Stephen's graphs show quite clearly that Canadian monetary policy must tighten before US monetary policy. I'm convinced. But what does monetary policy mean? In this context, I'm going to ignore other interpretations, and just focus on interest rates and exchange rates. What is the division of labour between increasing interest rates and appreciating exchange rates? Which one will do the tightening? Or will it be a bit of both?
Or, to put it another way, should exchange rates or interest rates move first, and why?
Or, given that the exchange rate is appreciating already, will the Bank of Canada need to raise interest rates before the Fed does?
The Bank of Canada talks about choosing the time path of the interest rate to target inflation, while watching the exchange rate as an indicator. But I am convinced there exists an alternate universe, observationally equivalent to this universe, except that there the Bank of Canada talks about choosing the time path of the exchange rate to target inflation, while watching the interest rate as an indicator.
Let's take a neutral perspective. Suppose that a b% appreciation of the exchange rate causes the same tightening of aggregate demand as a 1 percentage point increase in the interest rate. If Canadian aggregate demand and inflationary pressure rises relative to US aggregate demand and inflationary pressure, then we need either an increased positive interest rate differential, or an appreciation of the exchange rate relative to purchasing power parity, or a weighted bit of both. Let d be the interest rate differential, S be the exchange rate (relative to PPP?), and D be the aggregate demand (or inflationary pressure) differential.
Then the Bank of Canada must ensure that d+bS=D.
(Yes, this does look very much like the Bank of Canada's old, discontinued, and suppressed "Monetary Conditions Index". And the Bank of Canada thinks, or thought, that b=1/3.)
Under perfect capital mobility we know that any interest rate differential must reflect expected future exchange rate depreciation: d = S – E(t)[S(t+1)].
After some tedious arithmetic, you find the true division of labour between the interest rate and the exchange rate. Define "permanent D" just like Milton Friedman defined "permanent income", except you discount future D at rate b rather than at the rate of interest. Define "transitory D" as current D minus permanent D.
(The definition of "permanent D" is given by the formula: Permanent D = b.E(t)SUM to infinity of D(t)/(1-b)^t )
Then:
1. The exchange rate adjusts in response to changes in permanent D.
2. The interest rate differential adjusts in response to changes in transitory D.
So, what does this all mean? It means:
1. If D follows a random walk, so that all changes in D reflect changes in permanent D, then we see the exchange rate doing all the work, and the interest rate differential doing none. The exchange rate will follow the same random walk, and Canadian interest rates will follow US interest rates exactly, with no change in interest rate differentials.
2. If D is stationary but serially correlated (so if D rises it will tend to come back down eventually to the same average level) then any change in D will be partly a change in permanent D and partly a change in transitory C. That means that the exchange rate and interest rate differential will move in the same direction in response to news. The stronger the serial correlation, the more work will be done by the exchange rate, and the less work will be done by the interest rate differential.
3. At the other extreme, if all changes to D are very short-lived, and permanent D barely changes, then nearly all the work will be done by the interest rate differential, and nearly none by the exchange rate.
OK. So what does this mean right now?
That, I confess, is where I lose the thread a bit. So far, we've seen the exchange rate appreciate over the last year, with no change in the interest rate differential. This will continue as long as increases in D are expected to be permanent, or if D is expected to rise further in future before falling back to zero when both economies recover at the same rate.
But the US economy won't stay depressed relative to Canada's forever. D will eventually begin to fall. And that means the weighted (discounted at rate b) sum of expected future Ds must also begin to fall at some time. It is at that point that the exchange rate begins to depreciate again. And (if my head is straight on this), at some point before the exchange rate begins to depreciate, current D will be above permanent D, so transitory D will be positive. It's at that point the Bank of Canada should raise interest rates above the US Fed.
I really wish I could get my head around the implications of my model more clearly. Sorry.
But just because we see the Canadian economy recovering more quickly than the US doesn't mean the Bank of Canada should raise the overnight rate immediately relative to the US. The exchange rate is the forward-looking variable that is supposed to handle that job. It's only when the current recovery starts to look stronger than the future recovery (both relative to the US) that the Bank of Canada should start raising interest rates relative to the Fed.
Hoping Stephen might be able to put some empirical meat on these theoretical bones.
Worthwhile Canadian Initiative 
Nick, How does this relate to the “one tool, two targets” problem? If monetary policy is a single tool, then doesn’t it simultaneously affect interest rates and exchange rates? Suppose the BOC decides, “we’ll raise interest rates but not the exchange rate.” When they raise interest rates, won’t exchange rates go up as well? I’m sure I am missing something obvious here, as I am not used to doing open economy macro.
Perhaps this is what I am missing; the two instruments (interest rates and exchange rates) might convey very different messages about the future expected path of monetary policy. Is that what I am missing?
