I was expecting to hate Tim Hartford's piece, which essentially says that the math in economics "feels wrong" for the subject.
But I liked it! He's right. Today's economics does invest a lot of its mathematical effort in the wrong stuff.
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But I liked it! He's right. Today's economics does invest a lot of its mathematical effort in the wrong stuff.
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https://twitter.com/IsabellaMWeber/status/1971292262874370221
To take an example from the graduate curriculum, we spend a lot of time dealing with fixed points in large models (dynamic, stochastic, etc.)
But most students taught our toolbox could say nothing useful about how to model whether agents can find these equilibria.
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But most students taught our toolbox could say nothing useful about how to model whether agents can find these equilibria.
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Some famous work in computer science, e.g. by Daskalakis and Papadrimiou, has studied the complexity of finding equilibria in games and markets.
But economics has not absorbed much from the methods or concepts used in this work, and has mostly shrugged off the whole thing
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But economics has not absorbed much from the methods or concepts used in this work, and has mostly shrugged off the whole thing
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Phase transitions/emergent properties are a very important idea in network theory, which is one of the most exciting areas of economic theory.
But most economists regard the math behind all this as exotic - the vibes are that this stuff is weird/different
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But most economists regard the math behind all this as exotic - the vibes are that this stuff is weird/different
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To be clear, economics is not closed to these ideas. In each case discussed above, and many like it, economists have published papers using these "offbeat" methods.
But the mainstream toolkit in economics is not seriously expanding in any of these directions.
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But the mainstream toolkit in economics is not seriously expanding in any of these directions.
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If the math used in economics were more influenced by the other successful "applied math" fields (computer science, physics, mathematical biology) it would look different, and would, in my view, be much better.
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There's an argument that people like Hartford should be ignored, because they weren't smart enough to understand the math.
It's true some parts of his argument, like the skepticism about constrained optimization, are silly.
But the overall vibes of his argument are right.
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It's true some parts of his argument, like the skepticism about constrained optimization, are silly.
But the overall vibes of his argument are right.
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We need to be a little less conservative and have a toolkit that looks less like Bourbaki and more like modern statistical mechanics, computer science, statistical learning theory, etc.
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