Empirical Analysis of Purchasing Power Parity Big Mac

£ ₩ € Empirical Analysis$ of Purchasing Power Parity ₡ ¥ ₣ Big. Mac Index vs Exchange Rate 1

1. Purchasing Power Parity Compare the price of Big. Mac in two diferent countries, denominated in two different currencies ₩ 3, 000 in Korea Ø $ 2. 5 in US Exchange rates are determined to reflect purchasing power between two countries Ø 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 Big. Mac index 2

2. Purchasing Power and Exchange Rates Ø To compare purchasing power across countries, choose a homogenous product, like Big. Mac or Coca Cola, and compare prices denominated in local currencies. Ø Hypothesis to be tested: Exchange rates are determined by the Big. Mac index (or Coca Cola Index). 3

3. Big Mac Index Ø For each country, its Big. Mac index is the price, denominated in local curency, of “$1 value of Big. Mac. ” Ø The Economist compiles the Big. Mac index since 1986 Ø Compare Big. Mac index with the actual exchange rates 4

4. Data Ø Download the data on the Big. Mac Indices and the exchange rates from The Economist Website http: //www. economist. com Note: Click on Big. Mac Index located on the left-middle of the Home. Page. Then, you can obtain Big. Mac indices little bit outdated. If you are really serious about this kind of research, you can subscribe to the current ones. 5

5. Model I Ø Simple Linear Regresion (Exchange Rate) = + (Big. Mac) + Test whether “ = 0 and = 1” 6

5. Results (Exchange Rate) = - 57. 31 + 1. 81 (Big. Mac) Ø Test of =0 (not rejected) Ø Test of =1 (rejected) 7

5. Interpretation Ø is significantly different from one Reject the Null Ø Big. Mac Index, reflecting purchasing power, is not equal to the exchange rate. Why doesn’t Purchasing Power Parity hold? 8

5. Look into data existence of outlier Ø In most countries, Big. Mac index and exchange rates take a value in the range of 0 -1, 000. In a few countries, these values are quite extreme. Ø Absolute PPP vs. relative PPP.

6. Model II –logarithmic tranasformationØ Regress ln(Exchange Rate) on constant and ln(Big. Mac index). ln(Exchange Rate) = + ln(Big. Mac) + Test whether =1. 10

6. Model II (log transformed) Ø Due to log-transformation, the impact of outliers is reduced. Ø In line with relative PPP rather than absolute PPP, beta now measures the percentage changes in the exchange rates associated with 1% increase in the Big. Mac index (concept of elasticity).

6. Results from Model II ln(Exchange Rate) = 0. 29 +1. 01 ln(Big. Mac) Ø Test of = 1 (cannot be rejected) 12

6. Interpretation Ø is not significantly different from 1. Cannot reject relative PPP Ø Conclude that 1% increase in the purchasing power (as measured by the Big. Mac index) is associated with the 1% increase in the exchange rate. Ø PPP holds in relative version, but not in absolute version. 13