The Stages of Model Building in Economics

Abstract

Five successive stages are identified that characterize the process of explanatory model building in economics. Moving across the first three from an initial image, to the model’s preliminary formalization, and then to its operationalization, requires the successive introduction of assumptions that remove the model farther and farther from the reality on the basis of which the initial image was created. It is argued that by ignoring the first two stages, important implications of the Stage 3 assumptions may be hidden. The revelation of these implications may lead to the reconsideration or rejection of the model.

Keywords

Stages of the model-building process bridges to reality model falsity primary and secondary assumptions

Introduction

Models can be built for different reasons. They may be intended to suggest, according to Aydinonat (2008, p. 119), ‘… what may be possible in the real world, … show new ways … [to] look at the world, … or help … evaluate the plausibility of … conjectures about the world.’ They may be designed to identify the conditions under which certain outcomes might arise (Aydinonat, 2008, p. 163), or the logical possibility of the occurrence of a sequence of observable values over time. And, of course, they may be constructed to explain a particular phenomenon that has been observed.¹

An alternative role for explanation described by Sugden (2011) and not considered here is to create a model first and then look for something in the real world that it explains.

This last purpose is the focus of the present article.

Explanation and models that explain have been characterized in terms of such differing notions as causality, idealization, unification, credible worlds, etc. (Reiss, 2012). However, it is not necessary, at this point, to delve into the details that these categories present. Several of them will be briefly noted later on. For now, the following definitions are sufficient. By the term ‘explanation’ is meant, first, a statement of the economic significance of the main features and empirical characteristics of the phenomenon in view; second, revelation and clarification of the reasons why the observed phenomenon is what it is; and third, the degree to which the presence of the phenomenon in the economic system is likely to be continued, and the economic implications that follow from such continuation. To the extent that the viability of the model involved in explanation is supported by empirical testing against data culled from an appropriately relevant time period, it may also be useful as a basis for predicting future occurrences. The competence of such a model to produce an explanation depends, in substantial part, on the method of the model’s construction, on the suitability of its assumption content and on the accordance of its component parts with real economic elements, thereby avoiding spurious correlations with actual facts.

The economic phenomena, that explanatory economic models purport to address, largely consist of economic behaviour or the consequences of that behaviour. The models themselves can be constructed with one or more explanatory objectives in mind. One possible objective could be merely to centre attention on describing a structure that explains the phenomenon in question. Examples will be given shortly. Alternatively, or additionally, the objective could be to create a structure while focusing on its capability of producing observable outcomes relating to that phenomenon. The observable outcomes generated by models’ structures fall into at least two categories: When the consequences of economic behaviour are at issue, the model outcomes are typically collections of variable values as in the price and quantity outcomes of demand–supply models of isolated markets. If the underlying reasons or motivations for economic behaviour are under investigation, the model outcomes are often behavioural functions whose function values are usually regarded as the result of economic choice. From Hausman’s perspective (2012, p. 73), the structure of the standard model of choice consists of preferences (in the general sense of judging one alternative to be better than or equally as good as another), beliefs and constraints as determinants of choices. With respect to the traditional model of consumer demand, individual preferences and beliefs are combined into a preference ordering among baskets of commodities, and preference orderings and price–income constraints combine to determine choices and hence behaviour (Hausman, 2012, p. 19). In the case of the firm, the typical model sets out to show how the firm’s operating decisions are determined. First, its preference ordering among input mixes and output levels is developed as dependent on constraining prices and resource endowments, beliefs about technological possibilities and the firm’s desire for larger net returns. These preferences then generate the firm’s choices and behaviours (Hausman, p. 42). The models that produce the behavioural functions described here can be combined and enlarged to obtain the so-called general equilibrium model whose structure fabricates an outcome that is a collection of variable values consisting of prices and quantities across the microeconomy. Building the general equilibrium model could also be interpreted as having as its only objective the description of a structure to explain how the general microeconomy operates. This article is concerned with the procedure whereby these kinds of models are constructed.

A model of something, call it S, is a construct, having enough in common with S, so that insight into S can be gained by studying the model. Einstein and Infeld (1938, p. 33) gave the following illustration for physical models: Imagine a scientist is shown a watch with rotating hands and asked to explain how it works, but is not allowed to remove its cover. One way he might proceed is to obtain appropriate springs, gears and whatever else might be required, and build a model of the watch whose observable behaviour duplicates the observed behaviour of the original. It is then possible for him to give an explanation of how the original watch behaves by claiming that it works like, or as if it were the model. The objective in constructing this model may be taken to be that of describing a structure that explains the operation of the watch. Regardless, there are many different models, and hence explanations, that could be built. But all explanations (not only those whose sole objective is to describe a structure) operate by identifying something in the model (here, the movement of the model’s hands) with what is observed (the movement of the hands on the original watch). In economics, of course, explanatory models are usually mental formulations intended to relate to economic phenomena.

Boumans (2005, pp. 2–4) thinks of models as instruments of investigation that aid in achieving an understanding. They are built by ‘... fitting together elements from disparate sources.’ The latter include ‘... policy views, mathematical concepts and techniques, metaphors and analogies, stylized facts and empirical data.’ These pieces are homogenized and harmonized into a single form and merged into a single structure. It is a trial-and-error activity. The main thrust of present argument is to describe and explore some of the characteristics of the manner in which this homogenization and harmonization process in the construction of explanatory models such as are now in view can be carried out. Weisberg (2007, p. 209) identifies a three-stage procedure for the construction of models in general and which applies to explanatory economic models in particular: 'In the first stage, a theorist constructs a model. In the second, she analyzes, refines, and further articulates the properties and dynamics of the model. Finally, in the third stage, she assesses the relationship between the model and the world if such an assessment is appropriate.' The following considers a five-stage approach that builds on Weisberg’s structure and in which his first and third stages are each split into two parts. The possible problems that can arise by ignoring the initial steps of the proposed five-stage process are then described. In the same context, the relation of models to the reality they purport to explain, along with the empirical testing of them, is also considered. The article concludes with a brief discussion of the place of explanatory model building in the overall methodological scheme.

