Economics Has a Math Problem

http://www.bloombergview.com/articles/2015-09-01/economics-has-a-math-problem

by gedrap • 11 years ago

169 195 11 years ago

chrismealy• 11 years ago

If economists could manage to get themselves thought of as humble, competent people on a level with dentists, that would be splendid.

Gibbon12• 11 years ago

My beef is when I read economists claims about perfect markets I think, 'Wow! With markets I should be able to solve the traveling salesman problem in polynomial time'

dmichulke2• 11 years ago

Well, I am not a big fan of today's "more debt, more gov't spending = more prosperity" but markets only parallelize a process and the best ones at this process survive while the worse ones drop out of the market.

So, in a sense, if you assume ideal markets to have an "infinite number of participants", then yes, you can solve TSP in polynomial time but otherwise they will just evolve like bitcoin miners which as of yet still didn't solve the "find a decent hash" problem an order of magnitude faster even though there are many of them.

My beef with economists is that they themselves are not subject to markets so the bad ones and the good ones survive and you end up with lots of noise.

Hermel• 11 years ago

Actually, calculating equilibrium prices of markets is PPAD-hard (similar to NP-hard, but not quite) in general. See for example http://arxiv.org/pdf/0904.0644.pdf

triangleman• 11 years ago

Really, because I always think of dentists as inflating their own professional stature in order to promote their supposedly indispensable remedies, much like economists.

atmosx• 11 years ago

There are several problems with social sciences not just economics. Recently, I've read an interview by Yanis Varoufakis[1]. Here's an interesting excerpt:

---

Mariana Mazzucato, University of Sussex – How has the crisis in Greece (its cause and its effects) revealed failings of neoclassical economic theory at both the micro and the macro level?

Varoufakis: The uninitiated may be startled to hear that the macroeconomic models taught at the best universities feature no accumulated debt, no involuntary unemployment and, indeed, no money (with relative prices reflecting a form of barter). Save perhaps for a few random shocks that demand and supply are assumed to quickly iron out, the snazziest models taught to the brightest of students assume that savings automatically turn into productive investment, leaving no room for crises.

It makes it hard when these graduates come face-to-face with reality. They are at a loss, for example, when they see German savings that permanently outweigh German investment while Greek investment outweighs savings during the “good times” (before 2008) but collapses to zero during the crisis.

Moving to the micro level, the observation that, in the case of Greece, real wages fell by 40% but employment dropped precipitously, while exports remained flat, illustrates in Technicolor how useless a microeconomics approach bereft of macro foundations truly is.

----

I really don't know at what level of complexity someone must settle, in order to have a viable mathematical model to predict financial crisis... How many variables do you need? Then again a lot in economics depends on 'perception'. A FinMin will never discuss devaluation of his currency, the moment he does... The currency will drop. How can a mathematical model 'predict' such behaviours?

[1] https://theconversation.com/varoufakis-in-conversation-with-...

yummyfajitas13• 11 years ago

This interview is almost incoherent.

Note the contradiction: "no involuntary unemployment and, indeed, no money" followed by "real wages fell by 40% but employment dropped".

The latter statement only contradicts Keynesian economics, which don't have relative prices (Keynesian economics has only real and nominal dollars of GDP) and uses money combined with sticky prices to explain involuntary unemployment.

But although in one sentence he seems to think the Greek experience contradicts Keynesian economics, he turns around and appeals to Keynesian economics a few minutes later: "the 3.5% primary target for 2018 would depress growth today".

tP5n• 11 years ago

Why would a self-described 'erratic marxist' even be concerned about contradicting Keynesian economics?

bildung• 11 years ago

Note the contradiction: "no involuntary unemployment and, indeed, no money" followed by "real wages fell by 40% but employment dropped".

That contradiction quickly dissolves once you see that he first he talks about macroeconomics as taught in the university ("no involuntary unemployment and, indeed, no money") and then about microeconomics ("real wages fell by 40% but employment dropped").

crdoconnor12• 11 years ago

The latter statement only contradicts Keynesian economics

Uh, no, it contradicts neoclassical economics. Keynesian economics views unemployment as a deficit of aggregate demand and most CERTAINLY does not pretend that it doesn't exist.

But although in one sentence he seems to think the Greek experience contradicts Keynesian economics

A quick skim suggests he doesn't contradict Keynesian economists.

Probably he contradicts new keynesian economics somewhere, but then again, New Keynesian is an abortion that would have Keynes turning in his grave.

yk2• 11 years ago

Actually, Keynes called his book General Theory precisely because it included unemployment, in the context of Keynesian economics usually called the output gap. So "no involuntary unemployment and, indeed, no money" is a insult from a Keynesian against neo-classic models.

Second, "real wages fell by 40% but employment dropped," this is precisely what a Keynesian expects. The core insight of Keynesian economics is, that the employees are also the consumers, so that falling prices lead to falling demand.

Gustomaximus• 11 years ago

In my macro economics studies we absolutely included involuntary unemployment in models, this in itself broken into different forms like frictional vs structural unemployment. Similar inclusions for debt and pricing. As for crisis, then what are macro economic stress tests? Economists can be a overly theoretical in places, they have to be in a world of unlimited and often irrational variables, but this is a bit simplistic.

I have quite admired the way Yanis has handled his brief position in Greece. He's clearly an intelligent big picture thinker that was out to serve his peoples interests. This quote seems out of context to my expectations of his usually we'll considered statements. I wonder if there is some loss or context or other soundbite missing here.

niklasni12• 11 years ago

The Danish ministry for Finance has an official macroeconomic model that is used to evaluate policies.

To the best of my knowledge, it includes a small (I think fixed) amount of structural unemployment but anything else is assumed to be transient. We might have some unemployment now, but it's always assumed to right itself after a few years.

asgard10246• 11 years ago

I think, if you want to truly understand where Yanis Varoufakis is coming from in that comment, read the book Debunking Economics by Steve Keen. Although Varoufakis is probably even more critical to economic theories than Keen, the two guys agree a lot and admire each other.

Besides, Keen (and other postkeynesians) truly shows how the mathematical economics should be done, that is, by having a fully dynamic macro models with time and debt/money. I am afraid machine learning the article talks about is a similar distraction as econometrics. Unless mainstream economists will be willing to rework the theoretical foundations (give up on equilibrium, at least), and base it more on empiricism, mathematical approach, no matter how fancy, will always be a quandary.

