International Financial Markets
Prices and Policies
Second Edition ©2001
Richard M. Levich
4

McGraw Hill / Irwin
International Parity Conditions:
Purchasing Power Parity
4-2
Overview
 The Usefulness of Parity Conditions in
International Financial Markets

An Overview of International Parity Conditions in a
Perfect Capital Market
 Purchasing Power Parity in a Perfect Capital
Market
The Law of One Price
 Absolute Purchasing Power Parity
 Relative Purchasing Power Parity
 The Real Exchange Rate and Purchasing Power Parity

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4-3
Overview
 Relaxing the Perfect Capital Market Assumptions
Transaction Costs
 Taxes
 Uncertainty

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4-4
Overview
 Empirical Evidence on Prices and Exchange
Rates
Empirical Methods, or How to Test a Parity Condition
 Evidence on the Law of One Price
 Relative PPP: Evidence from Recent Quarterly Data
 Relative PPP: Evidence from Hyperinflationary
Economies
 Relative PPP: Evidence from Long-Run Data
 Empirical Tests of PPP: Is the Real Exchange Rate
Constant?
 Empirical Tests of PPP: The Final Word

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4-5
Overview
 Policy Matters - Private Enterprises
The Role of Parity Conditions for Management
Decisions
 Purchasing Power Parity and Managerial Decisions
 Purchasing Power Parity and Product Pricing
Decisions

 Policy Matters - Public Policymakers
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The Usefulness of Parity Conditions
4-6
in International Financial Markets
 Parity conditions can be thought of as
international financial “benchmarks” or “breakeven values”.

They are the defining points where the decisionmaker is indifferent between the two strategies
summarized by the two halves of the parity relation.
 Because parity conditions rely heavily on
arbitrage, a violation of parity often implies that a
profit opportunity or cost advantage is available
to the decision-maker.
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The Usefulness of Parity Conditions
4-7
in International Financial Markets
 We begin our analysis of international parity
conditions by assuming a perfect capital market
(PCM) setting:
no transaction costs
 no taxes
 complete certainty

 Based on the PCM assumptions, there are four
principle parity conditions in international
finance, of which only three are independent.
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The Usefulness of Parity Conditions
4-8
in International Financial Markets
1a. Purchasing Power Parity
Absolute Version
The price of a market basket of U.S. goods equals the
price of a market basket of foreign goods when
multiplied by the exchange rate.
PUS  PUK  Spot
Driven by arbitrage in goods.
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The Usefulness of Parity Conditions
4-9
in International Financial Markets
1b. Purchasing Power Parity
Relative Version
The percentage change in the exchange rate equals the
percentage change in U.S. goods prices less the
percentage change in foreign goods prices.
Spot  PUS  PUK
Driven by arbitrage in goods.
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The Usefulness of Parity Conditions
4 - 10
in International Financial Markets
2. Interest Rate Parity
The forward exchange rate premium equals
(approximately) the U.S. interest rate minus the foreign
interest rate.
F  S  S  i$  i£
Driven by arbitrage between the spot and forward
exchange rates, and money market interest rates.
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The Usefulness of Parity Conditions
4 - 11
in International Financial Markets
3a. Fisher Parities
Fisher Effect (Fisher Closed)
For a single economy, the nominal interest rate equals the
real interest rate plus the expected rate of inflation.

~
i$  r$  E PUS

Driven by desire to insulate the real interest against
expected inflation,
and arbitrage between real and nominal assets.
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The Usefulness of Parity Conditions
4 - 12
in International Financial Markets
3b. Fisher Parities
International Fisher Effect (Fisher Open)
For two economies, the U.S. interest rate minus the
foreign interest rate equals the expected percentage
change in the exchange rate.

~
i$  i£  E Spot

Driven by arbitrage in bonds denominated
in two currencies.
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The Usefulness of Parity Conditions
4 - 13
in International Financial Markets
4. Forward Rate Unbiased
Today’s forward premium (for delivery in n days)
equals the expected percentage change in the spot rate
(over the next n days).
Ft  St 
  
