# Guest Post: The Mathematicization Of Economics

*Submitted by John Aziz of Azizonomics*

**The Mathematicization Of Economics **

If one thing has changed in the last one hundred years in economics it has been the huge outgrowth in the usage of mathematics:

This is largely a bad development, for a number of reasons.

First of all layers of mathematics acts as a barrier to public understanding. While mathematics is a useful language for communicating complex ideas, those without training in mathematics will struggle to grasp what an author is trying to communicate if a paper consists mostly of equations untranslated into English. This is bad practice; it is easier to baffle with bullshit in an unfamiliar language than it is in plain English.

Second, mathematical models are always simplifications. Human action and economic behaviour is complex and unpredictable. While mathematical models can sometimes approximate a pattern quite well and so have some limited uses as toys, the complexity of human behaviour means that there are always unmodelled variables that can throw off a model’s output. Over-reliance upon or excessive faith in mathematical models can lead to bad forecasting and bad policy decisions. The grand theoretical-mathematical approach to economics is fundamentally flawed.

Third, attempting to smudge the human reality of economics into cold mathematical shackles is degenerative. Economics is a human subject. Human behaviour is not mechanical, it is not mechanistic. Physicists can very accurately model the trajectories of rocks in space. But economists cannot accurately model the trajectories of prices, employment and interest rates down on the rocky ground.

Economics would benefit from self-restraint in regard to the usage of mathematics. Alfred Marshall made some useful suggestions:

- Use mathematics as shorthand language, rather than as an engine of inquiry.
- Keep to them till you have done.
Translate into English.- Then illustrate by examples that are important in real life
Burn the mathematics.If you can’t succeed in 4, burn 3.This I do often.

I hope the blowout growth in mathematics in economics is a bubble that soon bursts.

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realtickWhen Goods Data Is Not Good

http://chartistfriendfrompittsburgh.blogspot.com/2012/10/when-goods-data...

Lohn JockeIn lay terms: people don't understand numbers and numbers don't understand people.

Alpo for GrannyOr thought of another way...Figures don't lie, but liars figure.

Nothing To See HereAziz becoming Hayekian/Misesian without being aware?!?

AzizI agree with Mises and Hayek on a lot of things, but I usually get to a similar conclusion via a different route.

Spirit Of TruthHowever, if you believe in free will you can't truly believe in social science and economic projection. You cannot predict how people will act. Except, of course, if there is a trick, and that trick is the cord on which neoclassical economics is suspended. You simply assume that individuals will be rational in the future and thus act predictably. There is a strong link between rationality, predictability, and mathematical tractability. A rational individual will perform a unique set of actions in specified circumstances. There is one and only one answer to the question of how "rational" people satisfying their best interests would act. Rational actors must be coherent: they cannot prefer apples to oranges, oranges to pears, then pears to apples. If they did, then it would be difficult to generalize their behavior. It would also be difficult to project their behavior in time.In orthodox economics, rationality became a straitjacket. Platonified economists ignored the fact that people might prefer to do something other than maximize their economic interests. This led to mathematical techniques such as "maximization," or "optimization," on which Paul Samuelson built much of his work. Optimization consists in finding the mathematically optimal policy that an economic agent could pursue. For instance, what is the "optimal" quantity you should allocate to stocks? It involves complicated mathematics and thus raises a barrier to entry by non-mathematically trained scholars. I would not be the first to say that this optimization set back social science by reducing it from the intellectual and reflexive discipline that it was becoming to an attempt at an "exact science." By "exact science," I mean a second-rate engineering problem for those who want to pretend that they are in the physics department - so-called physics envy. In other words, an intellectual fraud.- Nassim Taleb,The Black Swan: The Impact of the Highly Improbable, 2007From my thesis - http://www.spiritoftruth.org/Thesis/Intro/

jpmrwbNonregularity in the realm of human action also makes hopeless the other way in which many economists try to ape the physical sciences: their "quantophrenia" (an irrational haste to introduce mathematical analyses to their work).

First of all, measurements require constant relations. So, in contrast to the natural realm, the utter lack of constant relations in the realm of human action precludes any useful measurements.

