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					          Harvard Business School




                       International Financial Management
                             Purchasing Power Parity
                                   Final Paper
                                December 12, 2005


Kwabena Osei-Boateng
Santiago Izaguirre
Fabrice Ndjodo




Kwabena, Santiago and Fabrice                               Page 1 of 17
SECTION 1: INTRODUCTION

The objective of this paper is to better understand one of the key concepts and building blocks of macroeconomic

theory, the Purchasing Power Parity (PPP). We chose to focus on this topic because as more and more companies

are doing business globally, it becomes fundamental for managers taking international investment decisions to

gauge the impact that fluctuations in inputs prices and consumer good prices could have on the profitability of their

respective businesses. In Section 1 of this paper, we will define the concept of PPP, discuss the theory behind it and

elaborate on its relevance to global managers involved in cross-borders transactions. The next section clarifies the

nuances between absolute PPP and relative PPP, and tests the validity of the PPP theory over time. Finally, the last

section of this paper identifies explanations to deviations from PPP, both market-based and macro-economic factors

related to supply and demand.




Kwabena, Santiago and Fabrice                                                                         Page 2 of 17
SECTION 2: UNDERSTANDING PURCHASING POWER PARITY

In this section we will define purchasing power parity (PPP), use examples to illustrate how it works in real life and

discuss how it relates to exchange rates. Finally, we will discuss PPP relevance to managers as they consider cross

border investments.



What is PPP?

The theory of purchasing power parity is one of the most renowned and contended theories in macroeconomics. The

most fundamental form of the theory of purchasing power parity (PPP) suggests that the same good should cost the

same amount in different countries, when the prices of the good are converted to the same currency. The PPP

exchange rate is the rate at which the price in one currency would need to be converted to allow the goods to have

the same price in the common currency. This relatively simple theory has a long history in economic circles going

back several centuries.



This fundamental idea of macroeconomics is predicated upon the “Law of One Price (LOP)”. The underlying

principle for LOP is that once the price of a good has been converted to a common currency, if it had different

prices in different countries then because goods are assumed to be freely traded, market arbitrage would close the

gap between the prices. However it is clear that there are several factors that would prevent arbitrage from fully

closing the gap between the prices and these factors include tariffs and some non-tariff barriers that we will discuss

in later sections.



Law of One Price

As noted above, the LOP refers to the correlation in the prices of similar goods in different geographic locations.

This can thus be thought of as providing a framework to relate the currency in one market (the domestic market) to

currency in another marker (the foreign market). In algebraic1 form, the LOP posits that for any good i:



Pi = EPi*


1
    JIE: The purchasing power parity puzzle, pp 649; June 1996



Kwabena, Santiago and Fabrice                                                                         Page 3 of 17
where Pi is the domestic currency price of good I, Pi* is the foreign currency price and E is the exchange rate. Thus

if the LOP holds then the exchange rate is the rate at which good i will have the same price in both the domestic and

foreign currencies.



Perhaps the most useful way to discuss the theory of PPP through the law of one price is to use the Big Mac Index,

a tool that The Economist magazine has successfully used to discuss exchange since 1986.



For example, according to the LOP a Big Mac hamburger in its final form should cost the same amount in the UK

as it does in the US once its price is converted to a common currency. In this example, the PPP would therefore be

the exchange rate at which the Big Mac in the US and the UK have the same common currency price. For instance,

if the Big Mac cost USD3.50 in the US and a Big Mac costs GBP2.00 in the UK then the dollars per pound PPP

exchange rate in the case is 1.75. This PPP exchange rate can then be benchmarked against the current exchange

rates between the UK and the US. The reason of the discrepancy between this exchange rate and the real exchange

rate will be discussed in the next section.



