Hume's Sailing Ships correcting Samuelson's Icebergs

Paul Samuelson said (PITA gated) that David Hume's price-specie flow mechanism (ungated) was wrong. And I am saying, nervously biting my fingernails, that Samuelson was wrong.

Assume that durable sailing ships are costly to build, but have low (or zero for simplicity) operating costs. Assume apples are the only tradeable good, and one ship can transport one apple per year across the English Channel between Britain and France (the only countries in the world). Let P be the price of apples in Britain, P* be the price of apples in France, and R be the annual rental of a ship, (all prices measured in gold), then R=ABS(P*-P).

In this model, the Law of One Price (P=P*) will only hold if the volume of exports of apples (in either direction) is unconstrained by the existing stock of ships, so rentals on ships are driven to zero. But then no ships would be built to export apples if ship rentals were expected to be always zero, which is a contradiction of the Law of One Price because arbitrage is impossible without ships. But an existing stock of ships represents a sunk cost (sorry) and they keep on sailing even as rentals approach zero. They sail around Samuelson's Iceberg model (sorry) of transport costs.

If you are already familiar with Hume's essay, and have a good economic intuition, the rest of this post should be obvious.

Start with zero exports, zero ships, and P=P*. Then suppose, like Hume, that some of the gold in Britain magically disappears. (And unlike Hume, just to keep it simple, suppose that gold magically reappears in France.) The price of apples in Britain drops, the price of apples in France rises, and so the rent on a ship is now positive because you can use it to export apples from Britain to France. If that rent is big enough, and expected to stay big long enough, some ships will be built, and Britain will export apples to France in exchange for gold. Gold will flow from France to Britain, so the stock of gold will slowly rise in Britain and slowly fall in France, and the price of apples will likewise slowly rise in Britain and fall in France, so ship rentals will slowly fall, and the price of ships (the Present Value of those rents) will eventually fall below the cost of production, so no new ships will be built. But the ships already built will keep on sailing until rentals fall to zero or they rot (whichever comes first). Some clever grad student can do the math and figure out the parameter values for which the model converges all the way (rather than part way) back to the original equilibrium before all the ships rot. (My guess is that it depends on whether ships depreciate slower or faster than the rate of interest.) Should be a fun topic, combining irreversible investment with international trade and finance, plus there's data (see below).

The flow of exports and hence the flow of specie is limited by the stock of ships. And only a finite number of ships will be built. So we observe David Hume's price-specie flow mechanism playing out in real time.

This bugs me. Because it's all sorta obvious really. And my Sailing Ship model of transportation costs is a helluva lot more realistic than Samuelson's Iceberg model, where ships cost nothing to build but are fueled by burning apples (OK, the ship's crew could be fueled by eating apples). And it would have been a lot more likely to have been sorta similar to whatever was at the back of David Hume's mind when he wrote:

"What nation could then dispute with us in any foreign market, or pretend to navigate or to sell manufactures at the same price, which to us would afford sufficient profit?"

See that word "navigate"? Hume's gotta be thinking about sailing ships, right? And the Baltic Dry Index (equivalent to R in my model-sketch) fluctuates a lot, especially in times of international monetary disequilibrium, for the obvious reason that the stock supply of ships is very inelastic in the short run. It takes time to build new ships, and ships last a long time.

Prices don't just arbitrage themselves. Even if we take the limit of my model, as the cost of building ships approaches zero, we need to explain what process ensures the Law of One Price holds in equilibrium. Suppose it didn't...then people would buy low and sell high.....you know the rest.

Would introducing international finance (borrowing and lending gold) change the story? Yes, but not qualitatively. France would lend Britain gold, so prices would deviate less initially, so ship rentals would be lower, fewer ships would be built initially, and initial exports would be smaller, so we would observe Hume's price-specie flow mechanism for longer.

It doesn't have to be sailing ships. Any one-time investment cost of setting up in a new foreign market or expanding the volume of exports to an existing market could play the same role. Goods don't just export themselves. Hume's two century old essay is just as relevant today.

The volume of exports will not be a simple function of the current real exchange rate. It will be much more sensitive to changes in the real exchange rate that are expected to be longer-lasting than temporary. And there will be hysterisis, because the current stock of sailing ships will depend on a distributed lag of past expectations of future real exchange rates.

Thanks to C Trombley and David Glasner for letting me know about Samuelson's classic article. And to my daughter for helping me actually read it. This criticism of that article, and defence of Hume, can't be original, can it? Someone else should have thought of it earlier, shouldn't they?

Comments

[C Trombley]

On Twitter, I said I like Iceberg Models, but I have no problem with other models. I consider myself to be a Humean, also.

