Forward guidance, borrowing degrees of freedom, and the inflation target horizon

This is something I do not understand very well. I'm writing this to try to help me think about it more clearly.

Eight times a year, at each Fixed Announcement Date, the Bank of Canada does two things: it announces a target for the overnight rate until the next FAD; it provides some "forward guidance" about future targets for the overnight rate. That forward guidance receives as much attention as the current target. Here's a recent example from Kevin Carmichael at the Globe and Mail.

A good "dumb" question to ask would be: "Why does the Bank bother with forward guidance at all?"

1. Here is one simple explanation, that doesn't really work. If you looked at just one FAD in isolation, you would say that the Bank uses forward guidance because it gives the Bank more power. By saying what it plans to do over the next year, rather than just over the next 6 weeks, the Bank can shift the whole term structure of interest rates by influencing people's expectations of its own future actions.

But when you stop thinking of FADs in isolation, and see them as part of a repeated game, that simple argument doesn't work any more. The Bank only has one degree of freedom per FAD. If at each FAD it announces what it will do at the next FAD, it must then do what it said it would do, if it wants its forward guidance to remain credible. It has borrowed one degree of freedom from the future, and must then repay that loan by doing what it said it would do, otherwise nobody will believe it in future and nobody will lend it a degree of freedom again.

2. Here's a better explanation. Sure, the Bank has only one degree of freedom per FAD on average, but maybe sometimes it wants to spend two degrees of freedom at one FAD, and is willing to borrow one degree of freedom from the future and repay the loan at some future FAD by spending zero degrees of freedom. The Bank might want the extra power at some FADs much more than at other FADs. Forward guidance lets the Bank borrow extra power when it's most needed, and repay the loan when extra power is not needed.

3. Here is a quite different explanation. There is a difference between making a promise about your own future actions and making a prediction about your own future actions. Maybe forward guidance is a prediction and not a promise, and has nothing to do with borrowing degrees of freedom from the future. We are normally better than other people at predicting our own future actions. Markets normally work better when people can better predict the future. So by publishing its own predictions of its own future actions the Bank of Canada is helping markets work better.

4. Maybe it's a mixture of 2 and 3. Forward guidance is mostly a prediction, but occasionally in emergencies (like in 2009 when the Zero Lower Bound became a problem) it's a promise that borrows degrees of freedom from the future.

5. But there's something wrong with thinking that the Bank of Canada has any degrees of freedom in setting the overnight rate target. The Bank of Canada is targeting 2% inflation. If it is serious about trying to keep future inflation as close as possible to the 2% target, it cannot freely choose a target for the overnight rate. Once it has chosen the 2% inflation target, it has used up all its degrees of freedom. It has to do what (it thinks) it needs to do to hit that inflation target. If it sticks to the 2% target, any commitment becomes a conditional commitment. But then "I promise I will set the overnight rate at 1% unless I think I need to change it to keep future inflation at 2%" is no different from "I promise I will set the overnight rate at whatever I think is needed to keep future inflation at 2%, and I think 1% will work for some time". It's like making a "promise" to do whatever you think you will feel like doing. It's not a promise at all.

6. Here's yet another explanation. Maybe the Bank of Canada thinks there is a trade-off between short run and long run inflation targeting. (If I'm driving an underpowered car with poor brakes, trying to keep as close as possible to 100kms/hr, I might want to go faster than 100 when I see an uphill section ahead and go slower than 100 when I see a downhill section ahead.) In this case a conditional commitment might mean "I will set the overnight rate at 1%, even if it means inflation rises above 2% or falls below 2% in the short run, unless I think I need to change it to keep inflation at 2% in the long run."

If 6 is correct, then what the Bank of Canada is doing when it gives forward guidance is not borrowing degrees of freedom from the future, nor making a prediction of its own future actions. Instead it is announcing that it has temporarily lengthened its time-horizon for keeping inflation at the 2% target. It has borrowed a temporary extension on handing in the promised 2% inflation assignment.

It might be a mixture of 2, 3, and 6. But maybe 2 is really 6, deep down.

Comments

[Frances Woolley]

Great post. I like 2 and 6 (I know exactly what you mean about underpowered cars and long steep hills). I can see how 2 and 6 would converge with a rational, non-political central bank. Does this describe the B of C?

[Scott Sumner]

Nick, Why not interest rate smoothing? The economic shocks call for a 3/4 % rate increase, so you spead it out over three periods, in quarter point increments. Not sure why they'd want to smooth rates, but they seem to.

