# The Purchasing Power Parity Theory

## Introduction

PPP or the Purchasing Power Parity is a theory that is used to determine whether the exchange rates between currencies are equal when the purchasing power is equivalent in each of the two countries compared. Basically, it depicts the clarification between the fairness of how exchange rates are calculated through the equal ration of the price level of the two countries’ goods and services. Taking for example when the domestic price level of a country increases or when a country is experiencing inflation, the exchange rate of the country should decrease in value in order to maintain the PPP. The determinant of PPP is the law of one price.

Without transportation and other transaction expense, the competitive markets will be able to balance the price of the same good in two countries when the time the prices are converted in the same currency (Rogoff, 1996). Taking for example a laptop computer that costs 750 Canadian Dollars (CAD) in Toronto should cost 500 US Dollars (USD) in California considering the exchange rate between Canada and the US is 1.50 CAD/USD.

People would prefer to buy the laptop computer in Toronto if it cost lesser. This approach can be referred to as arbitrage and is accepted at a huge sense. The customers in US that buy Canadian products will proffer for a value of the Canadian Dollar which will make the Canadian goods more expensive to them. This is constant upon the products reach the same level of pricing. And this process is constant in anticipation of having the same level of prices among the products.

Purchasing power parity does not determine the exchange rates in a short term because of the fact that it is affected by the news. Declarations with regard to the interest rate changes alter through the approach of the growth path of the economies and the factors that motivate exchange rates in a short term sense. Comparisons of PPP illustrate the long run changes of the exchange rates. The significant forces in the economy in the rear of PPP will result to the equalization of the purchasing power of currencies. This may take a lot of years though and four to ten years is seen to be a normal span of time (Ethier, 1995).

## Discussion

### Theoretical framework

The means of exchange rate shifts has put the economists in some perplexities. Bretton Woods’ system is distinguished when monitoring the fluctuations of the exchange rates prevailed and this defines some answers to the questions of the economists. The exchange rates in developed countries have taken an interesting recurring path. There are many theories that describe the determinants of exchange rates such as the monetary framework of the exchange rate determination.

The portfolio equilibrium model describes the changes in the exchange rate through connecting them to the alterations in the relative potential returns on domestic and foreign financial assets with an exceptional accent on unforeseen influences and the part of news. Hence, Purchasing power parity is regarded as one of the oldest theories of determining the exchange rates. This explains the alterations in the level of prices between two countries (Froot, and Rogoff, 1995).

In retrospect, the theory of PPP was first introduced by a German economist Gustav Cassel way back 1922. According to the economist, the probability that products of the same are sold on the same prices in a global market, and this made the concept of linking prices and exchange rates (Azali et al., 2001). This approach is rational indeed considering the fact that prices change in an international manner. Regardless of its historical explanations and strong points, the PPP is seen to have some controversies.

According to Melvin (1997), though the theory of PPP presents the link between the price levels and exchange rates, it does not mean that this is the mere fact for the theory of exchange rate. Melvin (1997) stated that “the fundamental process for determining the exchange rate of freely traded currencies has not been well understood, and there are various theories that try to explain this process”. But this process of PPP is the one that is regarded as the oldest approach and largely used by many economists.

Furthermore, it is explained by Meher Manzur (1993) that “Some authors have held that PPP provides a basis for the determination of exchange rates with useful policy implications. Others have argued that PPP is an equilibrium relationship that leaves much to be explained. On an empirical level, many authors have found that PPP does not appear to hold very well, particularly over recent times since the return to flexible exchange rates among major currencies in the early 1970s”.

However, PPP and market exchange rates have differences such as the estimation of World Bank’s World Development Indicators 2005 in 2003 that a US Dollar was equal to 1.8 Chinese yuan though the purchasing power parity, which is seen to be very different because the nominal exchange rate of the two countries is 1 USD/7.6 yuan. This issue has illustrated a lot of insinuation like; the Gross Domestic Product per capita in the People’s Republic of China is about 1,800 US Dollar while on the view point of PPP, it reaches an amount of 7, 204 US Dollar.

