Capital flows vs Kapital flows (simpler version)

Let me try to make the intuition of my previous post simpler and clearer.

Suppose a country wants to invest more, because the profitability of investment has increased. It wants to increase the stock of kapital (machines) in its factories. There are three ways it could do this:

1 Divert some of its own production away from producing consumer goods towards producing investment goods, and consume less (save more).

2 Divert some of its own production away from producing consumer goods towards producing investment goods, but keep consumption (and saving) the same by importing consumer goods.

3 Import more investment goods, keep its own production of consumer and investment goods the same, and keep consumption (and saving) the same.

A closed economy can only do 1. And this will require an increase in the rate of interest (or something) to persuade households to postpone consumption. And it will require an increase in the price of investment good relative to consumption goods, to persuade firms to switch from producing consumption to investment goods.

An open economy can also do either 2 or 3. In both 2 and 3 there will be what economists call "capital flows" (borrowing from abroad, a surplus on the capital account of the balance of payments, matching a deficit on the current account). But only 3 has what I will call "kapital flows".

And the difference matters, because when we talk about "perfect capital mobility" in international finance/macroeconomics (and draw a horizontal BP curve in the Mundell-Fleming model and say a small open economy has the real interest rate pinned down by arbitrage at the world rate we are talking about capital flows (international borrowing and lending) and not kapital flows (importing or exporting machines).

If I understand Paul Krugman's model correctly, he assumes that 3 is impossible. A country cannot import investment goods, it can only import consumer goods. It must be self-sufficient in investment goods. Investment goods are non-traded goods. And he assumes that each country produces a different consumption good. The home country can only produce apples; the foreign country can only produce bananas. So if an open economy does 2, the price of apples must rise relative to the price of bananas, to persuade people to consume fewer apples and more bananas. And when the demand for increased investment goes back to normal, the price of apples will fall again, relative to the price of bananas. And if people expect this, the real interest rate in terms of apples (nominal interest minus expected apple inflation rate) must rise relative to the real interest rate in terms of bananas. And yet, if I understand Paul's model correctly, each country only produces one good, that can either be consumed or invested, so we have the simple "Neoclassical" production function Y=F(K,L)=C+I and I=dK/dt, so the price of the investment good is always the same as the price of the consumption good, because firms can switch from producing consumption to investment goods, at exactly the same cost of each, so the Marginal Product of Kapital is always equal to the real rate of interest in terms of the consumption good. (Otherwise, instead of r=MPK, we would instead have r=(MPK/Pk) + (dPk/dt)/Pk where Pk is the price of the investment good in terms of the consumption good, and the second term is the expected growth rate of that price.)

(Yes, I am reading things into Paul's post, to try to reveal his implicit assumptions, and I may be wrong on this.)

And I am saying there is a theoretical problem with this. Because it is hard to understand why the consumption good can be traded but the investment good cannot, if the two goods are the same good. Hard, but not impossible, because we could assume that each country can only use a very special type of investment good that can only be produced at home, and cannot be imported. (You can only invest in apple orchards by planting apples, which can't be grown in foreign climes.) But this does not seem generally plausible.

And I am saying that 3 is more likely, because investment goods can and do get imported. Or we could imagine 3', where the country exports fewer investment goods, so it can invest more at home, which amounts to the same thing. And if 3 is what happens, the world price of investment goods might rise, and world interest rates will rise, if the home country is a large country. But if the home country is small, relative to the rest of the world, these will not happen. And there is no reason why the apple rate of interest should rise relative to the banana rate of interest, because the mix of consumption need not change. (If the shock were a change in home country consumption and saving, rather than investment, this would cause relative interest rates to change.)

On the other hand, if the increased investment were an increase in investment in housing, I think 2 would be more plausible than 3, and Paul's model would be better. Because most of the work to build a new house must be done on site, even though the lumber and materials can be imported (I think that's right). But even then, there is a  problem with any model of kapital where the price of kapital goods never changes relative to the price of consumer goods. Especially if we are talking about houses, recently.

