Exchange rates and the economy
• In this lecture we will model the operation
of our IS-LM model in an open economy
with fixed or floating exchange rates.
• An open economy has two meanings here:
– Goods market: trades goods and services
– Financial market: allow the flow of investment
capital- this is often called “capital mobility”,
as capital is thought to flow to where it earns
the highest returns.
Fixed vs floating exchange rates
• Fixed exchange rates: the government
determines the nominal exchange rate and the
RBA moves to keep that rate in the market for
foreign currency- typically the exchange rate of
the A$ would be fixed in terms of another
currency like the US$- also called a “peg”.
• Floating exchange rates: the nominal exchange
rate of the A$ is determined in the market for
foreign currency- the current Australian policy is
a floating exchange rate.
Net exports
• In the last class we defined net exports as:
NX(Y, Y*, e) = X(Y*, e) – IM(Y, e)/e
(-, +, ?)
( +, -)
(+, +) +
• So NX is decreasing in Y, increasing in Y* and
ambiguous is e. We can’t sign e, as we can’t
sign IM(Y, e)/e.
• The Marshall-Lerner condition is the condition
that ensures that NX falls as e rises. If the
Marshall-Lerner is true:
NX(Y, Y*, e)
(-, +, -)
(Uncovered) interest parity
condition
• We derived this is the last lecture. Assuming
that capital is mobile, investors are free to put
their money in the country where it will earn the
highest return. In equilibrium it must be true
then that expected returns are the same across
all countries.
• Comparing Australian interest rates (i) versus
some foreign interest rates (i*), it must be true
that:
it = i*t – [Expected appreciation of A$]
Fixed exchange rates
• This is the case where the Australian
government fixes the nominal exchange rate of
the A$ to another currency, also called a
“pegged exchange rate”.
• If the peg is believed (“credible”), the expected
rate of appreciation/depreciation relative to the
pegged (or “anchor”) currency is zero.
• The [Expected appreciation of A$] term must be
zero if the peg is credible, so we will have:
it = i*t
Fixed exchange rates
• Since Australia is a “small” country, we
would imagine that the Australian interest
rate is then fixed at the pegged currency’s
interest rate, usually US i*.
• What happens if the peg is not credible?
– Answer: The expected future appreciation
then is a probabilistic term, with x chance of
depreciation of -dE, we have:
Expected depreciation = (x) (-dE) + (1-x) 0
Monetary policy under fixed rates
• What happens to monetary policy if the
government fixes the nominal exchange rate?
• Answer: Monetary policy becomes ineffective as
a tool for controlling interest rates under a fixed
exchange rate regime.
• Scenario: The government sells Aust bonds in
order to reduce the Aust money supply and raise
i. The sale of the bonds pushes down the bond
price and pushes up i.
• But the lower price of Aust bonds attracts foreign
investors wanting Aust bonds. The foreign
investors start purchasing A$ to buy Aust bonds.
Monetary policy under fixed rates
• The foreign investors buying A$ pushes the
nominal exchange rate, E, up.
• But the government can’t allow E to rise, as the
A$ is fixed. So the RBA has to supply A$ to the
foreign exchange market to keep the A$ price
down.
• How much A$ must the RBA provide? Enough
to prevent A$ from rising, so the RBA has to sell
back all the A$ that it bought with the bond sale.
Monetary policy under fixed rates
• The net result is that the RBA has issued more
bonds (sold bonds for A$) and then bought
foreign exchange (sold A$ for US$). The
amount of A$ is unchanged, but the RBA now
has more US$ reserves.
• Monetary policy can not change interest rates,
as long as the peg is maintained. It can only
affect what the RBA is holding.
• The Aust i is fixed at the US i*, for as long as the
peg is maintained.
Monetary instrument?
• Either:
– the RBA controls the exchange rate and has
no control over the interest rate (fixed
exchange rate); OR
– the RBA controls interest rates and lets the
foreign exchange market determine the price
of the A$ (floating exchange rate).
• The RBA can not do both as long as there
is capital mobility.
IS-LM under fixed rates
• Our goods market equilibrium is:
IS: Y = C(Y-T) + I(Y, r) + G + NX(Y, Y*, e)
• Our money market equilibrium is:
LM: (M/P) = Y L(i)
• We have our Fisher equation:
r = i - πe
• And since the nominal exchange rate is pegged
at E’, we have
e = E’P/P*
IS-LM under fixed rates
• We also have our interest parity condition:
i = i*
• Our IS-LM equations become:
IS: Y = C(Y-T) + I(Y, i* – πe) + G
+ NX(Y, Y*, E’P/P*)
LM: (M/P) = Y L(i*)
• We can use these two to solve for our AD
equation. We have to ask “what happens as P
rises?”
