In a previous post, I asked whether Adam Smith was a closet Bayesian, and I concluded that post with a reference to an obscure but intriguing paper titled “A study of Adam Smith’s original contributions to economic theory and decision making under uncertainty” by Michael Emmett Brady, a lecturer at the Dominguez Hills campus California State University. (See also his 2015 book of essays on Adam Smith and John Maynard Keynes below.)
Among other things, Brady’s 2016 paper identifies three passages in The Wealth of Nations as proof of “Adam Smith’s original contributions to economic theory and decision making under uncertainty.” (Brady 2016, p. 39) For reference, I reproduce the three relevant passages below:
PASSAGE #1:
The first passage Professor Brady cites is from Book V, Chapter 2 of The Wealth of Nations, where Smith is explaining why the business of insurance can be successfully carried out by a joint stock company in a free market, i.e. without monopoly rights:
“The value of the risk, either from fire, or from loss by sea, or by capture, though it cannot, perhaps, be calculated very exactly, admits, however, of such a gross estimation, as renders it, in some degree, reducible to strict rule and method. The trade of insurance, therefore, may be carried on successfully by a joint-stock company, without any exclusive privilege. Neither the London Assurance, nor the Royal Exchange Assurance companies have any such privilege.” (WN, V.ii.b.34, p. 756; Brady’s emphasis)
For Prof. Brady, this passage is evidence in support of the proposition that “probabilities are not precise.” This may not sound like a big deal, but it really is. See here and here, for example.
PASSAGE #2:
The next passage Prof. Brady mentions is from Book I, Chapter 10 of The Wealth of Nations, where Smith is explaining “inequalities” in the wages of labour:
“… the wages of labour in different. employments vary according to the probability or improbability of success in them.
“The probability that any particular person shall ever be qualified for the employment to which he is educated is very different in different occupations. In the greater part of mechanic trades, success is almost certain; but very uncertain in the liberal professions. Put your son apprentice to a shoemaker, there is little doubt of his learning to make a pair of shoes; but send him to study the law, it is at least twenty to one if ever he makes such proficiency as will enable him to live by the business. In a perfectly fair lottery, those who draw the prizes ought to gain all that is lost by those who draw the blanks. In a profession where twenty fail for one that succeeds, that one ought to gain all that should have been gained by the unsuccessful twenty. The counsellor-at-law who, perhaps, at near forty years of age, begins to make something by his profession, ought to receive the retribution, not only of his own so tedious and expensive education, but that of more than twenty others who are never likely to make anything by it. How extravagant soever the fees of counsellors-at-law may sometimes appear, their real retribution is never equal to this. Compute in any particular place what is likely to be annually gained, and what is likely to be annually spent, by all the different workmen in any common trade, such as that of shoemakers or weavers, and you will find that the former sum will generally exceed the latter. But make the same computation with regard to all the counsellors and students of law, in all the different inns of court, and you will find that their annual gains bear but a very small proportion to their annual expense, even though you rate the former as high, and the latter as low, as can well be done. The lottery of the law, therefore, is very far from being a perfectly fair lottery; and that, as well as many other liberal and honourable professions, are, in point of pecuniary gain, evidently under-recompensed.
“Those professions keep their level, however, with other occupations, and, notwithstanding these discouragements, all the most generous and liberal spirits are eager to crowd into them. Two different causes contribute to recommend them. First, the desire of the reputation which attends upon superior excellence in any of them; and, secondly, the natural confidence which every man has more or less, not only in his own abilities, but in his own good fortune.” (WN, I.x.b.21-23, pp. 122-123; Brady’s emphases)
For Brady, the above passage illustrates the problem of “unreliable probabilities with different weights of evidential support.”
PASSAGE #3:
Lastly, Brady refers to Adam Smith’s discussion of retaliatory tariffs in Book IV, Chapter 2 of The Wealth of Nations. According to Smith, whether country A should impose a retaliatory tariff on country B as a strategic device to induce the repeal of country B’s tariffs depends on the probability that such a retaliatory tariff will, in fact, succeed in persuading country B to repeal its tariffs. But who is in the best position to make such a probability calculus? Smith tells us in Book IV, Chapter 2:
“There may be good policy in retaliations of this kind, when there is a probability that they will procure the repeal of the high duties or prohibitions complained of. The recovery of a great foreign market will generally more than compensate the transitory inconveniency of paying dearer during a short time for some sorts of goods. To judge whether such retaliations are likely to produce such an effect, does not, perhaps, belong so much to the science of a legislator, whose deliberations ought to be governed by general principles, which are always the same, as to the skill of that insidious and crafty animal vulgarly called a statesman or politician, whose councils are directed by the momentary fluctuations of affairs. When there is no probability that any such repeal can be procured, it seems a bad method of compensating the injury done to certain classes of our people, to do another injury ourselves, not only to those classes, but to almost all the other classes of them. for that alone would seldom affect them considerably, but some other manufacture of theirs.” (WN, IV.ii.39, p. 468; no emphases by Brady)
QUESTIONS:
Do these three passages really amount to “original contributions” to decision making under uncertainty? Can a case be made that Adam Smith was a closet Bayesian? And, lastly (for now), why doesn’t Professor Brady cite Smith’s more extensive and prescient discussion of the psychology of lotteries and “the certainty or uncertainty of the returns” in Book I, Chapter 10 of The Wealth of Nations, especially paragraphs 27 to 33? I will return to and further discuss all of these questions in my next few posts later this week.
WORKS CITED:
Brady, Michael Emmett. 2015. Adam Smith: Essays on Adam Smith, John Maynard Keynes, and Their Interval Valued Approaches to Probability, Decision Making, and Uncertainty. Xlibris.
Brady, Michael Emmett. 2016. A study of Adam Smith’s original contributions to economic theory and decision making under uncertainty. International Journal of Business Policy & Governance, 3(3): 39-50, https://thescholedge.org/index.php/sijbpg/article/view/290
Smith, Adam. 1981. An Inquiry into the Nature and Causes of the Wealth of Nations (R. H. Campbell and A. S. Skinner, editors), 2 vols. Liberty Fund.
prior probability 