Tuesday, April 20, 2010

CUE CARD ECONOMICS: Mathematical economics

Open any contemporary economics textbook or journal, and you’ll find the pages inside littered with charts, graphs and mathematical formulae—all of them pretending to a precision that the alleged economists drawing them up simply don’t have.  These people, remember, were so busy in recent years looking at the results of their psuedo-economic equations and hypothetical mathematical models that they didn’t notice that the real economy outside was about to collapse in a way that showed their models to be so much useless garbage. Elaborate castles in the air broken on the incoming tide of reality.

Mathematical economics has several strikes against it underpinning its abject failure to do the job it purported to do.

First off, the formulae themselves are garbage.  They are not derived in the way a physicist or an engineer of materials derives his formulae describing real   scientific and engineering phenomena. Instead, they are merely hypothetical expressions of hypothetical relationships using either hypothetical or already irrelevant data.  And as Henry Hazlitt points out, “the mathematical economists . . . tend to forget that out of a merely hypothetical equation or set of equations they can never pull anything better than a merely hypothetical conclusion.” 

Or to put it more simply: Garbage in, garbage out.

    _Quote The deliberations which result in the formulation of an equation are necessarily of a non-mathematical character [points out Ludwig von Mises]. The formulation of the equation is the consummation of our knowledge; it does not directly enlarge our knowledge. Yet, in mechanics, the equation can render very important practical services. As there exist constant relations between various mechanical elements and as these relations can be ascertained by experiments, it becomes possible to use equations for the solution of definite technological problems. Our modern industrial civilization is mainly an accomplishment of this utilization of the differential equations of physics. No such constant relations exist, however, between economic elements. The equations formulated by mathematical economics remain a useless piece of mental gymnastics and would remain so even it they were to express much more than they really do.
    “A sound economic deliberation must never forget these two fundamental principles of the theory of value: First, valuing that results in action always means preferring and setting aside; it never means equivalence or indifference. Second, there is no means of comparing the valuations of different individuals or the valuations of the same individuals at different instants other than by establishing whether or not they arrange the alternatives in question in the same order of preference.”
Not everything that can be measured is worth measuring.  Not everything that is worthwhile is able to be measured. And not everything that pops out at the end of a string of calculations is a reliable predictor of the future. The econometricians make all three errors with their derivations of equations purporting to model systems and behaviour more complex than their ability to model them, and in their results that demonstrate their inability to meet the challenge.

The aim of the econometricians is to scientise a non-science—as one of their breed once said in the journal Econometrica, the goal is “to help make economics a more or less exact science as was the determination of atomic weights for the development of chemistry.” But economics deals with human beings, not with atoms or molecules—human beings whose individual actions, choices and values are not able to measured in the way atoms and molecules can be, and whose behaviour can be even less predictable than the atomic particles so beloved of physicists. 
    _QuoteTake the simple "Lagrangian Multiplier" that we use in basic graduate-school economics to ‘explain’ consumer behavior [suggests William Anderson]. Here, economists construct an equation in which one’s utility depends upon, say, goods ‘x’ and ‘y.’ The ability to accumulate such goods is constrained by one’s income and the prices paid for the goods.
    “In determining the "optimal" state that the consumer can enjoy, one uses tools of multivariable calculus to reach a point where ‘equilibrium’ is reached. At that point, the marginal utility of good ‘x’ divided by the price of good ‘x’ is equal to the marginal utility of good ‘y’ over the price of that good.  (I have not done the mathematical work on this page for obvious reasons.)
    “The problem here is that this ‘solution’ is nonsense. Utility (or consumer satisfaction) cannot be measured in cardinal terms. There is no way to take a cardinal measure of someone’s satisfaction. I can say that I like chocolate more than vanilla, but I cannot put that preference in cardinal numbers. An attempt to do so is nothing short of an exercise in fraud.”
The assumption of precision emerges out of the arithmetic, but it is nowhere in the derivation of the arithmetic.  Economic tinkerers over-simplify at the individual level (the bane of non-reality of “partial equlibrium”), while arithmeticising “utility maximisation” in the aggregate, apparently unaware that the aggregation of an error is simply its magnification. 

