The Role of Assumptions in Economic Modeling

1. Introduction to Economic Modeling

The purpose of this paper is to explore the role of assumptions in the modeling of economic behavior. Although the perspectives that have emerged in this literature vary in the stance that they take, most can be seen as resting on one of a number of themes.

A crucial feature of all models, be they simple or complex, is that they help to define the assumptions required in the analysis and provide a coherent logic. Consequently, assumptions are at the heart of the modeling exercise and yet, despite this, their use, scope and interpretation remain controversial and open to widely differing views.

Models play a central role in economics. They are applied to economic data in order to generate empirical regularities, used to forecast economic outcomes, inform policy, and employed to help understand the world and to underpin micro-economic theory. This use and abuse of models has attracted considerable attention, not just in economic literature but also in numerous writings aimed at a more general audience.

These are, in no order:

1. The most theoretical assumptions are also the least controversial: these assumptions follow logically from a definition, are axiomatic to a logical structure or are unreasonably modest and fall into the category of being the least that is required to generate significant or interesting conclusions.

2. Common or best practice assumptions: certain well-defined properties or assumptions give rise to a best practice criterion which may be seen as unambiguously useful.

3. Assumptions subject to important policy and welfare considerations: several important modeling approaches have models that are derived as a solution to policy or welfare questions.

4. Consistency: some assumptions have the status of being consistent with a larger modeling context.

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1.1. Definition and Importance

Consider a proposition of the form "If assumptions 1, 2, and 3 hold, then conclusion 4 follows." Mathematical proofs and analyses begin with assumptions and use them as building blocks. Many other fields also use models that begin with assumptions, such as the "agents' preferences are locally nonsatiated" assumption in consumer theory. The importance of assumptions in a context such as this is well known. Everyone knows that many applications will fail to hold the field's hypothesis, but fortunately, the conclusions have been derived under the assumption that the hypotheses do hold. Although assumptions are crucial building blocks in the process of reasoning about the consequences of economic quantities, they are often ignored or dismissed in modern economic practice. These assumptions form the basis for the economic models that economists use to make further predictions or to conduct counterfactual exercises.

The role of assumptions in economic modeling has two related questions: What is the role of assumptions in economic modeling, and how, if at all, should economists' values enter their modeling? I consider the second question in the next section of this paper. In this section, I consider the first.

1.2. Basic Elements of Economic Models

The informal verbal model consists of the description of things or factors within the model. These factors are critical to the model, and without them, the model would not work. These verbal assumptions do not necessarily have to be quantifiable, although it is often useful to have models that yield quantifiable implications. But, the assumption does have to describe something with some level of detail or depth. In other words, the definition has to be sharpened enough that others, our 'audience', can immediately grasp what we are trying to achieve in the model. This, of course, implies that the informal verbal model that constitutes an economic model is not universally applicable. The economic model must operate in a specific context, and that context is crucial in defining the informal verbal model.

The ceteris paribus assumption or the holding factors constant assumption holds that the only force influencing the relationship between two variables under study is the one explicitly identified. This is a very important and all-encompassing idea within economics, and indeed all science.

In more technical terms, every economic model, while not universally applicable, consists of five important elements: a 'ceteris paribus' assumption, informal verbal assumptions, a list of exogenous variables, a set of endogenous variables, and a functional form that relates the exogenous to the endogenous variables.

Economic models are, at an important level, miniaturized and simplified versions of reality communicated through formal or semi-formal mathematics. In many ways, creating models involves choices that we all make each day in communicating about various phenomena that interest us. When we tell a story, we have to simplify it to interact with the ideas of our audience. Economic models do this as well, and in doing so, offer us a language with which to understand and communicate about complex phenomena such as markets, profits, costs, consumer behavior, and so on.

2. The Significance of Assumptions in Economic Models

Paradigms differ, as do the assumptions that lie behind various economic models, tools, and paradigms. In this chapter, we explore the logic of a particular model and the role that its assumptions play. How are we to understand the nature, role, and significance of the assumptions that underlie economic models? There is no single "best" way for economists to approach this central question of model construction and model testing. Nor is there a consensus as to what constitutes a model, even within the economics community. In terms of model structure, model scope, and model application, there is no consistent, unified approach taken by economists for determining "what matters," or about how concepts crucial to the success or power of a particular model ought to be treated.

