It's like this: once a system is sufficiently complex it is impossible to describe with simple models, and one cannot get an intuitive understanding of its behaviour from staring at two or three equations. Biologists have found this out - living systems have layers of complexity bolted on layer of complexity that have evolved in geological time.
It's immediately obvious that economic systems are the same - the simple models taught to undergrads are simple, elegant - and they don't work to well in practice, their predictive power is limited. The practice of economy needs to change, it isn't that we didn't have the data or the computational power to deal with it.
>the simple models taught to undergrads are simple, elegant - and they don't work too well in practice
Also they have been very ideological for a long time.
The idea that real economic behavior will converge on a particular model as the real actors approach the assumed behavior of the actors in that model is a good way to think about models. The idea that distance from model behavior in real actors will smooth out to insignificance over the long term or at a larger scale is common, but denies the existence of nonlinearities and feedback effects resulting from the interactions between the differences between real behavior and model behavior. The effects of those nonlinearities can (and often do) subsume the model behavior entirely.
Hence, the importance of natural experiments. You can use them to find important deviations and build a new model. Unless you're from the Chicago school, in which case deviations are your cue to start hand-waving and appealing to nature, justice, and the character building nature of hard work.
Some very old and very well established models performed very well during all of the recent economic shocks. What they couldn't do was compete with a bunch of cornpone wisdom about spending within your means that was easily understood by people who have trouble with math.
I took Caltech/Coursera class "Principles of Economics for Scientists" this winter. I was struck by how lean and clear the concepts are once you bother to write them down mathematically. Much better than the hand-wavy explanations I had heard before.
I also took it a step further, and wrote them down as code. When you can explain something to a computer you know you have understood it; and you may even end up with something that other people can understand and play with. I believe something along the lines of what I ended up with (https://github.com/juanre/econopy) might be profitably used to teach economics to CS-type students.
As far as economics math not representing reality: I think it's obvious enough that humans don't behave the way these equations assume. However, they are a great framework from which to think about how humans actually behave.
As far as economics math not representing reality: I think it's obvious enough that humans don't behave the way these equations assume. However, they are a great framework from which to think about how humans actually behave.
There's a problem: the only reason you would build a model is to predict things from it. If the model can't do that for you what you are doing has stopped being science and had turned into something else. Again: if the "framework from which to think about how humans ... behave" can't predict how humans behave in actuality looking at such frameworks is an exercise in futility.
Lately I've developed a distaste for thinking of math as simply a representation of "something real", I'd rather think of it as a language in its own right. I'll just link this here because it explains the point way better than I could: http://onfoodandcoding.blogspot.fi/2013/04/completely-reliab... (the first 5'ish paragraphs especially)
> Lately I've developed a distaste for thinking of math as simply a representation of "something real", I'd rather think of it as a language in its own right.
I remember reading a SF story some time ago (forgot its title and author) where maths is the language of choice between us, humans, and the passengers of an alien ship who had just landed on Earth.
I also dream of other realities (call them parallel universes or whatever) where maths is just different, like for example the real numbers being one and the same as the natural number. It could still be called "maths" even though totally different from "ours", the same as the Basque language is totally different from a "classic" Indo-European language but they serve the same purpose.
Noah's spot on about the tedium and emotional frustration of studying macroeconomics-- of staying up to late hours to learn something that not only may not correspond to real-world behavior, but demonstrably doesn't.
I'll point out that at the University of Michigan, where I believe Noah was before Stony Brook, there's exactly one class available on the philosophy of modeling and economics. And it's for upperclassmen and grad students.
I happen to think this really sucks and that the methods of model construction and model-oriented thinking should happen much earlier in economics study. Is it different any where else?
As Dave Kollat told me way back in 1974, "Micro is trivial and macro is wrong." I went on to study a bit of economics anyway, attending some graduate seminars at Harvard. On one occasion, some grad student held forth "It is axiomatic that ...", whereupon I retorted "It may be axiomatic, but it happens to be incorrect."
My life would actually have been easier had I respected economics. I jumped from math all the way to business or public policy (I wound up as a Kennedy School post-doc); the only assistant professorship I was ever offered was at a B-school (Kellogg); I went to Wall Street instead; and have been in the business world ever since.
Sometimes something is not worthy of your respect! Something I thought was interesting is that the article is basically a rehashing of the Austrian criticism of modern macro. Although the austrians superimpose their own theology as well.
The only way that mathematics should be used to signal intelligence is if you can explain a mathematical idea in a way that makes it completely obvious and trivial. The kind of "signalling" that the author describes in macro (by obscurity and complexity) is the opposite, and it makes me sad.
Hmm. I'm not sure that's the case. Sure, it's preferable, if possible, to describe a mathematical idea in such a way that makes it completely obvious and trivial. But at a certain point, there are some ideas that will not be obvious and trivial; there is a huge amount of foundation which is needed to understand them.