[Frances Woolley]

Scott: "Not sure why they'd want to smooth rates, but they seem to." Movements in interest rates cause people to switch from equities to bonds or vice versa. If the B of C announces a large discrete change in interest rates, people will all move their money right away. If it announces a phased in change, the switch from one to the other will be more gradual (people have different thresholds for switching from stocks to bonds), and the effect on the stock market will be less extreme. That's my story anyways.

[Nick Rowe]

Frances: thanks! (I clicked on the link, first saw the E-type, and thought "Underpowered??" Then I saw the Marina!)

Scott: good point. I think that an AR(1) (MA(1)?) process for setting the overnight rate, to smooth interest rates, is isomorphic to a permanent loan of half a degree of freedom. Each basis point move has a bigger effect, because it is partially permanent, but you don't move it as much as you otherwise would. In principle, there's nothing to prevent the Bank of Canada choosing any fixed lead in setting the overnight rate. Each FAD it could announce the interest rate target of the next FAD, or the one after that......, or any weighted average of leads. It is not obvious (to me) which lead is best.

[Nick Rowe]

But presumably forward guidance would be better than some *fixed* degree of *silent* interest rate smoothing, because it lets the Bank adjust the weights over time?

[Frank Restly]

Nick,

"But when you stop thinking of FADs in isolation, and see them as part of a repeated game, that simple argument doesn't work any more. The Bank only has one degree of freedom per FAD. If at each FAD it announces what it will do at the next FAD, it must then do what it said it would do, if it wants its forward guidance to remain credible. It has borrowed one degree of freedom from the future, and must then repay that loan by doing what it said it would do, otherwise nobody will believe it in future and nobody will lend it a degree of freedom again."

There is such a thing as conditional guidance. Obviously monetary policy is just one part of broader economic policy (fiscal - spending and taxes) and the Bank of Canada is not the only central bank in town. Conditional on how the broad economy performs the Bank of Canada gives forward guidance on the future interest rate. The central bank sets a nominal interest rate (not a real one), because it has no control how debt is used - productively which puts downward pressure on prices or consumption / destructively which puts upward pressure on prices.

From Scott:

"Nick, Why not interest rate smoothing? The economic shocks call for a 3/4 % rate increase, so you spead it out over three periods, in quarter point increments. Not sure why they'd want to smooth rates, but they seem to."

Interest rate smoothing gives other credit markets time to adjust. Wild swings in short term interest rates could cause the yield curve to oscillate between positive and negative slopes if short term interest rates are already close to long term rates. A better question would be - Why doesn't the Bank of Canada (or any central bank) allow higher resolution interest rate adjustments on a continuous basis (hourly?), instead of 0.25% increments on a monthly basis?

In that way even miniscule changes provide forward guidance on future policy.

[JKH]

Nick,

“If at each FAD it announces what it will do at the next FAD, it must then do what it said it would do, if it wants its forward guidance to remain credible.”

Not really. It announces on a best efforts basis, which is better than nothing.

E.g. The Fed isn’t inextricably locked in to holding the funds rate as per its current longer term guidance. Look closely and parse every statement a central bank makes – ALL of them are hedged and conditional.

That doesn’t mean they don’t have credibility. It means they’re allowing for the facts to change - like Keynes maybe.

“Maybe forward guidance is a prediction and not a promise”

Yes, but it can be a prediction of economic conditions or policy, or both. Woodford talked about this is his recent paper, didn’t he?”

“it cannot freely choose a target for the overnight rate”

The monetarist in you will never die, Nick.

“any commitment becomes a conditional commitment”

Yes. Again, parse any statement by any central banker. That’s why God invented the subordinate clause.

"It's not a promise at all"

It is a promise. It’s a promise that the central banker is telling the truth about his conditional intentions – just giving you information about what constitutes those intentions based on today's information and best guesses about the future.

"I will set the overnight rate at 1%, even if it means inflation rises above 2% or falls below 2% in the short run, unless I think I need to change it to keep inflation at 2% in the long run."

A variation on Woodford’s history dependent stuff; on market monetarist level targeting stuff?

I have noticed Carney has been somewhat wishy washy over the past several years in trying to talk up interest rates via expectations, and gotten himself into a bit of a credibility bind IMO by doing so. He overdid it. The actual CHMC policy actions on mortgages (amortization constraints, etc.) have been very effective though.

[JKH]

P.S.

