Sunday, September 21, 2014

In the long run we are all Baroque

Terence Hutchinson concluded his appendix on "Some postulates of economic liberalism" in Significance and Basic Postulates of Economic Theory with the admonition, "It is high time to put these theories [laissez faire and equilibrium doctrines] firmly back in their place as Utopian constructions." He cited S. Bauer's 1931 article, "Origine utopique et métaphorique de la théorie du “laissez faire” et de l’équilibre naturel."

Prominent in Bauer's discussion is the role of the Spanish Baroque author, Baltasar Gracian's Oráculo Manual, which was translated into French by Amelot de la Houssaie in 1684, in popularizing both the notion and the term, laissez faire. Pierre le Pesant Boisguilbert is credited with introducing the term into political economic thought in a book published in 1707. It is conceivable that Keynes knew of the Gracian maxim because he used the image Gracian had used of tempestuous seas in his famous rejoinder about "the long run" being "a misleading guide to current affairs."

In his book Hutchinson noted that "several writers have argued that some such postulate as 'perfect expectations' is necessary for equilibrium theory." This observation lends a special note of irony to Gracian's coinage of laissez faire. In his discussion of Gracian's Oráculo, Jeremy Robbins highlighted the observation that:
Gracián’s prudence rests firmly on a belief that human nature is constant... In Gracián’s case, human nature is viewed as a constant in so far as he believes it to act consistently contrary to reason."
In fact, Robbin's chapter on Gracian is titled "The Exploitation of Ignorance." Gracian's maxims establish "a sharp distinction between the elite and the necios [that is, fools]." Assuming that most people are fools who act contrary to reason is obviously something quite different from assuming perfect expectations. For that matter, the prudence of a courtier seeking to gain power over others is something quite distinct the foresight required of a policy professional acting ostensively on behalf of the public welfare.

That metaphorical and Utopian notions of laissez faire and natural equilibrium have managed to persist and even prevail in economics -- impervious to Hutchinson's warning (or Keynes's) -- is testimony to the perceptiveness of Gracian's estimate of human nature.
_______________________

John Maynard Keynes, A Tract on Monetary Reform (1923)
Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is long past the ocean is flat again.
Baltasar Gracian, Oráculo Manual y Arte de Prudencia, Maxim 138 (1647), English translation: The Art of Prudence.
The Art to let things go as they can go, especially when the Sea is tempestuous. 
There are Tempests and Hurricanes in the life of man. It is Prudence to put into a Haven, to let them blow over. Most commonly the Remedies increase the Evil. When the Sea of humours is in agitation, let Nature work; if it be the Sea of Manners, leave it to Morality. There is as much skill required in a Physician, in not prescribing, as in prescribing; and sometimes the excellency of the Art consists in applying no Remedy. The way then to calm popular gusts, is to be quiet. Then to yield to the times, will get the victory afterwards. A Well will be troubled if it be in the least stirred, and its water becomes clear again, by ceasing to dabble in it. There is no better remedy for some disorders, than to let them alone. For at long run they stop of themselves.
Gracian,  Oráculo, French translation: « L'homme de cour »
L’art de laisser aller les choses comme elles peuventsurtout quand la mer est orageuse.
Il y a des tempêtes et des ouragans dans la vie humaine; c’est prudence de se retirer au port pour les laisser passer. Très souvent les remèdes font empirer les maux. Quand la mer des humeurs est agitée, laissez faire la nature ; si c’est la mer des mœurs, laissez faire la morale. Il faut autant d’habileté au médecin pour ne pas ordonner que pour ordonner ; et quelquefois la finesse de l’art consiste davantage à ne point appliquer de remède. Ce sera donc le moyen de calmer les bourrasques populaires, que de se tenir en repos ; céder alors au temps fera vaincre ensuite. Une fontaine devient trouble pour peu qu’on la remue, et son eau ne redevient claire qu’en cessant d’y toucher. Il n’y a point de meilleur remède à de certains désordres que de les laisser passer, car à la fin ils s’arrêtent d’eux-mêmes.
Gracian, Oráculo
Arte de dexar estar. 
Y más quando más rebuelta la común mar, o la familiar. Ai torbellinos en el humano trato, tempestades de voluntad; entonces es cordura retirarse al seguro puerto del dar vado. Muchas vezes empeoran los males con los remedios. Dexar hazer a la naturaleza allí, y aquí a la moralidad. Tanto ha de saber el sabio médico para recetar como para no recetar, y a vezes consiste el arte más en el no aplicar remedios. Sea  modo de sossegar vulgares torbellinos el alçar mano y dexar sossegar; ceder al tiempo aora será vencer después. Una fuente con poca inquietud se enturvia, ni se bolverá a serenar procurándolo, sino dexándola. No ai mejor remedio de los desconciertos que dexallos correr, que assí caen de sí proprios.

