Happy Paris Liberation Day! (And Happy Birthday to yours truly!) In my previous post, I introduced and surveyed three separate passages from The Wealth of Nations in which Adam Smith refers in one way or another to the concept of probability. (Hat tip to my colleague and new friend Michael Emmett Brady for re-bringing these probability passages to my attention.)

Today, I will return to the first of these three Smithian selections: the insurance business paragraph. To begin, this particular passage, which appears for the first time [1] in the last part of a 79-page pamphlet Smith published in 1784 (see Smith 1784a, p. 77) and which was then inserted into Book V, Chapter 1 of the third edition of Smith’s magnum opus (Smith 1784b, Vol. 3, p. 147, available here), reads as follows:

“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, my emphasis)

[1] The possible significance of the actual publication timeline of this short passage will become clear shortly.

One can certainly try to argue, as Professor Brady does, that Smith’s off-hand remark that “the risk … cannot … be calculated very exactly” anticipates the idea of “imprecise probabilities” (see here and here, for example), but I want to focus instead on the second part of the passage above, where Smith refers to two actual insurance companies: London Assurance and Royal Exchange Assurance. Historian Maurice Edward Ogborn reports that both of these companies were granted their corporate charters during the South Sea Bubble of 1720:

“In the troubled times of the South Sea Bubble, charters were granted to two corporations, the London Assurance and the Royal Exchange Assurance—in 1720 for the purpose of transacting marine insurance business and in 1721 for fire and life insurance business. The corporations granted life assurance contracts for a year at a time, similar to the contracts that were being granted for fire insurance business.” (Ogborn 2006, p. 21)

Although both the London Assurance and Royal Exchange Assurance companies “were permanent and substantial organizations” (ibid.), the fields of actuarial science and risk management — or what I like to call “applied probability” — were still in their infancy. Case in point: according to Ogborn, the schedule of premiums of the first life insurance policies ever issued by the London Assurance and the Royal Exchange Assurance companies “was at a flat rate for a wide range of ages”!!! (Ibid.)

Instead, it was another insurance company — alas, one that is not mentioned by Adam Smith, either in the passage above or anywhere else in The Wealth of Nations for that matter — that pioneered age-based premiums based on mortality rates and that laid “the framework for scientific insurance practice and development” and “the basis of modern life assurance upon which all life assurance schemes were subsequently based.” (See here.) That company was the Equitable Society:

“The original establishment of life assurance upon a sound basis was largely the achievement of one office and of the men who served her. This was the Society for Equitable Assurances on Lives and Survivorships, now known as The Equitable Life Assurance Society, and still affectionately called the ‘Old Equitable’. The Equitable was the first life assurance society to grant long-term contracts of life assurance for either a stated period or the whole of life, with premiums calculated according to age and type of assurance.” (Ogborn 2006, p. 19)

Moreover, in a plot twist that proves the old adage “truth is stranger than fiction”, one of the leading intellectual lights who served this company was none other than Adam Smith’s nemesis, Richard Price (whose portrait is pictured below). [2] In short, if the insurance business is now, to quote Adam Smith, “reducible to strict rule and method“, this happy state of affairs was in large part due to the ground-breaking work of Richard Price!!! (See generally Chapter 4 of Frame 2015 as well as Chapter 7 of Ogborn 2006.)

[2] On Adam Smith’s low opinion of Richard Price, see Smith’s letter of 22 December 1785 in The Correspondence of Adam Smith. I quote from that letter here.

Furthermore, it was most likely Richard Price’s early work on Bayes’s theory of inverse probability in 1763 that eventually led to his interest in life insurance. (See, e.g., Frame 2015, pp. 44-45; see also Ogborn 2006, p. 88) According to Ogborn (p. 90), “The earliest contacts between Price and the Equitable Society are recorded in copies of his correspondence between August 1768 and March 1771, and it was Price, applying Bayesian methods to life insurance, who “counselled that the Society, ought to have tables of values for all ages and every different term of years in order to guard against ‘careless or unskilful calculations’.” (Ibid.)

The Equitable Society was founded in 1762 — 14 years before the publication of the first edition of The Wealth of Nations and 22 years before the publication of Smith’s 1784 pamphlet — so her omission from Smith’s magnum opus is curious. Indeed, I would go as far as to say that this omission requires an explanation. After all, if this 1785 letter is any indication (see Corr. 251), Adam Smith knew who Richard Price was and both men ran in same social circles during their visits to London.

WORKS CITED:

Frame, Paul. Liberty’s Apostle: Richard Price, His Life and Times. University of Wales Press (2015).

Ogborn, Maurice Edward. Equitable Assurances: The Story of Life Assurance in the Experience of the Equitable Life Assurance Society, 1762-1962. Routledge (2006).

Smith, Adam. An Inquiry into the Nature and Causes of the Wealth of Nations (R. H. Campbell and A. S. Skinner, editors), 2 vols. Liberty Fund (1981).

The Correspondence of Adam Smith. (Mossner, E. C., and Ross, I. S., editors). Liberty Fund (1987).