It should also be pointed out that the main focus here is to marshal those considerations and logical relations which, taken together, point to what might be considered an optimal way of coming to grips with the problem of economic explanation. In that sense, the ensuing presentation may be interpreted as being connected to two distinct and alternative contexts. First, attention may be paid primarily to the ways in which economic model building is designed to elevate the more significant aspects in the explanation of actual phenomena. Since economic model builders attempting to explain economic phenomena have appeared, historically, not to have been seriously concerned with a detailed specification of the procedures involved in such an exercise, the ensuing discussion may be viewed as more normative than descriptive in that it provides a proposal for directing model building towards possibly more fruitful explanation. Second, from a purely methodological perspective, the following can be viewed as suggesting conceptual steps or stages that may be employed as an aid in describing and understanding explanatory economic model-building activities. These stages are heuristically relevant in clarifying the process of model construction and furnish a conceptual framework that rationalizes certain aspects of the model-building program.

I

As previously indicated, the concept of model building in explanation as contemplated here is described in terms of five procedural steps. The advantages and limitations of approaching model construction in this way will be considered later on. For now, it should be noted that the approach is quite distant from instrumentalism in that the relation of assumption content to the real-world activity under investigation is highly significant, and that, as suggested above, prediction is only a secondary by-product of explanation. The five steps or stages may be identified as follows:

1. Formulate an initial image of the phenomenon in question and its characteristics. According to Schumpeter (1954, pp. 561–561), ‘… the thing that comes first [in every scientific venture] is Vision. That is to say, before embarking upon analytic work of any kind we must first single out the set of phenomena we wish to investigate and acquire ‘intuitively’ a preliminary notion of how they hang together or, in other words, of what appear from our standpoint to be their fundamental properties.’ This will involve an accounting of various aspects of the phenomenon under review, recognizing that it may be described in terms of (a) measurable, (b) non-quantified or non-quantifiable, or (c) proxy variables. From such a vision, a process of abstraction will bring into focus a conceptual structure containing potential relations among those elements that appear to be most important for explanatory purposes. The abstraction procedure requires the isolation of certain elements thought to be most important for the purpose at hand from the influence of other elements deemed to be less important.²

This is Mäki’s notion of ‘essential isolation’. See Grüne-Yanoff (2012, p. 98).

2. Formalize these initial thoughts in a model that employs relations among appropriate variables. In this initial conceptualization of possible explanatory relations, it is not necessary to consider, in full detail, the extent to which the model is operational or the usefulness of the model for explaining aspects and possible iterations of the phenomenon. That is, specific answers to questions of measurement, if appropriate, of the empirical testability of the model, and of the availability of analytical techniques to manipulate and, assuming testability, to test the model, are ignored. Nevertheless, the potential correspondence between real-world occurrences and the model builder’s analytical conceptions will, of course, still be influential.

In the process of formalization, a number of assumptions, referred to below as primary assumptions, will have been made. It will subsequently emerge that an important relation exists between the assumption content of the model (including both primary and what will shortly be called secondary assumptions) in its full specification and its overall explanatory competence, coherence and empirical relevance. For that reason, it is useful at this point to clarify the distinction between what has been designated as primary assumptions and secondary assumptions.

Primary assumptions form part of the initial stage of formalization of the model and have to do with such things as the characteristics of human behaviour, possible institutional structures influential in economic outcomes, and human motivations for economic decisions and choices. Thus, consistent with frequently adduced assumptions relevant to the explanation of commodity market activity, the assumption may be made, for example, that decision makers behave in accordance with some appropriately specified objective of benefit or utility maximization. Such an assumption may derive from an underlying tenet of generalized economic rationality present in the cultural background of the individuals under consideration. Similarly, assumptions regarding institutional structures may reflect perceptions of the nature of competition and regulatory constraints, resource availabilities and their freedom of movement, and the availability of finance.

The model as constructed thus far, with the initial vision of Stage 1 taken into account and with its primary assumption content of Stage 2, provides an abstract depiction that makes sense as an incomplete representation of how the real world might actually operate or be described. (These two stages correspond to Weisberg’s first stage.) That representation, for example, may bring into focus individuals with particular preference orderings and motivations, pursuing their own self-interest, and facing institutional and resource limitations. But incompleteness arises because the description may not yet have sufficient substance to rigorously and logically assert that the behaviour to be explained could follow from the primary assumptions alone. The missing material is furnished by the secondary assumptions.

The purpose of secondary assumptions, to be introduced at the next stage, is to complete the model so as to render it capable of explaining the phenomenon under consideration. This will include, in part, making the model amenable to analytical exploration and empirical investigation. Illustrations of these kinds of assumptions might involve specifying, say, mathematical forms or properties of preference orderings and associated utility functions if such are contemplated in Stage 2; ignoring or modifying, in specific situations, some of the primary assumptions introduced at Stage 2; and introducing quantified proxy variables in place of unmeasured or ordinally measured variables present at Stage 2. In the latter case, it will be relevant to consider certain difficulties and possibilities of misinterpretation that may arise in the use of the calibrated proxies.

3. Operationalize the model (this relates to Weisberg’s second stage). This means both the possible introduction of new elements and the manipulation of the relations among the variables of the model to extend and complete the analysis, to examine the implications of the assumptions and to derive, if possible and not already present in the relations that structure the model, empirically testable hypotheses. Notwithstanding the care with which primary assumptions may be brought in at Stage 2, the process of operationalizing will usually involve the introduction of secondary assumptions of the sort indicated above.³

It is certainly possible for a model builder who is using or extending a model built by someone else to employ the same primary (Stage 2) and secondary (Stage 3) assumptions of the original model. But this does not absolve the copier of the need to discuss those assumptions and give reasons why they are relevant to explaining the phenomenon on which the copier’s attention is focused. Moreover, if the copier is making changes in the primary or secondary assumptions, those changes require explanation too.

