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 havee = 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.