To quote Henry Hazlitt again,
_Quoteif a mathematical equation is not precise, it is worse than worthless; it is a fraud.” 
Worse still, the illusion of precision is a nonsense turning the mathematical lacunae of the econometrician into a prescription for the planner.  If “the use of calculus and differential equations to describe economic phenomena represents a Procrustean bed, into which the discrete, discontinuous phenomena of actual economic life are mentally forced” (as George Reisman argues), then the results of that calculus and those differential equations are used to force human behaviour into a Procrustean bed described by the way economic planners and Reserve Bank economists (but I repeat myself) suppose it to be, not as it is.

Thus, when after consulting the entrails of equations they emerge to chant “market failure,” we should instead realise that the failure that is really evident here is an abject failure of theory.

Second, as Ludwig von Mises pointed out, “mathematics is silent as to causality.”   Human action (which is the field that economics studies) involves “the apprehension of causal relations” among entities and existents, and the purposeful actions human beings take to bring those entities and existents into a causal connection with human needs.  If it is to be taken seriously, the field of economics must describe and draw out the conclusions of all this human action. Yet mathematics itself is utterly blind to the existence of causality, and inherently confused about the direction of the causal “arrow.” 

In short, it scrambles cause and effect—a confusion more than any other that is responsible for the many destructive non-sequiturs of the likes of Keynesian pseudo-analysis, which constantly reverses cause and effect in a manner as destructive of real economic activity as the burning of the nation’s savings.  (Just one example will suffice: the absurd assumption that spending, as measured by GDP, is the cause of production rather than its effect—leading to the absurdly destructive notion that, when spending falls, governments must take money from producers to jack up spending in the hope and expectation this will (somehow)increase economic activity. Yet nothing could more successfully suppress it.)
    _QuoteThe claim is sometimes made that any relationship, including presumably causal relationships, can be expressed mathematically [notes Roger Garrison]. John Egger's attempt to give plausibility to this claim by offering a far-fetched example is noteworthy because the particular example he chose provides, if only inadvertently, a sound basis for rejecting the claim. Egger translates the old saw ‘absence makes the heart grow fonder’ into f'(x)>0. (The first derivative of fondness with respect to absence is greater than zero.) Tellingly, the word ‘makes,’ which indicates the direction of causality, is unavoidably lost in the translation. The exact same mathematical expression would result from a translation of the converse: ‘growing fonder makes the heart absent.’"
The blindness of mathematics to causality, and human relationships, could not be more obvious.

Third, mathematics is blind to real market processes. Because of the very nature of differential equations, the primary tool of the econometric tinkerer, imathematical economics concentrates its attention unduly upon final equilibrium, which as Reisman says, “are all that its differential equations are capable of doing.”
    _QuoteIt thus takes attention away from the real-world operation of the profit motive and of the market processes by means of which the economic system continually tends to move toward a state of full and final equilibrium without ever actually achieving such a state...
    “The effect of the dominance of mathematical economics and of the fact that it ignores market processes has been that all the major principles which explain how prices are actually determined, and which were discovered by the classical economists, have been completely forgotten…”
… and young students entering the field of economics never get to learn the real market processes by which human needs and wants are met (or, to paraphrase Bastiat’s famous example, “how Paris is fed!”), and as graduates they come to deny those processes actually exist.

No wonder they are so ready to describe (and accept) an economy as “a chaotic system.”

