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CLASS 9: THE EFFECTS OF ANTICIPATED CHANGES IN MONETARY POLICY
- in this class the forward looking nature of prices will play
a major role
- we will show that anticipated future changes in monetary
policy affect the current rate of inflation
- Let us consider the following situation: in periods
t=0,1,...,T-j money grows at
a rate
,
and people expect it to grow at that rate forever:
this implies that nominal money supply is equal to
,
real money balances
are equal to the equilibrium level
,
and therefore that the price level
is equal to:
(if we further assume that the level of public debt is zero (Bts=0, all t), we obtain that
transfers from the government to individuals (which are equal to seignorage) are
equal to:
)
- In period T-j it is announced that there will be a regime change in economic
policy in period T: it is announced (and the people believe it) that from period
T onward (for all
)
the money supply will be kept constant at the level
reached in period T, which is
(if the level of public debt is still kept at zero, Bts=0 all t, this means that
transfers from the government to individuals will be zero as well in all periods:
Tt=0)
- Given that people expect money supply to be constant forever after,
the equilibrium real money balances from period T onward will adjust
accordingly to the new stationary equilibrium. In particular, real money
balances will be equal to m*(0) (if
,
then
)
The price level will also be constant forever after:
![$p_t=\frac{M_T}{m^*(0)}=\frac{M_0}{m^*(0)}(1+\mu)^T$](img11.gif)
,
all
![$t \geq T$](img7.gif)
- The question is: what is going to happen between period T-j
and period T?
- This question is relevant to understand a number of issues, like:
- What happened to inflation in Europe in the years between
the announcement
of the Monetary Union and its actual implementation?
- What would happen to inflation in Mexico if the adoption
of the US Dollar was announced?
- Let us use the first order condition for money holdings (after
imposing the equilibrium conditions: ct=y and Mt=Mst, and
assuming that income is constant):
- when t=T-1 this equation becomes:
since we know that
,
we know the time path of the money
supply between T-j and T (that is, we know MsT and MsT-1), and we know pT
(
), this equation will deliver a value for pT-1.
But once we have pT-1, we can use the same equation to
find pT-2, and so on and so forth until we get to pT-j
- For simplicity we choose to use the same approach
to find the path for real money balances, instead of prices (we know that
it is equivalent).
Multiplying both sides for Mst, and multiplying and dividing the right
hand side for Mst+1, the above equation becomes:
that is:
- It is clear that the above equation is satisfied by
so that is the only point (if
is unique) where the function
mt+1=f(mt) crosses the 45 degree line.
- In order to understand whether the solution is stable, we have to see
what is the derivative where it crosses the 45 degree line:
where all derivatives are evaluated at
.
- If
m(uc+um) is an increasing function of m the
denominator is positive, and hence the whole expression is positive.
Furthermore, one can show that under the same condition that guarantees
that
is unique, namely
um ucm+uc umm>0 the numerator is larger than the denominator.
- In practice, this means that starting from
mT=m*(0) we
can solve the equation backward and obtain m(T-j).
- Notice that, unless
(the announcement is given many many
periods in advance), real money balances will jump at the time of
the announcement:
- Notice also that real money balances are growing from the time of the
announcement to the time of the actual implementation:
The announcement is enough to have inflation growing at a rate less
than the rate of money growth
- "Money, unlike regular goods like bread, derives its value
from convention, institution and, more than any other good, from
expectations
(Guillermo A. Calvo)
- In Germany (1923) money supply stops growing only in November,
but real money balances stop decreasing three months in advance
the announcement was given only the 15th of October, but the public was
expecting a change in regime since August (new government, fiscal reform,
refusal of the Central Bank to buy more government debt with maturity
greater than one month)
- The experiences of Greece and Hungary also suggest that a model
with adaptive expectations (inflation expectations depend
on past levels of inflation) cannot explain the increase in real money
balances before the change in the rate of growth of money supply
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Marco Del Negro
2000-02-19