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1

The Big Mac Index Two Decades On:

An Evaluation of Burgernomics

May 2009

by

​

Kenneth W Clements

Yihui Lan

Shi Pei Seah

​

Business School

The University of Western Australia

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Outline

  1. Purchasing Power Parity Theory
  2. The Big Mac Index
  3. Enhancing the BMI
  4. The BMI as a predictor
  5. More on the Oz
  6. Conclusions

2

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1. Purchasing Power Parity

  • A weaker version:

​

​

​

​

  • In logs:

​

​

​

​

​

3

1. PPP Theory

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Three Versions of PPP

where e is a random disturbance term with E(e)=0

4

Version

Intercept

Disturbance

k

e

1. Absolute

0

0

2. Relative

≠ 0

0

3. Stochastic

≠ 0

≠ 0

1. PPP Theory

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Absolute PPP

5

Undervaluation

s

r

45o

s2

r 2

s1

r 1

Overvaluation

B

A

1. PPP Theory

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6

Relative PPP

Undervaluation

A

s

r

-k > 0

45o

s2

B

r 2

s1

r 1

Overvaluation

1. PPP Theory

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7

Stochastic PPP

Consistent with SPPP

Y

-k+e2

-k+e1

r2

X

E (e) = 0

r

s

Consistent with SPPP

1. PPP Theory

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  • Define the real exchange rate as:

​

with E(q) = k, var(q) = σ2.

​

  • Chebyshev’s inequality:

​

​

  • The bounds are:

​

where α is the probability of a Type I error.

​

8

More on Stochastic PPP

1. PPP Theory

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9

2. Big Mac Index

Country

Big Mac prices

Implied �PPP of �the dollar

Actual $�exchange rate�30/01/09

Under/over valuation, %

In local currency

In dollars

United States

$3.54

3.54

-

-

-

Australia

A$3.45

2.19

0.97

1.57

-38

Britain

£2.29

3.30

0.65

0.69

-7

Canada

C$4.16

3.36

1.18

1.24

-5

Euro area

€ 3.42

4.38

0.96

0.78

+24

Japan

¥290

3.23

81.9

89.8

-9

Switzerland

SFr 6.50

5.60

1.84

1.16

+58

2. Big Mac Index

Source: The Economist (Feb 2009)

Equilibrium Exchange Rate

Should go to 0

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Mean

± 2 SE

10

(q x 100)

Australia

Japan

Canada

2. Big Mac Index

Deviations from Big Mac Parity I

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Mean

± 2 SE

11

Deviations from Big Mac Parity II

(q x 100)

Britain

Euro Area

Switzerland

2. Big Mac Index

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2. Big Mac Index

Deviations from Big Mac

Parity III

12

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  • There are substantial, sustained and significant deviations of exchange rates from the BMI

​

  • The BMI is biased

​

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Conclusion

2. Big Mac Index

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  • Adjusting the BMI for a bias we obtain relative PPP

​

where b is the bias

​

  • This relative PPP over horizon of h years:

​

,

​

is the annualised change over horizon h

​

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3. Enhancing the BMI

3. Enhancing the BMI

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  • Low inflation
  • Appreciating� currency
  • High inflation
  • Depreciating � currency

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A Scatter Plot

0

45o

0

3. Enhancing the BMI

Change in exchange rate

Change in exchange rate

Inflation Differential

Inflation Differential

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Evidence on Relative PPP�24 countries 1994-2008

16

3. Enhancing the BMI

Mexico

Czech Republic

Japan

1-year Horizon

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Evidence on Relative PPP�24 countries 1994-2008

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3. Enhancing the BMI

Poland

Russia

Polish Zloty redenominated 10,000:1

(1 January 1995)

Russian Ruble redenominated 1,000:1

(1 January 1998)

14-year Horizon

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Total and Annualised Volatility I

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  • Two types of deviations from parity:

3. Enhancing the BMI

Absolute

Relative

  • Volatility of deviations:
  • Under relative PPP,

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Total and Annualised Volatility II

19

  • Two types of multi-horizon volatility:

3. Enhancing the BMI

Annualised

Total

  • Example: The AR(1) case:

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Example I

20

3. Enhancing the BMI

B. Non-stationary

  • Annualised volatility when:

A. Stationary

Annualised

Volatility

Horizon (h)

Horizon (h)

