Chapter 10
The Purchasing-Power Parity Principle
The Law of One Price
Absolute Form of the PPP Condition
The Relative Form of PPP
An Alternative Derivation of PPP
The Empirical Evidence on PPP
Reasons for Departures from PPP
Restrictions on Movement of Goods
Price Indexes and Nontraded Outputs
Statistical Problems of Evaluating PPP
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The Law of One Price
1. The Purchasing-Power Parity (PPP) Principle states a long-run connection
between inflation and exchange rates.
Definition: The idea that exchange rates are determined by the amounts of
different currencies required to purchase a representative bundle of goods. p.606.
2. The law of one price states the connection between exchange rates and commodity
prices.
(1) Definition: The law of one price states that in the absence of frictions such as
shipping costs, tariffs, and so on, the price of a product when converted into a
common currency such as the U.S. dollar, using the spot exchange rate, is the
same in every country.
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(2) For example:
(10.1)
pwheatUS = S($/￡) × pwheatUK ,
where pwheatUS is the dollar price of wheat in the United States,
pwheatUK is the pound price of wheat in Britain, and
S($/￡) × pwheatUK is the dollar equivalent price of wheat in Britain.
(3) When the law of one price does not hold, buying decisions help restore the
equality.
3. Rationale behind the law of one price
(1) Opportunity for profit: If there is enough of a price difference, people
(commodity arbitragers) will begin to take advantage of it by buying
commodities in the cheaper market and then shipping them to and selling them
in the more expensive market.
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Arbitragers cease their activities only when all
profitable opportunities have been exhausted, which means prices of the same
product in different markets are equal.
(2) Transportation costs are involved.
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Absolute Form of the PPP Condition
1. The Absolute Form of the PPP Condition
(1)
(10.2)
PUS = S($/￡) × PUK ,
where PUS is the costs of the basket of goods and services in the United
States in dollars, PUK is the costs of the same basket of goods and services
in Britain in pounds.
(2) the spot exchange rate in terms of the relative costs of the basket in the two
countries,
(10.3)
S($/￡) = PUS /PUK ,
For example: PUS = $1,000, PUK = ￡600, then S($/￡) should be $1.67/￡.
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2. The Pros and Cons of the absolute PPP
(1) The pros
◎ a simple explanation for changes in exchange rates
(2) The cons
◎ It’s difficult to test the validity of PPP, because different baskets of
goods are used in different countries for computing price indexes.
◎ Even if the law of one price holds for each individual good, price
indexes which depend on the weights attached to each good, will not
conform to the law of one price.
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The Relative Form of PPP
1. Some definitions
S($/￡)-dot is the percentage change in the spot exchange rate over a year,
PUS-dot is the percentage change in the price level (annual rate of inflation) in
the United States over a year
PUK-dot is the percentage change in the price level (annual rate of inflation) in
Britain over a year
For example: PUS-dot = (dP/dt) / P
2. The derivation of the relative PPP condition
(1) the absolute PPP holds at some point in time
(10.2)
PUS=S($/￡)×PUK
(2) at the end of 1 year,
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(10.4)
PUS×(1+PUS-dot)=S($/￡)×[1+S($/￡)-dot]×PUK×(1+PUK-dot)
The LHS is the price level in the United States after 1 year, written as the price
level in the United States at the beginning of the year, multiplied by 1 plus the
U.S. annual rate of inflation.
(3) (10.4) / (10.2)
(10.5)
(1+PUS-dot)=[1+S($/￡)-dot]×(1+PUK-dot)
(4) the relative PPP condition
(10.7)
S($/￡)-dot=(PUS-dot - PUK-dot)/(1+PUK-dot)
For example: PUS-dot = 5%, PUK-dot = 10%,
S($/￡)-dot = (5% - 10%) / (1+10%) = -4.5%
If U.S inflation is 5 percent and British inflation is 10 percent, then the
pound should depreciate at a rate of 4.5 percent.
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(5) The approximate form
(10.8)
S($/￡)-dot=PUS-dot - PUK-dot
◎ Equation (10.8) is a good (poor) approximation of equation (10.7) when
inflation is low (high).
