Stolper-Samuelson for the real world

(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...

Comments

[Richard H. Serlin]

Dani,

I think the key overall point to make is this:

You can think of funny situations where one nations total GDP goes down from an increase in free trade. But, in the vast majority of real world situations, free trade will increase the total GDP of both sides -- and often tremendously over the long run.

But the free trade agreement will sometimes have to be intelligently constructed, and it's important to have some good key local laws and institutions in both countries to make the free trade work well. It's important to realize that with free trade there will be losers in each country, but in each country, in the vast majority of cases, the gainers gains will outweigh the losers losses – and often by a huge amount.

This will especially be true if you have the agreement well constructed and with good supplementary local laws and institutions. But usually, even if you don't, trade will do a lot more good than harm. The main reasons are it allows for more economies of scale, efficient specialization, greater competition, and less corruption.
Now the last two don't have to result from free trade. You can think of situations where the opposite will happen, but in the real world, it's more likely than not that freer trade will lead to more competition and less corruption. But this is precisely where the side agreements, local laws and institutions are so important – for example, smart anti-trust law with good enforcement.

It is also important to redistribute some of the gains of the gainers to the losers. The gainers gains almost always will outweigh the losers losses, so you can give some of their gains to the losers so that no one loses and everyone gains. This will also increase support for free trade, and make it more likely. Of course, try explaining this to today's Republican party, which believes that thinking beyond simple sound-bites is liberal and un-American.

An excellent case in point is Mexico. Total GDP has increased substantially due to a great increase in free trade, but the income of the vast majority who are poor has hardly increased. Almost all of the gains from free trade have gone to the wealthy. If Mexico had much more progressive taxes, as it should, it could be taxing those gains and using them to invest in education, infrastructure, public health, etc. for the vast majority. This would make essentially everyone gain from free trade, and these high return public investments would make the country much wealthier over the long run.

Dani, I think it's important to stress these things, along with the legitimate criticisms of free trade that you make. I know you make these criticisms not because you're against free trade overall, but because you want to make it better, with better constructed agreements and supplementary laws and institutions. But without stressing at the end that you think free trade is good overall, you risk doing a lot to help those who are fervently against it, and want extreme protectionism, which would hurt every country and devastate the poorest.

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http://richardhserlin.blogspot.com/

[Joe]

I really doubt, as you seem to do, that greater competition has caused improvements in productivity. What might explain this perhaps is the confluence in the 1990s of greater US-China trade with the spectacular technological revolution in information and communication technologies (ICT), which is known to have triggered a productivity boom. Which begs the question: whether the apparent negative impact of trade on unskilled workers would be transient or more permanent once the ICT-led technological revolution has run its course.

[Isaac]

In the last paragraph don't you mean "Stolper-Samuelson type dispersion" in wages, rather than compression?

In terms of wanting to see the mechanism of lay-offs when subject to import competition see any papers by Bernard/Jensen/Schott and others. The best paper for this question is Survival of the Best Fit: Exposure to Low-Wage Countries...(http://mba.tuck.dartmouth.edu/pages/faculty/andrew.bernard/bestfit.pdf)

[Peter]

Dani, you left out one teensy-weensy assumption that all trade theorems, including S-S, depend on: that trade balances at the margin, which is to say that any increase in imports is exactly matched by a corresponding increase in exports in the comparative static analysis. The last time I look at the numbers...., well, you get the drift. And, unfortunately, we don't have a micro-trade theory that tells us what happens to owners of factors for that other, unbalanced kind of trade. You'd think that an army of young doctoral students would be scribbling away at this, but there's no sign that this is happening.

[Mike Huben]

One thing that might make presentation of ideas like these better would be a systems diagram showing causes, effects, assumptions, and the sources of the arguments.

In economics, philosophy , and many other subjects, it takes innumerable paragraphs to present in a jumble what might be clear in a simple diagram.

A clear diagram could show what inputs increase, decrease, or are insignificant for the outputs, thus laying out most of the assumptions in a way we could rapidly assess. Having to juggle 10 or more paragraphs of reasoning in our heads makes this a difficult task.

[Bruce Wilder]

Ricardian comparative advantage is a very powerful argument, precisely because it posits a minimal rationale for specialization. And, it appeals to economists, in part, because it is purely a story of allocative efficiency.

There are stronger motivations for specialization, evident in the pattern of actual trade. One broad category could be called "fruits of the earth": the peculiar advantages of climate, soil or mineral endowments, which make one region an oil exporter and another a world-class vacation resort and a third, an exporter of wheat or bananas or dates or wine.

A second category of rationales for specialization could be called technological: the embodiment in sunk cost capital investment of high technical efficiency in manufacturing or services production. Think of Adam Smith's pin factory.

"Fruits of the earth" and technical efficiency are not, of course, at all mutually exclusive in practice. But, it is worth noting that some geographic regions with few natural endowments have, nevertheless, grown rich, by systematic investment in technically superior producion methods. Japan must lead the list of exemplars.

If, in calculating the "gains from trade" one is to restrict one's self to calculating the gains to Ricardian improvements in allocative efficiency, then, certainly, one is going to miss the gains from enhancing and extending technical efficiency. And, it has been the gains in total factor productivity in applying scientific and techological knowledge to the organization of production, which has driven the huge increases in production and income of the industrial revolution(s).

