Parity Conditions in International Finance

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• Parity Conditions in International Finance
• (Purchasing Power Parity)
• (Shapiro Chapter 4)

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• Purchasing power parity (PPP)
• Fisher effect (FE)
• The International Fisher Effect (IFE)
• Interest rate parity theory (FE)
• Forward rates as unbiased predictors of future
  spot rates (UFR)

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Purchasing Power Parity (PPP)

• A concept regarding the equilibrium value of a
  currency based upon its purchasing power in
  different countries
• General idea is that prices in different
  countries once converted to a common currency
  should be equal
• Condition on prices of goods that would preclude
  moving goods from one country to another to
  capitalize on price differences

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• Three concepts of PPP are used
• The Law of One Price for individual goods
• Absolute PPP for general price levels
• Relative PPP for changes in the general price
  level (inflation rates)

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The law of one price

• Equivalent assets sell for the same price
• Pd price of an asset in domestic currency
• Pf price of the same asset in foreign currency
• Pd / Pf sd/f Û Pd Pf sd/f
• (note e0 sd/f )
• seldom holds for nontraded assets
• may not hold when there are market frictions
• cant be used to compare assets that vary in
  quality

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An example of the law of one priceThe world
price of gold

• Suppose P 500/oz in New York
• P 550/oz in Berlin
• The law of one price requires
• P /P s/
• Þ (500/oz)/(550/oz) .91/
• If this relation does not hold, then there is an
  opportunity to lock in a riskless arbitrage
  profit.

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Big Mac Index

• Economists Big Mac PPP
• For the Big Mac price in the US was 2.49 and the
  price abroad ranged from 3.81 in Switzerland to
  about 0.78 in Argentina.
• EX
• Big Mac in China costs Yuan 10.50
• Big Mac in US costs 2.49
• Implied PPP exchange rate
• The Yuan was 49 undervalued on April 23, 2002
• (4.22-8.28)/8.28-0.4903 or -49.03

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• Whether PPP can hold may depend on the commodity
  in question
• Consider differences in prices of Coca-Cola sold
  around the world - or Duracell batteries or the
  price of a room at the Hilton Hotel
• Other factors that affect local prices
• Production inputs
• Tradability of the product
• Durability of the product
• Homogeneity of the product
• Substitutes
• .

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Absolute Purchasing Power Parity

• Example
• Let CPIUS PUS and CPIUK PUK
• PUS S(/) x PUK
• S(/) PUS/PUK
• This is referred to as the Absolute PPP

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Problems with Absolute Purchasing Power Parity

• Simplistic theory of the exchange rate
• Exchange rate is a function of not just the
  relative price level
• Price level in countries is a function of the
  consumption basked in that country
• PPP may not hold if prices of goods consumed only
  in one country increase
• Northern Europe consumes more heating oil that
  the Mediterranean countries
• If the price of heating oil increases the price
  level in Northern Europe will increase
• PPP may not hold since the price level in the
  Mediterranean countries will not also rise
  similarly given that they do not consume as much
  heating oil

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Alternative form of the PPP - Relative PPP

• Absolute PPP P S(/) x P
• ? S (/) (1IUS) / (1IUK) 1
  ? S (/)? e0
• ? S (/) (IUS - IUK) / (1IUK)
• E.g. If inflation in the US is 5 and that in the
  UK is 10 then the exchange rate S(/) should
  depreciate by about 4.5
• ? S (/) ? e0 (1.05 - 1.10) / 1.10
  -0.045 or -4.5
• Or ? S (/) IUS IUK 0.05-0.1 -0.05 -5
• the pound should depreciate by about 5

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Important Points

• If U.S. inflation gt U.K. inflation, the should
  appreciate against the , i.e. the should
  weaken
• If U.K. inflation gt U.S. inflation, the should
  depreciate against the , i.e. the should
  strengthen
• If U.K. inflation U.S. inflation, there should
  be no change in the exchange rate.

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• Or
• EX If the United States and Switzerland are
  running annual inflation rates of 5 and 3,
  respectively, and the spot rate is SFr 1 0.75,
  the PPP rate (exchange rate) for the Swiss franc
  in three years should be

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• Ex Between 1980 and 1985, the / exchange rate
  moved from 226.63/ to 93.96. During this same
  15-year period, the consumer price index (CPI) in
  Japan rose from 91.0 to 119.2 and the U.S. CPI
  rose from 82.4 to 152.4. If PPP had held over
  this period, what would the / exchange rate
  have been in 1995?
• Ans 160.51/

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Reasons for departure from relative PPP

• Traded goods and substitutes
• If the price of Japanese pearls increases and
  there is no substitute for this in the US, US
  consumers may still import these pearls and the
  demand for yen may be unaffected so the exchange
  rate may not adjust to reflect this
• Non-traded good
• If the price of land in the US increases, this
  may not affect relative exchange rates
• Haircuts cost 10 times as much in the developed
  world as in the developing world.
• Other factors affect exchange rates besides
  relative inflation levels Shipping costs as well
  as tariffs and quotas can lead to deviations from
  PPP. Transaction costs and restrictions on trade

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Empirical evidence on PPP

• Data does not in general support PPP especially
  the nominal version of PPP
• Empirical evidence supports PPP during
  hyperinflationary periods as in Germany during
  the 1920s when the exchange rate movement is
  dominated by changes in inflation
• A 50 overvaluation of the real rate relative to
  PPP takes 3-5 years to be reduced to half
• Obstfeld (1995) looks at exchange rate changes
  and inflation for 22 OECD countries over 20 years
  (1973-93) and finds that long run changes in
  exchange rates are related to inflation