Secondly, equations

alsorequire constant relations. So, again in contrast to the natural realm, the utter lack of constant relations in the realm of human action precludes the formulation of any meaningful equations.jpmrwbNonregularity in the realm of human action also makes hopeless the other way in which many economists try to ape the physical sciences: their "quantophrenia" (an irrational haste to introduce mathematical analyses to their work).

First of all, measurements require constant relations. So, in contrast to the natural realm, the utter lack of constant relations in the realm of human action precludes any useful measurements.

Secondly, equations

alsorequire constant relations. So, again in contrast to the natural realm, the utter lack of constant relations in the realm of human action precludes the formulation of any meaningful equations.hbjork1Seriously, it is good to see someone a post deditated to the difference between random events and human directed events as applied to statistical analysis. Human behavior maybe all over the chart but it is not necessairily RANDOM. Dice thrown are random(if they aren't fixed). Coin tosses are random, parts failures in equipment are random but people remember, communicate and plan. Yesterday's probability distribution may not be todays probability distribution.

Trading is the great Casino. Buying or selling goods or labor is an attempt to optimise use of available resources.

Thanks Spirit!

ParkAveFlasherAziz, kindly provide a useful example of point #2:

"While mathematical models can sometimes approximate a pattern quite well and so have some limited uses as toys, the complexity of human behaviour means that there are always unmodelled variables that can throw off a model’s output."

I have my own but I'd like to see what you would present.

verum quod liesI'll do it for him: the CAPM. For example, it is not just the "market" driving prices around.

ElementGot any numbers of that?

Cognitive Dissonance"I hope the blowout growth in mathematics in economics is a bubble that soon bursts."It's not just math in economics. It's the present day "belief" in all things science. If "science" says it is true then consider it spoken by GOD herself.

Let us

nevermistake the finger pointing to the moon for the moon itself.http://www.youtube.com/watch?v=sDW6vkuqGLg

UnpreparedIt has nothing to do with science. Every professional would greatly benefit with a dose of meta-thinking; what are the boundaries of their discipline and its tools? What is the purpose of their inquiries? Where do they stand in the scheme of things?

Mathematics is not a preset, crude language. It is a modelable set of logical codes and relationships with varying degrees of accuracy, meaningfulness and application. Every modeling technique ever invented by men has to suffer from a trade off between variations of Type I and Type II errors (statistics).

The difficulty with crude maths are equally relevant to other social science disciplines. However, few, like behavioral sciences went ahead using less math (statistics) and more experimentation.

Maths have enough tools to model systems as complex as markets, the problem is our (or our PhD's) expectations of what the model is supposed to provide; universal future projections as opposed to local/situation simulations.

Nothing To See Here"Maths have enough tools to model systems as complex as markets, the problem is our (or our PhD's) expectations of what the model is supposed to provide; universal future projections as opposed to local/situation simulations."

If a model can't predict, then it's because it can't model what it pretends to model. Starting from there, maths DO NOT have the tools to model complex systems. It can only make abstract, incomplete representations which hold according to various assumptions, which assumption are never entirely true in the real world.

ConfundidoThe problem is not the use of math.

The problem is that those who use the math don't understand economics! Even worse, they use assumptions that are wrong!For instance, EVERYONE uses national accounting to measure surpluses or deficits in flows, and then, then they speak of imblances, gaps out of equilibrium. However, that is a technique first proposed by Leo Walras, that worked during his years....you know why?? Because fucking Walras lived during the gold standard years! That's the only reason anyone could have come up with the fucking idea of a general equilibrium.

But we live in a Ponzi scheme, fuelled by shadow banking, that not even Gartman can figure out! He is bearish on gold because the monetary base, assuming he measured it right, is not growiing...So WHAT?? Shadow banking is growing, rehypothecation is growing...otherwise, how the fuck do you explain that over 95% of IG bonds and over 70% of HY bonds are priced above par??? You can't even hedge it with cds...you know why?? Because default expectations are fucked up. You know why? Because Ben is the fucking correlation here, given his FX swaps that manipulate the ccy EURUSD basis. That's why! Now, go back to model this Ponzi scheme with math. You can't! We live in an overdetermined algebraic system!

AetosAerosSuccint, to the point, but you forgot the most important thing:

'Fuck You Bernanke!'

ConfundidoOh, you're right...Here it goes: FUCK YOU, BERNANKE!