So maybe I should do the classic (and perfectly legit) economist's wimp-out and say: "It depends". But at least I've said something about what it depends on.

Comments

[Benoit Essiambre]

>A closed economy can only do 1. And this will require an increase in the rate of interest (or something) to persuade households to postpone consumption.

I'm sorry to diverge from the main point of the post, and I think I've had some of this debate here already but I have difficulty getting past this assumption.

As an individual, I invest to make it through my retirement years. This means that lower interest rates and lower returns means I need to invest more not less.

Lower interest rates make me buy a bigger house, a good that is mostly investment.

Businesses can finance new capital projects more easily in low interest rate environments. The "cost of capital" equation that they use to decide how much to put into investment tells them to invest more in lower rate environment.

On the aggregate, it seems to me that if investment goods have lower returns, that they wear out and depreciate faster, the natural reaction should be to divert more in investment goods and their maintenance just to maintain a reasonable level.

I realize that some forces go the other way. That in lower returns environment, people may not want to put too much resources where they will just be lost, but still... it seems to me the general trend should be the other way.

What am I missing?

Last time I think squirrels were mentioned in this debate.

[Nick Rowe]

Benoit: In an overlapping generations model you can sometimes get the result you are talking about (income effects dominating substitution effects, so saving falls when r rises). With a simple infinite horizon (people leave buguests for their kids) representative agent model there are only substitution effects (when r rises, future consumption becomes cheaper relative to present consumption, so we substitute away from present to future consumption). Remember that in a macro model there are really any income effects from price changes, because for every seller there's a buyer, and every borrower a lender, so one is made worse off and the other better off).

I did a post on this once, but can't find it. But I want to avoid saying more about that question here.

[Benoit Essiambre]

I sorta get what you are saying.

With these overlapping generation models, what if there is a large baby boom and in one period there are many workers relative to consumers and the next period after the large generation retires, it's the opposite? Also, what if, in between generations, we run out of a crucial natural resource like oil? What if there is a slow down in technological innovation between the periods? Wouldn't these things lower r and cause more investment relative to consumption in the first period? Are these part of income effects or substitution effects?

[Lord]

I am not so sure he is saying 3 can't happen, but he does note nontradables are 75%, and the adjustment period is long. And if most of the kapital is human, it won't be readily imported. I think it does depend, but the assumption 2 won't dominate in the short term seems highly unlikely.

[Lord]

I am not so sure he is saying 3 can't happen as that it takes time to happen. He does note 75% is in nontradables and the adjustment period is long. One can view 2 as the signal for 3 to happen in the first place. I agree it depends, it is just highly unlikely for 2 not to dominate in the short term under current circumstances of proposed trillion dollar deficits.

[Miguel Navascues]

In today world, it is perfectly possible kapital transactions, included transactions financed with leasing, which means a temporary import (export) of kapital.

[Roger Sparks]

It seems to me that your #1 assumes that the economy is fully deployed, with no spare capacity whatsoever. I think we come to your reasoning when we overlook the potential redeployment and more efficient use of time, labor, materials, and tools.

[Henry Rech]

"A country cannot import investment goods, it can only import consumer goods. "

It seems to me that Krugman is not saying this at all. He is saying the transfer process (the "conversion" of the capital inflow into a flow - net import - of goods) might be ineffective and slow. His blog post is about arguing why a corporate tax cut will not necessarily improve the share of income going to labour in hurry - it might take decades. For the tax cut to have immediate impact on labour incomes, immediate capital goods imports, attracted by the rate of return increase occasioned by the tax increase, would be required. Capital goods imports would proceed until the local rate of return on capital would again equalize with the international rate. The increase in domestic capital stock would reduce the marginal productivity of capital which would then drive down the local rate of return on capital. Krugman's post is all about discussing why an immediate flow of capital goods may not occur.

That's the way I see it anyway.

[Henry Rech]

The other thing that should be said is that he argues that because markets for goods and services are not "perfectly integrated" the the required changes in the real exchange to effect the flow of goods will not be forthcoming in the short term. He doesn't explain "perfectly integrated" - I'm not sure what he means by this - maybe there are still barriers to global trade which detain or limit the adjustment process.

