Forecast the target, not the instrument

Should the Bank of Canada announce what it expects the future overnight rate to be? There are two good articles in the Financial Post: Pierre Siklos argues "yes"; Andrew Spence argues "no". There's more by both authors in this C.D. Howe backgrounder (pdf).

I'm against it. I'm going to try to explain why I believe it would be a bad idea for the Bank of Canada to publish a forecast of where it will set the overnight rate in future. And I build a simple little model to help show why.

First thing to be clear on: we are not talking about the Bank making a promise, or commitment, about where it will set the overnight rate in future. We are talking about the Bank making a forecast of its own future behaviour. (Whether that distinction will be quite so clear in practice though, and whether the Bank would end up feeling obliged to do what it had predicted it would do, is less obvious.)

In general, I'm very uneasy about the Bank putting any more focus on the interest rate instrument. I have argued in the past that "setting an interest rate" is not what the Bank does; it's a social construction of what the Bank does. And it's a social construction that has undesirable consequences, precisely because the mere setting of an interest rate, especially a nominal interest rate, provides no nominal anchor to the monetary system. The only nominal anchor is people's belief that the Bank will adjust that interest rate, and adjust it by a large enough amount, in response to forecast deviations of inflation from target. (And at the zero lower bound, that's a belief that's no longer credible.) It's the inflation target that the Bank needs to focus expectations on, not the interest rate instrument. And anything that takes public expectations away from focusing on the 2% target is a bad thing.

But here, I'm going to lay out a simple model to try to explain more generally why I think it's a bad policy for the Bank to forecast its own future setting of the monetary policy instrument. I think my model works whether or not the instrument is an interest rate.

Here is a very simple model of an inflation targeting central bank:

Pt = Mt

Pt is the deviation of inflation from target at time t.

Mt is (no, not the money supply) the Mistake made by the central bank at time t in setting the monetary policy instrument.

If the Bank makes no mistakes, inflation stays exactly on target. If the Bank makes a (positive or negative) mistake (relative to the policy that would have been chosen if the Bank had a crystal ball) then inflation will deviate from target. Since the Bank does not make consistent mistakes, on average inflation will stay equal to target. The unconditional forecast is for the Bank to make zero mistakes and for inflation to stay on target.

E(Pt) = E(Mt) = 0

That model is just a little bit too simple for my purposes. Here's a slightly less simple model:

Pt = Mt + bEt[M(t+1)]

The current deviation of inflation from target depends on the Bank's current mistake, and also on the market's current expectation Et of the Bank's future mistake M(t+1).

Suppose initially that the Bank has exactly the right policy for today, and the market also expects that the Bank will have exactly the right policy in all future periods. So actual and expected future inflation are both equal to target. Then the market suddenly expects that future monetary policy will be too loose. That raises expected future inflation above target (and maybe causes expected future real output to rise as well, if prices are sticky), and this causes current inflation to rise above target as well. That is why the expected future mistake appears in the equation.

The Bank does not have a crystal ball, and so cannot reduce the unconditional variance of Mt below some minimum, that reflects the best it can do, given its models and judgment. It's the unconditional variance of Et[M(t+1)] that concerns us here.

Suppose the Bank makes purely random, uncorrelated, unforecastable mistakes. The market's best forecast of the Bank's future mistake is then zero. Et[M(t+1)=0. In that case, the variance of inflation around target equals the variance of the Bank's current mistake.

But suppose instead that the market has a crystal ball and is able to forecast the Bank's future mistakes with perfect accuracy. So Et[M(t+1)=M(t+1). If the Bank's mistakes were uncorrelated, the unconditional variance of inflation would now equal (1+b) times the variance of the Bank's mistakes. The variance of inflation around the target is higher if the market knows the Bank's future mistakes (provided those mistakes are not negatively correlated).

That's far too extreme an assumption of course. The Bank doesn't have a crystal ball, and neither does the market. But it does show the danger of giving the market extra information about the Bank's future instrument setting. The more information the market has about the Bank's future instrument setting, the more likely it is that the market's expectation of the Bank's future mistake is non-zero. And, except in the implausible case of negative correlation of mistakes, that will cause bigger fluctuations of inflation around the Bank's target.

Don't give the market any information about the Bank's future policy that would help the market predict the Bank's future mistakes. That's the lesson here. And if the Bank makes serially correlated mistakes, the Banks current forecast of its own future instrument setting may help the market predict the Bank's future mistakes, which we don't want.

