The Principle, Practise and Problems of Purchasing Power Parity Theory

Table of Contents

Introduction

I. Purchasing Power Parity theory
1. The Law of One Price and the Purchasing Power Parity
2. Absolute PPP and relative PPP
3. PPP and the mechanism of exchange rate determination

II. Looking for empirical evidence of PPP theory
1. Informal test of PPP theory
2. Formal tests of PPP theory

III. The Critics and Usage of PPP Theory
1. Limitations and Critics of PPP Theory
2. The Usage of PPP Theory

Conclusions

Appendices

References

List of Figures

Figure 1: Decrease in $/£ nominal exchange rate as a result of higher price level in the UK

Figure 2: Increase in $/£ nominal exchange rate as a result of lower price level in the UK

Figure 3: Over- and unevaluated currencies according to PPP theory

Figure 4: Dollar-Sterling PPP over two centuries.

Figure 5: PPP at various time horizons

Figure 6: Summary of formal tests for PPP

Figure 7: Limitations of absolute PPP

List of Abbreviations

illustration not visible in this excerpt

Introduction

"Under the skin of any international economist lies a deep-seated belief in some variant of the PPP theory of the exchange rate."^[1]

The purpose of this paper is to consider one of the most controversial theory in international economics – Purchasing Power Parity theory – its main idea, empirical evidence, limitations and practical application.

The main idea of PPP is price levels changes determine the exchange rate change between two countries. There are two versions of PPP theory absolute and relative. Stricter absolute version of PPP did not find confirmation in reality and relative version of PPP theory was proposed. Despite theoretical and practical inconformity, PPP is present in many models of international economics as an explanation of exchange rate changes.

The main apologist of PPP theory and its father was Gustav Cassel. He indicated that the exchange rate determined by price levels is not necessarily the actual exchange rate but the equilibrium one. Also Cassel mentioned that there is a tendency for the actual exchange rate to return to its equilibrium exchange rate. The original idea of PPP theory is described below:

“Our willingness to pay a certain price for foreign money must ultimately and essentially be due to the fact that this money possesses a purchasing power as against commodities and services in that foreign country.”^[2]

In this paper we considered the principle and two versions of PPP theory, discussed its empirical evidence and econometrical tests, and also tried to find possible reasons why PPP theory fails in reality and answered the question is this theory still useful for explaining exchange rates movements.

I. Purchasing Power Parity theory

Purchasing Power Parity (henceforth PPP) theory describes the relationship between currency exchange rate and price levels in two countries. The exchange rate of two currencies is positively related to the price level in foreign country and negatively related to price level in home country. Equilibrium is reached when the ratio of the two countries’ price levels of a fixed basket of goods equals the exchange rate between two countries.^[3] Another definition of the PPP theory as the citation below:^[4]

“…the nominal exchange rate between two countries should be equal to the ratio of aggregate price levels between the two countries, so that a unit of currency of one country will have the same purchasing power in a foreign country.”

This means in turn that if a country experiences an increase in its price level, i.e. inflation, then exchange rate of this country will be proportionally depreciated to restore the PPP between two currencies. To explain the PPP theory it is useful to give an idea about the “Law of One Price” as a basic of PPP theory and show its absolute and relative aspects.

1. The Law of One Price and the Purchasing Power Parity

In general the PPP describes the price relatives, which is expressed by the ratio of a national currency of the identical good or service in different countries.^[5] A popular example about the PPP is the “The Big Mac Index” published by The Economist Magazine. The Big Mac PPP shows the exchange rate that would mean that Big Mac’s cost abroad as much as in the United States (Appendix 1).^[6]

The LoOP is the foundation of the PPP theory. It assumes that goods in two different countries are sold for the same prices without taking into account an existence of transportation costs, tariffs, taxes and other barriers to trade. The LoOP states that the price of an identical good, which is traded on competitive markets, will have the same price in every trade-related country, when the price is indicated in the same currency. This statement shall be explained in the following example by means of the “iPod” price, , which is sold in two competitive markets without any significant trade barriers or transaction costs, like transportation costs or tariffs, for example in the United Kingdom (UK) as domestic market and in United States (US) as foreign market. If we say that the price for an iPod in UK is and in the US is, than it is possible to get the ₤-price of an iPod on the US market, depending on the exchange rate, like this:

illustration not visible in this excerpt

The LoOP implies in equation 1, that the ₤-price of an iPod must be the same as in the US.^[7] If we use the second equation below, in which is describing the amount of US dollars per one UK pound exchange rate, e.g. 2,0, and we assume the price for an iPod in the UK is 300 ₤ then in the US - 600 $.

illustration not visible in this excerpt

If we go further and assume that raises over 300 ₤, a clever trader would buy iPods more likely in the US market and sell them to the UK market. A kind of operations when one makes profit from price differences in different countries is called arbitrage. If those arbitrages happen in larger scales, the higher demand will raise the price of US iPods and will make this US product more expensive for the UK demanders. In the same way the iPods on the UK market will get cheaper because of increased supply of iPods from the US. This development will continue until the prices converge at the equilibrium which is expressed by the PPP between US dollar and UK pound.