This is usually used in order to declare that China is the second largest economy in the world though the prevailing calculation would just be accepted under the theory of PPP. On the other hand, the Gross Domestic Product per capita of Japan is approximately 37,600 US Dollar but in under the PPP approach, it just reveals to have 30,615 US Dollar (Husted and Melvin, 1997).

PPP is regarded as having controversial hold and it requires financial markets to be completely liquid, transparent and free without restrictions, taxes or any transaction expenses. Good markets are perfect with the consideration of the international shipment of goods that has the capability of taking place freely and with no cost (Ethier, 1995). PPP also needs a single consumption good which is usual to everyone and similar commodities appear in the same level of each country’s prices of goods.

These basically depict to be fictional for some economists. The suppositions for the PPP illustrate relative inflation differentials as being the only source of the variations in exchange. Although, in the short run, other non-monetary observable facts like the changes in relative prices, changes in the level and consumption of output and consumption affects the supply and demand for the foreign currency and hence, the exchange rate (Froot and Rogoff, 1995).

### Law of one price

The law of one price details the purchasing power parity and stipulates in three ways. The first is that, the PPP should significantly consider the factors such as transportation, costs, hindrances to trade and other expenses for transactions. The second stipulation agrees that there should be competitive markets for the products of the paired country. And the third approach states that the law of one price pertains to the tradable goods; stationary goods like houses, and a lot of services which are locally available, are certainly not exchanged between countries.

In addition to, the law of one price depicts that the differences of prices on the traded goods that tends to even out through the absence of tariffs, barriers for trading and high shipping rates. Therefore, the law describes that an effective market should have one price for all similar goods. However, the econometric analysis disrupts the hypotheses and provides other proposition for the PPP or exchange rte relationship according to the relative Gross Domestic Product. The Neoclassical economics that involves the Balassa-Samuelson effect theory explains that the PPP model adjustment gives the equilibrium of CPIs (Ethier, 1995).

It is disagreed that PPP theory had mislaid its rationalization power because of the comparative intransigence of the exchange rates in the Bretton Woods System (BWS) in 1944. Since 1973, BWS formally ended and the exchange rates became supple again in current years, yet, the PPP theory looks like recovered its theoretical power of the complicated justification of the determination of the exchange rate.

There are a lot of empirical studies with regard to the PP that have been carried out over the years. In 1978 and 1981, Frenkel carried out empirical studies and in the second study, it prevailed that the simple versions of PPP did not hold up. Other tests prevailed that PPP is a long-term supposition (Ethier, 1995). Prompted by the stimulating and interesting aspects of PPP, but concurrently distinguishing its contentious characteristic.

### Absolute PPP

Absolute purchasing power parity refers to the equalization of the price level between countries. It explains the exchange rate through the use of the price level ratios between two countries. Just like the citation made in the previous example made in Canada Dollar and US Dollar. Applying the law of one price, “the price level in the home country is equal to the price level in the foreign country multiplied by the exchange rate” as what Kulkarni and Ishizaki (2002) discussed in their paper.

The exchange rate between Canada and the United States represented by ECAD/USD is equivalent to the price level in Canada PCAN and divided by the price level in the United States PUSA. Suppose that the price level ratio PCAD/PUSD depicts a PPP exchange rate of 1.3 CAD per 1 USD. If the exchange rate today is ECAD/USD and 1.5 CAD per 1 USD, the PPP theory illustrates that the CAD will value more than the USD and thus the USD will depreciate against the CAD.

### Relative PPP

On the other hand, relative PPP is the rate of changes of price levels or the inflation rates. This supposes that the rate of appreciation of a currency is balanced to the difference in inflation rates of the foreign and home country. Specifically, this can be illustrated through this given example; if Japan has an inflation rate of 1% and the US has an inflation rate of 3%, then the US Dollar will depreciate against the Japanese yen by 2% per year. This holds well empirically most especially when the inflation differences are big.

