14
EXCHANGE RATES and
Purchasing Power Parity
(PPP)
(Chap. 14, section 1; plus pp. 525-527; 529)
1
Exchange Rates and
Prices in the Long Run
2
Money, Prices, and
Exchange Rates in the
Long Run
3
The Monetary
Approach
4
Money, Interest, and
Prices in the Long Run
5
Monetary Regimes and
Exchange Rate
Regimes
6
Conclusions
Motivation
• On July 26, 2008, the price of 1 big Mac is 280 Japanese
Yen in Japan, 2.29 pounds in U.K., 3.37 Euros in Euro
zone, and about $3 in the U.S.
• Should these price levels tell us something about spot
exchange rates?
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LEARNING OBJECTIVES
1. Exchange Rates and Prices in the Long Run
•
•
•
Understand long-run arbitrage in goods market
Understand law of one price (LOOP) and
purchasing power parity (PPP)
Understand real exchange rates
 Real exchange rate and relationship to PPP
 Real appreciations and real depreciations
 Overvaluations and undervaluations
•
•
Understand PPP as it relates to both price levels
P and rates of change of prices (inflation, p)
Understand how and why PPP works in the long
run but not in the short run
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Introduction to Exchange Rates and Prices
• Consider the prices and exchange rates in the U.S. and
Canada:
 Prices of a representative basket of goods (CPI basket) in
U.S. and Canada
 1970 PCAN= C$100
 1970 PUS=$100
1990
1990
PCAN=C$392
PUS=$336
 Exchange rates (C$/$)
 1970 EC$/$=1
1990
EC$/$=1.16
 Prices of baskets in common currency (U.S. $)
 Canada
1990
$338 (= C$392/1.16)
• Is it coincidence that the exchange rate and price level
adjusted in this way?
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Introduction to Exchange Rates and Prices
• Arbitrage
 Chapter 13: applied to the foreign exchange market
 Chapter 14: applied to the goods market
• The prices of goods and services in different countries is
related to the exchange rate.
• When the relative prices of goods changes, the exchange
rate adjusts to reflect this change.
• The monetary approach to exchange rates is a long run
theory linking money, exchange rates, prices, and interest
rates.
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The Law of One Price
• Key assumption – frictionless trade




No transaction costs
No barriers to trade
Identical goods in each location
No barriers to price adjustment
• General idea:
 Prices must be equal in all locations for any good when
expressed in a common currency.
 Otherwise, there would be a profit opportunity from buying
low and selling high.
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The Law of One Price
• Consider a single good, g, in 2 different markets.
• The law of one price (LOOP) states that the price of the
good in each market must be the same.
• This is a microeconomic concept, applied to a single good,
g.
http://www.x-rates.com/
• Relative price ratio for g:
g
E / US
q
relative price
of good g
in Europe
versus U.S.
 (E$ /€ P ) / P
g
E
g
US
European price U.S. price
of good g
of good g
expressed
expressed
in $
in $
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The Law of One Price
• If LOOP holds then:
This means the price of good g is the same in Europe and
in the U.S.
• What if LOOP doesn’t hold?
 Goods less expensive in U.S.
 Goods less expensive in Europe
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Purchasing Power Parity
• Macroeconomic counterpart to LOOP.
 If LOOP holds for every good in CPI basket, then the prices
of the entire baskets must be the same in each locations.
• The purchasing power parity (PPP) theory states that
these overall price levels in each market must be the
same.
• Relative price level ratio:
qE / US  (E$ /€ PE ) / PUS
relative price
of basket
in Europe
versus U.S.
European price U.S. price
of basket
of basket
expressed
expressed
in $
in $
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The Real Exchange Rate
• The relative price level ratio q is an important concept.
It is called the real exchange rate
qE / US  (E$ /€ PE ) / PUS
relative price
of basket
in Europe
versus U.S.
European price U.S. price
of basket
of basket
expressed
expressed
in $
in $
• The real exchange rate has some terminology in common
with the nominal exchange rate.
 exchange rate E is the ratio at which currencies trade,
 Nominal
 Real exchange rate q is ratio at which goods baskets trade.
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The Real Exchange Rate
qE / US  (E$ /€ PE ) / PUS
relative price
of basket
in Europe
versus U.S.
European price U.S. price
of basket
of basket
expressed
expressed
in $
in $
•
• Changes in the real exchange rate:
 If the real exchange rate rises
 