Fourth, and finally (for now), the use of mathematical economics has effectively become a means by which entry to the “priesthood” of economics is judged—it has erected (in Reisman’s phrase) “a sort of exclusive ‘Scholar’s Guild’ which, as was the case in the Middle Ages, seeks to shut out all who do not first translate their thoughts into its esoteric language.”
    _QuoteOne can say, for example, that the amount of bread people will buy at any given price of bread depends both on the price of bread and on the prices of all other goods in the economic system. Or one can say that the quantity demanded of bread is a mathematical function of all prices in the economic system, and then write out a nonspecific mathematical function using symbolic terminology.
    “If on merely writes such an equation and stops at this point, all that has taken place is an act of intellectual pretension and snobbery…  If, however, one goes further and believes one can actually formulate a specific equation—that, for example, the quantity demanded of bread equals ten thousand divided by half the square of the price of bread minus the price of butter and the average of grocers, then one is led into major errors…
    “The belief that an equation could be constructed that would take such changes into account [as the introduction of new goods technologies, and changes in ideas, incomes, populations and valuations] is totally opposed to reality.  It is tantamount to a belief in fatalistic determinism and implies, in effect, that a mathematical economist can gain access to a book in which all things past, present and future are written, and then derive it from the corresponding equation.  Whatever it may be, such a view is definitely not within the scientific spirit.”
Let me conclude with three pieces of advice from three economists who were no mean mathematicians themselves.
_Quote(1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This I do often."
- Alfred Marshall, letter to his friend and colleague Arthur Bowley
_QuoteMathematics is ... useful, though not an indispensable adjunct to economic studies; a finish to the training of an economist comparable with a knowledge of the classics as part of a general education…. Not much is gained by the translation into mathematical language."
- Francis Edgeworth, ‘On the Application of Mathematics to Political Economy

_QuoteThis is not a dispute about heuristic questions, but a controversy concerning the foundations of economics. The mathematical method must be rejected not only on account of its barrenness. It is an entirely vicious method, starting from false assumptions and leading to fallacious inferences. Its syllogisms are not only sterile; they divert the mind from the study of the real problems and distort the relations between the various phenomena.”
- Ludwig von Mises, in ‘Mathematics Versus Economic Logic

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24 Comments:

Anonymous Falafulu Fisi said...

What's the point of studying economics or even having economics departments if there's no analysis (mathematics) at all? Why not just integrate Economics into say, Sociology, i.e., they merge into just one department called Social science? What's the need for school of economics then, when in fact, they can be merged into social science? Anything else that is analytical in economics should be folded into statistics/maths. Is this something that you support? Kill economics and integrate it into sociology?

Abolished all economic schools in the world? What you say then? If economics theory can be condensed into just one book from say, the Austrian economics, then that just one book can be taught as an economic paper for half a semester from papers in say from Social Science department.

It is not the math that is the problem; it is those with authorities that used them unquestionably and not cautiously. Note, that bubbles & crashes will still happen with or without regulations & government interferences. Those will take place even in a perfect Austrian economic environment – but perhaps less mild than they’re in heavily regulated environments of today.

You've made a lot of references & quotes here, but they're just opinions. They're not founded in empirical evidence but you only rely on those you quoted from do think.

You go on about business cycle and how it was discovered by Austrians, but you’re wrong there. It was inferred from mathematical data analysis, i.e., statistical mathematics. Without quantitative analysis, then economics is pretty much useless. I think that you mean to criticize the wrong formulations of economic theories (like neo-classical, etc,…) rather than saying that mathematics can’t be applied to economics analysis. Can you see the difference between the 2 here? It seems to me that you've lumped them into one.

4/20/2010 12:14:00 pm  
Blogger PC said...

"What's the point of studying economics or even having economics departments if there's no analysis (mathematics) at all?"

Becuase the tool to study economics is not analysis by mathematics but analysis by mathematics.

"It is not the math that is the problem; it is those with authorities that used them unquestionably and not cautiously."

No, it's both.

"You've made a lot of references & quotes here, but they're just opinions..."

You would seem to have skipped straight past the arguments.

"You go on about business cycle and how it was discovered by Austrians, but you’re wrong there. It was inferred from mathematical data analysis..."

Well, no it wasn't.

"I think that you mean to criticize the wrong formulations of economic theories (like neo-classical, etc,…) rather than saying that mathematics can’t be applied to economics analysis."

No, I mean to say precisely what I've said.

The analytical tool of economics is not mathematics,it is logic.

4/20/2010 12:54:00 pm  
Anonymous Anonymous said...

As a not so young student studying first year economics I really enjoyed this post. So much of the course consists of differential equations and any actual application of them is put in the most subjective of terms. 'Economists disagree on..' is all you can find when the effect of say minimum wage price floors is discussed. Keynes was quoted three times in the first chapter though!

Del

4/20/2010 01:15:00 pm  
Anonymous Falafulu Fisi said...

PC said...
Well, no it wasn't.

