Sunday, July 30, 2017

Tim Johnson — Why mathematics has not been effective in economics

I have the opinion that almost all of the criticism of the use of mathematics in economics stems from a lack of understanding of what mathematics is, reflecting a general ignorance in economics that has led to the failure of mathematics in economics.…
The starting point of understanding the role of mathematics in finance and economics is to appreciate what mathematics is concerned with. Mathematics is concerned with identifying relations between objects: bigger smaller, to the left/right, symmetry, before/after and so forth. Top class mathematical research is concerned with discovering new ways of representing how things are related. More every-day research shows that A=B or how you go from A to B. Once the mathematicians have done their work, of "formatting the world as we experience it" by identifying how we see relations between objects, others then get on and do things.…
Mathematicians rely on other disciplines providing problems, mathematics, whatever the caricature of a mathematician dealing with abstract ideals will say. Mathematics then figures out a way of looking at the problem - the relations between its components - so that a solution can be found. The caricature of the mathematician is explained by how mathematics is presented. Rather than starting with the problem and then breaking it down into its components, mathematics is presented back to front. It starts with the components and then shows how these combine to deliver the observed phenomena.…

The effect in economics is most clearly seen in Friedman's argument, in theMethodology of Positive Economics, that the validity of an economic theorem should not rest on the realism of its assumptions. I will not dismiss Friedman as the arch-priest of neo-liberalism as I think the argument he makes has some merits (he focuses on the empirical outcome and would normally be regarded as 'anti mathematiciastion'). The attitude he shares with most economists, along with Kant, Hobbes and Spinoza, is that a 'mathematical' argument flows from assumptions to conclusions. A mathematician approach would be to try and tease out the correct assumptions from the observed behaviour. I would prefer the problem to be re-cast as "By fetishising synthetic a priori knowledge, economists turned economics into a highly paid pseudoscience".

The next question is why do economists do this. The answer is rooted in the observation that the 'mathematical' approach is powerful rhetorically: you can use it to convince everyone of almost anything, providing you can make the chain of arguments tricky enough to follow.…
Once mathematics has delivered ways of identifying relations in physics, 'invariants' can be identified, such as momentum, energy or the speed of light (Noether's Theorem is critical here). Physical theories are then tested on the basis of whether or not they adhere to a particular conservation law. Because economics is disinterested in using mathematics to identify relationships it has been unable to accomplish the next step of discovering invariants.…
Money, Maths and Magic
Why mathematics has not been effective in economics
Tim Johnson | Lecturer (associate professor) in the Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh

12 comments:

AXEC / E.K-H said...

Why economists have not been effective in economics
Comment on Tim Johnson on ‘Why mathematics has not been effective in economics’

Mathematics has not been effective in economics because economics is a cargo cult science. Feynman defined it as follows: “They’re doing everything right. The form is perfect. ... But it doesn’t work. ... So I call these things cargo cult science because they follow all the apparent precepts and forms of scientific investigation, but they’re missing something essential.”

What is missing among economists is a proper understanding of what science is all about. Aristotle gave a working definition 2000+ years ago: “When the premises are certain, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing.”

Economists apparently followed this methodology. Walrasian economics is axiomatized, the hard core premises are verbally given as follows: “HC1 economic agents have preferences over outcomes; HC2 agents individually optimize subject to constraints; HC3 agent choice is manifest in interrelated markets; HC4 agents have full relevant knowledge; HC5 observable outcomes are coordinated, and must be discussed with reference to equilibrium states.” (Weintraub)

It should be pretty obvious that the Walrasian axiom set contains THREE NONENTITIES: (i) constrained optimization (HC2), (ii) rational expectations (HC4), (iii) equilibrium (HC5). Every theory/model that contains a nonentity is A PRIORI false. And this is why economics is a cargo cult science. Economists do all the things scientists are supposed to do but it does not work.

Science is about invariances (Nozick) but there is NO such thing as behavioral invariances. Because of this, the Walrasian axioms are methodological madness, to begin with.

Economics suffers from the fact that the subject matter is ill-defined. Economists think that they are doing economics while they bungle amateurishly in sociology and psychology. What economists overlook is that their subject matter is the structure and behavior of the economic system and that all questions about Human Nature/motives/behavior/action are NOT their business.

The task of economics is to figure out how the economy works. Economics is a system science. Accordingly, the correct approach is not microfoundations but macrofoundations.#1

What we have at the moment is Walrasianism, Keynesianism, Marxianism, and Austrianism. Neither of these approaches satisfies the scientific criteria of formal and material consistency. Economists are PROVABLY false with regard to the two most important features of the market economy: (a) the profit mechanism, and (b), the price mechanism. Let this sink in: the profit theory is false since Adam Smith. Instead of having clarified their foundational concepts profit and income, economists have wasted their time fooling around with NONENTITIES.