Annualised

Volatility

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Example II

21

3. Enhancing the BMI

B. Non-stationary

  • Total volatility when:

A. Stationary

Total Volatility

Horizon (h)

Horizon (h)

Total Volatility

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22

The Area Under the Curve I: Stationary

3. Enhancing the BMI

Annualised

Volatility

Horizon

TV1

TV1

Total

Volatility

TV2

TV2

When β < 1, total volatility constant

TV1 = TV2 = … = TV14

TV14

TV14

Horizon

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23

The Area Under the Curve II: Non-Stationary

3. Enhancing the BMI

Horizon

TV1

TV1

TV2

TV2

When β = 1, total volatility increases

TV1 < TV2 < … < TV14

TV14

TV14

Total

Volatility

Horizon

Annualised

Volatility

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Stationary and Non-Stationary

  • When the real rate is stationary, the total volatility is constant as the length of the horizon expands.

​

24

Horizon

Total volatility

3. Enhancing the BMI

Non-stationary

Stationary

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�Evidence from 24 Countries�1994-2008

​

​

​

​

​

​

​

  • Real rates are weakly stationary
  • Relative PPP holds at longer horizons

​

25

Horizon (years)

Total volatility (%)

3. Enhancing the BMI

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​

  • Absolute PPP The Economist BMI

​

  • Relative PPP Bias-adjusted BMI

​

  • Stochastic PPP Stochastic Bias-Adjusted BMI

​

​

​

​

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4. BMI as a Predictor

Subsequent change

Current mispricing

4. The BMI as a Predictor

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Another Scatter

Subsequent change

Current mispricing

45o

0

  • Currently � undervalued
  • Subsequently � appreciates
  • Currently � overvalued
  • Subsequently � depreciates

0

4. The BMI as a Predictor

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Evidence on BMI Predictions �24 countries, 1994-2008

28

4. The BMI as a Predictor

1-year Horizon

2-year Horizon

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… and at longer time horizons

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4. The BMI as a Predictor

10-year Horizon

14-year Horizon

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Regression results

  • Full adjustment requires: and

​

Standard errors in parenthesis. Non-overlapping observations.

1

-0.055 (0.733)

-0.302 (0.041)

336

0.138

143.5

​

​

​

​

​

​

2

-0.346 (1.377)

-0.588 (0.075)

168

0.270

15.2

​

​

​

​

​

​

3

-2.199 (1.486)

-0.872 (0.086)

96

0.525

2.1

​

​

​

​

​

​

4

-6.439 (2.000)

-1.097 (0.096)

72

0.649

5.4

​

​

​

​

​

​

5

-6.009 (1.927)

-0.875 (0.113)

48

0.565

4.9

4. The BMI as a Predictor

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BMI versus a Random Walk

31

Horizon (years)

RMSE (Percent)

Random walk

Big Mac Index

Bias-adjusted BMI

4. The BMI as a Predictor

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5. More on the Oz

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5. More on the Oz

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  1. Conventional BMI, �q x 100, Australia

33

± 2 SE

Now 08/05/09 = -27%

Mean = -29%

5. More on the Oz

Absolute PPP, q = 0

(Conventional BMI)

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5. More on the Oz

± 2 SE

Now 08/05/09 = +3%

Mean = 0%

II. Bias-Adjusted BMI, � q x 100, Australia

34

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III. Now

5. More on the Oz

Country

Big Mac prices

​

$US cost of 1 $A

Under- valuation %

In local currency

In $A

Implied �PPP of �the $A

Actual�exchange rate�08/05/09

Australia

A$3.45

3.45

-

-

-

United States

US$3.54

4.72

1.03

0.75

-27

Big Mac Index

$US cost of 1 $A

Actual exchange rate 08/05/09

​

Implied �PPP of the $A

​

Over/Under-valuation

Conventional

0.75

less

1.03

=

-0.28 (-27%)

Bias-Adjusted

(15-year mean)

0.75

less

0.73

=

0.02 (+3%)

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  • BMI is biased.
  • Bias-adjusted BMI has considerable predictive power regarding future currency values.
  • Bias-adjusted BMI also looks nicer (see distribution).
  • Can predict future currency movements over longer horizons.

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6. Conclusions

6. Conclusions

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Distribution of Real ERs�24 countries, 1994-2008

Number

Number

6. Conclusions

Conventional BMI

Bias-Adjusted BMI

Note: Argentina 2002 omitted.