Well, how was it discovered then in the first place? Was there a survey or an interview of every economic agents in the whole economic systems at the time, and it was then found out from the facts revealed by those agents (i.e., in their actions) about the cause? Or was the economic data just being interpreted in a simple correlation, with no prior interviews of the agents that made up an economic system? If correlation was used, then sorry, that's math. It is no different to what other economic analysts of today. They use tools to probe economic data and see what comes out of them.

PC said...
The analytical tool of economics is not mathematics, it is logic.

But mathematics is logic. See, when someone is using mathematics to model an economic system, it is not the math that's illogical. It is the very formulations of the models (by whoever's doing it) that can be illogical (i.e., wrong formulations). Now, we know that Keynesian framework started with wrong formulations about market equilibrium, which we now know that it is false. But the math is always being blamed for disasters and not the wrong formulations of that theory to start with. You apply wrong formulations, then of course you will get wrong results/estimations, etc...

Market herding behavior is a collective phenomena and not an action of individual agents according to their own rational choices, and although we can argue that every individual thinks differently from other agents in an economic system, that very assertion breaks down when herding emerges.

4/20/2010 02:23:00 pm  
Anonymous Barry said...

Milton Friedman is quoted as saying that "all assumptions in mathematical economic models should be judged on how well the theory predicts reality, not how well the assumptions accord with reality.

If a theory can be shown to have a high correlation with actual circumstances. And this theory was made using logic. Then someone would not be called a fool for considering that this idea might have some merit. For this is the same method used by the natural sciences.

That is what the maths in economics is all about.

If you are charging that ALL the mathematical models in economics have been proved wrong by reality then you should provide some evidence to back this claim up. You didn't.

A market crash did not invalidate all models which may have been unrelated to that crash.

Many social disciplines utilise statistics. They are a tool. A tool of analysis. Statistics have proved useful in many cases in public health studies and sociology in pointing those who make decisions in the right directions - i.e. where to spend money, who might be at risk.

Since economics is a social discipline maths can be equally as useful.

It may disappoint you that you cannot read the economics literature, but that alone does not make it not valuable.

In the same vain just because you think that their underlying theories are incorrect, does not make their tools for testing it invalid.

4/20/2010 02:35:00 pm  
Anonymous Falafulu Fisi said...

Barry, are you talking to me or PC?

You said...
A market crash did not invalidate all models which may have been unrelated to that crash.

Equilibrium models don't involve or explain market crash. There is nothing in the model that says anything or something about market crash, ie, its not in the model. Complex system modeling of recent times, however have had some limited success in explaining bubbles & crashes.

4/20/2010 03:31:00 pm  
Anonymous Falafulu Fisi said...

PC said...
But economics deals with human beings, not with atoms or molecules—human beings whose individual actions, choices and values are not able to measured in the way atoms and molecules can be, and whose behaviour can be even less predictable than the atomic particles so beloved of physicists.

That's true that humans are not atoms or molecules, but humans & molecules/atoms behave similarly when they're acting collectively (herding) and not individualistically.

An interesting blog post shown below from a financial engineer, that may be interest to the discussion here on applying Ferro-magnetic Icing Models from statistical mechanics to economics/finance. The amazing thing is that such models (or similar ones to Icing) have reproduced the markets characteristics (stylized facts) that are observed in the real world, in which standard economic theories failed to reproduce.

Music, molecules and misanthropy (econo-physics part 1)

Individual agents in an economic system can still think as an individual, but he is interacting with other agents at the same time, which in its very nature it is complex and it continuously adapts. This is the main reason why forecasting is almost or completely impossible because of the very dynamical nature of an economic system.

4/20/2010 04:53:00 pm  
Anonymous LGM said...

FF

When you write about complex modelling, are you referring to complex algebra (like "i") or something different to that? Just interested, as I use complex algebra for control engineering purposes (it can also be used for vehicle NVH, mechanics of vibration and so on). The results are useful, but I've often felt this approach was more of a device than a description of a real physical system.

LGM

4/20/2010 06:01:00 pm  
Anonymous Falafulu Fisi said...

