Sometimes I like to make assumptions I know are totally false. Not (or not always) for simplicity, but just to see what happens. It helps me understand the world better. For example, sometimes I like to assume a barter economy; it helps me understand monetary exchange better to see what would happen if we didn't have monetary exchange.
In this case, what I want to understand better is cross-country interest rate differentials. And the effects of international trade, and the effects of a common currency, on those interest rate differentials.
The results are a bit weird, and I'm not quite sure what lessons to draw.
(Think for example of a standard Mundell-Fleming IS-LM-BP-AD-AS model, except that the IS curve is the same IS curve for a closed economy, because NX is always zero. What happens to the BP curve?)
Now lets look at this world under three different assumptions about the monetary system.
1. Barter. Within country A there is trade of one variety of apple for another variety, and there is also intertemporal trade (finance) where people buy and sell apples for promises to pay apples in future. There is both trade and finance within a country.
Suppose the rate of interest on apples in A were above the rate of interest on bananas in B. Because, for examples, the A's are less patient than the B's, so save less. Or because the A's have better investment opportunities than the B's. Would anyone be able to make a profit on the spread? (Would there be any international finance?)
Suppose I expected the exchange rate between apples and bananas to stay constant. I would then borrow bananas, exchange those bananas for apples, lend the apples, then next year exchange my apples for bananas, repay the loan, and pocket the difference. But who would take the other side of the trades in exchanging apples and bananas? Since there is no "natural" market in which apples are exchanged for bananas, the only person who would take the other side of my trades would be someone who expected the exchange rate of apples for bananas to fall. One of us will be wrong. One of us will gain, and the other will lose. Any "international finance" would be gambling on an intrinsically irrelevant event, like the roll of a die.
The market in which apples exchange for bananas would not exist if everyone had the same expectations. Even if people were risk-lovers, and liked to gamble, they would be as likely to create a market in the roll of a die instead. With barter exchange there would be no international finance in a world of no international trade. Except, maybe, sheer gambling.
Each country's interest rate would be independent of any other country's interest rate. There is no tendency for international finance to equalise interest rates across countries. Bonds can't flow from A to B unless some other good flows the other way from B to A in exchange for those bonds. And there is no other good in this case, because the people in country A don't like eating bananas.
2. Monetary exchange with national currencies and freely floating exchange rates. People in country A trade apples for A-bucks, and trade promises to pay future A-bucks for current A-bucks. Suppose the rate of interest on A-bucks in country A were higher than the rate of interest on B-bucks in country B. Would anyone be able to make a profit on the spread? (Would there be any international finance?)
If you expected the exchange rate between A-bucks and B-bucks to remain constant, you would want to borrow B-bucks, take them to the forex market to buy A-bucks, lend the A-bucks, then next year take your A-bucks to the forex market to buy B-bucks, repay your loan, then pocket the difference as pure profit. But who would take the other side of the trades in the forex market?
Again, there is no "natural" market in which A-bucks are exchanged for B-bucks, so the only person who would take the other side of my trades would be someone who expected the exchange rate of A-bucks for B-bucks to fall. One of us will be wrong. One of us will gain, and the other will lose. Any "international finance" would be gambling on an intrinsically irrelevant event, like the roll of a die.
Again, just like in barter, there is no tendency for international finance to equalise interest rates across countries. Bonds can't flow from A to B unless some other good flows the other way from B to A in exchange for those bonds. And there is no other good in this case, because the people in country A don't like eating bananas, and don't use B-bucks.
3. Monetary exchange with a common currency.
Under barter, and under national currencies, bonds could not flow across international boundaries because there were no other goods that could flow the other way in exchange. That all changes when we have a common currency. Everyone uses the same money. So bonds can flow one way and money can flow the other way.
Suppose the (nominal) rate of interest in A were higher than the rate of interest in B. Any individual could then make a profit by borrowing in B and lending in A. Nominal interest rates must be equalised across the two countries. Bonds are flowing from the impatient A's to the more patient B's, and money is flowing the other way, from B to A. But the A's don't borrow the money because they want to hold more money; they borrow the money because they want to spend it on apples and eat the apples. So the price of apples rises. And the price of bananas falls, because there is less money in B.
At this point, David Hume would start talking about the price-specie flow mechanism. He would say that the rise of prices in A, and the fall of prices in B, would mean that A imports more of B's cheaper goods, so that money flows back from A to B to pay for those imports, so we eventually reach an equilibrium. But we have ruled out David Hume's price-specie flow mechanism by assumption. The people in A don't like bananas, so they won't import B's bananas however cheap bananas get relative to apples. So there is nothing to stop the flow of money from B to A continuing forever.