more home goods are needed in exchange for foreign goods
 real depreciation.
 If the real exchange rate falls
 fewer home goods are needed in exchange for foreign goods
 real appreciation.
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Exercise 1
• If price increases in the U.S., other things equal,
there is a real depreciation for U.S. $. T/F?
• A: False. As PUS rises, U.S. goods become more
expensive. This corresponds to a real
appreciation.
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Exercise 2
• If the price decreases in Europe, other things
equal, there is a real appreciation for U.S. $. T/F?
• A: True. As PE decreases, European goods
become cheaper. This is a real depreciation for
Euros and a real appreciation for $.
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Exercise 3
• If there is a nominal appreciation for $, other
things equal, there is also a real appreciation for
$. T/F?
• A: True. A nominal appreciation means that 1 $ is
worth more Euros. Since 1 U.S. good is worth the
same number of $ (same for European good),
U.S. goods become more expensive. This is a
real appreciation.
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Purchasing Power Parity
• If PPP (Absolute PPP) holds then:
E$ /€ PE  PUS , or qE /US  1.
• This implies that a basket of goods purchased in two
countries should cost the same in a common currency


• Alternatively, under absolute PPP
E$ /€
exchange rate

PUS / PE
ratio of price levels
• Absolute PPP says that the real exchange rate = 1; or that
the spot exchange rate equals the relative price.
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Absolute PPP and the Real Exchange Rate
• What if absolute PPP does not hold?
 If the real exchange rate is above one (by x %)
 foreign (European) goods are relatively expensive
 foreign currency (the euro) is overvalued (by x %).
 If the real exchange rate is below one (by x %)
 foreign (European) goods are relatively cheap
 foreign currency (the euro) is undervalued (by x %t).
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Absolute PPP: Evidence
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Absolute PPP: Evidence
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Absolute PPP: Evidence
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Evidence on Absolute PPP
• According to absolute PPP, relative prices should be equal
to spot exchange rate.
• They are not equal, but move in the same direction
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Relative PPP, Inflation, and
Exchange Rate Depreciation
E$ / €  ( PUS / PE )qE / US
 log E$ / €  log PUS  log PE  log qE / US
  log E$ / €   log PUS   log PE
• Assumption: Δ log qE / US =0
 The rate of change in the exchange rate is the rate of
depreciation in the home currency (U.S. $):
 log E$ / € 
E$ / €,t
E$ / €,t

E$ / €,t 1  E$ / €,t
E$ / €,t
rate of depreciation
of the nominal exchange rate
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Relative PPP, Inflation, and
Exchange Rate Depreciation
 log PUS   log PE

PUS ,t
PUS ,t

PE ,t
PE ,t
 PUS ,t 1  PUS ,t


PUS ,t


 

rate of inflation in U.S.
p US ,t
 PE ,t 1  PE ,t

PE ,t




rate of inflation in Europe
p E ,t
• The rate of change in prices can be found by substituting
in the absolute PPP condition into the expression above.
• This is the home-foreign inflation differential:
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Relative PPP, Inflation, and
Exchange Rate Depreciation
• Relative PPP: This is another way to forecast the
exchange rate
E$ /€, t
E$ /€, t
 p US, t  p E, t
inflation differential
rate of depreciation
of the nominal exchange rate
• Relative PPP implies that the rate of depreciation of the nominal
exchange
rate equals the inflation differential.

