## Modelling consistency and real world non-coherence in mainstream economics

from **Lars Syll**

In those cases where economists do focus on questions of market or competitive equilibrium etc., the formulators of the models in question are often careful to stress that their theorising has little connection with the real world anyway and should not be used to draw conclusions about the latter, whether in terms of efficiency or for policy or whatever.

In truth in those cases where mainstream assumptions and categories are couched in terms of economic systems as a whole they are mainly designed to achieve consistency at the level of modelling rather than coherence with the world in which we live.

This concern for a notion of consistency in modelling practice is true for example of the recently fashionable rational expectations hypothesis, originally formulated by John Muth (1961), and widely employed by those that do focus on system level outcomes. The hypothesis proposes that predictions attributed to agents (being theorised about) are treated as being essentially the same as (consistent with) those generated by the economic model within which the same agents are theorised. As such the proposal is clearly no more than a technique for (consistency in) modelling, albeit a bizarre one. Significantly any assertion that the expectations held (and so model in which they are imposed) are essentially correct, is a step that is

additionalto assuming rational expectations.

It is a form of modelling consistency (albeit a different one) that underpins the notion of equilibrium itself. In modern mainstream economics the category equilibrium has nothing to do with the features of the real economy … Economic models often comprise not single, but sets of, equations, each of which is notoriously found to have little relation to what happens in the real world. One question that nevertheless keeps economists occupied with such unrealistic models is whether the equations formulated are mutually consistent in the sense that there ‘exists’ a vector of values of some variable, say one labelled ‘prices’, that is consistent with each and all the equations. Such a model ‘solution’ is precisely the meaning of equilibrium in this context. As such the notion is not at all a claim about the world but merely a (possible) property that a set of equations may or may not be found to possess …In short, when mainstream economists question whether an equilibrium ‘exists’ they merely enquire as to whether a set of equations has a solution.

Modern economics has become increasingly irrelevant to the understanding of the real world. Tony Lawson traces this irrelevance to the failure of economists to match their deductive-axiomatic methods with their subject.

It is — sad to say — a fact that within mainstream economics internal validity is everything and external validity nothing. Why anyone should be interested in that kind of theories and models is beyond my imagination. As long as mainstream economists do not come up with any export-licenses for their theories and models to the real world in which we live, they really should not be surprised if people say that this is not science, but autism.

Studying mathematics and logics is interesting and fun. It sharpens the mind. In pure mathematics and logics we do not have to worry about external validity. But economics is not pure mathematics or logics. It’s about society. The real world. Forgetting that, economics is really in dire straits.

The classical thinkers (Smith, Ricardo, and Marx) have, in general, given us a descriptive theory of economics. Their theory, especially Smith’s, not only described the current economic life of their time very closely but also related to coming events. Yet, their descriptive theories are based on solid philosophical and mathematical (logical) background. For example, Smith’s descriptive theory of general equilibrium might be considered as predecessor to Walras’s formalized (mathematical) theory. Marx, together with his famous Reproduction Schemes (simple and extended), has given a description of the relationship between industries, such that is equivalent to Walras’s theoretical version IO and to Leontief’s empirical (monetary) Input-Output Analysis. It is clear that today’s real economics is characterized by much more high technology and complicate reciprocal relationship between individuals, production sectors, financial and public institutions, and international trades, which increased a stochastic character of economic events. Role of mathematics today is much more significant than Walras’s time. Only by means of mathematics is possible to describe modern economics and planning and forecast its future.

Therefore, formalized (mathematical) theory for the twentieth economy should be accordingly much more complicated than the mathematical theory of economics of the nineteenth century, in conditions that it has to be compatible to contemporary economic reality. In practice, unfortunately, the opposite is true. Namely, today’s mathematical economics is very “technical” and it is far from to expound economic problems. Actually assumptions of contemporary mathematical models become them irrelevant to the practical recommendations. Moreover, sometimes these assumptions are “forgotten” and they are generalized as if those assumptions were not assumed.