It gets worse. As more of the world's stock of money flows to A, and the price of apples rises, people in A come to expect rising prices. That lowers the real interest rate in A, so the A's want to save less, invest more, and borrow even more. And the real interest rate in B rises with falling prices for bananas, so the B's want to save more, invest less, and lend even more. So even more bonds flow from A to B and even more money flows from B to A.
Lessons. I'm really not sure what lessons to draw from this counterfactual thought experiment.
The easy lesson to draw is that having a common currency is a dangerous thing for monetary stability unless there is high substitutibility between foreign and domestically-produced goods. But that lesson applies equally to provinces within a country like Canada as it does to countries within the Euro.
But there is a harder lesson about money hiding in here somewhere that I still can't quite get my head around. There is a fundamental difference between finance in a monetary exchange economy and finance in a barter economy. The basic purpose of finance is to transfer control of goods across time between people. When I borrow from you then I should eat more fruit now and you should eat more fruit later, and if there's no trade there should be no finance. But in a monetary exchange economy it doesn't seem to have to work like that. (I'm probably going to regret having written that, because it's like issuing an open invitation to all sorts of monetary cranks to parade their own pet confusions, but what the hell.)
I think you want to add commodities futures. What happens to the future price of apples? You've described impatient apple consumers which suggests that in the future production will be unaffected but more people want to exchange for cash to pay off loans and fewer will want to consume, so forward apples depreciate. This constrains A's ability to repay loans and credit to A dries up.
Meanwhile, the price of bananas will contango. If bananas can be stored this will compete for funds with apple consumption loans. Even if they can't, citizens of B will substitute into present consumption.
Posted by: fmb | March 22, 2012 at 11:45 AM
"Sometimes I like to make assumptions I know are totally false. "
Show me a mathematical economic model that isn't stuffed to the gills assumptions which are totally false?
All of the "givens" in the construct are totally false from the perceptive of embedded human's making unique evolving judgments in unique contexts; a mathematical formula for "uncertainty" is a total falsification of genuine uncertainty; the equilibrium conditions of the models are totally false, etc.
So your technique, Nick, is not only common in economics, it is nearly universal.
Posted by: Greg Ransom | March 22, 2012 at 12:00 PM
"Sometimes I like to make assumptions I know are totally false. Not (or not always) for simplicity, but just to see what happens. It helps me understand the world better."
Economists have built equilibrium constructs and all else to "see what happens." What every tenured professor of economics has failed to do is show or even suggest how these fictional constructs allow us to "understand the world better", e.g. how a tautological construct built out of mathematical "givens" could possibly provide us with any sort of causal understanding addressing a problem raising empirical pattern in our experience.
Posted by: Greg Ransom | March 22, 2012 at 12:13 PM
@Nick: what about international migrations? Low price bananas growers going to high price apple regions. Which is happening to Greece and Ireland...
Posted by: Jacques René Giguère | March 22, 2012 at 12:13 PM
I am wondering how this would change if there were explicit real investment opportunities (rather than just people with different levels of patience or temporally different income streams) - perhaps a wheat economy and a corn economy where you could sow the wheat or the corn for a crop the next year?
Posted by: primedprimate | March 22, 2012 at 12:21 PM
Why aren't they using bonds as money in B?
why aren't they buying bananas in B or why aren't they investing B in what is needed to create more banana tree?
Your model seems to assume that the people in B have a preference for hoarding claims to money over the consumption of goods.
"More patient" in traditional economics means an exchange of a bit fewer goods now for many more goods later -- it doesn't mean a preference for claims to money over increased in consumption down the road.
Or have I misread the hypothetical?
And at some point the flow of money changes direction, correct? Back from A to B, as the bonds pay off.
Posted by: Greg Ransom | March 22, 2012 at 12:27 PM
Make that:
why aren't they exchanging bonds in B for what is needed to create more banana trees?
Posted by: Greg Ransom | March 22, 2012 at 12:28 PM
Nick, you did well, you made it clear that you were saying "If A then B", so you haven't been deluged with comments that say "not A."
Instead, you've got comments that say "Not 'If A then B'".
Posted by: Frances Woolley | March 22, 2012 at 12:28 PM
fmb: in my barter version I do have commodity futures. The apple bonds are promises to repay apples. I don't see how having both apple bonds and money bonds makes any difference in the two monetary versions of the "model", unless we introduce uncertainty. You can just buy a money bond, and then trade the money for apples at the expected future price.
In my third version, with a common currency, the A's have a larger and larger stock of debt, but also a larger and larger stock of money. They repay their debt with money, not apples.
Maybe I'm not following you here.
I think of costless storage as just a perfectly elastic investment demand curve at a 0% real interest rate.
Greg: we all make false assumptions for simplicity. Here I'm not doing it for simplicity. I want to explore a counterfactual.