Saturday, September 20, 2014

Don't Pay Any Attention -- Paul Krugman edition

"Don't pay any attention..." [correction: this is not a quote from Krugman but Mark Thoma's characterization (correct, in my view) of Krugman's argument]

This is advice from Paul Krugman in his column Errors and Emissions. Professor Krugman obviously hasn't paid any attention to the analysis underlying the critique of "growth".

Lovely.

teach this stuff at university. I pay a great deal of attention to arguments that the "strong measures to limit carbon emissions would have hardly any negative effect on economic growth, and might actually lead to faster growth."

Krugman says "This may sound too good to be true, but it isn’t. These are serious, careful analyses." If, as Krugman suggests you don't pay any attention to the critiques, you can just take his word for it that these are "serious careful analyses."

The fact is, though, that "serious careful analysis" would pay close attention to criticism. These too-good-to-be-true sounding arguments don't pay any attention to the criticism. They are not serious and careful analyses.

Don't pay any attention to what Roefie Hueting wrote about asymmetric accounting entries 20 years ago. Don't pay any attention to what Nicholas Georgescu-Roegen wrote about energy and materials 40 years ago. Don't pay any attention to what Simon Kuznets wrote about national income accounting 60 years ago. Don't pay any attention to what John Maurice Clark wrote about overhead cost shifting 90 years ago. Don't pay any attention to what Jevons wrote 150 years ago about fuel efficiency and consumption. Don't pay any attention to what Tim Jackson and the U.K.'s Sustainable Development Commission wrote about prosperity without growth 5 years ago.

Just don't pay any attention.

The corporate bureaucrats have your best interests at heart and have everything under control. Nothing can go wrong... go wrong... go wrong...

Move along, now. Nothing to see here.

Update: David Nemerson of Baltimore, MD posted the following comment to Krugman's column. It has received 67 "recommends", so far (don't pay any attention to David or to what Bobby Kennedy said 46 years ago):
Until we break the fetish of growth, we are in for a very bumpy ride indeed. Bobby Kennedy's critique of GDP stated it beautifully in 1968: 
"It counts napalm and counts nuclear warheads and armored cars for the police to fight the riots in our cities. It counts Whitman's rifle and Speck's knife, and the television programs which glorify violence in order to sell toys to our children. 
Yet the gross national product does not allow for the health of our children, the quality of their education or the joy of their play. It does not include the beauty of our poetry or the strength of our marriages, the intelligence of our public debate or the integrity of our public officials.
It measures neither our wit nor our courage, neither our wisdom nor our learning, neither our compassion nor our devotion to our country, it measures everything in short, except that which makes life worthwhile.
And it can tell us everything about America except why we are proud that we are Americans."

Rest of the quote here.

Friday, September 19, 2014

MAXimizing Utility?

At MaxSpeak, Max responds to comments on his earlier posts on Universal Basic Income.

Bud Meyers wrote:
With ever more robotics and automation putting people out of work, how will they live without a Universal Basic Income, when human labor becomes obsolete?
To which, Max replied:
I totally disagree with the idea that jobs will be displaced by automation. The composition of jobs will change, but there is still quite a bit of useful work to be done. People were talking this way in the 1950s. There is always more automation, and always other kinds of new jobs.
Whoa, Max! You just invoked the lump-of-labor fallacy claim!

Logically, the premise that “there is still quite a bit of useful work to be done” is true by definition. Empirically, the statement is vacuous. That doesn't mean it is untrue, just that it has no empirical content. The effort to fill it with pseudo-content leads inevitably into self-contradiction, as shown by the “dispute” in the 19th century between Cairnes and Thornton over the wages-fund doctrine. See "Ceteris paribus, Dr. Jekyll tans his own Hyde"

The methodological issues here don’t have to do with whether or not there is “work to be done” but with uncertainty, rational expectations and the fundamental assumption of “maximizing utility” (stated by Nassau Senior as “That every man is desirous to obtain, with as little sacrifice as possible, as much as possible of the articles of wealth.”) See my new post "On Deducing Faith and Redemption from Usury with the Help of Automata."


Thursday, September 18, 2014

On Deducing Faith and Redemption from Usury with the Help of Automata

"That every man is desirous to obtain, with as little sacrifice as possible, as much as possible of the articles of wealth." -- Nassau Senior, 1827
In "Expectation and Rational Conduct" (1937) Terence Hutchison argued that Senior's "first fundamental proposition" shared "one remarkable characteristic" with "almost all" formulations of the utilitarian doctrine: "they appear further to postulate, and only are applicable if the further postulate is made, that all expectations are perfectly correct."

