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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.

Nick, How does this relate to the "one tool, two targets" problem? ... 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

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.

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