Krugman, Heckscher, Ohlin, Samuelson, Autor, Dorn, and Hanson

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Robert Waldmann
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Paul Krugman has been wondering why stock market indices fell so sharply soon after Trump began trade-war-mongering. (also less wonkily here) He starts by noting that it’s a mugs game to try to explain stock market fluctuations, but then tries all the same.

The puzzle is that according to the very standard Heckscher Ohlin Samuelson model, the effect even of a severe trade war on GDP is fairly small. On the other hand the decline in the Dow (which he pegs at 6%) is large. Also Autor, Dorn and Hanson famously estimated a large effect of “The China Syndrome” on local labor markets (pdf warning).

His argument is basically

there is a reason why stock prices might overshoot the overall economic costs of a trade war. For a trade war that “deglobalized” the U.S. economy would require a big reallocation of resources, including capital. Yet you go to trade war with the capital you have, not the capital you’re eventually going to want – and stocks are claims on the capital we have now, not the capital we’ll need if America goes all in on Trumponomics.

Or to put it another way, a trade war would produce a lot of stranded assets.

For this post, it is even more necessary to click the link and read Krugman. I can’t summarize competently.

This post turned out to be really bad, so I am putting the rest after the jump.

To try (and fail) Krugman says a standard model implies a long run cost of 30% tariffs of just 1.5% of GDP. Here the standard HOS model assumes that capital and labor can be costlessly shifted from sector to sector. Sectors differ only in capital intensity. Trade affects wages and the return on capital. Protection by a capital rich country causes a shift to labor intensive sectors causing higher wages and lower returns on capital (that’s the point). It also reduces GDP by a Harberger triangle of deadweight loss(so it would be better for workers and investors to lump sum seize some capital and give it to workers). The deadweight loss is (to a linear approximation) equal to the area of a triangle whose height is the tariff and whose base the reduction in imports due to the tariff. I really just should cut and paste Krugman

So, what would a trade war do? Suppose the US were to impose a 30 percent tariff across the board, with other countries retaliating in kind so that there’s no improvement in the U.S. terms of trade (more technical stuff I don’t want to get into.) How much would this reduce trade? It depends on the elasticity of import demand; a reasonable number seems to be around 4. This would mean a fall in imports from 15 percent of GDP to around 5 percent – a 10-point reduction. And that in turn means a reduction in US real income of around 1.5 percent.

Krugman also appealed to an even longer post in which he suggests that Heckscher Ohlin Samulson (HOS) works in the long run, but in the short run, capital (and labor) are committed to a firm and reallocation is costly. I’m trying to figure out if this makes sense. I can think of three possibilities

1) as Krugman tends to suggest, there might be high costs for shareholders but not for the country as a whole, so the market reaction (down 6%) is actually rational this time (for once) and Krugman’s calculation that 30% tariffs would cause a loss of 1.5% of GDP is also accurate.

2) The 1.5% calculation is based on assumptions which might (or might not) describe the effect on a long run steady state but aren’t reasonably described as corresponding to the economic cost of a trade war.

3) the 6% decline is not total noise, but it is based on a more excusable than usual mistake by investors.

I will try each possibility.

1) Krugman is definitely not suggesting that the cost will be born by investors not workers. He stresses that workers have sunk costs too. Their stranded assets are sector specific skills and knowledge, their houses, their social network of friends and neighbors. So he is not guessing that the cost might be 6% of the value of shares, because it is all (or more than all) born by shareholders not workers.

He might be suggesting that the gains to capital don’t show up in stock market indices because they will go to firms which are not publicly traded (yet). This would work arithmetically. The idea is that total market capitalization will not be 6% lower because of the trade war, but there will be IPOs of labor intensive firms (the hot new shoemakers) and shareholders will have to buy the shares, hence the shares they own are worth less. But even if it could work arithmetically it is clearly silly — the US firms which would replace Chinese imports are almost certainly the ones outsourcing to China. They don’t have US factories now, but they do have patents, trademarks, and expertise. They would have a valuable option to invest in China competing factories with an advantage compared to new entrants.

It is certainly possible that part of the gain which balances the loss to shareholders is public revenue. 30% tariffs on 5% of GDp = 1.5% of GDP — the gain to the Treasury (coincidentally) equals the deadweight loss. If there is Ricardian equivalence, this doesn’t matter (and pigs fly). This means the cost to the private sector is 3% of GDP which is (very roughly) 2% of stock market capitalization. But shareholders would bear only part of this risk. this helps but doesn’t get close to 6%.

I’m pretty sure that I can’t make a plausible case for possibility 1.

2) the 1.5% calculation may be misleading (or wrong).

The argument is that there are costs of shifting factors from one sector to the other. In the long run these costs have been paid and are irrelevant, but shareholders face those costs now, hence the 6% market decline.

I have two concerns.

First, there is a difference between the long run in a model with adjustment costs and the short (and long) run in a model without adjustment costs. In the HOS model, the national amounts of labor and capital are taken as given, while in the long run, capital is accumulated. There is no reason to assume that the costs of reallocation won’t affect capital accumulation. A more reasonable assumption is that the marginal return on capital will converge to the same constant (this is true of growth models even with closed economies). That means a shift towards labor intensive sectors will cause a lower capital to labor ratio which is an additional effect on GDP.

Also the deadweight (money metric) cost of tariffs is not equal to the long run effect on GDP. The adjustment costs are social costs. Their present value isn’t zero even if they don’t last forever. The long run effect on GDP isn’t an estimate of the dead weight loss. I note Krugman didn’t say it is. It is easy to put a very high upper bound on these costs — private sector agents pay them to reduce the tariffs they have to pay. They could just pay 30% on 15% of GDP imported, so the present value of the adjustment costs must be less than 4.5% of GDP which is less than 6% of market capitalization. The option to reallocate resourses is very valuable, so the present value of adjustment costs is much lower than the present value of 4.5% of GDP forever.

3) Funny business related to share prices (other than the usual noise). it could be that managers’ incentives concentrate the costs on shareholders. Managers want their firms to survive even if it shareholder value would be maximized by liquidating them.

If the adjustment costs are paid in the medium run and the gains are extremely long run, then there could be shareholders displeased that firms pay those costs because the shareholders discount the future more than managers. This is similar to the story about managers wanting their firm to survive.

Update. Now I remember an interesting possible investment error. Even though many people invest in index funds, many still try to pick stocks. They include sophisticated investors who don’t necessarily do a bad job. But the point is that a significant fraction of shares are owned by people (or firms) who don’t have fully diversified portfolios. Trump’s trade tirades imply large possible transfers (say from steel using to steel making firms). Even if they sum up to a loss of much less than 1.5% of GDP, they make stock less attractive to those who pick individual shares. This uncertainty is diversifiable risk, but, in the real world, not all such risk is diversified. The sector specific risk created by Trump might reduce stock indexes even if the gains and losses add up to zero in the end.