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Note: Purchasing Power Parity

Nhat M. Nguyen

IFM, Section 01

Fall 2005

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INTRODUCTION

An important concept to understand when evaluating the economic health ofnations and the relative dynamics between international markets is the idea of purchasingpower parity (PPP). The basic theory asserts that the prices of common goods betweentwo countries should be equal once prices have been converted to a common currency.

Distilled to its basic form, purchasing power parity is a ratio that displays the relative price level differences across two countries for similar products or group of products.PPP is used as a first step in making inter-country comparisons based in real terms ofgross domestic product (GDP) and its component expenditures. GDP is commonly usedas a economic indicator for size, growth, and health of a nation. PPP allows countries tobe viewed through a common reference point.1 Taken as a long-term theory, one shouldexpect a convergence of all prices for common goods around the world in order forequilibrium to take affect and mitigate cost arbitrage opportunities. This note willprovide the reader a deeper understanding of how the theory of purchasing power parityworks, the practical application of PPP, flaws surrounding the application, and therelationship between PPP and real exchange rates.

BUILDING THE THEORY OF PURCHASING POWER PARITY

To begin to understand PPP, one can start at how the theory is developed from thelaw of one price and then translated or generalized to the concepts of absolute purchasingpower parity and relative purchasing power parity.

Law of One Price

The foundation of purchasing power parity is grounded in the law of one price.The theory states that barring frictional or complicating factors such as tariffs, taxes, andtransportation costs, the price of a internationally traded good in one country should

achieve the identical price in another country, once the price is adjusted to a commoncurrency.

To provide an illustrative context, a frequent example of purchasing power paritymanifests itself in the form of the McDonalds Big MacTM. Quite often, the Economistwill publish a light-hearted survey concerning the prices of a Big MacTM from differentcountries in order to: (1) evaluate exchange rates based upon differences in the prices ofthis nearly ubiquitous good, (2) get a comparative sense of economic output and healthacross countries.

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As an example, consider a basic ingredient to the Big MacTMlike a beef patty.

Assume the price for a beef patty in the United States is represented as pbp$

and the priceof the same beef patty in the France is represented as pbp

, the law of one price can beexpressed mathematically as follows:

pbp

=Expbp$ (Equation 1)

here, E is the exchange rate between the euro/dollar. Assume the cost of a pre-formedbeef patty in the U.S. is $1.00 per patty. If the euro/dollar exchange rate is 0.845316 (thespot rate as of 12/07/2005), then the price for the same beef patty in France should be0.85. An arbitrage opportunity could arise if the pre-formed patty sold for anything lessthan 0.85 in France. A shrewd trader could then purchase pre-formed beef patties inFrance and resell them in the U.S. for an tidy profit until supply and demand forces took

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hold and drove down the prices in the U.S. market while driving up the prices in theFrench market. This process would repeat itself until price convergence is achieved.Thus, the law of one price holds true within this iterative pricing cycle for a discreteproduct like the beef patty.

Absolute PPP

Using the intuition built by the law of one price for a discrete product, one canapply the principle across an aggregate of products and prices. Or put another way, onecan imagine a common basket of goods that can be traded and prices compared acrosstwo countries- this is also known as the consumer price index (CPI). By using priceindices, one can rewrite equation (1) to make a relative comparison of overall price levelsbetween France and the U.S., P and P$:

P

=E/$x P$ (Equation 2)

once againE/$, is the exchange rate between the euro and the dollar. If PPP holds true,then equation (2) can be rearranged to derive the form ofabsolute PPP:

P

P

The left-hand side of equation 3.1 can also be referred to as the real exchange rate or theexchange rate that has been adjusted for relative pricing levels. In the alternate form ofequation 3.2, one can see that for purchasing power parity to hold, a very strict definitionof the basket of goods must be met or the composition of the CPI must be identical.However, in empirical usage, one finds international price indices are varied in goods anddifferent weights assigned to those goods. Another complication associated withinternational indices is that they must be constructed from similar base years.