Now, this perfect expectation postulate can be -- and has been -- shrugged off as a merely heuristic "convenient approximation" that enables the economist "to study in isolation, tendencies which in the world of reality operate with many others" (Robbins, 1935). But, as Hutchison emphasized, the consequences of such a "simplification" are not so easily waved aside. He cited Frank Knight:
"With uncertainty absent, man's energies are devoted altogether to doing things; it is doubtful whether intelligence itself would exist in such a situation; in a world so built that perfect knowledge was theoretically possible, it seems likely that all organic readjustment would become mechanical, all organisms automata."
Hutchison followed this quotation with the observation that it is misleading to attribute rationality to "this sort of conceptual marionette" because the decision process becomes superfluous when results are known beforehand. In one example, he compared the logical impossibility of perfect expectation to the liar's paradox: "A person's conduct cannot both be given to someone else who may adjust his own accordingly, and still be adjustable by the person."

1937 was a banner year for economic articles addressing uncertainty. In addition to Hutchison's article, the following were published: Coase's "The Nature of the Firm," Hayek's "Economics and Knowledge" and Keynes's response to critiques of his General Theory in The Quarterly Journal of Economics. In his article, Keynes observed that uncertainty about the indefinitely distant future renders the accumulation of wealth "a peculiarly unsuitable subject for the methods of the classical economic theory." Of course that "peculiarly unsuitable subject" happened to be none other than the very one the classical theory purported to illuminate -- with, as Senior put it, "certainty and universality."
"Exactly a year before Nassau W. Senior discovered at Manchester, that the profit (including interest) of capital is the product of the last hour of the twelve, he had announced to the world another discovery. 'I substitute,' he proudly says, 'for the word capital, considered as an instrument of production, the word abstinence.'" -- Karl Marx
Abstinence was the basis of Senior's theory of interest. Interest is a payment to the lender of money for the service of abstaining, for the time being, from consumption. According to Waterman, Senior "was the most important writer on scope and method among the classical economists, and the one whose work was most influential for the twentieth century development of economic methodology."

Some 26 years after Senior delivered his inaugural lecture at Oxford, Cardinal Newman, in his inaugural lectures at the Catholic University of Ireland, rebuked Senior for the presumptuousness of the claims he had made on behalf of political economy. Newman characterized Senior's argument as "just so far true, as to be able to instil what is false."

Newman quoted Senior's assertion that "The endeavour to accumulate the means of future subsistence and enjoyment, is to the mass of mankind, the great source of moral improvement." Newman interjected to exclaim that Senior had rated the pursuit of wealth as "not merely a source, but the great source" of not merely "social and political progress—such an answer would have been more within the limits of his art,—no, but of something individual and personal, 'of moral improvement.'"

That was only the warm up. To Senior's claim that "No institution could be more beneficial to the morals of the lower orders... than one which should increase their power and their wish to accumulate..."  Newman observed that this excluded Christianity, "for it expressly says, 'Lay not up to yourselves treasures on earth... for where thy treasure is, there is thy heart also."

"But it is not enough that morals and happiness are made to depend on gain and accumulation," Newman exclaimed, continuing:
"...the practice of Religion is ascribed to these causes also, and in the following way. Wealth depends upon the pursuit of wealth; education depends upon wealth; knowledge depends on education; and Religion depends on knowledge; therefore Religion depends on ‘the pursuit of wealth.'"
Thus did Nassau W. Senior deduce faith and redemption from usury, while redefining usury as "abstinence." Medieval canon law strictly condemned usury and prescribed excommunication as the punishment for usurers, excluding them from the sacraments of the church and the from society of other Christians. How did such a remarkable doctrinal reversal, from sin to sacrament, come about?