Absolute and Relative PPP

Although initiating a discussion on PPP is helpful when done through the framework of the law of one price of a

good, that model is relatively restrictive and therefore any fuller discussion of PPP would require a more

generalized form of the framework. Thus the theory can then be generalized to take into account for the general

basket of goods and in this case it is referred to as Absolute PPP. Absolute PPP suggests that “the national price

levels, not just the individual goods’ prices, are equal when expressed in a common currency” and therefore the

exchange rate that allows this relationship to hold is the absolute PPP exchange rate. In algebraic2 form, the LOP

equation can be modified to:



ΣPi = EΣPi*


2
    JIE: The purchasing power parity puzzle, pp 650; June 1996



Kwabena, Santiago and Fabrice                                                                        Page 4 of 17
where the sums are taken over a consumer price index (CPI)3 to reflect the price of a basket of goods. In this case,

there are a number of other baskets of goods that could be used in stead of CPI, including producer price indices

(PPP)4 and unit labor costs.



The dynamics of the absolute PPP are analogous to that of the LOP. In the absolute case, we will replace the Big

Mac with a price index obtained from a basket of goods. Thus the price of that average basket of goods should be

the same in any two countries when the prices have been converted into a common currency. It should be noted the

basket approach in itself is not perfect given that the consumer price (or producer price) indices used in absolute

PPP are typically constructed in different ways in different countries. Although ‘baskets’ are supposedly quite

similar, they are still not quite the same, which would, at a first approximation, prevent the theory from holding true.



The discussion about absolute PPP has thus far been a static discussion where we take the prices of the baskets of

goods in the countries in question at a point in time and analyze the exchange. This presents a few problems. The

main one is that the indices are usually provided by governments relative to a base year. However, the static data

that is used under absolute PPP gives little indication of how large or small PPP deviations have been in relation to

the base year. In order to get around this, one could focus on a relative PPP. This effectively takes the rates of

change of the price levels (i.e. inflation) and the depreciation of the currency level over time and in so doing,

converts the absolute PPP into the relative PPP, which states that a currency’s exchange rate depreciates over time




3
    The Consumer Price Index (CPI) is a measure of the average change over time in the prices paid by urban consumers for a

market basket of consumer goods and services. The CPI is the most widely used measure of inflation and is sometimes viewed as

an indicator of the effectiveness of government economic policy. It provides information about price changes in the Nation's

economy to government, business, labor, and private citizens and is used by them as a guide to making economic decisions. In

addition, the President, Congress, and the Federal Reserve Board use trends in the CPI to aid in formulating fiscal and monetary

policies.
4
    The Producer Price Index (PPI) program measures the average change over time in the selling prices received by domestic

producers for their output.




Kwabena, Santiago and Fabrice                                                                                   Page 5 of 17
at a rate equal to the difference in inflation rates in the two countries under consideration. In algebraic5 form, this

can be represented as:



ΣPit /ΣPit-1 = (Et/ Et-1)(ΣPit*/ΣPit-1*)



where t refers to time. The above equation is very similar to the equation we put forward for absolute PPP, the only

difference being that we are taking the rates of growth of the various values as opposed to taking the values

themselves. Indeed, given that the equation above holds, we can extend the idea of relative PPP to account for a

currency exchange rate. This states that a currency’s expected exchange rate depreciates over time at a rate equal to

the expected difference in inflation rates (relative) in the two countries under consideration. This extension can

serve as a strong predictive tool for economists, managers and others interested in investing in foreign currencies. It

is this predictive power that makes PPP particularly interesting because using this, macroeconomists, managers and

other entities that have vested interests in cross-border situations try to forecast the long run performance of various

currencies with respect to others.



What is PPP’s relevance to managers?

It is worth asking why we would spend time discussing PPP. Well, it is clear that PPP is a useful framework for

macroeconomists. However, the concept is also important for managers and those wishing to invest in different

geographic territories. Given the theories assertion that exchange rates in the long run will move ensure that the

purchasing power of currencies are aligned, the theory, if it holds, can give managers useful insights on the likely

long run performance of various currencies and this information would be extremely useful in certain long term

investment decisions. For example if the difference between the exchange rate as currently derived from PPP and

the actual current exchange rate observed in the market suggest that a currency is overvalued, then management

would know that an investment in that currency at this stage would not be such a wise idea. The reverse to this is

also clearly true. One other area in which PPP is useful to multinational companies is in assessing compensation

packages for employees at similar levels within the company but who work in different countries. A useful example


5
    JIE: The purchasing power parity puzzle, pp 650; June 1996



Kwabena, Santiago and Fabrice                                                                           Page 6 of 17
is the situation in which a company, like McKinsey & Company, employs two Harvard Business School graduates:

one into their Johannesburg office and the other into their New York office. In this case, the PPP framework

provides a useful tool through which the company can set the compensation levels of the two graduates given that

they are living in different countries and will have differing costs of living. The tool will ensure that although the

nominal salaries may differ, the purchasing power of their salaries would be comparable. Other entities, including

governments, would also be able to make better policy decisions if they had a better sense of the long term

performance of their currencies as predicted by the theory of PPP.