Hence, it is not accidental that modern authors have tried to persuade us that current economics “became” mathematical science (Debreu; Weintraub). Supposedly, these claims are based on the well-known law of the dialectics whereby quantitative changes (publications) become qualitative changes. For this to happen, these works must research real economic problems, which, unfortunately, are not the case.

To make their argument more convincing the modern authors have been trying to delegitimate Walras’s mathematics claiming that it is primitive, clumsy, dubious, and even incorrect. Almost every author who has written about Walras and his economics has felt obliged to emphasize this fact.

The following main erroneous claims have been made against Walras’s mathematics in post-Walras mathematical economic literature:

(1) Walras’s general equilibrium theory has only contained equalities;

(2) Walras did not discuss existence of equilibrium and reduced existing problems to the equality of the numbers, of variables and independent equations of the model.

(3) Walras did not consider the problem of comparative static.

(4) Walras’s tâtonnement is clumsy and primitive.

(5) Walras’s model is only characterized by the market clearing principle where the total offer is equal to its total available quantity.

(6) Walras’s general equilibrium theory does not know “Walras’ Law”.

(7) Walras’s tâtonnement is the process of adjustment only of prices without of quantities.

The trouble with modeling of the economics of the nation is that either the model is oversimplified and does not cover the whole of the subject, or that it is too detailed and due to the need to calculate it exactly the computational results have almost no meaning due to difficulty in their interpretation. The answer is to view the macro-economy from a greater distance and perspective so that only the most basic aspects are in focus and can be resolved. Such a model was proposed in my new book “Consequential Macroeconomics–Rationalizing About How Our Social System Works”. Write to : chesterdh@hotmail.com and I will send you a review copy (for private use).

From one roadside ditch straight into the other

Comment on ‘Modelling consistency and real world non-coherence in mainstream economics’

Walras has to be credited for making great methodological progress in comparison to what he called the English School, or, what may be called with more accuracy the Cambridge School of Loose Verbal Reasoning.

What Walras correctly pointed out was (i) that partial analysis does not allow for generalizations and therefore had to be replaced by total analysis and (ii) that the forbidding wish-wash of his contemporaries had to be replaced by rigorous argument.

The methodological credo of the Cambridge School of Loose Verbal Reasoning comes in different wordings but always with the same irresistible message for muddle heads.

“Marshall followed the maxim: Better to be ambigous and relevant than precise and irrelevant.” (Colander, 1995, p. 283)

“Another danger is that you may ‘precise everything away’ and be left with only a comparative poverty of meaning. … Such a problem was avoided, said Keynes, by Marshall who used loose definitions but allowed the reader to infer his meaning from ‘the richness of context’.” (Coates, 2007, p. 87)

“For Keynes as for Post Keynesians the guiding motto is ‘it is better to be roughly right than precisely wrong!’” (Davidson, 1984, p. 574)

The Elements are quite clear on multiple occasions about Walras’s take on proto-scientific economics.

“To state a theory is one thing; to prove it is another. I know that in economics so-called proofs which are actually nothing more than gratuitous assertions are doled out and find acceptance again and again. And precisely for this reason, I submit that economics will not attain the status of a science until economists are compelled that which they have hitherto been content, in the main, mainly to assert.” (Walras, 2010, p. 427)

Walras’s critique, no doubt, was valid and still is. He got economics out of a deep roadside ditch — but only to steer it into the other. He based his approach on assumptions like utility, optimization, perfect foreknowledge, production function, supply/demand function, perfect competition, capital, equilibrium, etcetera. All these notions are nonentities.

Now the problem is: one can formulate a green-cheese assumption as vivid or colorful or suggestive or or precise or rigorous as one likes — it does not help.

As Lawson put it: “It is a form of modelling consistency … that underpins the notion of equilibrium itself. In modern mainstream economics the category equilibrium has nothing to do with the features of the real economy.” (See intro)

To paint dancing angels on a pinpoint or supply-demand-equilibrium does not make either real. The crucial methodological mistake, however, is not so much in the painting or the formalism but in the underlying green-cheese assumptions.

Equilibrium is a nonentity and therefore all equilibrium models are false. There are many differences between Walras and the post-Walrasians. These do not count at all. Both approaches are based on the same set of nonentities. Therefore both are irrelevant.

