Wednesday, June 07, 2006

More On The Incorrect Heckscher-Ohlin-Samuelson (HOS) Theory

I have some comments in "Unregulated International Trade Unjustified By Comparative Advantage (TOC)". Radek offers an admittably speculative explanation of why there is a loss from trade in my numeric example:
"Increasing returns isn't the correct term. Nonconvex production set is what I'm guessing."

I think that explanation is wrong. I pointed out in the comments that the numeric example is not a reswitching example. Radek comments on this observation:
"I think Metcalfe and Steedman emphasized reswitching as necessary for this kind of result then later folks realized that reswitching wasn't it. But like I said, I'm not too familiar and it's been awhile.

Ok - I think I found the MS article and will read up on it (JIL May'77)."

The phrase "this kind of result" is doing too much work here. As I mentioned, Metcalfe, Steedman, and others have a variety of criticisms of the logic of HOS theory. The criticism illustrated by my example is from Metcalfe and Steedman (1974). Steedman and Metcalfe (1977) is a different criticism, a criticism that stretches my knowledge of trade theory by the by. They conclude:
"We have examined a version of the familiar H-O-S analysis, with two countries, two commodities and two factors; we have made all the normal assumptions except that, instead of a common zero rate of profit, we have assumed a common positive rate of profit. Since the existence of a positive profit rate does not affect the properties of the familiar relationship between commodity-prices and factor-prices it does not affect the factor-price-equalisation and Stolper-Samuelson theorems. In general, however, nothing can be said a priori about the relationship between factor-prices and the factor-intensity of production methods, when the profit rate is positive, and it follows that nothing can be said a priori about the shape of the relative supply curve. This does not prevent the H-O-S theorem about the pattern of trade from holding in its 'quantity' form, but does make the theorem invalid in its 'price' form, does mean that trade need not 'harm' a country's scarce factor, and does mean that uniqueness of international equilibrium is to be regarded as a special case when the common rate of profit is positive." - Steedman and Metcalfe (1977)

The demonstration in Steedman and Metcalfe (1977) draws on an earlier analysis of a closed economy, Metcalfe and Steedman (1972). Here M. and S. present a reswitching example with two homogeneous unproduced inputs, labor and land. They find, at a certain given positive rate of profit, that the technique of production that minimizes cost at the higher ratio of the rent to wage will be more land-intensive. I think of this example as analogous to one of capital-reversing. It too is destructive of supply and demand explanations of prices.

I don't recall if they say so explicitly, but this article certainly gives the impression that this counter-intuitive result - at least to those who believe in the out-dated neoclassical theory of value and distribution - is due to the presence of reswitching. If I recall correctly, this result was later shown to be compatible with the absence of reswitching. I believe Steedman selected the article first demonstrating this compatibility for republication in Steedman (1989).

If I ever get around to discussing recent empirical results on the labor theory of value, I will point to some criticisms of Steedman.

Update: Radek reminds me that Montet (1979) demonstrated that the results in Metcalfe and Steedman (1972) and in Steedman and Metcalfe (1977) are compatible with the absence of reswitching.

  • Metcalfe, J. S. and I. Steedman (1972). "Reswitching and Primary Input Use", Economic Journal (Reprinted in Fundamental Issues in Trade Theory (edited by I. Steedman), Macmillan, 1979).
  • Steedman, I. and J. S. Metcalfe (1977). "Reswitching, Primary Inputs and the Heckscher-Ohlin-Samuelson Theory of Trade", Journal of International Economics (Reprinted in Fundamental Issues in Trade Theory (edited by I. Steedman), Macmillan, 1979).
  • Metcalfe, J. S. and I. Steedman (1974). "A Note on the Gain From Trade", Economic Record (Reprinted in Fundamental Issues in Trade Theory (edited by I. Steedman), Macmillan, 1979).
  • Montet, C. (1979). "Reswitching and Primary Input Use: A Comment", Economic Journal, V. 89, N. 355 (Sep.): 642-647.
  • Steedman, I. (editor, 1989). Sraffian Economics (2 volumes), Edward Elgar.


radek said...

Hmmm, I still think nonconvexity has something to do with it. Positive rate of profit may be just a different way of saying the same thing. The fact that all the relevant examples in Metcalfe and Steedman are based on funky supply curves also suggests the link, since usually convex production set => monotonic supply curve. (Except here we're talking relative supply curves and I forget all the topology details from way back when)

As far as the 'is it reswitching?' question. A quick search finds this Comment by Montet, which points out that MS go through without reswitching: The Economic Journal, Vol. 89, No. 355 (Sep., 1979), pp. 642-647

One thing I'm not clear on in the MS 77's paper is whether the result is still Pareto Efficient - obviously, since there are mutliple equilibria they will differ in their Social Welfare ranking. I'm not sure if this is relevant to your example.

Finally, as MS point out, the existance of a positive rate of profit pretty much implies that there is a third unspecified factor. So you're really in a 3-factor, 2-commodity, world, not the standard 2x2x2 HO world. This is why your example has the feel of the specific factors model (though obviously it isn't). And in 3x2 world all kinds of crazy things happen - but again, I don't know if the term 'comperative advantage' makes sense here.

Currently I don't have access to the Steedman book.

dsquared said...

It's not so much nonconvexity as noncontinuousness of the production function. It's like the beef/leather model - for a lot of the range of the production function, there are some proportions in which you can't produce corn and ale.

Robert Vienneau said...


Thanks for the Montet reference. You'd have to show some work to show nonconvexity; I don't think it's there.

Some of Steedman's later criticisms of neoclassical theory do not depend on a positive rate of profits/interest, if I recall correctly. I plan on blogging about them sometime. He has sustained a critique of partial equilibrium across a decade of papers.

I think the structure is chosen to give the number of degrees of freedom to make the example work. I plan on blogging sometime about an example in the theory of international trade that has only one non-produced input ("labor") and produced inputs (finance "capital").

Robert Vienneau said...


Thanks for the comment. I think the loss from trade could result from smooth microeconomic production functions. At the level of the economy, not every proportion of ale and corn can fully use the non-produced inputs - you are correct there.

I once thought of creating an example with more processes. I wanted to get segments za and bc, as well as ab, along the Production Possibilities Frontier in which all resources are used. This would be a closer discrete approximation to a continuously differentiable PPF. But even I got bored with that before going to far.

Obviously statements about what's compatible with what are most convincing with examples.

radek said...

You know it actually sort of occured to me what was going on here - I think, still not 100% sure. So let me come back to this long long long ago post. Anyway I think I was wrong. It's not nonconvexities it's just factor intensity reversal which the HOS theorem rules out by assumption. But if you wanted to you could do all this with neoclassical tools.
Man, it's been a long time since I took International Trade and hadn't paid much attention to it recently. Strangely enough that's what got me interested in economics in the first place.