LGM, it is the domain of Complex System Theory or CST (which is multidisciplinary field) and although feedback control theory is included in CST, I haven't seem much use of the complex number 'i' in their published researches. There may be, but I haven't come across one yet.

4/20/2010 07:09:00 pm  
Blogger Paul Walker said...

"“The problem here is that this ‘solution’ is nonsense. Utility (or consumer satisfaction) cannot be measured in cardinal terms."

Just a small point, utility isn't measured in cardinal terms, its measured in ordinal terms.

4/20/2010 07:22:00 pm  
Blogger Paul Walker said...

"Alfred Marshall, letter to his protégée, A.C. Pigou"

AFAIK the letter was to A. L. Bowley.

4/20/2010 07:29:00 pm  
Blogger Paul Walker said...

The point about maths in econ is that maths is just a tool. Like all tools it can be used well or badly, so the argument isn't that we shouldn't use maths when doing economics, its that we should use maths well when doing economics.

4/20/2010 07:31:00 pm  
Blogger Paul Walker said...

Pete. You may want to check out just how much maths is used in Austrian econ these days. Checkout Nicolai Foss, "Austrian Economics and Game Theory: An Evaluation and a Stocktaking," Review of Austrian Economics, 13: 41-58. (2001) for a look at just one math tool used in Austrian econ.

4/20/2010 07:48:00 pm  
Blogger gregster said...

Ha! I knew you'd be the first to bite FF. :)

I agree with PC, muchly.

4/20/2010 07:49:00 pm  
Blogger PC said...

@Paul, "You may want to check out just how much maths is used in Austrian econ these days. Checkout Nicolai Foss, "Austrian Economics and Game Theory: An Evaluation and a Stocktaking," Review of Austrian Economics, 13: 41-58. (2001) for a look at just one math tool used in Austrian econ."

Crikey, that's frightening. Mind you, I was heartened to see this admission in the abstract: "...admittedly some aspects of game theory don't square easily with Austrian economics."

4/20/2010 11:47:00 pm  
Blogger PC said...

"AFAIK the letter was to A. L. Bowley."

Oops, yes you're right. It was Pigou who included it in his memoriam to Marshall.

4/20/2010 11:55:00 pm  
Anonymous Falafulu Fisi said...

Paul, I found a free copy on the net. I am interested in the last sentence of the abstract that says:

Moreover, a major stumbling block for an Austrian acceptance of game theory may lie in the traditional resistance to formal methods.

I agree with that comment and this is precisely of what PC and his Austrian ilks are doing.

Another quote from the paper:
A further reason is that game theory has been argued to address exactly the dynamics of the market process that Austrians have so vigorously criticized mainstream economics for neglecting.

Game theory comes under the general umbrella of complex system theory.

Austrian Economics and Game Theory : An Evaluation and a Stocktaking

Austrians should move forward from thinking in the way of 17th century, because they definitely missed the boat and being left behind. There is a default position for Austrians that I have noted. If its' mathematical economics (whatever that math originated from) it must be bullshit.

Some econophysicists had already identified Heyak as the pre-cursor of modern economic complex system theory, but some die-hard Austrian economists & followers with 17th century mentality, just don't make a connection, ie, they refuse point blank to even connect the dots. It is sad to see them miss the boat completely in the evolution of economics, because what they do advocate for is good .

4/21/2010 12:44:00 am  
Anonymous LGM said...

FF

Ah, it's a different topic.

I'm using complex algebra, mostly as the result of employing Laplace Transforms when dealing with differential equations. What is interesting is that sometimes you don't need to actually solve the d.e. since the transform provides sufficient information to know about some characteristics of a problem/situation (e.g. whether the system is going to be unstable etc.).


Ta for the clarification.

LGM

4/21/2010 07:19:00 am  
Anonymous Falafulu Fisi said...

Nash/Von Neuman type games which are still equilibrium-based models are not the only ones in town. Econophysicists have developed the Minority Games (MG) which is the mathematical modeling of the El Farol Bar problem.

The minority games (MG) is not based on equilibrium at all (which is more realistic) compared to other classical games such as Nash game theory model and the likes which are in fact they were formulated based on equilibrium. Equilibrium in the real world doesn't exist (fact), this is why everyone today (including economists) agrees that neoclassical failed because it is based on equilibrium (which is false).

