jerry S-L :

"Consider the diagram below, which represents the simplest possible model.

Real interest rates are always constant, which is the 45 degree line.

Monetary policy follows the Taylor principle,

but nominal rates cannot go below zero,

so the bold monetary policy line kinks.

There is

one ‘locally stable’ equilibrium at the inflation target

(let us call that the ‘intended’ equilibrium),

and

one ‘indeterminate’ equilibrium when we are at the ZLB

(which involves negative inflation).

It is often said that the intended equilibrium is ‘globally unstable’.

By this is meant that,

*in the absence*of imposing an endpoint constraint
that has to be met

there are infinitely many rational expectations solutions to the model

many rat ex solutions involve inflation exploding.

tracing one:

we start at A

the monetary authority raises nominal interest rates

but

for constant real rates

expected inflation next period is even higher etc etc.

John Cochrane says:

“Transversality conditions can rule out real explosions, but not nominal explosions.”

. Hyperinflations occur when monetary policy makes no attempt to stabilise inflation.

Here we have a model that attempts to stabilize inflation

so it makes sense to impose an endpoint on any dynamic path.

For example,

when interest rates and inflation go up when we are at A.

Do agents say to themselves ‘hyperinflation here we come’.

Of course not.

This is inconsistent with the model, which involves an inflation target.

They say instead ‘that was unexpected - we must have got something wrong’.

We only travel along the unstable path

for as long as agents do not revise their ‘beliefs’

(in this case, expectations about the inflation target and the real interest rate).

Once agents revise their beliefs, whether it is their belief about the inflation target

or the real interest rate, inflation is likely to fall towards the intended steady state. "

---------------------------------------------

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NOW COMES CLIO :

"Note that we cannot just say - suppose we start at A,

as if history put us there.

History does not put us there:

in this forward looking model history is irrelevant.

Given the Taylor principle

there are only two reasons we could be at A

within the context of this model:

agents get the real interest rate wrong,

or the inflation target wrong.

Once we allow beliefs to be revised,

it seems inconceivable that hyperinflations

would occur within the context of this model.

In looking at how beliefs change

we are applying a simple notion of learning.

The fact that learning helps stabilise inflation

around the intended steady state should not be surprising

what we are in effect doing is

adding some backward dynamics into the model.

A locally stable steady state with forward looking dynamics

will tend to flip

to a stable steady state with backward dynamics.

This property is helpful

we probably do not know the mixture

of backward and forward looking dynamics

we have in the real world,

It is good that policies should be robust to this.

----------------------------------------------------------

CLIO STRIKES THRU BACKWARDS DYNAMICS

---------------------------------------------------

A consumer

has to eventually get on to their stable saddlepath

because it is stupid for them to accumulate infinite wealth

and stupid for others to carry on lending them more and more (no Ponzi games).

But things in this model are not so very different

- all we are saying here is

we are working with a model in which

we rule out hyperinflation

because that is a stupid thing for central banks to allow.

But unlike the consumer case,

it is not

*impossible*that central banks could allow it,
which is why we sometimes see hyperinflation.

------------------------------------------------------

If we start off with inflation below the inflation target,

we can apply a symmetrical argument.

Nominal interest rates will fall.

This is inconsistent with agents’ beliefs,

so if they revise these beliefs

it seems likely that inflation will rise rather than carry on falling.

But suppose they do not revise their beliefs.

In that case we do not shoot off to hyper negative inflation.

This path will converge on the ZLB steady state.

This steady state is not ‘locally stable’, but ‘indeterminate’.

--------------------------------------------------------------

Indeterminacy means that the model does nothing to tie down the initial point.

We could start anywhere below the intended steady state

a solution of the model would get us to the indeterminate steady state.

While this may sound desirable

it is not desirable

we normally

*want*the model to give us a unique dynamic path"
-------------------------------------------------

enters here CLIO again

". With a forward looking model

where history does not matter

we need something to give us our starting point

. Often indeterminate steady states

flip to

unstable points

if we change from forward looking

to backward looking dynamics.

This is where the desirability of the Taylor principle comes from

------------------------------------------------------

. If we replace the Taylor rule plus the Taylor principle

by a constant nominal interest rate

that passes through the intended steady state,

this steady state would be indeterminate

a very strong argument

*against*constant nominal interest rate policies.
The ZLB is just a particular constant interest rate policy.

-------------------------------------------------------------------

RE-LOOPING

" in this purely forward looking model history is irrelevant.

We cannot say ‘history means we start somewhere,

and then we converge to the indeterminate steady state’.

Now incorrect beliefs could start us anywhere,

but beliefs are not completely independent

of the model and subsequent dynamic paths.

All along the approach to the ZLB equilibrium,

events are contradicting those initial beliefs.

---------------------------------------------------------------------

" it's as unrealistic to assume beliefs are continually revised

as it is to assume they are never revised. "

"Suppose the initial belief involves an inflation target

which is below the actual target.

leads to interest rates falling,

which

if real rates are constant implies

still lower inflation next period.

If beliefs do not get revised, we do not go to hyper disinflation,

but to the ZLB steady state.

Suppose agents only revise their beliefs

once they get close to the ZLB steady state.

What will happen then?"

---------------------------------------------------------

ZLB means asymmetry

" originally agents thought that the inflation target

was a bit below the actual target

(1% rather than 2%, say).

Inflation has now fallen much further (to -3%, say).

Is it possible that they might conclude

they originally

*overestimated*the true inflation target?
If they ignored the fact that the ZLB is a constraint

they might decide

current stability implied that the inflation target was -3%.

The central bank cannot demonstrate

that this is incorrect by lowering nominal rates,

because of the ZLB. "

deflation can never get to hyper deflation

so very different

"from the hyperinflation case. "

------------------------------------------------------------------------

caveats

"In a model this simple we stretch credibility a bit

to get us to a point where we stay at the ZLB steady state."

" Agents ignore all the observations on the path towards that position

each of which was inconsistent with a -3% inflation target."

" But

if you add in additional uncertainty

allowing the real interest rate to temporarily change

things get more complicated.

Agents could interpret falling nominal rates

when inflation was 1%

as being due to temporarily lower real interest rates."

"So for a time, at least,

we could stay at the ZLB steady state

because of ‘self-fulfilling’ but mistaken expectations."

" If we allow real interest rates to change,

at some point real interest rates will rise

and agents will recognise this. "

"Instead of nominal rates rising

(as they should if the inflation target was -3%),

they will stay at zero,

which should make agents revise their belief about the inflation target.

So the ZLB steady state remains transitory.

But we could stay stuck in the ZLB steady state

:

for as long as beliefs remain unchanged

or

no information arrives that makes them change. "

-----------------------------------

now he tosses his model to the fairies

" I think it is difficult to argue that something like this applies today

to countries like the US or UK. "

"Expectations of inflation are still positive,

and central bank inflation targets are clearly positive and pretty credible"

------------------------------------

now the moral of the toy model

" if we take the idea seriously at all"

" it does suggest that one-sided inflation targets are dangerous."

" Central banks that have a target of 2%

*or less*
invite speculation that they would settle for zero inflation if that came around,"

" which would make falling into an expectations driven liquidity trap

that much easier."

think

" Japan ".