## The vanity of rigour in economics

13 December, 2016 at 20:22 | Posted in Economics | 5 CommentsReasoning is the process whereby we get from old truths to new truths, from the known to the unknown, from the accepted to the debatable … If the reasoning starts on firm ground, and if it is itself sound, then it will lead to a conclusion which we must accept, though previously, perhaps, we had not thought we should. And those are the conditions that a good argument must meet; true premises and a good inference. If either of those conditions is not met, you can’t say whether you’ve got a true conclusion or not.

Mainstream economic theory today is in the story-telling business whereby economic theorists create make-believe analogue models of the target system – usually conceived as the real economic system. This modeling activity is considered useful and essential. And it’s used both in micro- and macroeconomics. Since everything the economist wants to know is put in to the model, it’s a piece of cake to prove whatever in a ‘rigorous’ and valid way. Deductive certainty is achieved — in the model. Unfortunately, the price one has to pay for getting at ‘rigorous’ and precise results in this way, is making outright ridiculous assumptions that actually impair the possibility of having anything of interest to say about the real world.

Since fully-fledged experiments on a societal scale as a rule are prohibitively expensive, ethically indefensible or unmanageable, economic theorists have to go for something else. To understand and explain relations between different entities in the real economy the predominant strategy is to build models — the preferred stand-in for real experiments — and make things happen in these ‘analogue-economy models’ rather than engineering things happening in real economies.

Mainstream economics has since long given up on the real world and contents itself with proving things about thought up worlds. Empirical evidence only plays a minor role in economic theory, where models largely function as a substitute for empirical evidence. The one-sided, almost religious, insistence on axiomatic-deductivist modeling as the only scientific activity worthy of pursuing in economics, is a scientific cul-de-sac.

Avoiding logical inconsistencies is crucial in all science. But it is not enough. Just as important is avoiding factual inconsistencies. And without showing — or at least warrantedly arguing — that the assumptions and premises of their models are in fact true, mainstream economists aren’t really reasoning, but only playing games. Formalistic deductive ‘Glasperlenspiel’ can be very impressive and seductive. But in the realm of science it ought to be considered of little or no value to simply make claims about the model and lose sight of reality.

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Economic malpractice seems to have given “axiomatic-deductive” methods a bad name, but claims that this malpractice constitutes any sort of “rigor” ought to be rejected and ridiculed. Economists are misapplying analysis whenever they wave their hands out the classroom window, insisting that the world can be “like” their analytic models.

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The point of analysis is to work out conceptually the necessary and sufficient elements of a systemic order and the logically necessary relation of those elements to one another. This

a prioriactivity is vital to developing an understanding of how actual mechanisms work, because we can not directly observe how things work nor can we sort out willy nilly what is related to what in the chaos of immediate experience. Functional relations do not identify themselves nor do they usually come prepackaged as neatpost hoc propter hocregularities (at least not without a lot of noise)..

I worry when I see someone write about “true premises”. Premises are not “true”. Truth is a quality of a statement about facts concerning the state of the world and its past. Is it true you went to Chicago last Saturday? Premises are not facts. The axioms of a deductive argument typically express some abstract and essential idea, because analysis is ultimately about trying to work out what is essential in a set of functional relationships. The premises of Euclidean geometry cannot be “true” in the sense of being statements of fact, because they abstract from fact. Nobody expects to find a dimensionless point lying around their kitchen or a two-dimensional right triangle lying in the street.

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Euclidean geometry is far from useless. Maps are useful because of Euclidean geometry. Maps are descriptive. But, no one doing geometry confuses the theorem with a map. A good geometer never takes a measurement for a reason. And, a good surveyor and map maker never stops taking measurements. It seems to be only in economics that people practicing the profession get fatally confused.

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An analytic model (a theory) is never in and of itself a synthetic model (a map). And, the epistemic standard of an analysis is of course logical consistency, but also logical completeness. Economists brag on having vetted the first, but many seem almost unaware of the need to meet the second standard. The idea in analysis is to identify the necessary and sufficient elements and the functional relations of those elements in a system. It is no rigor to ignore this second standard for analysis, but economists have all kinds of excuses that the mainstream of the profession inexplicably accepts.

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A classic example is the textbook analysis of production, which posits output as a function of factor input. Output is not actually a mathematical function of inputs, as a moment’s careful thought will confirm (yes, thought experiments are sufficient for some purposes!), but economists introduce a particular assumption to make the production function a relation of maximum output to constrained input, in effect assuming away all the problems of management and engineering in order to focus exclusively on allocative efficiency. Nothing wrong with that choice in analysis; that’s what analysis is for — to work out such distinctions as the conceptual meaning of allocative as opposed to technical efficiency. Nothing wrong until you are proposing an aggregate production function with an accumulating tangible Capital as the Solow Growth Model and giving its progenitor a faux Nobel. Then, with a macroeconomics based on such a growth model, everything is wrong. You have abandoned the habit of critical thought with regard to your analysis. What is this “capital” that accumulates? (Shall we answer Sraffa? I guess not.) If you’ve used a numéraire to add the aggregate capital and aggregate output up, what creates the numéraire? To wit, where is money and finance and economic rent and political power? And, in physical production, where is error and entropy and waste? You’ve left necessary elements out of your analysis and what you have is fatally incoherent. And, that’s before you’ve so much as even looked out the window.

