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.
Interesting. What's the best study you have, with scatterplots, that shows that the "very old" models performed "very well"? Insofar as we have seen actual quantitative predictive modeling by Keynesians of macroeconomic quantities, the plots tend to look like this:
Neither seem particularly textbook, but you're obviously thinking of something. Given that people who think differently from you invented Bitcoin (and thus have at least a glancing familiarity with advanced mathematics, if the solution of the Byzantine Generals problem means anything) it would be great to see some plots to the contrary. Not just models, but X/Y plots or tables in which Keynesians predict something and nail it. It's not hard, after all to find many examples of Krugman, Bernanke, Goolsbee, or Orszag making quantitative predictions that turned out flagrantly wrong [1].
It's very difficult for me to figure out what you're trying to say here. The first graph seems to be about Obama, the second a time series of the monetary base, and the link in the footnote long statements from random people. Only the last mentions a model, and only in terms of how well it worked[1].
>Given that people who think differently from you invented Bitcoin (and thus have at least a glancing familiarity with advanced mathematics, if the solution of the Byzantine Generals problem means anything) it would be great to see some plots to the contrary.
I don't know what Bitcoin has do do with anything, or what it is being presented as an example of.
>Not just models, but X/Y plots or tables in which Keynesians predict something and nail it.
You're the first person to mention Keynesians, I mentioned economists. If you want to find something that Krugman nailed, though, try the unemployment rate from your first graph.
Ha. Methinks you doth protest too much. But I'll be very precise. Show me the equations and code that Krugman wrote in 2009 that predicted the unemployment curve over the last four years. OMB (full of economists!), to their credit, at least essayed a quantitative prediction. As the first graph showed, it was completely wrong.
So: what "very old" models performed "very well"? You must be thinking of something here. I'm not talking about a Krugman blog post where he says the stimulus was too small. I'm talking about an actual scatterplot, a time series prediction with the X axis as time, the Y axis as the dependent variable, and actual empirical measurements plotted vs. the predictions of theory.
You can see the graph halfway down the page, with theoretical predictions as the red line and actual empirical measurements as the black line. The Nature article admits they don't match well. But in other fields they do match well. For example:
In ballistics the predicted time series match experimental results very closely. So I ask again: what "very well established models" in economics performed "very well"? Which of them nailed the curve?
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.
A classic example of irrationality is mental accounting. Say you are going to the theater. You have a $100 ticket and a $100 bill, and on the way to the theater you lose the ticket. Would you spend your $100 to buy another one? Most people wouldn't, because they would be assigning a $200 cost to the theater department.
Now imagine that you only have a $100 bill with which you are going to pay the ticket, and you lose it on the way to the theater. Would you take out your credit card and pay for the ticket anyway? Most people would.
We know that if people were rational the two scenarios would be identical. But they differ, and this is interesting because we have a framework from which to look into it, and we can see it doesn't fit the framework, and therefore we can infer new and unexpected facts about the economic agents. Models inform in interesting ways how we go about trying to understand reality, even when they are poor predictors.
But those aren't identical. If I lose the $100 bill, I'm out those hundred bucks whether I buy a ticket or not. Whereas if I lose the ticket, I get to keep the money if I don't buy a replacement.
Scenario A: The setup is (1) lose $100, gain 1 ticket (current state is -$100, +1 ticket); (2) lose 1 ticket (current state is -$100, 0 tickets). The choices are (a) lose $100, gain 1 ticket (yields state -$200, +1 ticket) or (b) do nothing (yields state -$100, 0 tickets).
Scenario B: The setup is (1) lose $100 (current state is -$100, 0 tickets). The choices are the same as above.
The final 'state' at the end of each setup is the same, and the choices are the same, so the argument is that a rational actor would make the same choice in both situations. Maybe there's an argument that the state should include more than just $ and tickets though?
This explains a particular heuristic bias, i.e., it's a finding of cognitive psychology. The comment you're responding to talks about whether the mathematical models of economics have any correspondence to reality, and if anything, this finding shows that it's difficult to make such a model (rationality cannot be assumed).
Although that might be true in a roundabout way, I don't think that all models are required to be directly prognostic. Models can be useful without having much predictive power if they nevertheless lend insights into how different concepts (physical entities, energies, presumably something equivalent in economics...) interact, even if only in the idealized model world.
I don't think that's quite true. You create a model not necessarily to predict, but to understand. A good model - which is by definition not intended to be exactly right - helps one to come to insights that can in turn help to come up with predictions that can be tested.
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.
You might be thinking of Carl Sagan's _Contact_. There a set of construction instructions are constructed from first principles using mathematical notation.
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.
I think mathematics at least strives to achieve that goal. But then when I say obvious and trivial I mean it in a mathematical sense: it's obvious and trivial if you understand all of the obvious and trivial groundwork needed to understand how obvious and trivial the idea at hand is.
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.
> 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).
One quibble. Unlike the empirical sciences, mathematics doesn't have to agree with reality, only with the rest of mathematics. Mathematics need only be internally consistent, where successful empirical science theories need to be both internally and externally consistent, i.e. they must agree with established theories* as well as survive reality-testing.
* = Or overthrow them entirely, as relativity did to the ether theory
> This does not mean that better theories will necessarily be simpler.
Yes, true, but Occam's razor favors simple theories, and there's plenty of empirical support for the idea that a simple explanation is more likely to reflect reality than a complex one.
Sorry, when I used "mathematical" in the quoted paragraph I did not mean an actual theorem in mathematics, I meant a scientific theory that involves heavy use of mathematics to describe some aspect of the world.
> Yes, true, but Occam's razor favors simple theories, and there's plenty of empirical support for the idea that a simple explanation is more likely to reflect reality than a complex one.
All Occam's razor tells us is that all else being equal, the simple theory is more likely to be correct than the more complex. I was not objecting to this observation, just pointing out that in only applies when all else is equal. There are some cases in which Occam's razor does not help you; when the problem being modeled is complex enough that you really do need a difficult, complicated model to accurately model it.
I think the big issue that OP has with economics is that it is neither beautiful, like much of pure mathematics, nor particularly grounded in empirical results, so it essentially winds up being a bunch of complexity for complexity's sake. That's the problem, not just the fact that a theory is complex and difficult to understand.
> Sorry, when I used "mathematical" in the quoted paragraph I did not mean an actual theorem in mathematics, I meant a scientific theory that involves heavy use of mathematics to describe some aspect of the world.
Yes, that's different, and for that case, my reply was misdirected. A theory in mathematical physics must certainly acquire empirical support, and must remain falsifiable in perpetuity.
> I think the big issue that OP has with economics is that it is neither beautiful, like much of pure mathematics, nor particularly grounded in empirical results, so it essentially winds up being a bunch of complexity for complexity's sake.
I agree completely, and the consequences are sometimes severe, as when quants use questionable economic theories to make phony risk estimates that backfire.
> That's the problem, not just the fact that a theory is complex and difficult to understand.
Yes, both difficult to understand, and difficult to test in any meaningful sense.
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.
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.