This is the other way of stating the exchange rate behavior. Through the relative PPP, exchange rate is viewed as a percentage change and is presented to be equal to the difference between inflation rates in two countries. Therefore, not like the absolute PPP, relative PPP centers on the percentage change in the price levels of two countries. The percentage change in the price levels is normally regarded as the rate of inflation. And through the use of the consumer price index, an estimation of the inflation rate can be determined. The theory suggests that the change in the exchange rate is determined through the price level changes the two countries (Ethier, 1995).

### Calculation of PPP

The easiest way to calculate purchasing power parity for the paired country is through the comparison of the price of standard good that is similar across countries. Each year, the Economist Magazine publishes a version of PPP which is called the hamburger index. This compares the price of a McDonald’s hamburger around the world. More refined versions of PPP are viewed at a large number of goods and services. However, a problem is seen because people in different countries especially the consumers, they set various approaches for pricing goods and services which makes the comparison of purchasing power of countries difficult.

The calculation for the PPP exchange rate has been an issue because of the difficulties of determining comparable goods to compare purchasing power parity. Assessment of the purchasing power parity is indeed too complicated with the use of the specific formulas and taking consideration of the facts that the countries do not just differ in a uniform price level. Food prices may be greater than the housing prices while less than the entertainment process.

People who are in different countries normally consume different goods. And it is significant to compare the cost of goods and services through the price index. Indeed, this is seen to be a difficult task because the buying behavior and goods vary from place to place. Therefore, it is important to consider the differences in the quality of products that are involved in the transaction process. More statistical difficulties come up with the multilateral comparisons when more than two countries are being compared. Inflationary effects should be accounted properly if a PPP comparison is to be made over some period of time (Wang, 2000).

### Empirical evidences in PPP

Trading and non-trading goods, short and long-term, and the comparison between the developing and non-developing countries reveal the empirical evidences of purchasing power parity. Prices of the trading goods are assumed to be on a similar level where in the countries involved in trading goods would posses an exchange rate that would follow the trend of changing the price of the goods at any given point in time.

It depicts that the behavior of the exchange holds the evidence for the trading goods while non-trading goods thus are not intended for assessing the price valuation of certain goods. Movements in the market exchange does not affect the non-trading goods and services because those are usually set to lower prices and prevails lower incomes. The low cost of living is considered by the PPP though but the income is considered in a different manner.

The comparison between short and long-term approach for the PPP favors more on the long-term side. The theory of purchasing power parity uses a long-term equilibrium exchange rate of the two countries in order to balance its purchasing power. The exchange rate balances the purchasing power of many currencies and this cannot take effect in short term equilibrium. Purchasing power parity does not recognize the exchange rates in a short term considering the effect of media.

The declarations regarding the changes in the interest rates change the concept of the goals of economies. Many factors can affect and motivate the exchange rate in a short term process. The important factors in the economy will result to the equalization of the purchasing power of the different currencies of the countries (Either, 1995). And this is said to be taken in a long term process.

There are studies that found some minimal support for the suppositions of PPP. It is found to be a profound divergence from the law of one price in the market commodities. If the law of one price consequently does not hold, PPP is more likely not to hold as well. Although, there are series of studies that found PPP does not hold but time lag should be considered (Milanovic, 2002). Others suggest that PPP is usually desecrated in the short run though but holds up in the long run. Usually tests are done through longer periods of time or on times when inflation rates are high in the economy because it gives a stronger link for the PPP.

In spite of the arguments with regard to the significant grounds of PPP, the agreement that emerges from a wide literature on this matter suggests that relative PPP is valid in the long run. Husted- Melvin (1997) justifies these findings. “In high inflation countries, changes in exchange rates are highly correlated with the inflation differential because the sheer magnitude of inflation overwhelms the relative price effects, whereas in low inflation countries the relative price effects dominate exchange rate movements and lead to discrepancies from PPP.”

It means that if the inflation rate is relatively high, people do not have to pay more attention to the relative price effect. With regard to the clarification for the period, it is said that the longer period of time will tolerate for more inflation. Therefore the unsystematic relative price effects are comparatively irrelevant and exchange rate changes are very much connected to the inflation differentials (Chinn, 2000).

