Math without beauty or truth
noahpinionblog.blogspot.com.au
noahpinionblog.blogspot.com.au
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.
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.
http://affordablehousinginstitute.org/blogs/us/wp-content/up...
And the independent variables of course tend to like this:
http://m.research.stlouisfed.org/fred/series.php?sid=BASE&sh...
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].
>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.
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.
Here is another example from a different field:
http://www.nature.com/news/climate-change-the-forecast-for-2...
http://www.nature.com/news/499139a-i2-0-jpg-7.11335?article=...
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:
http://physics.info/projectiles/practice.shtml
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?
1 - (mostly easily and cheaply) run experiments
2 - is described by a stationary distribution, unlike most of economics
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.
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.
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.
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?
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.
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?
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.
This is the opposite, unfortunately, of academia in general, not just economics.
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.
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.
> 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.
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 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...