[Nick Rowe]

Henry and Lord: fair points. We notice that Purchasing Power Parity does not hold (and therefore real interest rate parity will not hold, if real exchange rates are expected to change). Now why might this be (why aren't markets for goods & services "perfectly integrated")? In this post I have assumed it's because the home and foreign countries produce different goods. But there might be other explanations. A traded/non-traded goods model might be an alternative. Or some sort of transport costs. But I don't think the iceberg model of transport costs will give Paul's results (if transport costs are 5%, then real interest rates are bordered by a 5% differential). One alternative model is where there's some fixed cost to setting up a new export market. I call this the "Sailing Ships" model (ships are costly to build, but sail for free once built). Or maybe there are adjustment costs in changing the mix of goods you produce (so all goods are perfect substitutes in production in the long run, but not in the short run).

[Henry Rech]

It doesn't look as if Krugman has anything specific in mind but your suggestions seem to be the sort of things that might fit the bill. He says in his blog post:

"And because markets for goods and services are still imperfectly integrated - most of GDP isn't tradable at all - it takes large signals......."

So he is saying that "imperfectly integrated" equates with small tradable goods sectors in the world economy. There has been an inertia in developing tradable goods sectors despite the globalization of the last 30 years. This results in a slower adjustment process (which is what his blog post is all about) i.e. the real exchange rate needs larger movements for it to effect adjustment - there is no "immaculate transfer" process.

If you scan some of Krugman's papers on international adjustment, he is never specific about why markets are imperfectly integrated.

Looking at the world as it is, there are bilateral and multilateral trade agreements everywhere. Why are these necessary in a globalized world? Maybe the world trading system isn't as globalized as is made out? Perhaps international factor mobility has a long way to go? (Personally, I think that is a good thing. Globalization has its costs.)

[Nick Rowe]

Henry: I tend to agree. But think the degree of immaculatelessness(?) depends on what goods will be transferred. Transfers of machine tools, because of changes in investment, might be fairly smooth. Transfers of haircuts, because of changes in consumption, will be the opposite. (But there might be other examples where investment goods are non-traded, and consumption goods traded.)

[john]

I appreciate you are trying to theoretically model, but in a real economy if kapital ROI rises you're starting from a situation of underutilization, in which case there is no kapital/consumption goods tradeoff. In addition, if there is no underutilization, then the expected ROI you measure is in fact likely declining, just mis-expected, which later becomes clear in writeoffs.

[Nick Rowe]

john: yes, but it is easier to work through these questions if we assume the central bank is controlling aggregate demand, and will offset any such effects.

[Majromax]

Isn't scenario #3 just a combination of #1 and #2? Since we don't care about the eventual ownership of the factories, importing more factories and maintaining the same domestic consumption seems to me much like producing more factories in lieu of apples but importing more banapples instead.

Krugman's core point in the article was about how long it would take for the kapital to actually be built and hence improve the labour share of income. It's obvious that it takes time if the kapital must be built domestically, so his argument isn't contingent on "we can't import machines" as much as "we won't import machines orders-of-magnitude faster than we would have built them domestically."

[Bob Murphy]

Nick, great stuff! I'm working on a journal article on this stuff. If I find anything "important," you will be (one of) the first to know about it...

But regarding your post here, for what it's worth, I didn't take Krugman to think that each country produced a different consumption good. You're right, maybe he HAS to be thinking that, deep down, in order to make sense of everything else he wrote, but I don't think he had that in mind. Especially because a big part of his argument is that the tradeable goods sector is small relative to the whole economy, I think he was picturing many consumption goods, only some of which had tolerable shipping costs. (And none of the capital goods could be shipped.)

[Nick Rowe]

Bob: Thanks!

On rethinking: yes, I don't think my model is what Paul Krugman has in mind. But I'm not sure what he really has in mind, deep down. And at least my model does give interest rate differentials, in response to some shocks. (As you know, it's the same as the Sraffa interest rate differential.)