Economics needs a paradigm shift from false Walrasian microfoundations and false Keynesian macrofoundations to true macrofoundations. Economics is NOT a social science but a system science. A system can be objectively and precisely defined. This is the very condition for the application of mathematics.

When the premises are not correctly defined mathematics cannot work its magic and as a collateral damage econometrics becomes a senseless exercise.#3 When utility maximization is put into the premises no testable proposition ever results. Scientifically incompetent economists do not understand this elementary methodological fact since 140+ years. And this is why mathematics has not been effective in economics.

Egmont Kakarot-Handtke

#1 New Economic Thinking: the 10 crucial points
https://axecorg.blogspot.de/2017/07/new-economic-thinking-10-crucial-points.html

#2 Profit theory in less than 5 minutes
http://axecorg.blogspot.de/2017/07/profit-theory-in-less-than-5-minutes.html

#3 Morons on math
https://axecorg.blogspot.de/2017/06/morons-on-math.html

Neil Wilson said...

Economics uses mathematics in the same way medieval religions use Latin. It is to give an air of mystery and power to the charlatans doing the 'interpretation'.

Kaivey said...

I'm not a mathematician, although I loved calculus at college, but economics is about psychology and I doubt whether that can be measured without conjecture and assumption.

AXEC / E.K-H said...

Economists: just too stupid for counting

The mathiness problem of economists does not consist in the application of advanced mathematics but in the incapacity to apply the straightforward arithmetic of accounting.

Imagine we have two accountants, one for the business sector, Mr. B, and one for the household sector, Mrs. H. Mr. B is supposed to make an entry every time the firm makes a wage payment and every time the firm sells its output. To make matters simple, the condition of market clearing holds, that is, quantity sold = output, that is, there is no change of inventory. Mrs. H is supposed to make an entry every time one of the households receives wage income and every time a household buys the firm’s product.

Nobody could be more down to earth and historically accurate than Mr. A and Mrs. B. At the end of the first period, they meet at the Honest Accountant Bar and compare their numbers, which are shown in the form of accounts on Wikimedia.

(a) National accounts, pure consumption economy, two sectors, initial period, consumption expenditures = wage income, C = Yw.
https://commons.wikimedia.org/wiki/File:AXEC94.png

The accountants are pleased that their respective numbers are exactly equal. This means that both have captured reality, i.e., every single transaction in the period under consideration, accurately.

At the end of the second period, they meet again and compare their numbers. This time they have:

(b) National accounts, consumption expenditures greater than wage income, C > Yw.
https://commons.wikimedia.org/wiki/File:AXEC95.png

The accountants are again pleased that their respective numbers are exactly equal but this time their accounts show balances.

Says Mr. B, I call my balance profit or loss, as the case may be, more specifically I define monetary profit as Qm ≡ C - Yw.

Well, says Mrs. H, I call my balance saving or dissaving, as the case may be, more specifically I define monetary saving as Sm ≡ Yw - C.

Then they calculate their respective balances and find out, to nobody’s, surprise that Qm=-Sm. Note that NO real transactions and transaction entries correspond to the balances. To draw the balances is an ex-post exercise that is NOT backed by a real world transaction.

See part 2

AXEC / E.K-H said...

Part 2

Next day, the two accountants hand their numbers = Figure (b) over to the economist. Says the economist, hmm, for my purposes I have to rearrange the accounts, after all, profit has to be treated as the income of capital analogous to wage income. I define Gross Domestic Income as GDI ≡ Yw + Qm. He does NOT realize that he puts a flow and a balance together, something no accountant worth his salt would ever do. Now the accounts look like this:

(c) National accounts, consumption expenditures greater than wage income, with profit redefined as a kind of income.
https://commons.wikimedia.org/wiki/File:AXEC97.png

The economist now says to himself, obviously, Gross Domestic Income GDI is ‘equal’ to consumption expenditures, which follows from the definitions GDI ≡ Yw + Qm and Qm ≡ C - Yw. Let us call the right-hand side of the business sector’s account Gross Domestic Product GDP for the general case of the sum of consumption expenditures and investment expenditures, i.e. GDP ≡ C + I. . Then we have always GDI ≡ GDP. This, Gross Domestic Income is ‘equal’ to Gross Domestic Product, is the fundamental macroeconomic accounting identity ― the unassailable quantitative/empirical bedrock of economics.

The economist’s exercise is, of course, futile because profit is NOT the income of capital but the mirror image of dissaving, i.e. the household sector’s increase of debt. Income is a flow and profit is a balance of flows and to lump the two together is sheer stupidity.

