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Clarification and Elaboration on Stolper-Samuelson

(Prefatory Note: This post and the earlier one on which it is an elaboration are wonkier than is typical for Cafe Hayek.  For that I apologize.  Each of these posts is also a bit more speculative than is typical for my blog posts.  While I believe that my reasoning here is correct, I’m still pondering the intricacies of the arguments.  I confess to a possibility of error that is even higher than usual.)


The point I try to make in this earlier post on the Stolper-Samuelson Theorem warrants further elaboration.  Let’s begin by running through a quick example of Stolper-Samuelson.

Suppose that there are two goods (chemicals and shoes) and two inputs (high-skilled labor and low-skilled labor).  Both kinds of labor are used to produce both chemicals and shoes, but in different proportions.  Suppose that the production of each pair of shoes requires relatively more low-skilled labor compared to high-skilled labor than does the production of a liter of chemicals.  (“Requires” is a bit misleading because the optimal proportion of inputs used to produce any good or service depends upon the relative prices of inputs.  So, to be more precise, assume that at current wages the efficient production of shoes is low-skilled-labor intensive while the efficient production of chemicals is high-skilled-labor intensive.)

If the U.S. has a relative abundance of high-skilled labor compared to China, Americans will have a comparative advantage over the Chinese in the production of chemicals and the Chinese will have a comparative advantage over Americans in the production of shoes.  As trade opens up between these two countries, the demand for chemicals produced in America rises and the demand for shoes produced in America falls.  (In China the opposite happens.)  Because the production of chemicals uses relatively more high-skilled labor than does the production of shoes, the wages of high-skilled workers in America are bid up with freer trade.

In contrast, because the production of each liter of chemicals uses relatively less low-skilled labor than does the production of each pair of shoes, as shoe production falls in America a greater number of low-skilled workers are released from shoe production than are absorbed into chemical production – unless, that is, the wages of low-skilled workers fall sufficiently to encourage chemical producers to employ greater numbers of low-skilled workers.  In the U.S., in this very simple example, freer trade causes the wages of low-skilled workers to fall not only relative to the wages of high-skilled workers but also absolutely.  And because even before trade became freer the wages earned by high-skilled workers were higher than were the wages earned by low-skilled workers, freer trade further increases this income difference.  Freer trade increases income inequality in a country with a relative abundance of high-skilled workers.

The above is a standard account of Stolper-Samuelson’s identification of the process through which freer trade increases income inequality in a rich country (or, alternatively, of how judiciously imposed tariffs can not only raise the real incomes of the poorest workers in countries such as the U.S., but also make incomes more equal than they would be under free trade).

One problem with this standard account is its assumption of only two kinds of labor (“high” skilled and “low” skilled).  In reality each country has a wide range of many different qualities of labor, but with countries differing in their particular distributions of the different qualities of labor.

Suppose the U.S. is the only country in the world with hyper-super-duper talented managers.  Suppose also (as is reasonable) that the number of hyper-super-duper talented managers in the U.S. is nevertheless very small relative to the total U.S. workforce.  In this case, hyper-super-duper talented managers are nevertheless relatively abundant in the U.S. compared to in other countries.  Freer trade will further raise the labor income of such singularly skilled workers.

But in reality the bulk of U.S. workers have skill levels somewhere between those of the hyper-super-duper talented managers and those of low-skilled workers such as motel maids and handymen.  It is reasonable to suppose that if the bulk of American workers are employed in what we may call ‘middle-skill-level’ jobs, then America has a relative abundance of such middle-skill-level workers.

It is unquestionably true that, within America, there is an abundance of middle-skill-level labor relative to very high skilled and very low skilled labor.  But the question that is relevant for Stolper-Samuelson is this: In what kinds of labor does America have an abundance compared to other countries?  While it’s possible that, compared to other countries, the only kind of labor that America has in abundance is very high skilled labor, in reality this situation is implausible – or, at least it’s not obviously so.  Precisely because the great bulk of American workers are, in America, middle-skill-level workers, the relative abundance of such workers in America suggests that America has, compared to its trading partners, a relative abundance of many varieties of middle-skill-level workers.

America does have, for example, large numbers of skilled machinists, accountants, actuaries, medical technicians, web designers, educators, and engineers of all sorts.  Very few, if any, workers in these fields earn incomes that put them in top one-percent of income earners.  Many earn incomes that rank them at or near the middle of the income distribution for workers in America.  Therefore, if and to the extent that America has an abundance of such middle-skill-level workers relative to that of our trading partners, then Stolper-Samuelson predicts that freer trade will raise the wages of these middle-skill-level workers.

Whether or not freer trade raises the incomes of these middle-skill-level workers relative to any trade-induced increase in the incomes of America’s highest-skilled and highest-paid workers is a different question.  It might not do so – but it also might.

Bottom Line: In a world with a wide range of many different skill levels – from unskilled to hyper-super-duper skilled – it is a mistake to conclude from the Stolper-Samuelson Theorem that freer trade necessarily increases income inequality in rich countries.  It might do so.  But if the rich-country’s workforce is especially abundant in skills that, for that rich country, are considered middle level but which are relatively more scarce in the rich-country’s trading partners, then freer trade is likely to decrease income inequality in that rich country.  It will do so by swelling the incomes earned by the bulk of workers in that rich country – workers who, by the standards of that rich country, have middle-level skills.