But as other have said, the problem is that many economists are pretty much the prophets of the free market (or status quo in general). If you want to somehow claim a moral basis of society, then you can't have a model which allows multiple different solutions, and so you need to stick to equilibrium instead of allowing a dynamical solutions.

pdkl95• 11 years ago

I like Mark Blyth's brief summary[1] of this problem. Not only is it important to base your theories on actual data, it is also vitally important to remember that the map is not the territory. All models are an imperfect representation of reality, so they should always be viewed with appropriate scepticism, even when the math seems to work out elegantly.

[1] https://www.youtube.com/watch?v=hmWbkPezgtU

georgeglue1• 11 years ago

Pure economics should be about applying abstractions to help us understand the world. The world is pretty sophisticated, so I'm fine with mathematically sophisticated abstractions. Even when those abstractions fail intuitively, they can be useful and extended for other subareas of economics or are simply philosophically fascinating. More often than not though, a lot of prominent theory seems impracticable or intractably limited. This is a valid criticism.

Noah Smith is slightly misdirecting his complaints though. If we're looking at applied economics or policy, the amount of math is not intimidating to anyone who has taken a couple of years of non-introductory statistics. The most important econometrics papers of the past few years apply basic regressions with only a few additional valid statistical techniques.

runarberg• 11 years ago

I'd think economics should be about describing systems in terms of cost, and finding how much a certain action will cost or profit the system. There is tons of economy to be found in the natural world, and it is mostly shunned by economists, and left to the naturalists. I don't know of any other science that ignores the natural world like that. And yes I see a problem with that. The probability of being wrong becomes huge. What good is an abstraction if it's wrong?

ThePhysicist4• 11 years ago

I was always interested in both Physics and Economics and did studies in both disciplines.

As a physicist, the models that I encountered in economic theory always left me quite disappointed. The main reason for this was that -like the article says- most of the models used in Economics are based on abstract reasoning about "ideal" markets and actors (or more recently on game-theoretic ideas) instead of experimental data. One reason for this is of course that when many of those models were developed (in the 50s or earlier) there simply was no reliable (micro-)data available that one could develop a theory against. Another big problem that kept Economics from taking a more experimental stance towards model generation is of course that until recently it was very hard or outright impossible to conduct large-scale experiments, which are the main instrument to validate (or better, not falsify) a given theory in other disciplines such as Physics or Biology.

That said, the recent computerization of all aspects of business and the creation of virtual economies -like Eve Online, World of Warcraft- and "transparent" markets -like Bitcoin- should provide ample data to develop "real" models of economic behavior against, and I think that many researchers actually already make use of this data.

The theories that will result from this will probably be more like those developed in statistical mechanics though -i.e. making statements about the aggregate behavior of the system- rather than those developed e.g. in electrodynamics, where we usually can predict the behavior of even a single particle. Would love -and be at bit scared- to be proved wrong about this of course :)

brc3• 11 years ago

The best theories on economics date back much further than the twentieth century. The history of economics is far more interesting than trying to run experiments. A talented economist has to be able to come up with explanations for things they observe, which can then be proven out with further data.

The mistake is in thinking it should or could be a hard science like physics.

jevgeni7• 11 years ago

Exactly. I'm also doubtful that taking a more real science approach to economics (hypothesis -> experiment -> result -> rule) will work. It's a science about societies and societies change.

For example, the financial markets are the most measured markets out there, with the most microscopic details recorded. One interesting thing that happens after financial crashes are crises of theory. For example prior to 1987 American options didn't show [volatility smiles](https://en.wikipedia.org/wiki/Volatility_smile). After the crash the smiles appeared, making the markets a very different place. The same happened after Subprime and the LIBOR scandal, when the notion of a "risk-free rate" suddenly disappeared: governments now had to compensate for their default risk and market quotes were unreliable. Academics still struggle with the whole notion, although it seems that the current practice is settling around OIS discounting and CVA/DVA.

The point is, rules change. Hence in economics you can't just empirically deduce a rule and let it be, you constantly have to recalibrate it.

analog31• 11 years ago

The mistake is in thinking it should or could be a hard science like physics.

That's fair, so far as academic research goes, as there are plenty of academics doing respectable work in in non-scientific fields such as music and poetry.

But it's another matter to decide if and how to ethically apply the results of soft-science research (likewise music and poetry) in ways that affect society.

lottin3• 11 years ago

All theories are abstract, that's the whole point of a theory. Without abstraction there's only observation and no reasoning. That's why I'm highly sceptical of the claim that it is possible to understand something simply by "letting the data speak" without "committing to a theory".

sklogic10• 11 years ago

Without abstraction there's only observation and no reasoning

This is what the real science is. Observation and only observation. Reasoning is secondary and unimportant.

ThePhysicist4• 11 years ago

I don't say that having abstract theories is bad, after all one of the most successful theories in Physics, general relativity, was formulated without much data or even experimental hints to work with. The difference is that this theory was later put to scrutiny by performing experiments and by observing natural phenomena (e.g. light bending by gravity), which have failed to falsify the theory so far.

So what I'm saying is that a theory that cannot be falsified experimentally is not very useful.

The real danger here is that these theories -most of which are supported by no or very slim experimental evidence- are used by governments to formulate economic policies, which in turn affect the life of millions or billions of people. For me, this is a bit like developing an "idealized" theory of nuclear physics and then trying to build a nuclear power-plant based on it. I, personally, would not want to live near one of these ;)

donkeyd• 11 years ago

I would be very surprised if banks and big trading companies aren't doing this already, in order to predict markets. Sharing this information, however, would eliminate their competitive advantage, so I assume they just do it secretly.

TheSpiceIsLife• 11 years ago

Great comment. Incidentally, have you come across Deirdre Mccloskey, I've been reading her book 'Bourgeois Dignity: Why Economics Can't Explain the Modern World' and finding it really interesting. Economics is a social science, taking measurements / accumulating data and theorising on that data causes changes in behaviour. Just sitting around talking about economics, or your weekly budget, drives changes in behaviour.

As a layperson with a bit of an interest in economics I don't really see how, as the article says "econ is now a rogue branch of applied math". More like economics uses applied maths, or something like that. It's a 'social science', we can't reveal the laws (let's call them 'habits') of economics like we do The Laws of Nature, because circumstances change -both globally and locally (macro / micro)- and new economic phenomenon emerge.

