(II)PPP Using BigMac

7/31/2019 (II)PPP Using BigMac

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Empirical Analysis ofPurchasing Power Parity

BigMac Index vs Exchange Rate


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1. Purchasing Power Parity

Compare the price of BigMac in twodiferent countries, denominated intwo different currencies

3,000 in Korea $ 2.5 in US

Exchange rates are determined to reflect purchasing

power between two countries

In the hypothetical example, solve \3,000=$2.5 to get

$1=\1,200, which is the won-dollar exchange rate as

determined by the BigMac index


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2. Purchasing Powerand Exchange Rates

To compare purchasing power across countries,

choose a homogenous product, like BigMac or Coca

Cola, and compare prices denominated in local

currencies.

Hypothesis to be tested: Exchange rates are

determined by the BigMac index (or Coca Cola Index).


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For each country, its BigMac index is the price,

denominated in local curency, of $1 value of BigMac.

The Economist compiles the BigMac index since 1986

Compare BigMac index with the actual exchange rates

3. Big Mac Index


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4. Data

Download the data on the BigMac

Indices and the exchange rates from

The Economist Website

http://www.economist.com

Note: Click on BigMac Index located on the left-middle of the

HomePage. Then, you can obtain BigMac indices little bit

outdated. If you are really serious about this kind of

research, you can subscribe to the current ones.
http://www.economist.com/http://www.economist.com/http://www.economist.com/


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5. Model I

Simple Linear Regresion

Test whether = 0 and = 1

(Exchange Rate) = + (BigMac) +
http://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EC%9B%90%EC%9E%90%EB%A3%8C.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EC%9B%90%EC%9E%90%EB%A3%8C.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EC%9B%90%EC%9E%90%EB%A3%8C.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EC%9B%90%EC%9E%90%EB%A3%8C.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EC%9B%90%EC%9E%90%EB%A3%8C.xls


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5. Results

Test of =0 (not rejected)

Test of =1 (rejected)

36.105.42

31.5731.57

t

12.2104.0

181.181.1

t

(Exchange Rate) = -57.31 + 1.81 (BigMac)
http://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EB%A1%9C%EA%B7%B8%EB%B3%80%ED%99%98%EC%A0%84.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EB%A1%9C%EA%B7%B8%EB%B3%80%ED%99%98%EC%A0%84.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EB%A1%9C%EA%B7%B8%EB%B3%80%ED%99%98%EC%A0%84.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EB%A1%9C%EA%B7%B8%EB%B3%80%ED%99%98%EC%A0%84.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EB%A1%9C%EA%B7%B8%EB%B3%80%ED%99%98%EC%A0%84.xls


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5. Interpretation

is significantly different from one

Reject the Null

BigMac Index, reflecting purchasingpower, is not equal to the exchange

rate.

Why doesnt Purchasing Power Parity

hold?


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5. Look into data

existence of outlier

In most countries, BigMac index and exchangerates take a value in the range of 0-1,000. In a fewcountries, these values are quite extreme.

Absolute PPP vs. relative PPP.


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6. Model IIlogarithmic tranasformation-

Regress ln(Exchange Rate) on

constant and ln(BigMac index).

Test whether =1.

ln(Exchange Rate) = + ln(BigMac) +
http://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EC%9B%90%EC%9E%90%EB%A3%8C.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EC%9B%90%EC%9E%90%EB%A3%8C.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EC%9B%90%EC%9E%90%EB%A3%8C.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EC%9B%90%EC%9E%90%EB%A3%8C.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EC%9B%90%EC%9E%90%EB%A3%8C.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20%EC%9B%90%EC%9E%90%EB%A3%8C.xls


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6. Model II (log transformed)

Due to log-transformation, the impact of outliers is reduced.

In line with relative PPP rather than absolute PPP, beta nowmeasures the percentage changes in the exchange ratesassociated with 1% increase in the BigMac index (concept of

elasticity).


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6. Results from Model II

Test of = 1 (cannot be rejected)

5.002.0

101.101.1

t

ln(Exchange Rate) = 0.29 +1.01 ln(BigMac)
http://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20log-log%20%EB%AA%A8%ED%98%95.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20log-log%20%EB%AA%A8%ED%98%95.xlshttp://ezstat.co.kr/real_life_sample/%EA%B5%AC%EB%A7%A4%EB%A0%A5%ED%8F%89%EA%B0%80%EC%84%A4/BigMac%EC%A7%80%EC%88%98%20%ED%9A%8C%EA%B7%80%EB%B6%84%EC%84%9D%20log-log%20%EB%AA%A8%ED%98%95.xls


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6. Interpretation

is not significantly different from 1.

Cannot reject relative PPP

Conclude that 1% increase in the purchasing power

(as measured by the BigMac index) is associated with

the 1% increase in the exchange rate.

PPP holds in relative version, but not in absolute

version.


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THE END

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(II)PPP Using BigMac