It doesn't even matter whether the market is right or wrong about the Bank's future mistakes. We don't want the market to even think the Bank will make a mistake in future. We want the market to just shrug its shoulders and say "Dunno. Who know where the Bank will set the overnight rate next year? My best guess is that the Bank will set it at whatever's needed for 2% inflation; could be too tight, could be too loose, there's just no way of telling which way it will make a mistake".

We don't need to assume that the market has superior information to the Bank, or a superior model. Just that the market has some information the Bank doesn't have (even if the Bank might also have some the market doesn't have). Or a different model.

(And I expect Scott Sumner will say that we should just leave it to the market to decide on what setting of the instrument is needed to hit the target. Not because the market has a crystal ball. But because the market's expectation of its own future mistake will always be zero. And I expect that Scott's got a valid point. Funny, I didn't expect to be writing about Scott's policy when I started writing this post. Might depend on which market we are talking about though. There's more than one, and they don't always all expect the same thing.)

I'm not sure if any of this is really original. Probably not. Someone is bound to have said it before. Maybe not as simply?

Comments

[Stephen Gordon]

My impression is that much of the pressure on the Bank to publish interest forecasts comes from private sector types whose job is to forecast interest rates.

[Nick Rowe]

Stephen: Dunno. Wouldn't that help put the private forecasters out of business?

[Stephen Gordon]

Well, their job is to produce forecasts for the short- and medium-terms. If the Bank gave them the first few months, then their job is made easier.

This point came up when I was talking to a journalist once about what the Bank's outlook might be, and he mentioned that the private-sector people he had talked to were frustrated that the Bank hadn't given more concrete indications about where its overnight rate was going to be in the next few months. Apparently, at least one of them said words to the effect of 'Carney should be able to give us something for the salary he's pulling down.' My response was that Mark Carney's job was to hit his inflation target, not provide interest rate forecasts.

I come down on your side of this debate. Forecasting the interest rate in the short term only makes sense if the Bank is *really* certain about how the short term will evolve. If it's not, then the forecast will only make it harder and more painful to adjust its stance if need be.

[Sina Motamedi]

I agree, except I think it might be more useful for the bank to target a price level instead of an inflation rate.

i.e. the bank would target higher/lower inflation in certain periods to get to a price level that, on average, rises 2% a year, if that makes sense...

[K]

If your policy instrument is an asset you can't target the path (except by targeting the path of rates). The expected return is determined by rates plus risk premium. So you can only target the current level. I assume you were thinking of stocks or other liquid assets as possible policy instruments?

[Adam P]

monetary policy mistakes are the only reason inflation ever deviates from target, seriously?

The bank is likely thinking that there are large and persistent shocks to inflation that can take a good long time for them to correct. In that they'd be correct (Scott Sumner's silly ideas aside). The arrival of such shocks would not indicate they made a mistake.

They probably think they'd just be giving their opinion on how long it will take them to restore things, a guess at future policy can be a help in communication. If the fed replace "low for longer" with "low for about 5 years" it might have helped a lot.

That said, I agree with you points about the politics. Lots of people would interpret the forecast as a commitment (or at least act that way to try to pressure the bank) and the bank may feel a bit committed ex-post.

[Nick Rowe]

sina: "i.e. the bank would target higher/lower inflation in certain periods to get to a price level that, on average, rises 2% a year, if that makes sense..."

Yes, that makes sense. That's "2% Price Level Path Targeting". It has advantages, and disadvantages.

K: a crawling peg for an exchange rate is one example of a level path target of an asset. So is the gold standard. Either can be done with monetary policy.

Adam: "monetary policy mistakes are the only reason inflation ever deviates from target, seriously?"

Yes, if the Bank is an "inflation nutter" (Mervyn King's technical term), and we define "mistake" as "a policy different from what the Bank would have done with a crystal ball".

But sure, if the Bank is a soft inflation targeter, rather than an inflation nutter, and so cares about output and other fluctuations as well, we would have to define "inflation target" as the momentary target, or flexible target, rather than 2% at every point in time. But that just complicates my talking about my simple little model.

[anon]

I find the target/instrument language to be very ambiguous/confusing, which doesn't help interest in the subject, IMO.

Can't you say something like "forecast the inflation target, not the interest rate target"?

An interest rate is not "an instrument".

An instrument is a t-bill or something, isn't it? OMO is not even "an instrument".