Unfortunately, heterodox methodologists simply do not get the crucial point. “Tony Lawson traces this irrelevance to the failure of economists to match their deductive-axiomatic methods with their subject.” (See intro)

The irrelevance of economics since Walras is not due to the deductive-axiomatic method but to green-cheese assumptionism.

Note in passing that Walras’s general equilibrium is a zero profit economy (2015). Since his time economists have not become tired of presenting and discussing models which every intelligent layman could immediately dismiss as irrelevant.

Economics is still in the scientific roadside ditches — one half of economists is trapped in the Cambridge ditch the other in the Laussane ditch, neither moves along the real-world road.

Egmont Kakarot-Handtke

References

Coates, J. (2007). The Claims of Common Sense. Moore, Wittgenstein, Keynes and

the Social Sciences. Cambridge, New York, NY, etc.: Cambridge University Press.

Colander, D. (1995). Marshallian General Equilibrium Analysis. Eastern Economic

Journal, 21(3): 281–293. URL http://www.jstor.org/stable/40325642.

Davidson, P. (1984). Reviving Keynes’s Revolution. Journal of Post Keynesian

Economics, 6(4): 561–575. URL http://www.jstor.org/stable/4537848.

Kakarot-Handtke, E. (2015). Essentials of Constructive Heterodoxy: Profit. SSRN

Working Paper Series, 2575110: 1–18. URL

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2575110.

Walras, L. (2010). Elements of Pure Economics. London, New York, NY: Routledge.

“Modern economics has become increasingly irrelevant to the understanding of the real world. Tony Lawson traces this irrelevance to the failure of economists to match their deductive-axiomatic methods with their subject”.

As Egmont’s reaction shows, this doesn’t do justice to Tony’s position. The point is, WHY does he reach it? He agrees with Egmont on “green cheese” mainstream assumptionism. However, his argument is not so much AGAINST deductivism as FOR retroductivism in the case of economics. In order for deductive logic to work the objects have to remain in consistent and stable relationships, and conversely, as Tony argues, models deduced from axioms are “closed” in the sense of always producing the same set of possibilities, without new possibilities emerging. But economic situations are rarely (if ever) like that.

Ezra is very helpful when he says (rightly) that “The classical thinkers (Smith, Ricardo, and Marx) have, in general, given us a descriptive theory of economics”. By contrast, Tony is arguing for explanatory theory, capable of explaining how the system works and develops – and thus how it can fail to – in terms of what it is, i.e. an ontology more fundamental than that of economics. I’ve put my own slant on this recently in the thread on Paul Romer.

It seems to me lack of appreciation of the difference between descriptive and explanatory theory – the one offering knowledge, the other understanding – is at the root of most of the cross-purposes on this RWER blog.

Egmont Kakarot-Handtke concludes: ‘Economics is still in the scientific roadside ditches — one half of economists is trapped in the Cambridge ditch the other in the Lausanne ditch, neither moves along the real-world road’ (see Comment 24 May).

This conclusion is based on two common erroneous statements. First, Walras’s general equilibrium theory is identified with Pareto’s general equilibrium theory; however they are different, because Pareto’s theory is irrelevant not only to real economics but also to hypothetical economics; while Walras’s theory derived from reality and is compatible to hypothetical economics.

There are eight significant differences between Walras’s and Pareto’s General Equilibrium Theories:

1. According to Walras’s approach the individual economy and the entire economy are separated for all four of economy: exchange, production, capital formation and money. Pareto combined them within one model and considered only the exchange and the production economies. Therefore, Walras’s economy is a decentralized economy, while Pareto’s economy is a centralized; yet, even if there is a theoretical solution to Pareto’s model, it is impossible to realize practically, as Pareto frankly confessed;

2. Walras has used cardinal measure of utility; while Pareto from the very beginning has used ordinal measure of ophemility, but later has passed to cardinal measure;

3. Walras has used separable utility functions; whilst Pareto has used the utility function included all goods and services together in one function, which from the practical point of view is problematic, if not impossible;

