Interest rates, exchange rates, and the Bank of Canada

Last week the Bank of Canada cut the overnight rate of interest from 1.00% to 0.75%. The exchange rate dropped 2 cents (about 2.5%) on the news. [Update: I forgot to add (because I figured Canadians already knew it, but then remembered others probably wouldn't) that the Bank of Canada has "done nothing" (with interest rates) for the last 4 years, but the exchange rate has dropped about 20% over the last 2 years. And that's important background for my story.]

Consider a very simple economy with only two goods: apples and bananas. It's a non-monetary economy; apple producers and banana producers swap apples and bananas because people produce only one good but like to consume both goods. So there's a relative price of apples to bananas, Pa/Pb. People borrow and lend apples at a real interest rate Ra (I give you 1 apple today, you promise to give me 1+Ra apples next year); and borrow and lend bananas at a real interest rate Rb (I give you 1 banana today, you promise to give me 1+Rb bananas next year). If people expect (strictly, expect with certainty) that Pa/Pb will stay the same in future, then Ra and Rb will be exactly the same. Because if Ra < Rb, all borrowers would want to borrow in apples, and all lenders would want to lend in bananas, so it couldn't be an equilibrium.

Suppose a shock causes Pa/Pb to fall. How will that shock affect the difference between Ra and Rb? That depends.

If it's expected to be a permanent shock, so that Pa/Pb is expected to stay permanently lower, we will continue to see Ra=Rb.

But if it's expected to be a temporary shock, so that Pa/Pb is expected to rise in future back to its original level, we will see Ra<Rb. (If you lend in apples you get a lower interest rate, but that's offset by a rising price of apples.)

The longer the shock is expected to last, the smaller the effect on the difference between Ra and Rb. And if the shock is expected to get bigger over time, Ra will need to rise relative to Rb.

Now let's call the apple producers "Canadians", and the banana producers "foreigners". And suppose there are transport costs, so that Canadians eat mostly apples and foreigners eat mostly bananas, but there is some trade in apples and bananas. And suppose that Canadians use the Canadian dollar as money, and foreigners use the foreign dollar as money. And suppose the Bank of Canada targets the Canadian inflation rate, which is mostly (but not totally, because Canadians do eat some bananas) the apple inflation rate. And the foreign central bank targets the foreign inflation rate, which is mostly (but not totally, because foreigners do eat some apples) the banana inflation rate.

Let S be the nominal exchange rate between the Canadian dollar and the foreign dollar, so a fall in S means the Canadian dollar depreciates. The relative price between apples and bananas is now SPa/Pb, where Pa is the Canadian dollar price of apples, and Pb is the foreign dollar price of bananas.

Again, suppose there is a shock that requires the relative price of apples to bananas, SPa/Pb, to fall. The only way that can happen, if both central banks stick to their inflation targets, is if S falls. (In the limit, as transport costs became very high so that Canadians eat only apples and foreigners eat only bananas, S would do all the adjustment so Pa would not fall and Pb would not rise.)

How will that shock affect the difference between Ra and Rb? That depends.

If it's expected to be a permanent shock, so that SPa/Pb is expected to stay permanently lower, we will continue to see Ra=Rb.

But if it's expected to be a temporary shock, so that SPa/Pb is expected to rise in future back to its original level, we will see Ra<Rb.

The longer the shock is expected to last, the smaller the effect on the difference between Ra and Rb. And if the shock is expected to get bigger over time, Ra will need to rise relative to Rb.

Neo-Wicksellians think of the central bank as setting a rate of interest, and trying to keep the actual real interest rate equal to the natural real interest rate so that actual and expected inflation can remain on target. In a small open economy, it would make more sense to think of the central bank as setting an exchange rate, and trying to keep the actual real exchange rate equal to the natural real exchange rate so that actual and expected inflation can remain on target. Because if a small open economy is hit by a permanent shock, the domestic interest rate needs to stay equal to the foreign interest rate, and it is only the exchange rate that needs to adjust. The only case in which the exchange rate does not need to adjust is if the Canadian economy and world economy are hit symmetrically with an identical shock, and even in this case the Bank of Canada simply needs to ensure the Canadian interest rate follows the world interest rate, and it will do this automatically if the Bank of Canada holds the exchange rate fixed when a symmetric shock hits. And if a negative shock hits, but is expected to get even worse in future, the exchange rate needs to fall, but the Bank of Canada needs to raise the rate of interest (temporarily).

