of assumptions presented in this paper is neither exhaustive (Nagel (1963), Musgrave (1981), and Kuorikoski and Lehtinen (2009) provide much more detailed accounts in this regard) nor is it easy to define at first glance, we can get an idea of the role they play by asking ourselves the range of questions *what would happen under different circumstances?* If an assumption S₁ meets a tractability role in a model M, then the model results should not change if we replace it by another tractability assumption S₂.<fnref n="4" /> But what usually occurs in the discussion about realisticness is not so much about these kinds of assumptions, but especially about those that do make a difference to the result. The same results are not inferred if unemployment is assumed instead of full employment; the same conclusions are not reached when assuming animal spirits instead of rational expectations; assuming Say's Law or assuming effective demand lead us to different results. Mainstream economists have consistently steered the discussion toward tractability assumptions, and in some cases they have suggested methods such as derivational robustness analysis as an attempt to justify the exaggerated deductivism in their models. In this regard, asking *what would happen if things were different?* allows us to get at least an initial idea about the role of a particular model assumption. Therefore, in the face of any attempt to immunize an assumption S₁ by treating it just as a tractability assumption, a good counteroffensive would lie in asking *what would happen if S₁ were replaced by S₂?* If the answer involves a change in the inferred results, we can get the idea that it is not a tractability assumption at all.

Similarity and the use of models

The logic of possibility trees proposes rethinking, among other things, the knowledge provided
by economic models, as well as their use for different purposes (such as representing,
predicting, explaining, intervening, etc.). Let A be an agent that uses a model M with purpose P
to learn something about a selected part of the world or target system T. For this to happen,
some degree of resemblance (or similarity) between M and T must be achieved. The issue is
that there is a menu of possible models for T. Which of them should the agent choose?

<footnote n="3">³ Note that I use interchangeably Kuorikoski and Lehtinen’s definition of “substantive assumption” and Musgrave’s definition of “domain assumption”, for they meet a similar role under the logic of possibility trees.</footnote>

<footnote n="4">⁴ In any case, a possible problem with this change is the loss of internal validity or deductive capacity of a model in replacing S₁ for S₂.</footnote>
One option is to rely on the predictive and/or explanatory capacity of models (F53's approach). Let us suppose two models $M_1$ and $M_2$ which are expected to account for a target system T. According to this premise, A would choose the model that provides the most accurate predictions. However, such a model will only give us information about facts that have happened in the past, so we have no basis to expect that such facts will continue to hold in the present or in the near future. This situation is associated not only with the typical epistemic problem of making inductive inferences, but also with the ontological issue that what prevails in the realm of economics are not stable causes but possibility trees. In other words, it is possible that a model $M_1$ has provided better predictions than $M_2$. But this is not because $M_1$ is necessarily "better" than $M_2$, but because its domain of applicability has been more in line with what has hitherto happened in the real world.

This leads us to a second option: not choosing models according to how accurate they have been in the past, but rather to their similarity with the selected part of the world from which it is expected to learn something. This similarity can be understood in comparative terms with respect to the structures that underlie both T and the menu of models. Following Weisberg (2013), a model M and a target T are similar when the variables and/or assumptions that describe them have close values. The smaller the distance between these values, the greater the similarity.

In each model a different set of substantive assumptions is specified. Because of this, it may be said that different models involve different targets or scenarios. Therefore, if A is interested in learning something about a selected part of the world T, they are to choose the model which structure resembles more the structure of T. This can be done by comparing different substantive assumptions with certain features of the real world. Therefore, what A intends is to find the model M* that maximizes its similarity with the selected target (see appendix for more details). Once M* is chosen, its implications may be useful to know what events could occur under circumstances specified in such a model. Note that the use of model implications changes significantly. For F53, predictions are taken as a previous step to choosing the best model. What in the present paper is proposed is the other way around. Specifically, the first step consists in examining the (structural) similarity between different models and the target. And once the model that maximizes its similarity with that target is found, then implications are to be taken into consideration.