Jacques Rene: you are quite right. If labour is mobile, there can be flows of labour to exchange for the flows of bonds. It's a way to bring international trade back in. That's why I had to assume zero factor mobility, as well as no flows of goods.
Posted by: Nick Rowe | March 22, 2012 at 12:31 PM
Sounds like a ponzi scheme. A is insolvent in your description. Rates will adjust up accordingly (witness Greece). So you should add a risk premium to your model; then I think it will stabilize.
Posted by: Jon | March 22, 2012 at 12:37 PM
primed, and Greg. Just suppose the natural rates of interest are different between A and B, either because of different intertemporal preferences, or because of different intertemporal production (investment) opportunities.
In terms of the Mundell-Fleming: the IS curves in A and B intersect the LRAS curves at different levels of r. But those IS curves can't shift when the real exchange rate changes, because exports and imports are identically zero. But the BP curve is horizontal, because there's perfect capital mobility.
Posted by: Nick Rowe | March 22, 2012 at 12:41 PM
"But there is a harder lesson about money hiding in here somewhere that I still can't quite get my head around. There is a fundamental difference between finance in a monetary exchange economy and finance in a barter economy. The basic purpose of finance is to transfer control of goods across time between people. When I borrow from you then I should eat more fruit now and you should eat more fruit later, and if there's no trade there should be no finance. But in a monetary exchange economy it doesn't seem to have to work like that. (I'm probably going to regret having written that, because it's like issuing an open invitation to all sorts of monetary cranks to parade their own pet confusions, but what the hell.)"
Nick,
At the risk of sounding as a crank: I am reminded of the dichotomy Marx made between what he called C-M-C and M-C-M. Where the former is Commodities (C) exchanged for Commodities (C) with Money (M) and where the latter is Money exchanged for Money with Commodities (Bonds in this case) in between.
I believe Post-Keynesians as in Circuitists following Sraffa and Marx, are the ones you want to consult on this.
I am also reminded of the tread-mill effect in finance (bubbles), where shares are bought not to transfer control or to obtain right to the cash flow, but to instead be able to sell it on.
Posted by: Martin | March 22, 2012 at 01:01 PM
Sorry, to be clear I was responding to #3, and in particular your conclusion (which I tentatively dispute) that money would just continue flowing from B to A.
In fact, I don't think money would flow at all.
What I think I'm getting at is that individuals in the 2 countries may face the same nominal interest rate but they face different real interest rates (in the fruit that they respectively care about), and it's the latter that drive their savings behavior. However patient Barry is, there's a future price of bananas high enough to induce him to consume more today instead of lending. Future apple & banana prices adjust to set local real interest rates at a level where there's still no intl finance.
Posted by: fmb | March 22, 2012 at 01:10 PM
Jon: "A is insolvent in your description. Rates will adjust up accordingly (witness Greece). So you should add a risk premium to your model; then I think it will stabilize."
Maybe. Here's the paradox (I think). Each individual in A can be solvent, because each individual in A can always consume fewer apples and produce more apples to get the money to repay B. But the A's in aggregate cannot do this. If the stock of debt that A owes B grows at i% interest, but the stock of money A bought from B grows at 0% interest, then the A's, collectively, cannot repay the B's, collectively. So we can't decentralise borrowing and lending???
Martin: "At the risk of sounding as a crank: I am reminded of the dichotomy Marx made between what he called C-M-C and M-C-M."
That's sort of what it remined me of, too. ;-)
fmb: "What I think I'm getting at is that individuals in the 2 countries may face the same nominal interest rate but they face different real interest rates (in the fruit that they respectively care about), and it's the latter that drive their savings behavior."
I agree, but I think the effect goes the wrong way to bring the countries back to autarky. You see, the relative price of apples and bananas (the real exchange rate) is indeterminate. Sure, for any given expected future real exchange rate, there's a current level of the real exchange rate that satisfies the nominal interest rate parity condition while keeping the two countries' real interest rates equal to their (different) natural rates. But I don't see any way to pin down that expected future real interest rate. If there's any sort of adaptive expectations, so that expected inflation responds to past actual inflation, the effect takes us even further away from equilibrium. A has an actual interest rate below its natural rate, which causes inflation to increase, which causes expected inflation to increase, which causes the actual real rate to fall even further below the natural rate.
Posted by: Nick Rowe | March 22, 2012 at 01:28 PM
"At this point, David Hume would start talking about the price-specie flow mechanism. He would say that the rise of prices in A, and the fall of prices in B, would mean that A imports more of B's cheaper goods, so that money flows back from A to B to pay for those imports, so we eventually reach an equilibrium."