In this section we have, at a high level, discussed theory of purchasing power parity and its relation to exchange

rates. In doing so we started with the law of one price and on that basis discussed the other variants of purchasing

power parity: absolute PPP and relative PPP. We have also seen that, if we believe PPP to hold over any time

period, then it can be a powerful predictive tool in helping managers and investors think through potential cross-

border situations. Much of our discussion however has been predicated on the fact that PPP does indeed hold and

that exchange rates will change to allow currency purchasing power for any two currencies to align. However, the

view the PPP holds at all, or over certain time periods, is one that remains controversial and there continues to be a

significant amount of debate, particularly in macroeconomic circles. In the next two sections we discuss whether or

not we believe the theory holds, and if so over what time periods and under what circumstances.




Kwabena, Santiago and Fabrice                                                                         Page 7 of 17
SECTION 3: SHORT VERSUS LONG RUN VIABILITY OF THE PPP CONCEPT

While there is a great discrepancy in how economists regard PPP as a valid short term proposition, much greater

accordance is found in terms of considering PPP as an anchor for long-run real exchange rates. Citing diverse

factors as causes for movements in short-term real exchange rates, economists, on the other hand, have weighed in

with persuasive evidence that real exchange rates tend towards purchasing power parity in the very long run. The

reason for this is simple, just like the law of one price explains how market arbitrage provides broad parity in prices

across individual goods, it should also provide parity across aggregate price levels.



Consensus suggests, however, that the speed of convergence is very low. Deviations appear to dwindle at a rate of

15% per year. Second, short-run deviations from PPP are large and volatile, stretching this convergence point even

further.



The existence of other factors, however, might seem to totally challenge the validity of this concept. Although LOP

suggests that arbitrage mechanisms (buying cheap and selling expensive) bring discrepancies in prices towards an

equilibrium, the presence of transactions costs, tariffs, even physical distance between countries, among other

factors, might all prevent this convergence between exchange rates and PPP from ever happening. We will look

closely at some of the factors that cause PPP to fail in the next section.



As we presented before, a mechanism broadly used to discuss the purchasing power of a country’s currency is the

Big Mac index. As we saw earlier, the LOP is represented in its algebraic form as:



           Pi = EPi*



If 1 USD (USA) = 107 YEN (JAPAN)



Thus according to the formula, a Big Mac selling for USD 2.39 should sell for the same in Japan (once converted to

US dollars) and for YEN 255.73. Finding differences in prices of the Big Mac around the world should give us a

sense that PPP is different among countries and LOP is not always valid. Using the U.S. dollar as a reference point


Kwabena, Santiago and Fabrice                                                                          Page 8 of 17
we find the following prices published in The Economist newspaper (Table 1)6. Using this chart we can estimate if

the currency is overvalued or undervalued against the U.S. dollar.


        TABLE 1
        Relative Prices of Big Macs
        Across selected countries

       Country             Price of Big Mac (in Dollars)


      Switzerland          5.20
      Denmark              4.92
      Japan                4.65
      Belgium              3.84
      Germany              3.48
      United States        2.32
      Canada               1.99
      Russia               1.62
      Hong Kong            1.23
      China                1.05



      Source: The Economist, Apr 15, 1995


Why are Big Mac values different after being converted to the common currency?



The tradable or non-tradable condition of a good or any of its components might explain for the differences in

above prices. The frozen beef patty, represents a good that is easily traded and transported, however, the inputs

required and labor costs involved in its preparation, the space rented to sell it, the local taxes and transportation

costs to distribute it, are not. All these components add up to the final price of a Big Mac. Other reasons might

involve bundles. For instance, condiments like mustard, salt, cheese, mayonnaise, might come freely with the final

product in some countries, whereas in other places might not. Nevertheless, for highly traded commodities the Law

of one price holds very well. Table 27 illustrates this fact for gold.