The exchange rate is the thing that Canadians should be watching, far more than the interest rate.

Apples are oil. Oil caused the exchange rate to drop. The Bank of Canada needed to allow that to happen, which it did. It only needed to cut the interest rate because the fall in price of oil is probably, at least partly, temporary.

Comments

[Market Fiscalist]

If the CB just said "we are going to adjust the size of the monetary base as needed to keep inflation on target" - would both interest rates and exchange rates take care of themselves through market forces ?

[Nick Rowe]

MF: I think so.

[Andy Harless]

What MF said. Actually, I think there's a real-life mystery here. Why did the exchange rate have to wait for explicit monetary policy action before falling 2.5%? The BoCs objective is well known. The price of oil is well known. Maybe people think the BoC has better information about the future trajectory of the price of oil? But I think that goes the wrong direction: cutting the interest rate implies the BoC thinks the oil shock is (partly) temporary, so the effect on the exchange rate should, if anything, be smaller than if it were permanent, and the observation of a rate cut by the BoC with better information should cause the exchange rate to reverse partly. Or was the rate cut actually smaller than expected? It almost seems as if people don't have confidence in the BoC's objective -- they're reacting the way they would to a central bank that didn't have a clear objective. But that doesn't seem plausible at this point. Maybe they thought the BoC would delay its interest rate action? But the delay would have to be implausibly long to justify taking a loss of 2.5% on the exchange rate. I don't get it.

[Derivs]

"Maybe people think the BoC has better information about the future trajectory of the price of oil?"

that would be a definite NO.

"Why did the exchange rate have to wait for explicit monetary policy action before falling 2.5%?"

Personally, I would rephrase that as "the market used the monetary action as a reason to fall another 2.5% "Appears that falling is the direction the market likes since mid- 2014, and likes even more since mid-Dec. Give it an excuse to continue, and it appears to be more than happy to oblige. Like it or not, the CAD, in the mind of Wall St., is now linked to the CRB.

[Nick Rowe]

Andy: yes. I've been thinking about that. Haven't got my head clear on it yet (too much teaching and admin today).

" Or was the rate cut actually smaller than expected?"

I think we can rule that out, from survey data. Most watchers didn't expect the cut.

[Nick Rowe]

OK, Iv'e now had my second coffee, and I think my brain is working again.

Why did the exchange rate drop on the news?

Because people thought:

Either, the BoC is right, and the economy is weaker than we thought, and it's partly transitory and partly permanent, so the real and nominal exchanges rate need to drop.

Or, the BoC is wrong, and future inflation will rise above target, so the future price level will be higher than we expected, so the nominal exchange rate needs to drop.

Either way, the nominal exchange rate needs to drop.

[JCE]

You (and Brad DeLong also) are the best teacher of economics I've ever had. And I've had many

[Roger Sparks]

Do I have these base assumptions correct?

1. A two commodity economy with equal distribution of either apples or bananas to every participant.
2. A desire for unequal distribution results in one participant promising future sacrifice in exchange for current excess consumption.
3. Condition 2 is so common that a fixed rate of interest has evolved and that ratio is the ratio between availability of the two commodities.

Assuming I have the basic assumptions correct, I next try to imagine a real life parallel.

1. Why would there be a desire to unbalance distribution.
2. Why would the unbalanced distribution have a need for interest which is an additional unbalance but in the opposite way?

I can not imagine any parallels. The desire for unbalance creates an inherently unbalanced economy, defeating the initial equal distribution. The existence of an interest rate increases the unbalance coupled with the promise that the unbalance will (sometime in the future) reverse.

