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An Evaluation of PPP in terms of The iPod Index: A Possible Replacement of the Big Mac Index?

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Ernest E. (Rick) Walker

An Evaluation of PPP in terms of The iPod Index: A Possible Replacement of the Big Mac Index?

Background:

Introducing the iPod Index

- Like Big Macs, Apple’s iPod had become widely available internationally (simplifying cross-country comparisons).
- iPods are assembled in mainland China (i.e. a single country).
- iPods are thus both more homogenous and more tradable than Big Macs—which means that this product complies much better with the requirements set out by PPP.

- And as we will see, most of the other ‘non-arbitrage’ deviations from PPP in iPods are also much more easily controlled for than in the prices of Big Macs.

- The same cross-section of 39 countries (for both Big Macs & iPods) in a balanced panel dataset ranging from 2007 to 2009.
- Main Data Sources:
- Various The Economist Publications (for Big Mac prices)
- Various CommSec corporate reports and internet archives (for iPod prices).

Panel Regression Analysis:

DEVIATIONS FROM PPP AND THE ADJUSTMENTS TOWARD IT

- We start with the basic Law of One Price (LOP) otherwise known as absolute PPP:
- This equation carries the implicit assumption that there are zero barriers to trade that could potentially result in a wedge between the two prices.

Relative to the United States (US$) for 2007 to 2009

100%

50%

0%

Percentage Over (+) or Under (-) Valuation

-50%

-100%

2007

2008

2009

Big Mac Index Valuations

iPod Index Valuations

- Does PPP holds equally well for both indexes when controlling for some of the possible exogenous factors that may directly influence the size of the wedge between domestic and international prices; e.g.
- Tariffs
- Taxes
- Transport Costs
- The effect of non-tradable components, (i.e. The Balassa-Samuelson effect).

- We therefore develop a formal model with which one can test for PPP while controlling for these deviations:
- Some of the factors contributing to this price-wedge are observed and can be controlled for.

- Observed Factors:
- Tariffit- denotes the domestic country’s import tariff rate (in percent) for electronic music players imported from China.
- Taxit- represents the applicable sales tax (in percent) for each of the respective economies, whether it is a General Sales Tax (GST) or a Value Added Tax (VAT).

- Unobserved Factors:
- εit - represent the remaining unobserved factors that we were not able to empirically observe (like actual transport costs or the Balassa-Samuelson effect).

- With a bit of mathematical manipulation and by using a few proxies for the unobserved components we obtain the testable equation:

Asterisks indicate levels of statistical significance of the respective F-statistics: * (90%), ** (95%) and *** (99%)

Unrestricted Panel VARs with

Cholesky Impulse Responses

- We now evaluate:
- How the logarithmic domestic-U.S. price ratio responds to a standardized shock in the logarithmic ER of both Big Macs and iPods; and,
- How the logarithmic ER responds to a standardized shock in the logarithmic price ratio.

- The Confidence Bounds were calculated via a Monte Carlo simulation with 10,000 repetitions.

- It was found that at least one cointegrating relationship existed among the following Big Mac and iPod variables: the log domestic-price; the log US$-price; and, the log nominal domestic-US$ exchange rate.
- VECMs are extremely valuable to assess several aspects of the adjustments of a RER as they converge towards their long-term equilibrium values.

- For the Big Mac structural-VECM the estimated ‘coefficient of adjustment’ according to my model equalled 0.94. This means that about 94% of the PPP-discrepancy in year should be eliminated by the RER-adjustment in the following year.
- In the iPod structural-VEC this figure was found to be 1.41. This either suggests that the discrepancy is eliminated in less than one year; or, that the ER overshoots the theoretical model.

Adjustment Speeds of the two Indices

Half-Lives of RER Movements

- According to Taylor & Taylor (2004:146) “One way to get a feel for how fast the real exchange rate mean reverts is by asking how long it would take for the effect of a shock to die out by 50 percent—in other words, we can compute the half-life of shocks to the real exchange rate.”
- This can be done by evaluating the -coefficient in (where qit is the RER for country i at time t):
- Consensus estimates for the rate at which PPP deviations damp suggest a half-life of three to five years.

Asterisks indicate levels of statistical significance of the respective t-statistics: * (90%), ** (95%) and *** (99%)

Big Mac & iPod Index

Conclusion

- It appears as though for iPods, it is significantly easier to control for some of the exogenous factors driving these international ‘price wedges’ than it is in Big Macs.
- All of the econometric techniques employed in my paper—including VECMs a CV analysis, an evaluation of half-lives, etc—all seem to reaffirm that RER-corrections according to the iPod-index are notablyquicker—in addition to being more significant—than those according to the BMI.

Big Mac & iPod Index

Q&A