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• 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
r$-r&
)4
1](&)/($
&)/($&)/($[4 &41 r
S
SF
A
B C
E
E
$r &)/($S
&r &)/($41F
International Financial and Exchange Rate Adjustments
D&
London money market& $
Forward market&
E$/&,fwd
D&,fwd
S&,fwd
Spot market&
E$/&
D&
S&
e0
Interest rate
S&
iL
New York money market
Interest rate
D$
S$
iNY
e0,fwd
The interdependence of the parity conditions
&$ rr
&)/($eS
(Uncovered)
interest parity
eUK
eUS PP
(Expected) PPP
Fisher
-open
Interest parity in the presence of transaction costs
r$-r&
)4
1](&)/($
&)/($&)/($[4 &41 r
S
SF
Unprofit
able
arbitr
age
Unprofit
able
arbitr
age
Incentive to borrow in pounds and invest in dollars
Incentive to borrow in dollars and invest in pounds
-0.005
0.005
Round-trip covered interest arbitrage
$ borrowing ----& investment
$0 $n
&0 &n
Br$
&)/($ askS
Ir&
&)/($ bidFn
$ borrowing ----& investment
&0 &nBr&
$0
Ir$ $n
&)/($ bidS
&)/($ askFn