Tuesday, August 13, 2013

simple simon lewis discovers ...Clio

yes history

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),
 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
 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. "
"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.

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.

" 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,
 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. "

"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
 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."
 " Japan ".