My conclusion is that I can not take this example to the destination that you found. I think that competition between competing apple producers, each seeking bananas would be a much better path to explore the ratio of apples to bananas.

[Nick Rowe]

Roger: No.

The only bit that is correct there is the two good economy assumption, with some people producing apples only, and others producing bananas only.

[Andy Harless]

"Either, the BoC is right, and the economy is weaker than we thought, and it's partly transitory and partly permanent, so the real and nominal exchanges rate need to drop."

So IOW the BoC doesn't necessarily have better information about the future price of oil but it does (or might, anyhow) have better information about how the current price of oil affects the aggregate economy. I guess I can buy that.

"Or, the BoC is wrong, and future inflation will rise above target, so the future price level will be higher than we expected, so the nominal exchange rate needs to drop."

OK, because base drift means the price level change, even due to an random one-time error, will be permanent. Presumably with price level targeting this wouldn't happen unless people doubted the BoC's credibility.

[Derivs]

I would think, from your above example, economists would discuss the effects of a diversified economy on recessions more. An all apple economy is extremely vulnerable.

It seems from your example, if you take unavoidable hit in rGDP (drop in apple prices), CAD obviously falls, then you get inflation from devaluation, forcing up rates in your effort to keep actual inflation = expected.
Answer seems - to get money out of system equivalent to negative delta rGDP. Then your currency would hold flat. Inflation would meet target, raising rates would be unnecessary although, unfortunately you still take unavoidable rGDP hit. Does a CB have a button to burn money?

The same period as the CAD dropped you had a very similar move in AUD and an even bigger one down in CRB. It appears pretty clear to me that it is the GDP to commodity link that is worrying the market.

[Derivs]

Actually your inflation might be dependent on domestic utilization. But your currency would be all that mattered in that case.

[Nick Rowe]

Andy: yes, I think that's (roughly) right.

Derivs: don't take the apple metaphor too literally. It's just a way of saying that Canada is not identical to the rest of the world, and that the goods we produce aren't exactly the same as the goods we consume, because of exports and imports.

[Derivs]

I americanized my entire example anyway. Was thinking in dollars with commodities in dollars. In cad you could avoid the rgdp drop because of the currency drop. Its doing the dirty work.

[Mike Sax]

Hey Nick. If I could ask you an admittedly unrelated question, this has been on my mind. If markets are rational-so that in predicting a market move we have no good reason to expect to be any more accurate than a coin flip-why do participants continue to try to predict market moves? Whether in the equity and commodity markets, sports betting etc. Is that rational on their part?

Again, this has been on my mind so I figure the best way forward is to ask an economist.

[Nick Rowe]

Mike: a fine old conundrum.

this is my best attempt to explain it clearly. (I ripped off an old Brad de Long paper.)

BTW, if you want to "take" my course, you can watch it here, on streaming video. I think I'm on Monday eveings:

http://carleton.ca/cuol/access-your-courses/
http://carleton.ca/cuol/courses-lecture-schedules/cuol-fall-winter-courses/?term=201430&crn=31742

[Mike Sax]

Cool. TK Nick

[Nick Rowe]

JCE: I just found your comment in the spam filter. Sorry about that. But I'm very glad I found it! Thank you for saying that! You made my day.

[Derivs]

Nick,
A simple Yes or No. Do you agree that if both the U.S. and Canada were identical producers of only apples, the same fundamental circumstances hitting the U.S. where apples are quoted in USD would show a huge drop in US GDP whereas the currency offset results in no change to Canadian GDP. The entire change hides itself in the currency. The U.S. would look like it was in a recession, Canada would look unscathed, and only when you drove to Florida, for the winter, would you wonder why prices were so high in the U.S.

Essentially we both produce 1,000 apples and at CAD:USD of 1 and apple prices =USD 1 then both have identical GDP. Now if Apple prices go to 50 cents at the same time USD/CAD goes to 2. US GDP, being in dollars, gets cut in half. Since the USD is now 2:1 vs CAD. The apple in Canada still remains 1CAD per apple. No drop in GDP in CAD. If this is true, what I see is even funnier than the fact that GDP is a poor metric. Although inadvertently, for another reason, I used to say this about revenue and why Canada has to pull twice the molecules of gas out of the ground to equal the same revenue a molecule provides in the U.S.