It may also be the case that a causal relationship holds for a period of time, that is to say, that we are able to find invariant regularities. But it just does mean that a certain causal structure has remained invariant in the real world. Nothing guarantees that such a structure will continue to hold in the near future. F53 would propose to use such a causal relationship, for it provides the most accurate predictions so far. But he would be missing something important: that what counts is not so the invariance of causal relationships, but the very structures that underlie such invariances.

In order to clarify this point, let us consider once again the Keynes effect example. Once the increase in quantity of money takes place, Keynes proposes the existence of a positive causal relationship between quantity of money and income. However, far from being a universal mechanism, certain conditions have to be met. Keynes, aware that other conditions may take place, also proposed alternative scenarios (or deviations from the initial path). Therefore, let us assume that the liquidity preference is increasing, and might grow more than the growth of the quantity of money. If so, then in some moment the causal nexus between quantity of money and income will not hold anymore. Instead, we may analyze the structure of the target system, and choose the model whose structure (or set of substantive assumptions) is the most similar to such a target. Thus, if, for instance, the liquidity preference is high in the real world, it is likely that the increase in money supply will not be followed by a decrease in the interest rate. This
implication is not related to past information –which involved a low liquidity preference and allowed, among other things, to the Keynes effect to work– but rather to what we expect to happen given the current features of the system under study. Thus, if for example the monetary authority was interested to increase the quantity of money in order to trigger the Keynes effect and consequently to reach an increase in employment and production, such a decision should not be necessarily based on past successes or failures of the policy, since the current scenario might be substantially different from past scenarios. On the contrary, the decision should be based on the implications derived from the model which structure (or set of substantive assumptions) resembles the structure of the target system the most.

This way of understanding what kind of information economic models provide leads us to a discussion about their use in different situations. Regardless of whether models are conceived as fictions, metaphors, representations of isolated mechanisms and so on, it is usually said that, when building such models, economists intend to say something about the real world. The issue is that (1) what economic models say about the real world is not only approximate but also about a selected part of it, and (2) those who use these models can make undue extrapolations.

Let us examine these two points. (1) refers to what is asserted in relation to a particular target, which can be more or less broad in its domain of applicability. This should not be in principle a source of criticism. Properly speaking, any researcher has the right to investigate any aspect of reality, no matter how small or narrow it may be. It must be said, however, that a model with a very narrow domain of applicability is to be very difficult to apply under different circumstances, that is to say, it is very likely that its similarity with a great variety of different target systems is quite small. In such a case, models quite unrealistic in their substantive assumptions might be dismissed as they are not useful for representing, explaining or predicting most of the economic phenomena of interest.

However, on many occasions the problem lies not only on the models' domain of applicability, but especially on their very use, that is, under what circumstances modelers end up extrapolating the model implications to different domains of reality. This idea is in line with Pfleiderer (2018), who warns about the chance of using models that try to bypass the relevant filters, that is, to use them in domains that exceed their range of applicability. The author examines, among other things, an economic model whose central thesis is a defense of leveraging in banks. Pfleiderer shows that, leaving aside many aspects of reality, leverage is optimal as long as the assets of a bank are riskless (or 100% funded by deposits). However, despite not saying anything about what could happen if the circumstances were different, the authors of that model make claims about the benefits of leverage even when the risk is present. This model does not tell us anything about what would happen if the assets of banks were risky, so agents who use this model under these new circumstances are very likely to fail in representing, explaining or predicting the phenomenon under analysis. In cases like this, the problem is not related to the (however small) contribution of an economic model, but to the "undue" extrapolations of its contributions.