6
    The Purchasing Power Parity Puzzle, Roggoff, June 1996, page 3
7
    The Purchasing Power Parity Puzzle, Roggoff, June 1996, page 4


Kwabena, Santiago and Fabrice                                                                        Page 9 of 17
     TABLE 2
     Relative Prices of Gold
     Across selected countries

     Country              Price of One Troy Ounce (in Dollars)


   Hong Kong              379.35
   London                 379.25
   Paris                  378.81
   Frankfurt              378.87
   Zurich                 379.10
   New York               379.10


   Source: The Economist, Apr 15, 1995


Therefore, we find a strong correlation between the “non-tradable” condition of a good and its discrepancy in price

around the world. Moreover, using the concept of “substitutes” rather than “tradables” we can easily see that there

are certain types of goods that though easily tradable will still not be able to substitute other goods and therefore

will not foster an arbitrage opportunity. (i.e. all 220V domestic electronics wouldn’t do well in USA, as right-hand-

side UK cars wouldn’t do well in Latin America because standards are different in these respective regions).



Relative vs. Absolute PPP

In the previous section we discussed a couple of variants of the PPP hypothesis: Absolute PPP and Relative PPP.

One important thing to note here is that given the nature of absolute and relative PPP, then if absolute PPP holds,

then relative PPP must also hold, but if relative PPP holds it does not necessarily mean that absolute PPP will, since

it is possible that common changes in nominal exchange rates are happening at different levels of purchasing power

for the two currencies (due to transaction costs, for example).



To test if the relative or absolute version of PPP is a good approximation of the real world we can use the figure 1.

The Curves represent the US and UK consumer price indexes (CPIs) over a period 1820-2001. Both are expressed

in U.S. dollar terms. (UK CPI was multiplied by the number of US dollars exchanging for one UK pound at that

point in time). Figure 2 represents the producer price indexes (PPI) between UK and US over the period 1791-1991.

From these graphs we can see that absolute PPP did not hold perfectly and continuously: no strong correlation

between lines. Therefore, there are short-run deviations from PPP. Second, the national price levels (expressed in


Kwabena, Santiago and Fabrice                                                                        Page 10 of 17
common currency) tended to move together over long periods. And lastly, there is a stronger correlation between

PPIs than CPIs. In other words, although neither absolute nor relative PPP appear to hold in the short-run, both

appear to hold reasonably well in the long run.


Fig 18




Fig 29




In the following section we will explore some of the main circumstances that help determine whether or PPP will

hold.



8
    The Purchasing Power Parity debate, Taylor & Taylor, June 2004, page 32
9
    The Purchasing Power Parity debate, Taylor & Taylor, June 2004, page 32



Kwabena, Santiago and Fabrice                                                                     Page 11 of 17
SECTION 4: CONDITIONS FOR PPP FAILURE

Deviations from the PPP are best analyzed through two contexts: market based deviations and structural deviations.




Market explanations to deviations from PPP10

In this section, we will discuss anomalies to the PPP theories to see under which circumstances it might fail. The

main issue with the PPP theory is the fact that PPP conditions are rarely met within a country, or between countries.

Below, we are going to examine one at a time some of the reasons why the PPP theory may not hold, both in the

short run and in the long run.



Transportation costs and trade restrictions on traded goods

Since the PPP theory is derived from the law of one price, the same assumptions need to hold for both theories to

be valid. The law of one price assumes that there are no transportation costs and no differential taxes applied

between markets. In fact, this means that there can be no tariffs on imports or any other type of restrictions on the

trade of goods. Since transport costs and trade restrictions do exist in the real world, this would tend to drive prices

for similar goods apart in different markets. On average, transport costs make a good cheaper in the exporting

market and more expensive in the importing market. By the same token, an import tariff will create an upward

pressure on the prices of an identical good in two trading countries' markets, raising it in the import market relative

to the export market price. In short, the greater are transportation costs and trade restrictions between countries’

markets, the less likely for the costs of identical market baskets to be equalized. Therefore, the less likely is the PPP

theory to hold.