New variants of MG have emerged in recent years thus improving on the original model of MG. It has far outreaching conclusions, because the model reproduced what we see in the real markets of today, eg: The outcome of the MG model produced the stylized facts in economics that we observe today. The spontaneous order that emerges from the cooperation amongst agents in an economic system is also observed in the MG framework, note that this is what Austrian like Hayek had exactly proposed.

In the real world, there is no such thing as a perfect model and I think that this is what Austrian are opposed to, which is the economic imperfect models of today, however as any other invented model, MG is always improving (been modified over time in recent years) upon its original model.

Here is an excellent article on MG:

Minority Games -
What happens when physicists start doing economics


Ideas borrowed from ferro-magnetic Icing Model were applied in the development of MG. See, humans do show frustration & cooperation in their behavior in the real work markets which are similar to frustration & cooperation of particles & molecules in the Icing Model.

I agree with Nicolai Foss (author of : "Austrian Economics and Game Theory : A Stocktaking and an Evaluation"), that Austrian should start embracing game theory (under complex system umbrella) because it is closer to what Hayek advocated for in his time.

4/21/2010 07:26:00 am  
Anonymous Falafulu Fisi said...

LGM, do your engineers at work developed or designed complex/complicated control systems? If they are and you think that they may need some help, then I can give them some software libraries that I have already developed for my own use (in other areas mainly in finance). If they find it useful to be used in any commercial product development for your company then I can charge them a one-off fee this including any consultant work that I may do for them ie, some custom code development or perhaps coaching them on the library functionalities itself. I have a fuzzy logic library and also a non-linear control one ie, neural-network & fuzzy hybrid (all written in Java). Ask your engineers if they want to just flick me an email as an informal chat to find out if what I have already can be of any use to them.

4/21/2010 07:44:00 am  
Anonymous Falafulu Fisi said...

One of the major reason that I am a skeptic over global warming, is that the main foundation that it is built upon is based on equilibrium physics of radiative heat transfer. In actuality, equilibrium doesn't really exist in climate system at all. It is an adaptive complex system that doesn't settle at a stable point long enough, which makes its whole formulation started off wrong footing. Neoclassical economics is based on equilibrium, which in reality, equilibrium doesn't exist and this is why keynesian economic framework and all its neoclassical fellow models are unworkable because their formulations were based on a wrong assumption.

Hurricane/storm is physical phenomena which characterized by self-emergence/self-organization property of a climate dynamical system. AFAIK, there is none whatsoever in today's climate models that reproduce hurricane dynamics. I mean there is no single model that when a simulation is run, then hurricane will emerge out of the model. We have models to explain what they are, but no model has ever been invented or formulated to reproduce hurricane phenomena yet. WHY? Because such model is difficult, since scientists must have to drop their beloved equilibrium models that they cling to religiously and we know from experiences/results so far in complex system dynamic modeling such as general game theories including minority games, that observed market dynamics of today, equilibrium-based neoclassical economics have failed miserably. Equilibrium dynamics cannot explain spontaneous order of emergence and self organization, none whatsoever. As a commenter on the econophysics forum stated:

...no one can teach old dogs new tricks, no matter how many millions generously spent.

This is true regarding both warmists (equilibrium radiative heat transfer model) and neoclassical economists with their equilibrium based economic theories.

4/21/2010 08:50:00 am  
Anonymous LGM said...

FF

Will call.

LGM

4/22/2010 06:23:00 am  
Anonymous Greg said...

Milton Friedman is quoted as saying that "all assumptions in mathematical economic models should be judged on how well the theory predicts reality, not how well the assumptions accord with reality.

In other words, "make shit up, and if you happen, by some complete fluke, to get the right answer, you, too, can win a Nobel prize."

What a bass-ackwards way to run a planet!

4/22/2010 11:59:00 am  
Blogger Paul Walker said...

"In other words, "make shit up, and if you happen, by some complete fluke, to get the right answer, you, too, can win a Nobel prize.""

No because flukes only happen once. To win the Nobel you have to be right often and about big things. Hence Friedman's win.

4/22/2010 09:31:00 pm  

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