3. The relative PPP condition is not necessarily violated by sales taxes or shipping
costs that makes prices higher than their static form PPP levels.
(1) For a given exchange rate and price level in Britain, U.S. prices are (1-) of
the British price level
(10.9)
PUS=S($/￡)×PUK×(1-)
After 1 year,
(10.10) PUS×(1+PUS-dot)=S($/￡)×[1+S($/
￡)-dot]×PUK×(1+PUK-dot)×(1-)
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(2) By (10.10) / (10.9), the relative PPP can hold even if the absolute PPP is
(consistently) violated,
S($/￡)-dot=(PUS-dot - PUK-dot)/(1+PUK-dot)
is the same equation as equation (10.5).
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An Alternative Derivation of PPP
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The Empirical Evidence on PPP
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Reasons for Departures from PPP – Restrictions on Movement of Goods
1. Transportation Costs
(1) The price difference must exceed the transportation costs in either direction
before arbitrage occurs.
(2) A possible deviation from the absolute PPP for commodities within a neutral
band that spans twice the costs.
2. Import Tariffs
(1) The effect of tariffs is different from the effect of transportation costs
(2) Tariffs do not have a symmetric effect. As a result of tariffs, prices can
move higher only in the country which has the import tariffs.
3. Quotas
(1) Quotas are limits on the amounts of different commodities that can be
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imported.
(2) Arbitragers are limited in their ability to narrow the gap of price difference.
Quotas provide a reason for persistent departures from PPP.
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Price Indexes and Nontraded Outputs
1. Untraded Outputs
(1) The “untraded” items can allow departures from PPP to persist when we
measure inflation from conventional market-bundle price indexes.
(2) Categories
◎ Immovable items such as land and buildings
◎ Highly perishable commodities such as fresh milk, eggs
◎ Services such as hotel accommodations and repairs
(3) The movement of buyers tends to keep prices in different countries in line
with each other.
2. The relative prices of traded versus nontraded items
(1) The relative prices of traded versus nontraded outputs will be similar
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between countries if producers within each country can move into the production
of the nontraded outputs when their prices are very high.
(2) If the prices of traded goods satisfy PPP, then so will the Prices of nontraded
items if they move with the prices of traded goods.
(3) Even when producers can move, the price adjustment can take a very long
time, during which departures from PPP can persist.
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Statistical Problems of Evaluating PPP
1. Estimation procedure
(1) Regression equation
(10.13) S($/￡)-dot=0+1(PUS-dot – PUK-dot)+
where  is the ex ante regression error.
(2) Testing for the validity of PPP
If PPP is valid, then in estimates of equation (10.13), 0 should be close to zero,
1 should be close to 1, and the ex post regression errors should be small.
2. Statistical Problems that can incorrect rejection of PPP
(1) Errors in measuring the inflation differential
◎ will bias regression coefficient (1) toward zero
(2) Simultaneous determination of the dependent and explanatory variables
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◎ will bias regression coefficient (1) toward zero
3. Literature Review
Data errors are responsible for rejection of PPP
(1) Rush and Husted (1985)
◎ departures from PPP are due to poor measurement of inflation
◎ Long-term trends should reduce or remove the unsystematic errors in
calculating inflation because the errors should average out and become less
important as the interval of measurement increases
◎ long-run PPP holds
(2) Hakkio (1984, 1990)
(3) Cointegration
◎ If two economic variables move together, then differences between
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them should be more stable than the original series.
◎ If the spot exchange rate and the inflation differential do move together
according to long-run PPP, then even though the two series may
temporarily move apart, they must move back eventually theough their
cointegration.
(4) Kim
◎ applied the cointegration technique
◎ annual data in CPI and WPI for Britain, France, Italy, Japan, and
Canada
◎ PPP holds except for Canada
(5) McNown and Wallace (1989)
◎ applied the cointegration technique
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◎ countries with very high inflation rates such as Israel, Argentina, Brazil,
Chile
◎ long-run PPP holds
4. Casual support of long-run PPP – Figure 10.1
A simple plot of the spot rate between the Mexican Peso and the U.S. dollar
versus the inflation differential between these countries
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