By borrowing from B, A's are seeking to eat more apples now and fewer apples in future. Assuming perfect price flexibility, any such aim must ultimately be frustrated, and prices will instead adjust to preserve monetary equilibrium and market clearing at all times.
Assuming monetary disequilibrium, I think there is a specie flow mechanism hiding in there. With prices and incomes being expected to fall in B, we should expect demand for money to rise temporarily, so B will sell bonds back to A in exchange for money. The opposite process will occur in A: the hot-potato effect will lead to increased demand for all goods, included bonds, so long as the disequilibrium persists.
Posted by: anon | March 22, 2012 at 01:32 PM
Nick, model 3 is quite useful for understanding Eurozone, and may also apply to isolated islands that are a part of a currency union.
A and B may join a monetary union, if both fit Maastricht criteria, and especially if banking regulators in B say that bonds in A have zero risk weight.
Ultimately it is unsustainable, and one of the following happens:
- currency union collapses, bondholders in B take losses.
- currency union becomes a fiscal union between A and B, whereby taxpayers in B permanently subsidize bondholders in B
- there is a hyperdeflationary crisis in A, after which apples are so cheap that the assumption of no trade no longer holds.
Your model perfectly illustrates the absurdity of the fiscal union solution for the Eurozone.
Posted by: 123 (TMDB) | March 22, 2012 at 01:40 PM
anon: "With prices and incomes being expected to fall in B, we should expect demand for money to rise temporarily, so B will sell bonds back to A in exchange for money."
Hmmm. Dunno. Let's assume a standard money demand function, and monetary equilibrium. Ms=Md=P.L(Y,i). As P falls in B, and rise in A, the stock demand for money should fall in B and rise in A. Which encourages B to lend more and A to borrow more money.
Posted by: Nick Rowe | March 22, 2012 at 01:48 PM
123: that's sort of what I was thinking it might do. Good to hear you thinking along the same lines. But what about provinces like Newfoundland? Saved by labour flows?
My model violates the Marshall/Lerner condition massively, of course. I can't remember the latest thinking on the relevance of the M/L condition.
Posted by: Nick Rowe | March 22, 2012 at 02:04 PM
Nick, if you assume that monetary equilibrium holds at all times (perfect price flexiblity), then I suppose that the price level _might_ fall indefinitely in B - however, this has no macro consequences. I am assuming disequilibrium occurring due to price stickiness.
Posted by: anon | March 22, 2012 at 02:06 PM
anon: OK. Let's run with that. Keep the assumption that Ms=Md=P.L(Y,i), but now assume that Y adjusts, as well as P. As both Y and P fall in B, and rise in A, Md will fall in B and rise in A. I think we get the same results. That makes B want to lend even more, and A to borrow even more.
Posted by: Nick Rowe | March 22, 2012 at 02:20 PM
Nick: I doubt that such mechanism could work indefinitely. First, if we assume that there exists finite ammount of money in A and B respectively, and that the long-term level of inflation is based on the amount of money in circulation, then there is a ceiling to how much price level can rise in A. If we assume that A and B start with same ammount of money and that they have similar patterns of money velocity, then the overall price level can only double in A. So there is no reason why people in A should expect higher inflation (forever). So this refutes the second part.
Posted by: J.V. Dubois | March 22, 2012 at 02:49 PM
Obviously, i think the price spiral stops sometime.... If nothing else, at some time the entire stock f money has to pass hands for each trade. At that point only one trade occurs per unit time, except to the extent that trades can be regulated by promises. I think people would start trading in promises instead of money in this case.
I think that this is the solution. Money and debts are really about information more than transferring consumption a cross time. As the price rises without bound a greater share of trades are recorded in ledgers to keep track of who owes what to whom as money is becoming less available for the purpose. Eventually the cost of maintaining the ledgers destroys the gain from the spread and the process terminates.
So your confusion, if I'm right, comes from assuming cost less ledgers. I don't know if that's right, but awesome example.
Posted by: BSEconomist | March 22, 2012 at 03:20 PM
J.V. Dubois, right, inflation in A cannot go on indefinitely, so this refutes the simplified case from Nick's post. However, money flows between regions could be a cause of instability nonetheless, in the absence of high trade integration.
Nick, OK. It's an interesting puzzle though: I'm not clear either what exactly is happening here, in terms of overall principles.
Posted by: anon | March 22, 2012 at 03:21 PM
"But what about provinces like Newfoundland? Saved by labour flows?"
Don't know much about Newfoundland (actually I've never been in Canada or US), but I guess labor mobility would equalize the price of human capital to some extent. It might also be useful to allow one-way flow of goods financed via fiscal transfers in your model if you analyze Newfounland.
The lesson of your model for Quebec separatists is that they should engineer a local real estate mega-bubble and a corresponding double digit provincial current account deficit, so the rest of Canada would want to kick Quebec out after the bubble collapses.