The history of double-entry bookkeeping offers a clue. Surely one of the motivations for early modern merchants to adopt the novel and challenging technique was to "prove an alibi" against suspicions of usury. Some of the financial instruments for evading the prohibition were complicated, to say the least:
"The canonist doctrine on usury had a profound influence on business practices, since interest could not be charged openly but had to be concealed under some form or other. As a result of the usury prohibition, bills were never discounted but were bought at a rate of exchange which fluctuated up and down according to the conditions prevailing in the money market. There is no doubt that interest was received by the banker who invested his money in the purchase of bills, for a hidden interest was included in the rate of exchange. Because of this subterfuge, the structure of the money market was such that exchange fluctuations were caused either by a change in the rate of interest or by a change in the terms of international trade."
... 
"The ledgers of medieval bankers do not contain any account called Interest Income. Nor is there any account for Interest Expense. It is true that the Italian merchant-bankers often paid interest on time deposits, but it was called deposit, discrezione, dono (gift), guadagno (gain), or provedigione (commission). The use of the word 'interest' itself was avoided like the plague. 
True, interest was concealed in the exchange rates, but the presence of the interest factor was boldly denied. The merchants argued -- and the canonists agreed -- that exchange transactions did not involve a mutuum or a loan of money for certain gain. It is quite true that the profit on individual exchange transactions was uncertain.
And so, we return at last to uncertainty, this time as an alibi for the certain gain of usury. But I have interrupted de Roover's narrative. There is more:
"As the analysis of our data reveals, it did happen that occasionally the lender lost. Nevertheless, the reasoning of the canonists was fallacious: they overlooked an essential point, namely, that the presence of the time factor tipped the scales in favor of the banker. While he suffered a few losses, the banker was bound to gain on most transactions, if he was a clever and cautious manager. Losses occurred only when the exchange rates were not in a position of equilibrium. Such a condition could not persist over a long period of time, for the economic forces of the money market automatically tended toward the restoration of equilibrium."
de Roover possibly overstated the case for the automatic restoration of equilibrium. But his point remains valid that the usual tendency toward equilibrium in the foreign exchange market favored the banker "if he was a clever and cautious manager."

Sections 5 and 6 of Hutchison's article address, respectively, "Perfect Expectation and Equilibrium" and "The Assumption of a 'Tendency' Towards Equilibrium." "The position of equilibrium," he argued at the beginning of section 6, "has always been the very central concept of economic analysis." In section 5 he had cited Oscar Morgenstern's argument that the postulate of perfect expectations "may give a nonsensical indeterminate situation the very reverse of equilibrium." Conversely, Knight, Hicks and Pigou argued that the postulate of perfect expectation is necessary for equilibrium theory.

Leaving aside some ostensively universal political economy and thinking instead in terms of Venetian merchant-bankers' interest on loans -- interest concealed within rates of exchange -- uncertainty, perfect expectation and the tendency toward equilibrium all play their roles in assuring both probable profit and usurious deniability to the bankers. The probability of gain is a qualitative one and thus not calculable. All the better to allay suspicion.

This just in: At the end of an appendix to Significance and Basic Postulates of Economic Theory, Hutchison remarked, "It must always be remembered that laissez faire and equilibrium doctrines had their origin in rationalistic Utopia-building." In the footnote to that comment, he cited the 1931 article by S. Bauer, "Origine utopique et métaphorique de la théorie du “laissez faire” et de l’équilibre naturel." Below is an abstract of that article:
9538. BAUER, STEPHANE. Origine utopique et métaphorique de la théorie du “laissez faire” et de l’équilibre naturel. [Utopian and metaphoric origin of the theory of 'laissez faire' and of natural equilibrium.] Rev. d’Êcon. Pol. 45(6) Nov.-Dec 1931: 1589-1602.
A re-examination of the origins of laissez faire gives rise to three observations: (1) the theory of laissez faire was originally conceived as a utopia; (2) it developed as an abuse of a metaphor; (3) this utopian metaphor has perpetuated itself into the 19th century in the guise of a theory of equilibrium. Economic laissez faire was utopian, i.e. far from the facts, and purely intellectual in origin, since both in France and England the corn markets of the 18th century were regulated. The metaphoric use of laissez faire carried over from the Pyrrhonean theory of medicine was current not only in Boisguillebert, d'Argenson, Gournay, and the Marquis of Casaux but is found in and old Spanish book by Balthasar Gracian, Oraculo Manual (1647) which was translated into French and was very popular in the 18th century. Indeed the whole concept of the sovereign and perfect character of nature can be traced through the Renaissance back to the Stoics. The medical analogy marks the work of the Physiocrats, of Adam Smith and of Cournot. Rodbertus protested against this point of view by setting "anthropocracy" in opposition to "physiocracy." Further protests are coming from those who explain economic phenomena in terms of economic institutions rather than in terms of deviation from a rigid system of equilibrium.