Clearly, because every model is a simplified representation of reality, the real issue centers on what particular structure makes an assumption useful or essential in one model and not in another. Aren't all models somewhat arbitrary in the sense that assumptions are made and conclusions reached based on those assumptions? Everything depends on the accuracy of the assumptions. After all, no model is really correct. Rather, each model has limiting conditions restricted by its assumptions. If good predictions are obtained under given assumptions, the model is successful. Why then should we worry about the assumptions? The devil is in the small print. If one pays careful attention to the assumptions, the results may not be so unreasonable. Errors in the assumptions are likely to carry over to the policy implications of the model.

2.1. Definition and Purpose of Assumptions

Assumptions matter to us, and hence it is important for us to try to figure out where the problem is. In this section, we will try to understand and explain more carefully what assumptions are and what purposes they are supposed to serve. For a start, let us consider the functions of a few axioms. A basic one of an axiom is supposed to give us those few highly powerful tools with which we can prove a great variety of propositions. They provide the oil without which the mathematical disciplines would grind to a halt.

Neoclassical assumptions also have a methodological role. What we write down initially may be only a very partial or stylized version of the reality we are interested in. The purpose is to define the central elements (that are expected to capture most of the relevant information) of the phenomena being analyzed and their principal interrelationships so that the data, as they become available, can be understood.

As knowledge improves over time, it will usually be necessary to add additional complications or relax some of the restrictions built into the original version of the story in order to obtain a more accurate account of what goes on. The method used by the classical school to study the economic world is essentially the same as that used in Euclidean geometry or in its relativistic extension. First, one makes some uncontroversial assumptions about human behavior or about the world. Then, by unflinching logical rigor and by applying these assumptions, one deduces from them a number of striking and surprising conclusions about the way in which the economic world must be organized.

This approach attempts to understand economic phenomena by combining simple and plausible hypotheses into a logical framework, and then by deducing the conclusions that follow from these hypotheses. That is, it is an axiomatic-deductive method. It is this final characteristic that distinguishes the scientific method of the ancient Greeks from the inductive or statistical methods used in most other scientific traditions.

2.2. Different Categories of Assumptions Utilized in Economic Modeling

The economic model is an abstraction from reality. While its abstract nature implies that it is not entirely 'true' in the sense of accurately representing the intricate state of the world, assumptions play a pivotal role in linking the model to reality. These assumptions serve as the critical building blocks upon which the model is constructed, ensuring that it captures the multifaceted complexities of the real world in a comprehensive and representative manner. By incorporating various assumptions, economists strive to make the model as inclusive and robust as possible, enabling a deeper understanding of economic phenomena and paving the way for more precise analysis, informed decision-making, and effective policy implementation. Connecting the abstract world of the model with the messiness and nuances of reality relies on the formulation of robust relationships that economists structure in the form of assumptions. These assumptions not only give clear content to the model but also provide essential links between its elements and the world, enabling economists to empirically assess and validate the model's applicability. Without these assumptions, the economic model would be devoid of content and provide capricious guidance to understanding and policy, rendering it ineffective in informing decision-making and formulating policies. Furthermore, it is vital to note that assumptions in economic modeling play a crucial role in shaping the outcomes and predictions derived from the model. By meticulously analyzing and considering the validity of these assumptions, economists can further refine the model, enhancing its capacity to yield valuable insights into the complex dynamics of the economic landscape. Through robust empirical assessment and the incorporation of diverse methodological approaches, economists ensure that the model remains comprehensive, insightful, and applicable. Moreover, the connection between the economic model and reality extends beyond assumptions. Economists employ a range of methodologies that encompass statistical techniques, empirical data analysis, and mathematical frameworks to bridge the gap between the simplified model and the intricacies of the real world. These methodologies enable economists to validate and refine the model's predictions, addressing the inherent complexity and uncertainties of real-world dynamics. By utilizing this comprehensive approach, economists ensure that the economic model is not a mere speculation but a potent analytical tool that can guide decision-making and policy formulation with a nuanced understanding of the intricate economic landscape. In summary, assumptions serve as the vital foundation that links the economic model to reality. They provide the necessary structure, content, and logical underpinning to ensure the model's validity and applicability. By acknowledging and incorporating assumptions, economists transform the abstract realm of modeling into a powerful tool that captures the essence of the real-world complexities. With diligent empirical assessment and the use of diverse methodological approaches, economists can constantly refine and enrich the economic model, paving the way for precise analysis, informed decision-making, and effective policy implementation. Thus, the economic model, bolstered by robust assumptions and comprehensive methodologies, emerges as an invaluable tool that empowers economists to navigate the intricacies of the ever-evolving economic landscape and make meaningful contributions to the world.