It'd be interesting to see what future historians have to say about present day economics.

hammock• 11 years ago

Much denser, but if you enjoyed mccloskey, I recommend The Romantic Economist by Richard Bronk. It also repudiates the rigid but unrepresentative models of the average economics lesson, and explores the role of imagination and creativity (novelty) in the dynamic nature of economics that you've described.

asgard10246• 11 years ago

Economics is a social science, taking measurements / accumulating data and theorising on that data causes changes in behaviour. Just sitting around talking about economics, or your weekly budget, drives changes in behaviour.

Funny - you could say the same about physics. For example, knowing that the coming car may kill a person causes the human behaviour to change, namely the driver will stop the car. Does that invalidate Newton's laws?

Yes we probably cannot predict universe totally. But we can do scenarios (of complex emergent systems of interacting agents with bounded rationality), just like in physics. In fact the whole point of doing that analysis is to change behaviour of people, one way or another.

ThePhysicist4• 11 years ago

I was not aware of this work actually, thanks so much for sharing this!

rodgerd2• 11 years ago

most of the models used in Economics are based on abstract reasoning about "ideal" markets and actors (or more recently on game-theoretic ideas) instead of experimental data.

Essentially it's like pre-Enlightenment Natural Philiosophy, in that it's a discipline that claims to explain the way the world works, but actually explains who has the most sway in getting their ideas accepted.

...should provide ample data to develop "real" models of economic behavior against, and I think that many researchers actually already make use of this data.

I suspect reality will get about as much traction against idealogues of e.g. the Chicago School as actual climate science does agains useful idiots like Bjørn Lomborg. It's about providing views that happen to be useful to moneyed interests, not reality.

CWuestefeld5• 11 years ago

I suspect reality will get about as much traction against idealogues of e.g. the Chicago School

This is an odd criticism. I could see it applied to Chicago's cousin, the Austrian school, which clearly relies more on ideas (viz. the work of Hayek and Mises, both of whom considered themselves political philosophers as much as economists).

But Chicago is just the opposite. It's been criticized for being too tied up in the mathematics of it all. Chicagoans love numbers.

ashark• 11 years ago

I see an awful lot of from-a-state-of-nature fairy tales in economics, which is usually employed to justify a bunch of garbage moralizing about how markets are supposed to be. It's almost as bad about it as political philosophy—and oh, god, when political philosophers write about economics...

wodenokoto• 11 years ago

Greatcomment, very insightful.

I think another reason is that in business you need models you can reason about.

One example is from a bank that advises customers on investment. They have to algorithms doing machine learning on the market, a decision tree and a deep neural net. Over time they can see that the neural net outperforms the decision tree, yet they cannot use the results to advise customers because it is a black box.

Why should you buy this investment? "Because the computer said so" isn`t an answer that makes it sound like you know what you are talking about.

fennecfoxen• 11 years ago

As a physicist, the models that I encountered in economic theory always left me quite disappointed. The main reason for this was that -like the article says- most of the models used in Economics are based on abstract reasoning about "ideal" markets and actors

I recall my family's PhD. economist relating an anecdote about an colleague explaining that he's making the usual set of assumptions like, say, "people live forever", before doing some math for students. :)

Assume a spherical cow: https://en.wikipedia.org/wiki/Spherical_cow

pachydermic• 11 years ago

Experiments are pretty damn crucial to the entire scientific process, right? What if you couldn't do controlled experiments? That's where economics is right now. Until we either get enough data or economists can run actual experiments (ie those that don't just rely on fabricated mathematical models) I don't think we'll have real rigor in economics.

In the meantime, we still have to do our best. People still want ways to predict the future which suffer less from human interference (which is ideally what a mathematical model will let you do). That's still better than just asking people what they think (in some ways).

A lot of simplifying assumptions have to be made to say anything useful about a system which includes billions of intelligent actors trading trillions of dollars. There's obviously room for improvement, and I think that'll happen once people are given the proper tools to make it happen.

logfromblammo• 11 years ago

We are almost to the point where an entity like Facebook or Amazon could do controlled economic experiments. Or they could gather so much data, that when filtering them based on the experimental criteria, whatever remains could show a significant result.

Aside from the technical possibility of doing economic experiments, there is also the ethics of doing them. You are not only involving humans, but doing so on a grand scale. To prove a point, you would not only need to possibly send an economy into a recession, but you would have to do so dozens of times to get significant results. The people you are experimenting upon might get a little murdery.

rebootthesystem3• 11 years ago

Assume a cow is a uniform sphere of milk...

And sometimes that's how economics feels. Absolutely agree with your comment. Coincidentally, I was thinking about this yesterday as I watched one of many economists explain the market on TV. At some level I feel they grab onto one of N plausible ideas and go with it. They have to say something, right? After all, they are economists.

I haven't failed to notice that there are very few (not one?) massively wealthy economists. That has to say something. If you look at the people who have made fortunes they are all practitioners, not theorists. In other words, they "touch and feel" the economy every second of the day for years and understand how it moves, at least at the relevant micro level, to gain advantages.

This one thing has always bothered me about economics. Lots of economists publishing books and claiming all sorts of events and effects and none of them have significant financial success to show for their understanding of the economy. Fake Jedi's who talk about the force but can't use it.

I'd like to see an economist on TV who starts their opinion of the economy in a Trump-esque way with: "I am very rich. I understand the economy and because of that I make $400 million per year".

In terms of using models and simulations, well, we do a lot of FEA, mostly for thermal and fluid dynamics. I had a poster printed and hung in the lab. It reads: "The only person who believes the results of these simulations is the one who wrote the code". I stole that from my friends in aero who always talk about how careful you have to be with aero "codes", particularly at the extremes (low and high RN).

Of course, FEA has gotten better and better over the years, yet it is true that you have to be very careful with how you interpret results. That's why we verify expected results experimentally by building a prototype every N variants of a design based on various criteria. I remember thermal management design to cool over 1,000 Watts of high power LED's concentrated within a small surface area. It took eight months of FEA and dozens of prototypes to get it right. Some of the proto's didn't behave anything like the simulation. Some behaved better. It's an art.

And so my point is that we are likely to have a new crop of economists who will base their opinions on simulations without, perhaps, understanding just how imperfect they can be.

Mikeb854• 11 years ago

Plenty of economists work as traders, in banks, and have money and success to show for it. But they're not making economic policy, nor creating theories in academic settings. They're just using complex models to predict things, they have no interest in creating policies. In general, the economists who are successful are mostly ignored.

