Weekly Philo of Economics: Adam Smith and Proportions (as well as good judgment)

“An effect always holds proportion with its cause,” David Hume, “Of Interest.”

Whatever be the actual state of the skill, dexterity, and judgment with which labour is applied in any nation, the abundance or scantiness of its annual supply must depend, during the continuance of that state, upon the proportion between the number of those who are annually employed in useful labour, and that of those who are not so employed. The number of useful and productive labourers, it will hereafter appear, is every where in proportion to the quantity of capital stock which is employed in setting them to work, and to the particular way in which it is so employed. The Second Book, therefore, treats….--Adam Smith (1776), Introduction and Plan of the Work, The Wealth of Nations (WN; emphases added).

In the passage above and throughout WN Smith appeals to "quantity" and "number." In light of this, consider, for example, this famous passage:

The real price of every thing, what every thing really costs to the man who wants to acquire it, is the toil and trouble of acquiring it. What every thing is really worth to the man who has acquired it, and who wants to dispose of it or exchange it for something else, is the toil and trouble which it can save to himself, and which it can impose upon other people. What is bought with money or with goods is purchased by labour, as much as what we acquire by the toil of our own body. That money or those goods indeed save us this toil. They contain the value of a certain quantity of labour which we exchange for what is supposed at the time to contain the value of an equal quantity. Labour was the first price, the original purchase-money that was paid for all things. It was not by gold or by silver, but by labour, that all the wealth of the world was originally purchased; and its value, to those who possess it, and who want to exchange it for some new productions, is precisely equal to the quantity of labour which it can enable them to purchase or command. (WN. I.v; emphasis added)

Adopting the language of "precisely equal"  Smith seems to imply to many readers that that such magnitudes enter into an exact theoretical model that is capable of being reconstructed by a series of equations. (Here is a famous example by Paul Samuelson.) Of course, such a model would have to be implicit because -- curiously enough -- explicit equations are lacking in WN.

In fact, even explicit computations are extremely rare throughout WN. Strikingly enough, right at the start of book, just after introducing the first main idea -- the division of labor -- Smith writes, "Observe the accommodation of the most common artificer or day-labourer in a civilized and thriving country, and you will perceive that the number of people of whose industry a part, though but a small part, has been employed in procuring him this accommodation, exceeds all computation." (WN I.1; emphasis added) Rather than offering a ringing endorsement of quantitative methods in his science, Smith calls attention to our epistemic limitations here.  And this fits with other evidence that Smith is deeply skeptical about applying mathematics to political economy. (Recall my treatment of this passage in WN, "I have no great faith in political arithmetick, and I mean not to warrant the exactness of either of these computations.")

So, what's going on here? I have come to think the key resides in Smith's embrace of "proportions" (see the second quote at the top of the post). Recall Hume's claim that “An effect always holds proportion with its cause” (“Of Interest,”). I call this Hume's "ninth rule of reasoning." If one assumes (or prescribes) that linear causal relationships are the only possible ones, this ninth rule allows Hume to rule out competing claims that posit the existence of causal relationships that are not 'proportional.' Hume uses the rule as a constraint on theory. For example, in context it plays a prominent role in  Hume's rejection of Mercantilism.

This is not the place to explore the Humean foundations of proportional (moral) reasoning. (Somewhat annoyingly Hume does not mention proportionality either among the natural nor among the philosophical relations.) But one can understand Hume’s attraction to proportionality. For, reasoning with proportions does not permit exaggerated claims to exactitude. (This is not to deny that one can make very precise claims through proportions. Newton's Principia is written in the language of geometric proportions, after all--and so is much classical science.) In the absence of precise measures, a judgment of proportion also requires some (contextual) judgment; one cannot just follow a mechanical rule.

In Smith we find lots of proportions in the absence of exact measures. For example, in his moral theory Smith writes,

It has already been observed [TMS 1.1.3.5,--ES], that the sentiment or affection of the heart, from which any action proceeds, and upon which its whole virtue or vice depends, may be considered under two different aspects, or in two different relations: first, in relation to the cause or object which excites it; and, secondly, in relation to the end which it proposes, or to the effect which it tends to produce: that upon the suitableness or unsuitableness, upon the proportion or disproportion, which the affection seems to bear to the cause or object which excites it, depends the propriety or impropriety, the decency or ungracefulness of the consequent action; and that upon the beneficial or hurtful effects which the affection proposes or tends to produce, depends the merit or demerit, the good or ill desert of the action to which it gives occasion.” (The Theory of Moral Sentiments 2.1.Intro.2, 67).

Smith embeds judgments of proportionality at the core of his moral theory; for Smith when we make a moral judgment we do so after mentally inspecting, as it were, the proportionality of the relata that enter a cause-effect relation. Such judgments are very sensitive to context. There is no exact measure of propriety. 

Now, there is one exact measures in WN: "At the same time and place, therefore, money is the exact measure of the real exchangeable value of all commodities." But the theoretical significance of this gets undercut in the very next sentence: "It is so, however, at the same time and place only." No other measure is called exact in WN! By contrast, even though "labour be the real measure of the exchangeable value," it is not an exact measure. As Smith goes on to explain:

It is often difficult to ascertain the proportion between two different quantities of labour. The time spent in two different sorts of work will not always alone determine this proportion. The different degrees of hardship endured, and of ingenuity exercised, must likewise be taken into account. There may be more labour in an hour’s hard work than in two hours easy business; or in an hour’s application to a trade which it cost ten years labour to learn, than in a month’s industry at an ordinary and obvious employment. But it is not easy to find any accurate measure either of hardship or ingenuity. In exchanging indeed the different productions of different sorts of labour for one another, some allowance is commonly made for both. It is adjusted, however, not by any accurate measure, but by the higgling and bargaining of the market, according to that sort of rough equality which, though not exact, is sufficient for carrying on the business of common life. (WN 1.7)

Now, this is not the place to explain how data that is merely sufficient for common life can be deployed with real, albeit inexact measures that enable causal, even counterfactual reasoning. (Before I saw any of this clearly, I have tried to do so here and here.) All I hope to have made plausible is that even reasoning with quantities and number in Smithian political economy generally requires good judgment and cannot be reduced to mere mechanical rules.