From the graphics, it is immediately obvious that Keynes’ foundational identity “Income = value of output” is false. Why? Because Keynes did not come to grips with profit: “His Collected Writings show that he wrestled to solve the Profit Puzzle up till the semi-final versions of his GT but in the end he gave up and discarded the draft chapter dealing with it.” (Tómasson et al.)#1

Because economists ― Keynes, Keynesians, Post Keynesians, Anti-Keynesians and all the rest ― cannot even do the elementary mathematics of accounting the profit theory is false since Adam Smith.#2 This means because economists cannot do their little math ALL of economics is proto-scientific rubbish.

Egmont Kakarot-Handtke

#1 See also ‘Economists do not solve problems, they are the problem’
https://axecorg.blogspot.de/2015/01/economists-do-not-solve-problems-they.html

#2 For more details see cross-references Accounting
http://axecorg.blogspot.de/2016/12/accounting-cross-references.html

Postkey said...

" . . . profit is . . . the mirror image of dissaving, i.e. the household sector’s increase of debt."

You have the figures for 'profit' and 'the household sectors increase in debt' for the US economy and/or the UK economy?

Andrew Anderson said...

Due to extensive privileges for depository institutions, their liabilities wrt to the non-bank private sector (i.e. the rest of us) are largely a sham now and shall be entirely a sham should physical fiat ever be abolished, i.e. try to "cash a check" if cash no longer exists!

Yet somehow we are supposed to have an honest, at least, economic system with sham accounting!

Who benefits from sham liabilities? ans: the banks themselves and the more so-called creditworthy at the expense of the less so-called creditworthy of what is, consequently, the PUBLICS credit but for private gain.

jrbarch said...

Which comes first: - the relation or the expression of the relation? The husband loves the wife – he buys her flowers. The husband hates the wife – he beats her. You could argue about what ingredients make a mix in the relation. So, economics is a relation between two human beings first – then comes the expression? All the rules are made up in line with the relation. Ever seen two little babies put into a room together without any toys. They smile, goo, laugh at each other, enjoy each other, and start relating. If greed and power are the relation (between adults?), what do you expect the rules to look like?

What if everyone practiced kindness and were civilised? Your economic ‘science’ would reflect that accordingly; so would the rules. Of course the expression impacts back on the relation, but the quality of the relation is the initial determinant. Is that about right Tom? We are dealing with human beings?

It all swims around in the soup of human consciousness: - change that and the expression changes.

AXEC / E.K-H said...

Neil Wilson

Economics is a failed science because economists are scientifically incompetent. The proof is in the misapplication of mathematics. Of course, this is NOT how economists explain their failure. They come up like a Pavlovian dog with explanations = excuses#1 like these:

“In mathematics, an object is something we can quantify. Now comes the problem: in economics, what we need to identify is the relation between emotions (greed, fear of loss, investor euphoria, etc.) and behavior (buying, selling, tolerance for risk, and so forth). Alas, this requires that we mathematize emotions. To my knowledge, no one has succeeded in doing this in some 8,000 years of recorded history.”

“Isn’t the problem just the level of complexity of the system? The fundamental agents in economic models, people, all have huge variation in possible actions. We then have self-consciousness and reflexivity. We react to each other’s actions; then, as a system, react again to the changed situation.”#2

“What economists ought to do is take a more inductive (historical) approach. This is exactly what the tradition’s best thinkers have done, but the approach is not currently popular in academia.” (Cavalla)

“Economics uses mathematics in the same way medieval religions use Latin. It is to give an air of mystery and power to the charlatans doing the ‘interpretation’.” (Wilson)

All this sounds plausible but demonstrates only a poor understanding of science. Economics suffers from the fact that the subject matter is ill-defined. Economics is NOT a social science but a system science. The subject matter is the structure and behavior of the economic system, and all questions about Human Nature/motives/behavior/action are the business of other disciplines (psychology, sociology, anthropology, political science, history etc.). The beauty of the correct systemic approach is that a system is mathematically unambiguously defined.#3 So, there is no mathiness problem but only the problem of blatherers that pointlessly gossip about other peoples’ motives and behavior but cannot tell since 200+ years what profit is.

Egmont Kakarot-Handtke

#1Failed economics: The losers’ long list of lame excuses
https://axecorg.blogspot.de/2017/01/failed-economics-losers-long-list-of.html

#2 Complexity and stupidity
https://axecorg.blogspot.de/2017/01/complexity-and-stupidity.html

#3 The Economics God Equation
https://commons.wikimedia.org/wiki/File:AXEC25.png

jrbarch said...

... oh, the other result of the baby experiment was to throw a toy into the room. The babies each started trying to possess the toy, take it off one another; in some instances one baby clocked the other over the head with it. Sound familiar? Then a little later they come up with a 'science of toys'. Hmmm - to me it looks very much like the relation babies .... !

jrbarch said...

Economic Rule No.1: - 'play nicely and enjoy each other - share'.

Matt Franko said...

"Mathematics is concerned with identifying relations between objects"

I wouldnt say stochastic analysis does this...