And you can't deny that the bank targets the ON interest rate, according to some reasonably normal use of the English langugage.

[Nick Rowe]

anon: yes, the language is confusing. That's why I avoided using the words "overnight rate target".

The Bank's target for the overnight rate is a short-term "intermediate target", in the old "target, instrument, indicator" language.

At a very short-term horizon, settlement balances are the instrument, and the overnight rate the target. At a longer term horizon, the overnight rate is the instrument, and inflation the target. Stepping way back and taking a big picture view, inflation is the instrument, and the well-being of Canadians the target.

[Nick Rowe]

And please change your handle from "anon"! Every Tom, Dick, and Harry calls himself "anon". Think up a real fake name ;-)

[anon]

Nick,

thanks, I might return later on the Dark Age

good encapsulation of the other, although I might not entirely agree

i prefer to remain within economic definitions and conventions as far as the accounting in concerned; defining income at the micro level different at the macro level just doesn't illuminate anything about the economics

it's similar to your distinction about demanded/bought etc. - you don't need to define capital gain as income in order to understand that capital gains can have an effect on quantity demanded or aggregate demand for example

[Adam P]

Nick: "Yes, if the Bank is an "inflation nutter" (Mervyn King's technical term), and we define "mistake" as "a policy different from what the Bank would have done with a crystal ball"."

that's just so very wrong...

[Nick Rowe]

anon "you don't need to define capital gain as income in order to understand that capital gains can have an effect on quantity demanded or aggregate demand for example"

Yep. And, if the marginal propensity to consume out of capital gains is not the same as the mpc out of other income, it might not be *useful* to define capital gains as income, even at the micro level.

[anon]

Nick,

"Yep. And, if the marginal propensity to consume out of capital gains is not the same as the mpc out of other income, it might not be *useful* to define capital gains as income, even at the micro level."

YES! (agree)

[Angelo Melino]

Any complaint with publishing the interest rate projections with a lag (say six months, or even a year)? I can see several advantages:

1. It forces the Bank to think about the entire path of its response. That's hard, but it's what GC should be doing, even if it only announces one target point at a time.

2. Specialists can pour over the projection errors and provide feedback on the model's forecasting abilities (both the projections provided by staff and the value-added by the modifications made by GC).

3. When we're as far away from "neutral" as we are now, it's important to have some idea of where the nominal interest rate is heading. If the Bank always thinks that the overnight rate should be heading back to 4.5% within a couple of years, then that information that would help households and firms.

BTW, the Bank spends a lot of time talking about the evolution of the output gap, developments around the rest of the world, commodity prices, etc. Should it suppress this discussion because it distracts attention and simply report "the Bank will do whatever is required to hit its 2% inflation target"?

[K]

Nick: " a crawling peg for an exchange rate is one example of a level path target of an asset."

But, the forward price of the asset directly implies the difference between the interest rate yield and the convenience yield of the asset.  So unless you are trying to set expectations for the convenience yield (e.g. the interest rate of the other currency, the dividend policy of the TSX, whatever) then all you are doing is targeting the yield curve.

[Phil Koop]

Nick, Adam has been a bit cryptic, but here is how I interpret him.

Your opening premises are exactly wrong: what the the bank actually does is to set interest rates, the social construction of what the bank does is to control inflation. This is a social construction because the rate of inflation is beyond the bank's control. That fact is only partly accounted for by introducing the market expectation of bank mistakes; the variance of inflation is due in some part to factors that are entirely exogenous to bank actions or market expectations of bank actions.

In this interpretation, your responses to Adam have been begging the question; perhaps that accounts for his brevity :-)

For my part, although I agree that there are obviously exogenous factors that affect inflation, I don't, on first reading, see why that should vitiate the model - I like the model. As for your premises, it is the fact that they are wrong that makes your conclusion correct. Because what the bank actually does is to set an interest rate, "forecasting" this rate has the character of a commitment. I could as easily "forecast" that I am going to have eggs for breakfast. Forecasting inflation, on the other hand, is merely a pious wish.

[Nick Rowe]

Angelo: The logic of my model does seem to say that the Bank should stay mum about everything, except keep on repeating that it is targeting inflation.

I don't see much harm if it publishes its past forecasts, for the reasons you say. And if it were common knowledge that the private sector's information were a proper subset of the Bank's information, then there would be no risk of the market thinking the Bank will be wrong, and there would only be benefits from the Bank publishing its forecasts, to help private sector decisions.

