An understanding of Purchasing Power Parity is essential to evaluate the economic health of nations and to make the first comparison among different countries. The basic theory is that the price of same goods between different countries should be equal when the price of goods are measured in a common currency.1 PPP has an important role in the international finance . Firstly, PPP is a good tool to convert some economic indicators around the world and it also provides a point of reference for these countries to be compared. Secondly,PPP theory can be used as an important measurement and basis to evaluate the current real exchange rate .Actually, the current exchange rate always fluctuate around the PPP rate .So when we compare these two exchange rate ,there have been both substantial and prolonged deviations from PPP rate. 2
The note will provide the reader a wider understanding of how the concept of ppp perform , the practical econometric tests of PPP, limitations about PPP theory.
The literature review on econometric tests of PPP
The empirical evidence on PPP is huge,so it is wise to divide these empirical evidence into six different groups:the early empirical literature on PPP;tests of the random walk hypothesis for the real exchange rate ; cointegration studies ; long span studies ; panel data studies and studies employing nonlinear econometric techniques.
The early empirical literature on PPP ,in the early literature, people tested PPP based on the ordinary least squares ,but economists found that there were a serious problem ,that is if nominal exchange rates and price indices are nonstationary variables , the testing based on OLS is invalid (Granger and Newbold,1974) . Until the mid 1980s , with the development of advanced econometric techniques, the research on PPP theory and its relationship with real exchange rate make new progress. Including these ,the tests for a unit root in the real exchange rate and cointegration tests are most widely used.
As to the tests for a unit root in the real exchange rate, it is used to test the stationarity of the data of time series. When the data of real exchange time series displays nonstationary,it do not support purchasing power parity theory.Conversely,if it displays stationary,we can believe that the real exchange rate can return to the mean value in the long term,it can also return to the long-term equilibrium value at last. Lothian and Taylor (1993) used the unit root to test Dollar-Pound rate and Pound-French franc rate over 200years.It proved that the test support the purchasing power parity in the long term. Frankel (1987)used the unit root to test the real exchange rate of Pound-Dollar rate.when the sample periods are 1973-1984 or 1945-1984, it can not reject the random walk hypothesis .when the sample period is 1869-1984, it can reject the random walk hypothesis,and the real exchange rate return back the purchasing power parity at a rate of 14% per year.
Another way is to test the cointegration of the variable sequence of real exchange rate .For example, we can test the relationship of nominal exchange rate ,the price indices expressed in the domestic currency and the price indices expressed in terms of foreign currency.In general, we can confirm that the real exchange rate is stationarity when it exists the relationship of cointegration. In this day,the cointegration studies support the long -run purchasing power parity at the state of the adoption of generalized floating .
xu(2003)states that the importance of choosing the correct price index in PPP tests. In his study,it shows that the half -life of deviation from PPP is lower than Rogoff's three-five-years. Kim (1990)use EG-test to test whether regression residuals of purchasing power parity exists the unit root. It shows that if wholesale price indices are used,the real exchange rate are all stationarity for the five industrialized country.But when the consumer price indices are used, only one exchange rate is stationarity.
Building the theory of purchasing power parity
The theory of purchasing power parity derive from the law of one price. To better understand of the theory of purchasing power parity, we should know about the law of one price and discuss the concepts of absolute purchasing power parity and relative purchasing power parity later.
Without the limitation of transport costs and other barrier to trade and with a competitive market, the price of same goods in different countries will be same once the price is measured in a common currency.
The most famous application of the law of one price is the MCDonald's Big Mac. The magazine launched a survey of Big Mac index.they choose hamburgers because they fit the concept of the theory of purchasing power parity
Assume that the price of the hamburger in the USA is P$ ,then the same hamburger in other countries is P€. According to the law of one price ,we can get the equation as follows:
P€ =E* P$
E is the exchange rate between other currencies/dollar. It easily can compare the price of the hamburger to obtain the measurements of overvaluation or undervaluation of the dollar in terms of the theory of purchasing power parity against other currencies.
