Purchasing Power Parity, Realistic in the 21st Century?
Kai Huang
University of Amsterdam, Economics and Business, Netherlands
Abstract
In 1918, Gustav Cassel (1918) first mentioned Purchasing Power Parity in how to determine exchange rates. Since the collapse of the Bretton Wood system and the introduction of floating exchange rate regime, plenty of researches have been conducted to test the validity of PPP. Although the early results rejected it, more recent studies tend to find some support for PPP. This paper uses the simple unit root model to test the monthly U.S. dollar/U.K. pound, Canadian dollar/U.S. dollar and Japanese yen/U.S. dollar real exchange rate data for the period January 2000 to December 2014 in order to see whether PPP gives a better prediction of the exchange rates for the period.
Introduction
Purchasing power parity, broadly known as PPP, is a preliminary economic theory of determining the nominal exchange rate between any two given countries. Since 1918 when Gustav Cassel formalized the PPP theory into what we generally know today (Cassel, 1918), there have been dozens of papers published in discussing and testing the validity of the theory, especially during the post Bretton Woods period of the previous century. This paper consists of four main parts. In Part One, the concept, two deferent forms namely the Absolute PPP and Relative PPP as well as the underlying idea will be reviewed. In Part Two, the main theoretical problems for both the Absolute PPP and Relative PPP will be reviewed and these problems have led to the empirical tests of PPP especially after the collapse of the Bretton Woods system. Part Three is going to review these empirical tests and results, mainly the ones using monetary approach and the unit root test. We will see that although the short-‐run exchange rate is volatile, some literatures support the long-‐run PPP. Moreover, recent literatures tend to find more evidence of PPP. This leads to Part Four, my own test of PPP in the 21st Century using the simple unit root model, which is a model used in many recent existing literatures. The reason I do this test is because as the world steps into a new century, accompanied with an increasing maturity of information technology and a faster pace of integration of the global economy since the start of floating exchange rate period, it gives a potential opportunity for PPP to play a practical role in the new era since international arbitrage, one key factor underlying the theory, is more likely to be satisfied than it was in the past. I applied monthly U.S. dollar/U.K. pound, Canadian dollar/U.S. dollar and Japanese yen/U.S. dollar real exchange rate data for the period January 2000 to December 2014 to the test and the result I have achieved reject the validity of PPP. Therefore, I suggest a longer period of data should be tested
in order to justify whether the usefulness of PPP has really improved or not in the new century.
Statement of Originality
This document is written by Student Kai Huang who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Literature Review:
Part One: Revision of the purchasing power parity
Concept of Purchasing Power ParityPurchasing power parity (also known as PPP) states that without barriers of trade (tariffs, quotas etc.) or transaction costs, the exchange rate between any two countries should be determined by the ratio of their aggregate price levels. The concept of PPP was first introduced by British political economist David Ricardo, but formally named and popularized by the Swedish economist Gustav Cassel in 1918. In his famous published work “Abnormal Deviations in International Exchanges”, Gustav (1918) first mentioned that he referred to such a situation as the “purchasing power parity ” in which the actual exchange rate would not deviate from the quotient between the purchasing power of two countries’ monies, if free movement of goods for trading is not disturbed.
The underlying philosophy of PPP is the Law of One Price and the key determinant of it is international arbitrage.
Alan M. Taylor and Mark P. Taylor (2004) elaborate that the Law of One Price indicates people are only willing to pay the same price for the same goods. Thus, as long as traded internationally, one good should sell at a same price when expressed in a common currency no matter where it is being traded. If this is not the case, then there exists an arbitrage opportunity under which one can simply buy the good where it is selling at a lower price while at the same time sell it to the countries where it could be sold at a higher price and yield the price difference. This situation is called international arbitrage and the way to eliminate international arbitrage is to find a certain level of the exchange rate between any two currencies that ensures the prices expressed under different currencies will be transformed in the same level of price under one common currency. For the same logic, if countries construct their aggregate market baskets in the same way, the Law of One Price implies each country’s aggregate price level should become the same when using the exchange rates to transfer them into a common currency. This is how exchange rates should be determined
and it is exactly what PPP means.
Forms of Purchasing Power Parity
PPP can take two different forms, either the Absolute PPP form or the Relative PPP form.
Absolute PPP takes form of
𝑆 = 𝑃𝑃∗ Where,
S is the equilibrium spot exchange rate between two currencies (here it represents units of domestic currency per unit of foreign currency),
P is the price index for the domestic country, P* is the price index for the foreign country.
Absolute PPP claims that the exchange rate between two countries is determined by the quotient of the two countries’ price indices.