As will be argued below, secondary assumptions often have implicit assumption counterparts that may be implied at the level of the primary assumptions of Stage 2. That is, these counterpart assumptions that are now seen to be relevant because of the operationalization at Stage 3 may significantly alter the initial structure of assumptions introduced at the earlier stage. And such counterparts may not have been acknowledged or taken into account at Stage 2. Of course, had such implicit primary-level assumptions been explicitly introduced as primary assumptions at Stage 2, they would frequently (though not necessarily) imply, respectively, the corresponding secondary assumptions. In any case, the presence at the level of Stage 2 of implicit assumption counterparts to the secondary assumptions raises the issue of how well these counterparts fit with the earlier initial image and its initial formalization in Stages 1 and 2. This matter plays an important role in judging the cogency, relevance and usefulness of the model in Stage 5.

4. When appropriate, subject the model to empirical tests. Where quantified variables are employed, this will be accomplished by using standard statistical and econometric techniques. For instances when the explanatory model is structured by nonquantifiable variables, a variety of alternative methods are also available (Katzner, 1983, Chapters 12 & 13). It should be noted, however, that all empirical tests compare model properties with observed data—quantified or unquantified. And the construction of that data may involve considerable abstraction which removes it a significant distance from reality, often farther than the vision of Stage 1 or the preliminary formulation of Stage 2. To identify in the general automobile market, say, the number of automobiles sold at a particular price, requires the condensation, respectively, of quantities of many different products and their varying prices into a single pair of numbers.

It should be further noted that models whose outcomes are variable values (such as the demand-supply models of isolated markets or the general-equilibrium models of the microeconomy) may not admit of direct tests of their explanatory competence.⁴

Of course, the component relations of the supply-demand model and certain component relations of the general equilibrium model are testable in isolation. And there are, moreover, special formulations of the general equilibrium model extended by letting endowments vary that can also be tested for explanatory competence. With respect to the latter, see Brown and Matzkin (1996).

Apart from other possible connections, these models are linked to reality in that observed prices and quantities are interpreted as equilibrium prices and quantities in the relevant model. Even without empirical testing, the usefulness of these models in explanation is clear: Their explanatory competence exists at a high level of intuitive satisfaction even in the absence of empirical tests, and the models themselves are robust by reason of their apparent continued empirical relevance. Indeed, the model explaining observed prices and quantities in an isolated market has passed into the public domain and stands as the basis for often-seen-and-heard assertions of the form, ‘Reductions in supply have led to price increases.’ And the general equilibrium model is typically regarded as a way of thinking about the microeconomy as a whole, and as a part of the theoretical basis for capitalism—the economic system that is thought to largely structure economic behaviour in the Western world today.

5. In light of any empirical tests that have been undertaken, make a judgment of the explanatory significance of the model including its cogency (that is, the manner in which its parts fit together to provide explanatory significance) and its relevance to the real phenomenon under investigation, and its possible usefulness for purposes of prediction. Of course, judgments of cogency and relevance are highly personal in nature and reflect the values and interests of the person undertaking the investigation. Thus a model may be judged cogent if it provides, in the view of the investigator, a satisfactory explanation of the phenomenon it was constructed to explain. Cogency may also require that the elements of the model be internally consistent. The judgment of relevance necessitates a determination by the investigator as to the extent to which the various constituent parts of the model do, in fact, directly or indirectly reflect what are thought to be observable real-world relationships and economic structures. In particular, it has to take into account the ‘bridges’ to reality that are present or absent in the model. A bridge establishes a direct connection between an element of a model and the observable real world. Examples will be provided shortly. The notion of bridge encompasses not only those connections to reality that relate to the primary-and secondary-assumption content present in the model, including whatever implicit assumption counterparts present at the level of Stage 2 that are implied by the secondary assumptions added at Stage 3. It also includes those connections that appear upon subjecting parts of the model to empirical estimations and tests.

It should be emphasized that bridges can arise either as a result of an empirical estimation or test, or when an element of the model appears, in the judgment of the investigator, as a sensible representation of a real-world object. Bridges can be present at each of Stages 1–4 of the model-building process. They can exist as links between established cultural tenets of societies and assumptions of motivation directing behaviour in economic models (e.g., the cultural value of self-interest arises in the assumption that individuals buy what they most prefer or maximize utility) as well as between model conclusions and observed facts (e.g., the macroeconomic conclusion that under certain conditions income tax cuts will stimulate the growth of GDP can be associated with the increase in GDP observed after the US income tax cuts of 1964). Relevance would likely require, in at least one of the first four stages above, at least one link to reality that is sufficiently adequate for an investigator to accept the model as a possible explanation of the phenomenon in question. The more links and the more stages at which such links are present, the greater the confidence the investigator might have in the model’s explanatory competence. (Stages 4 and 5 as described here correspond to Weisberg’s third stage.)

In all of this, the knowledge, skill, and imaginative insight of the investigator is critical. Such elements, to the extent that they are present, could enhance the meaningfulness and persuasiveness to the investigator of the explanation secured and might lead to acceptance of the model by others as an adequate statement of what is going on.

It is important to point out that passage from the second to the third stage does not necessarily imply transition from an unquantified to a quantified state. Operationality, in the sense employed here, means that the model has been developed to the point at which it is, at least in principle, linkable to potential empirical observations that are identifiable with, and thought to be representative of, the phenomenon being explained. These observations could be represented and expressed in terms of either numbers or words. In the latter case, they would consist of verbal descriptions of realizations of various forms of such things as, for example, security or freedom (Katzner, 2001, pp. 63–64).