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Relative PPP, Inflation, and
Exchange Rate Depreciation
• Relative PPP is derived from Absolute PPP
 If Absolute PPP holds (i.e. qE/US = 1) then Relative PPP (i.e.
ΔqE/US = 0) must hold also.
 But the converse need not be true: one could imagine a
case where a basket always costs a fixed amount more, say,
10% in common currency terms in one country than the
other—Absolute PPP fails, but Relative PPP holds.
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Relative PPP, Inflation, and
Exchange Rate Depreciation
• The PPP theory, whether in absolute of relative form,
suggests that price levels in different countries and
exchange rates are tightly linked, either in levels or in
rates of change.
 Where do price levels come from?
 Do the data support the theory of purchasing power parity?
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Evidence on Relative PPP: Long Run
• According to relative PPP, the percentage change in the
exchange rate should equal the inflation differential.
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Zimbabwe Hyperinflation
•
Factiva Search: Zimbabwe Central Banker Answers to Mugabe, Bible
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Zimbabwe Hyperinflation
• Background
 Inflation = 100,580% in Jan., 2008 and 8,000,000% in
June 2008. (source: WSJ)
 Starting in Nov. 2008, the monthly inflation rate is 13.2
billion percent (i.e. price doubles every 15.6 hours)
(source: wikipedia.org)
 Factories operating at 30% of capacity or less
 Unemployment at 80%
• The government's role
 Wage and price controls have created shortages.
 In addition, real income has decreased as the
government seized white-owned farms, disrupting
production.
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Hyperinflation: Other Countries
Yugoslav dinar of 1993.
Daily inflation rates of 100% in 1993.
Jan. 1994, 1 DM = 6 trillion dinars.
See also http://www.rogershermansociety.org/yugoslavia3.htm
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Hyperinflation: Other Countries
Hungary pengo of 1946.
Denomination: 100 million B-pengo = 1026 pengos
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Currency Reform
• Death of currencies
 Cases where countries have been or become “dollarized”
 Often a result of hyperinflation (in some developing
countries)
 Unilateral adoption of foreign currency
 No influence over monetary policy
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Evidence for Relative PPP: Hyperinflations
• Hyperinflation occurs when the monthly inflation rate
equals 50% or more over a sustained period.
 Relative PPP predicts the high inflation differentials should
lead to sharp depreciation in the currency.
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What Explains Deviations from PPP?
• Transaction costs
 Recent estimates suggest transportation costs may add about 20%
to the cost of goods moving internationally.
 Tariffs (and other policy barriers) may add another 10%, with
variation across goods and across countries.
 Further costs arise due to the time taken to ship goods.
• Nontraded goods
 Some goods are inherently nontradable;
 Most goods fall somewhere in between freely tradable and purely
nontradable.
 For example: a cup of coffee in a café. It includes some highly-traded
components (coffee beans, sugar) and some nontraded components
(the labor input of the barista).
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What Explains Deviations from PPP?
• Imperfect competition and legal obstacles
 Many goods are differentiated products, often with brand names,
copyrights, and legal protection.
 Firms can engage in price discrimination across countries, using
legal protection to prevent arbitrage
 E.g., if you try to import large quantities of a pharmaceuticals, and
resell them, you may hear from the firm’s lawyers.
• Price stickiness
 One of the most common assumptions of macroeconomics is that
prices are “sticky” prices in the short run.
 PPP assumes that arbitrage can force prices to adjust, but
adjustment will be slowed down by price stickiness.
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The Big Mac Index
HEADLINES
• For over 20 years The Economist newspaper has
used PPP to evaluate whether currencies are
undervalued or overvalued.
 Recall, home currency is x% overvalued/undervalued
when the home basket costs x% more/less than the
foreign basket.
 It is really a LOOP-based test because it relies on a
single good.
• The Economist uses a very simple “basket”
consisting of just one globally uniform,
standardized product: The Big Mac
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The Big Mac Index
HEADLINES
• Invented in 1986 by economics editor Pam
Woodall.
• Ask correspondents around the world to visit
McDonalds and get prices, then computes the
price in each location relative to the U.S.:
Big Mac
q
1 
“Big M ac index ” =
Big Mac
E $/local currencyPlocal
Big Mac
US
P
1
 The % deviation (+/–) from the U.S. price measures the
over/under valuation of the local currency based on the
burger basket.

 Updated every year:
http://www.economist.com/markets/Bigmac/
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The Big Mac Index
HEADLINES
• In 2004 The Economist tried using a new globally
uniform, standardized product.
Starbucks tall latte
“Big M ac index ” =
“tall-l atte index ” =
q Big Mac  1 
q tall latte  1 
Big Mac
E$/local currencyPlocal
Big Mac
US
P
tall latte
E $/local currencyPlocal
tall latte
US
P
1
1

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The Big Mac Index
HEADLINES
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Summary: PPP as a Theory of Exchange Rate
• In levels - Absolute PPP:
E$ /€
exchange rate

PUS / PE
ratio of price levels
• In rates of change: Relative PPP

E$ /€, t
E$ /€, t
 p US, t  p E, t
inflation differential
rate of depreciation
of the nominal exchange rate
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Chapter Outline
1. Exchange Rates and Prices in the Long Run:
Purchasing Power Parity and Goods Market
Equilibrium
 Goods Market Equilibrium



The Law of One Price (LOOP)
Purchasing Power Parity (PPP)
The Real Exchange Rate
 Implications of PPP



Absolute PPP and the Real Exchange Rate
Absolute PPP, Prices, and the Nominal Exchange Rate
Relative PPP, Inflation, and Exchange Rate Depreciation
 Empirical Evidence on PPP


How Slow is Convergence to PPP?
What Explains Deviations from PPP?
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Key Points
1. Purchasing power parity implies that the
exchange rate should equal the relative price
level in the two countries, and the real exchange
rate should equal 1.
2. Evidence for PPP is weak in the short run, but
more favorable in the long run.
 In the short run, deviations are common and changes
in the real exchange rate do occur.
 The failure of PPP in the short run is primarily the
result of price stickiness and market frictions and
imperfections that limit arbitrage.
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