Purchasing power parity (PPP) states that in the absence of transaction costs and barriers to trade, the nominal exchange rate between two countries should equate the aggregate price levels of the respective countries. Since its formal introduction in 1918 by Gustav Cassel as a means of stabilising the exchange rates of the major countries after WW1, PPP theory has been extensively scrutinised and investigated by researchers to determine its relevance as a practical theory in exchange rate determination. Starting with the testing of the most basic relationship of PPP in the 1970s till the recent use of more advanced econometric techniques like Co-integration or Fractional Integration, the results gathered from the numerous literature have not been consistent. But even with the mixed results, there was always belief by academia or interested parties that the PPP holds the potential to be the cornerstone for the determination of exchange rates. As a result this paper attempts to join the plentiful literature on PPP, by investigating the convergence of long run PPP for two of most advanced economies in the world, United States of America and United Kingdom respectively. Co-integration and Johansen test have been correspondingly employed to the data set that spans from 1968 to 2010. The findings from both tests were contrasting where Co-integration advocating that PPP does not hold in the long run while Johansen Co-integration test shows the existence of one co-integrating relationship. Nevertheless, this result is consistent with existing literature where different econometric models have produced different results, even on similar dataset.

1. Introduction

Purchasing Power Parity (PPP) points out that in the absence of transaction costs and barriers to trade, the nominal exchange rate between two countries should be equal to the aggregate price levels of the respective countries. Although the term Purchasing Power Parity (PPP) was apparently first proposed by Gustav Cassel in 1918 as a means of stabilising the overly-inflated exchange rates of major industrialised countries after World War 1, the origination of the underlying idea has a history dating back to the Spanish scholars of 15th & 16th centuries. To the scholars, PPP serve as reliable measure to comprehend the interaction between the trade between the Spanish and other economies and the monetary impact on the exchange rate. But to current users of this theory, PPP offers an easily understood economic theory for the determination of exchange rate and the relation of the countries’ price level to exchange rate.

Since its introduction, PPP theory has been extensively scrutinised and investigated but results have not been consistent. Even with the contrasting literature, there was always belief that the PPP theory holds the potential to the theoretical solution to exchange rate determination. Dornbusch and Krugman (1976 p.540) stated that “Under the skin of any international economist lies a deep-seated belief in some variant of the PPP theory of the exchange rate”. It was further pointed out by Rogoff (1996), that even with the mixed results from the various literatures, there was “a surprising degree of consensus on a couple of basis facts” First, real exchange rate will tend to purchasing power parity in the long run but the speed of convergence is extremely slow. In addition, the deviation in the short run is large and volatile which eliminates its role for exchange rate determination in short term. It is this significant deviation of the exchange rate form PPP in the short run that presents the “Purchasing Power Parity Puzzle” to researchers and interested parties alike.

They have searched and investigated different aspect of PPP and improved their statistical approaches in the hope of explaining the deviations in the short run and how it could be reconciled with the long run exchange rates. In the earlier studies like Gailliot (1970), Lee (1976) and Friedman (1980), they have used a simple method of using the basic PPP relationship as the null hypothesis to test for the relevance of PPP. As expected due to the stringent criteria, most studies failed to find the validity of PPP in the long run. Surprisingly, Frenkel (1978) found that the PPP theory holds for countries undergoing hyper-inflation phase but was less successful for countries with stable economic conditions. With the unsuccessful attempts in the early days, researchers started to revisit the issue from another perspective by testing the null hypothesis that the real exchange rate does not revert to its mean but instead follows a random walk (Roll 1979; Darby 1983; Edison 1987 etc). Some techniques to test for unit root included the Dickey-Fuller and Augmented Dickey-Fuller test and Variance ratios. These techniques did not seem to improve the probability of rejecting the null hypothesis of random walk and that PPP holds in the long run. More recently, methodologies like co-integration and fractional integration & co-integration have entered the picture. Corbar and Ouliaris (1988), Taylor (1988), Kim (1990) applied co-integration techniques but most found that the null hypothesis of non co-integration cannot be rejected in most cases while Rogoff and Froot (1994) compared the 3 techniques used to determine PPP and concluded that although the co-integration test have been more successful in rejecting the null hypothesis, it is still unclear whether this technique produces a benefit over the simple PPP hypothesis or random walk test. On the other hand, Cheung and Lai (1993), Masih and Masih (1995) and Soofi (1998) employed the fractional integration approach and found relatively favourable results. Regardless of the mixed results from different methods and econometric techniques, purchasing power parity theory remains an important aspect in exchange rate determination as it is simple to comprehend and intuitive.