The limitations of empirical testing also deserve comment. On the one hand, an explanatory model that survives empirical tests may be thought of as provisionally confirmed as one possible explanation of the phenomenon under investigation. But that by itself does not signify that a different model, and hence an alternative explanation, might not also pass similar tests. Nor does it provide a final guarantee that the explanation generated by the model is correct and relevant to the matter at hand. Of course, and as will be seen in the illustration that follows, the absence of such a guarantee does not mean that the model is not useful. But in light of this particular limitation, cogency and relevance, as judged by the investigator need not rely on full correctness. They could also be based, in addition to the results of tests, on further considerations involving judgments as to the meaningfulness and appropriateness of both primary and secondary assumptions and the theoretical results that ensue from them. To illustrate, a model concluding that sunspot activity causes economic activity, even if consistent with observed data, may be rejected on the grounds that the correlation between sunspot and economic activity is spurious. Generally, of course, correlation does not imply causality. In the sunspot case, the judgment may be made that the correlation does not provide an accurate causal explanation of what is actually going on. On the other hand, conditions may exist in which a model that is apparently refuted by a test could nevertheless be adjusted in certain ways to enable it to be viewed as a cogent and relevant explanation. Such a situation may arise because of acknowledged deficiencies in the test or inadequacies in the manner in which the Stage 2 specification of the model was operationalized. In the latter instance, the model’s explanatory competence could be improved by the adjustment of the third-stage specifications, i.e., the secondary assumptions, that led to its operationality.

An example will serve to illustrate the methodological procedure that is here in view. Consider the standard utility-maximization model of consumer purchasing behaviour in which elements such as uncertainty, savings, and altruism are ignored. Imagine this model is to be constructed from scratch. The modelling process begins (Stage 1) by envisaging the consumer as an individual who buys different commodities at various prices, whose choices are constrained by the prices of goods and the amount of money he has to spend, and whose behaviour is a reflection of his own self-interest. At the level of Stage 2, an initial model is developed that contains two primary assumptions: The consumer has a preference relation among baskets of commodities that is consistent, i.e., reflexive and transitive,⁵

A relation such as ≥ defined on D is reflexive when x ≥ x for all x in D. It is transitive if x' ≥ x'' and x'' ≥ x''' imply x' ≥ x''', for all x', x'' and x''' in D.

and, in each purchasing situation, he buys that basket that is the most preferred among the options available to him. Since baskets of commodities are already quantified, there is no measurement issue. In Stage 3, the model is often operationalized by first introducing secondary assumptions to permit the expression of preferences in terms of a utility function that is to be maximized, and also to guarantee the existence of unique utility-maximizing baskets. One collection of such assumptions is that the preference relation is also total⁶

The relation ≥ on D is total provided that, for all x' and x'' in D, either x' ≥ x'' or x'' ≥ x'.

and representable by a continuous (utility) function defined over a Euclidean commodity space, and that the utility function is increasing, and strictly quasi-concave. Then the model is manipulated to derive, from the constrained maximization of utility, demand functions and their empirically testable properties. Observe that the assumptions of totality and continuous representability are already expressed at the same level (i.e., the level of preferences) as the primary assumptions, while those of increasingness and strict quasi-concavity can easily be reduced to, or expressed at that level. To follow through on Stage 4, appropriate empirical tests are undertaken and an analysis is made of the extent to which the model fits the available data.

In the last stage (Stage 5), a judgment has to be made as to the cogency and relevance of this model. It turns out that in the present example, a number of qualifying considerations imply that the results of empirical tests or analyses may not help with such a judgment. On the one hand, since observations of buying behaviour are necessarily taken over time, any instance that might be thought to contradict or refute the model through inconsistencies with the derived properties of demand functions can always be explained away in terms of changing preferences from one observation to another (Caldwell, 1982, pp. 156–157).⁷

Of course, there may be reasons why, in particular situations, inconsistencies revealed by empirical tests might be taken as evidence that the theory should be rejected.

At the same time, of course, it must be born in mind that problems may arise regarding the quality of the empirical data set against which the model is being tested or estimated. As a case in point, the very definition of a commodity represented in data across time and its availability and desirability in relation to competing or complementary goods may vary due to technological innovation. Such modifications provide additional reasons why observed data may contradict the properties of demand functions derived from constrained utility maximization.

On the other hand, confirming instances, as previously noted, do not necessarily guarantee that the model is an accurate explanation of what is really going on. But the vision of Stage 1 and the primary assumptions based on it of Stage 2 may, on several grounds, still seem appropriate in many cases: first, because of the bridge to reality linking the buying circumstances in the model (i.e., the limits imposed by prices and money available) to circumstances similar to what a real consumer actually faces when making purchases; second, because of the bridge between preferences in the model and the seemingly plausible fact that real individuals actually have preferences among buying options; and third, because of the bridge, present at least for Western economies, generally linking the effort in the model to buy the most preferred option with self-interest in the real Western world. (Self-interest is a fundamental tenet of the cultural milieu in which actual purchasing behaviour takes place in the West and hence, as a rule, may be understood as a driving force behind behaviour in Western economies (Katzner, 1999⁸

This is not to say that motivations other than self-interest might not drive behaviour in particular circumstances and cannot be represented by utility maximization.

). Account should also be taken of the fact that the secondary assumptions and their implicit assumption counterparts at the level of Stage 2 are logically necessary to ensure that preference or utility maximization can take place. As such, the secondary assumptions do not seem to interfere significantly with the main thrust of the explanation produced by the model. Therefore, in the context of this example (with uncertainty, saving, and the possibility of such elements as altruism ignored), the utility-maximization model may be judged as both a cogent and relevant explanation of numerous instances of consumer purchasing behaviour.

To illustrate how a specific study might fit into the five-stage methodological structure proposed here, consider the model of herd behaviour developed by Banerjee (1992). The purpose of Banerjee’s model is to provide an explanation of why it might be ‘rational’ for an individual making a decision to be influenced by the decisions that others have made. The discussion of his Stage 1 vision suggests that the reason why such a procedure could be rational is that the decisions of others may mirror information that the decision-maker in question does not have. Reflecting back on the Stage 1 vision, the model, upon analysis, shows that a consequence of everyone relying on the information contained in the observed decision of others in making their own decisions is herd behaviour—everyone does what everyone else does even though their own information might suggest doing something different.

In Stage 2, Banerjee sets out a game-theoretic model in which individuals make decisions sequentially in a fixed order. Each person knows the choices of those who made decisions before him, but not the information upon which those decision were based. In Stage 3, the model is analyzed to determine the unique decision rule adopted by all participants. Welfare properties are also considered, and the model is extended to consider such things as alternative payoff structures and making the order of decisions made endogenous. There is no attempt at Stage 4 empirical testing and no Stage 5 overall judgment of the model is provided, although some of the model’s weaknesses are described.