Looking into the perspectives of the developed and developing countries would require further explanations and studies that present empirical data for evaluating the evidences that holds PPP for certain countries as will be discussed in the following context. Comparisons for the world income depict the differentiation between the developed and developing countries. It needs to set the level of economic growth where in it signifies the vital forces for assessing the purchasing power parity.

Accordingly, developing countries are illustrated by the government through the innovations and limitations for trade than any other developed equivalent. Asian countries’ structure of government attempts to be different from the alterations that occur in the developed countries. It is expected that the developing countries presents more divergence on the exchange rates from PPP (Kaminsky and Reinhart, 1998).

However, smaller divergence from PPP is more likely seen in the developing countries as a result of the predilection in putting capital limitation. Limitations are for exchange and it impacts the reduction of the presumptions from the currency that provides lower instability of the exchange rate. It is regarded as an approach to test the PPP for the developing countries most especially in Asia. Certainly, considerable divergence from PPP in countries where there is a high foreign exchange rate assumption and movements for capital (Wu and Wu, 2001). Exchange rate misalignment is also taken into account for some developed and developing countries over a time frame of 16-18 years (Alba and Park, 2003). Thus, PPP holds for the developed countries because the economic growth is affected by the increase in the exchange rate which typically brings problem for the developing countries to be stable.

### Testing Theory: A Case of Japanese Yen and US Dollar Exchange Rate

There are a lot of studies with regard to the determination of empirical evidences of the PPP between particular countries. Featuring this study would make this paper be more liable and help comprehend the approach of PPP through a specific scenario. Primarily, tests are made on the PPP theory and are conducted with the use of different econometric ways. Kulkarni (1991) conducted a test for the case of US Dollar and Japanese yen.

The paper aims at testing the Purchasing power parity and explains the behavior of exchange rate. Significant data such as the US Dollar and Japanese yen are used and apparently concluded that the explanation of PPP has a profound explanatory power for the behavior of the exchange rate. The paper accepts the difference between real and absolute purchasing power parity, survey-related literature and carries out an econometric analysis of the arguments in the PPP theory.

In this paper, a new approach is used which is based from the Divisia index numbers and illustrates a number of attractive features. This concludes into the idea that even though the short term data do not back up the PPP, the long term data can be taken account for supporting the theory of PPP rather. The use of PPP theory for the determination of exchange rate is somehow put into a controversial issue during the early years as some of the economists have backed it up, though others do not. Different methods have been used by a lot of economists but this paper use a casual observation with the help of the tables and graphs and the statistical methods.

Association between the exchange rate that is affected by the PPP and the actual exchange rate are carried out for the testing of speculations of the researchers. An ordinary least squared is also used in the paper in order to estimate methods (Papell and Theodoritis, 2001).

Controversies on the aspect PPP, it is undeniably true that some of the economists support those ideas. Among the different methods for the hypothesis testing, some prevailed to be appropriate and some are not. There are economists who use different data such as the whole price index or the Gross Domestic Product deflators rather than the consumer price indexes that can also be used in order to come out with a different conclusion.

But this study conducted by Kulkarni and Ishizaki (2002), used two methods and find out the satisfactory outcomes in order to back up relative PPP. Through the results, it can be said that there is a statistical significant link between the change in the exchange rate and the percentage change in the level of prices of two countries. PPP explains the change in the exchange rate between the countries Japan and US. Moreover, the explanation of the factors that causes divergence from PPP and many divergences can be taken as invalid for the concept of PPP. There are factors that are lastingly stoppable like the effect of big economic announcements in the news.

Consideration of the aspects mentioned can not dismiss the fact of having differences on the results through the use of different data, periods, countries and methodologies. PPP can still be utilized as a basis for an economic policy discussion because it can bear satisfactory results for particular countries. Kulkarni (1991) presented that the case of Japan yen and US Dollar during the periods of 1973 up to 1997 through testing the links between the actual exchange rate and the exchange rate affected by the PPP and through the Ordinary Least Squared methods, it is then concluded in the paper that a relative PPP can hold its theory.

