Purchasing Power Parity

FIN 40500: International Finance

The relationship between exchange rates and prices starts with a very basic idea – ANY PRODUCT SHOULD COST THE SAME EVERYWHERE.

Suppose that a BMW sells for $40,000 in the United States and E 30,000 in Germany. The current exchange rate is $1.25 per Euro.

1 Borrow $37,500 and convert it to Euros at $1.25/Euro.

$37,500$1.25

= E 30,000

2 Buy a BMW in Germany for E30,000 and ship it back to the US.

3 Sell the car in the US for $40,000

500,2$)500,37$000,40($* ePP A 6.7% return

The act of arbitrage should eliminate the profit opportunity

Suppose that a BMW sells for $40,000 in the United States and E 30,000 in Germany. The current exchange rate is $1.25 per Euro.

*ePP

1 Increased demand for Euros should increase the price of a Euro.

2 Increased demand for BMWs in Germany should increase the German price .

3 Increased supply in US should drive down US price

The Law of One Price (LOOP) states that, given a domestic and foreign price, there is only one arbitrage free exchange rate

$40, 000= $1.33 per Euro

E30,000

As in the previous example, if the Euro is undervalued relative to LOOP, buy in Europe and sell in the US

if the Euro is overvalued relative to LOOP, buy in US and sell in Europe

*ePP

PeP *

The arbitrage free exchange rate is given by the ratio of prices

*P

Pe

Domestic Price

Foreign Price

Purchasing Power Parity (PPP) refers to the same concept as the Law of One Price, with specific prices replaced by general price indices

England

CPI = 195.0 (March 2006)

USA

CPI = 199.8 (March 2006)

PPP Exchange Rate

e = CPI (USA)CPI (UK)

199.8195.0

= = $1.025/L

Currently, the British Pound is trading at $1.786

$1.786 – $1.025$1.205

X 100 = 74%Is the British pound really overvalued by 74%?

One problem with this method had to do with how the CPI (in both the US and Britain) are calculated:

Suppose that we have two goods: BMWs and Computers

000,3$

000,40$

C

BMW

P

P

2006

250,2$

000,30$

C

BMW

P

P

1992

A price index is defined as a weighted average of individual good’s prices

500,21$000,3$5.000,40$5. PCPI2006

1992

CBMW PPCPI 5.5.

125,16$250,2$5.000,30$5. CPI

The prices are then normalized by a ‘base year’

1001992 CPI 3.133100125,16$

500,21$2006

CPI

We can correct for this by looking at PPP in relative terms

England

Inflation = 2.4%

(12 months)

USA

Inflation = 3.4%

(12 months)

*% e4.24.3

%1The dollar should depreciate by 1% against the pound

12 months ago, the British pound was trading at $1.904

$1.904 ( 1.01) = $1.923

$1.786 – $1.923$1.923

X 100 = -7.1% Now, it looks like the British pound is undervalued

Its easy to calculate currency values with the PPP method. Just compare inflation differentials with actual currency price changes!

What’s a better currency predictor, Coffee or Burgers?

The right answer is “neither!”

Country Exchange Rate (12/2003)

Inflation Differential

(US-Foreign)

PPP implied exchange rate

Actual Exchange Rate (12/2004)

JPY/USD .00928 3.5% .00960 .00963

EUR/USD 1.23 -.5% 1.224 1.34

GBP/USD 1.75 1.5% 1.776 1.93

CAD/USD .761 -.5% .757 .820

CHF/USD .791 1% .799 .872

AUD/USD .740 .5% .7437 .768

Overall, it turns out that inflation differentials alone provide a relatively poor forecast of the exchange rate

The exception would be countries with notoriously high inflation rates – Zimbabwe has a 585% annual inflation rate (2006). From 1998 to 2006, the Zimbabwe dollar fell from 24 per US dollar to 96,000!!!

Alternatively, we could estimate a forecasting equation using inflation differentials

*% ttte

Percentage change is exchange rate (dollars per foreign currency) – an increase is a depreciation

Parameters to be estimated – PPP implies that alpha is zero and beta is one

Typically, estimated values for beta are close to zero and statistically insignificant

The real exchange rate is the price level adjusted exchange rate. Its meant to capture the relative value of goods and services across countries

P

PeRER

*

Nominal Exchange Rate

Domestic CPI

Foreign CPI

By definition, the PPP explanation of exchange rates assumes that the real exchange rate is constant (and equal to one)

50

100

150

200

250

300

Jan-85 Jan-89 Jan-93 Jan-97

Yen/$ Real

Empirically, real exchange rates are clearly not constant. In fact, the correlation between real and nominal exchange rates is nearly one. This casts some serious doubt on PPP.

In reality, there are costs that will inhibit arbitrage of goods between countries. Let’s take another look at our BMW example.