II

While the general methodological statement of the stages of explanatory model building set out above, may seem rather straightforward and even obvious, many investigations in economics do not appear to follow the pattern it sets out. Economists may recognize and acknowledge one or more of these stages, and perhaps even give lip service to them. But without taking full cognizance of the entire scheme of stages and their implications, they may fail to address the question of how their constructions relate to and explain real economic phenomena. And this leaves them vulnerable to their critics.

Whatever the difficulties in dealing with Stages 1 and 2 of the methodology set out above, those difficulties can be compounded by the fact that in economics it often happens that many, if not all of the variables of the model at those stages, are not capable of appropriate quantification. Some are not even ordinally quantifiable. Since techniques for handling the unquantified in a formal way, though available (Katzner 1983, 2001), are not well known, a lack of ability to quantify may make coming to terms with Stage 2 and possibly even Stage 1 seem intractable. This may be one reason why scholars have often tended to ignore those stages and proceeded directly with the operational models of Stage 3.

But regardless of the reason, in many instances Stages 1, 2, and 5 are ignored and attention focuses only on Stage 3 and possibly on Stage 4. That is, a model in operational form is assumed, manipulated and, perhaps, tested. (For instance, the inquiry might begin by assuming the presence of a functional relation with certain properties or, more particularly, of a functional relation of a specific form.) And little attention is paid to many of the assumptions at the primary level or Stage 2, both those that are implied from the introduction of secondary assumptions and those that, being primary, are not, and both of which are now mostly implicit in the operational statement of the model. But without explicit expression of all Stage 2 level assumptions, it is not possible to know the full extent of the assumption content of the model. Moreover, since the primary-level assumptions are located at Stage 2 and are in that sense ‘nearer’ to reality than the secondary assumptions and the operational model of Stage 3, and since the primary-level assumptions are therefore more closely related to the initial contemplations of Stage 1, they are critical in judging the cogency and relevance of the model. It follows that without knowing all primary-level assumptions of the model, the ability to carry out the judgment of Stage 5 can be significantly impaired.

Because, as indicated at the outset, models generally can be built for different purposes, none of this is intended to imply that successful model building must, of necessity, always take Stages 1 and 2 considerations into account.⁹

As an example of constructing a model first and looking for something for it to explain (cf. Note 1), Volterra ‘... began his investigation of Adriatic fish by not looking directly at those fish or even at the statistics gathered from the fish markets, but by constructing a model… [in which] he imagined a population of predators and prey, each with only two properties… [He then discovered] some very general properties of predator–prey models, ones that apply far more widely than the particular case he had in mind’ (Weisberg 2007, pp. 222–223).

But it does suggest the dangers of not doing so.

To illustrate the problem and see what is often at stake, suppose, in the standard utility-maximization model described above, the further secondary assumption of an additive utility function

u (x) = f^{1} (x_{1}) + \dots + f^{I} (x_{I})

(where u and the fⁱ are functions and the x_i are scalars, i=1,…,I) with positive first-order and negative second-order derivatives of each function f ⁱ, is included as part of the operationalizing process of Stage 3. It is well known that with such a utility function, as the individual’s income rises his demand for each good increases, that is, there are no inferior goods (Katzner, 1970, p. 91). Although, as indicated earlier, characteristics such as the absence of inferior goods cannot be conclusively refuted (or affirmed) by observing demand behaviour, this still seems rather strange. But it could also be demonstrated that the implicit assumption counterpart at the level of Stage 2 of the secondary assumption of additivity is that the individual’s preference ordering is such that preferences among quantities of each commodity alone are independent of the quantities of the other commodities that could be held by that individual.¹⁰

The argument is similar to that establishing the relationship between ‘additive preferences’ and the existence of an additive utility function representing them. See Katzner (1970, pp. 29–31).

And as part of the initial Stages 1 and 2 formulation, this might not seem to be appropriate in many cases. By looking at the Stage 2 implication of this secondary assumption, then, possible grounds are obtained for arriving at the judgment in Stage 5 that the model is inadequate.

This is not to say that additive utility functions are never to be employed under any circumstances.¹¹

Nor is it to accuse the classical economists such as Jevons, Walras and Marshal of bad modelling because they assumed additive utility functions. Their models, after all, were based on the knowledge complex of the time. It was the subsequent advancement of knowledge that made it possible at a later date to see that additive utility comes with some potentially unfortunate baggage.

For example, the assumption of additivity could be invoked to demonstrate that even under such a severe restriction, certain confounding issues (such as, say, the presence of asymmetric information) could arise, thus suggesting that without that restriction, matters could be even more complex and difficult to deal with (e.g., Sugden, 2000, p. 9). But when confining interest to the explanation of an individual’s demand behaviour, such an assumption might not, in the judgment of the investigator, seem to be suitably representative of his preferences.

The issue raised by this example, namely that ignoring the implications of secondary assumptions at the primary level can exclude vital information necessary to arrive at a judgment of the cogency and relevance of a model, may arise in many different ways in model building directed towards explanation. As a second illustration, turn attention to the standard long-run model of the perfectly competitive firm. The Stage 1 vision consists of such elements as technology playing a role in the production of outputs, and the firm reacting to market dictates in its own self-interest. In Stage 2, a production function is introduced, input and output market prices are taken to be fixed and, given these parameters, the firm is assumed to hire inputs and produce outputs so as to maximize profit (total revenue minus total cost). At the operational level of Stage 3, at least, two significant secondary assumptions arise. First, a distinction is drawn between durable physical capital and nondurable inputs so that normal profit (the minimum return on the investment in durables necessary to keep the owners of the firm from removing their investment in it) can be characterized as the economic reward of the physical capital inputs. Second sufficient properties on the production function are imposed to enable the maximization to take place. Implicit in the distinction between physical capital and nondurable inputs is the further secondary assumption that the two kinds of inputs can be treated identically in determining the firm’s profit-maximizing position in the sense of equating the first-order partial derivatives of the profit function to zero.¹²

Other problems associated with this approach to physical capital are not considered here.