An example of an economist who is successful would be Jan Hatzius, Goldman Sach's head economist.

scottlocklin• 11 years ago

Samuelson attempted to develop a sort of thermodynamics of economics. As far as I can tell it was a miserable failure.

https://en.wikipedia.org/wiki/Foundations_of_Economic_Analys...

I'm a fan of using physics models for predicting behavior of large groups of people, but economics .... they do occasionally come up with nice statistical tools. Sort of like psychological researchers; those fellows whose papers can only be reproduced around 1/3 of the time.

saosebastiao• 11 years ago

Those theoretical models have held up to quite a bit of empirical scrutiny, and almost perfectly so in highly competitive markets like crops, energy (production, not distribution), housing, etc. I would say that the models have remained simplistic because economists have been trained to recognize the conditions when the theoretical models break down.

Competition (or lack of it) is absolutely the number one area where the simplistic models break down, with psychological phenomena being a close second. Even where there is demonstrated and measured irrationality in individual decisions though, in aggregate the distortion effects tend to be minimized.

Outside of these known areas of completixity and modeling deficiency, there have been several major breakthroughs in modeling and understanding other seemingly puzzling factors. Matching problems, search frictions, moral repugnance, game theory, asymmetric information, and discrete choices. There have been huge advances since the 1950's, it just takes some time to catch up with it all.

DanielBMarkham2• 11 years ago

I love watching smart people argue, so I love economics. Economics is a great source for jokes. "Economics is astrology for people who know calculus", "How many economists does it take to reach a conclusion?", and so on.

As much as I like picking on economists and watching them bicker, there's actually a method to the madness. (Except for the shills, I'm looking at you, Krugman[1]). When done correctly, economics becomes kind of a cross between a courtroom and a bullshitting session. People present various theories and sets of measurements. Lots of discussion around instrumentation and epistemology takes place. At the end of the day, the discussion wraps up to be something like "Given that most of us agree that these kinds of initial conditions mostly lead to these kinds of results, do most of us think that these kinds of initial conditions currently exist?" (Note that the "most of us" can very well be different sets of folks)

Oddly enough, it turns out that this kind of discussion has lots of real-world value.

Machine learning and deep learning especially has a pretty cool new role here, but it will never take of this dynamic ongoing discssion.

So no, economics doesn't have a math problem. It doesn't work like that. Perhaps a better way of putting is this: people who expect the world to be deterministic have a problem with economics. That situation is unlikely to change.

[1] I pick on Krugman because his shtick is already knowing the answer, no matter what the question is. He also likes showing us his Nobel. Somebody said once that every Krugman column should begin with "Damn fools!" In this way, this isn't economics; as far as I can tell it's personal aggrandizement using economics as a prop. A huge ego is a terrible thing to waste. But damn, it sure is entertaining!

[Several edits for clarity]

brc3• 11 years ago

Good comment - I remember while studying economics (a subject I have always enjoyed) I got into an argument with some fellow students who felt that it was too 'fluffy' and 'not enough meat'. They wanted to do equations and get hard answers.

The truth is that Economics is the study of choices in a world of limited resources, and that the process is exactly as you have said : observing initial conditions, material decisions and subsequent outcomes. It is, as laid out by Adam Smith, also dependent on certain initial inputs (theory of moral sentiments) which produce rational actors.

The amusing thing for me is that, despite repeated tests and outcomes, people continue to think that they can wander off the reservation and get better outcomes with the same humans by trying different things to try and control the flow of limited resources. The results are rarely pretty, but the siren song of being able to improve things and be hailed a hero draws people into thinking the rules do not apply.

Krugman wandered off the reservation a while back and hasn't been worth reading since at least 2008.

The point is, you don't have to agree on economic policies to agree that it's not a hard science and shouldn't be treated as such.

DanielBMarkham2• 11 years ago

The best part about Krugman is reading real economists try to figure out how to deal with him. Mostly they try not to engage, but every now and then you'll see several try to band together to "patch up" some statement he's made that's out of line (in their minds). Always a mistake.

It is not a hard science, but out of all of the soft sciences, I think economists understand just how tenuous their situation is. This is probably because they are using very hard tools to get a handle on a very fuzzy situation.

ADD: One of the bad things over the past 10-15 years has been the use of economics as a political weapon. It was bad enough when professors got stuck in one system or another and you had to wait an entire generation for new ideas to take hold. Now you're seeing a lot of laymen using economics as a way of arguing politics. Doesn't matter to me one way or another what kind of politics people have, but at least if you're an academic you have some notion of the realities of this field of study. In political discourse it's all just throwing dog poop around and supporting your team. That's going to make the serious study of economics even more difficult in the years ahead.

niklasni12• 11 years ago

We recently had a parliamentary election here in Denmark, and economic models featured rather prominently as arguments on both sides. One particular party would consistently refer to the economic model they used as a "calculator", which obviously in most people's mind is something that cannot be wrong. This went unquestioned and even seems to have caught on.

igravious2• 11 years ago

2008? That's a coincidental year. Around about the time of the last crisis and the beginning of austerity politics. The worst economic period since the Great Depression arguably. The rich getting ever richer. Real wages for most people stagnating or falling. Massive unemployment and under-employment. Quantitative Easing not creating real jobs and fixing infrastructure. Low interest rates (still!) Multinational corporations with so much money through tax evasion schemes that they literally don't know what to spend it on. The ongoing privatisation of public services which rarely if ever benefits the public. Essentially, ongoing class warfare and levels of inequality not seen in practically a century. Regulatory and political capture and political collusion. Trade agreements on the horizon being negotiated in secret that would exacerbate every issue already mentioned.

And you say Krugman has wandered off reservation? Rubbish. He's got to keep banging the same drum because nothing's getting fixed.

_FKS_• 11 years ago

Indeed, what is funny that while resources are limited (and declining), economics are still considering as resources were unlimited. This video has a great re-interpretation of what economics really are, just managing energy in a productive system: https://www.youtube.com/watch?v=3w6ruZ_5nPE

seliopou• 11 years ago

What your advocating is precisely what the article argues is wrong with economics as it's praticed today. Debating mathematical models is one thing, and debating the application of mathematical models while ignoring empirical facts is another.

Machine learning and deep learning especially has a pretty cool new role here, but it will never take of this dynamic ongoing disucssion.