Scott: you are right that monetary policy still has just one tool. But that tool can be thought of as the exchange rate, or as the interest rate, or (as I prefer) as a weighted sum of the two. (A weighted sum of two tools is still just one tool, just as NGDP can be thought of, in logs, as just the sum of P and GDP). If the Bank chooses the weighted sum of interest rate and exchange rate, then the market decides on the division of labour between the two. Just as if the Bank chooses NGDP, the market chooses how that gets divided between P and GDP.
I’m sticking basically to an open economy of the Neo-Wicksellian framework here. There’s an IS curve, but it has the exchange rate as well as the interest rate as arguments. Plus a BP curve. Plus some sort of Phillips Curve.
I stayed out of the ‘social construction of monetary policy’ stuff, except for that one paragraph about alternate universe. The Bank insists that monetary policy is is is setting interest rates, while watching the exchange rate. I think we can also see it as the converse, or as setting a weighted sum of interest rate plus exchange rate.
In the Bank’s defence though, it daren’t ever talk about setting the exchange rate for fear of US accusations of “manipulating the exchange rate”. Since Canada has no exchange controls, such an accusation would be unfounded in any case, but it might not be easy to convince US politicians of that.
I can’t say that I quite understand your model (especially the math part), but I like the concept of using either interest rates or exchange rates to control monetary policy. But I’m a little confused on how it would be implemented. Given that Canada has an open economy, the BoC can’t effectively influence the exchange rate except by changing the interest rate. Even then, it’s the market that will decide how much the exchange rate will move in response to a change in interest rates.
For instance, in your original post you wrote: But just because we see the Canadian economy recovering more quickly than the US doesn’t mean the Bank of Canada should raise the overnight rate immediately relative to the US. The exchange rate is the forward-looking variable that is supposed to handle that job. It’s only when the current recovery starts to look stronger than the future recovery (both relative to the US) that the Bank of Canada should start raising interest rates relative to the Fed.
As I understand it, during the initial part of the recovery, the exchange rate will rise as the Canadian economy outperforms the US economy and your model suggests that this change will provide sufficient tightening of monetary policy. Then, as it becomes apparent that the US economy will start to catch up, your model suggests the BoC should start to raise relative interest rates. But if the BoC starts to raise rates above the US, won’t this in turn increase the exchange rate, which will further tighten monetary policy?
I guess I’m echoing Scott’s comment, but won’t any increase in interest rates also affect the exchange rate?
Or perhaps your model could provide a basis for estimating how the change in exchange rate in response to a change in interest rates in turn affects monetary policy?
Kosta: I wish I understood it more clearly myself! 😉
The conventional way of describing what happens is that the Bank of Canada sets the time-path of the interest rate, and that time path determines the exchange rate. But if the Bank chooses an interest rate reaction function, which includes the exchange rate as an argument, like i=D-bS, (and it needs to follow a reaction function something like this if it wants to look at all information, including the exchange rate, to keep inflation on target), then we can always just re-write that reaction function as set S = (D-i)/b. So we can’t really tell the difference between:
1. setting i, watching S, letting the market determine S given i
2. setting S, watching i,letting the market determine i given S
3. Some mixture of 1 and 2.
“But if the BoC starts to raise rates above the US, won’t this in turn increase the exchange rate, which will further tighten monetary policy?
I guess I’m echoing Scott’s comment, but won’t any increase in interest rates also affect the exchange rate?”
My short answer is “no”. That’s the conventional view, but I think it’s wrong. Here’s a longer answer from an earlier post: http://worthwhile.typepad.com/worthwhile_canadian_initi/2009/10/cheap-talk-and-the-exchange-rate.html
Actually, I’ve now figured out something that I should have figured out when I wrote the post. If events unfold as expected, then the Bank of Canada will start to raise interest rates relative to the US just an instant before the exchange rate starts to depreciate. So rising Canadian interest rates (relative to the US) will be followed by exchange rate depreciation, not appreciation. It is only if events don’t unfold as expected, if there’s “news” of temporarily stronger demand, will we see the Bank raise interest rates and the exchange rate appreciate.
Could you define time-path? It’s a concept you use a lot but I:ve yet to understand. actually any path, what is a path.
Maybe not in the short-run? ‘i’ is set in the reserves market and is a clearing price of present supply and demand. Maybe the forex rate is manipulated by transactions in the options market. If the CB refuses to discount those options, then the markets will become isolated.
edeast: “time-path” as in “The Weather Channel has a graph showing their forecast for the hour-by-hour time-path of temperature over the next 48 hours.”
Jon: Dunno. Maybe at very high frequency (hourly, daily?)
Isn’t it also handy to think of the interest and exchange rates as two ends of the same lever? Because each suffers from bounds: the BoC can only cut interest rates to zero, and it can only spend its foreign currency reserves to bid up the exchange rate. It can’t impose negative nominal interest rates or carry negative foreign currency reserves. But these constraints are binding in opposite directions: if one is binding, you can resort to the other lever to meet your policy goal.
I think that cleared it up for me.
Also: I agree that CAD won’t necessarily appreciate against USD if we tighten more quickly, except to the extent strength of our economy surprises positively or the US’ negatively.