"My model violates the Marshall/Lerner condition massively"
I'm still thinking about your second model, and have no firm opinion yet.
Posted by: 123 (TMDB) | March 22, 2012 at 03:26 PM
JV: Hmmm. I think that's right. In the limit, all the world's money ends up in A, and B owns A's bonds, but no money. So it's not that A's prices go to infinity, but B's prices do go to zero, along with its stock of money.
Posted by: Nick Rowe | March 22, 2012 at 03:43 PM
"Maybe. Here's the paradox (I think). Each individual in A can be solvent, because each individual in A can always consume fewer apples and produce more apples to get the money to repay B. But the A's in aggregate cannot do this. If the stock of debt that A owes B grows at i% interest, but the stock of money A bought from B grows at 0% interest, then the A's, collectively, cannot repay the B's, collectively. So we can't decentralise borrowing and lending???"
Isn't this the A + B fallacy though? (pun intended, of course.) The stock of money can repay any amount of debt, depending on its velocity of circulation. So perhaps this paradox occurs because there is no trade in goods, so money can only be redeemed through the bonds channel.
Posted by: anon | March 22, 2012 at 03:45 PM
So A's inflation rate must ultimately converge to zero (assuming zero growth in the world money stock and zero real growth), but B's deflation rate does not need to converge to zero. B's stock of money can keep on halving (say) every 10 years forever. Eventually, looked at in purely nominal terms, A is the country with the whole world's nominal GDP, and B's NGDP shrinks towards zero, even though nothing real has changed.
Posted by: Nick Rowe | March 22, 2012 at 03:48 PM
anon: "Isn't this the A + B fallacy though? (pun intended, of course.)"
Normally, if the money circulates quickly enough, $1 of money can payoff $1 trillion in debt, because the money comes straight back to the debtors in exchange for goods, then gets reused to pay a second $1 of debt, and so on. But yes, in this case, it's different, because the creditors in B never buy goods from the debtors in A.
BSE: "Eventually the cost of maintaining the ledgers destroys the gain from the spread and the process terminates."
I'm not sure. I think it terminates when everyone in B wakes up to the fact that everyone in A cannot repay the debt to everyone in B, even though each individual in A can repay his debt to each individual in B. A credit crunch?
Posted by: Nick Rowe | March 22, 2012 at 04:02 PM
Another way of looking at this model:
1. In the Mundell Fleming model with flexible exchange rates, Ms held constant, the elasticity of the AD curve in {P,Y} space equals the reciprocal of the income elasticity of the demand for money. So the AD curve is roughly a rectangular hyperbola.
2. In the M-F model with fixed exchange rates, and endogenous Ms, (or common currency) the elasticity of the AD curve equals (IIRC) the elasticity of demand for domestic output wrt the real exchange rate. That's zero in my model, so the AD curve is vertical, so it can't intersect the LRAS curve, except if by sheer fluke both countries have the same natural rate and the vertical AD curve lies on top of the vertical LRAS curve.
Posted by: Nick Rowe | March 22, 2012 at 04:13 PM
informational problems do have a tendancy toward regime change, so yes I think in the real world what happens is that there is a crisis at some point. Porbably at the point at whcih the ledgers require too many real resources to maintain. Presumably someone would be specializing in ledger maintainance and they would have to eat themselves.
As time goes on and ledger maintainance becomes more valuable, a greater share of national NGDP goes toward the pure informational problem of maintaining the ledgers. In the limit, you might expect all the debt to flow through these specialists, but it would be clear long before that time that they are essentially running a ponzi scheme. When this becomes common knowledge, money stops flowing between the countries and there would be a credit crisis as the hopelessly intertangled ledgers would be hard to unwind. At this point, the market couldn't clear until the price comes back down.
Or a simpler solution would simply be for people to make up their own money and circulate that. Still, it would be possible to game the ledgers so that at least some people would benefit. When the ledger system collapses the debtors are left holding the real goods. Maybe. I'm getting off topic anyway so I'll leave it at that.
Posted by: BSEconomist | March 22, 2012 at 04:31 PM
"I think it terminates when everyone in B wakes up to the fact that everyone in A cannot repay the debt to everyone in B, even though each individual in A can repay his debt to each individual in B. A credit crunch?"
Yes. Credit crunch and the crash of a bubble.
Posted by: 123 (TMDB) | March 22, 2012 at 05:13 PM
Me (as snipped by Nick): "What I think I'm getting at is that individuals in the 2 countries may face the same nominal interest rate but they face different real interest rates (in the fruit that they respectively care about), and it's the latter that drive their savings behavior."