The "Ceteris Paribus" Assumption

From The Significance and Basic Postulates of Economic Theory by T. W. Hutchison (1938, 1960), pp. 40-46:
As an example of the use of the ceteris paribus assumption we may take the proposition "If the price at which a good is sold rises, ceteris paribus the amount of the good demanded declines." Is this an empirical generalisation which can conceivably be false without any contradiction, or is it an analytical-tautological proposition? 
This, usually, is not made clear, and perhaps such propositions are sometimes meant in one way, sometimes in another. One can only ask in each particular case whether the validity of the ceteris paribus proposition in question depends on facts, or whether, on the other hand, the denial of it simply shows that one does not understand by the terms "rise in price" and "amount demanded" what the language of economists understands. 
If the proposition "If the price at which a good is sold rises, ceteris paribus the amount of the good demanded declines" is an empirical generalisation, so it can only have a clear scientific meaning if it is indicated under what conditions it would be true, or under what false. Further, it is desirable that the difference be shown between this empirical generalisation (with ceteris paribus) and the other empirical generalisation, "If the price at which a good is sold rises the amount of the good demanded declines" (without ceteris paribus). 
Ceteris paribus propositions can be interpreted in this way. But if they are to be so interpreted—as empirical generalisations—then they are usually very vaguely and unclearly formulated. For no attempt is made, usually, to indicate under what conditions they are true and under what false, and the meaning of the vital qualification "ceteris paribus" is left hopelessly imprecise. The ceteris paribus assumption, just as much as any other, must be precisely formulated if the propositions it qualifies are to have any clear meaning. The intention of the assumption obviously is to lessen the falsifiability of the too often falsified generalisation "If the price of a good rises, the amount sold declines." But exactly how far is its falsifiability thus lessened, and if it remains an empirical proposition, what conceivable possibilities of falsification remain? 
On the other hand, it seems more probable that ceteris paribus propositions are frequently treated as analytical-tautological propositions, the example taken in this case explaining a relation between the definitions of "rise in price" and "amount demanded" at different points on a demand curve of a particular shape—a purely logical or geometrical relation. Then it is inconceivable that its truth or falsity (as against its applicability) can be established by any facts, since it is without factual content. In this case one simply determines whether, in fact, the ceteris paribus assumption is true or false, by observing whether or not the price has risen appropriately or not—a circular procedure. This appears to be the interpretation favoured by Menger, though it involves a very elastic conception of "cetera." For example, if the well-known case of poor people buying more bread when the price of it rises in no way falsifies our proposition, this involves a considerable stretching of the assumption "ceteris paribus." 
Thus interpreted the ceteris paribus clause is an accessory assumption of pure theory, and ceteris paribus propositions may be analysed in the same way as the propositions of pure theory have been. The ceteris paribus assumption makes out of an empirical proposition that is concerned with facts, and therefore conceivably can be false, a necessary analytical-tautological proposition. For a mathematical solution (by tautological transformations) the number of equations must be equal to the number of unknowns. The ceteris paribus assumption sweeps all the unknowns together under one portmanteau assumption for a logical "solution."
In Physics and Chemistry, where there are far more discovered empirical regularities, the ceteris paribus assumption is not used in the same way. For if the assumption is broadly true, or if, as is rather the case, the "cetera" in the natural sciences themselves act in accordance with known laws, then the ceteris paribus assumption is more or less a given one, and a true premise can always be dropped. For in a certain sense it is only necessary to make an assumption when one does not know it is true, or knows that it is untrue. This is the peculiar dilemma—apparently unique throughout science—of the "isolating," "assumption-making" procedure of economic theory where there are few empirical generalisations known to be true 
In the natural sciences certain fundamental propositions can be taken either to be analytical-tautological or to be empirical generalisations, exactly as the ceteris paribus propositions may be so taken. For example, originally the proposition "All gases expand on warming" was probably arrived at by empirical experiments. But if to-day an experiment was made with something which as regards the other ways in which it was tested behaved like a "gas" but did not expand on warming, one would at first be inclined to suggest that some mistake had been made in the experiment. But if after repeated experiments this "gas" did not expand, scientists would be faced with a choice. Either they must say "Our law that all gases expand on warming is destroyed, and we must find a new law," or they could say "This stuff which does not expand on warming is no 'gas ', for by definition a 'gas 'must expand on warming; we must find some other name for this." The choice of this second course on all conceivable occasions would mean that the proposition "All gases expand on warming" was not an empirical law at all, but an analytical-tautological definition which was always true because it was not allowed to be false. From the mere wording and form of the proposition one cannot say whether it is the one or the other. One can only find out by a test case when scientists are forced to choose one alternative or the other. 
According to Edgeworth, "The treating as constant what is variable [e.g., supply, margin, wages-fund] is the source of most of the fallacies in political economy,"  and it is the danger of the ceteris paribus assumption that it particularly facilitates such fallacies. It is quite probably true that in more cases than not a rise in price is in fact followed by a decrease in demand, but this of course might not be so; and whether it is so or not can only be decided by statistical investigation. Our proposition with ceteris paribus does not tell us this. In fact the ceteris paribus clause seems sometimes so to be used that one might equally significantly and correctly advance the proposition that ceteris paribus a rise in price is followed by an increase in demand, as the proposition that ceteris paribus it is followed by a decrease. "Ceteris paribus this follows that" seems to come to mean simply "In many cases this follows that," and however often it may not, the reply is that the proposition only said "in many cases" (or ceteris paribus), and this was simply one of the other cases (or "ceteris paribus" did not hold). 
In the recent developments of the "dynamic" pure theory of employment the ceteris paribus assumption appears sometimes to have been applied to propositions which standing alone (without "ceteris paribus") are quite probably more often empirically false than true, but when it is added are meant to get away with some kind of exact and significant empirical content. 
Mr. Keynes gives an example of the use of the ceteris paribus clause on these lines. He contrasts the two propositions: (1) "A decreased readiness to spend... will ceteris paribus increase investment," and (2) "A decreased readiness to spend... will ceteris paribus diminish employment." Are these empirical or analytical propositions—that is, what is the precise content of "ceteris paribus"? If they are empirical, then it is difficult to see what the qualification "ceteris paribus" can mean other than "usually." Then we have two propositions: "A decreased readiness to spend will usually" either (1) "increase investment" or (2) "diminish employment"—two rather vague impressionist generalisations; and though one may be more often true than the other, neither is of much scientific value compared with statistical investigations as to what, in fact, does follow a decreased readiness to spend in. different cases, pending the results of which it seems difficult to justify an exclusive insistence on one as against the other. 
If, on the other hand, these propositions are analytical, there is of course no question of one being "true" and the other "false," and no particular reason for contrasting them, since neither says anything about what in fact follows a decreased readiness to spend. "Ceteris paribus" is simply used differently for the two equations. In the first total outlay is included among the "ceteris" that remain the same, so that a decrease in one division of it (consumption spending) mathematically implies an increase in the other division (investment). In the second equation employment on capital goods is assumed to remain the same, so that a decrease in employment on consumption goods mathematically implies a decrease in total employment. 
Either of these interpretations is possible and there may be others. In the first place such a use of the "ceteris paribus" clause leaves it quite ambiguous as to what kind of proposition is being put forward. In the second place it appears to give to what is either simply an empirically empty analytical proposition, or a very vague and statistically unsupported empirical generalisation, an air of some kind of precise and widely valid empirical content. 
We suggest that the ceteris paribus assumption can only be safely and significantly used in conjunction with an empirical generalisation verified as true in a large percentage of cases but occasionally liable to exceptions of a clearly describable type.
Conclusion (p. 163):