### Empirical Evidence of PPP in Asian Countries

Another study in this paper will further be discussed in order to come up with a conclusion as to PPA should be hold or not for a lot of considerations. The paper aims at testing the validity of the PPP theory for six Asian countries and be able to detail the perspectives regarding the PPP’s empirical evidences. The study is conducted through the Panel Unit Root test. The paper caters to the creation of a multilateral real effective exchange rate with the use of dynamic export, import and trade weights for the countries and the outcomes present that the unacceptable theory of the PPP’s failure cannot be dismissed until the cross sectional links are put down.

The economic explanations for the marginal variations in the integration about the PPP due to the different system of measurement used in the formation of real effective exchange rates of the six Asian countries are given. This illustrates that the PPP does not hold a case of two-sided real effective rates of the featured countries with one big trading partner. Looking into the point of view of the policy, PPP can be utilized to evaluate the levels of exchange rates. It also considers the premise of whether the theory of PPP holds in six Asian countries which relates on being the trading partners of India (Rogoff, 1996).

The data used in the study came from the International Financial Statistics and Direction of Trade Statistics. Accordingly, it is stated that “Bilateral Exchange rates between any two countries are computed from bilateral exchange rates of each of these countries with the US. This is the potential source of cross sectional dependence. Real exchange rate series has been constructed with the CPI series and the exchange rate series for the price of US dollars in respective currencies” (Shoup, 1998).

The study covered the periods of 1970 up to 1998 for India, Korea, China, Malaysia, Singapore and Thailand. Factors such as export, import and trade are considered for the tests and the CPI of the countries included are needed to reduce the insignificant exchange rates (Allsopp and Zurbruegg, 2004).

Conclusions of this study points out to the acceptance that PPP theory is a vital supposition for many aspects in the international economics. The PPP theory puts highlight in the essential factors that largely affects the movements of the exchange rate. It is considered to be useful for the determination of exchange rate levels and also to measure up the income levels between the countries. The study established one most recent method which is the panel test in order to test the PPP for six South East Asian Countries. Many methods of testing PPP in the long run have resulted from time to time but the method used in the study has conquered the context (Rogoff, 1996).

## Conclusion

Purchasing power parity largely takes an approach for the determination of whether exchange rates are equal for two countries involve. It considers two concepts which are the absolute and relative PPP. The theory commonly uses the United States currency in order to make comparisons because US currency serves as the major currency that leads the finance market in the world. Assumptions for the theory of PPP accounts for the ideas defined by the law of one price and establish a basis on how to test PPP of significant countries. The evaluations for PPP have given important details in many areas of the international finance and economics.

Specifically, it helps to present a comparative analysis between countries on many diverse issues. The area of development economics has been used broadly in order to set up the degree of income inequality where in an area of increasing consensus such as globalization has become a reason for arguments. It has tolerated making up conclusions with regard to the links between the economic growth and real exchange rate valuations (Shoup, 1998).

With regard to the international finance, evaluation for PPP has been influential in guiding the policy makers in their choice of exchange rate administrations and the decisions to create monetary unions. Moreover, supposing the existing difficulties in accounts liquidity crisis are covered by the assessment of PPP. As prevailed by a lot of literatures and studies, the conclusions gave mixed ideas and various concepts. The popularity of PPP serves as a policy tool for central banks and treasury departments around the world that helps to distinguish probable existing account dilemmas before it results to a bigger problem for the country.

In relation with few other economic, political and legal factors, PPP then can give an early warning system to be able to help the government foresee any future economic crisis in a country. PPP have played important roles in comprehending with many economic scenarios. Thus, it justifies economic and financial circumstance change, the need to constantly test for the PPP becomes an important matter.

Empirical evidences for the purchasing power parity accounts for the long-term assessment of the countries involve. The economic growth and issues relating to the developed and developing countries should also be accounted because it defines an important ground for the determination of the country’s inflation rate. Thus, purchasing power parity holds with the consideration of the aspects justified in the context that are revealed on the empirical evidences for trading goods, long-term and developed countries.

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