There is something especially problematic about publishing its interest rate forecast though, just because an interest rate is not a nominal anchor, and a fixed interest rate path is an unstable equilibrium for inflation.

K: The higher the inflation rate targeted by the Bank, the higher will be the whole set of nominal yields on all assets (except 0% interest currency). Roughly 1% for 1%, according to the Fisher equation. That works for the CPI, it will also work for the exchange rate, gold price, or any asset price.

Phil: lets agree to disagree on the whole "social construction" bit. Past arguments on that point have not been fruitful, and my model doesn't depend on it.

Suppose I added a random error term Vt to the right hand side of my model. So it reads (in the simple case): Pt=Mt+Vt. That presumably would satisfy you and Adam. But then, if the Bank had a crystal ball, it would observe Vt, and would set Mt=-Vt, and keep inflation perfectly on target. Remember, I am defining "mistake" as "mistake from the POV of someone with a crystal ball".

Or, we could just add Vt to the RHS of my models, and I don't see how it would affect the conclusions, if nobody has a crystal ball to observe Vt. That's perhaps what you had in mind.

anon: I'm going to delete your last comment above, now you have re-posted it on the other thread. No worries.

[Gregor]

Nick,
Can't we test this hypothesis by checking to see if the variation in (core) inflation around the target is higher for countries that publish interest rate forecasts than for those (with firm tragets) that publish only inflation forecasts? Also, we could test whether Sweden and New Zealand's inflation became more volitle around the traget after they started publish interest rate forecasts.

The first question might be distorted by country size (it's mostly small countries that publish interest rate forecasts) and the second by the Great Recession (inflation might be more 'volitile' in the 2008-2010 period) but it might be interesting nevertheless.

[K]

Nick: "The higher the inflation rate targeted by the Bank, the higher will be the whole set of nominal yields on all assets"

Yes.  But the forward price is exactly determined by the interest rate and convenience yield. So setting forward prices amounts exactly to setting the yield curve. And if the bank is effectively controlling the asset, then there will be zero volatility, no risk premium and the expected price will be exactly the forward price.  So setting the path of the price of any capital asset with a known convenience yield will amount exactly to setting the path of rates.  All of which amounts to agreeing with you that your model works whether or not the policy instrument is an interest rate.  For the purpose of this discussion all policy instruments are interest rates.

[Nick Rowe]

Gregor: yes, we could. Given all the other things changing, and differences across countries though, I wouldn't put much confidence in the results of the test, whichever way the results went.

K. Yep. I think I follow you now.

Angelo: Here's a thought: Maybe, just maybe, all the bank is really doing when it talks about output, what's happening in the rest of the world, and all that stuff, is simply saying to the market: "Look, we are aware of all that stuff that you know about. We're not stupid, and we've got a good information set, and good models, so don't even think that you can second guess us and predict which direction our future mistake will be!" In other words, the Bank is signaling that it has a big information set.

[vimothy]

Nick, but don't you now have two error terms?

[Nick Rowe]

vimothy: yep. And I want to add them together. But if someone really wants to separate the "avoidable error conditional on market information" from the "unavoidable error, without a crystal ball"?

[Phil Koop]

Nick, I see that you're the sort of fellow who won't take yes for an answer!

[Nick Rowe]

Sorry Phil! I'm a little sensitive about my little model. I'm fond of it. I wasn't sure you liked it. Adam doesn't. Sniff.

[dlr]

The more information the market has about the Bank's future instrument setting, the more likely it is that the market's expectation of the Bank's future mistake is non-zero

I don't understand why this is true. The market (pre-forecast) already has some information about the Bank's future mistakes: past actions, other communications, political considerations, governor-psychology, etc. Isn't is possible that the market expects a particular mistake (not a random mistake) based on this information, which expectation might be mitigated by yet more information, such as a rate forecast? If it were possible to literally give zero information, I could see your point. Then by definition the market (pre-forecast) would have no basis to expect mistakes in a particular direction. But it isn't. So how do you know that less information is better, when the type of information that is disclosed isn't necessarily neutral, because it wasn't created to be so (maybe it tends to lean toward creating expectations for either loose or tight mistakes by virtue of the kind of partial information that tends to be publicly available)?

[Nick Rowe]

dlr: It would take someone with better technical skills than me to do a proper formal analysis.

I could certainly imagine particular cases where the market thinks the Bank will make a particular mistake, and then when the Bank says what it expects it will do, the market is surprised to learn that the Bank will not be making that particular mistake after all. But I don't think that could happen on average.