4. According to Walras’s approach, the demand and supply of goods and services are obtained directly from the solution of models. The offer quantity of a certain good (service) must be less or equal to its available quantity. In the Pareto’s approach the final endowment is directly determined for all commodities and their sum is equal to the sum of their initial endowment; which prevent discussing employment-unemployment problem in the macro level;

5. Walras first formulated a macro model, a simultaneous equation system, for the equilibrium state. He then formulated the disequilibrium (working) model, where the number of unknowns is larger than the number of equations and described the process of equilibrium establishment by means of his well-known algorithm – tâtonnement, which transforms the initial disequilibrium model into a final equilibrium model. Pareto did not use tâtonnement;

6. According to Walras’s approach all prices are unknown for the macro model, but they are known for the micro model; yet, they are strictly positive. In Pareto’s model all prices are unknown and some of them might be equal zero;

7. Walras had a certain success in showing that general equilibrium exists. Pareto, however, ignored the issue of whether equilibrium exists, and reduced it to comparing the number of independent equations and unknowns;

8. Walras used two categories of money: (1) money (money commodity-numéraire) serves as the functions of money, and its price is one; (2) money (money commodity-numéraire or fiat money) is used for circulation, and its price is the rate of interest. Pareto ignored money issue. Second, Marshall’s theory is separated from Walras’s one; however they are generally equivalent:

(1) Walras used the original (ordinary) demand curve (function); and the derived (general) demand function. Marshall also used both types of demand curves (function); however he did so in a very simplified and vague manner.

(2) Walras used a common method of equilibrium establishment and re-establishment of equilibrium for all four types of economies. First, he discussed the problem of equilibrium establishment using initial basic data. Second, Walras starts the adjustment process by using a model to describe the equilibrium state. He then describes the process of equilibrium establishment from a position of disequilibrium, by the use of his famous algorithm – tâtonnement. Finally, Walras discussed the problem of the variation of prices, or the problem of the re-establishment of equilibrium, as a result of changes in the initial basic data for any individual or any group of individuals. Marshall also used the same method, but in an incomplete form. Despite that, Marshall did not formulate the model for individual economies, he discussed the conditions of its optimality; and discussed the process of equilibrium establishment. Furthermore, despite the fact that Marshall described verbally the complete model for the whole (macro) economy in a similar way to Walras, he did not formulate mathematically that model. Marshall also discussed the problem of the re-establishment of equilibrium, as a result of changes in the initial basic data. Therefore, the statement that they are alternative theories is mistaken.

Objective Principles

Comment on ‘Modelling consistency and real world non-coherence in mainstream economics’

You write: “This conclusion is based on two common erroneous statements. First, Walras’s general equilibrium theory is identified with Pareto’s general equilibrium theory; …”

Pareto has not been mentioned at all in this thread until your recent post. Hence no conclusion has been based on Pareto.

Anyway. Let us take the opportunity and do away with Pareto. He obviously was a Subjectivist.

“The foundation of political economy and, in general, of every social science, is evidently psychology. A day will come when we shall be able to deduce the laws of social science from the principles of psychology …” (Pareto, 2014, p. 20)

Subjectivists cling to the naive idea that the understanding of human behavior somehow leads to the understanding of how the economic system works. Since Pareto, Walras, Jevons, Marshall, Menger et al. we have sufficient experience with this approach. And it is pretty obvious that it has failed completely.

Psychologism/sociologism inverts the Midas touch of science — to turn whatever it might touch into knowledge — into a curse: it turns everything it touches into balderdash.

So let us paraphrase Pareto.

“The foundation of theoretical economics is evidently different from every social science. A day will come when we shall be able to deduce the laws of economics from the Principles of Objectivity, that is, from a handful of elementary structural axioms.”*

Egmont Kakarot-Handtke

References

Pareto, V. (2014). Manual of Policical Economy. Oxford: Oxford University Press. URL http://books.google.de/books?hl=de&id=M3ZYAwAAQBAJ&q=psychology#v=snippet&q=psychology&f=false.

* For a start see the new heterodox curriculum

http://axecorg.blogspot.de/2015/04/new-curriculum-cross-references.html