~
St  E St  n  St St
Driving force: Market players monitor the difference
between today’s forward rate (for delivery in n days)
and their expectation of the future spot rate
(n days from today).
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Purchasing Power Parity
4 - 14
in a Perfect Capital Market
 Purchasing power parity (PPP) is built on the
notion of arbitrage across goods markets and
the Law of One Price.
 The Law of One Price is the principle that in a
PCM setting, homogeneous goods will sell for
the same price in two markets, taking into
account the exchange rate.
PUS,wheat  PUK,wheat  S$ / £
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Purchasing Power Parity
4 - 15
in a Perfect Capital Market
 Let PUS and PUK represent the weighted average
price level for goods in the U.S. and U.K.
market baskets respectively.
 Absolute PPP predicts that these two price
measures will be equal after adjusting for the
exchange rate: PUS = S$/£  PUK
 Absolute PPP requires that the consumption
baskets are identical across the two countries.
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4 - 16
Purchasing Power Parity
in a Perfect Capital Market
Suppose absolute PPP is violated. Introduce K so that:
PUS, t +1 = K  S$/£, t +1  PUK, t +1
(a)
PUS, t = K  S$/£, t  PUK, t

where
s
p
P
= ,sp + PpUK P+ s, p pUK
S$/£, t US
1  S $/£, t
S$/£, t
(b)
US, t 1
US
PUS, t
UK, t 1
US, t
UK
 PUK, t
PUK, t
For small % changes, or when continuous rates are
used, the cross-product term s  pUK can be ignored.
% exchange rate = % U.S.prices – % U.K.prices
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Purchasing Power Parity
4 - 17
in a Perfect Capital Market
 Often, we are interested in the level of the
exchange rate that satisfies PPP.
 The PPP spot rate reestablishes PPP relative to
a base period. It is the exchange rate that would
just offset the relative inflation between a pair
of countries since the base period.
(a)

(b)
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S PPP,t 1  S$ / £, t
PUS, t 1 PUS, t
PUK, t 1 PUK, t
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Purchasing Power Parity
4 - 18
in a Perfect Capital Market
Example
Base period nominal exchange rate = $1.50/£
Prices of U.S. goods had risen by 8%
Prices of U.K. goods had risen by 4%
PPP spot rate = $1.50/£  1.08/1.04 = $1.5577/£
 A nominal exchange rate of $1.5577/£ would
reestablish PPP in comparison to the base period.
 Nominal exchange rates greater than $1.5577/£
represent £ “overvaluation” ($ undervaluation), while
rates less than $1.5577/£ represent $ “overvaluation”
(£ undervaluation).
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Purchasing Power Parity
4 - 19
in a Perfect Capital Market
PPP conditions do not imply anything
about causal linkages between prices and
exchange rates or vice versa.
 Both prices and exchange rates are jointly
determined by other variables in the economy.
 PPP is an equilibrium condition that must be
satisfied when the economy is at its long-term
equilibrium.
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Purchasing Power Parity
4 - 20
in a Perfect Capital Market
 Real magnitudes are constructed from nominal
magnitudes by adjusting for the appropriate
price levels or inflation rates.
Example
Nominal income in 2000 (base year) = $55,000/year
Real = $55,000/year = 220 market baskets/year
income $250/market basket
Nominal income in 2001 = $60,500/year
Real = $60,500/year = 224.07 mkt baskets/year
income $270/market basket
Index (2001) = 224.07/220 = 1.0185
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Purchasing Power Parity
4 - 21
in a Perfect Capital Market
 The real exchange rate is calculated by
correcting the nominal exchange rate for the
price levels in the two countries.
 When absolute PPP holds:
$1.50/£ =
$1,500/US good
£ 1,000/British good
.
LHS = 1 US good / British good
RHS
 When PPP holds, the real exchange rate is
constant.
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Purchasing Power Parity
4 - 22
in a Perfect Capital Market
 An index of the real exchange rate is defined as:
Spot (Real, t) =
Spot (Nominal, t)
Spot (PPP, t)
.
Example
Today’s spot exchange rate is $1.80/£
PPP spot rate is $1.50/£
Real exchange rate index = 1.80/1.50 = 1.20
 At 1.20, the £ is “overvalued” on a PPP basis.
1.0 British good can be exchanged for 1.2 U.S.
goods. So, sellers of British goods have “lost
competitiveness” on international markets.
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Relaxing the
4 - 23
Perfect Capital Market Assumptions
 Transaction Costs

Transport and menu costs lead to a neutral band
around the PPP line, within which it is not profitable
to execute arbitrage transactions.
 Taxes

Tariffs have an effect similar to transaction costs.
 Uncertainty

Arbitrageurs will seek a greater profit to compensate
for risks, thus leading to a wider band around the
PPP line before arbitrage becomes profitable.
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Empirical Evidence on
4 - 24
Prices and Exchange Rates
 A parity condition can be viewed as a 45° line
passing through the origin with the LHS and
RHS variables plotted on the x and y axes.
 Thus, parity conditions can be tested by running
the simple linear regression:
LHSt =  +  RHSt + t
 Parity holds when the data cannot reject a null
hypothesis where  = 0,  = 1, and the error
terms have classical properties.
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Empirical Evidence on
4 - 25
Prices and Exchange Rates
 In reality, seemingly “homogeneous” goods may
differ in a number of important respects which
undermine tests of the Law of One Price.
 One test of the Law of One Price is the Big Mac
index, which has been published annually in The
Economist since 1986.

