Exchange Rates

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C h a p t e r 1 8
Exchange Rates
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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.

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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 e denote the nominal exchange rate between
  RMBs and dollars.

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Example Chinese Yuan
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Different Currencies and Exchange Rates
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Different Currencies and Exchange Rates
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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.

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Purchasing-Power Parity
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Purchasing-Power Parity
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Purchasing-Power Parity
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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.

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Purchasing-Power Parity

• The PPP Condition and the Real Exchange Rate
• 1/P e(1/Pf)
• quantity of goods that can be bought in U.S.
• quantity of goods that can be bought in
  China

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Purchasing-Power Parity

• purchasing-power parity
• e Pf/P
• nominal exchange rate
• ratio of foreign price to home price

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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.

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Purchasing-Power Parity

• The PPP Condition and the Real Exchange Rate
• real exchange rate (e/ 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).

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Purchasing-Power Parity

• The Relative PPP Condition
• The PPP condition says that the nominal exchange
  rate, e, equals the price ratio, Pf/P
• e Pf/ P
• real exchange rate e/(Pf/P)

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Purchasing-Power Parity

• The Relative PPP Condition
• growth rate of Pf/P ?Pf/Pf - ?P/P
• growth rate of Pf/P pf - p
• growth rate of real exchange rate
• ?e/e - (pf - p )

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Purchasing-Power Parity

• The Relative PPP Condition
• purchasing-power parity, relative form
• ?e/e pf - p
• growth rate of nominal exchange rate
• foreign inflation rate- home inflation rate

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Purchasing-Power Parity
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Purchasing-Power Parity
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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 et(1if)/et1

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Interest-Rate Parity

• 1i et(1if)/et1
• return on holding U.S. bond
• return on using exchange market and holding
  Chinese bond

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Interest-Rate Parity

• 1if (1 i) (et1/et )
• The growth rate of the nominal exchange rate is
• ?et/et (e t1- e t)/et
• ?et/et (e t1/et )- 1
• 1 i f (1 i)(1 ?et/e t)

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Interest-Rate Parity

• i f - i ?et/et
• interest-rate differential
• growth rate of nominal exchange rate
• i f - i ?(et/et)e
• ?e/e pf- p

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Interest-Rate Parity

• In terms as expected rates of change
• ?(et/et)e (pf)e-pe
• if - i (pf)e-pe
• interest-rate differential
• difference in expected inflation rates
• if - (pf)e i- pe
• foreign expected real interest rate
• home expected real interest rate

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Interest-Rate Parity

• real exchange rate e/(Pf/P)
• If it is smaller than 1
• The expected growth rate of the nominal exchange
  rate, (?et/et) e , must be greater than the
  expected growth of Pf/P, which equals the
  difference between the expected inflation rates,
  (pf)e - pe

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Interest-Rate Parity

• Instead of the equality in equation we have the
  inequality
• ?(et/et)egt (pf)e- pe
• If we substitute this inequality into the
  interest-rate parity condition in equation
• if - i gt (pf)e- pe

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Interest-Rate Parity

• if - (pf)egt i- p
• foreign expected real interest rate
• gt 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.

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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, e, between their
  currency and the U.S. dollar.
• Each countrys central bank stood ready to buy or
  sell its currency at the rate of e units per U.S.
  dollar.

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Fixed Exchange Rates

• Purchasing Power Parity Under Fixed Exchange
  Rates
• e Pf/P
• Pf eP
• if the nominal exchange rate, e, is fixed,
• pf p

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Fixed Exchange Rates

• Purchasing Power Parity Under Fixed Exchange
  Rates
• i f - i ?et/et
• Under fixed exchange rates
• if i

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Fixed Exchange Rates

• The Nominal Quantity of Money Under Fixed
  Exchange Rates
• Mf Pf L(Yf,if)
• Pf eP.
• Mf e P L( Yf, i)

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Fixed Exchange Rates
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Fixed Exchange Rates

• Two possible results of increasing M under
• fixed exchange rate regime
• The decline of the international reserves, even
  devaluation.
• Trade barriers to limit free trade.

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Fixed Exchange Rates

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

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Fixed Exchange Rates

• Devaluation and Revaluation
• An appreciation of the Chinese currencyan
  increase in 1/e, the number of dollars that
  exchange for each yuan is called a revaluation.

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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, e, is not a
  fixed number. Because of adjustments of e in a
  flexible-rate regime, Pf need not move in
  lockstep with P even if the absolute PPP
  condition always holds.

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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.

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