HoofHeartedOK, that's the best thing that can be said, though I'd include "Fuck you, S.E.C. Leave Sean Egan alone!"

The problem isn't the math at all. The problem is us. We have these ASSumptions built into the way people are going to act. And we all know what we do when we ASSume. People do whatever the hell they please. Maybe they are trying to maximize some utility function, maybe they are just braindead trying to make it through the day. Likely they don't understand any math and wouldn't know how to maximize anything very well.

Our biases cause the biggest problems in all of this. And when some rogue tries to ask why someone chose a certain model (whether neo-Keynesian with some parameters or DGSE or...) they typically ask said person to either shut up or leave the conference. Yes, I know that guy well. And I've enjoyed cities instead of listening to bullshit based on ridiculous assumptions or biases.

Bay of Pigs"go back to model this Ponzi scheme with math"

+1 spot on...

verum quod liesActually, Minsky was pretty close but wasn't so focused on the math.

HardAssetsWell stated. Those fabricating the models don't know economics, and most of the economists don't know the day-to-day markets.

It is a rigged system run by criminals. They pay the academics to come up with all the b.s. 'models' & 'theories' to confuse the suckers, who believe its all much too complex for them to understand. (Its simple . . . theyre stealing from you.)

There are plenty of 'A students' who prefer to stay in school forever, rather than make a real living in the real world. They are very capable at memorizing and learning . . . . . what is wrong.

insanelysaneReality: Infinity = Infinity

Hope: Infinity = Infinity + 1

silver surferOk, hmmm

Mathematics in economics works great as long as people act like machines then...

HardAssetsMacro level isnt micro level. Mathematics has been very useful at the micro level - down to the level of the firm. It can be used to optimize processes. Just use the tool appropriately, and youre fine.

Benjamin GluttonIs Legal Tender Next?

It’s going to be illuminating to see whether the government appeals the big ruling on judges’ pay that was handed down last week at Washington. The case is called Beer v. United States. The Sun has written about it here and the editor of the Sun here. The plaintiffs are Judge Peter Beer and a rainbow coalition of some of the most distinguished judges on the federal bench. They have just won a ruling that prohibits Congress from suspending a system of automatic pay increases designed to protect their honors from inflation.

The United States Court of Appeals for the Federal Circuit, sitting en banc, handed down the ruling on Friday. The ruling hasn’t received much coverage in the press, though — at least in our view — it’s one of the most important cases of our time. The reason is that it has to do not only with the question of need for Congress to keep its promises and the need to attract a first class judiciary but also the question of constitutional money.

The judges turn out to be a special case because it is unconstitutional ever to diminish their pay. This is American bedrock that was laid down by the Founders because of the British tyrant George III. The king made judges dependent “on his Will alone, for the tenure of their offices, and the amount and payment of their salaries,” as America’s revolutionaries put it in the Declaration of Independence. So it was written into the United States Constitution that the compensation of judges “shall not be diminished during their Continuance in Office.”

It turns out, though, that the historical record is clear what the Founders thought dollars were. They used the word “dollars” twice in the Constitution. By a dollar they meant 371 and ¼ grains of pure silver or a 15th as many grains of gold. That’s the way Congress defined a dollar in law under the Articles of Confederation and the way Congress defined it in law in the first Coinage Act of the constitutional era.

The idea that a dollar could be worth a different number of grains of silver or gold at the end of a contract than it meant at the beginning of a contract would have horrified George Washington and nearly all of the other Founders (Benjamin Franklin, a printer, had a vested interest in paper money). So would the idea that the dollar would be permitted to decline over a decade to but a sixth of the number of grains of gold at which it was valued at the start of a decade. That is what has just happened in America.

The court deciding Beer didn’t get into legal tender per se. But the legal tender question is the elephant in the courtroom, so to speak. If a dollar can’t be diminished for judges — that is, if the legal tender laws are not good enough for judges — why should they be good enough for the rest of us? If they are not good enough for the contract between the government and judges, why should they be good enough for contracts between private parties?

complete article...http://www.nysun.com/editorials/is-legal-tender-next/88019/

onebirConflicted Aziz meme:

Says burn the maths

...

Shows Hodrick-Prescot filter 'trends'.

