Macroeconomics Chapter 181 Exchange Rates C h a p t e r 1 8

Macroeconomics Chapter 18 1

Exchange Rates

C h a p t e r 1 8

Macroeconomics Chapter 18 2

Different Currencies and Exchange Rates

Each country issues and uses its own currency, instead of using a common currency.

To keep things simple, pretend that there are only two countries.

Think of the home country as the United States and the foreign country as China.

The China nominal quantity of money, Mf, is measured in RMB. The U.S. nominal quantity of money, M, is in Dollars.

Macroeconomics Chapter 18 3

Different Currencies and Exchange Rates

Exchange market, on which participants trade the currency of one country for that of another.

the nominal exchange rate is the number of RMBs received for each dollar.

Let ε denote the nominal exchange rate between RMBs and dollars.

Macroeconomics Chapter 18 4

Example: Chinese Yuan

100美元

0. 00

200. 00

400. 00

600. 00

800. 00

1000. 00

Macroeconomics Chapter 18 5

Macroeconomics Chapter 18 6

Different Currencies and Exchange Rates

Macroeconomics Chapter 18 7

Different Currencies and Exchange Rates

Macroeconomics Chapter 18 8

Purchasing-Power Parity

Sometimes countries allow their nominal exchange rates to move freely in response to market forces. These systems are called flexible exchange rates.

In other circumstances, countries try to maintain a constant nominal exchange rate with respect to another currency, often the U.S. dollar. These systems are called fixed exchange rates.

Macroeconomics Chapter 18 9

Purchasing-Power Parity

Macroeconomics Chapter 18 10

Purchasing-Power Parity

Macroeconomics Chapter 18 11

Purchasing-Power Parity

Macroeconomics Chapter 18 12

Purchasing-Power Parity

The PPP Condition and the Real Exchange Rate The U.S. price level, P, is measured in dollars

per unit of goods. We denote the Chinese price level (or foreign price level) by Pf , measured in RMB per unit of goods.

Assume that the goods produced and used in both countries are physically identical.

We also ignore any transportation or other transaction costs for buying and selling goods in the two countries.

Macroeconomics Chapter 18 13

Purchasing-Power Parity The PPP Condition and the Real

Exchange Rate

1/P = ε·(1/Pf)

quantity of goods that can be bought in U.S. = quantity of goods that can be bought in China

Macroeconomics Chapter 18 14

Purchasing-Power Parity

purchasing-power parity

ε = Pf/P

nominal exchange rate = ratio of foreign price to home

price

Macroeconomics Chapter 18 15

Purchasing-Power Parity

The PPP Condition and the Real Exchange Rate purchasing-power parity (PPP). This condition means that the

purchasing power in terms of goods for dollars (or RMB) is the same regardless of whether households buy goods in the United States or China.

Macroeconomics Chapter 18 16

Purchasing-Power Parity

什么时候 PPP Condition 不一定成立？

各国产品不一样。（想一想，上海的麦当劳和波恩的麦当劳产品真的是一样的吗？）

非贸易商品的存在。（例如，住房）

Macroeconomics Chapter 18 17

Purchasing-Power Parity

The PPP Condition and the Real Exchange Rate real exchange rate= (ε/Pf) / (1/P)

real exchange rate is the ratio of goods that can be bought in China (say, with $1) to goods that can be bought in the United States (also with $1).

Macroeconomics Chapter 18 18

Macroeconomics Chapter 18 19

Purchasing-Power Parity

GDP的国际比较

中国 2004年的名义人均 GDP是 12336元按照 1 ： 8 计算，折合 1542美元这样的计算有什么问题？

如果考虑 PPP呢？这样的计算又有什么问题？

Macroeconomics Chapter 18 20

Purchasing-Power Parity

The PPP Condition in long run ε = Pf/ P

real exchange rate= ε/(Pf/P) 1

预测一下人民币汇率的走势： 4.3 1 ε 下降 Pf/P 上升

Macroeconomics Chapter 18 21

Purchasing-Power Parity

growth rate of Pf/P = ∆Pf/Pf − ∆P/P

growth rate of Pf/P = πf − π

growth rate of real exchange rate = ∆ε/ε − (πf − π ) E.g. 30years from 4.3 to 1 implies -4.8%

Macroeconomics Chapter 18 22

Purchasing-Power Parity

The Relative PPP Condition purchasing-power parity, relative form:

∆ε/ε = πf − π

growth rate of nominal exchange rate = foreign inflation rate− home

inflation rate

Macroeconomics Chapter 18 23

Purchasing-Power Parity

Macroeconomics Chapter 18 24

Purchasing-Power Parity

Macroeconomics Chapter 18 25

Interest-Rate Parity

Option 1: Hold U.S. bond dollars received in year t+ 1 = 1 + i

Option 2: Use exchange market and hold Chinese bond dollars received in year t+ 1 =

εt·(1+if)/εt+1

Macroeconomics Chapter 18 26

Interest-Rate Parity

1+i =εt·(1+if)/εt+1

return on holding U.S. bond = return on using exchange market

and holding Chinese bond

Macroeconomics Chapter 18 27

Interest-Rate Parity

1+if = (1+ i) · (εt+1/εt )

The growth rate of the nominal exchange rate is ∆εt/εt = (ε t+1− ε t)/εt

∆εt/εt = (ε t+1/εt )− 1

1 + i f = (1 + i)·(1 + ∆εt/ε t)

