A good model makes the right strategic simplifications...mathematics turns out to be a very efficient way to express the structure of a simplified model and it is, of course, a marvelous tool for discovering the implications of a particular model...the mathematics in these models is almost never deep. There are exceptions, of course. Nevertheless I venture the estimate (safe because it is unverifiable) that there is little or no correlation in fact between the difficulty or mathematical depth of an economic model and its value as science.
...The interesting question is why...model-building took over as the standard intellectual exercise...technique and model-building came along with the expanding availability of data, and each reinforces the other. Each new piece of information about the economy, especially if it is quantitative information, practically sits there and begs for explanation. Someone will eventually be clever enough to see that it is now feasible to construct a model. Reciprocally, alternative models have to compete on some basis. They are not usually fancy enough to compete on the basis of elegance or depth or the intellectual equivalent of pectoral development. They compete on the basis of their ability to give a satisfying account of some facts. Facts ask for explanations, and explanations ask for new facts.
I would remark parenthetically that this experience with model-building may explain my willingness to challenge the consensus on global warming. As an economist, if you keep your eyes open, you tend to learn something about what can happen when you combine prior beliefs, simplified models, and data. Climate science is an exercise in model-building, and I think that economists have a lot of model-building experience that is relevant.
Based on my experience, I would say that the pressure to create a "consensus" forecast for climate change is absurd and counterproductive. All of the important action is in the tails of the distribution--the events that have a relatively low probability of occurrence. I do not care whether the consensus thinks that sea levels in the year 2200 will be 25 centimeters higher or 30 centimeters higher. Instead, I want to know about what sequence of events could lead to sea levels that are higher by 4 feet by the year 2025, how likely or unlikely is that sequence of events, and how soon one could detect that sequence starting to occur.
Changing the subject to macroeconomics, Solow writes,
The textbook writers before 1940 had neither the theory nor the data required to give a coherent account of macroeconomics as part of the core of the subject.
Keynes more or less invented macroeconomics. He was not much of a model-builder himself, but he opened up a gold mine for those who came after...
The General Theory was and is a very difficult book to read. It contains several distinct lines of thought that are never quite made mutually consistent. It was an extraordinarily influential book for my generation of students...but we learned not as much from it - it was, as I said, almost unreadable - as from a number of explanatory articles that appeared on all our graduate-school reading lists. These articles reduced one or two of those trains of thought to an intelligible model, which for us became "Keynesian economics."
I think it is worth emphasizing that Keynesian economics did not emerge fully-hatched from The General Theory. It took decades to create a logical framework for Keynesian macro. In the meantime, the notion that deficit spending might be used to fight a recession was based mostly on intuition. This is very much on my mind, having just read a pre-publication version of Amity Shlaes' illuminating new history of the Great Depression.
In the nature of the case it will often happen that two quite different models can fit the facts just about equally as well. No doubt the right way to proceed is to think of circumstances in which the two models give widely different predictions and to look around for real-life situations that offer the opportunity to discriminate between them. But that may not be possible...So naturally the temptation becomes irresistible to compete by adding variables, making slight changes in formulation, looking around for especially favorable data, and otherwise using the tricks of the trade. It can become very difficult ever to displace an entrenched model by a better one. Clever and motivated - including ideologically motivated - people can fight a rearguard battle that would make Robert E. Lee look like an amateur.
In the late 1980's, the controversies in macroeconomics more or less ended in a stalemate, because each side had learned how to make its model fit the data. Models with totally opposite microfoundations and policy implications could be shown nonetheless to be "observationally equivalent."
Finally, after defending model-building, Solow offers this explanation of how mathematics can go overboard.
There is a tendency for theory to outrun data. (This includes statistical theory as well as economic theory.) Theory is cheap, and data are expensive...
In economics, model-builders' busywork is to refine their ideas to ask questions to which the available data cannot give the answer. Econometric theorists invent methods to estimate parameters about which the data have no information. And, of course, people are recruited whose talent is for just these activities, whose interest is more in method than in substance. As the models become more refined, the signal-to-noise ratio in the data becomes very attenuated. Since no empirical verdict is forthcoming, the student goes back to the drawing board - and refines the idea even more.
In my recent post on graduate study in economics, I made a suggestion that students take an in-depth look at an applied topic, and that writing books should be valued more highly than it is today, with journal articles valued somewhat less than is the case today. It may be a stretch, but I would draw support for this view from what Solow says here:
there is a lot to be said in favor of staring at the piece of reality you are studying and asking, just what is going on here? Economists who are enamored of the physics style seem to bypass that stage, to their disadvantage.