Can Grigori Perelman describe to you his proof of the Poincaré conjecture in a way that is completely obvious and trivial? Well, no, otherwise he probably would have done that. Rather, he explained it as succinctly as possible, in a series of papers totaling about nearly 70 pages of fairly dense math, building on nearly a century of earlier work on the problem.
Does the fact that he was not able to express this completely obviously and trivially mean that he is not brilliant? No. It means that it's a really hard problem, which doesn't have a really obvious and trivial solution.
Now, it's absolutely true that mathematical complexity has nothing to do with how correct a theory is. You can have a complex, difficult mathematical theory that is bullshit, and you can have a complex, difficult mathematical theory that is a damned good approximation of reality (remember, in all of science, we are building models or approximations of reality, so even the best theory is never expected to be "right" in some absolute sense). And likewise, you can have a simple, easily explained theory that is bullshit, and you can have a simple, easily explained theory that is a damned fine approximation of reality.
Part of the beauty of physics is that since you are just studying the most fundamental of forces and interactions in the universe, it's a lot easier for a simple mathematical theory to model it quite accurately. Newton's laws are a damn good approximation of many physical phenomenon that we can observe directly, even if we now know that at large scales and high speeds they are not quite accurate due to relativistic effects.
It's just hard to find that kind of beauty in economics. The systems involved are just so much more complex; remember, you are trying to model not just the a single human, but a complex system of humans operating in both cooperative and competitive ways. So, asking that they boil down theories into something completely obvious and trivial may be asking too much. It may be the case that no obvious and trivial theory provides anything close to an accurate model of reality.
Now, the issue seems to be that there are a lot of theories in economics that are simply not grounded in any sort of empirical evidence at all, and are merely more mathematical manipulations applied to other theories that haven't been well substantiated. And this may be a problem; it's also a problem in physics, where ideas like string theory take hold and lead to complex, opaque mathematical manipulations that seem to be almost entirely independent of any kind of empirical evidence.
This does not mean that better theories will necessarily be simpler. There are plenty of theories in physics which have been well tested which are quite mathematically complex and non-obvious, like quantum electrodynamics.
The problem with economic models isn't that they don't work, or that they're made up.
The problem is that economies, especially on a global scale, are so complex, they can't possibly be modeled with a few equations. To keep things reasonably simple, you need to make assumptions that may or may not be BS.
There's a reason economists, quantitative analysts, and people who come up with economic/financial algorithms often make a ton of money, why the algorithms are very closely guarded secrets, and why hedge funds and banks go to such lengths to develop their models.
Another thing to keep in mind, is that applying math and programming to something so dynamic as human behaviour on a macro scale is very difficult. Scientists and economists employ massive supercomputers, and entire teams of researchers to test their models. Not something that can be taught in an undergrad economics class...
I'm surprised that he compares the quality of economic models with those from physics. No matter the discipline it's still just a model -- with all their strengths and weaknesses. If he liked the rigor of physics in school, why not pursue a career in mathematics with a stronger focus on concepts? I get the feeling that he would enjoy the purity of it. If that lacks practical benefits, theoretical physics might be a good choice.
[+] [-] HarryHirsch|12 years ago|reply
It's immediately obvious that economic systems are the same - the simple models taught to undergrads are simple, elegant - and they don't work to well in practice, their predictive power is limited. The practice of economy needs to change, it isn't that we didn't have the data or the computational power to deal with it.
[+] [-] pessimizer|12 years ago|reply
Also they have been very ideological for a long time.
The idea that real economic behavior will converge on a particular model as the real actors approach the assumed behavior of the actors in that model is a good way to think about models. The idea that distance from model behavior in real actors will smooth out to insignificance over the long term or at a larger scale is common, but denies the existence of nonlinearities and feedback effects resulting from the interactions between the differences between real behavior and model behavior. The effects of those nonlinearities can (and often do) subsume the model behavior entirely.
Hence, the importance of natural experiments. You can use them to find important deviations and build a new model. Unless you're from the Chicago school, in which case deviations are your cue to start hand-waving and appealing to nature, justice, and the character building nature of hard work.
Some very old and very well established models performed very well during all of the recent economic shocks. What they couldn't do was compete with a bunch of cornpone wisdom about spending within your means that was easily understood by people who have trouble with math.
[+] [-] x0x0|12 years ago|reply
1 - (mostly easily and cheaply) run experiments
2 - is described by a stationary distribution, unlike most of economics
[+] [-] juanre|12 years ago|reply
I also took it a step further, and wrote them down as code. When you can explain something to a computer you know you have understood it; and you may even end up with something that other people can understand and play with. I believe something along the lines of what I ended up with (https://github.com/juanre/econopy) might be profitably used to teach economics to CS-type students.
As far as economics math not representing reality: I think it's obvious enough that humans don't behave the way these equations assume. However, they are a great framework from which to think about how humans actually behave.
