From Hilbert’s hotel to Hilbert’s method

Comment on ‘Infinite Debt, Future Generations, and Hilbert’s Hotel’

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There are many ways to abuse economics, the three most popular are politics, entertainment, and kindergarten. In the economics kindergarten, they love to play with tiny toy models. And, you know, kids are a bit ad hoc; they start with beer, add the medium of exchange and then IOUs, introduce interest out of the blue, and finalize with the Erlang number. However, what looks like utter confusion is the well-established economic method: “... twentieth-century neoclassical theory resembles nothing so much as the child's game of Mr. Potatohead — the fun comes in mixing and matching components with little or no concern for the coherence of the final profile.” (Mirowski, 1995, p. 294)

Coherence and consistency were never the strong points of the representative economist (2013). But infinite gallimaufry is the privilege of the philosophical economist.

It should be, first of all, clear that there is no such thing as a ‘real’ economy. Because the economy comes into being as the interaction of real and nominal variables, all real models are garbage — even beer models. Second, in economics, infinity should not be used to push a problem out of sight. It is silly to argue that debt is not a problem if it never has to be redeemed.

Hilbert’s hotel is a fine example of all that is wrong with economics. The irony is that Hilbert was the most famous proponent of the correct scientific method, which came to be known as the axiomatic-deductive method. It works as follows.

“When we assemble the facts of a definite, more-or-less comprehensive field of knowledge, we soon notice that these facts are capable of being ordered. This ordering always comes about with the help of a certain framework of concepts... The framework of concepts is nothing other than the theory of the field of knowledge. ... If we consider a particular theory more closely, we always see that a few distinguished propositions of the field of knowledge underlie the construction of the framework of concepts, and these propositions then suffice by themselves for the construction, in accordance with logical principles, of the entire framework. ... The procedure of the axiomatic method, as it is expressed here, amounts to a deepening of the foundations of the individual domains of knowledge — a deepening that is necessary for every edifice that one wishes to expand and to build higher while preserving its stability.” (Hilbert, 2005, pp. 1107-1109)

Needless to say that Hilbert’s method has never been applied properly by either orthodox or heterodox economists. Both camps are still stuck with the ‘child's game of Mr. Potatohead.’ This explains why economics is a failed science.

The fundamental mistake in the actual discussion of debt is that the pivotal relationship between increase/decrease of debt and profit/loss is entirely missing. For the correct theory see (2014).

Egmont Kakarot-Handtke


References
Hilbert, D. (2005). Axiomatic Thought. In W. Ewald (Ed.), From Kant to Hilbert. A Source Book in the Foundations of Mathematics, Vol. II, 1107–1115. Oxford, New York: Oxford University Press.
Kakarot-Handtke, E. (2013). Confused Confusers: How to Stop Thinking Like an Economist and Start Thinking Like a Scientist. SSRN Working Paper Series, 2207598: 1–16. URL
Kakarot-Handtke, E. (2014). Mathematical Proof of the Breakdown of Capitalism. SSRN Working Paper Series, 2375578: 1–21. URL
Mirowski, P. (1995). More Heat than Light. Cambridge: Cambridge University Press.

For more about Hilbert see AXECquery.

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Twitter Nov 28, 2021 Privatdozent David Hilbert's influence on economics

Accounting matters

Comment on ‘Accounting for ****’

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Since theories have an architectonic structure it is clear that if there is a fault in the formal foundations the whole superstructure is bound to collapse eventually. Accounting matters because it provides the natural reality check for economic theories; it plays the same role in economics as a sophisticated measuring instrument in physics.

The first thing to realize is that there is no such thing as a ‘real’ economy. Hence economic phenomena are only explicable as the outcome of the interaction of real and nominal variables. A good number of nominal variables reappear in national accounting.

With regard to saving this means that all ‘real’ models of intertemporal shifting of consumption are pointless. In the monetary economy, the process of saving and dissaving is independent of real output in different periods.

For the correct theory of saving/dissaving see (2013).

Egmont Kakarot-Handtke


References
Kakarot-Handtke, E. (2013). Settling the Theory of Saving. SSRN Working Paper Series, 2220651: 1–23. URL

Relates to Unaccountable

How markets work

Comment on axdouglas on ‘Macroeconomic Theory and Operational Reality’

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“I often wonder whether other subjects suffer as much from textbook writers.” (Hahn, 1980, p. 127)

Economists think they can explain economic phenomena by painting a supply-demand-equilibrium cross or what Leijonhufvud has ironically called the totem of the micro/macro. However, already Schumpeter found it necessary to diffuse doubts about the scientific content of the whole exercise.

