The term “model” can mean many things.
1. To an engineer, a model might be something like a flight simulator. It attempts to replicate actual conditions so well that it can be used to train a pilot who then moves on to operate in the real world. Economists sometimes treat their models this way. Think of models used to forecast the impact of tax changes, or think of Jonathan Gruber’s model used to predict the impact of Obamacare on the health insurance market. In my view, most of the time the accuracy of these sorts of exercises is often far over-stated.
2. In economics, models are often used for a different purpose. The economist writes down a model in order to demonstrate or clarify the connection between assumptions and conclusions. The typical result is a conclusion that states
All other things equal, if the assumptions of this model hold, then we will observe that when X happens, Y happens.
For example, X could stand for “a firm raises its price” and Y could stand for “the demand for its product goes down.”
3. Model failure is usually more interesting than model success.
Suppose that we observe a situation where X happens and Y happens. Does that confirm the model? Because there typically are other models that can explain such a pattern, we usually do not draw strong conclusions based on such evidence.
However, suppose that we observe a situation where X happens and Y does not happen. Does that refute the model? I would say that what it refutes is the prefatory clause “other things equal, if the assumptions of this model hold.” That is, we may conclude that other things were not equal or that the assumptions of the model do not hold.
In my book, I use the example of a college that raised its tuition and experienced a subsequent increase in applications for admission. I do not say that the law of demand fails to hold. Instead, I say that other things were not equal. In particular, the college also raised its level of financial aid. Thus, although its “list price” went up, the discounted price faced by many applicants went down.
The prefatory clause in economic models makes it difficult to draw scientific conclusions from real-world observations. When X and Y occur as predicted, we cannot confirm any one model, because other models are consistent with result. When they do not occur as predicted, we only know that the prefatory clause was violated–the assumptions of the model were not met or other things were not equal.
Often, we cannot say anything very interesting about which assumptions were not met or which things were not equal. For example, the model of an aggregate production function is used to predict that differences in output per worker will be proportionate to differences in capital per worker. When this fails, there are many possible reasons: workers may differ in their human capital; physical capital may not be measured or aggregated correctly; output may not be measured or aggregated correctly; institutional differences may matter. etc.
In fact, the primary use of the aggregate production function model is to examine its failure, which is called “the residual.” Economists place an interpretation on this residual, calling it “total factor productivity.” They interpret the rate of change in this residual over time as “productivity growth.” They interpret the change in the rate of change in this residual as “change in the trend rate of productivity growth.”
Too often though, the model is treated as the reality and reality ignored.
“All other things equal, if the assumptions of this model hold, then we will observe that when X happens, Y happens.”
Right before I read this I was thinking this is more like how engineers usually think of models than like flight simulators. Maybe this recurring analogy is only irksome to other engineers, so if your model of engineering models is effective, carry on as you were.
The problem with engineers is ultimately we have to ship, so that forces us to ultimately relief on the model, but the majority of total effort is in feedback testing and tweaking, in my limited experience.
In the former life, we had numerous models for the consumer product. There was the finished product model that wa used to predict performance. Ther was the model that predicted how the assembly would be formed into the finished product. The design that wedded the two together. There were process models that estimated the effects of the process on going from the build to the finished product. Then the perfirmance models. All these models were always being tweaked with constant feedback, feature upgrades, rebuilds and replacements. I never got the impression that people believed the map was the territory, but you had to have a measure of faith, but everyone was scared.
Arnold, I think you are slowly converging on my views about engineering and non-linear systems. “All other things equal, if the assumptions of this model hold…” is how engineers solve non-linear systems. You restrict enough variables until you have an approximation of a linear/deterministic system. You make assumptions about what variables are critical and what range of values the equations remain valid for.
The early models are always terrible and they fail miserably in unexpected ways in the real world but with each failure you can improve the model. The problem is not with attempting to model non-linear systems, the problem is the assumption that unproven models are deterministic enough to be usefully applied.
A good model captures essential and persistent properties of the system. Almost all models in economics are not models at all. Rather, they are heuristics. They capture in the form more resembling a “rule of thumb” some properties of economic systems holding sometimes under some conditions.
A good model is also good for something – to explain or to predict.
The law of electromagnetic induction is a good model. It operates with well-measured quantities such as currents, electromagnetic fields, properties of materials. And it can explain why a strong magnets slows down its fall in a copper tube https://www.youtube.com/watch?v=lnY9u8TfFKI. This law holds everywhere and every time because it deals with fundamental properties of matter.
Models in economics are heuristics and the laws of economics are not fundamental. For the law of demand to “hold” there needs to be a fundamental process to produce the result. Such fundamental processes do not exist. Good, plausible stories and rules of thumb are not fundamental.
One last thing. A decent airline or hotel reservation system is a well-designed engineering system built around “the law of demand”. A decent reservation system never assumes “all other things being equal”. Rather, it takes “the law of demand” as a good starting point, a story, and attempts to build predictive heuristics and rules of thumb and make probabilistic inferences around it.