Costs of non-traded goods

Similar goods can sell for different prices in comparable markets because they require non-traded inputs in the

production process such as labor, rent, etc. The prices of these non-traded inputs can vary vastly from one market to

the other, and therefore impact the selling prices of the final goods. For example, let’s consider why the price of a

McDonald's Big Mac hamburger sold in Manhattan is higher than the price of the same product in the New York




Kwabena, Santiago and Fabrice                                                                          Page 12 of 17
City suburbs. The main reason is that the rent for restaurant space is much higher in Manhattan than in the suburbs;

and the restaurant located in Manhattan will pass through its higher costs to its customers in the form of higher

prices. Substitute products in Manhattan (other fast food restaurants) will be subject to the same high rental costs

and thus will charge higher prices to their customers as well. Because it would be impractical, and expensive to

produce burgers at a cheaper suburban location and then transport them for sale in Manhattan, competition would

not drive the prices of burgers to converge in Manhattan and in New York City suburbs.




Perfect information

The law of one price assumes that consumers have unrestricted access to perfect information about the prices of

goods in other markets. If that is the case, then in theory, there will be opportunities for arbitrage for profit-seekers.

These profit-seekers will begin to export goods to the market with high prices, import goods from the market with

low prices and pocket in the difference in prices. Over time, everybody will have access to the information that

profit-seekers have access to, and the prices will tend to converge between markets and opportunities for arbitrage

will disappear. And eventually, prices will be the same in all markets. In practice, this does not happen because

there is asymmetry of information in the real world. Some price deviations are known to some traders but other

deviations are not known. Alternatively, a small group of traders may know about a price discrepancy between

markets but is unable to achieve the scale of trade needed to equalize the prices for that product, because it lacks the

capital to execute trades that would swing the market. In any case, traders without information about price

differences on a specific commodity will not respond to arbitrage opportunities, thus prices will not be equalized

over time in different markets. Therefore, the law of one price may not hold which would imply that PPP would not

hold either.




Other market participants

In the PPP theory, it is the behavior of profit-seeking importers and exporters that forces the exchange rate to adjust

to PPP levels. These transactions are generally recorded on the current account of a country's balance of payments.

Therefore, it is fair to say that the PPP theory is based on current account transactions. This contrasts with the


10
     International Finance Theory and Policy Analysis, Steven Suranovic; Chapter 30


Kwabena, Santiago and Fabrice                                                                           Page 13 of 17
interest rate parity theory in which the behavior of investors seeking the highest rates of return on investments

induces adjustments in the exchange rate. Since investors are trading assets, these transactions would appear on a

country's capital account of its balance of payments. Thus, the interest rate parity theory is based on capital account

transactions.

It is estimated that there are approximately $1 trillion dollars worth of currency exchanged every day on the

international foreign exchange markets. This $1 trillion estimate is made by counting only one side of each currency

trade. This represents approximately one-eighth of the US Gross Domestic Product. That is an enormous amount of

trade. If one considers the total amount of world trade each year and then divide by 365, one can get the average

amount of goods and services traded daily. This number is less than $100 billion dollars. This means that the

amount of daily currency transactions is more than ten times the amount of daily trade. This fact would seem to

suggest that the primary effect on the daily exchange rate must be caused by the actions of investors rather than

importers and exporters. Thus, the participation of other traders in the foreign exchange market, who are motivated

by other concerns, may lead the exchange rate to a value that is not consistent with PPP, and therefore question the

validity of the theory.




Structural explanations to deviations from PPP11

All the evidence that we have looked at so far to explain deviations from PPP has been based on price and exchange

rate data. In this section, we discuss alternative explanations which are more related to fundamental factors such as

productivity, government spending and strategic decisions by firms.