Nick: I agree, but I think the effect goes the wrong way to bring the countries back to autarky. You see, the relative price of apples and bananas (the real exchange rate) is indeterminate. Sure, for any given expected future real exchange rate, there's a current level of the real exchange rate that satisfies the nominal interest rate parity condition while keeping the two countries' real interest rates equal to their (different) natural rates. But I don't see any way to pin down that expected future real interest rate.
And now back to me:
I agree the real exchange rate is indeterminate. And the sentence I bolded is an accurate restatement of my point (though I’d switch “future” and “current” between the first 2 clause). I lose you on the next sentence, though. To me, there’s an exchange rate today (known), time preferences of each population (known), and a nominal interest rate and this leads to inflation expectations that are *higher* in B than in A such that the bond market can clear without need for int’l finance.
That said, I think I’ve found an issue in my reasoning: I haven’t kept real money supply in each country in equilibrium. Even if we find ourselves in the equilibrium I described, real money balances will decrease in B relative to A, which is similar to the outcome you described.
I still feel like there’s a way to fix that. Initially B lends almost everything to A, apples instantly almost double, bananas fall to near zero, and then A pays back a weird annuity. Say B is 2% more patient than A, then initially B experiences 2% inflation a year to keep their real interest rate correct. That only requires a small interest payment since B starts with very little money. If there’s any short-term lending going on, it happens at a nominal rate nearly equal to A’s (higher) real rate.
Eventually B accumulates most of the money, and in the limit A’s money supply is very low and bleeding close to 2% per year. Banana prices are stable, the nominal rate is close to B’s lower real rate, and apples are perpetually depreciating at close to 2% a year.
A & B in aggregate reach this arrangement to avoid bubbles, crashes, and monetary disequilibrium. Obviously a plethora of possible frictions could prevent that from happening, but I don’t see why sufficiently rational agents (except for the bizarre choice to have a single currency) couldn’t find and reach this equilibrium.
Posted by: fmb | March 22, 2012 at 07:05 PM
It gets worse.
Or does it? If the amount of B's currency drops by 2% per year, and all exchange mechanisms are closed, it will be an extremely long time until B is devalued all the way to zero.
More likely, we would see the wealth "A" types seeing that they could retire in B-land with huge wealth, if they could just import a few years' supply of apples. Now B is exchanging housing, health-care and other non-exportable services in which they have a HUGE relative price advantage, for apples.
Posted by: Walt French | March 22, 2012 at 11:03 PM
I can't grasp even the first model. As I understand it, in country A the only things traded are apples and IOUs for apples; and in country B the only things traded are bananas and IOUs for bananas. No one from country A has any intrinsic desire for bananas and no one from country B has any intrinsic desire for apples.
Well to me that seems to be the end of the matter. There would be no international market at all exchanging apples for bananas, full stop. The economies would be completely isolated one from the other. There would also be no speculating apple-jobbers from B, and no speculating banana-jobbers from A. The only thing a speculator from A could acquire in country B would be either bananas or IOUs for bananas. Both are utterly worthless to him, even as intermediary exchange goods. What does it matter to the clever trader from A to be able to trade up a less valuable basket of bananas and IOU's for bananas for a more valuable basket of bananas and IOUs for bananas. He can never escape from the circle of bananas, which are of no value to him.
There would be no "exchange rate of apples for bananas", natural or otherwise. You might as well be comparing the economies of Earth and Mars. The only reason some clever trader from Mars would have to come to Earth and mess around in our economy would be if there was at least one good here on Earth that that trader wanted to get his hands on, either because he intrinsically desires it, or because someone back on Mars intrinsically desires it and is willing to trade something the trader intrinsically desires for that good.
If there is no market at all exchanging apples for bananas, then there would be no expectations regarding the exchange rate of apples for bananas, and no possibility of engaging in speculative bets relating to those exchange rates and expectations on the exchange rates. It's not just that such bets would be arbitrary zero-sum rolls of the dice in which one loses and one gains. Rather there would never be any such bets and no possibility of even chance gain or loss.
Model Two seems to add nothing important to Model One. Allegedly there is some additional item in each economy you are calling "money". But given that there are no other differences, this A-money just seems to be another name for certain kinds of IOUs for apples, and the B-money just seems to be another name for certain kinds of IOUs for bananas. The money in A is a sort of demand-claim on apples where other IOUs are future claims of various durations.
Posted by: Dan Kervick | March 23, 2012 at 12:26 AM
We see something like that in Greece: The clearly collective debt became worthless--there is no guy behind the tree--but private debtors could still borrow.
I'm not following your concluding remark though. You seem to be suggesting that an individual bond issuer is solvent, and therefore the bond will be issued, and therefore the system is insane.
I agree that sounds like a paradox, but therefore I choose to discard the assumption that individual bond holders would be treated as solvent. My sense is that they mustn't be but the risk prima might move violently--i.e., the system is bistable.