That ceteris paribus propositions are frequently hopelessly ambiguous and that the ceteris paribus assumption should be used less often and more cautiously.

Thursday, September 4, 2014

Ceteris paribus, Dr. Jekyll tans his own Hyde

"In too many cases one is unsure of exactly what restraints are being imposed and by what authority the exercise is legitimated. Fittingly, the history of ceteris paribus is a history of studied ambiguity." – Joseph Persky
Let us not worry about too many cases. Let's focus on the paradigmatic case. Persky identified Alfred Marshall's role in "spreading the word" of ceteris paribus:
"It is very likely that Alfred Marshall picked up his use of ceteris paribus from Cairnes. Although he doesn't cite Cairnes in his methodological discussions of the phrase, Marshall does use the following quotation from Cairnes in a discussion of the wages-fund theory: 'the rate of wages, other things being equal, varies inversely with the supply of labour.' 
"Whatever its origins, the fact remains that Marshall was the one to popularize ceteris paribus."
The phrase was actually "other things being the same," which appears eleven times in Cairnes's Some Leading Principles of Political Economy: Newly Expounded. Notice that Marshall cited Cairnes "in a discussion of the wages-fund theory." More specifically, Marshall was criticizing Cairnes's attempt to "resuscitate" the wages-fund theory, in which Cairnes avoided the old pitfalls "only by explaining away so much which is characteristic of the doctrine." Apparently, though, Marshall must not have noticed that it was precisely the infernal ambiguity of the ceteris paribus device that enabled Cairnes to explain away the pitfalls in the doctrine. Marshall went on to promote the use of the ceteris paribus "pound" in static analysis.

Persky's article mentions the methodological critique of ceteris paribus by twentieth century philosophers of science and cites Daniel Hausman's introduction to those arguments. A subsequent ceteris paribus "industry" has blossomed in philosophy in which "hardly a year passes without the appearance of at least a few articles on this topic in major journals." Although it would be an exaggeration to call it a consensus, there are cogent arguments "that extant attempts to save ceteris paribus laws from vacuity are massive failures." In a recent article, T. V. Carey has proposed Galileo's method of successive approximation as a "partial solution to the ceteris paribus problem."

While the philosophers are busy resolving the methodological difficulties raised by ceteris paribus, I would like to turn my attention to the political consequences of this magical clause. Cairnes's attempt to revive the wages-fund doctrine was a response to William Thornton's apparently decisive repudiation of it in On Labour Its Wrongful Claims and Rightful Dues; Its Actual Present and Possible Future. The wages-fund doctrine had lent pseudo-scientific legitimation to fierce partisan polemics against trade unionism.