To get from the LoOP to PPP theory instead of the price of identical good, like iPod in our example of LoOP, we need to use price of a basket of goods and services which represents the price level of an economy as whole in certain period of time:

illustration not visible in this excerpt

whereas is the weight of an individual product or group of products i in a basket of goods which represents a whole economy;stands for the price of product i; t certain period of time.

If we change the variables of the item priceandfrom the LoOP equation into the commodity basket prices and we can describe the equation for the absolute PPP, like:

illustration not visible in this excerpt

The equation 6 states that there is an equilibrium when, the nominal exchange rate, equals, PPP exchange rate. The PPP exchange rate in itself is equal to the ratio of the price levels and . The reciprocity of that equation is also valid but for indirect exchange rate, i.e. =.

The PPP can be calculated in three stages. The first stage is gathering data of prices on product level (prices of iPod in the US and in the UK); the second stage is aggregating the data of prices on product level to the product group level (food, clothes, etc.). On the third level the data for prices on product group level is aggregated using some weights for every kind of product group to the level which represents an economy as a whole. Hence, contrary to LoOP, PPP is represented by averaged and weighted prices of product groups.^[8] The annual calculation is done in the joint OECD-Eurostat PPP Programme, in which the Eurostat calculates the PPPs for the EU countries, including the European candidate countries, like Turkey, Croatia, etc. The OECD is taking over the part in calculating the PPP figures concerning the non-European Union countries, like Ukraine, Russia etc., which are also included in the PPP Programme.^[9]

2. Absolute PPP and relative PPP

Up to this point we were focused on the absolute values of price levels and currency exchange rate as determinants of PPP theory equilibrium. But PPP theory equilibrium can also be expressed in terms of price level and currency exchange rate relative changes. According to this we can say that there is absolute and relative PPP. As we showed above absolute PPP aims on the exchange rate equalisation according to the price level of two countries. The relative PPP focuses on the equalisation of relative changes in price levels, i.e. inflation rates in two countries, and currency exchange rate. For example, if the price level in the US is raising about 10 % within a year and the UK price level is raising about 5 % in the same year, than the relative PPP would forecast a 5 % depreciation of the US dollar against the UK pound.^[10] Because relative PPP is focused on relative price changes, it requires using of price indices and instead of price levels. For price indexes we can use Consumer Price Index (CPI), Producer Price Index (PPI)^[11], GDP-Deflator^[12] or other indexes which represent changes of the general price level in an economy during some period of time.^[13] The following example is focusing on the CPI. The CPI covers the changes of the average price for a group of individual products consumed by households in different time periods and measures the changes in price level of a base time unit.^[14] The UK CPI () can be calculated as follows:

illustration not visible in this excerpt

whereas andstand for base year and t year respectively.

To measure the relative change of US dollars / UK pound exchange rate using CPI first there is a need to have a look on the ratio of the year 2007 of the US and UK CPIs in terms of price levels:

illustration not visible in this excerpt

The ratio of the CPI is formed in the division of the very left-hand side. According to equation 8 we can get the purchasing power parity exchange rate of 2007 divided by the PPP exchange rate 2006 in the next equation.

illustration not visible in this excerpt

To get the PPP exchange rate using the CPI of the US and the UK according to the base year 2006 is done by a rearranging of equation above, like in equation 9.

The inflation rate of an economy is measured as a percentage change of the CPI during a year, for example we want to calculate inflation rate, , in 2007:

We also can rearrange equation 10 by using inflation rates in the US and the UK instead of price indexes:^[15]

The importance of the relative PPP derives from that case, if the absolute PPP does not hold than the relative PPP is still valid, because the factors for the absolute PPP may change over time and are not stable. Whereas relative price levels changes allow a rough approximation about relative changes in exchange rates.^{[16] [17]}

3. PPP and the mechanism of exchange rate determination

The PPP equilibrium condition is reached when equation 6 is valid. If there is an inequality in nominal exchange rate and PPP exchange rate then we can assume that general price level in UK is higher then in the US (equation 12).