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The adaptation of the law of one price to PPP brings a particular nuance or wrinkle. Inthe beef patty arbitrage example cited above, the trader would take advantage of the pricedifferences between two markets and the exchange rate was assumed constant. Here,there is an attempt to hold the price levels constant and it is the exchange rate thatfluctuates. This becomes basis of the idea that PPP as a determinant of the exchangerates.4

Relative PPP

One sees from the discussion above, in order to control for a constant pricedifferential between the two countrys indices, one can focus on measuring the relativepurchasing power parity. Using a relative PPP allows for a different basket of goods andvarying weights to be applied towards the goods within the CPI. This is because relativePPP states that fluctuations in the pricing levels will be related to the fluctuations in theexchange rates. Changes in relative exchange rates are attributed to varying inflationrates across countries. Thus, relative PPP can be expressed as follows:

P$

= E/$P

$=

E/$

1 or PPP(Equation 3.1) (Equation 3.2)1x PPP

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in equation 4.1, one sees that the percent change in exchange rates over a given range oftime will be equal to the differences in inflation of the euro, , and the dollar, $.

5 Putin a slightly different manner, equation 4.2 expresses the differences in percent changesin price levels in France and United states, also known as changes in relative inflation, asdirect determinant in the relative changes in exchange rates between the two countries.6It is the calculation of relative PPP that many economists and theorist will anchor theirempirical tests in order to prove out the validity of PPP.

INHERENT PROBLEMS WITH PPP

There are an number of errors surrounding PPP theory. While significant, theyare still not compelling enough for scholars to discard a theory that makes strong intuitivelogic. Below are some reasons why PPP may not hold.

Transportation costs The theory of the law of one price assumed that transportationcosts were negligible and PPP requires the same assumption. However, getting productsto and from different markets can add significant costs to goods. This will causeadditional divergence in any price comparison when the product is applied to the basketof goods in a CPI. There is research that estimates transportation costs add 7 percent tothe price of U.S. imports of meat, 6 percent to the import of price of diary products, and16 percent to the import price of vegetables7.

Tariffs and Taxes Once again, for PPP to hold, another key assumption underlying thelaw of one price is the abstraction of taxes and tariffs. There can be no imposition ofunequal taxes or tariffs in goods imported or exported across countries, otherwise thiswould tend to cause further separation of true price levels between markets. A notedscholar on PPP, Cassel (1918), stated that If trade between two countries is morehampered in one direction than in the other, the value of the money of the country whoseexport is relatively more restricted will fall, in the other country, beneath the purchasingpower parity.8 Export restrictions were particularly relevant during Cassels time due totheir widespread use during the first World War. The effect of export restrictions

translates into the currency of a country with high export tariffs to be undervaluedrelative to PPP of another country with lower export tariffs. Conversely, a country withhigherimportrestrictions will be overvalued on PPP basis.

During the early nineties, Japan imposed quotas and tariffs on beef imports that went ashigh as 70 percent. Likewise, Korea imposed a 30 percent tariff as well as quantityrestrictions from 1989 through 1994. Trade barriers such as these erected an obstructionto natural price equalization of beef across the world markets, not to mention the impactupon the domestic prices of beef within Japan and Korea. Imposed barriers to trade may

or %E/$ = %P

- %P$= - $

E/$1

E/$2 -

E/$1

(Equation 4.2)(Equation 4.1)

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be a partial explanation to the overvaluation of the yen and the won against the US dollaruntil the late 1990s.

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Taxes also have the same effect as tariffs upon deviations away from PPP. Many priceson goods that make up the composition of the consumer price index are inclusive of taxesor value added taxes. For instance, countries with higher rates of taxation (in comparisonto the U.S.) on like goods such as beef patties will appear to have an overvalued currencyrelative to the U.S. dollar.