It follows that the firm’s optimal input mix and optimal output level depend only on input and output prices and the firm’s production function. It is also concluded that even though the free entry of perfect competition drives profit to its designated normal level and above-normal profit to zero, the firm is content to continue to hire inputs and produce outputs.

However, the secondary assumption of treating physical capital inputs in the same way as nondurables implies, at the level of Stage 2, that significant consequences of the manner in which physical capital has been incorporated in the model are not usually consistent with observable fact. In particular, the practice requires that the firm’s revenue at any instant in the model be sufficient to cover the full cost of the physical capital inputs—a characteristic that is often incompatible with reality. For in real-world situations, the cost of physical capital will generally be amortized over its useful life and, were this accounted for in the model, the optimal input mix, and optimal output level would be influenced, in addition to prices and the production function, by the cost, at the margin, of carrying the physical capital inputs over those inputs’ lives (Katzner, 2006, pp. 551–553). Once again, by looking at the implications of the secondary assumptions significant properties of the model are revealed that may lead to the judgment that the original model should be rejected or at least modified.

Robinson’s criticism (1953) of the aggregate capital variable in the neoclassical production function may be interpreted in similar terms. That is, neoclassical analyses of economic distribution and growth at the time might be said to have started at the operational level (Stage 3) by postulating such a production function without considering the meaning of the capital variable at the lower Stage 1 and 2 levels:¹³

For example, see Stigler (1968, especially Chapter 12). Harcourt (1972, p. 11) considers this volume to be a ‘case-book’ example of neoclassical economics during the period.

... the production function has been a powerful instrument in miseducation. The student of economic theory is taught to write O = f (L,C) where L is a quantity of labour, C a quantity of capital and O a rate of output of commodities. He is instructed to assume all workers alike, and to measure L in man-hours of labour; he is told something about the index-number problem involved in choosing a unit of output; and then he is hurried on to the next question, in the hope that he will forget to ask in what units C is measured. Before ever he does ask, he has become a professor, and so sloppy habits of thought are handed on from one generation to the next. (Robinson, 1953, p. 81)

Robinson’s paper draws out the unfortunate consequences of ignoring the Stage 1 and 2 issues.

To provide an example in the more recent literature, consider the market for used automobiles as analyzed by Akerlof (1970, pp. 489–492). Akerlof presents his model as a ‘... finger exercise to illustrate and deepen … [certain] thoughts …rather than for importance or realism.’ From that perspective, Akerlof begins with a Stage 1 description of his vision of the market. He notes the price difference between new and used automobiles and the presence of what he later refers to as asymmetric information, viz., that the seller of the used car typically knows more about it than the buyer.

Akerlof’s analysis then specifies a Stage 2 demand–supply model for the used car market in which the ‘average quality’ of used automobiles traded and the market price is determined. His Stage 3 extension of the model adds two types of utility functions, cars with uniformly distributed quality, and the derivation of the market demand and supply functions from the maximization of utility.

If now, notwithstanding Akerlof’s important contribution on the level on which his analysis was presented, it was desired to move his model further towards realism, a number of obstacles arise. To begin with, creating a model with market demand and supply functions requires additional abstraction from that already present in the vision of Stage 1. And the presence of an unmeasured quantity variable requires employment of different abstract conditions (which Akerlof ignores) to ensure the existence of solutions than are normally required (Katzner, 1983, pp. 91–94; 2001, pp. 65–67). However, this movement away from the real phenomenon being explained by these Stage 2 constructions is normal in many analyses and cannot be overcome. But in Stage 3, Acherlof assumes an additive utility function and, implicitly, that average quality can be measured on a ratio scale. The potential difficulty with the first of these Stage 3 assumptions has already been discussed; that with the second arises from the considerable arbitrariness introduced by taking a variable to be ratio measured when, at best, it is only ordinally measured (Katzner & Skott, 2004). Both assumptions tend to push the model considerably farther from reality than the distance already present in Stages 1 and 2 and might, even if some empirical corroboration were available, lead to a Stage 5 rejection of the model as an explanation of the used automobile market.

III

Consider now in the context of the stages of model building described here, how models generally explain and relate to the real world. Clearly, in moving across Stages 1–3, more and more abstraction takes place. Models become increasingly idealized and ‘false’ as accurate representations of reality in the sense that they are less and less closely related to what is actually present in the real world. The most significant and extensive deviations from reality are likely to occur in the transition from Stage 2 to Stage 3 with the introduction of secondary assumptions and possible measures of particular variables.¹⁴

Adding assumptions to those of Stage 2 to arrive at Stage 3 may make it easier to fit the model to a given set of data. But, as pointed out earlier, data already involve substantial abstraction from the real phenomenon at issue. Hence, such a movement from Stage 2 to Stage 3 is properly regarded as increasing the distance of the model from reality to at least that already present in the data.

According to Wimsatt (1987, pp. 28–29), this distancing from actual existence due to the process of abstraction can be attributed to a variety of sources, including the constructing of the model as an approximation that cannot be fully applicable to any situation and ignoring certain relevant variables so that the model lacks coverage of significant aspects of the real phenomenon under investigation. In spite of their falsity, however, false models, as is implicit in earlier discussion, are often judged by investigators to be cogent and relevant, and therefore accepted as explanations of that which is to be explained. Indeed, Wimsatt (1987, pp. 30–32) suggests that the construction of false models can help in the search for alternative models (still false) that provide better explanations of the reality under consideration. In terms of the present proposal, Wimsatt’s suggestion might mean consideration of the extent to which the construction of a false model conforms to the five-stage procedure described here and the implications that that holds for the possible testing of the model and its coherence. In light of these considerations, changes might be made to make the false model more satisfying.

There are also a number of other ways to approach models and model falsity that can make a false model acceptable as an explanation of an observed phenomenon. These alternatives are entirely independent of the five-stage procedure, although many are still consistent with it. Four of the latter approaches are now considered as illustrations.

