The purchasing power parity theory is one of the most influential exchange rate determination theories, and it is raised by the Swedish economist Gustav Cassell (1922). The theory is an old, but the most basic theory of exchange rate determination. It is a significant basis for governments to formulate economic policies, and some international organizations also employ the purchasing power parity theory to compare the situation of macroeconomic development among countries. For instance, the World Bank analyses the PPP and the form of capital to produce the International Comparison Program report. No doubt the effectiveness of the policies or reports is based on the assumption -the PPP theory is valid in practice. However, regarding the issue - whether the PPP theory is effective or not is challenged by various viewpoints and tests since it is proposed. A great many of the economists have tested PPP theory through different methods, and they have got various results and conclusions. In this essay, the results of the econometric tests of the PPP theory will be examined, and through the survey, the limitations of the PPP theory will be pointed out from my perspective.
The construction of the essay is as follows. Section 2 documents a general review of literature involving the past tests of the PPP theory. Section 3 presents the key points and framework of the theory, including the fundamental concepts and assumptions, etc. Section 4 provides the findings after surveying the results of the econometric tests, while Section 5 summarises the whole paper.
2. Literature review of past econometric tests of the purchasing power parity theory
Economists have tested PPP theory for countless times via various kinds of means these years, but sometimes they get totally different conclusions. For example, Froot and Rogoff (1995) provide the empirical evidence which supports the effectiveness of PPP theory, whilst Benigno and Thoenisse (2008) argue that PPP theory is not valid in practice. In addition, the ways of testing have always been improving. In the early, the ordinary least squares (OLS) regression is simply used for testing. Then, they examine whether the PPP theory is a random walk. After that, as the econometric techniques are increasingly developing, the time series' method becomes maturer, and many test techniques such as the unit root test and the co-integration test are widely used. Afterwards, some non-liner models are proposed. Apart from the economists employ various test methods, the different periods of time which are tested is another reason that causes different results and conclusions.
With the development of time series' method, the empirical ways to test PPP theory are often under a linear structure. One is the unit root test, because the performance of time series of the real exchange rate is severely related to the validity of the PPP theory, the effectiveness can be tested by analysing whether the real exchange rate is constant. Roll (1979), Adler and Lehmann (1983), Mark (1990) have all utilised this test, and the result cannot reject the null hypothesis that the real exchange rate is a random walk. The other is the co-integration test, which is proposed by Engle and Granger (1987). It tests whether there is a long-term equilibrium relationship between exchange rate and domestic and foreign price level. Abuaf and Jorion (1990), Pippenger (1993) have all employed the test, and the principal argument lies in if the dissimilar Exchange rate systems, price levels or data frequency have influence on the long-term equilibrium relationship of PPP.
Dumas (1992) states that due to the transaction costs, the change of exchange rate should be non-linear. Therefore, the traditional unit root test and the co-integration test is not appropriate, and they may produce errors. The analysing of the real exchange rate behaviour should be under the non-linear structure. In addition, Chen and Wu (2000) present the similar point of view through analysing the non-linear behaviour that the real exchange rate deviates from the PPP theory rate between Japan and the United States via STAR (smooth transition auto-regressive) model.
Taylor and Peel (2000) point out that the reason why the real exchange rate deviates from the equilibrium exchange rate, and the equilibrium change is non-linear is that under the impact of investors' technical analysis, the exchange rate does not change exactly as the variation of the economic foundation.
The non-linear variation may derive from arbitrage cost, government intervention or the implement of investors' technical analysis. The government intervention is mostly carried out gradually, so the adjustment process of the exchange rate is likely to be smooth. The smooth transition autoregressive model (STAR) can describe the adjustment process, and there have been much literature realise this, testing the variation behaviour that the exchange rate deviates from the economic basis via this model. For instance, Sarantis (1999), Killian and Talor (2003), Paya et al. (2003).
3. The fundamental key points and framework of the purchasing power parity theory
The basic idea of the purchasing power parity is that the value of money is determined by its purchasing power, and the domestic price level may represent the purchasing power of its currency to a certain extent, so the exchange rate is determined by the contrast of different price levels among countries.
The law of one price is the precondition of the purchasing power parity. The law of one price means that without taking into account the factors such as transaction costs, the prices of tradable goods in different countries are identical in terms of the same currency. That is
pi = S ·pi*,
In the meantime, the law of one price has its own preconditions: the currency convertibility is in the same degree in different countries; currencies, commodities, services and capital flows are totally free; the information is complete; there are no transaction costs and tariffs; the prices of commodities are completely elastic.
Based on the law of one price, the purchasing power parity theory has some key assumptions: the international trade is completely free without any transaction costs such as tariffs, quotas or taxes; all the prices of goods change in the same range; price is the only factor that influences the exchange rate; the factor which affects the purchasing power is merely the quantity of money.
