• 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.

Focus on PPP

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.

• 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.

PPP in practice

Is there McParity?

Cross-country comparison of Big Mac prices:– prices of Big Macs in 41 countries (published in the

Economist (1986- ))

advantages:homogeneous good, quality control over inputs

disadvantages: imperfect competition (strategic pricing), are inputs the same? (nontradables?), government regulations may affect product pricing

Empirical Evidence on Prices and Exchange Rates

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

Isra

el

Den

mar

k

Japa

n

Swed

en

Uni

ted

Stat

es

Chi

le

Ger

man

y

Mex

ico

Spai

n

Sing

apor

e

New

Zea

land

Aus

tral

ia

Cze

ch R

ep

Sout

h A

fric

a

Pola

nd

Chi

na

Source: The Economist, April 29, 2000

Sw

itze

rlan

d

Bri

tain

Sou

th K

orea

Fra

nce

Arg

enti

na

Eur

o A

rea

Tai

wan

Ital

y

Can

ada

Indo

nesi

a

Bra

zil

Tha

ilan

d

Hon

g K

ong

Rus

sia

Hun

gary

Mal

aysi

a

Ratio of Big Mac Prices in US$ Relative to U.S. PriceU.S. Price is $2.51/Big Mac

Researchers have investigated whether current deviations for Big Mac Parity help forecast future changes in exchange rates.

Answer: Yes, sort of. The Economist claims that the Big Mac method predicted the depreciation in the Euro following its introduction in 1999.

Persistent deviations from PPPA manager may really only care about the duration of deviations from PPP…do they last several months? Years? Forever?

Key question: Is there mean reversion in the real exchange rate; does it tend to go back to q=1?

Let’s look at a graph of the real exchange rate, which also clearly indicates the deviation from PPP

The Real $/DM Exchange Rate

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.41973

1974

1975

1976

1978

1979

1980

1981

1983

1984

1985

1986

1988

1989

1990

1991

1993

Mean reversion: RER tends to return to q=1

Empirical Evidence on Prices and Exchange Rates

• A parity condition can be viewed as a 45° line passing through the origin with the Left Hand Side (LHS) and Right Hand Side (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.

Regression test of relative PPP

• If relative PPP true, s$/peso = pUS – pmex

• This is expressed in % changes• Run regression of the form:• s$/peso,t = + ( pUS,t – pmex,t) + t

Regression test of relative PPP means testing the “null hypothesis” =0, =1.

Remember: we may reject or fail to reject the null hypothesis. We are not allowed to say we accept it!

Test for US-Germany: Quarterly data, 1973-93.

Estimates, with standard errors in parentheses: = 0.005 (se=0.010) = 0.50 (se=1.05) R2 = 0.003

Null hypothesis: PPP true: =0, =1.

Construct t-statistic; if absolute value of t < 2, cannot reject null hypothesis.

t = (estimate-true value under null)/se

Test =0: t = (.005 – 0)/0.01 = 0.50 cannot reject

Test =1: t = (0.50-1)/1.05 = -0.476 cannot reject

Conclusion: These data do not reject relative PPP for US-Germany over this period. But…we will see that the data can’t reject the alternative hypothesis that =0, =0 either!

Alternative hypothesis: exchange rate changes are completely unrelated to inflation differentials: =0, =0

Construct the t-statistics:

=0: t = (.005 – 0)/0.01 = 0.50 cannot reject=0: t = (0.50-0)/1.05 = 0.476 cannot reject

The 95% confidence interval for is the estimate plus/minus two standard errors:

0.50 – 2(1.05) < < 0.50 + 2(1.05)-1.60 <

These data are very uninformative about

Quarterly Deviations from Relative PPPCPI: Germany and the United States, 1973-1999

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999

(US-German)Inflation

Spot Rate Changes

= 0.003 = 0.15 R2 = 0.003 N = 107 (0.007) (0.83) D–W = 1.83

% D

evia

tion

s

AverageInflation

Difference

More Empirical Evidence on PPP

• During a hyperinflation period, even the demanding regression-style test tends to support PPP. This means: fails to reject PPP, while not failing to reject =0, =0. – But, this is mainly due to the fact that monetary

influences on prices completely dominate “real” influences on product prices.

More Empirical Evidence on PPP

• 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. This long-run tendency is called mean reversion.

• Definition: A variable follows a random walk if upward and downward movements are always equally likely; if the future path of the variable is completely unpredictable from past information.

Empirical Evidence onPrices 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.

Empirical Evidence onPrices 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.

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.

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.

The covered interest parity diagram

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International Financial and Exchange Rate Adjustments

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The interdependence of the parity conditions

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Incentive to borrow in pounds and invest in dollars

Incentive to borrow in dollars and invest in pounds

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