---

Otherwise pretty sensible, other than "Third, attempting to smudge...' which is bald assertion.

(Note: over-reliance on HP filters for estimating trend GDP was probably a major contributing factor to underestimation of structural deficits & the developed world's current fiscal debacle.)

machinehWhy would we expect a cyclical component in economics publications anyway?

Are mathematical economists like cicadas, emerging every 17 years from under their rocks to mate and die?Vlad TepidSort of, except for the mating part. I learned on NatGeo that female humans are repelled by the pheremones of mathematical economists.

DUNTHATEconomists are not mathematicians.

THEY PRETEND TO BE.

machineh'illustrate by examples that are important in real life'Recently I read an economic paper exploring the commonplace observation that VIX tends to rise when stocks decline.

The authors performed a heroic amount of calculation on an enormous database, fitting multiple models and reporting them with statistical panels.

Ultimately, all they showed was that VIX tends to rise when stocks decline, a fact known to every trader.

Not a single thing in the paper was useful to a practitioner. In blunt terms, enough computing to dim the lights nationwide didn't make any money.

NidStylesI do not pretend to be. I'm a Physicist and Economist though.

epwpixieq-1Mathematics is a Language, one can express whatever one wants with it!

One either understands Nature (humans are part of Nature) and can speak in a such a way that the Reality will CONFIRM the description, or one can write something totally useless has nothing to do with the Natural (Nonlinear) Dynamics and Reality will (of course ) diverge. Nothing more and nothing less.

An interesting quote, that can express the above idea, in a more visual way:

"An unsophisticated researcher uses mathematics as a drunken man uses lamp-posts -- for support rather than illumination."

Turin Turambar"Mathematics is a Language, one can express whatever one wants with it!"

I guess I'm a little dense and need some help. Would you mind please demonstrating to me how mathematics can describe and predict the impact of a person's dreams on Human Action?

Thanks in advance. It'll be such a relief to know the answer. ;-)

sebmurrayA rather crude attempt:

HA = f(a.D + b.R)

Where D = dreams and R = reality, a and b are weighting factors based the importance an individual places on dreams vs. reality.

That of course doesn't predict anything, because the number of variables is probably infinite at any one time.

One could of course also rephrase it to say that this model describes Human Action as a function of Dreams and Reality but it just looks cooler in an equation doesn't it?

Turin TurambarLOL, very nice! I'll let the equation speak for itself.

Your next project is a perpetual motion machine. ;-)

verum quod liesThe key in mathematical economics and finance are the assumptions. By assuming the right assumptions you can get any mathematical result you want. For example, assume perfect capital markets (e.g., no taxes, no transaction costs, etc.) and a serious of other unrealistic assumptions apply some math and you get Modiglinai and Miller's assertion that firm value is independent of its capital structure. Of course, there are taxes, transaction costs, etc. and actual people in the actual markets act as if the firm's value is dependent on its capital structure (i.e., at least in part). Anyway, it's the assumptions that tend to drive economic and financial economic "model" results.

sebmurrayWell put, one can talk shit in any language and it will still be shit. The problem is the more eloquent you sound, the more likely people are to believe you...

sitenineWhat a complete and utter load of shit! Economics does not acknowledge the existence or implications of the exponential function. There can be NO math in economics, or the entire fucking myth of perpetual growth implodes into the reality of limited resources. Economics is nothing more than a tool used to perpetuate the ponzi or illusion of promises that will not, indeed CAN NOT, be delivered.

socalbeachA little math could have helped you in your recent hyperinflation article. You approximated inflation as the % change in M2 money supply minus the % change in GDP. It turns out that is almost the exact same as the negative of the percent change in M2 velocity. Your inflation graph (M2NS-GDP) had inflation falling in the mid to late 70's.