Cairnes's response encompassed both defense and attack. It is in his defense of the wages-fund doctrine that the passage cited by Marshall appears. In a later chapter on trades unionism, Cairnes attacked a statement by Thornton to the effect that "the quantity of industrial work to be done is… 'at any give time a fixed quantity.'" Cairnes objected to this assumption vehemently:
"...I must make bold to say that, within the range of economic reasoning, no more profound fallacy finds a place than is contained in this inference; nor, I must add, is there one more pregnant with practical consequences of a pernicious kind."
The review of Thornton's book in The Edinburgh Review for July 1869 took a more good-natured and humorous view of Thornton's gaffe:
"That the rate of wages is governed, as Adam Smith and his followers have conceived, by the proportion between the capital disposable for the payment of labour and the number of the recipients of that capital, is a notion that Mr. Thornton scouts with contempt, and he consigns the chimerical 'wages-fund' to the lowest limbo of unrealities. Yet, while attacking the name, we find him occasionally, under the pressure of facts, using language which virtually admits the thing, as when he says, 'that at any given time the whole quantity of work to be done is a fixed quantity, and the uttermost which employers can afford to pay for having it done is a fixed amount'; and in other places his language recognises the inevitable fact that employment must be limited by the amount of capital which at the time being sets it in motion, that amount being the thing to which Smith, McCulloch, Fawcett, and other writers have assigned the offensive name."
Thornton erred in "virtually admitting" the chimerical notion that he "scouts with contempt." Cairnes compounded error by not noticing that the "profound, pernicious fallacy" he bitterly denounced on page 251 of his book was none other than a restatement of the wages-fund doctrine he had stoutly defended back on page 174.

How is it possible that both Thornton and Cairnes could commit the identical errors while taking diametrically opposite positions on the question of the wages-fund? The answer lies in the ineluctable vagueness and ambiguity of the ceteris paribus clause. In the hall of mirrors where "other things remain the same," what "other things" are included in or excluded from the ceteris paribus pound is tacit as is exactly how they are "the same."

Adding intrigue to irony, Persky credited William Petty with introducing the term ceteris paribus into economic discourse. It is also quite possible the Petty wrote the earliest version of Thornton's "fixed quantity of work to be done." Except in Petty's version it was "a certain proportion of work to be done," not a fixed quantity. There is a world of difference between a fixed quantity and a certain proportion. No doubt part of the shape-shifting magic of ceteris paribus arises from its equivocation on whether it is quantities or proportions or both that are being the same.

Maybe ceteris vertigus (other things being dizzy) would be a better name.

Monday, September 1, 2014

Lump of Labor Day Special: Advanced (Elementary) Concepts in Mathematics

"…if there be but a certain proportion of work to be done; and that the same be already done by the not-Beggars; then to employ the Beggars about it, will but transfer the want from one hand to another…" – John Graunt, 1662.
In a previous post, Graunt Work, I discussed the theological foundations of John Graunt's Natural and Political Observations made upon the Bills of Mortality and hinted at the unacknowledged survival of assumptions of divine providence in expectations of a harmonious social order. This post is concerned with the distinction between the "certain proportion of work" assumed by Graunt (or possibly inserted by Petty) in his discussion of employing beggars and the "fixed amount of work" assumption, alleged by economists to be a widespread fallacy.

Proportion and number are two distinct concepts in mathematics. The distinction is fundamental to mathematical reasoning. The title of Fra Luca Pacioli's classic Summa de Arithmetica, Geometrica, Proportioni et Proportionalita suggests the importance of the concept of proportion.

"One of Graunt's prevailing concerns," Philip Kreager has argued, "was to show that the body politic was integrated in the divine order in virtue of the numerical symmetry, intrinsic proportionality, and correspondences which could be found in its constituent parts." The word "proportion" appears 40 times in Graunt's text, where it consistently refers to the relation of one part to another or of a part to a whole -- not to simple quantities or amounts. "Quantity" occurs only once in the book and "amount" not at all. Quantities and amounts are indicated in Graunt's text by the word "number."

There has been some conjecture regarding the extent of William Petty's contribution to Graunt's book. In his 1939 introduction, Walter Willcox suggested passages may be ascribed to Petty:
"...wherever conjectures, whether numerical or not, are made but no evidence offered in support of them… Furthermore, numerical statements which apply to matters of popular or political interest, but are of no importance for science, are supposed to be his." 
Using Willcox's criteria, the passage about employing beggars is arguably Petty's. Petty shared with Graunt the idea of a unique and profound significance to proportionality. Petty was educated as a physician and had been an anatomy instructor at Oxford. In his preface to The Political Anatomy of Ireland, Petty wrote:
"Sir Francis Bacon, in his Advancement of Learning, hath made a judicious Parallel in many particulars, between the Body Natural, and Body Politick, and between the Arts of preserving both in Health and Strength: And it is as reasonable, that as Anatomy is the best foundation of one, so also of the other; and that to practice upon the Politick, without knowing the Symmetry, Fabrick, and Proportion of it, is as casual as the practice of Old-women and Empyricks."
So if proportion has such a conspicuous significance, how does it get confused with quantity? For example, after citing Graunt on the "proportion of work to be done," historian Peter Buck went on to state that "Graunt presupposes that there is only a fixed amount of work to be done…" apparently oblivious to the crucial distinction between a certain proportion and a fixed amount.

