Model Building: A Primer

Model building as a research tool has long flourished in the physical sciences, and has led to enormously powerful insights. More recently, with the advent the high-speed computer, model building has taken root in the social sciences as well. Indeed, a model is early obligatory in the usual doctoral insertation in economics (and increasingly in the other social sciences too).

What are models? How do they differ from each other? What is their purpose, and how well do they fill it? Any flow chart or schematic diagram can be called a model since it is intended to show how two or more parts of a whole are related. Economists have used models for some time (though not always by that name) as a method of theorizing about the particular type of human behavior they were studying. Such models differ in marked degree from the highly complex structures built today—but the difference is in degree, not in kind. Modern models use much more real-world data, and include a vastly greater number of variables than, example, Keynes's simple representation of the consumption function—with. its vertical axis showing income and its horizontal axis showing demand.

To define the term model is almost impossible, since it is used so loosely to cover so many different constructs. Wasily Leontief, the father of one well-known kind, the input-output model, defines the term as "essentially a theoretical construct," which starts with some "actual or hypothetical data to arrive at some interesting empirical conclusions." In his chapter in William Vogely, ed., Mineral Materials Modeling: A State-of-the-Art Review.)

Clearly there is room for a great many different kinds of constructs under this definition. Even so, it fails to include a whole class of models with which laymen are most familiar—physical models—such as children's model ships and airplanes. Physical models have also been extensively used in science and engineering research, on subjects ranging from the study of aeroplane fuselage shapes to America's Cup hull designs under different wind and wave conditions. Social scientists some-times construct physical models too—of a region or an urban area, perhaps—but most social science models are of the intangible, conceptual variety that Leontief's definition covers.

But what is their purpose: Why should models be constructed at all? The reason is that the reality of human behavior is too complex to be studied in place. Even the most complex relationships observed in the study of inanimate matter are simple compared with those involved in any single aspect of human behavior. To even begin to deal with the material, the social scientist must limit the number of variables or observations he deals with to the "most significant" ones; he must limit himself in time and space, and perhaps use only a sample to represent a whole class. But first, of course, the problem to be solved must be defined.

Suppose we were concerned with the fact that wilderness areas in this country, which were established in part to provide a wilderness experience for those who wished to have it, were being so overrun with campers, hikers, and riders in the peak season that the experience of being "alone with nature" was totally lost. How would we go about giving sufficient information to forest managers to allow them to solve this problem intelligently.

We might start by listing the kinds of variables we thought were significant, and we might define significant variables as those which affected "encounters," that is, people who wished to be alone, unwillingly meeting other people of like mind. This encounter variable would be the variable which all the other interacting variables would influence. On this assumption, the number of hikers, campers, and riders admitted to the area in each hour of each day of each week of each season (already twelve variables) would be first. Then the number of trails, their length, and their distance from each other must be considered. But how far can we go in this list? Clearly, the inclusion of what is or is not significant is a subjective (intuitive) decision. But beyond that, after the variables to be considered are decided upon, comes the collection of data. Immediately, we are confronted with the fact that there are hundreds of wilderness areas. Which ones can we consider average (we have no time to collect data from all of them)? And for how many years must we collect data, to feel that we have "average" seasons?

All these decisions—and many more—must be made. And then, with the vast amount of data accumulated (if we are lucky enough to obtain all we need) we must construct the right kind of model for our purposes. How do we choose?

A readers' guide or taxonomy of models can be constructed on several bases, just as can a taxonomy of flowers. One can classify a model by (1) its intended use; (2) its subject matter; (3) how it handles time; (4) its intended closeness of fit to the outside world; (5) the techniques used to construct it; and in other ways as well.

Under the first method of classification—by intended use—we would have subclasses based on the answers to certain questions. For example: Is the model descriptive? Input-output models are of this type, as are simulation models and behavioral models. Descriptive models are basically designed to show how the parts (variables, usually) in a specific activity or process fit together, and how they would fit together if some of the parts were changed. If the model is intended to be used for management purposes or to develop policy, we would want something more than this: we would want to know the "best" or "optimal" alternative. Models designed to show this are called optimization or normative models, of which linear programming models are a subvariety. The kind of problem that a linear programming model can solve is shown in the accompanying illustration.

To recapitulate, if models are classified by use, they can be described as trying to do one (or more) of three things: first, simply to classify the variables (the data) and show how they relate to each other; second, to predict on the basis of these interrelationships how the variables will behave when one or more of them are changed; and third, given the observed interrelationships of the variables, to determine the best way of combining them, or changing them, to achieve some desired result. Many models can be modified to do all three of these things. The wilderness travel simulation model may simply be used to show how many people use how many trails at what hours and what days and what seasons in a particular wilderness area. Or, using much of the same data, the model may be used to predict how many people would use the wilderness area if there were fewer trails, or if the season was extended, or curtailed. And finally, if one wished to establish some kind of norm—to say, for example, that the wilderness experience demands that only X number of people be on any one trail at any one time, then one could build this value into the model. In short, using the same data, a simulation model can be converted to a normative model.

When classifying models by subject, one refers to energy models, materials models, ecological models, industry models, fiscal policy models—in short, to whatever subject areas they are intended to elucidate. These models may fall into any of the other classifications as well.

A third classification could be based on whether the model is concerned with an equilibrium situation or one that changes over time. Accordingly, the model is described as static or dynamic (there are in-between types also). These models will also have designations in one or more other categories.

