Immaterial Models: How Models in Economics might Fail
by Shaun Terry
Boumans aims to assuage concerns over the appropriateness of models. He wants to draw a clear distinction between theories and models, and that seems appropriate enough to me. However, I have questions that I am not sure he answers here.
First off, on pg. 265, Boumans informs us: “The relation of a dynamical model to the system of which it is regarded as the model, is precisely the same as the relation of the images which our mind forms of things to the things themselves.” It may be similar in some sense to how our eyes form images to represent reality, but there are surely many differences. Notably, we generally do not have to concern ourselves with whether or not we can rely on the images we see. Of course there are exceptions, but there is generally no need to continually test the abilities of healthy eyes to produce reliable images. This seems generally different from the case of models.
On pg. 262, Boumans explains that models are meant to provide us with a mathematical middle ground between oversimplifying to the point of losing track of the reality we aim to explain and overcomplicating the model to the point of discouraging critical inquiry into the accuracy of the model. I think that this is a mistake.
Here is the problem that I see: if a theorist can be convinced that they need not concern themselves with accurately explaining the reality of phenomena, this discourages possible progress, i.e. why move forward if we can be satisfied with apparently close approximations? If the point is not to get closer to realism, then why persist?
Then, on pg. 263, Boumans states, “In other words, to the extent that two physical systems obey laws with the same mathematical form, the behavior of one system can be understood by studying the behavior of the other, better known, system. Moreover, this can be done without making any hypothesis about the real nature of the system under investigation.” I see a few problems with what Boumans has to say here. First off, he assumes that some physical systems might obey laws with certain mathematical forms. He may be right, but his assertion here depends on that and he does not seem to prove the assumption true. Worse, when he describes how we can understand one system by virtue of understanding the other, in what way does he mean for us to understand the yet unexplained system? If he means anything beyond the fact that they appear to produce outcomes that are predictable by the same formula, he does not seem to show us how. If he does not mean anything beyond that the formula is predictive of outcomes, then what is his point? Is he saying that we should assume that the systems share commonalities because they produce the same patterns? If he is, then why? Finally, Boumans seems to assert that we can understand the behavior of the system being explained without making a hypothesis about the nature of the system, but how? If he means to say that we can predict the outcomes, then this merely seems to be a tautology: If we observe a pattern in outcomes, we can model the pattern to predict the pattern of outcomes. If, by “behavior,” he means something more essential to the system, then I do not see how he explains this.
On pg. 266, Boumans quotes Boltzmann (1892  pg. 9): “It seemed that nature had built the most various things on exactly the same pattern; or, in the dry words of the analyst, the same differential equations hold for the most various phenomena.” What does Boltzmann mean here, when he says that nature “seems” to do this? Does he mean that nature might or might not? Or are we right to read that Boltzmann thinks that the systems built on the exact same patterns seem “most various?” When Boltzmann attributes the second half of his statement to the dry analyst, what he says stands on firmer ground, and I find this part to be more egregious.
How do we know that these equations hold for the most various phenomena? How do we know that any equation holds for any phenomena? The theorist may be tempted to assert something like, “Well, very many phenomena seem to be consistent with equations that we attribute to them, so surely some of those appearances must reflect actual reality,” but is this not simply the makings of Popper’s infinite regress? Of course I am not so naïve as to suggest that nothing we discover could ever count as progress or knowledge, but I think it important that we take steps to acknowledge the limitations in our ability to discern any such thing.
Later, on pgs. 272 and 273, Boumans explains that mathematical models in economics are meant to help see reality, but I would argue that these models are limited. One problem arises as economists suppose to better understand economic behavior by closely inspecting the model. If we concede that the model need not be able to explain the mechanics in order to make predictions, then the economist who looks at the model in order to try to understand economic behavior can only do so in a particular arrangement of conditions. To repeat, if Boumans means that models somehow explain the mechanics of the system and can, therefore, predict behaviors in various conditions, I do not find his explanation here.
It seems to me that the recognition of patterns from one area to another can create distortion——it may be too tempting to stand pat, even if only temporarily, with a “close enough” approximation that seems apparent. It seems to me that this could lead to confirmation biases separate of the confirmation biases that are already likely. In this sense, there may be an advantage in developing a theory or model from observing the phenomena directly, even if there might be less efficiency in doing so. That is to say that there is a tension between rigor/potential precision and ease of exposition.
Also, as before, I take issue with the idea that trying to make predictions, without explaining why the predictions might work as they do, should be a wise thing. For example, if we do not try to explain the mechanisms underlying a phenomenon as best we can, then I believe that we are less likely to be able to predict what might happen given a shock to the system.