000,30

000,40$* EP

P

Let’s assume that it costs $5,000 to ship a BMW from Germany to the US (12.5% of the purchase price)

0000,5$* ePP

For arbitrage to occur, it must be profitable

Buy in Germany, Sell in the US

Insert the appropriate prices and solve for the exchange rate

0000,5$000,30000,40 e 17.1$e

In reality, there are costs that will inhibit arbitrage of goods between countries. Let’s take another look at our BMW example.

000,30

000,40$* EP

P

Let’s assume that it costs $5,000 to ship a BMW from Germany to the US (12.5% of the purchase price)

0000,5$* PeP

We also have to consider the alternative strategy

Buy US, Sell in Germany

Insert the appropriate prices and solve for the exchange rate

0000,5$000,40000,30 e 50.1$e

In reality, there are costs that will inhibit arbitrage of goods between countries. Let’s take another look at our BMW example.

000,30

000,40$* EP

P

Let’s assume that it costs $5,000 to ship a BMW from Germany to the US (12.5% of the purchase price)

Time

e

17.1$

50.1$

The shipping cost provides a range within which arbitrage can’t occur

No Arbitrage Possible

Buy in US, Sell in Germany

Buy in Germany, Sell in US

This range represents a 24% change in the value of the dollar !!

A 24% band encompasses much of the EUR/USD movement!

Suppose that there are two goods in each country; haircuts and beer. Note that haircuts are a non-traded good.

15205105

20

10

*

*

*

E)(E.)(E.P

EP

EP

H

B

18$24$512$5

24$

12$

)(.)(.P

P

P

Price indices in Europe and the US are defined equally (50% Beer, 50% Haircut)

Europe United States

At an exchange rate of $1.20 per Euro, LOOP holds for each individual good and PPP holds for the index – the real exchange rate equals 1

20.1$**

H

H

B

B

P

P

P

P1

18

1520.1

*

P

ePRER

Now, suppose that the price of a haircut rises in Europe to E30 – because a haircut is not traded, there is no need for the exchange rate to adjust

20305105

30

10

*

*

*

E)(E.)(E.P

EP

EP

H

B

18$24$512$5

24$

12$

)(.)(.P

P

P

Europe United States

The 25% inflation should cause a 25% depreciation of the Euro (i.e. a fall in the EUR/USD to $.90, but this doesn’t happen.

33.118

2020.1

*

P

ePRER

Instead, the Euro appreciates in real terms by 33%!!

Education & Communication

5%

Tobacco & Smoking Products

1%

Recreation6%

Medical6%

Housing40%

Food & Beverage16%

Apparel5%

Personal Care4%

Transportation17%

US CPI

The previous example represented an increase in the relative price of a non-traded good. This causes a real appreciation of a country’s currency

When you consider that over 50% of the US CPI is non-traded, these relative price changes are important!!

Now, suppose that the two goods are beer and peanuts – assume that more beer is consumed in Europe than in the US

95201080

5

10

*

*

*

E)(E.)(E.P

EP

EP

p

B

2.7$6$8012$20

6$

12$

)(.)(.P

P

P

Europe United States

At an exchange rate of $1.20 per Euro, LOOP holds for each individual good, but PPP does not hold!

20.1$**

p

p

B

B

P

P

P

P 50.120.7

920.1

*

P

ePRER

Now, suppose that the price of beer in increases by 50% worldwide

135201580

5

15

*

*

*

E)(E.)(E.P

EP

EP

p

B

40.8$6$8018$20

6$

18$

)(.)(.P

P

P

Europe United States

Europe experiences a 36% inflation rate while the US experiences a 15% inflation rate. The nominal exchange rate is constant, LOOP still holds for each individual good but the Euro experiences a real appreciation

20.1$**

p

p

B

B

P

P

P

P 85.140.8

1320.1

*

P

ePRER

% Change in Nominal Exchange Rate

=% Change in Real Exchange Rate

+Inflation Differential

Relative Price Movements

Given the importance of relative prices (real exchange rate movements), we can use a modified version of PPP.

The two major relative price movements are:

Relative price of non-traded goods (causes a real currency appreciation)

Terms of Trade (relative price of imports) – an increase in the relative price of imports (worsening of the terms of trade) causes a real depreciation

The competing alternative explanation deals with differing adjustment speeds across different markets.

P

PeRER

*

Exchange rates are determined in asset markets – new information is incorporated rapidly into prices Prices are determined in commodity

markets – new information is incorporated slowly into prices.

Therefore any nominal movement will be reflected in the real exchange rate until commodity prices can “catch up”

How can we tell the difference between “sticky prices” and relative price movements?

RER

RER

Time

Time

1

1

If the “sticky price” story is correct, then the real exchange rate should be mean stationary

If the “relative price” story is correct, then the real exchange rate will not be mean stationary – i.e. real exchange rates are unpredictable!