Your pagerank is strong.

crdoconnor12• 11 years ago

There are worse economists out there than Krugman. Larry Summers, Mankiw. Anybody from the Chicago School.

im3w1l• 11 years ago

I don't think a model based purely on empiricism will work. Because people will read about the model and try to correct for their biases.

On the other hand a purely game theoretic model is not satisfactory either because a lot of people wont read about the model, and wont act optimally.

Maybe a two-tiered model, with "fish" and "sharks" could be a solution.

ancap2• 11 years ago

Your comment demonstrates beautifully how economics is not an empirical science. Much of what is taught in economics is founded on a flawed premise.

endzone7• 11 years ago

google the "lucas critique"

tim333• 11 years ago

The use of machine learning seems promising. One of the troubles with using regular mathematical equations is that at the end of the day economics is about human behaviour and that doesn't fit. Take a recent phenomenon like the 2008 crash. Banks increased lending, bankers made big bonuses while passing the risk on to various other parties and used some of the money to lobby politicians and keep the whole thing going until it suddenly collapsed leaving the other parties with the bill and the bankers with their bonuses. You're not going to capture that in a simple equation but running machine learning on say 50 previous crashes might get wise to what's happening.

I'm guessing you could run something like face recognition software but instead of faces it could recognise effects like the above and flash some politicians being paid off to turn a blind eye to high risk - give 'em a kick, warning or similar.

crdoconnor12• 11 years ago

That would make the techniques less interesting to many economists, who are usually more concerned about giving policy recommendations than in making forecasts.

Therein lies the real reason for the panoply broken economics models. They are more often used for the purpose of lobbying rather than for impartial prediction.

Much of the profession (particularly the elites) only exists as an intellectual pretext for maintaining and perpetuating existing power structures. It's about as scientific as the departments of Marxist economics were in the former Soviet Union or the Vatican in 15th century Italy.

Vagelis• 11 years ago

Considering financial policies are the de-facto social discussion around the Globe, and progress of the human species is being discussed and perceived in financial terms, it is no wonder the role of philosophy has fallen to economists.

One can hope that data-driven economics could improve predictions, but keeping the theory discussion alive is vital, if we are to ever understand our goals as something more than increasing production and consumption (quantitative).

Using the correct set of data, has long been the main issue with economic theory conflicts, and data-driven economics can only make a difference (and a huge one) if that changes.

qewrffewqwfqew• 11 years ago

Doesn't (over-applied) machine learning just lead towards a variation of exactly the same problem?

Instead of "this model fits the curve and sounds attractive and sciencey" it becomes "this model fits the curve and was done by computer!"

Not really the "empiricism coming to economics" that the author claims, but I guess it could support better outcomes. For a while.

pjc502• 11 years ago

Economics has an honesty problem. Financially motivated obfuscation is a problem in other sciences: global warming denialism, sponsored studies claiming that cigarettes aren't carcinogenic, all manner of food health and safety claims, and so on. Generally the evidence is overwhelmingly against them and the battle is mostly over PR and communicating to the public.

Economics is different; arguments that are very convenient to people who are wealthy under the status quo are very difficult to challenge, resulting in failed austerity programmes, "trickle down", and so on.

jevgeni7• 11 years ago

It is safe to say, that the economic theory a person subscribes to is highly related to their income.

Unless, of course, you're a politician, in which case it is related to vote count.

logicchains• 11 years ago

It is safe to say, that the economic theory a person subscribes to is highly related to their income.

This is an overly pessimistic view that ignores the philosophical aspects of economics. E.g. I lived on under $15k per year for a couple of years before I moved into software development, but during that time I still supported a very liberal approach to economics. This is because I hate violence (I can't even bring myself to crush spiders that wander into the house), and view redistributive economics as necessarily violent, as in a roundabout way it's forcing people to give goods/services/tokens of exchange to me that they may not want to give (since they're forced to give it via taxation lest they face imprisonment, I cannot assume it's voluntary). Other people may not care so much about this and take a more utilitarian approach, focusing on maximising some particular metrics (such as GDP or income equality), so they'll reach different conclusions.

Assuming people subscribe solely to the theories (economic or otherwise) that maximise the financial benefit to them is ironically a rather economics-style view of the world, and I'm fortunate enough to say that most of the people I'm close to don't fit this characterisation.

In terms of actual data, there's a correlation, but it's far from being the strongest factor: http://www.theatlantic.com/business/archive/2012/11/does-you...

obrero• 11 years ago

trickle down

I was just reading the convention speech of the Democratic candidate for president in 1896, William Jennings Bryan. In his speech ( http://historymatters.gmu.edu/d/5354/ ) he says "There are two ideas of government. There are those who believe that if you just legislate to make the well-to-do prosperous, that their prosperity will leak through on those below. The Democratic idea has been that if you legislate to make the masses prosperous their prosperity will find its way up and through every class that rests upon it." So some Democrats had to counter this trickle down nonsense even back then.

As an aside, in the speech he says "we shall fight them to the uttermost, having behind us the producing masses of the nation and the world". Can you imagine a Democratic presidental nominee saying that today, even if by some miracle it was Bernie Sanders? It's impossible - the heirs, and rentiers, and LPs and VCs and "job creators" and other parasites on those of us who work and create wealth have gained too much control of the system. And for the past two weeks signs are around that it could be entering one of its periodic crackups.

justincormack3• 11 years ago

Thats a much better argument, trickle up, than people make today.

mindcrime2• 11 years ago

The Democratic idea has been that if you legislate to make the masses prosperous

Assuming that were even possible. Whether it is or not is a pretty big open question. More to the point, can you do it without needing the hammer of government sanctioned violence (or threat of violence).

toyg2• 11 years ago

I partially agree with this view; however, to be fair, this is not a problem with academic economics, but rather with "pop economics".

There is no lack of academic economists who can (and do) prove how austerity programs and trickle-down are wrong; in fact, they're the only ones really leading the charge on this matter in the political world at the moment.

The problem is that policy leaders not trained in advanced economic studies (most of them lawyers by trade, as you would expect in the business of writing laws) are awash in "pop economics", cheap literature peddled by suspect gurus sponsored by interested parties. This creates a hegemonic but distorted view of the field that is then very hard to shake.

JupiterMoon2• 11 years ago

There is no lack of academic economists who can (and do) prove how austerity programs and trickle-down are wrong; in fact, they're the only ones really leading the charge on this matter in the political world at the moment.

