Next: About this document ...
CLASS 13: FIXED EXCHANGE RATES AND 'CRAWLING PEG'
- Implications for monetary policy of fixed exchange rate regime
- ... and of so called 'crawling peg': in a 'crawling peg'
system the Central Bank has a 'moving target' for the exchange rate.
- This was the case of Mexico before 1994.
The Equilibrium under 'Crawling Peg'
- The case of fixed exchange rate is a special case of
'crawling peg' because the target for the exchange rate is fixed rather than
moving. So we may as well study crawling peg first.
- In a 'crawling peg' regime the the Central Bank has a moving
target for the exchange rate: the depreciation of the exchange rate has to
be equal to a prespecified amount :
and conducts monetary policy consistently with this target.
- As you may anticipate, for the crawling peg to be successful fiscal policy has
to follow suit.
- Note in the first place that the Law of One Price implies that prices have to
grow at the same rate as the planned depreciation: since
and since pw is constant, then:
therefore in equilibrium inflation will be constant.
- Note that the no-arbitrage condition:
becomes:
- We can substitute this condition in the first order condition with respect
to money holdings, namely:
to obtain:
- Since in the foreign country inflation is 0, we know that this implies
that:
So we obtain that:
- From the no-arbitrage condition we see that this implies:
- Let us focus -for the time being- only on stationary equilibria, that is, equilibria where
the total amount of foreign activities of the country do not change over time, that is:
If the total amount of foreign activities of the country do not change over time, then the current
account,
is constant. But this implies that consumption is constant because:
and in particular:
- Since both equation have to hold at the same time, it is clear that, if
ct=ct+1=c*,
then:
- If real money balances are constant, and prices are growing at the rate ,
it must be that money supply is also growing at a rate :
- if money supply is growing at a rate ,
and if real money balances and
consumption are constant, we know from the equilibrium relationship:
that real money balances are equal to
The Impossible Trinity (Mundell?)
- The Impossible Trinity is the following:
- Fixed (or predetermined) exchange rates
- Open capital markets
- Independent monetary policy
- Our model says that the Impossible Trinity is indeed impossible:
If the no-arbitrage condition holds, once the government has chosen the path for
the exchange rate the growth in the money supply (monetary policy) is determined by
the equilibrium of the model - there are no more degrees of freedom.
- Note that fixed exchange rate means ,
so that money supply and the
price level must be constant.
- This is a lesson Asian countries, and Mexico, learned the hard way:
some chose to have the exchange rate floating (Mexico, most Asian countries), some chose
to impose capital controls (Malaysia, Chile).
- Let us try to understand why.
If the Central Bank wants to have a predetermined level of the exchange rate, it is
fixing the price of one currency against another.
Therefore it must be ready to exchange Peso denominated assets for $ denominated
assets at the given exchange rate: at the given exchange rate the supply of
foreign currency must be flat.
- With perfect capital mobility, the demand of real money balances
is given by the no arbitrage condition:
which says that the return from holding domestic currency has to be equal to
the return from holding foreign denominated assets.
- For given consumption, the above equation determines real money balances. But the law of one
price determines the evolution of prices! So the demand for nominal money balances is determined.
- Since in equilibrium demand must meet supply, the supply of money is also given - no longer a choice of the
Central Bank.
The Implications for Fiscal Policy
- Fiscal policy as a fourth element of the impossible trinity.
- Let us look at the intertemporal budget constraint of
the government:
- Given that real money balances are equal to
,
seignorage
in real terms is constant and equal to
- The intertemporal budget constraint of the government becomes:
or
- This condition pins down the discounted present value of real transfers
from the government to the private sector.
- The implication is that once the rate of devaluation is chosen, fiscal
policy is also constrained.
For instance, with fixed exchange rates, at any period the present discounted
value of future real transfers is a function of the current amount of activities
owned by the government:
- If real transfers are constant over time at a level ,
then
the real amount of activities owned by the government also has to be
constant:
so that the equilibrium level of transfers is equal to:
where Ag0 is the initial amount of activities owned by the government.
- Of course real transfers do not have to be constant over time.
In general, the path for real transfers will determine the path for
the reserves of the Central Bank:
If real transfers are above seignorage plus the interest from reserves, then
reserves will decrease.
- Remember that
Apt+Agt=Ap0+Ag0, all t.
The total amount of foreign assets in the country is constant, so if
the government is decumulating reserves, the private sector must be accumulating them.
- This simply reflects the identity:
CA=Sp+Sg
since CA is constant, if Sg is going down, then Sp must be increasing.
- The government cannot be decumulating reserves forever, because of the
no-Ponzi game condition: since the present value of real transfers is given, if
the government chooses to increase transfers today, it must increase them tomorrow.
- However, if fiscal policy is not consistent with the equilibrium, at some
point the fixed exchange rate must be abandoned.
Next: About this document ...
Marco Del Negro
2000-03-27