[+] [-] HarryHirsch|12 years ago|reply
There's a problem: the only reason you would build a model is to predict things from it. If the model can't do that for you what you are doing has stopped being science and had turned into something else. Again: if the "framework from which to think about how humans ... behave" can't predict how humans behave in actuality looking at such frameworks is an exercise in futility.
[+] [-] tsiki|12 years ago|reply
[+] [-] paganel|12 years ago|reply
I remember reading a SF story some time ago (forgot its title and author) where maths is the language of choice between us, humans, and the passengers of an alien ship who had just landed on Earth.
I also dream of other realities (call them parallel universes or whatever) where maths is just different, like for example the real numbers being one and the same as the natural number. It could still be called "maths" even though totally different from "ours", the same as the Basque language is totally different from a "classic" Indo-European language but they serve the same purpose.
[+] [-] unknown|12 years ago|reply
[deleted]
[+] [-] nooron|12 years ago|reply
I'll point out that at the University of Michigan, where I believe Noah was before Stony Brook, there's exactly one class available on the philosophy of modeling and economics. And it's for upperclassmen and grad students.
I happen to think this really sucks and that the methods of model construction and model-oriented thinking should happen much earlier in economics study. Is it different any where else?
[+] [-] CurtMonash|12 years ago|reply
My life would actually have been easier had I respected economics. I jumped from math all the way to business or public policy (I wound up as a Kennedy School post-doc); the only assistant professorship I was ever offered was at a B-school (Kellogg); I went to Wall Street instead; and have been in the business world ever since.
[+] [-] dnautics|12 years ago|reply
Sometimes something is not worthy of your respect! Something I thought was interesting is that the article is basically a rehashing of the Austrian criticism of modern macro. Although the austrians superimpose their own theology as well.
[+] [-] j2kun|12 years ago|reply
[+] [-] cynicalkane|12 years ago|reply
This is the opposite, unfortunately, of academia in general, not just economics.
[+] [-] lambda|12 years ago|reply
Can Grigori Perelman describe to you his proof of the Poincaré conjecture in a way that is completely obvious and trivial? Well, no, otherwise he probably would have done that. Rather, he explained it as succinctly as possible, in a series of papers totaling about nearly 70 pages of fairly dense math, building on nearly a century of earlier work on the problem.
Does the fact that he was not able to express this completely obviously and trivially mean that he is not brilliant? No. It means that it's a really hard problem, which doesn't have a really obvious and trivial solution.
Now, it's absolutely true that mathematical complexity has nothing to do with how correct a theory is. You can have a complex, difficult mathematical theory that is bullshit, and you can have a complex, difficult mathematical theory that is a damned good approximation of reality (remember, in all of science, we are building models or approximations of reality, so even the best theory is never expected to be "right" in some absolute sense). And likewise, you can have a simple, easily explained theory that is bullshit, and you can have a simple, easily explained theory that is a damned fine approximation of reality.
Part of the beauty of physics is that since you are just studying the most fundamental of forces and interactions in the universe, it's a lot easier for a simple mathematical theory to model it quite accurately. Newton's laws are a damn good approximation of many physical phenomenon that we can observe directly, even if we now know that at large scales and high speeds they are not quite accurate due to relativistic effects.
It's just hard to find that kind of beauty in economics. The systems involved are just so much more complex; remember, you are trying to model not just the a single human, but a complex system of humans operating in both cooperative and competitive ways. So, asking that they boil down theories into something completely obvious and trivial may be asking too much. It may be the case that no obvious and trivial theory provides anything close to an accurate model of reality.
Now, the issue seems to be that there are a lot of theories in economics that are simply not grounded in any sort of empirical evidence at all, and are merely more mathematical manipulations applied to other theories that haven't been well substantiated. And this may be a problem; it's also a problem in physics, where ideas like string theory take hold and lead to complex, opaque mathematical manipulations that seem to be almost entirely independent of any kind of empirical evidence.
This does not mean that better theories will necessarily be simpler. There are plenty of theories in physics which have been well tested which are quite mathematically complex and non-obvious, like quantum electrodynamics.
[+] [-] losethos|12 years ago|reply
[deleted]
[+] [-] Mikeb85|12 years ago|reply
The problem is that economies, especially on a global scale, are so complex, they can't possibly be modeled with a few equations. To keep things reasonably simple, you need to make assumptions that may or may not be BS.
There's a reason economists, quantitative analysts, and people who come up with economic/financial algorithms often make a ton of money, why the algorithms are very closely guarded secrets, and why hedge funds and banks go to such lengths to develop their models.
Another thing to keep in mind, is that applying math and programming to something so dynamic as human behaviour on a macro scale is very difficult. Scientists and economists employ massive supercomputers, and entire teams of researchers to test their models. Not something that can be taught in an undergrad economics class...
[+] [-] omn1|12 years ago|reply
[+] [-] xanth|12 years ago|reply
[+] [-] tunesmith|12 years ago|reply
[+] [-] losethos|12 years ago|reply
[deleted]