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Costs of Non-tradable goods The theory of PPP asserts that after the barriers to tradeare expunged, the cost of a good such as the BigMacTM should be the same across allcountries in which the BigMacTM is traded. However, the local price of a BigMacTMconstitutes more than simply the ingredients by which it is composed. Also embedded inthe local price is the cost associated with selling and marketing. Even within the samecountry, the cost of the BigMacTM can vary depending upon costs to lease or rent therestaurant space and pay for utilities such as power, water, and heat. Rents and utilitiesare examples of non-tradable goods. While it is possible for titles and deeds to be traded,the location of a property cannot. Thus it may be cheaper to rent a space for a restaurantin Boise, Idaho than in Manhattan, NY, however, it is a useless comparison if one desiresto sell BigMacsTM to the population in Manhattan.

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Another component incorporated in the prices is the cost to serve, market, and sell theBigMacTM, which may be significantly different from country-to-country. Wages havealways been understood to be a non-tradable good in economic terms. There are inherentbarriers to peoples ability to move across borders to take advantage of wage differences.Costs of non-tradable goods can have a significant impact on pricing. Ong (1997)estimates that non-traded goods account for 94 percent of a BigMacs price.12

Productivity A theory developed by Balassa and Samuelson (1964) states thatthe non-tradable goods have a systemic impact on the deviation from PPP due itscorrelation to the productivity of a nation.13 By incorporating non-tradablecomponents into the goods that comprise the CPI, the inherent effect is to alsoincorporate the productivity differences across regions or countries. Anunderlying assumption of the Balassa-Samuelson theory is that high per-capitawages are an indicator of higher productivity. Thus, countries with high-wageswill be overvalued relative to countries with lower-wages. There is furthersupportive arguments that differences in productivity is most pronounced in thetraded goods sector. Therefore, high-productivity in traded goods will manifest inhigh-wages across all sectors - tradable goods and services - as companies within

a country compete for workers. Higher wages paid for services in high-incomecountries relative to lower-income countries will cause higher prices for servicesin the high-income countries. There is a trickle-down affect of high prices intradable goods to services within a high-income country. Thus, even if there wereidentical prices for tradable goods across countries, there would still be anovervaluation of currency in the high-income country.14

Government Spending Another contributing factor for deviations from PPP aredifferences in government spending on non-tradable goods across different

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countries. There is evidence that governments spend more on non-traded goodsthan does the private sector. For instance, if the U.S. government increasedexpenditures relative to another government, the price of non-traded goods in theU.S. will increase along with the overall price levels, akin to the discussion above.Had PPP held prior to the expenditure, the dollar would now be overvalued

relative to its PPP level. This phenomenon is particularly prevalent in high-income nations.15

Current Account Deficits There is another related notion that purports a similarlogic of the trickle-down price effects of non-tradable goods. Krugman, annoted economist, theorizes that governments who establish current accountdeficits are spending more on traded goods than other countries. Hence, this willresult in a drop in the price of non-traded goods in the deficit country. Here, hadPPP held previously, there will be a situation where the deficit countrys currencywould be undervalued compared to its healthier neighbors.16

Information Asymmetry The law of one price also assumes that traders have access toall of the same information regarding prices across all markets. Armed with thisknowledge, any trader could move to make a profit by selling product in a higher pricedmarket until the supply and demand forces discussed earlier would take effect and workto create a state of equilibrium in the price of a good. Should there be imperfections withinformation flow or only partial information, traders would not be able to act. Even withthe knowledge, they may not be able to create an effective scale of trade to make animpact on equalizing a price. Without the information, traders are unable to make a playtowards profits and prices will not converge through natural market forces. Thus, the lawof one price would fail to hold along with PPP.

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Pricing to Market Another contributing factor to deviations from PPP is a firms ability

to mark their products at different price points across different markets. Basic businesstheory states that profit maximization can be achieved by pricing as high as is appropriateconsidering the elasticity of demand for a product.

18For instance, pharmaceutical

companies often charge higher prices in the U.S. than in other countries for the sameexact drug. This is partially attributed to higher incomes found in the U.S. and thecorresponding willingness-to-pay. Another important factor that allows pricing to marketis the ability to resell the product to another country. There are heavy restrictions onselling drugs within the U.S. and there has been increased debate on whether people canpurchase prescription drugs from countries such as Canada.