The general objective of assumptions, then, is to make the basic ideas in the model relevant for understanding important phenomena in the world. In this sense, assumptions fulfill some of the same roles in economic theory as the carefully planned conditions of laboratory experiments or the clear-cut definitions of variables and initial conditions for much of the exclusively data-driven or case-oriented empirical work in the social sciences.

3. The Impact of Assumptions on Model Outcomes

We have seen how assumptions enter into economic modeling, and we have also seen how such assumptions frequently involve beliefs about the behavior of agents in some sense. The purpose of the present chapter is to examine in somewhat greater depth the question of how important the particular set of assumptions used in that exercise actually is to the outcome of a modeling exercise. That is, do different sets of assumptions lead to different conclusions, and if they do, what do these conclusions have in common? Theories of behavior are aspects of each assumption that can be altered. The choice of discrete models that are formed as combinations of particular aspects of these assumptions matters.

The procedures used to form models are always limited. The outcome, therefore, is never going to be an accurate representation of reality. What is represented is, at best, just a collection of some of the facts of interest. Behavioral differences across models may suggest that the model results might be sensitive to the theoretical structure used. At least, that is what Francis Bacon says he would do. Indeed, if substantially different theories reach similar conclusions, then this fact is offered as evidence of the robustness of the result. If models with similar assumptions reach substantially different conclusions, then each claim is called into question. In the absence of further evidence, one would then have to revert to judgment, and only small degrees of confidence would be justifiable.

3.1. Sensitivity Analysis

A basic ingredient of scientific research is sensitivity analysis. This involves examining how outputs respond to variations in inputs. Frequently, there are multiple channels along which the relationship between output variables and input variables can work, and the key question is not simply: what are the values of particular inputs? The key questions are: for what reasons are these inputs important and how tight is the relationship between these and the outputs? Sensitivity analysis provides important insights into the structure of the model and into how a variety of effects might operate.

This is not to argue that the precise values of specific model inputs should be considered to be entirely arbitrary or that the treatment of these inputs should not be based on available evidence to a useful level of precision. However, it would be foolish to shell out for expensive empirical work to refine particular inputs, without sensitivity analysis being undertaken as to how a range of inputs would affect outputs. Such work could be wasteful, revealing a variety of empirical results concerning specific inputs, of which only one precise numerical value is of interest to the modeler, and none shed particular light on the channels along which the range of effects could operate.

3.2. Scenario Planning

Scenario planning refers to the process of identifying the major drivers and major uncertainties about the future, identifying the main scenario, and depicting a few other relevant scenarios to compare possible outcomes. This process may be used in economic models to investigate structural breaks in economic dynamics for forecasting, policy analysis, or to extract the underlying information about future uncertainty contained in economic data. This process is very important in econometric modeling because there is always some end point to research.

Scenarios must be built around major issues and strong forces that are important for model structures. Simply changing some exogenous variables in the model is not equal to this process for revealing structural shifts. In econometric search, serious thought must be put in on what these key driving and uncertainty variables are, how the modeling structure reflects the properties of these variables, and choosing a set of scenarios that could reasonably happen. Forming these scenarios stresses the creativity of econometric modeling.