The thing is you can pretty much find an academic economist to back up whatever argument you want to make.

pjc502• 11 years ago

It's not just lawyer-politicians, but economic organisations like the IMF and the ECB. Stiglitz' book on the subject is excellent, including the anecdote about how we know that their advice is the same whatever the country and situation because someone once forgot to search-and-replace the country name before sending it out.

Then there's the Rheinhart-Rogoff excel error: http://www.nytimes.com/2013/04/19/opinion/krugman-the-excel-...

mcguire2• 11 years ago

The membrane between academia and pop economics (i.e. the suspect gurus) is exceedingly porous.

gadders• 11 years ago

Careful, I think your politics is showing.

Shivetya• 11 years ago

Most austerity program fail because there is no true austerity. Outside of Greece which has had to make real cuts simply because it hasn't the money the vast majority of countries which claimed some form of austerity never actually cut spending, some kept increasing it.

In the US it is all a shell game where the deceit of baseline budgeting allows Congress and the President to claim cuts when spending increases. The US could balance its budget in a manner of years if budgeting were honest and they actually reduce spending increases below inflation.

JackFr• 11 years ago

To summarize, "I represent truth in the service of mankind. Those with whom I disagree if not stupid, must be acting out of the most base self-interest."

Mikeb854• 11 years ago

Plenty of economists argue against things like austerity, trickle-down, etc...

The problem is that politicians aren't interested in implementing the most ideal economic policies, they're interested in policies that give the effect they want - which is often at odds with the common good.

DanBC• 11 years ago

One real world example is whether there are educational benefits to deworming a child population in developing world countries.

If you use economist math you see a benefit. If you use epidemeologist math you don't.

http://www.cochrane.org/news/educational-benefits-deworming-...

http://www.cochrane.org/CD000371/INFECTN_deworming-school-ch...

http://www.theguardian.com/society/2015/jul/23/research-glob...

http://www.bbc.co.uk/programmes/b0659q1f

igravious2• 11 years ago

Economics is fascinating because it is where ideology meets math.

Economics has a math problem only if you're not honest about your mathematical models reflecting an ideological position rather than "reality" (whatever that's meant to mean in the context of economics).

_pmf_• 11 years ago

Economics is like fantasy football league. I predicts the future based on isolated personal preferences and ideologies of the "scientist", optionally sprinkled with small scale observations of data with dubious accuracy.

HSO• 11 years ago

I shouldn't even comment on this BS article but here we go, duty calls ( https://xkcd.com/386/ )…

1) First of all, let's make clear that there are no "the economists" and there is no "economics" that could be identified with whatever peeve du jour of "the journalists". Economics as a field, understood as the study of exchange between decision-making agents in more or less large systems[1], is marked by an extreme diversity of approaches and opinions on even basic questions. From my superficial understanding of other fields, this seems to be a big difference between economics and the sciences, and on the other hand rather similar to the humanities. If you're going to criticize something, better make it specific and name names.

2) It is fashionable for "technical" people to scoff at the mathematics used in economic theory (basically, analysis, optimization, linear alg, and measure-theoretic prob), pretending that the problems arise because the tools are too primitive. First, perhaps they should remember that a lot of the foundations of mathematical economics were laid by people way above their paygrade. I'm talking about von Neumann, for example, or Fischer Black. Usually, when smart people do something that does not make sense to you, you take a step back and ask what you might be missing, and usually there is a nontrivial answer to that question. Paul Romer, sorry, is a good economist but he has a BS in math. I would say that's my definition of a "lightweight when it comes to equations". That's not to say he shouldn't criticize, he should! But let's not pretend that there was no reason to "go formal" in economic theorizing or that there were/are easy modeling choices.

3) In my experience, most of the criticism of economic models comes from ignorance of the goal and context of a model and a too literal reading of the math. For example, if you take Markowitz's portfolio optimization (mean vs variance of a linear combination of a multivariate normal), it is correct that individual returns have non-exponentially decaying "heavy" tails, the copula is not (unconditionally) Gaussian, and risk is therefore not captured in variance and correlations (not least because they may in fact be undefined). But that is completely beside the point of the model, which is simply to express the idea that the risk of a portfolio is not necessarily additive and that there is a tradeoff between risk and return. The point being, although it is expressed in mathematical language, it is actually a qualitative model. Once you realize this difference to more descriptive models in the sciences, economic theory starts to make a lot more sense.

4) The real problem of economic theory may be the disconnect between how many people have a stake in it and how many people have the time and leisure and inclination and background to understand what the theorists are actually saying.

5) Side comment and half-reply to ThePhysicist's complaint: The reason to go with the "perfect gas"-type models in economic theory, I think, is that you are dealing with self-interested, utility-maximizing particles or "agents" -> acting particles. The thinking being that if you put in constraints of some form, say a short-sales constraint in a financial market model, you make the model very special. But in the messy real world agents would find a way around this particular constraint eventually. So the unconstrained general equilibrium models are trying to give you a big picture, "this is where the market tends to" type of result. There is so much more to be said on this point but I'm already way above my allocated time for this "duty call"...

6) Last but not least, let me state my opinion that there is nothing inherently noble about science. It is a method to gain knowledge, and it is contingent on the affordances of the field to which it is applied. In economic theory, your basic problem is lack of data. Now that may change in some subfields, and that's great. So the scientific method can be applied in those subfields eventually. But we need answers or opinions today for practical problems. I see economics as akin to philosophy how Russell [2] understood it. Let me quote him:

“Philosophy, as I shall understand the word, is something intermediate between theology and science. Like theology, it consists of speculations on matters as to which definite knowledge has, so far, been unascertainable; but like science, it appeals to human reason rather than to authority, whether that of tradition or that of revelation. All definite knowledge—so I should contend—belongs to science; all dogma as to what surpasses definite knowledge belongs to theology. But between theology and science there is a No Man’s Land, exposed to attack from both sides; this No Man’s Land is philosophy. Almost all the questions of most interest to speculative minds are such as science cannot answer, and the confident answers of theologians no longer seem so convincing as they did in former centuries.”

One should be aware of the limits of this approach but one should also not assume that there was a choice between science and this. If there was, it wouldn't even be a contest! The realm of science may get bigger over time, as more and more data is gathered, but again, we need answers today and in real time, not in 100 years, to decide on regulations, interest rates, portfolios or budgeting decisions. In almost all the big economic questions, your sample size is one and the possibility to experiment is nil. The world is arguably nonstationary on time-scales that matter, economic mechanisms change, and every statistical test and computational experiment is always a joint hypothesis test of your assumptions, about which I said in (1) above that there is and perhaps can be no consensus.

