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In a recent post I responded to this claim by Paul Krugman:

I’ve already argued that the fall in the euro is much bigger than you can explain with monetary policy; it seems to reflect the perception that Europe is going to be depressed for the long term. And if that’s what drives the weak euro/strong dollar, it will hurt US growth.

I said (without reading the linked to post):

I agree with the reasoning process in the last sentence. But I don’t think it applies to the current case, as it seems very unlikely that lower growth expectations are what is depressing the euro. Here’s what we do know:

1. Eurozone growth expectations have been in the toilet for years.

2. The euro was valued at about $1.35 for years, and then gradually fell to about $1.05 over the past few months.

3. During the past few months the growth forecasts of the eurozone have been revised upward, as the euro has been falling.

You don’t need to be an EMH fanatic like me to see a problem with Krugman’s argument. Kudos to him for not reasoning from a price change, for not lazily assuming that a weaker euro meant more growth. But I think’s he’s gone too far in the other direction, in assuming that the cause of the weaker euro was lower growth expectations.

Vaidas Urba suggested I do look at the linked post. And I was quite shocked to find it began as follows:

Watch that plunging euro! Actually, it’s good news for Europe. European growth numbers have been better lately, and the weak euro “” which makes EZ manufacturing and other tradables more competitive “” is surely a large part of the explanation. Not so good for Japan or the US. But how should we think about this?

Wait, that’s my argument—the weaker euro is associated with stronger eurozone growth. Therefore it’s monetary stimulus at work. But if you read the entire post you’ll see Krugman does actually have a good argument, albeit one that raises as many questions as it answers. And I might add that it’s one I’m pretty sure that 99% of his readers would not have understood.

Let’s first discuss Rudi Dornbusch’s (1975) overshooting model, which is sort of lurking in the background. Dornbusch thought about the impact of monetary stimulus in a world of interest parity, PPP and sticky prices. The result is quite odd. Suppose the ECB does a once and for all permanent 10% increase in the money supply. The quantity theory says this will raise prices by 10% on the long run. And PPP says that will depreciate the euro by 10% in the long run. So far, so classical. But sticky prices imply a liquidity effect, thus the monetary injections lower nominal interest rates for a few years. And because of the interest parity condition, lower interest rates imply a higher expected rate of appreciation in the euro. But didn’t I just say the euro would depreciate? Yes I did, and there is no contradiction. If you are not seeing the answer, you need to think outside the box. First do some brain exercises. Connect these 9 dots with 4 lines, without taking your felt tip pen off the paper:

For simplicity, suppose we started with US and eurozone interest rates being equal. After the monetary injection the eurozone rates are lower. So the euro is expected to appreciate. But in the long run it’s expected to be 10% lower. That means the immediate effect of a monetary stimulus shock must be a more that 10% decline in the euro. Dornbusch called this exchange rate overshooting. The model is composed of 4 theories (QTM, PPP, IPT, liquidity effect.) Most of us are not as adept at juggling 4 theoretical balls in the air at the same time as Krugman, so we struggle with the concept. As for empirical evidence, these things are hard to test. I’d argue that each component is pretty well established, and that’s good enough (and I suspect Krugman would agree.) In any case, it’s too beautiful a theory not to use once and a while. Here’s Krugman:

So, can we say anything about how the recent move in the euro fits into this story? One way, I’d suggest, is to ask how much of the move can be explained by changes in the real interest differential with the United States. US real 10-year rates are about the same as they were in the spring of 2014; German real rates at similar maturities (which I use as the comparable safe asset) have fallen from about 0 to minus 0.9. If people expected the euro/dollar rate to return to long-term normal a decade from now, this would imply a 9 percent decline right now. What we actually see is almost three times that move, suggesting that the main driver here is the perception of permanent, or at any rate very long term European weakness. And that’s a situation in which Europe’s weakness will be largely shared with the rest of the world “” Europe will have its fall cushioned by trade surpluses, but the rest of us will be dragged down by the counterpart deficits. Now, this is not how most analysts approach the problem. They make a forecast for the exchange rate, then run this through some set of trade elasticities to get the effects on trade and hence on GDP. Such estimates currently indicate that the dollar will be a moderate-sized drag on US recovery, but no more. What the economic logic says, however, is that if that’s really true, the dollar will just keep heading higher until the drag gets less moderate.

Krugman’s looking at real rates to abstract from inflation. While the Dornbusch overshooting model does a nice job of explaining the recent dramatic plunge in the euro, the model also predicts that the real exchange rate is unaffected in the long run. But that’s because interest rates are unaffected in the long run. Krugman’s readers don’t know this, but unless I’m mistaken he’s arguing that the recent fall in long-term interest rates in Europe is the income effect, not the liquidity effect. I actually like that argument, but it’s not the way Keynesians usually look at changes in long-term rates occurring in close proximity to QE. Most Keynesians would say the ECB is driving bond long term bond yields lower.

So Krugman’s arguing that the big fall in the expected 10-year future exchange rate reflects worsening prospects for long term European growth, not just monetary stimulus. That argument makes sense to me. But he’s also arguing that this increasing long-term pessimism occurred at almost exactly the same time that expectations of short-term growth became more optimistic. That might be true, but I kinda doubt it. And yet I can’t think of a better explanation for the fall in the future expected value of the euro.

So I’ll file this under “unresolved problems.”

PS. He ends up relying on liquidity trap arguments to draw policy conclusions for the US. But as I argue in today’s Econlog post (later this afternoon), those arguments are rapidly approaching their “sell by date.”

PPS. The eurozone demand side recession is likely to be over in 10 years. That means Krugman’s hypothesis implies severe structural problems in Europe—bad news for a continent with 7% of the world’s people, 25% of the world’s GDP, and 50% of the world’s social spending.

PPPS. Oh yeah, the puzzle. Because Ray claims his IQ is only 120, he probably provided answer #2. But answer #1 is correct. I’m sure Rudi would have been able to solve the puzzle. My dad did it first in a competition among friends back in 1962.

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