Then, according to increased benefits from arbitrage due to price level differences, demand of US households for UK goods and services will decrease resulting in lower demand for UK pounds (leftward shift of the demand curve for UK pounds on Figure 1) on foreign currency exchange market (FOREX). At the same time for the same reason UK households will increase demand for US goods and services resulting in higher supply of UK pounds in exchange for US dollars (rightward shift of supply curve for pounds on Figure 1) on FOREX. Therefore the nominal exchange rate of US dollar / UK pound will decrease. In other words, the UK pound will depreciate, while the US dollar will appreciate. This process will continue until there will be equal price levels again and the PPP exchange rate is reached. The amount of pounds on the market will not change because we assume that changes in its supply and demand are proportional.

illustration not visible in this excerpt

Figure 1: Decrease in $/£ nominal exchange rate as a result of higher price level in the UK

[Source: Suranovic (1999), chapter 30-2)].

The opposite can be caused by a higher general price level in the US market, like in equation 13:

Then, according to increased benefits from arbitrage due to price level differences, demand of US households for UK goods and services will increase resulting in higher demand for UK pounds (rightward shift of the demand curve for UK pounds on Figure 2) on FOREX. At the same time for the same reason UK households will decrease demand for US goods and services resulting in lower supply of UK pounds in exchange for US dollars (leftward shift of supply curve for pounds on Figure 2) on FOREX. Therefore the nominal exchange rate of US dollar / UK pound will increase. In other words, the UK pound will appreciate, while the US dollar will depreciate. This process will continue until there will be equal price levels again and the PPP exchange rate is reached. The amount of pounds on the market will not change because we assume that changes in its supply and demand are proportional.

illustration not visible in this excerpt

Figure 2: Increase in $/£ nominal exchange rate as a result of lower price level in the UK [Source: Suranovic (1999), chapter 30-2)].

Knowing the showed above mechanism of PPP theory equilibrium we can conclude that it is rather simple to earn money on FOREX deals. All we need to do for that is just to determine what currencies have undervalued and overvalued nominal exchange rates compared to their purchasing power and then place buying and selling orders for both groups of currencies respectively. The Figure 3 below shows a list of PPP of different currencies compared to the US dollar. The bars going to right are the currencies, which are overvalued by the percentage given on the abscissa of the graph. This means that according to PPP theory these currencies will depreciate against US dollar in the long-run. Whereas the bars going to the left side are undervalued and according to PPP theory will appreciate in the long-run.

illustration not visible in this excerpt

Figure 3: Over- and unevaluated currencies according to PPP theory [Source: Antweiler (2007)].

II. Looking for empirical evidence of PPP theory

As we can see from Figure 3 there are a number of currencies which nominal exchange rates are strongly deviate from their purchasing power parity. There are two opposite conclusions that we can make from that. If our logic about PPP theory in the first part sounds reasonable and convincing then one should immediately begin to trade on FOREX because it is possible to earn money just buying undervalued and selling overvalued currencies. But if the meaning of under- and overvalued currencies is nothing else but the bias of PPP theory? Then one might want to find some empirical evidence of PPP theory prior to applying it to its own bank account.

1. Informal test of PPP theory

To see weather PPP in its relative version is an acceptable approximation to the real world we will consider the following example.^[18] In the Figure 4 left graph plots data on the US and the UK consumer price indices (CPIs) over the period 1820-2001. Both indexes are expressed in US dollars. This means that UK CPI was multiplied by US dollar / UK pound exchange rate (number of US dollars per UK pound) at specific point in time. The right graph shows exactly the same relationship but instead of CPI it uses producer price indices (PPI) for the period 1791-2001. Each of the price indexes equals to 100 in 1900.

[...]

^[1] Taylor/Taylor (2004), p. 135.

^[2] Cassel (1922) in: Officer (n.d.), p. 68.

^[3] Antweiler (2007).

^[4] Taylor/Taylor (2004), pp. 135-158.

^[5] Schreyer/Koechlin (2002), p. 1.

^[6] The Economist (2007).

^[7] Krugman (1996), p. 400.

^[8] Schreyer/Koechlin (2002), p. 2.

^[9] OECD (n.d.).

^[10] Krugman (1996), p. 401.

^[11] The PPI is a selection of data concerning price indices of materials and fuels purchased by the manufacturing industry to run their business.

^[12] The GDP-Deflator is the indicator for price changes within all components of the Gross Domestic Product.

^[13] Officer (n.d.), p. 6.

^[14] OECD (2007).

^[15] Krugman (1996), p. 391.

^[16] Ibid., p. 402.

^[17] Suranovic (1999), chapter 30-2.

^[18] Taylor/Taylor (2004), p.139-140