Relative PPP takes form of
𝑆!!!
𝑆! =
1 + 𝜋! 1 + 𝜋! Where,
𝑆! is the spot exchange rate at time t between two currencies (again here it represents units of domestic currency per unit of foreign currency),
𝜋! is the percentage change of domestic price index from time t to time t-‐1, 𝜋! is the percentage change of foreign price index from time t to time t-‐1.
Relative PPP claims that the change of exchange rate between two countries for a certain period is perfectly offset by the difference between the two countries’ inflation rates during the period.
However, both forms of PPP face some theoretical defects and the next part is going to deal with these problems.
Part Two: Theoretical issues related with PPP
Although the underlying logic behind PPP seems to be concise and explicit, it suffers from potential over-‐simplicity and over-‐idealization by its restrictive conditions, and thus lacking practical value.
Problems specific with Absolute PPP
For Absolute PPP, Rogoff (1996) concludes two of the main possible problems of it in practice:
First, Rogoff (1996) argues the price indices used in Absolute PPP formula are assumed to be standardized all over the world. That means, every country’s government constructs its basket of goods using exactly the same goods and assigning exactly the same weights to the goods included, which is hardly the case in the real world. For instance, even though Germany and the U.S. are believed to share a fairly similar basket of goods, they still construct their price
indices in quite different ways.
More importantly, Rogoff (1996) points out each country’s price index is the aggregate price level relative to that of a base year, for example, if we set 1900 as the base year, then the price index for any given year is the percentage value of the aggregate price level for that year relative to that for 1900. However, if the quotient of two countries’ base year aggregate price levels has already deviated too much from the true exchange rate at the time in reality, the whole series of equilibrium exchange rates for the testing period estimated by Absolute PPP based on these two countries’ price indices would also deviate significantly from the true levels in reality. For instance, if the U.S. dollar/U.K. pound exchange rate in 1900 was 2 and the quotient of U.S. aggregate price level and U.K. aggregate price level was only 1, then 1900 is not a good choice for being the base year. Instead, we have to find another year as the base year in which the exchange rate did not significantly deviate from the quotient of their aggregate price levels. Absolute PPP makes the assumption that we can always find such a base year. Additional objection to PPP may focus on the existence of transaction costs, which includes transportation costs, taxes, tariffs and non-‐tariff barriers etc. For example, Engel and Rogers (1994) have found that physical distance plays an important role in varying prices of two different locations, both within the U.S. market and within the Canadian market, from the empirical evidence that distance has a positive effect on differentiating prices of 13 out of 14 goods investigated within these two markets, and for 11 of them, distance has a significant effect at a 5% significance level. The possible reason for domestic price dispersion is the existence of transportation costs. However, for the international market they have found evidence that the border instead of distance plays the dominant role in explaining the price dispersion of cross-‐border goods in the two markets for the possible reasons including tariffs and other trade restrictions. These findings pose another potential restriction to PPP being practical.
For the potential problems mentioned above, the relative version of PPP theory, which does not focus on the absolute level of the equilibrium exchange rate but on the change of level in exchange rate, has been indorsed since the 19th Century so as to avoid these problems and achieve exchange rates estimation by PPP matching better to that in reality. As Lafrance (2002) suggests that relative PPP gets rid of the problems related with the prediction of the absolute level of exchange rates by just focusing on the change of exchange rates.
However, there are still a couple of possible issues applying to Relative PPP and Absolute PPP in common that could not be avoided by Relative PPP.
Additional problems of Absolute PPP in common with Relative PPP
Beach, et al. (1995) summarize three fundamental issues related with both Absolute and Relative PPP that may prevent the usefulness of PPP.
The first issue is not all goods are tradable goods. As Obstfeld and Stockman (1983) demonstrate, the world market for tradable goods and for non-‐tradable
goods are two separate markets, and international commodity arbitrage only happens in the world market for tradable goods instead of that for non-‐tradable goods. However, as Balassa (1964) verifies, non-‐tradable goods such as services do have a significant positive correlation with the overall price level of a country, and thus the price index of a country partially reflects the price level of its non-‐tradable goods. Therefore, it is incorrect to use PPP, which involves price indices that take account of both tradable and non-‐tradable goods as a whole to calculate what the equilibrium exchange rate level should be because no international arbitrage can be made on those non-‐tradable goods included in the calculating process.