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This is not rigor. No one could make a useful “map” with “a geometry” this impoverished. Other problems of empiricism can scarcely be considered; no wonder they rely on an econometrics that distills vast storehouses of data into a time-series of annual summary statistics with no remaining degrees of freedom and are left scratching their heads, waiting on a millennium to unfold before there will be enough data to resolve basic controversies.

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This, that the standard Solow-Swan economic model of long-run economic growth set within the framework of neoclassical economics is conceptual crap, is consequential practically. This poverty of thinking caused the GFC of 2008 and the prolonged aftermath of policy ineffectiveness. The same poverty of thinking is preventing the political world from thinking thru the economic problem of resource depletion and global climate change that threatens an extinction event of geologic significance within this century. But, hey, why worry?

Comment by Bruce Wilder— 14 December, 2016 #

Hi Bruce,

You cannot use Euclidean geometry as an analogy to formal economic models since economies are consisted of

time-series data. Thus, any formal economic model is actually consisted of many temporal logic assertions with temporalquantifiers such as ∀(for all time periods), ∃(exist a specific time period), etc.

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All conventional equilibrium and behavior equations are implicitly assumed with ∃ quantifier. That means that any solution from equations at a particular time period tx may not be true at different time period ty. Also, there is no transitivity laws for equations with ∃ quantifier.

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For example,

(1) Logic assertion “∃ tx (supply (tx) = demand (tx))” does not imply any other particular time period ty such that supply (ty) = demand (ty).

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(2) Logic assertions: ∃ tx (P(tx) = Q (tx)) and ∃ ty (Q(ty) = R(ty)) do not imply that logic assertion “∃ t (P(t) = R (t))” is valid for any particular time period t.

Comment by Peiya Liu— 15 December, 2016 #

Well done Bruce. You have explained much of what I believe to be true and what in my approach is taken for granted! I use a model which is based on logic and is deliberately made as simple as possible without oversimplification, to show how macroeconomics works. see SSRN 2600103 for a diagram and mechanical expression of it or write to me for a 320 page e-book about it. chesterdh@hotmail.com

Comment by David Chester— 14 December, 2016 #

Hi David,

I read your SSRN 2600103 and suggest that you should be able to make it compliant to NIPA/FOFA accounting system based on economic circular flows

https://www.bea.gov/national/pdf/nipa_primer.pdf

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Economic growth model should use this derived accounting identity:

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∀ t (Y(t) = POP(t)*PR(t)*(1-UR(t))(1+ULC(t)+UCC(t))*LP(t)).

It reads as ” production growth is based on three factors: (a) payroll employment (POP(t)*PR(t)*(1-UR(t)), (b) units of labor/CFC costs, and (c) labor productivity(LP(t). Detailed in https://larspsyll.wordpress.com/2016/12/03/econ-101-theory-of-labour-markets-not-very-scientific/#comments.

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In Solow-Swan Model( ∃ t (Y(t)=K(t)^a (A(t)L(t))^(1-a))), it may exist a time period t such that Solow-Swan’s Y(t) = NIPA-FOFA’s Y(t). But this equal value during a specific time period t cannot assume to be true for another time period, for example, GFC 2008 in Solow-Swan Model.

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This example illustrates the issue about

formal axiomatic systemin mainstream economics. In NIPA/FOFA, we only have two axioms (my expense is your income and my liability is your asset for all time periods). In mainstream economic models, they assume many falsified axioms. For example, Solow-Swan Model implicitly assumes this falsified axiom( ∀ t (Y(t)=K(t)^a (A(t)L(t))^(1-a))) when starting with equation Y(t)=K(t)^a (A(t)L(t))^(1-a) without a temporal quantifier.

Comment by Peiya Liu— 15 December, 2016 #

The fundamental issue in economic modeling is about

time-series economic data..

Variable t in time-series data D(t) should be viewed as a logic variable instead of a

functional or statistical variable. Time-series data D(t) in economies should be viewed as an interval-based temporal logic assertion with time quantifier such as ∀ (for all time periods), ∃(exist a specific time period), etc. This is a pretty standards treatment in technical area of temporal data management.

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All accounting identities are equations or logic assertions based on

∀ quantifiersuch as ∀ t (GDP(t) = P(t) Q(t))..

All supply/demand equilibrium or behavior assumptions are equations based on

∃ quantifiersuch as ∃ t (M(t)V(t) = GDP(t)).

Thus we can derive ∃ t (M(t)V(t) = P(t) Q(t)) or ~ ∀ t (M(t)V(t) = P(t) Q(t)), But this derived logic assertion has quite different meaning from QTM formula M(t) V(t) = P(t) Q(t) with either functional or statistical variable t. Do you think QTM formula what you think you think?

This QTM example just illustrates why we could easily misapply our equations by using deduction/induction/abduction without correct time variable treatment at first place. Many existing economic models are just like. It is not deduction wrong. It is due to overstretched equation meaning by wrongly modeling the time variable.

Comment by Peiya Liu— 14 December, 2016 #