The purchasing power parity theory can be divided into two forms; one is the absolute purchasing power parity theory, whilst the other is the relative purchasing power parity theory. The formula of the absolute PPP theory is
S = P / P*,
S is the exchange rate (direct quotation), P and P* represent the domestic and foreign price level of an identical bundle of goods respectively. The absolute purchasing power parity means that when the domestic price level increases relatively, the purchasing power of the domestic currency declines accordingly. That is to say, the currency devalues and the exchange rate falls, and vice versa. While the formula of the relative PPP theory can be derived from the formula mentioned above,
%-S = %-P - %-P*,
%-S is the rate of change in the exchange rate, %-P and %-P* are the domestic and foreign inflation rate respectively. It says that the change rate of the exchange rate equals the difference between the domestic and foreign inflation rate. Compared with the absolute PPP, the relative PPP is more valuable, and its data is easier to obtain.
In summary, the purchasing power parity theory is the most influential exchange rate determination theory, and it is based on the quantity theory of money, interpreting the exchange rate behaviour from the quantitative point of view. Moreover, it starts to analyse the issue from the basic function of money (purchasing power), and is easy to understand. The formula is simple as well. Nonetheless, the PPP theory is not a complete theory of exchange rate determination. It does not state the cause-effect relationship between the price and the exchange rate clearly.
4. Empirical findings
Having surveyed the relevant literature, I find that the early classical economists emphasise that the price can be adjusted freely through the market mechanism, thus the theories of exchange rate determination following the spirit of classical school assume that the purchasing power parity is always correct. Nevertheless, since Keynes suggests that the price and wage are of rigidity, the theories of exchange rate determination which derive from the price rigidity theory imply that the purchasing power parity theory cannot hold in the short run, but it can in the long run. Because the price level is the commodity market price while the exchange rate is the price of the capital market, and the adjustment speed of the capital market is faster than that of the commodity market, the exchange rate can hardly reach the level determined by the purchasing power parity in the short term. However, in the long term, in one hand, if the disturbance is temporary, the influence will gradually disappear as the time goes by, hence the real exchange rate may move back to the equilibrium level, and the purchasing power parity theory holds. In the other hand, if the interference is constant, the real exchange rate may deviate, and the purchasing power parity fails to hold. As a consequence, it has reached a consensus that the PPP theory is not valid in the short run, but in the long run, it is still a debatable issue.
The past empirical tests to most industrial countries have suggested that when the international trades run in an open enough context, the exchange rate can be described by the PPP theory to a certain extent. Nonetheless, in the real world, the levels of economic development and the economic systems vary in different countries. Moreover, many factors may affect the domestic price such as shipping costs, tariffs, the incomplete flow of goods, trade barriers, monopolies, changes in industrial structure and technological progress, etc. When these factors play an important part in the economy, the law of one price, which is the basis of the purchasing power parity theory, and other relevant assumptions may fail to hold.
In the empirical tests, many sources of data are used, but usually they do not provide that what are the specific goods which they use to calculate the purchasing power parity. They utilise different indices, calculation methods or samples to produce the results. In addition, the indices may not reflect the prices of non-tradable goods and services, but the non-tradable goods occupy a considerable part in the calculation of price index, so it may affect the test results. Therefore, the statistical deception may emerge. We can choose different samples of goods or indices to produce the deceptive outcome.
Some of the relative early econometric tests of PPP theory literature tend to employ the augmented Dickey-Fuller (ADF) unit root test, Engle and Granger co-integration test or Johansen co-integration test. However, due to the lack of power of the traditional unit root test and the co-integration test, the PPP theory is likely to be not valid. Domas (1992) suggests that because of the transaction costs, the adjustment behaviour of exchange rate should be non-liner. After that, Kapetanios, Shin and Snell (2003) propose a new model (KSS) based on the smooth transition auto-regressive model (STAR). Accordingly, the literature which carries out the non-liner test tends to get a positive result of the PPP theory. As a consequence, from my perspective, it is just because that some assumptions of the PPP theory such as the international trades are completely free or the price is the only factor to influence the exchange rate may fail to hold under certain conditions, the non-liner model which has taken into account these factors influencing the exchange rate behaviours is likely to produce reasonable results.
5. Conclusions
The purchasing power parity theory is one of the most classic exchange rate determination theories, but it cannot be supported well by the empirical tests since it was raised. This paper outlines the fundamental concepts and framework of the PPP theory, and examines and summarises the past econometric tests of it during decades. We find that some key assumptions of the PPP theory fail to hold in the short run, and certain elements will impact the effectiveness of the theory in the real economy of the world. Besides, the survey of the literature suggests that the test methods and techniques will affect the outcomes, correspondingly, the conclusions of the effectiveness of the purchasing power parity theory vary as well.