Hausman (2009, p. 41) is content as long as the false model provides knowledge of the real world despite its distant-from-reality perspective. That very problem, of course, has been addressed in the successive stage model-building procedure previously explored in which the possibility of bridges from model assumptions to the empirical world speaks to questions regarding the degree of closeness to reality of the model’s conclusions.

To consider the ability of a model to provide knowledge in a particular case, focus on the static geometric supply–demand model explaining how the observed price of a single commodity is determined and how it rises and falls during a period when rapid inflation is not present. (Here, the identification of assumptions with the various stages of model building is left to the reader.) The commodity at issue is assumed to be homogeneous and bought and sold in a single isolated market. This, as previously noted in a different context, is already an abstraction which, necessarily, is not present in reality. Thus, gasoline, even within a single country, is not homogeneous and is sold in many places and under varying circumstances. The same is true of the ‘observed price’ which, at the empirical level, is often taken to be an average of observed prices over a collection of locations and similar products. Regardless, demand and supply curves are postulated that relate single quantity values to single price values and that are assumed to be stable for the period or moment of time in question. Of course, such curves are further abstractions that do not exist in actuality. Moreover, all other forces that may be operating in the market are ignored. When an observed price–quantity point is to be explained, both demand and supply curves are assumed to pass through that same observed point. The observed price is then viewed as the equilibrium outcome of the interaction of these geometric representations of demand and supply. Furthermore, an observed rise in price, say, is said to be a consequence of either an increase in demand or a reduction in supply.

In spite of its abstract nature and its distance from actuality, most economists would probably agree that this false model still yields knowledge of real economic activity. And, as pointed out earlier, the explanation it provides is so useful and resonates so strongly as an understanding of what is going on that it has passed from the realm of academic economics into the public domain. Of course, when the media write or speak of demand and supply, they do not explicitly refer to curves. But the model is certainly lurking in the background and imparts substance and meaning to their assertions.

False models are admissible as explanations to Mäki (2009, p. 78) because, to him, they are idealizations that exclude, in the judgment of the investigator, the presumably less significant real elements from involvement and influence in their analytical structures, thereby permitting a sharper focus on the key factors or what is thought to be most important with respect to the phenomenon being explained. That is, it is the isolation arising in Stage 1 of model building that gives models their significance. Even with false assumptions, models still represent real phenomena by resembling them ‘... in relevant respects and sufficient degrees…. Thanks to this resemblance, the examination of … [the model] will convey information about … [the reality under investigation]’ (Mäki, 2002, p. 11]).

Sugden (2000) accepts false models as explanations since, from his perspective, they create credible worlds, that is, ‘... descriptions of how the world could be’ (Sugden, 2000, p. 18). Gaps between the credible worlds and reality are filled by what Sugden refers to as inductive inference. The more credible the model, the more confidence in the inferences. What counts in determining credibility is a ‘... harmonious relationship between the assumptions of the model, and between the model and what we know about the causal structure of the [real] world.’¹⁵

This is Mäki’s (2002, p. 12) interpretation of Sugden’s position.

Evidently, for Hausman, Mäki, and Sugden, the degree of acceptability of a model notwithstanding its falsity would depend on how well, from their individual perspectives, the model relates to and explains reality. That determination, again, is precisely what is presented as the objective of the five-stage model-building methodology elucidated above. To a considerable extent, the ability to relate and explain rests on the nature of the Stage 3 secondary assumptions and what they imply at the nearer-to-reality Stage 2 level. Thus, regardless of what is thought about what models are and how they explain, model building that neglects Stages 1 and 2, and begins at Stage 3 leaves important questions concerning its viability and acceptability somewhat in doubt.

According to Morgan (2002, p. 178), false models are acceptable as explanations because, from her vantage point, they aid in understanding the real world by telling stories about that world. ‘Modelling involves a style of scientific thinking in which the argument is structured by the model, but in which the application is achieved via a narrative prompted by an external fact, an imagined event or question to be answered. Economists use their economic models to explain or understand the facts of the world by telling stories about how those facts might have arisen.’To illustrate in the demand–supply model described above, the structure of the argument or model is the intersecting demand and supply curves, and the stories consist of such narratives as how an observed outcome is a consequence of the interaction of the forces of demand and supply, or how an increase in price has come about through an enlargement in demand or a decline in supply. The stories form a bridge as described earlier that spans the gaps between model structures and the realities the models purport to explain. Both the structures and stories emerge from the vision described in Stage 1 of model building set out earlier.

It is, of course, always possible to develop a story to enhance a model’s argument after the model has been built. This was certainly the case with the auctioneer story associated with Walras’ general equilibrium model of price determination which was created long after Walras set out his model.¹⁶

Fisher (1987, p. 26) suggests that the auctioneer story was invented by Schumpeter in his lectures to students and introduced into the economics literature by Samuelson.

But from what seems to have emerged from Stage 1 considerations, Walras (1954, p. 84) had his own story of price determination based on ‘brokers or criers’ who negotiate market transactions. In any case, the dangers of adding a story after a model is built in which Stage 1 considerations are not taken into account are similar to those of starting model construction at Stage 3: Irrelevancies can be introduced that tend to push the model farther from the realities of the phenomenon the model purports to explain and may impair the ability to reach a positive judgment of the model in Stage 5. Although the auctioneer story that currently accompanies the general equilibrium model allows easy visualization of the mathematical workings of that model, it still adds further unrealism to it.

IV

Previous discussion has focused on the relations between the various elements or content of models as they occur at different stages of their construction. In addition to the observations made in that connection, a number of further comments will serve to clarify and summarize earlier results. It is convenient to begin by returning to the method of explanatory model building in economics described at the outset. As suggested there, such models are generally built to explain observable phenomena. Apart from such items as prices and quantities, there are circumstances in which the phenomena being observed consist of unquantified elements with respect to which the attribution of numerical measures is not evident. Thus, the necessity is frequently imposed on an investigator to model real-world phenomena in such a way as to somehow achieve explanation in the face of measurement difficulties.

