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I think the spot rate setting is more effective.

And that the ineffectiveness of a forward rate commitment is an increasing function of the length of the time period.

E.g. if the CB set the rate in either regime as a 1 day floating rate, it wouldn't make much difference. It's vaguely analogous to the difference between trade date and settlement date timing in the existing payment system. The tighter the standard time period for the rate reset, the less difference it makes to the outcome when comparing "spot" versus "forward" set/guidance regimes.

Your last post about power borrowing reminded me of the Fed's setting of long term rates during WWII. Borrowing equals setting the yield curve (or the end points of the curve) instead of setting just the short term rate.

JKH: "I think the spot rate setting is more effective."

In the sense that dY(t)/dr(t) is bigger than dY(t)/dE[r(t+1)] ? That is probably true. But it might not be true in a model where E[Y(t+1)] is an element in X(t). (Future interest rates affect future demand, which affects current demand.)

And if that were true, it would mean the central bank in the second world would need to make bigger movements in E[r(t+1)] to offset movements in X(t) than the central bank in the first world.

(Yep, adding forward guidance is a way of controlling the whole term structure this period. But next period you have to carry out your previous commitment, and can no longer control the short end as you want.)

Is this the answer: if dY(t)/dr(t) is bigger than dY(t)/dE[r(t+1)], then you would get explosive oscillations in r in the second world?

But if the reverse were true, if dY(t)/dr(t) were smaller than dY(t)/dE[r(t+1)], does that mean you would get explosive oscillations in r in the first world?

I wish my brain worked better.

Nick,

I'm not really responding to your precise question

But to clarify

This post is about a binary choice between setting a current period rate and a future period period rate, isn't it?

Applying your last post to WWII is a bit different - I think

The CB pegs the long rate

It still has flexibility to float the short rate

So it can use supply/demand signals in the long market as input to setting the short rate

E.g. if the market wants to sell long bonds at a pegged rate to the CB, that would be an indicator at the margin to tighten at the short end - i.e. hike short rates?

> and on the expected interest rate next period E[r(t+1)]

Nominal or real?

I'm being pedantic, but I think the distinction is too important to gloss over here. Central banks set a nominal rate to achieve an inflation target, but in a model without price rigidities expected inflation is irrelevant.

That means that central bank errors cause errors in expected inflation and errors in the expected real rate to be anticorrelated. Even a correctly-predicted nominal rate could hide the combination of inflation being low and the real rate being high versus expectations (or vice versa).

This is something of a problem, because optimal behaviour is different in the event of unanticipated inflation or an unanticipated increase in the real rate.

Imagine a world where target inflation is zero, the expected interest rate is zero, and our agent has one money to save for consumption next period. The agent can do so in the form of a bond (paying a mix of today's nominal rate and tomorrow's nominal rate) or in the form of a twinkie (paying a guaranteed 0% real rate).

The agent wakes up in the following period to be surprised that the interest rate is actually 1%. Which savings option was superior depends on why the interest rate was 1%: a Central Bank that kept inflation at 0% by raising interest rates would favour the bond, but one that let inflation reach 1% and kept the real rate at 0% would favour the twinkie.

This means that agents' behaviour depends on a mental model of how the CB is likely to be surprising. A highly-credible CB that always hits its inflation target will see errors in its expectations show up as errors in its expectations of the real rate; a less-credible CB will see a mix of real rate and inflation errors.

JKH: "This post is about a binary choice between setting a current period rate and a future period period rate, isn't it?"

Yes.

"The CB pegs the long rate

It still has flexibility to float the short rate"

No.

To keep it simple, there is a one-month interest rate (short) and a two month interest rate (long). This month, the central bank can set both the long rate and the short rate, by setting a short rate this period, and promising a particular short rate next period. But next month it must carry out the promise it made last month, and so is no longer free to set the short rate where it wants to set it.

Now, if the central bank does Operation Twist, or Reverse Twist, (changing the mix of long and short bonds on the asset side of its balance sheet) that gives it additional leverage over the term structure (assuming the pure expectations hypothesis is false). But I am assuming here it can only set the overnight rate, and make promises about the future overnight rate. No Operation Twist allowed.

Majromax: For this particular question, I don't think it matters if we interpret r as nominal or real. New Keynesian models have sticky prices. But if you think it does matter, interpret r as nominal, and include expected inflation in the vector X(t).

Maybe then it's a matter of information? E[r(t+1)] is always in our agents' model, but the interesting thing about forward guidance is that the estimate is now based on an explicit policy announcement by the Central Bank. The question is then not really what E[r(t+1)] gives us but instead what the announcement gives us.

I think the answer boils down to information: what does the announcement say about the Central Bank's thinking that isn't already obvious? This can come from a few factors:

*) The Central Bank could be acting on private information: I(t) is not contained within X(t) that the agent itself knows. The announcement of a future interest rate then gives the agent a glimpse into that additional information.
*) The Central Bank could be specifying its interpretation of economic information. Even if X(t) = I(t), there may be multiple plausible future economic paths. Concrete forward announcements pick one of those interpretations. This is relevant in recent experience, where forward guidance from the BoC and Fed contains a very explicit "... and we don't see inflation picking up quickly in the near future."
*) The Central Bank could be voluntarily reducing its discretion. The BoC has a flexible inflation target, so forward guidance is a way of saying "even if we're wrong and inflation increases faster than expected, we will tolerate that for a longer term (by one period) than otherwise."