Posted by: Jon | March 23, 2012 at 02:51 AM
Just additional comment, it seems that the example stands and falls on the assumption that interest rate is permanently higher in B compared to A. Since we already know that if this is the case, all the money would flow from A to B, meaning that the price level would steadily decrease in A (in B it would increase and then stop)
1) People in A would feel increase of their wealth. This means that at some point the wealth effect would have to kick in, like for example it would be less appealing to "save" one apple today to increase my already impressive savings from 1000 to 1002 apples in the future.
2) If people expect that interest rate in B will be higher, then I would imagine that there should be some real investment into banana plantations. So in short, there should be increase in real capital stock. I think such increase should cause lower real returns on capital and unless there is a technology change (or if technology change is the same in A and B) that should lower returns on capital and thus it should lower interest rates in B in the long run.
Posted by: J.V. Dubois | March 23, 2012 at 06:17 AM
fmb: "Initially B lends almost everything to A,..."
OK, I think I see where you are going. B swaps almost all its money for bonds from A, and the price of bananas jumps down to nearly zero and the price of apples jumps up to nearly double. Trouble is, if A pays only the interest on the debt, sooner or later A is collectively insolvent, because it will run out of money. Plus, if prices are sticky, they can't jump like that.
Walt: I'm still thinking that through.
Jon: "I'm not following your concluding remark though. You seem to be suggesting that an individual bond issuer is solvent, and therefore the bond will be issued, and therefore the system is insane."
Some sort of externality, maybe? The more I borrow/lend, the riskier it becomes for you to borrow/lend.
JV: OK. If they were borrowing real goods, that might work. But they are only borrowing money, and the more they borrow the higher the price level, so the real stock of money they hold stays the same.
Posted by: Nick Rowe | March 23, 2012 at 07:45 AM
I agree if prices are sticky my equilibrium isn't achievable.
However, there's an interest schedule (that I described) which doesn't lead to A's insolvency. Near the end when A has very little money, there's a long tail of very small payments of about 2% of A's money supply. These are tiny compared to the original principle, but enough to keep apples depreciating at 2% a year indefinitely (while bananas appreciate hardly at all).
Posted by: fmb | March 23, 2012 at 08:14 AM
Dan: sorry, your comment got stuck in spam.
For the purposes of this post, I am quite happy to accept your conclusions that in versions 1 and 2 there would be no markets in which apples trade for bananas (or A-bucks trade for B-bucks). Because nobody wants to trade in those markets. My talking about the possibility of speculators trading in those markets, and creating those markets, is a side-issue for this post. For example, if everyone were identical (and there were no economies of scale) as in a representative agent model, there would be no trade, and no markets. But we can still talk about the prices that people *would* be prepared to pay or accept in such markets, and the equilibrium price, at which no trade takes place, because quantity demanded = quantity supplied = 0 at that price, is still a useful concept.
One day I will write a post exploring this more. I already have the title: "Markets in nothing".
Posted by: Nick Rowe | March 23, 2012 at 08:41 AM
Dan: think about it this way.
Normally, we add up all the sellers' supply curves to get a market supply curve, then add up all the buyers' demand curves to get a market demand curve, then find the equilibrium where the two curves cross.
Let's do it slightly differently. Define supply as just negative demand. Each individual has an "excess demand" curve. Excess demand is negative if he wants to sell at that price. Add up all the individuals' excess demand curves to get the market excess demand curve. Equilibrium price is where the market excess demand curve cuts the vertical axis. Now suppose all individuals are identical. No trade takes place at that equilibrium. In my model, the market excess demand curve happens to be vertical, and coincides with the vertical axis. Any price is an equilibrium.
Posted by: Nick Rowe | March 23, 2012 at 08:50 AM
I think I can reframe my point in a more useful way.
Start with Nick's #2, where each country has its own currency.
1. Imagine (unbeknownst to each country) that there's a single central bank coordinating both money supplies. Surely this central banker could have their 2 nominal rates be the same simply by adjusting the money supply (assuming constant Y & V) so that they have different inflation rates.
2. In particular, imagine that the natural real rates are 3% for A and 1% for B. Then any single nominal rate between 1 & 3 could be achieved if deflation in A + inflation in B = 2%. (other rates are also achievable)
3. Now add a constraint on this central bank. Unbeknownst to A & B, the CB has to use the same token for both countries: it can only increase Ma by decreasing Mb or vice versa, and has to increase/decrease them the same amount (M = Ma+Mb is constant). It is still possible to satisfy #2: always drain money from A and increase M in B such that delta-M/Ma + delta-M/Mb = 2%. If Ma & Mb are similar, Ma shrinks by 1%, Mb grows by 1%, and the nominal rate in both is 2%. If Ma>>Mb, only 2% of Mb (a tiny amount of Ma and M) needs to flow in order for B to have 2% inflation while A has very tiny deflation. Nominal rates will be near 3%. Similarly, if Mb>>Ma, 2% of Ma, which is a tiny amount of Mb, will lead to 2% deflation in A with very slight inflation in B and a nominal rate near 1%.