I'm not 100% sure what you're saying. I don't see how it concerns Samuelson's criticism. Iceberg costs aren't Samuelson's correction. He assumes 0 transportation costs (and, implicitly, 0 transaction costs) in his first run through. Also, your argument seems kind of partial equilbrium. If the price of apples goes down, then there is a rent on a ship goes up as a transaction cost of arbitrage. Okay. But the falling of an apple isn't a falling of the price level.

Hume & Samuelson's point of contention is a bit recherche, at least to me.

Hume *invented* equilibrium thinking, and we're still picking up his scraps on it. Hume's account is very sophisticated general equilibrium thinking about price level shocks and monetary policy. He was inventing M / P = k Y as a macro semiequilibrium condition. The way I understand him is through Mundell-Fleming. Let's say gold disappears in England but nobody has a money illusion so all the prices and savings accounts are all similarly altered. Jack English has saved up k Y , like Pigou told him to. Then comes Jerry German and he sees that the price of everything is low, so he buys. He makes a guaranteed profit (minus transaction costs, such as paying for a ship) by sending a fleet of gold and coming back with a consumption basket of apples. If the IS & LM curves don't move, then we'll go left and right on the BoP curve until we're back at the same equilibrium, exactly as Hume said. Ho-hum

Samuelson doesn't have a refutation of Hume, merely a correction. He writes a little too strongly. Samuelson was a child prodigy that never grew up. In equilibrium, the relative prices of goods ought to be the same everywhere or else arbitrage. Let's say Jerry German can't export gold. So Jack English comes up with a scheme: he buys English apples with English gold, sells them to Jerry German for German gold, buys German apples and ships them back. He's made a profit - he has more apples than he did before. But why? All he did was pay extra buy something that he could get around the corner. Samuelson claims that changes in price level are an unnecessary part of the above story. Samuelson claims that even if the price level on every good (except) was the same, we would still have an equilibrium distribution of gold. The equilibrium can happen via purely gold-for-gold trade. I am not 100% on Samuelson's model. I don't know what determines M(\infty) in his model. But the important point is that in Samuelson's model, equilbriation is *monetary*, rather than real. If England gets too much or too little gold, BoE and not Johnny English fixes it.

Hume's broader points against the Mercantilists - that desire for gold will prevent us from losing all gold if we allow its export, that long gold balances are equilibrium phenomena (and that, therefore, there is no policy that ends up with one country holding all the gold), that changes in price level have monetary corrections - all of these stand. All of these points are important, possibly the most important qualitative things we know about macroeconomics. And I think maybe Samuelson goes to far - Hume's analysis could work but it isn't the only way it works. Glasner, Eichengreen, McCloskey and others make a convincing case that it isn't how it did work after Hume. If you worked at the Bank Of England under the gold standard, then the maintenance of short run gold price stability matters a lot more on how you buy gold from Germany than trade arbitrage constraints between England & Germany i.e. Samuelson was right. The Gold Standard was managed, not automatic.

These "corrections" are footnotes to Hume, of course.

[Nick Rowe]

CT: the Iceberg model of transport costs is from an earlier Samuelson paper. In this paper he only applies it to transporting gold, noting that it leaves an indeterminacy to P/P* (which can lie anywhere on or between the two "gold points"), but you get exactly the same non-Humean results if you assume the iceberg model applies to transporting apples. The sailing ship model (whether applied to apples or gold) gives us Hume's results, where P/P* jumps down, then slowly rises back to one.

The/an alternative equilibrating mechanism is the real balance effect; P and P* stay equal, and M and M* slowly adjust back to their original ratio, as Brits and French slowly accumulate or run down their stocks of M.

It doesn't really matter much whether apples are the only good in my model, or the only traded good. All prices in Britain and France will move in the same direction, even if not always exactly by the same amount, depending on details like substitutability between apples and other goods in production and consumption.

I remember David Laidler teaching me in 1978/9? that Hume was wrong about the price-specie flow mechanism. I hadn't known about Samuelson's 1980 "correction" of Hume until you tweeted it, and then David Glasner tweeted it soon after, saying he agreed with Samuelson that Hume was wrong in this point. So I'm going up against some heavy-duty economists in this post (and ones I normally agree with and have learned a lot from)!

[Lorenzo from Oz]

I like to divide the history of trade into 4 (well, 3 1/2) eras.

(1) Network continental: Afro-Eurasia does not know about the Americas or vice versa, transport costs are high, trade over a distance is limited to high value (non-competing) items along thin networks.
(2) Global networks: Europe connects everyone, Columbian exchange happens (which is mainly about contact and spread of crops, diseases to new places), transport costs remain hight, trade over a distance is limited to high value (non-competing) items along thin networks, mostly driven by silver being plentiful in the Americas, but output scarce, silver being scarce in Asia (particularly China) but output relatively plentiful, Europe being intermediate and intermediary.
(3) Atlantic transitional: With canal production and expansion in sailing ships, quantity has a quality all its own such that the Atlantic economy begins to head towards mass trade (even though transport technology does not change all that much), to the extent there is major convergence in wheat prices from late C15th to early C19th and the Netherlands becomes the first famine-free society.
(4) Globalisation From the 1820s onwards, steamships and railways drive down transports costs to the extent that mass trade happens and global prices begin to happen. From 1830s onwards, electrical telegraphy separates communication costs from transport costs for the first time (apart from the French semaphore system, 1790s onwards).