Guest Post: Explaining Hyperinflation

NidStylesIt was falling then. The Interest rates were as high as 15% in 1978. This was dropping Inflation.

socalbeachHere's a plot of Mr. Aziz' inflation estimate (blue) vs the CPI inflation rate (red) from Jan, 1976 thru Dec, 1979. They are almost exact opposites of one another. Just for fun I added a line of -1*the % change in the velocity of M2 (green), and you can see it's almost the exact same as the blue line. That similarity validates the comment I made in Mr Aziz'

Explaining Hyperinflationarticle.http://research.stlouisfed.org/fredgraph.png?g=bIL (%changes: CPI vs M2NS-GDP vs -1*M2 velocity)

This essay plus the

Guest Post: Explaining Hyperinflationarticle = FAIL.NidStylesThat you decided to display CPI as if had any real bearing on Inflation rather than with the full spectrum of M-values it's telling that your argument hasn't a leg to stand on. M-values display the Inflation clearly. That there is a lag between the initial expansion and what the doctored information that the CPI show's is well known already. Even the pre-'82 CPI figures were screwed up and lousy. Half of them were weighted estimates and in no way shape or form were complete.

Put the chartology away and start learning actual Econ before you embarass yourself further.

marriedgeordieWish I could follow this advice. But then, my papers would not get past he editor's desk

Variance DocOh shit, here we go again - another one of these ignorant "math is evil and get rid of the math" type articles.

There is nothing wrong with using math to describe the world we live in, whether it is a physical system with known laws (e.g. physics) or a system with more hazy laws, but laws never-the-less (e.g. economics). Humans

collectivelyDO actually follow laws/patterns that can be mathematically/statistically modeled. And this is an ongoing area of research by people like myself. By the way, if someone is too stupid to understand math, it's not math's fault. Whie you are trying to get over that concept, here's a coloring book, try to stay in the lines ------------------------------>I can imagine having a conversation with your type back in the 1850s:

me: "You know someday, man will fly just like birds. It's a matter of math and engineering."

Aziz: "Hey Ezekiel, this thre fella thnks weowil will fly like dem birds. Hahaha, what a ignoraumous. Son, ain't no way whell fly. Math? Why, that's no good. We need shit in english terms 'n stuff."

Yes Aziz, those "silver birds" in the sky you see today are called airplanes. A result of math and engineering, and not a result of English.

NidStyles"Humans

collectivelyDO actually follow laws/patterns that can be mathematically/statistically modeled. "No they do not. That you admitted to using them yourself to try and measure this show's that you have no clue what you are talking about. One only needs to see the Econ 211 example of modelled cereal consumption to understand that Mathematical Models do not represent reality in the least. Humans do not fit your cute little model you are trying to force them into.

This was the whole argument Mises made.

Economics =/= Engineering.

Variance DocRight, I no clue about what I'm talking about. Trouble with your type is you have a tough time with complexity and deep thought, so that cereal consumption models in econ classes is state of the art in your view. Any deviation from the model is termed a failure by your type. But really, it is not a failure of the model per se, but a failure of you to understand science. You need to understand the error process, e.g. measurment, etc. Just because the model does not follow reality exactlly, does not mean the model is wrong. If the model follows reality within an acceptible error, then the model is OK.

Think deeper if it is at all possible. Think about how humans at an individual level become a collective dynamic. Think about phase transitions, such as water turning to ice; where molecules have many degrees of freedom in the liquid state and are restricted to a lattuce in the solid state. Now apply that to human behavior.

You see, it's really your mental limitations and your limited thought process that is the problem; much like people who thought space travel was impossible and turned to TV instead of solving problems.

"This was the whole argument Mises made."

You sound like that dopy chick from the other day: http://www.zerohedge.com/news/2012-10-09/woods-murphy-refute-11-myths-ab....

“Some Federal Reserve critics claim that the Fed has devalued the U.S. dollar through a massive expansion of the amount of currency in circulation,” says Kavoussi. “But not only is inflation low; currency growth also has not really changed since the Fed started its stimulus measures,

as noted by Business Insider’s Joe Weisenthal.”Do you actually have some thoughts of your own, or do you just parrot?

Nothing To See HerePhysical laws are constant. Human laws evolve. This is the fundamental difference that you ignore.

This evolution of human/social laws occurs through a very complex process which maths cannot fully capture. If maths could, it could predict their evolution.

Your beliefs in the power of maths are nothing more than scientism. The very root of central planning and all that's immoral with the world. People pretending to "know" how best to run the world throgh charlatanistic science.

Variance Doc"Physical laws are constant." Right. Please see https://en.wikipedia.org/wiki/Oil_drop_experiment.

FlakmeisterBeg pardon?