(Warning: This is a long and wonkish entry, aiming at self-comprehension, and the product of one too many long plane ride.)
The Stolper-Samuelson theorem is a remarkable theorem: it says that in a world with two goods and two factors of production, where specialization remains incomplete (plus a few more technical assumptions), one of the two factors--the one that is "scarce"--must end up worse off as a result of opening up to international trade. Not in relative terms, but in absolute terms. But the theorem is also quite limited in its applicability. It applies only to a case with two goods and two factors, and so its real world relevance is always in question.
But there is a version of the theorem that is remarkably general and powerful. It says that regardless of the number of goods and factors, at least one factor of production must experience a decline in real income from trade as long as trade induces the relative price of some domestically produced good(s) to fall (and as long as the productivity benefits from trade are restricted to the traditional, inter-sectoral allocative efficiency improvements, about which more later). All that this result requires is a very mild assumption, namely that goods be produced with varying factor intensities (i.e., use different combination of factors). The stark implication is that someone will lose, even if the nation as a whole becomes richer.
(Here is the proof. Take the good whose price falls with respect to all other goods' prices in the economy. The percent change in that good's price must be a weighted average of the percent change in the prices of its inputs. This means that there must be at least one input or factor whose price falls by more (in percentage terms) than the output price. The owner of this particular factor must be worse off then in relation not only to that good's price, but in relation to all other prices as well.)
The theorem does not identify who exactly will lose out. The loser in question could be the wealthiest group in the land. But if the good in question is highly intensive in unskilled labor, there is a strong presumption that it is unskilled workers who will be worse off. And before you curse economic theory, note that this is really accounting--not economics at all.
I have been thinking about this result in connection with Broda and Romalis's remarkable finding that
the rise of Chinese trade has helped reduce the relative price index of the poor by around 0.3 percentage points per year. This effect alone can offset around 30 percent of the rise in official inequality we have seen over this period.
The puzzle here, at least on the face of it, is that one would expect China's trade to have had the largest price impact on labor-intensive goods. And if so, wages of unskilled workers must have fallen even more, along the lines of the Stolper-Samuelson logic sketched out above. Can we still say that trade with China has helped reduce U.S. inequality?
The first thought that comes to mind is that Broda and Romalis are talking about consumer prices, and Stolper-Samuelson effects depend on changes in producer prices--i.e., prices of goods that are actually produced in the U.S. If nobody in the U.S. produces the garments and toys that China exports to the U.S., then it is conceivable that the relative price of labor-intensive goods will fall without hurting real wages.
But then this is unlikely, given substitutability between Chinese- and U.S.-made goods. And indeed another paper, by Raphael Auer and Andreas Fischer, employs a clever technique to document a sizable negative impact on U.S. producer prices from trade with China and other labor-abundant countries. So the benign effect of Chinese exports, if any, is not due to the fact that the U.S. no longer competes head-to-head with that country in similar products.
What gives? The Auer and Fischer paper underlines another important result. What lies behind the decline in U.S. producer prices in trade-affected sectors is not wage or other input price reductions but mostly increases in total factor productivity. So perhaps what is going is that the Stolper-Samuelson logic is defeated by increases in sectoral productivity induced by import competition. The mechanical link between prices and factor costs--which I appealed to above in the proof of the generalized S-S theorem--breaks down whenever there is productivity change. After all, if TFP increases, employers can afford to pay unchanged wages even if the prices they face decline.
The next question inquiring minds will want to know is how and why this TFP improvement comes about. The available economic theory on the impact of market competition on firm-level efficiency is notoriously inconclusive and ambiguous. (Profit-maximizing firms should want to minimize costs regardless of how tough competition is.) Perhaps what is happening is a kind of industry rationalization--exit of the least efficient firms--in which case we should see this restructuring and the associated layoffs in the data as well. Moreover, labor does not exactly come out unharmed in this case either. It is after all job loss, and the threat thereof, that workers complain about.
But if this line of reasoning is correct, the main threat to workers is not a Stolper-Samuelson type permanent compression in wages, but the more temporary (and limited) wage losses incurred by displaced workers. This is the kind of problem that wage insurance is ideally suited for.
Stay tuned--if you managed to read this far...