Here's my attempt at a sketch of a formal analysis:

Suppose the Bank and Market have independent equally imperfect information. They both make an independent draw from the urn. In that case, if the Bank makes no announcement, the market doesn't know what the bank's information is, and Et[M(t+1)]=0.

But if the Bank makes an announcement, the Market knows what the Bank's information is. So the market now has more information than the Bank. The Market will use both bits of information to estimate the best instrument setting, and it will almost always be different from the Bank's estimate. So Et[M(t+1)] /=0.

That's not as clear as I want it to be.

You and the Bank are both trying to estimate the average height of the population. You each draw a sample of 100 people at random. If you don't get to see the Bank's sample, your estimate of the Bank's estimate will be the same as your own estimate. Et[M(t+1)]=0. But if your estimate is 5', and the Bank tells you that its estimate is 7', you revise your estimate to 6', and now think that the Bank will estimate too high. Et[M(t+1)]=1.

[Adam P]

But Nick, in reality doesn't the bank have a pretty good idea what the market is estimating. The BoE has devoted substantial resource to the problem of inferrring market inflation expectations. Perhaps that resource was not entirely wasted.

In the average height problem suppose we think that the bank knows that the market's sample yielded an estimate of 5 while its own sample gave an estimate of 7. Clearly 6 actually is the best estimate and that's what the bank will go on.

Now we have a situation where the bank's estimate, and the best estimate, is 6 but the market estimate is still 5. It will make the bank's job easier if the market also estimates 6, in this case wouldn't it be better for the bank to say something about its own estimates?

[Adam P]

Sorry, my third paragraph should start with "If the bank doesn't report its own estimate then we have a situation where..."

Also, it would seem that the bank needs to say its best estimate is 6 and explain clearly that it came to the estimate by incorportating its own data collection with its observation of the markets estimate. Perhaps even report its own internal estimate of 7 (the one that doesn't try to account for market forecasts).

[Nick Rowe]

Adam: good counterargument.

First best: Bank and Market pool information, and come up with a common estimate of what future instrument setting is needed. It's best because: the Bank knows more; the Market knows more; and Et[M(t+1)]=0

Second best: If the Bank cannot learn what the Market thinks, the Bank should not tell the Market what it thinks. Both get less accurate information, but Et[M(t+1)]=0.

Third best: The Bank cannot learn what the Market thinks, but the Bank tells the Market what it thinks, and Et[M(t+1)] /=0.

So, can the Bank observe the Market's belief? If it can observe the Market's belief in real time, i,e. if the Bank can observe Et[M(t+1)] in real time, it can adjust its own projection until Et[M(t+1)]=0. But I think what this amounts to is letting the Market choose the instrument setting, a la Scott Sumner. Certainly, the Bank should announce its own internal estimate of 7, to help the market, but then let the market choose the instrument.

[Nick Rowe]

Adam: I'm still getting my head and words straight:

Let's call 5 the market prior, and 7 the bank prior.

If the bank can observe the market's prior, the Bank will announce it's own prior, and also announce it's projection of 6, and the market adjusts its posterior to 6 too. Problem solved.

But if the Bank cannot observe the market's prior, but only the market's posterior, then I think we get the "circularity problem", unless we let the market set the instrument?

[Scott Sumner]

Please ignore this if others already mentioned the point. My first reaction is that there are two possible types of errors. Suppose the central bank (CB) uses a Taylor Rule. Then the CB might err by misforecasting future levels of prices and output gaps, or else the Taylor rule itself might be non-optimal. Since you assumed the CB doesn't make systematic errors, then if they are using the Taylor rule, we'd have to assume it's optimal. In that case if the CB forecasts differently from the public, then the market would assume that difference reflects a difference of opinion about where prices and output will be when future instrument settings occur. In that case if they thought the CB's opinion was worthless, they'd assume their forecast was right, and that in the future the CB would see the light and set the instrument exactly where the market now expects it to be set. If they think the CB forecast is useful, they'd slightly modify their own forecast.

[Just visiting from Macleans]

hah. end of my comments.

[The Money Demand Blog (123)]

CB's forecast of future interest rates makes the nominal anchor more effective at the zero rate bound. At the zero bound CB has to be very active in changing the forecast of future interest rates in response to forecast deviations of inflation from target. At least this is what Lars Svensson was doing in the Riksbank during the crisis.