Economists, overly impressed by the comparative advantage argument, often look for allocative efficiency as a driver of trade: China is said to dominate "labor-intensive" manufacturing, (just as the same thing was said of rising Japan in the 1950's and 1960's). The demands of technological advance, however, don't seem to advantage labor-intensive anything. Capital, embodying advanced technology, tends to economize on labor by removing the purely mechanical and concentrating the locus of control. Pareto, I think, may have observed that tractors only have one driver seat -- and designing a multi-driver tractor for labor-intensive agriculture does not make much sense.

Smith observed the relation between trade and specialization, noting the technical efficiency gains from specialization, and noting the specialization was limited only by the extent of the market. "Globalization" -- the combination of a favorable political environment with low-cost transport and tremendous communication capabilities -- maximizes the extent of the market. And, aside from the "fruits of the earth", the goods and services, which dominate trade, tend to be those where specialization yields the greatest productivity gains. In others words, industries demonstrating increasing returns, almost without limit, will become prominent in international trade.

Industries, where increasing returns do not obtain beyond some modest limit, are the province of local trade.

The critical question for income distribution is unlikely to be the one posed by Stolper-Samuelson. The critical juncture is between local trade and international trade. No one in Los Angeles or Seattle is bemoaning the inability of those cities to manufacture and export, say steel and automobiles. The question ought to be, how do the gains from international trade trickle down from software and aircraft (in Seattle) to barbers and restaurants and real estate agents. Ditto, in Los Angeles, how do gains from DVD sales or television licensing trickle down to gardeners and auto dealers and computer repair persons?

I don't know that the model of the profit-maximizing firm is of much use, in this context. If we are to consider a firm managing the allocative efficiency of a production function, where maximal technical efficiency is simply assumed, we are going to miss entirely the critical factors of technology and organization in achieving and advancing technical efficiency.

I would suggest that a way to think abstractly about technical effiency, without getting lost in engineering details, would be to adopt the cybernetic model of control as the task of the firm. See for example the work of W. Ross Ashby, Introduction of Cybernetics. Principal-agent models are a subset of the cybernetic model of control of process. In the abstract, technical efficiency, then, is increasing control over production process to reduce error and waste: in other words, the reduction in error and waste, facilitated by sunk cost investments, produces the gains in total factor productivity.

The theoretical firm, tasked with cybernetic control of a production process, lives in a world of uncertainty and risk. Practically, such a firm can no longer be a profit-maximizer; it must be a rent-seeker, because it must seek returns on sunk cost investments, and such a firm will endeavor to maximize returns on the resources it owns and controls.

Returning to the topic of international trade, and trade in general, the conservation and/or conquest of rents must become a paramount political issue. Recast in terms of rents, Stolper-Samuelson regains its relevance.

[don]

I wonder how the researchers you cite dealt with the problem of determining factor intensities of traded goods. As Krugman points out, you can't use the regular trade and production goods classifications, because production is broken down within the classifications - For example, in producing one of the goods, you may have part of the production done here, part done in China and part done in other countries.

[Bruce Wilder]

For Michigan and Ohio, where the loss of rents and quasi-rents associated with auto production, have been considerable, I would think there are problems that go far beyond what wage insurance can handle.

The progress of manufacturing technology dictates declining manufacturing employment. If you think there's such a thing as high-tech, labor-intensive manufacturing, you have your head stuck in an unpleasant place.

The problem for displaced workers can be confounded by inadequate capital investment. Progress requires a renewal of capital investment and new capital investment embodying advancing technology, to lift labor productivity.

70% of U.S. workers are employees of organizations employiing more than 20, and 50% are in organizations with more than 100 employees. The managerial efficiency of those organizations, and the meta-organization of the society in which they are embedded, is critical to labor productivity. If the necessary capital investments are not being made, productivity and wages will decline.

Another critical factor is energy consumption. Increasing energy expenditure per worker helped to boost labor productivity by amplifying effort in the post-WWII era; that stopped around 1973, and if energy expenditure per worker is to decline, to protect the environment, that amplification of effort will not be happening. All the technical gains will be from applying communication technology to improve control and reduce error, and from, say, substituting cheap communication for business travel. The increased productivity from improved control will tend to flow to people in managerial roles, without affecting people in the so-called "unskilled" roles.

[Winton Bates]

There is another interesting complication to SS when the scarce factor is unskilled labour that comes predominantly from other countries. The highly protected industries in Australia had a high proportion of immigrants in their labour force. This suggests that some of the effect of high tariffs on wage rates would have been dissipated by attracting more unskilled migrants.

Incidentally, Paul Samuelson apparently acknowledged that comments in the Brigden report on the effects of tariffs on wages in Australia (in the late 1920s) helped to set off the analytical controversy that resulted in development of the SS theorem.

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don't all these assumptions depend on everyone operating above board and by the rules. I understand that is is theory but how does theory account for the fact that most resource providers in this equation will cheat the system so in all practical terms the tests of the theorem will always be inconclusive.

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