Role of productivity in the relative price of non-traded goods

Balassa and Samuelson (1964) have developed a model to explain long-term deviations in PPP. They demonstrate

that, after adjusting for exchange rates, CPIs (Consumer Prices Index) in rich countries will be high relative to those

in poor countries, and that CPIs in fast-growing countries will rise relative to CPIs in slow-growing countries. They

argue that technological progress has historically been faster in the traded goods sector than in the non-traded goods


11
     “Perspectives on PPP and Long Run Exchange Rates”, Kenneth Froot and Kenneth Rogoff, NBER Working

Paper Series, Working Paper No. 4952, December 1994.


Kwabena, Santiago and Fabrice                                                                         Page 14 of 17
sector and, that this traded goods productivity bias is more pronounced in high income countries that boast more

technology-oriented industries. As a consequence, CPI levels tend to be higher in wealthy countries. This is due to

the fact that a rise in productivity in the traded goods sector will increase wages in the entire economy; producers of

non-traded goods will only be able to meet the higher wages if there is a rise in the relative price of non-traded

goods. To take an example, consider the fact that non-traded goods are cheaper in Ghana than in the UK. Although

the UK’s absolute level of productivity is higher than that of Ghana, the productivity in its non-traded goods sector

relative to its traded goods sector is lower.



One important caveat to the Balassa-Samuelson paper is the persistence of the effect of income growth on PPP in

really long-run data. Even though technology can differ across countries for extended periods, the free flow of

ideas, together with human and physical capital produces a tendency toward convergence of incomes in the long

run.



Demand factors and the real exchange rate

According to the Balassa-Samuelson model, the real exchange rate depends entirely on supply factors; demand

factors do not come into play. This property of the model depends on several assumptions:

       •   The country is small and cannot affect the world interest rate;

       •   Capital is mobile internationally;

       •   Both capital and labor are instantaneously mobile across sectors internally



If, for example, capital and labor are mobile across sectors in the long run but not in the short run, demand factors

can have a short-run impact on the real exchange rate. However, over the long run, the productivity differentials

continue to be significant whereas the effects of demand factors (government spending and income) become less

important.



Pricing to market

One of the main theories on why there can be deviations from the law of one price in traded goods is the “pricing to

market” theory of Krugman and Dornbusch (1987). In the pricing to market model, oligopolistic suppliers are able


Kwabena, Santiago and Fabrice                                                                         Page 15 of 17
to charge different prices for the same good in different countries: thus the prices of BMWs can differ between

Germany and the United States. If the BMWs are tradable, why isn’t this gap closed through arbitrage as discussed

earlier? According to the model, there are cases where companies as price-makers can separately license the sale of

goods at home and abroad. In practice, the ability to price discriminate across markets may be very limited.



In addition to potentially explaining longer-run deviations from the law of one price, “pricing to market” theories

also have implications for the transmission of currency movements assuming there is stickiness in nominal prices.

Let’s assume that in the short run, costs are set in nominal terms in the currency of the supplier. Then, if there is an

appreciation in the home country’s nominal exchange rate due to an external shock, the real costs of exporting

goods will rise. If demand elasticity were equal to 1, the markup of price over cost would not be affected, but the

markup on goods destined to be exported will fall if the foreign price elasticity of demand is greater than 1.

Consequently, domestic prices and export prices for the same goods will differ and PPP theory will not hold

because prices will not converge in comparable markets.




Kwabena, Santiago and Fabrice                                                                          Page 16 of 17
SECTION 5: CONCLUSION



In this paper we have endeavored to give an overview of PPP. We saw that the concept is based on the law of one

price which advocates there being one common currency price for the same good, irrespective of where it is

purchased. The paper went on to discuss relative and absolute PPP, important variants of the original PPP

framework. We noted that despite its usefulness at a first approximation, users of PPP need to be mindful of the

time horizon over which it may or may not hold. In our paper, we found that although it appears to hold in the long

term, its short term viability remains very questionable. Having established that PPP may not be viable in the short

term, we then turned our attention to the conditions under which PPP fails. Here, we realized that there are a number

of market based and structural conditions that can cause PPP to fail, some of which include transportation costs, the

lack of perfect information and the role of productivity in the relative price of non-traded good. In all, it is evident

that despite its flaws, the theory of PPP is a very useful tool for assessing several cross border transactions.




Kwabena, Santiago and Fabrice                                                                           Page 17 of 17

				
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