In short, it's not that people don't know there is a problem. It's that there has so far been no better solution.

______________________

[1] I'm just making this definition up on the fly but if someone has a better one, I'm all ears.

[2] B. Russell. A History of Western Philosophy. George Allen & Unwin, 1945.

amelius3• 11 years ago

Any recommendations on economics books with just the right amount of math, for non-economists with a college degree?

I'm looking for the economics equivalent of Feynman's lectures on physics.

justincormack3• 11 years ago

If you want readable economics, there is Keynes. No maths at all though.

asgard10246• 11 years ago

The book I got recommended from Steve Keen, when I asked him a similar question, was J.M.Blatt: Dynamic Economic Systems. Although he has beautifully simple approach, it is really outside the standard economic theory and apart from Keen and perhaps few other individuals, sadly no one really follows in Blatt's footsteps.

endzone7• 11 years ago

keen is a complete charlatan and the laughing stock of the economic world. he doesn't even understand the basic economic theory he attempts to criticize

ndonnellan• 11 years ago

I'm working my way through "Thinking Fast and Slow" by Kahnemann. It doesn't have much (or any) in the way of heavy math, but it references many experiments, and the tone in general is about how easy it is to "disprove" standard economic theory.

I like it.

ancap2• 11 years ago

If you want to learn why math does not belong in economics at all you should read Human Action by Mises.

pjkundert• 11 years ago

You might be interested in "Christian Economics in One Lesson", a modernization of Henry Hazlitt's "Economics in One Lesson" by (in my opinion) the greatest living economist of our age, Dr. Gary North.

http://www.garynorth.com/public/department181.cfm

dovereconomics• 11 years ago

While pursuing PhD in Economics, I've supported myself working as a data scientist and, like ThePhysicist says, it's fairly disappointing that many are oblivious of datasets, APIs, libraries,..

A good example of what can be done (http://econprediction.eecs.umich.edu/)

On the other side, the claim "literary types who lack the talent or training to hack their way through systems of equations" is groundless and mostly fallacious. The "literary types" have grasped many politicized inconsistencies and dedicate their research by deductive reasoning. Most of them are not 9/11 truthers.

hrzn• 11 years ago

The maths models used in economics are rarely checked against real-world data, but when they are they often turn out to be wrong.

A major instance of this problem comes from models used for trading, which often assume Gaussian distributions and Brownian-motion behaviors. According to those, extreme moves such as the ones occurring during economic crises such as the one of 2007 are several sigmas away from the mean -- making them supposed to happen perhaps once every 10^10 years. Yet they happen every 20 years. Taleb's book "Black Swan" is an interesting resource on this topic, for those interested.

endzone7• 11 years ago

gosh, i wonder why those traders use those simple, outdated models to make extraordinarily expensive decisions every singly day when they could just read the "black swan"

RA_Fisher• 11 years ago

Meanwhile machine learning is the high interest credit card of technical debt, what could go wrong? http://research.google.com/pubs/pub43146.html

I entered stats through econometrics. I love econometrics. Econometrics is seriously hampered relative to other applied math fields by the inability to apply large scale casual experiments. For this reason parsimony is soooo important in modelling. Machine learning is the opposite of parsimony. Machine learning is wonderful for many applications, it lets us shrug off a first error of model selection, but it's not a panacea to the math problem and I think it actually might make it much worse.

twitchard2• 11 years ago

I think there's a fundamental misunderstanding of what it is theoretical economists are doing.

A medical scientist runs experiments on rats, to gain insight into what the effects of a certain phenomenon might be on humans. Rats aren't humans, of course, but we think they share important characteristics with humans. Of course, human trials would be better---butbecause there are ethical and practical difficulties in performing human experiments in controlled environments, we are happy to accept the insights that come from studying rats.

Theoretical economics studies the interactions of idealized 'rational' actors. These aren't humans, of course, but like rats, we think they might share important characteristics with humans. Like rational actors, humans have things they want, and do respond to incentives. Economics is largely the study of systems of incentives.

You can gain insight into the systems of rational actors---and insofar as you believe the analogy between rational actors and humans, into human economic systems---by writing equations and proving theorems.

I'm sick of this theme that theoretical economists are these dogmatic lunatics who write equations on the board that have nothing to do with reality. They are in the business of crafting powerful arguments about human nature by analogy, which yes, aren't always accessible to those of us who haven't steeped ourselves in the math, but I think that is no reason to dismiss their insights as nonsense and saying they have a 'math problem'.

jal2782• 11 years ago

The issue is that assumptions such as perfectly rational actors can diverge so far from reality that it renders the resulting idealized conclusions meaningless from the perspective of actual human economies. The abstract study of incentives is of course interesting in its own right, but may have little to do with economics in practice -- i.e. the important practice of how actually should we run an economy.

What theoretical economists do is not 'nonsense' but can become nonsense when it naively forms the rationale for real-world policy.

twitchard2• 11 years ago

Rats are, in some ways, very different from humans too. But if it's impossible to run human trials, or there are severe deficiencies in the way we are able to execute them, studying rats is still the best argument.

If there is a convincing empirical economic study that widely contradicts a theoretical consensus---yes, that evidence should be preferred. But that is not often the case, and otherwise the theoretical argument is simply the best argument there is.

What drives me bonkers, though, is the people who dismiss the math and its conclusions as being 'meaningless', but then what they substitute is not superior empirical arguments of their own, but their own emotional sentiments and undisciplined intuitions (typically decorated by cherry-picked historical observations).

KingMob• 11 years ago

As a former cognitive neuroscientist with a master's in psychology, I will just point out that psychology departments look at the massive amount of data demonstrating human irrationality, and conclude that economists are mistaken or wildly naive to extrapolate from "rational actors" human beings.

You don't have a "math problem", you have a "data/science problem". And saly, at least at the micro-level, economists could have disabused themselves of the accuracy of rationality decades ago (e.g., Kahneman and Tversky's work in the 70's).

Much modern economics is like the elaborate math of epicycles, close enough, but still missing key insights. And this won't change until data is valued more.