What has been referred to above as the Stage 1 level of model construction is the vision leading to an initial collection of elements abstracted from real situations to focus attention on what is deemed to be important and significant. It is among these elements that, in passing to Stage 2, inaugural variables are defined and relations among them first postulated. Properties of the relations may also be introduced as additions to these primary assumptions. At the operational level of Stage 3, numerical measures may (or may not) be brought in to quantify what is not quantified, and analytical techniques that require numbers like the calculus (or those that do not) can be applied to manipulate the relations. But, in the sense described earlier, the taking of each of these subsequent actions removes the model or analysis one step farther from the reality it purports to explain. Clearly, the Stage 1 and 2 levels are those parts of the analysis that usually come closest to the actual real-world phenomena under scrutiny. For this reason, then, the content of the primary assumptions introduced at Stage 2 would typically have to be a part of what is kept in mind in order to make a conclusive judgment of the relevance of an analysis to the real-world question being addressed.

It should also be recalled that what constitutes empirical corroboration of a model or its testing against reality often occurs at a higher level of abstraction from reality than that of Stages 1 and 2. That is because secondary assumptions of convenience are frequently introduced to manipulate the model so as to obtain empirically testable propositions. In addition, numerical measures of economic variables, when present, are often proxies that, at best, only approximate what is supposed to be measured. And, notwithstanding the fact that some proxies reflect what is intended to be measured more effectively than others, the exact relationship between what the proxies are supposed to measure and what they actually measure is not known. It follows that, in such cases, what passes for a test is actually not a test at all, but rather, only a way of obtaining an empirical conjecture of what might be. The relevance of the model still depends on a Stage 5 judgment by the investigator based on the content of the model at the levels of Stages 1 and 2.

Unfortunately, as suggested earlier, many practitioners of explanatory economic model building do not pay much attention to these first two stages in building their models. Analyses frequently start by specifying operational or partly operational models with only quantified variables. Functional relations among them with specific properties are postulated and analytical manipulation proceeds from there. Questions about the meaningfulness of the measures employed and the relation of the structure to the levels of Stages 1 and 2, and hence to the real phenomenon under investigation, are not considered. But until those questions are given serious attention, no judgment can be made about the relevance of the analytical endeavour to the real phenomena at issue. In many cases, the arbitrariness of such an approach is clear and its usefulness may be questionable.¹⁷

Forms of arbitrariness, different from those suggested here, that arise from using inappropriate forms of measurement (e.g., cardinal measures where only ordinal measures are warranted) have been described and analyzed by Katzner and Skott (2004).

Alternatively, greater relevance and less arbitrariness may be easier to achieve by actually starting model construction at the level of Stage 1 itself. Assumptions might then be introduced at Stage 2 that, at the outset of the analysis, seem to fit the reality at issue, and argument at later stages would then proceed from those assumptions. This approach, however, might necessitate, in the later-stage arguments, the keeping of the analytical structure in unquantified form and the using of the rules (developed elsewhere) of analysis without measurement to pursue the manipulation of functions and derive conclusions (Katzner, 1983, 2001). In that case, manipulative tools requiring quantification, such as the calculus, could not be employed. But at least from this perspective, the relevance of the model or the analysis based on it would be determined up front and would not become an issue that might cause the entire endeavour to be discarded later on.

Discussion to this point has been substantially confined to questions relating directly to model building addressed to economic explanation, and, following from that, the respects in which the explanatory competence of a model can be adjudicated by the investigator in the light of relevant observable or empirical phenomena. It will be useful, in conclusion, to comment briefly on the broader question of the location of present argument in the larger complex of issues having to do with appropriate methodologies for economic analysis in general. The relation of the five-stage procedure of model building developed here to instrumentalism has already been noted at the outset.

Leaving aside mere description and focusing only on attempts at analytical economic explanation, two alternative methodological approaches to economic explanation can, in rather broad strokes, be referred to as ‘rationalist’ on the one hand or ‘positivist’ on the other. Rationalism, of course, comes to expression in the view that economic explanation properly proceeds by deductive implications from a given set of initial assumptions about human behaviour and the environment in which that behaviour takes place. The positivist perspective elevates the necessity for the derivation of testable hypotheses to enhance the competence of economic explanation in explaining real phenomenon. Without delving into these methodological approaches in detail, it is clear that at the initial stages of model building, i.e., Stages 1 and 2, elements of rationalism are apparent. That is so to the extent that the primary assumptions of Stage 2 refer in general to basic postulates underlying human behaviour, as well as to specific assumptions about real-world environmental or contextual structures. The deductive procedures that are generally associated with a rationalist approach are reflected in Stage 3 of model building, where the progress to the derivation of a testable hypothesis is carried out, preparatory to empirical testing at Stage 4. But it should be equally clear that the procedure of model building proposed here is in no sense simply or solely deductivist in its starkest rationalist sense. To the contrary, that procedure makes every necessary nod to positivist persuasions in significant twofold respects.

First, what should be seen as a highly significant aspect is the bridges to the real world, which are intended to fasten the analysis to genuine observable or empirical phenomena at appropriate points. As such, they often illuminate the way to the construction and content of appropriate empirical tests of Stage 4. Second, the insistence on testing the model at Stage 4 is in itself designed to incorporate in the model-construction process, the possibility of a genuine correspondence to real-world occurrences in the sense that the relevance as well as the explanatory cogency of the model is thereby ascertainable.

The deliberate introduction to the model-building argument of elements of both a priori rationalism and positivism rescues the argument from the aridity of severe rationalism that might not necessarily have any relevance to real-world situations and conditions at all, and from the mere descriptive handling of so-called facts of economic reality which, in itself, will generally be without explanatory content. Moreover, what is to be seen as a highly significant aspect of the model-building process is the need for reactive relations between the secondary assumptions that appear at Stage 3 and the primary assumptions at Stage 2. The examples of that interrelation that have been given confirm the way in which the robustness of the model is preserved, as necessary adjustments in the contours of the model are made, and the ways in which, as a result, the explanatory competence of the model is, hopefully, maximized.

Acknowledgments

The author would like to thank D. Wade Hands, Roberto Veneziani, Douglas Vickers, and anonymous referees for their help.

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