If the above is true, I would have to wager that velocity is NOT constant in the long run.

Mike, doubt you read this but... from a non-economist ex-trader... 1- I have never seen anyone able to determine current fair value of an asset. I highly recommend that accepting current market price as the best indicator of FV is a good thing to do. 2- I have no problem accepting EMH, I'd possibly interject some bad humor and modify it to say - results in most people losing. 3- Markets do not appear to me to be a random walk "pure coin flip"

[Nick Rowe]

Derivs: No.

[ThomasH]

This is a great analysis of why Greece will need a more devalued exchange rate (leave the Euro) if foreigners try to impose a shock (large primary surplus) on them.

It's also a good reminder that inflation targeting ought to be targeting of the prices of non-traded goods.

[Giovanni Zibordi]

all small and open economies, including those that do not export commodities, Sweden, Singapore, Korea, Poland, Czech, Hungary, Israel, New Zeland have seen their exchange rates drop against the dollar and almost as much as Canada on average. It is pretty much the Dollar going up against the all world (ok, not CHF..) whether are commodities economy or not. Some of these countries countries have deflation such as Sweden or Poland and some are "on target" (2%) inflazion such as Australia and NZ and also Israel. Some countries cut rates as much as the USA and some did not.
Are markets thinking at what the Central Banks of all small open economies one by one and finding out since the summer of 2014 that they are all doing things that imply a lower exchange rate ?
The explanation of this simultaneous global exchange rate movement across the world seems to have more to do with : a) the end of QE in the US b) global deflation and the global slowdown outside the US. Is is hard to model global capital flows driven by carry trade, relative investment opportunities and (for instance) dollar debt problems in the EM. I know this is fuzzy talk but what the CB of the many small open economies do seems to have little do with this global currency movement. Like Canada they have been doing very little, not even "adjust the size of their monetary base"

[Derivs]

Time A
Apples = 1 USD and 1 USD =1 CAD

Company Canada 1,000 Apples @ 1 CAD = $1,000 CAD
Company USA 1,000 Apples @ 1 USD = $1,000 USD

Time B
Apples = .50 USD 1 USD = 2 CAD

Company Canada 1,000 Apples @ .50 USD = 1 CAD = $500 USD or $1,000 CAD
Company USA 1,000 Apples @ .50 USD = $500 USD

Canada Company reports no change in Revenue in CAD
American Company reporting in USD shows huge revenue losses.

How no?

[Nick Rowe]

Derivs: You asked for "A simple Yes or No.", so that's what I gave you.

Recall that NGDP = P x RGDP, where NGDP is nominal GDP, RGDP is real GDP, and P is the price level. (You were using the term "GDP" to refer to both real and nominal).

You are implicitly assuming either:

1. The Fed targets inflation (or the price level) and the Bank of Canada targets NGDP.

or.

2. The US dollar price of apples is sticky and the Canadian dollar price of apples is perfectly flexible.

In either case, the two economies are not identical, which violates your initial assumption.

"Oil is priced in US dollars" is a BS phrase that confuses thought, by creating a special form of money illusion.

[Nick Rowe]

Giovanni: I think you are at least partly right. The strengthening of the US economy is part of the story, and oil (and similar commodities that Canada exports) is the other part (I don't know how much of each, and that will depend on the country).

If something causes US demand (and hence demand for US-produced goods) to increase (to which the Fed responds by reducing QE and then raising R) we would expect to see the US dollar strengthen against other currencies.

Really, as ThomasH notes, the "oil" story is just one example of an asymmetric shock, that hits some countries (Canada) differently than other countries (the US). And Greece is another example of this. If Greece must reduce domestic demand, to create a budget and current account surplus, that requires a depreciation of Greece's real exchange rate. Which is a problem if the nominal exchange rate is fixed. In Greece it wasn't oil, or apples, but it's the same thing.