Absolute Purchasing Power Parity
Absolute PPP assert that the price of goods in one country when compare with the price of the same goods in another country once measured in a common currency, the price should be equal.For instance, if the price of goods is ₤50 in the UK,and the same goods is $100 in the USA, so the exchange rate will be ₤50/$100=₤0.5/$1,the equating can be displayed as follows:
S=P/P*
Where S is the exchange rate,P is the price of goods displayed in the domestic currency , P*is the price of same goods expressed in the foreign currency.
In terms of absolute Purchasing Power Parity ,a fall in the domestic price relative to the other price will give rise to a appreciation of the domestic currency compared with the foreign currency.
Relative Purchasing Power Parity
In the absolute version of Purchasing Power Parity,we assume that at a state of without transport costs and other barriers to trade and in the presence of a perfect capital and goods markets.
But in fact , transport costs and other barriers to trade will always exist. Relative theory assert that the exchange rate will adjust by the number of the inflation in different countries,which can be expressed as follows:
%∆S=%∆P- %∆P*
Where the left side means the percentage change in the exchange rate , the right side means domestic and foreign inflation rate respectively.
Limitations to the theory of PPP
There are two main flaws around the theory.firstly, the flaw of the theory itself. Secondly,the problem about the test itself.
The limitation to the theory of PPP
On the one hand,the theory assert that the fluctuation of the exchange rate depend upon the purchase power of two currencies,namely price affects exchange rate only,and other factors have no direct influence on the exchange rate . But the fact is not the case, the change of many macroeconomic factors can affect the fluctuation of the exchange rate ,such as money supply, Interest rate ,fiscal policy,balance of payments etc. Apart from these factors,psychological factor , politics and conflict have an important influence on the fluctuation of the exchange rate.It is incomplete to regard the price as the only factor of the exchange rate .
On the other hand,the speed of the price to external impact is much slower than price to financial markets, so the exchange rate would departure from price in reality.when the moment see the important economic information is declared ,the moment see the exchange rate departure from purchase power parity.the price can not catch up with the exchange rate in time. With the extension of time,the gap between the price and the exchange rate will be narrowed.So the random effect of relative price appear less important.This is the reason PPP can hold in the long run.
The technical problems of the tests
Firstly, the theory of PPP demand the same price system to make sure the comparison of the two countries. But in fact,many reasons lead to the poor comparison between two countries,such as economic system ,economic structure etc.A number of empirical evidence show that the applicability of PPP is pretty good within the industrialized countries ,especially in the members of the European Union .the applicability is much worse between the industrialized countries and the developing countries.
Secondly,there are many correct price index in PPP tests.As mentioned above,IMF have six indices.PPP is much more likely to hold if one uses a tradables price index (TPI), than if wholesale price indices(WPI)are used; much worse is consumer price indices(CPI).
Thirdly,as for the statistical methods,they differ from each country,which mainly display in sampling method and the determination of weights.In practice,these factors can affect the comparison between two countries to some extent.It may lead to the different results due to different statistical methods.
Fourthly, another problem in testing for PPP is the choice of the base period. If the exchange rate can not reflect the purchase power parity between two countries at that time ,the test will make no sense finally.In fact, we can not make sure whether the exchange rate of the base period is reasonable or not,so we can get different results when we choose different base periods.
At last,the determination of price adjustment lag and time periods can affect the results of the test.because different countries exist various differences, different countries have different actions on the external shock.for the industrialized countries ,because they own developed capital and goods market, they can exchange items and service freely and quickly. The lag of the price adjustment in these countries will be much shorter than counterpart in those developing countries. We also can get different results due to different time periods. We can find the big differences by testing on a monthly data, quarterly data and yearly data.In general, if we test the theory of PPP on a yearly data , the gap about price adjustment lag between the developed countries and those developing countries will be narrowed. So it is veryimportant to determine time periods,which can affect the results of the test substantially.
conclusion
In a word ,there are a number of literatures about purchasing power parity ,and there are also a variety of methods and results of econometric tests.Most of results can not hold the theory of purchasing power parity.Even though,the value of the theory and forecast in the long term are widely concerned.especially when a nation is at the state of high inflation,after that,the theory of purchasing power parity will become the important basis of various financial policy in these countries.It is essential to understand that purchasing power parity is a useful tool that evaluate the health of economics and the current state of various countries.Just like the same tool and indices, we must know the limitations and take measures to deal with these weakness and limitations.