“The primitive apparatus of the theory of supply and demand is scientific. But the scientific achievement is so modest, and common sense and scientific knowledge are logically such close neighbors in this case, that any assertion about the precise point at which the one turned into the other must of necessity remain arbitrary.” (Schumpeter, 1994, p. 9)

As a matter of fact, the ‘primitive apparatus of the theory of supply and demand’ is a thoroughly faulty construct: “There is little or nothing in existing micro- or macroeconomics texts that is of value for understanding real markets. Economists have not understood how to model markets mathematically in an empirically correct way.” (McCauley, 2006, p. 16)

The familiar microeconomic SS-DD cross is built on NONENTITIES like utility, equilibrium, well-behaved production functions, decreasing returns, rational expectations, simultaneous adaptation, etcetera, and consequently, has to go out of the window. The same holds for macroeconomic versions like IS-LM. For the refutation of Krugman’s silly model see (2014): “What is now taught as standard economic theory will eventually disappear, no trace of it will remain in the universities or boardrooms because it simply doesn’t work: were it engineering, the bridge would collapse.” (McCauley, 2006, p. 17)

Because the textbooks are wrong, it is one of the first tasks of Constructive Heterodoxy to deliver the correct formal depiction of a market (2015). It is high time that economists learn how the market system works.

Egmont Kakarot-Handtke


References
Hahn, F. H. (1980). General Equilibrium Theory. Public Interest. Special Issue: The Crisis in Economic Theory, 123–138.
Kakarot-Handtke, E. (2014). Mr. Keynes, Prof. Krugman, IS-LM, and the End of Economics as We Know It. SSRN Working Paper Series, 2392856: 1–19. URL
Kakarot-Handtke, E. (2015). Essentials of Constructive Heterodoxy: The Market. SSRN Working Paper Series, 2547098: 1–10. URL
McCauley, J. L. (2006). Response to "Worrying Trends in EconoPhysics". EconoPhysics Forum, 0601001: 1–26. URL
Schumpeter, J. A. (1994). History of Economic Analysis. New York: Oxford University Press.

For more about the economic totem see AXECquery.

For more about Constructive Heterodoxy see AXECquery.

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Twitter/X 21 Aug 2023 Long obsolete, the silly totem of economics

Unaccountable

Comment on ‘Accounting for ****’

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Being very busy, economists as confused confusers did not miss the opportunity to mess up accounting, too. It started with Keynes. He gave the following elementary formal description of the economy: “Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment.” (Keynes, 1973, p. 63)

Since theories have an architectonic structure it is clear that if there is a fault in the formal foundations the whole superstructure of the theory is vulnerable. Actually, the fault in Keynes' syllogism is in the premise income = value of output. This equality holds only in the limiting case of zero profit in both the consumption and investment good industry.

Profit does not appear in Keynes' elementary formalism. That is, he in effect talks about capitalism without profit. Note well that Walras' economy was also a zero profit economy. Weird, isn't it?

Keynes' conceptual problems started 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 and Bezemer, 2010, p. 12)

This failure kicked off the chain reaction of errors/mistakes because when profit is not correctly defined, income is not correctly defined, and then saving is not correctly defined. By consequence, all I=S models are logically defective.

The root cause of all accounting errors/mistakes is a complete lack of understanding of what profit is. Total income is not the sum of wage income and profit but of wage income and distributed profit income. The conceptual error carries over to national accounting (2012).

To make it short, what, then, is the — minimal, objective, consistent, testable — common conceptual ground of all of the economics?

Total period income in an extremely simple monetary economy with only one firm is given by the sum of wage income and distributed profit, i.e. (1) Y=Yw+Yd. Total consumption expenditures are equal to the product of price and quantity sold, i.e. (2) C=PX. More is not needed for a start.

Monetary profit of the business sector as a whole is then defined as the difference between consumption expenditures and wage costs, i.e. Q≡C−Yw. Monetary saving of the household sector is then defined as the difference between total income and consumption expenditure S≡Y−C. Hence, S≡−Q if, for a start, Yd=0. In simple words: saving S is equal to loss −Q, or, dissaving −S is equal to profit Q.

Generally speaking, it holds for the pure consumption economy that Qre≡−S, i.e. retained profit Qre is equal to dissaving −S. And for the investment economy holds Qre=I−S, i.e. retained profit is equal to the difference between investment and saving (for details see 2014a).

Because the profit theory is false the loanable funds theory, too, is false (2014b).

Egmont Kakarot-Handtke


References
Kakarot-Handtke, E. (2012). The Common Error of Common Sense: An Essential Rectification of the Accounting Approach. SSRN Working Paper Series, 2124415: 1–23. URL
Kakarot-Handtke, E. (2014a). Economics for Economists. SSRN Working Paper Series, 2517242: 1–29. URL
Kakarot-Handtke, E. (2014b). Loanable Funds vs. Endogenous Money: Krugman is Wrong, Keen is Right. SSRN Working Paper Series, 2389341: 1–17. URL
Keynes, J. M. (1973). The General Theory of Employment Interest and Money. The Collected Writings of John Maynard Keynes Vol. VII. London, Basingstoke: Macmillan.
Tómasson, G., and Bezemer, D. J. (2010). What is the Source of Profit and Interest? A Classical Conundrum Reconsidered. MPRA Paper, 20557: 1–34. URL

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