Using the fourth method of classification, models that are intended to fit as closely as possible to the outside world are called empirical models. There are many kinds of empirical models, including all the types mentioned earlier. In contrast, theoretical models are developed to see how the parts of a model can be fitted together. Here, the main effort is on the inner workings of the model itself. In the actual world of modeling (rather than in this limited "model" of modeling) the varieties are often blended together. An empirical hypothesis becomes abstracted into a theoretical model; once a firm theoretical understanding of the conceptual parts of the model is achieved, the model is recast as an empirical model—to be fitted against the data. The back and forth process can happen many times, and the steps to and from modeling abstractions are efforts to come closer to the outside reality, which is too complicated to be perceived directly.

One way to describe the empirical—theoretical model relation is to look at an example in the physical sciences rather than the social or behavioral sciences. Consider an aircraft designer who designs a new wing to enhance airplane performance. Assume that cost considerations make it impossible to build an entirely new airplane to fit the wing. To determine how the new wing could be fitted to existing planes, the designer might take the following steps:

1. Abstract what he considers the pertinent aerodynamic and mechanical properties of an existing airplane and arrange these data to indicate the inter-relationships among them. This would be an empirical (conceptual) model-4 simplified version of the actual inter-relationships of all the properties in the real airplane.
2. Substitute the properties of his new wing design for those of the wing the empirical model, and observe how these new properties would theoretically affect the interrelationships of the other properties. This would now be a theoretical model; it may bear no relationship to reality, since the new interrelationships are no longer even a simplified version of the real properties of an existing airplane.
3. Build a small-scale physical model, based on the new interrelationships, and test it in a wind tunnel.
4. On the basis of the results, go back and adjust the model—and again test it with a small-scale physical model.

In social science, the problem is more difficult, since no physical models can be built to test the theoretical, model. Instead, the modeler tries to find some hypothetical implications of his model that can be tested by referring to real-world conditions. His new empirical model, however, cannot be as satisfactory as a physical model, since no matter how close to the real world he gets, he may never learn for certain the model actually "works."

Finally, models are often described in terms of the techniques used to construct them. Social scientists use the term mathematical model to describe models whose content is numerical. Most economics models are of this type. One technique often used in empirical economic models is econometrics, a, branch of statistics especially developed to handle problems frequently encountered in economic modeling. Econometric models are, therefore, rather common. Linear programming models (see illustration) are also mathematic in this sense. An input-output model so called because of the way the data are displayed in tableau form. Both input-output and linear programing models use the mathematics of algebra.

All of these types of models have other properties which assign them one or more of the classes previously mentioned.

This is by no means intended to be an exhaustive list of all the names given to models. It merely classifies some the more common ones and gives some idea of where to place the others. For example, an "environmental" model to clearly being classified by subject; a "management" model is just as clearly being classified by end use.

How well do models do the job they were intended to do? This might depend on how complex the job is. Some models are almost as simple as the folded paper airplane; others achieve the complexity of the full-scale prototype airplane—and of course some are greatly more complex than that. To the extent that the model builder can avoid or overcome major difficulties, he will often construct an extremely useful tool in explaining a complex real-world set of relationships. On the other hand, there are often disappointing failures, ror a variety of reasons.

The essential difficulty is that models cannot be one-for-one maps of reality; they must omit much of the detail in the hope of identifying the most important parts and relations among parts. Obviously there are dangers in this attempt. If the purpose is to understand something not well understood in the first place, how does one know which are the less important details to be suppressed which are the relationships to be built into the model? This is where much of the art (and abuse) of conceptual model building comes in. But there are other problems in social science model building due to the enormous number of variables that studies of human behavior must contend with. The economists solve this problem by some kind of statistical averaging, but this in itself can abstract from reality in an undesirable way. Leontief (ibid.) says, ". . . biologists . . . sometimes have five or six hundred thousand variables, and . . . they are not permitted to average. Each variable has its name; each has its address. It is like dealing with a telephone book. . . . If you average, you kill it, because ultimately you must give individual addresses. It is no use sending something to an average address. Some people do—but very seldom does the letter arrive."

Partly because of the complexity and quantity of data, most models that are constructed deal with only one small segment of the world. RFF's study of energy modeling, as its name implies, deals only with variables that model builders consider of direct significance in energy studies. But, of course, energy problems are related, and sometimes significantly related, to a great many other resource problems (and, indeed, to problems well beyond the resource field). In limiting modeling efforts to individual resource problems, much less may be accomplished than is hoped for. For example, in the wilderness travel simulation model, the number of airplanes flying over the area was not introduced into the model as a variable. Yet, this could clearly affect the quality of the wilderness experience.

Again, as Leontief puts it: ". . . one of the practical uses, in economic and social fields, of models is to design policies to recommend actions. From what I observe reading newspapers in Cambridge about Washington, what happens very often is this: you have an oil problem so you build an oil model, on the basis of which you prescribe your oil actions. Then you have a food problem; you set up a food commission. It has a food model; it prescribes action. When you have a copper problem, again you have a separate model. Essentially, you build a separate model for each type of trouble you have. And then, mind you, you design policies based upon that particular model.

What happens usually is: the immediate objective of a policy is realized, because most obvious things you can solve really without a model, and model just sounds better. But the secondary effects of one policy very often . . . clash with a primary effect of another policy. You solve your price problem, and you get an employment problem. You solve your fuel problem, but you get into metal production problems . . . you have not enough energy; and so on.

My feeling is that the main purpose of a model (or a very important purpose) is to introduce consistency in our actions, so that we do not come to cross purposes. . . ."
Perhaps the greatest inhibitor of the future development of models is the unavailability of data, and the unreliability of much of the data we do them.

Model builders are hindered not only by the degree to which they can choose the most significant variables, but also by the degree to which they can successfully generalize from the poor data available to them. Model building is still—rightly—called an art.