## Final remarks

The realism of assumptions does matter. Not just because of some sort of "naive" stance that advocates for realisticness *per se*. There are ontological, epistemic and methodological reasons that justify the turn towards the use of more realistic assumptions. In economic modeling a major argument in favor of using unrealistic assumptions has been associated with F53's idea that models cannot be judged by their assumptions, but only by their predictive capacity. Nevertheless, this approach tacitly presupposes either an ontology of stable causal factors or an
epistemology of invariant regularities. Both presuppositions have been put into question in the present paper. On the one hand, an ontological approach where economic phenomena are understood as possible paths of a possibility tree has been proposed. More precisely, depending on what decisions people make, how they interpret the signals from the world, which background conditions underlie people's decision making, etc., different causal paths will take place. This calls into question a very popular view in methodology of economics of thinking of causes as entities that, properly isolated from disturbing factors, provide information about their pure contribution. On the other hand, even if we were able to find regularities in the economic realm, they depend on an underlying structure. And any change in those structures will break such regularities.

Being predictive success questionable from this perspective, a similarity-based approach has been suggested. Economic models can be more or less similar to a target system. It all depends on which selected part of the world is expected to be examined. It is this similarity between the model substantive assumptions and the target system that would allow economists to choose, among a set of possible models, the one that best fits the problem in question. Model inferences are not the benchmark for choosing among them. In any case, these inferences would allow us to understand what would happen if the structure of a model resembled the structure of the selected part of the world.

## Appendix

The purpose of this appendix is to add more formality to the way in which the similarity account can be used to link the model world and the real world, that is, to link models to a target system. Let A be an agent that uses a model M to learn something about a selected part of the world or target system T. Following Weisberg (2013), a model M and a target T are similar when the attributes they share are greater than the attributes they do not share. The greater the difference between the shared and not-shared attributes, the greater the similarity.

Then let $E_{mi}$ be the structure of a model $M_i$. According to what has been asserted in the present paper, each $E_{mi}$ is not arranged by the whole set of assumptions of each model $M_i$, but only by its substantive assumptions. Hence, let $E_{mi}$ be a set such that $E_{mi} = \{B_1, B_2, ..., B_i\}$, where each of the $B_k$ is a substantive assumption of model $i$.

Likewise, let $C = \{M_1, M_2, ..., M_n\}$ be a set of economic models, and let $E = \{E_1, E_2, ..., E_n\}$ be the set of structures that underlies each of these models. The task of A is to find the model $M^*$ that “maximizes” the similarity with respect to T. To carry out this task, A is to appeal to the several models in C and compare them to T.

In this sense, Weisberg (2013) asserts that the similarity between two objects depends both on the features they share and on the features they do not share. If the structure $E_{mi}$ is the set of features of a model $M_i$, and the structure $E_t$ is the set of features of the target system T, then the similarity between $M_i$ and T will depend on how close the values of their features are. Weisberg also argues that the selection of features and their relative importance are contextual-dependent. In other words, A ponders subjectively both shared and non-shared features. Therefore, the similarity between a model $M_i$ and a target system T can be expressed by the following equation (see Weisberg 2013, p.144):

$$S_i(M_i, T) = \theta f(E_{mi} \cap E_t) - \alpha f(E_{mi} - E_t) - \beta f(E_t - E_{mi}) \quad (1)$$
where $S_i$ ($M_i$, $T$) represents the value of similarity of a model $M_i$ regarding the target $T$, $f(\cdot)$ is a weighting function, and $\alpha, \beta$ and $\theta$ are term weights. Equation (1) means that the similarity of $M_i$ to $T$ is a function of the features they share ($\theta f(E_{mi} \cap E_t)$), penalized by the features that they do not share ($\alpha f(E_{mi} - E_t)$ and $\beta f(E_t - E_{mi})$).

The goal of A consists in maximizing the similarity between some $M_i$ and $T$. To do so, let $H$ be a set by which its elements are all the values of similarity given by each of the functions (1), that is, $H = \{S_1, S_2, ..., S_n\}$, where the $S_i$ represents the value of similarity of each model with respect to the target $T$. Also, let $g$ be a function that selects the element of $H$ with maximum value. Function $g$ will provide us the model which similarity to the target system $T$ is maximum, that is

$$M^* = g(S_1, ..., S_n) \quad (2)$$

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