I.e. Carney wasn't quite nuanced enough in making those kinds of prediction statements about interest rates - too much Goldman Sachs, not enough central banker.

[Nick Rowe]

Frank: I interpret you as putting forward a variant on 3. The Bank makes a prediction (not a promise) of it's own future actions, and makes that prediction conditional on various things that might or might not happen, to give people better information.

On interest-rate smoothing: the key question is whether or not interest rate smoothing comes at the expense of keeping inflation on target.

JKH: the promise the Bank makes is to try to keep inflation at the 2% target. If you take any macro model, which contains both inflation and interest rates, then set inflation at 2% for every period, the model will tell you what interest rates will have to be to be. The Bank can't make two promises; it can't make a promise about inflation and make an independent promise about interest rates. I can't freely choose *both* the speed of my car and where to put the gas pedal.

[Frank Restly]

Nick,

"The Bank can't make two promises; it can't make a promise about inflation and make an independent promise about interest rates. I can't freely choose *both* the speed of my car and where to put the gas pedal."

The bank can't make any kind of promise about inflation. The only promise it can make is the Bank's reaction function to higher inflation. The central bank is not is the credit allocation business. Meaning it does not get to determine how credit is used - productively which puts downward pressure on prices or consumptively / destructively which puts upward pressure on prices.

[Gregor Bush]

Nick,
In July of 2009, shortly after the BoC announced its "conditional commitment" to keep the overnight rate at 0.25% I was at a meeting with an unnamed official and a bunch of unnamed economists. One of the economists (astutely) asked "if you're targeting 2% inflation why do you need a conditional commitment? Doesn’t your 2% target already imply a conditional commitment?".
To which the official answered:
“Well yes, one would have thought so, but when we looked at private sector forecasts, we saw forecasters projecting increases in the policy rate by the end of the year despite their own forecasts of inflation remaining below our target 2 years hence. When we asked them why they would show a forecast like this, they responded: “surely monetary policy has to be tightened to some degree with rates at such extremely low levels. These are emergency rates and the emergency is now over. But this policy tightening will result a relatively sluggish recovery and inflation remaining below 2% for an extended period” “
The official continued:
“So when we heard this we decided to include the conditional commitment as a way of reiterating our commitment to our target and reminding people that it’s the forecast of the target, and not any particular level of the instrument, that guides our policy.”

[Min]

"Here's a better explanation. Sure, the Bank has only one degree of freedom per FAD on average, but maybe sometimes it wants to spend two degrees of freedom at one FAD, and is willing to borrow one degree of freedom from the future and repay the loan at some future FAD by spending zero degrees of freedom."

Here is a translation into English. If announcing a target means borrowing a degree of freedom from the future, and spending a degree of freedom means meeting the target, what does it mean to borrow two degrees of freedom? It means announcing two targets. Then it spends two degrees of freedom by meeting both of them. Spending zero degrees of freedom means meeting no target at all.

I don't think that's what you mean. :)

[Nick Rowe]

Gregor: that's a fascinating and important story. Makes a lot of sense.

Min: in the second FAD the Bank can only do what it promised it would do at the previous FAD. It has no choices left, because it made 2 choices at the last FAD.

[Min]

Nick Rowe: "Min: in the second FAD the Bank can only do what it promised it would do at the previous FAD. It has no choices left, because it made 2 choices at the last FAD."

IIUC, the choices are borrowing DFs. So if it makes two targets at one FAD, what is to prevent it from making other targets at the next one? Meeting a target is spending a DF. If it does not meet the target, it loses the DF, anyway, right? Use it or lose it.

[wh10]

JKH - I am not sure it's the monetarist in Nick. It's the natural rate.

[Frank Restly]

Nick,

Another way to look at this is to consider both the rate of interest that the central bank sets and the rate of change in that rate of interest over time.

Degree of freedom #1 - i(t)
Degree of freedom #2 - di(t)/dt

That is why I mentioned high resolution interest rate adjustments. This has the potential to allow for a second degree of freedom.

This only works when the difference between the interest rate at time period t1 and time period t2 offered by the central bank is smaller than the interest rate spread offered in the private credit markets. It would have the effect of creating a microspread between a private bank's borrowing cost and lending returns. Meaning the central bank may charge 0.756928% for overnight money while a private bank may round that up to 1% (being the next highest 1/4% increment when it lends to another bank on an overnight basis. What it also allows the central bank to do is adjust both i(t) and di(t)/dt independently from each other.