Points one and two have the strongest first-order effects, since they will change the central estimate of E[r(t+1)]. All of these points also reduce the expected error between r(t+1) and the agents' estimate, which can change behaviour if the agent is risk-averse or if agents believe that the central bank is risk-averse (especially with point three).

This is somewhat like driving a car around a curve on an unknown road.

If we know the road, we can predict the curve and the motions needed to navigate the curve. Not so if we do not know-the-road.

Majromax:

But in both the first and second world the central bank is revealing its information about (or part of its information) about X(t).

And in both the first and second worlds, the Bank could depart from strict inflation targeting, if it wishes.

Roger: but the current speed of the car does not depend on what the car expects us to do with the gas pedal next period.

"The CB pegs the long rate

It still has flexibility to float the short rate"

No.

...............

I was referring to the WWII situation where that would have been the case

I thought that might have been interpreted in the context of your previous post - not in the sense of this post with its constraints on forward period rate commitment - there was no forward commitment of period rates in the WWII context - only a commitment to a (current) rolling long period

@Nick:

> But in both the first and second world the central bank is revealing its information about (or part of its information) about X(t).

True, but what it reveals is a bit different in each case.

Look at the example of US businessfolk who believe that hyperinflation is just around the corner. The US Fed's forward guidance clearly establishes that they do not in any way agree with that view.

A secondary effect of forward guidance is that it transfers some of the expectation-risk. Agents gain more certainty over the interest rate, but this comes at the expense of certainty over the inflation rate (in normal times). Forward guidance by a credible central bank in a "normal" monetary policy regime would be expected to increase inflation volatility, since if they stick to their guidance the CB would have to act with a greater lag.

However, in times where conventional monetary policy is believed to be less effective (that is, near-ZLB according to political will), a greater (upside) uncertainty on inflation is something of a good thing, via virtuous cycles and such.

This also explains the BoC's withdrawal of forward guidance. If the Bank believes that inflation is properly returning to target, there's no advantage to the tradeoff of uncertainties.

> And in both the first and second worlds, the Bank could depart from strict inflation targeting, if it wishes.

How do we define "strict" inflation targeting? It seems that every inflation-targeting central bank has some degree of flexibility within that target, since departures from the target rate are tolerated to a degree. Some of that is even probably by necessity, since typical central bank actions do not in practice instantaneously change the price level or inflation rate.

JKH: Ah! I understand you now (I think). Yes, the central bank can choose the 1 month rate every period, or it can choose the 2 month rate every period, or the 3 month rate every period, etc.

That leads to a slightly different way of asking a very similar question to the one I am asking here: which of those many rates should it use as its instrument?

Nick,

Again, not an answer to your precise question, but thinking out loud around it:

As an example, suppose the Bank of Canada sets the overnight rate every 6 weeks, but sets it for the 6 week period beginning in 6 weeks’ time.

An example of the risk in doing this is that the Bank sees incoming data on the economy early in a rate set period but can’t act on that data - in terms of a rate that would be currently applicable - for another 12 weeks. It’s currently operating with a rate that was set 6 weeks ago and has already locked in the rate it will enforce starting in 6 weeks’ time.

That 12 weeks is a fair stretch. Also, this forward rate setting system suggests a discipline that makes it a bit more cumbersome for “emergency” meetings where a CB can reset rates right away due to extreme market conditions. Such emergency resets do happen from time to time in the system we have.

So I’m not sure I see any advantage to this. In fact, it suggests less control and more volatility in the way in which the market reacts to these various rates that have been committed to (the current rate and the next period rate).

The CB rate is only an anchor, and market expectations can adjust all other rates that are set by the market using the CB rate as a base. So any “damage” done by such a constrained system would be limited by the freedom the market has to determine various yield curves.

I see the WWII model as quite different. It is not forward short term rates that are being committed in step-wise fashion, but spot long term rates on a continuous basis. The long term rates extend well beyond the short term horizon of a short term rate commitment. This is a more powerful model I think. The long term government financing cost can be fixed according to what seems reasonable under a given inflation (or NGDP) target and that will hold provided the CB has the fortitude to impose its (Chuck Norris) capability at the short end. Something like a gold standard defense. I think this would result in cycles of normal and inverted yield curves.

Also, I think 2 characteristics of the rate set system/process are important:

a) Its really an overnight rate - whether for the current period or the forward period - because its applicable to variable balances. That's not the case for a single term rate for example.

b) The overnight rate is committed for a term period - with exceptions for emergency meetings, so I guess there's some tail risk on that commitment. If you compress the 6 weeks to 1 day, you get something close to a true variable rate applicable to variable balances. And the forward commitment system converges to the current system in the limit (almost). That's why I said any "damage" due to loss of flexibility would be minimized as the period term goes to zero.

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