NumberCruncher• 11 years ago

There is a main difference between Physics and Economics. Physics tries to explain the laws of nature which do not change over time. But Economics tries to explain the laws of a system based on human knowledge and believes which is anything but robust. Using modeling techniques borrowed from Physics/Mathematics in the field of Economics can work very well but only if the laws you are investigating are robust over a given period of time.

Edit: typo

gooseus• 11 years ago

I feel like Nassim Taleb (Fooled By Randomness, Black Swan, Antifragile) has been making a similar point for years now.

Unfortunately I don't know enough about economics to comment any more than that.

k2enemy• 11 years ago

If anyone is interested in something other than shitting on economics...

The other half of the article seems interesting. Does anyone have handy references (besides the Athey and Varian papers in the article) to how machine learning is being used to establish causation rather than focusing on prediction? I've heard several places that there have been big strides lately in this area, but I'm not sure where to look.

marketforlemmas• 11 years ago

Here's a link to the slides that she used for the NBER talks. I've flipped through them and there seems to be some references to working papers (that Googling should be able to surface):

https://onedrive.live.com/?cid=351055fdce7d0ff1&id=351055FDC...

WorldMaker3• 11 years ago

My insight in college taking some economics courses side by side higher level physics and engineering courses was that economics has mostly gotten stuck in algebra and has thus far failed to develop its calculus.

The easiest analogies for me to make are to electronics. Talking about cash/debt is like talking about instantaneous voltage. It's sort of interesting, but it isn't doing any actual work. In electronics it is the flow of that voltage, the current, that is more often more important and more interesting and more directly applicable to the "work" of a circuit...

I think you get a very different view of economics if you model it more like electronics circuits than just about any of the other economics models I see discussed. I've often wondered what would happen if someone actually bothered to attempt such a model and apply some deep scientific rigor to it.

nobbis• 11 years ago

Economists were modeling the economy using circuits in 1949 (see MONIAC), before the Integrated Circuit was even invented.

WorldMaker3• 11 years ago

Thanks for the interesting reference to look up. I had not heard of the MONIAC before. Looks like this is also a sideways referent in Terry Pratchett's Making Money which draws in some interesting dots in that book.

endzone7• 11 years ago

comments like this are amazing. you are completely ignorant of the current state of economics yet wonder if economists have bothered to construct dynamic models of the economy. i guess your intermediate macro course didn't get that far...

WorldMaker3• 11 years ago

Do you have any links for what you consider to be the current state of economics? I will the first to admit that I am not an economist, but I do try to at least keep an ear out for what may be current and certainly in terms of what I've been hearing from a layman's perspective, for the most part my comments remain valid against current economics work. That said, it's also why I prefaced my comments that they were primarily centered from several years ago back when I was in college and that the analogy was mostly personal opinion. If it is personal opinion founded in ignorance, I am happy to be proven wrong or shown cool things, if you are interested in a deeper discussion beyond insults.

Certainly, the models that we see in day to day political discussions and popular/lay culture have not seemingly progressed much beyond the macroeconomics courses I took in college, but again I'm willing to admit I certainly have my biases/blinders. Also, I'm sure that dynamic models exist, I was more curious if there are economists that have played with models more closely aligned with my physics analogies, specifically.

Thus far the one of most interesting things in economics right now, to myself at least, is I have done some reading on some of the work of theorists in Modern Monetary Theory (MMT) and I liked where it seemed to be heading (not to mention its ties to turn of the last century Social Credit theories/works). That certainly seems close to what I'd expect/like to see more of in economics, but correct me if I'm wrong, it still seems "fringe" in the current state of economics.

Mikeb854• 11 years ago

This is really the important part of the article:

Their overview stated that machine learning techniques emphasized causality less than traditional economic statistical techniques, or what's usually known as econometrics. In other words, machine learning is more about forecasting than about understanding the effects of policy.

And it's true. Economists care more about forecasting than 'understanding the effects of policy' because the money is to be made forecasting while working for a bank or a large corporation.

Economics can't be codified the way physics can because economics models human behaviour (which is constantly changing), not physical laws than can be tested and retested.

clavalle• 11 years ago

I find it interesting that many economists tend to ignore the limits of their own theories.

For example, the dogma that markets tend toward efficiency.

This is true -- as long as certain axioms are not violated. But they seem to forget about the axioms on which their conclusions are built and march forward as if their conclusions are absolutely true and apply that assumption to problems where they simply do not hold because the axioms on which they are built are violated.

To continue with the 'markets tend toward efficiency' conclusion: it does not hold when there are negative expectations for a party for not making a transaction. And they invented a fudge factor to get around this a bit (that still doesn't work for all cases) which is to make sure the equations when taken in aggregate do not generally lead to negative expectations for not making a transaction. This holds in many more cases but still not all.

Where does it fail and why does it matter? Well, the axioms underlying the 'markets tend toward efficiency' work great in capital markets. They tend to completely fail when pain or death is potentially involved in a transaction (severe negative expectations) but they may look like they should work and you can find limited cases that do work. So, basically war or crime or relationships or corruption or or poverty or healthcare or any other of those human interactions pain or death tend to come into play. A huge swath of sectors where politicians and special interests and the economists that inform them try to craft policy to fit a misapplied theory. Yet, economists march on pretending the theory holds from the axioms to the conclusions and on to the further conclusions built on those hold because 'mathematics' -- who can argue with mathematics?

mamon• 11 years ago

Capitalism is a greedy and cruel system where 2 + 2 = 4. Socialism is a a blessed system claiming that in a name of social responsibility and justice 2 + 2 should equal 7 (at least)

endzone7• 11 years ago

reminder: noah has never published an academic paper in economics and it looks unlikely that he ever will. he is simply not a competent guide to the field. this entire thread is a perfect example of the blind leading the blind: a journalist (noah) presents an entirely one sided view of the field, and intellectually lazy posters take it as a cue to dump on an entire academic field while freely admitting their ignorance of any of the details.

newsflash: most economists are acutely aware of the imperfections in their models. sure, you can find the blinkered and dogmatic, but that is unsurprising in such a large and varied field. the subject encompasses a serious variety of subjects and methods you (the hn poster) simply know nothing about. for example, machine learning techniques are really nothing new. theorists have been aware of the kahneman/tversky result for decades. please bear this in mind before you lazily declare the intellectual bankruptcy of the entire field.

p.s so-called econophysics was a direct attempt to apply models from hard science to economics and it has been a complete failure, since it lacks an underlying model of human behaviour. turns out this is quite important...

Economics Has a Math Problem

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