If the CB is transparent about money supply and the citizens are smart about MV=PY, then both countries can experience their appropriate real rate, with fluctuating inflation/deflation and the same nominal rate. I think this satisfies all equilibrium conditions:
a) same nominal rate
b) each country faces its appropriate real rate
c) MV=PY
d) Ma + Mb is constant.
e) Ma and Mb each > 0 at all times
I'm handwaving about the step where the countries do know about eachother and there's no CB, but any initial loan from B to A with a goofy repayment schedule matching the above would still work. There's an additional constraint that the loan principal must match the NPV of the repayment schedule, but that's probably achievable.
Finally, I think this all breaks if apples can be stored for lower cost than the necessary deflation in A when Mb>>Ma.
Posted by: fmb | March 23, 2012 at 09:05 AM
Wouldn't there be a limit to the flow of money from A to B , as there would also be flows from B to A in the form of interest payment? Eventually an equilibrium would be reached where the sun of new loans moving in 1 direction would be matched by the sum of interest payment moving in the other.
If one introduces business loans then I think the story is different. Assume all the capitalists are in A. They will invest wherever monetary profit rates are highest which will mean they will invest in both A and B. However all the profits flow to A who only eat apples , which will tend to increase the profits on Apples and lead to to A having a more capital intensive structure than B and correspondingly higher long-term consumption.
Posted by: Rob | March 23, 2012 at 10:24 AM
Nick, I get that. I was making two points.
1. About the explanatory failure / explanatory strategy failure dominant in mainstream economics.
2. You method is universal in economics.
My third point would be that we learn _most_ in economics by figuring out the significance of what has been left out.
What is _always_ left out is open-ended learning and adaptive changes in individual situated understandings of the significance of local conditions and relative prices.
This is the _core_ causal explanatory element missing from "Top 5" mainsteam department microeconomics and macroeconomics.
And it matters.
Nick writes,
"Greg: we all make false assumptions for simplicity. Here I'm not doing it for simplicity. I want to explore a counterfactual."
Posted by: Greg Ransom | March 23, 2012 at 01:23 PM
Nick,
I know of one paper that studies "nominal" interest rate differentials in a monetary exchange model with national currencies, freely floating exchange rates, and no trade in goods:
Fernando Alvarez & Andrew Atkeson & Patrick J. Kehoe, 2009. "Time-Varying Risk, Interest Rates, and Exchange Rates in General Equilibrium," Review of Economic Studies, Wiley Blackwell, vol. 76(3), pages 851-878, 07.
The cool idea is that you may wish to hold internationally traded assets because money is traded and international bonds may provide a hedge against domestic risk (even if goods are not traded).
Posted by: Martin Boileau | March 23, 2012 at 01:41 PM
"My model violates the Marshall/Lerner condition massively"
Your model is a financial model that shows the limitations of Marshall/Lerner. Elasticity of current account with respect to changes in the financial distress in country A is more important than the elasticity to forex rate. Changes in the A bond prices is an important equilibrating mechanism. For example, before the crisis Lithuania, Latvia and Estonia had double digit current account deficits that disappeared rapidly when bond prices dropped. And when foreign trade equilibrium was regained, bonds rallied. This all has happened without any devaluation against euro.
I still think it would be useful to allow one way trade in order to make the model more realistic.
Posted by: 123 (TMDB) | March 23, 2012 at 05:03 PM
So why is it they aren't using bonds as money to invest in more apple production in B?
Posted by: Greg Ransom | March 24, 2012 at 05:19 PM
I'm trying to think of a natural experiment that would allow you to test this idea empirically. Off-hand, what about the 17th century. Larry Neal's book, The Rise of Financial Capitalism is able to show that there was financial market integration between the Dutch and English. At the same time, mercantilism restricted trade between countries (though, of course, it still happened).
Posted by: hosertohoosier | March 25, 2012 at 05:30 PM
But my pet confusions are so cute. It's like an upside down umbrella with adjustable supports outside of an n-gon mesh which captures utility. Or so goes my constructive interpretation of hicks(V/C chapter2). I want to add (non composable good)money in, or the von mises' preference relation switching for use of a good in trade but I am hitting a wall. Anyway that's it. I can't get to is/lm if can't get past part1.
Posted by: edeast | March 25, 2012 at 10:28 PM