Macroeconomics Chapter 18 28

Interest-Rate Parity

i f − i = ∆εt/εt

interest-rate differential= growth rate of nominal exchange rate

i f − i = ∆(εt/εt)e

Macroeconomics Chapter 18 29

Interest-Rate Parity

Real interest-rate

∆ε/ε = πf− π

In terms as expected rates of change:

∆(εt/εt)e= (πf)e−πe

Macroeconomics Chapter 18 30

Interest-Rate Parity

if − i = (πf)e−πe

interest-rate differential = difference in expected inflation rates

if − (πf)e= i− πe

foreign expected real interest rate = home expected real interest rate

Macroeconomics Chapter 18 31

Interest-Rate Parity

real exchange rate= ε/(Pf/P) If it is smaller than 1: The expected growth rate of the

nominal exchange rate, (∆εt/εt) e , must be greater than the expected growth of Pf/P, which equals the difference between the expected inflation rates, (πf)e − πe

Macroeconomics Chapter 18 32

Interest-Rate Parity

Instead of the equality in equation we have the inequality:∆(εt/εt)e> (πf)e− πe

If we substitute this inequality into the interest-rate parity condition in equation

if − i > (πf)e− πe

Macroeconomics Chapter 18 33

Interest-Rate Parity

if − (πf)e> i− πforeign expected real interest rate > home expected real interest rate

i.e., we expect that the price level in those countries whose real exchange rate smaller than 1 will decreases.

Macroeconomics Chapter 18 34

Fixed Exchange Rates

The fixed-exchange-rate regime that applied to most advanced countries from World War II until the early 1970s was called the Bretton Woods

Under this system, the participating countries established narrow bands within which they pegged the nominal exchange rate, ε, between their currency and the U.S. dollar.

Each country’s central bank stood ready to buy or sell its currency at the rate of ε units per U.S. dollar.

Macroeconomics Chapter 18 35

Fixed Exchange Rates

Purchasing Power Parity Under Fixed Exchange Rates ε = Pf/P Pf = εP if the nominal exchange rate, ε, is

fixed, πf = π

Macroeconomics Chapter 18 36

Fixed Exchange Rates

Purchasing Power Parity Under Fixed Exchange Rates i f − i = ∆εt/εt

Under fixed exchange rates: if = i

Macroeconomics Chapter 18 37

Fixed Exchange Rates

The Nominal Quantity of Money Under Fixed Exchange Rates

Mf = Pf· L(Yf,if)

Pf = εP.

Mf = ε P · L(Yf, i)

Macroeconomics Chapter 18 38

Fixed Exchange Rates

Macroeconomics Chapter 18 39

Fixed Exchange Rates

Two possible results of increasing M under

fixed exchange rate regime:

1. The decline of the international reserves, even devaluation.

2. Trade barriers to limit free trade.

Macroeconomics Chapter 18 40

Fixed Exchange Rates

a devaluation, which is a reduction in the value of RMB compared to the dollar.

Macroeconomics Chapter 18 41

Fixed Exchange Rates

Devaluation and Revaluation An appreciation of the Chinese

currency—an increase in 1/ε, the number of dollars that exchange for each yuan— is called a revaluation.

Macroeconomics Chapter 18 42

Flexible Exchange Rates

Since the early 1970s, most advanced countries have allowed their currencies to vary more or less freely to clear the markets for foreign exchange.

The difference from the fixed-exchange-rate setup is that the nominal exchange rate, ε, is not a fixed number. Because of adjustments of ε in a flexible-rate regime, Pf need not move in lockstep with P even if the absolute PPP condition always holds.

Macroeconomics Chapter 18 43

Fixed and Flexible Exchange Rates: A Comparison

An extreme form of fixed nominal exchange rate is a common currency.

a fixed-exchange rate system precludes an independent monetary policy, at least in the long run.

Macroeconomics Chapter 18 44

Fixed and Flexible Exchange Rates: A Comparison

One advantage of a flexible nominal exchange rate is that it introduces an additional way to satisfy the PPP condition, Pf = εP

The independence of monetary policy under flexible exchange rates is not always desirable.

Macroeconomics Chapter 18 45

Extra: Mundell-Fleming Model

Open economy NX(e) is net export

e is the exchange rate

Small country r=rf

Fixed price

Macroeconomics Chapter 18 46

Extra: Mundell-Fleming Model

IS : r=rf Y=C(Y)+I(rf)+NX(e)

e

Y

Macroeconomics Chapter 18 47

Extra: Mundell-Fleming Model

LM: M/P=L(Y,rf)

e

Y

r

Y

r=rf

Macroeconomics Chapter 18 48

Extra: Mundell-Fleming Model

IS : r=rf Y=C(Y)+I(rf)+NX(e) LM: M/P=L(Y,rf) e

Y

Macroeconomics Chapter 18 49

Extra: Mundell-Fleming Model with floating exchange rate

LM: M/P=L(Y,rf) M increases

e

Y

Macroeconomics Chapter 18 50

Extra: Mundell-Fleming Model with floating exchange rate

M increases

Closed economy: r decreases and Investment rises. Y increases.

Open economy: r is fixed, hence, capital flows out. e decreases and net export rises. Y increases.

Macroeconomics Chapter 18 51

Extra: Mundell-Fleming Model with fixed exchange rate

e=e*

e

Y

Macroeconomics Chapter 18 52

Extra: Mundell-Fleming Model with fixed exchange rate

e=e* M increases ?? e

Y

Macroeconomics Chapter 18 53

Extra: Mundell-Fleming Model with fixed exchange rate

Summary

Floating Fixed

Y e NX Y e NX

Monetary policy M