Once you have mass transport and extensive distance communication, the price-specie-flow mechanism is not needed anymore, because there is a global market in gold and silver which does not require the gold or silver itself to move for the prices to shift (though the gold and silver could still be moved to protect and "ratify" ownership shifts, it is not required for the price adjustments, merely its ready possibility).

While transport costs are so high, there is no law of one price over any distance, because there is not enough transport to achieve the equalising arbitrage or allow sufficient disparate point production in traded goods. Trade patterns can be strikingly stable for centuries, even millennia, because prices never converge: one only trades over any distance in things not produced locally (i.e. non competing goods).

The price-specie-flow mechanism occurs when transport costs are low enough to support converging price arbitrage but not separate from communication costs so prices cannot shift until the transporting happens. So, Hume was right until he wasn't (but hadn't been previously).

So, I agree with you Nick, but I come at it historically rather than via model reasoning as such.

[C Trombley]

Lorenzo From Oz: Read the Samuelson paper, "high speed -> no price-specie-flow mechanism" is not a theoretically well grounded argument. Or go straight to the horses mouth, see 41-43 (esp 43) here:

http://www.econlib.org/library/NPDBooks/Viner/vnSTT6.html#VI.41

[Nick Rowe]

Hi Lorenzo!
Interesting way of looking at it. Hume would have been thinking about the end of your 3rd period, I think.

"Once you have mass transport and extensive distance communication, the price-specie-flow mechanism is not needed anymore, because there is a global market in gold and silver which does not require the gold or silver itself to move for the prices to shift..."

I disagree with you there. Even if (paper/electronic) "gold" has zero transport costs, the real goods and services that get exported and imported do have transport costs (and sometimes the fixed cost of opening up a new export market, which is not strictly a "transport" cost, but acts just like my sailing ships in a model). So we will see international price differentials, even if "gold" flows at zero cost.

[rsj]

Yes, transportation will bound price differentials, but once you can move gold around at zero cost, wouldn't the residents Germany not spend all their increased wealth in period 1 but also also make investments in England, thereby obtaining a permanently higher lifetime consumption even as prices equilibrate? For example, they can be absentee landlords in England.

It seems to me the question Hume was addressing was not prices per se, but whether a one time movement of gold from England to Germany (say as war reparations) had any real long term effect on the relative well-being of the two nations. Once you allow for international capital flows, which were well known to Hume, it does have a real long term effect even in the case of zero transportation costs. IMO omitting capital flows is incredibly disingenuous on Hume's part. The mention of Ireland is particularly grizzly, as by then 1/4 of total Irish output was sent each year as rental payment to absentee landlords in the UK, resulting (both directly and indirectly) in many Irish starving to death even in Hume's day. Moreover the long term impoverishment of the Irish forced them to change their economy and focus on growing cheap food staples such as potatoes. All of this was known to Hume, so how could he argue that removing gold from one country while keeping it others wouldn't result in any long term effects? The British did just that to Ireland.

[Nick Rowe]

rsj: Samuelson's attack on Hume's price specie flow story was based on the law of one price, rather than capital flows.

But yes, it is possible that a one-time transfer of wealth from Britain to France could make a permanent difference to exports. You get that with infinitely-lived agents and homothetic preferences in a simple model. You don't get it in an OLG model. It depends.

But that question is really a side issue. There are various monetary and financial shocks and savings/investment shocks that would require a change in net exports to re-equilibrate the global economy. Think Germany and Greece recently. Hume's imaginary disappearance of gold is just a simple metaphorical thought-experiment, that allows him to hold everything else constant, because it was a fairy who disappeared the gold. The question is: does there need to be a change in international relative prices (P/P*) to allow that increase in net exports to happen, and what is the exact relationship between net exports and P/P*? And I'm saying that Hume's Sailing Ships model gives a very different and better answer to that question than Samuelson's Iceberg model (which I think Paul Krugman's work also uses).

[Frances Woolley]

Interesting post.

[Lorenzo from Oz]

Nick: but once we have telegraph globalisation, we have these things which can trade for gold which don't cost anything to move. And the informed possibility of moving the gold means that the prices will move in tandem, including differentials due to transport costs. The difference is between a situation where the prices change as the good moves (Hume) and one where the interaction between the good moving and prices changing is more complex.