One might suppose that economics has inherited a special concern for proportion from Graunt and Petty, the pioneers of political arithmetic. Unemployment and interest rates; productivity and price indices; efficiency, equality and inequality; elasticity of demand and of substitution are all proportional. Even the intersection of supply and demand is a proportion (an equality). So where does the attributed assumption of a "fixed amount of work" fit in with all this proportionality?
"There is, say they, a certain quantity of labour to be performed. This used to be performed by hands, without machines, or with very little help from them. But if now machines perform a larger share than before, suppose one fourth part, so many hands as are necessary to work that fourth part, will be thrown out of work, or suffer in their wages. The principle itself is false. There is not a precise limited quantity of labour, beyond which there is no demand." – Dorning Rasbotham, 1780. 
"In accordance with this theory it is held that there is a certain fixed amount of work to be done, and that it is best in the interests of the workmen that each shall take care not to do too much work, in order that thus the Lump of Labour may be spread out thin over the whole body of work-people." – David F. Schloss, 1891. 
"Economists have historically rejected the concerns of the Luddites as an example of the 'lump of labor' fallacy, the supposition that an increase in labor productivity inevitably reduces employment because there is only a finite amount of work to do." – David H. Autor, 2014.
Characteristic of the hundreds of denunciations of the supposed lump-of-labor fallacy (Sandwichman has amassed over 500 examples) is a obstinate refusal to substantiate allegations of such a belief with documentary evidence. "We don't have to show you any stinking badges!" Oddly enough, the denunciations also omit reference to particular authorities on the fallacy claim, settling for allusions to a nebulous view held by unnamed "economists" -- the above Autor quote is typical. Moreover, various arguments offered as "proof" of the fallacy of the assumption of a fixed amount of work evaporate with the simple substitution of a "certain proportion" for the conventional "fixed amount."

Of course a "certain proportion of work" is also vague. It might refer to a proportion of work to population, to industrial output, to resource consumption or to virtually anything else. Nevertheless, the alternatives of an "infinite amount of work to do" or of demand for labor that automatically adjusts to changes in the supply of labor are even less tenable.

One might also suppose that the increasing reliance of economics on mathematical modeling would make economists sensitive to the not-so-subtle distinction between quantity and proportion. Such a supposition would be premature, however. Liping Ma's study of math teachers' understanding of math fundamentals in China and the United States, reviewed by Roger Howe, found that:
"…successful completion of college coursework is not evidence of thorough understanding of elementary mathematics. Most university mathematicians see much of advanced mathematics as a deepening and broadening, a refinement and clarification, an extension and fulfillment of elementary mathematics. However, it seems that it is possible to take and pass advanced courses without understanding how they illuminate more elementary material, particularly if one’s understanding of that material is superficial."
So much for rigor. In addition, it's not a sure thing that understanding of math guarantees an unbiased use of it. Kahan et al. found that "more numerate subjects would use their quantitative reasoning capacity selectively to conform their interpretation of the data to the result most consistent with their political outlooks."

In a reply to comments from four economists on his General Theory of Employment, Keynes doubted that "many modern economists really accept Say's Law that supply creates its own demand. But they have not been aware that they were tacitly assuming it." Similarly, although economists may not have expressly believed, "that every individual spends the whole of his income either on consumption or on buying, directly or indirectly, newly produced capital goods," nevertheless, they tacitly assumed it. "They have discarded these older ideas without becoming aware of the consequences."

Keynes was wrong. Economists didn't "discard" the older ideas, they renounced the form in which they were expressed and devised new bottles in which to store the coveted old wine.

The tacit assumptions that Keynes highlighted are assumptions of inherent proportionality (the divinely ordained harmonious social order). Say's Law can be restated as: demand increases in proportion to an increase in supply. The tacit assumption about spending is that an increase in income will result in proportional increases, respectively, in consumption and investment.

One of the inevitable consequences of these tacit assumptions is that the proportion of work to be done must also be a constant. In other words, the alleged lump of labor, which in its distorted "fixed amount of work" formula is refuted by Say's Law is, in its original form of a "certain proportion of work," a corollary to Say's Law!