The objective of this paper is to investigate the relevance of the PPP theory on the exchange rate of two advanced economies, U.S and UK respectively. This analysis will be conducted using co-integration test, a common time series methodology in the PPP literature. Furthermore to ensure the robustness of the results, Johansen test will also be applied.

The rest of this paper is organised as follows; Section 2 presents the introduction of purchasing power parity and law of one price, discuss the debate of PPP and the test of unit root and random walk as well as explaining of some improved techniques for the testing of PPP in last decade. Section 3 describes the data and empirical framework. Section 4 will show the findings from the analysis while section 5 will conclude the paper.

2. Literature review

2.1 Purchasing Power Parity and Law of One Price

Purchasing Power Parity states that in the absence of transaction costs and barriers to trade, a commodity should cost the same regardless of the location of its purchase. If the prices of similar goods are different between countries, the exchange rate will adjust to be equal to the ratio of the price levels of the countries, so as to offset any possible arbitrage opportunities. If this scenario were to exist, three economic reactions will be subsequently observed (Arnold 2008);

Being relatively expensive, the demand of the particular commodity will fall, forcing price down. (Domestic)

Being relatively cheaper, the demand of the particular commodity will increase, increasing the price. (Foreign)

The demand for the foreign currency relative to domestic currency would increase

Eventually, the exchange rate and the price levels of the two countries will adjust until they converge at equilibrium again and PPP will hold again.

Before exploring further into PPP, it will be beneficial to mention the law of one price theory as it forms the foundation for Purchasing Power Parity (PPP) theory, which explains the long-run equilibrium relationship between nominal exchange rates and price levels.

The law of one price states that in the absence of transaction cost and barriers to trade, identical goods in 2 countries should sell for the same price at the same time. The law of one price applies to individual commodities while purchasing power parity is relevant to a basket of goods (ie. CPI or WPI). Consequently, if the law of one price holds true for all the commodities, PPP theory will hold too.

Where is price of good I in dollar , is the nominal exchange rate and is price of good i in British Pounds. Thus, the exchange rate between the two countries equates the relative ratios of the countries’ price levels. (Shown below)

Therefore, an increase in the domestic purchasing power will be associated with a proportional appreciation of the currency in the foreign exchange market, vice versa. Moreover, PPP is implying that all countries’ price levels are similar when compared in similar currency. (Krugman and Obstfeld, 2006)

2.2 Relative & Absolute PPP

The absolute PPP states that exchange rate is equal to the national price levels in two countries and the purchasing power would be the same in the two countries if expressed in a common currency. On the other hand, Relative PPP focuses on percentage changes in the price levels and the exchange rate and assets that the relative change in exchange rate must be matched by the same change in price levels in order to keep the ratio constant.

Where is the percentage change in the nominal exchange rate and denotes the inflation rate.

Froot and Rogoff (1994) pointed out that discussions relating to re-establishing exchange rate to equilibriums using PPP, referred exclusively to relative PPP. They further argued that real shocks can lead to changes in the relative prices of different commodities, especially so for low inflation economies. Moreover, there is not much evidences to support that the relative PPP will exhibits a greater robustness than the absolute PPP.

2.3 Debate of PPP and Tests for Unit root and Random walk.

In July of 1944, delegates from 44 countries met in Bretton Woods, where they drafted and signed the Articles of the International Monetary Fund (IMF). The objective of this coming together was to propose an international monetary system that will ensure internal (full employment & inflation) and external balances of the countries. The Bretton Woods agreement called for fixed exchange rates against the US dollar whilst the US dollar was tied to the price of gold. Subsequently, the “monetary approach” was commonly used during that period of time to determine exchange rates. This approach advocates that exchange rate between countries should be determined by the relative price of two monies, which is further influenced by the demand and supply factors in their respective money market. More importantly, this approach is based on the assumption that purchasing power parity does hold continuously.

From 1970s, there have been numerous studies to determine the empirical relevance of purchasing power parity theory. But due to the lack of theoretical and advanced statistical models, the results were largely disappointing. Early studies of PPP have mostly based on the simple empirical model shown below.

Where is the logarithm of the domestic currency price of good i, is the logarithm of the foreign-currency price and is the logarithm of the domestic-currency price of foreign exchange. They test the null hypothesis that = 1 and and if the null cannot be rejected, it meant the exchange rates and relative prices follows the PPP theory. On the other hand when, Purchasing power parity does not hold.

Frenkel and Johnson (1978) found some relative success for