The most important philosopher of science of the 20th century, Karl Popper, argued that economics was the only social science that had turned into a real science. To him, economics was the queen of the social sciences just as physics was the king of the physical sciences.
But why did he think this? Because economics was, to him, the only social science that engaged in systematically testing hypotheses about how the world works. Doing so is actually much easier if you engage in a lot of mathematical modeling. Why? Because in a math model it is crystal clear what your assumptions are, and also what implications follow from those assumptions.
Thus, you can say: “under assumptions X, Y, and Z, we get outcome B but not outcome A.” That sort of very clear statement allows for experimental science.
You simply go out into the real world and find a situation where X, Y, and Z are happening and see if indeed the outcome associated with them is B rather than A. If it is, then this actual phenomenon is consistent with your hypothesis. That doesn’t mean your hypothesis is right, just that it hasn’t been overturned yet by the facts. And if people go out year after year after year constantly trying to overturn the hypothesis and they can’t, then it gains more credence. It never becomes truth; but it gains credibility and may pass into becoming referred to as a theory or even a law.
On the other hand, if you observe outcome A — the outcome that the model said wouldn’t happen — then you know the model is wrong and that you have to start over trying to find some other model of how things work.
Economics was the social science that most early on embraced math modeling and therefore was the social science that led the way in terms of making very precise, testable predictions that could be compared with the real world to see if they held up. That is why economics got the reputation of being more of a real science than psychology.
To see what I mean, think about any of the Sigmund Freud’s writings. Is it at all clear what his assumptions are? What are his X, Y, and Z? And then, is the logic that he uses to get from his vague assumptions to his often-vague conclusions totally air tight? Not really. And then, are his predictions about human behavior in a given situation very precise? No. So, if we went out to test his “model” against what happens in an actual situation would we be able to? Not at all.
But before I get slammed by sociologists, anthropologists, psychologists, and others, let me say that much has changed. All the social sciences are now very much more mathematical and precise and thus very much more able to produce models that make precise, testable predictions. So these days, I can’t really say that economics is more of a real science than many of the others. But I would say that we were first, and that we led the way, and that that was a very good thing.
Freakonomics has a Q&A with Sean Masaki Flynn, author of Economics for Dummies. The whole thing is interesting but I thought his response to a question about "why is economics considered more of a real science than psychology?" was one of the best explanations of this issue that I've seen. It's a long quote but I think worth repeating:
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