IS-LM under fixed rates
• As P rises, the RBA must move M so as to keep
i = i*, so the nominal interest rate will be
unaffected. However the real exchange rate will
change, as E’ and P* are fixed. As P rises, e
rises as:
e = E’P/P*
• So a change in P affects the economy only
through the change in the real exchange rate.
• As P rises, e rises, so NX must fall if the
Marshall-Lerner condition is satisfied. We can
use this fact to trace out our AD curve.
AD under fixed rates
• As P falls, NX rises, so AD increases. This
means our AD curve is downward-sloping.
• Our AD curve holds constant G, T, E’ and P*.
We can express our AD curve as:
AD: Y = AD(E’P/P*, G, T)
• Changes in G, T, E’ and P* will shift our AD
curve. A rise in G and P* shift the AD right. A
rise in T and E’ shift the AD left.
• [Note: Be sure that you understand why!]
AS under fixed rates
• Our aggregate supply
relation is the same
as before:
AS: P = Pe (1+μ) F(1(Y/L), z)
• All of these variables
are the same as
previously discussed.
• Let’s say P* dropped,
shifting AD left.
Medium-run dynamic under fixed
rates
• Let’s say we start at A,
with Y < Yn. What moves
us back to Yn?
• Same dynamic as before,
excessive unemployment
leads to lower W, so P
drops as W drops.
• As P drops, e drops, and
NX rises, shifting us down
and along AD to B.
Medium-run dynamic
• However this requires wages being flexible. In
many countries, wages are slow to adjust (long
contracts, unions, etc). This could mean that we
would have a long period of low Y/ high u before
we move back to natural rate of Y.
• Is there an easier/faster way to restore
equilibrium? Previously, we would use G to shift
AD out and move us back to equilibrium faster.
Medium-run dynamic
• Instead of raising, G, the
government could lower
E. This would lead to a
drop in e and an increase
in the NX.
• The AD curve would shift
to the right when E
dropped, and so we move
from A to C.
• E adjusts faster than W
and P.
Medium-run dynamic
• But this means that the government has broken
its own fixed exchange rate. This act could
affect future credibility of the government in
fixing a new peg.
• Fixed exchange rates require a flexible labour
market in which wages can adjust quickly to
external shocks, such as to P*.
• If labour markets are slow to adjust and the
exchange rate is fixed, recessions could last.
Flexible exchange rates
• The interest parity condition requires that:
1 + it = (1 + i*t)Et/ Ee
• For a fixed expected future exchange rate
Ee and foreign interest rate i*, the current
exchange rate is a function of the
domestic interest rate:
Et = (1+ it) Ee / (1 + i*t)
• The higher is the domestic interest rate,
the higher is the exchange rate today.
Flexible exchange rates
• So holding constant future E, the higher is i, the
higher is today’s E. How does this work?
• A higher i means that foreign investors will want
to buy Aust bonds. To do this, they will have to
buy A$, so this will raise today’s price of A$, E.
• Holding the future exchange rate fixed, raising
today’s E means that we expect a higher
depreciation of the A$ between today and the
future.
Flexible exchange rates
• In general the flexible exchange rate model is
too complex for this class, so we will just
concentrate on a few features of the equilibrium.
• One feature is what is called “exchange rate
overshooting”. This is the idea that exchange
will over-adjust in the short-term to changes in
monetary policy.
• Assume there is a long-term equilibrium in, Yn
and en to which the economy will return over the
medium-run.
Overshooting exchange rates
• Say the government wants to stimulate the
economy through an expansionary monetary
policy. The government lowers i in the short-run
(but will return to in in the medium-run).
• In the medium-run, P will now be lower in than
P*, and so to return to en, we have to have E
higher than expected before.
• But in order to have interest parity:
it = i*t – [Expected appreciation of A$]
• The A$ must appreciate during the medium-run!
Overshooting exchange rates
• So how can future exchange rates be lower than
expected before, but we have to experience an
appreciation between now and the future?
• Answer: Today’s exchange rate has to
depreciate by even more, so that there is room
for the A$ to appreciate.
• So an expansionary monetary policy will cause
exchange rates today to drop so far that they
rise in the future.