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4-1
Purchasing Power Parity
 Purchasing Power Parity and Exchange Rate
Determination
 PPP Deviations and the Real Exchange Rate
 Evidence on PPP
Purchasing Power Parity
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$ / £
4-2
Purchasing Power Parity
 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$/£  PUK
 Absolute PPP requires that the consumption
baskets are identical across the two countries.
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4-4
Purchasing Power Parity and
Exchange Rate Determination
 The exchange rate between two currencies
should equal the ratio of the countries’ price
levels:
P$
S($/£) =
P£
For example, if an ounce of gold costs $300 in
the U.S. and £150 in the U.K., then the price of
one pound in terms of dollars should be:

P$ $300
S($/£) =
=
= $2/£
P£ £150
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Relative Purchasing Power Parity
Suppose absolute PPP is violated. Introduce K so that:
PUS, t +1 = K  S$/£, t +1  PUK, t +1
(a)
PUS, t = K  S$/£, t  PUK, t

(b)
%ΔpUS = %Δ s + %Δ pUK + %Δ s  %Δ pUK
S$/£, t 1  S$/£, t
PUS, t 1  PUS, t
PUK, t 1  PUK, t
%s 
, %pUS 
, %pUK 
S$/£, t
PUS, t
PUK, t
For small % changes, or when continuous rates are used, the crossproduct term %Δ s  %Δ pUK can be ignored.
% exchange rate = % U.S.prices – % U.K.prices
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Relative Purchasing Power Parity
 Note that %Δp = π, the rate of inflation
 Relative PPP states that the rate of change in
the exchange rate is equal to the differences in
the rates of inflation:
%Δs =
($ – £)
(1 + £ )
≈ $ – £
If U.S. inflation is 5% and U.K. inflation is 8%, the pound should
depreciate by 2.78% or around 3%.
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Ex-Ante PPP
 Ex-Ante PPP says that relative PPP will hold
in an expected value sense, i.e.
E (% st 1 )  E ( t 1 )  E (
*
t 1
)
Where E is the expectations operator signifying
that E(·) is an expected value.
Purchasing Power Parity
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.
4-8
PPP Deviations and the Real Exchange
Rate
St Pt
The real exchange rate is  t 
Pt
*
 The real exchange rate is calculated by correcting the
nominal exchange rate for the price levels in the two
countries.
If PPP holds then
Pt
St  *   t  1
Pt
 When PPP holds, the real exchange rate is constant.
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4 - 10
Real Exchange Rates
Purchasing Power Parity
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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4 - 12
The Big Mac PPP Standard
4 - 13
Evidence on PPP
 PPP probably doesn’t hold precisely in the real world
for a variety of reasons.
Haircuts cost 10 times as much in the developed world as in
the developing world.
 Film, on the other hand, is a highly standardized commodity
that is actively traded across borders.
 Shipping costs, as well as tariffs and quotas can lead to
deviations from PPP.
 Productivity differences in traded and non-traded goods.

 PPP-determined exchange rates still provide a valuable
benchmark.
How Large is China’s Economy
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Purchasing Power Parity
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.
4 - 15
Relaxing the
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
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:
yt =  0 + 1 xt + u t
 Parity holds when the data cannot reject a null
hypothesis where 0 = 0, 1 = 1, and the error
terms have classical properties.
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4 - 18
Some Terminology
 In the simple linear regression model,
where yt = 0 + 1xt + ut, we typically
refer to y as the
Dependent Variable, or
Left-Hand Side Variable, or
Explained Variable, or
Regressand
4 - 19
Some Terminology, cont.
 In the simple linear regression of y on x,
we typically refer to x as the
Independent Variable, or
Right-Hand Side Variable, or
Explanatory Variable, or
Regressor, or
Covariate, or
Control Variables
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A Simple Assumption
 The average value of u, the error term, in the
population is 0. That is,
 E(u) = 0
 This is not a restrictive assumption, since we
can always use 0 to normalize E(u) to 0
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OLS estimated slope is
n
ˆ1 
  x  x  y
i 1
i
i
n
 x  x 
i 1
i
 y
2
4 - 22
The Intercept Estimate
ˆ
ˆ
y   0  1 x ,
or
ˆ
ˆ
 0  y  1 x
4 - 23
Summary of OLS slope estimate
 The slope estimate is the sample
covariance between x and y divided by the
sample variance of x
 If x and y are positively correlated, the
slope will be positive
 If x and y are negatively correlated, the
slope will be negative
4 - 24
More OLS
 Intuitively, OLS is fitting a line through the
sample points such that the sum of squared
residuals is as small as possible, hence the term
least squares
 The residual, û, is an estimate of the error term,
u, and is the difference between the fitted line
(sample regression function) and the sample
point
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Sample regression line, sample data points
and the associated estimated error terms
y
.
y4
û4 {
yˆ  ˆ0  ˆ1 x
y3
y2
y1
û2 { .
.} û3
û1
}
.
x1
x2
x3
x4
x
Empirical Evidence on
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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 $27.00 at Amazon.de (Germany).
Empirical Evidence on
Prices and Exchange Rates
 To examine the relative PPP condition, we can
compare the exchange rate change to the
contemporaneous inflation differential:
Δst = 0 + 1 (Δp$ – ΔpDM)t + ut
 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).
4 - 27
Quarterly Deviations from Relative PPP
CPI: Germany and the United States, 1973-1999
0.20
 = 0.003  = 0.15 R2 = 0.003 N = 107
(0.007)
(0.83) D–W = 1.83
0.15
% Deviations
Spot Rate Changes
0.10
0.05
0.00
-0.05
-0.10
-0.15
Average
Inflation
Difference
(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 - 29
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.
Empirical Evidence on
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 - 31
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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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.
4 - 33
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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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.