It was devised as a light-hearted
guide to whether currencies are at
their “correct” level, based on PPP.
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Empirical Evidence on
4 - 26
Prices and Exchange Rates
1.60
1.40
Ratio of Big Mac Prices in US$ Relative to U.S. Price
U.S. Price is $2.51/Big Mac
1.20
1.00
0.80
0.60
0.40
0.20
Israel
Switzerland
Denmark
Britain
Japan
South Korea
Sweden
France
United States
Argentina
Chile
Euro Area
Germany
Taiwan
Mexico
Italy
Spain
Canada
Singapore
Indonesia
New Zealand
Brazil
Australia
Thailand
Czech Rep
Russia
South Africa
Hong Kong
Poland
Hungary
China
Malaysia
0.00
McGraw
Hill
/ Irwin April 29, 2000
Source:
The
Economist,
 2001 by The McGraw-Hill Companies, Inc. All rights reserved.
Empirical Evidence on
4 - 27
Prices and Exchange Rates
 With the rise of e-commerce, investigating the
Law of One Price becomes easier and violations
more puzzling.

A recent Wall Street Journal article highlighted the
case of a popular book that sold for $16.20 at
Amazon.com (U.S.), for $13.52 at Amazon.co.uk
(Britain), and for $27.00 at Amazon.de (Germany).
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Empirical Evidence on
4 - 28
Prices and Exchange Rates
 To examine the relative PPP condition, we can
compare the exchange rate change to the
contemporaneous inflation differential:
st =  +  (p$ – pDM)t + t
 It seems that PPP is a poor explanation of
exchange-rate changes on a period-by-period
basis.
 However, there is a tendency for PPP to reassert
itself as time passes (mean reversion).
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Quarterly Deviations from Relative PPP
4 - 29
CPI: Germany and the United States, 1973-1999
 = 0.003  = 0.15 R2 = 0.003 N = 107
(0.007)
(0.83) D–W = 1.83
0.20
0.15
% Deviations
Spot Rate Changes
0.10
0.05
0.00
-0.05
Average
Inflation
Difference
-0.10
-0.15
(US-German)
Inflation
1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999
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Empirical Evidence on
4 - 30
Prices and Exchange Rates
 During a hyperinflation period, even the
demanding regression-style test tends to support
PPP. This is due in some degree to dollarization.
 Long-run data indicated that the real exchange
rate did not evolve as a random walk, but
demonstrated a clear tendency to revert back to
its central value.
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Empirical Evidence on
4 - 31
Prices and Exchange Rates
 Note that the real exchange rate itself may not
be constant.
It may change on a permanent basis if a real shock
affected one country but not its trading partners.
 The Balassa-Samuelson hypothesis states that
countries that have experienced high productivity
gains, higher real income growth and higher real
incomes should have appreciating real exchange
rates.

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Empirical Evidence on
4 - 32
Prices and Exchange Rates
 Empirical tests confirm that ...
PPP is a poor descriptor of exchange rate behavior
in the short run, where the rates are quite volatile
and domestic prices are somewhat sticky.
 But in longer-run analysis, it appears that PPP offers
a reasonably good guide.

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4 - 33
Policy Matters - Private Enterprises
 If managers can identify the deviations from
parity that are growing larger or likely to
persist, then profit-maximizing decisions can be
made.
 Knowing that deviations from parity occur,
managers may adopt strategies that reduce their
exposure to the risks of such deviations.
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4 - 34
Policy Matters - Private Enterprises
 In a number of instances, international price
differentials in some commodities have been
both large and persistent.
 More interesting perhaps are the international
price differentials across “branded goods” like
McDonald’s Big Mac and The Economist,
whose prices are set by brand managers rather
than by market forces.
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4 - 35
Policy Matters - Public Policymakers
 Deviations from PPP, by definition, measure
changes in a country’s international
competitiveness, and reveal whether a currency
is overvalued or undervalued relative to a
simple standard.
 However, there are limitations on the usefulness
of PPP in policy decisions, as real
macroeconomic disturbances call for a change
in the real exchange rate.
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