CONCLUSION: Purchasing power parity puzzle

There have been numerous studies to prove out the various theories surrounding PPP andits efficacy along particular time horizons. There has been a long standing belief thatPPP is an effective tool to understand real exchange rates and their natural equilibriumstates in the long-run. There is a consensus that the speed of convergence is relativelyslow compared to the rampant shifts to exchange rates in the short-term (some experts believe the half-life of shocks exhibited by short-term exchange rates fluctuations isanywhere from two to three years)19. However, there has been much debate on thecauses of the volatile nature of the short-run exchange rate. So, the conundrum is: how

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do we reconcile the erratic, and enormous volatility of short term exchange rates with theextremely slow rate of the corrective force of PPP? We have already touched on Balassa-Samuelsons theory attributing deviations from PPP to the attributes of non-tradablegoods, incomes, and productivity difference across nations.20 There is a more recentstudy by Engel (1999) that argues against this view by entirely attributing the deviations

to the other errors to the law of one price and none to relative prices of non-tradablegoods.21

Regardless, it is important to understand that purchasing power parity is a powerful toolthat provides us a common lens by which to view the economic health and condition ofdifferent countries. Just as with any tool or device, we must be cognizant of thelimitations and weakness of PPP and understand how we can control those limitationswithin a particular data set.

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References

1 Organisation for Economic Co-operation and Development, Purchasing Power Parities (PPP),Purchasing Power Parities (PPPs) Frequently Asked Questions, 2005,http://www.oecd.org/faq/0,2583,en_2649_34357_1799281_119678_1_1_1,00.html, accessedNovember 2005.

2 Michael R. Pakko and Patricia S. Pollard, Burgernomics: A Big MacTM Guide to Purchasing PowerParity, 2003, The Federal Reserve Bank of St. Louis., pp. 9-12.

3 Steven Suranovic, "International Finance Theory and Policy: Purchasing Power Parity," TheInternational Economics Study Center, 1997-2006,http://internationalecon.com/v1.0/Finance/ch30/ch30.html.

4 Ibid.

5 Ibid.

6 Pakko and Pollard, pp. 14.

7 Ibid, pp. 16.

8 Gustav Cassel, (1918), Abnormal deviations in international exchanges, The Economic Journal, pp.28.

9 John Dyck. U.S.-Japan Agreements on Beef Imports: A Case of Successful Bilateral Negotiations, inMary E. Burfisher and Elizabeth A. Jones, eds.,Regional Trade Agreements and U.S. Agriculture.Chap. 9. Market and Trade Economics Division, Economic Research Service, U.S. Department ofAgriculture, Agricultural EconomicsReport No. 771, November 1998.

10 Suranovic, Problems with Purchasing Power Parity.


12 Li Lian Ong, The Big Mac Index: Applications of Purchasing Power Parity. New York: PalgraveMacMilan, 2003.

13 Bela Balassa, The Purchasing-Power Parity Doctrine: A Reappraisal.Journal of Political Economy,December 1964, 72(6), pp. 584-96.


15 Ibid, pp. 21.

16 Ibid, pp. 21.

17 Paul R. Krugman, Equilibrium Exchange Rates, in William H. Branson, Jacob A. Frenkel, andMorris Goldstein, eds.,International Policy Coordination andExchange Rate Fluctuations. Chicago: University of Chicago Press, 1990, pp. 159-87.


19 Kenneth A. Froot and Kenneth Rogoff, Perspectives on PPP and Long-Run Real Exchange Rates,NBER Working Paper Series, pp. 2-7.

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20 David C. Parsley and Shang-Jin Wei,. A Prism into the PPP Puzzles: The Micro-foundations of BigMac Real Exchange Rates. August 2003, pp. 1-9.

21 Engel, Charles, 1999, Accounting for U.S. Real Exchange Rate Changes,Journal of PoliticalEconomy, V107, pp.507-38.

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