4. Challenges and Criticisms of Assumptions in Economic Modeling

When we examine economic models or theories, we see that we make assumptions. At times, our models use very strong and restrictive assumptions. These can be necessary and useful. Without the assumptions of the zero profit condition of perfect competition, chaos and disorder in economic life would reign. Yet at the same time, our assumptions can be inadequate and lead our economic models to produce what appear to be results that have little to do with life in the real world. What principles should or do we follow in making assumptions in our models? Be clear about the issue at hand, always ask yourself for what purpose will the theory be used. Take guidance from real-world phenomena, whichever sector of economics, approach (neoclassical, post-Keynesian, and so on) you advocate. Keep the model as simple as possible but no more so. We have no doubt that these are better principles than ones linked to specific contents of assumptions.

One criticism of these guidelines is that they may encourage thoughtless or politically motivated assumptions, that is, neglecting an examination of assumptions are crucial to any economic model. Indeed, there are many popular criticisms of assumptions made in models. Popular wisdom teaches us to "beware of false assumptions". E. Ostrom, a Nobel Prize-winning economist, explained in her Nobel lecture that "it is my belief that one does not enhance understanding by automatically building a plethora of assumptions into models. Unique cases may be unique and may be difficult to pattern to existing cases. A political scientist or economist who maintains that the richness of human beings and their interactions with one another should be ignored most of the time when one builds models in their professional work is making a grievous error".

4.1. Over-simplification

This is the idea that the assumptions necessary to construct a model that can provide insight to a particular question are an oversimplification. By this, we mean that the assumptions inherent in economic modeling are too removed from real-world phenomena for considerations to hold. That is, we cannot make assumptions that are a 'thin' exaggeration of the world and expect the resultant models to hold. Perhaps such oversimplified models have some value as thought experiments that involve unrealistic descriptions of the world to illustrate some qualitative notion, but such exaggerations should not be mistaken for carefully constructed explanations.

Well, yes and no. It is certainly the case that many economic models contain some assumptions that are unrealistic in an absolute sense. But this is not the point. The critical question for any economic model is not whether any particular assumption is realistic. The right question is whether a model is capable of providing insight about some idea. When you put a model aside because you say the assumptions imply that it is severely unrealistic, you are using the wrong criterion for model selection. Your measure for models should not be whether they are realistic in some absolute sense but whether holding a group of assumptions yields insights that are approximately applicable in the world.

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4.2. Ignoring External Factors

Because of the difficulty in simultaneously analyzing the numerous necessary factors in a complex system, the assumption that factors that are held constant or ignored are unimportant or irrelevant is a frequent convenience of many models. The effect of this assumption is to limit the model's relevance to the real world where these ignored associations may exist. This assumption, sometimes called ceteris paribus, is the starting point of any economic analysis and enables the economist to simplify the entire complex world into a sufficiently manageable form so that some reason-based analysis may occur. The result should not be shocking, though. It is the basic point of all models that they only seek a limited understanding.

The separation of external factors from the company of decision-influencing factors depends upon the rest of the model. That is, external factors are devoid of influence on the situation to be analyzed only to the extent that they are ignored in the model. If a particular association excluded from the model is necessary for a complete understanding, then a resultant bias will be identified.

5. Conclusion and Future Directions

In this note, we have examined several key assumptions and their economic importance. A careful examination of these assumptions indicates the deep restrictions on what economic models capture. They suggest meaningful ways to modify economic models, expanding the range of "real world" problems that they can be used to address. Used in this capacity, assumptions provide sharp tools, rather than prison cells, for the economic research process.

Of course, beyond the abstraction necessary when using models per se, these assumptions facilitate value judgments when applied to building models. Desiderata from economic theory are thus a critical component of the model-building process. We have discussed how these desiderata can render straightforward positive analysis considerably more complex. But as a general matter, the presence and impact of these assumptions complicates empirical measurement, testing, and estimation. A deeper understanding of these issues and the many interesting directions for future research that they present is clearly needed. Whether they are direct questions that have been opened here or the kind of curiosity that stimulated the research, economic modeling is a fertile ground for the economist interested in the critical links between nudging and regularity.

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