The second issue associated with PPP is that besides the volatility of the relative inflation rates between two countries, exogenous factors in the real economies can also result in a change of the equilibrium exchange rate between them. An example is given by Beach et al. (1995) to illuminate such a situation. Suppose if there is a technological revolution happening in Canada that increases the production capacity as well as the quality of its agricultural goods, consumers in the U.S. will stop buying agricultural goods in their own country and instead start buying them from the Canadian market. This leads to an appreciation of Canadian dollar relative to US dollar because now people need more Canadian dollars to purchase goods from Canada and fewer U.S. dollars to purchase goods from the United States. However, because both the demand and supply of the Canadian agricultural goods are shifted up, there will be no significant inflation in the Canadian market of agricultural goods. In the U.S. market for agricultural goods, the lower demand will lead to a permanent left-‐ward shift of long-‐run supply, as Bashar (2011) verifies that aggregate demand shocks did result in a change of long-‐run aggregate supply permanently for the G-‐7 countries, and thus there is no significant deflation in the U.S. agricultural goods market either. Therefore, as Buiter and Eaton (1980) and Cooper (1986) conclude, when the relative demand for one country’s currency changes because of asymmetric shocks in the two countries’ real economies, a new equilibrium exchange rate will be introduced without an equal-‐size change in price levels in both countries. Last but not least, capital movements between two countries can also result in a change of the equilibrium exchange rate. When central banks conduct monetary policies, the resulting changes of the overnight interbank interest rate will have a further pass-‐through effect to retail banking markets and lead to capital movements between countries (Kleimeier and Sander, 2006). In the research of Helliwell and Padmore (1982), they have found that capital movements led to variation of the exchange rates among the seven major OECD countries without corresponding inflation rates changes during the period 1974-‐1977. This implies there is no reason expecting PPP to accurately calculate either the short-‐term or the long-‐term exchange rates that match the ones in the real world if there are frequent and unexpected capital movements between countries.
Considering all the potential problems mentioned earlier, there exists dozens of empirical studies testing whether these problems are valid and whether PPP
holds in reality. The next part will review some of the key studies.
Part Three: Empirical Tests for PPP
Many empirical studies were introduced so as to whether the potential problems mentioned in Part Two are valid, especially in the last three decades of the 20th Century. This is because before the collapse of the Bretton Woods system, the U.S. dollar was tied up to gold and members of International Monetary Fund agreed on fixing the exchange rates of their own currencies against U.S. dollar as the key currency (Dammasch, 2007). However, due to the rising payments imbalances and growing inflation in the United States after 1965, the system collapsed between 1971 and 1973 (Bordo, 2014). Since then the floating exchange rate regime has been adopted and researches on how exchange rate should be determined and how well PPP theory works began to flourish.
A variety of approaches have been chosen to test whether PPP holds in practice and both positive and negative empirical results have been found.
Monetary Approach
In the mid to late 1970s, monetary approach was the dominant approach in determining exchange rates. Under monetary approach, shocks such as changes of fiscal policy and monetary policy lead to changes of the aggregate price level of the former country relative to the latter one and therefore the current accounts of both countries, and monetary approach assumes that PPP holds continuously in reality that the exchange rate is actually the aggregate price of one country’s asset relative to that of the other’s (Boughton, 1988). Thus, to test whether PPP holds requires testing whether a change in fiscal or monetary policy leads to a one-‐to-‐one change in the exchange rate.
Jacob A. Frenkel (1976) tested the relationship between the German mark/U.S. dollar exchange rate and the German money supply during the German hyperinflation period from February of 1920 to November of 1923 using the following model:
𝑙𝑛𝑆 = 𝑎 + 𝑏!𝑙𝑛𝑀 + 𝑏!𝑙𝑛𝜋 + 𝑢 Where,
S is the spot exchange rate, M is the nominal money stock,
𝜋 measures the expected inflation plus 1 and it is a variable measuring expectation. The reason for an additional one added is to make sure that it is always a positive number.
Frenkel (1976) assumes during the period tested, the domestic influences dominated the foreign influences on the change of German mark/U.S. dollar exchange rate. Therefore, the null hypothesis is 𝑏!=1. The result shows at a 5% significance level, the null hypothesis cannot be rejected and thus there is not sufficient evidence to reject PPP did hold continuously during the pre-‐Bretton Wood time.
for the monetary approach.
For the data covering both the Bretton Woods period and the post Bretton Woods period, John F. O. Bilson (1978) applies the monthly exchange rate data from April of 1970 to May of 1977 between the Federal Republic of Germany and the United Kingdom to the monetary model and also failed to reject a continuous PPP.
In addition, Rudiger Dornbusch (1979) applies the post Bretton Wood period German mark/U.S. dollar exchange rate data from March of 1973 to May of 1978 to the model and the again there is no sufficient evidence to reject a continues PPP.
Thus, from the early researches, the monetary approach of determining exchange rates cannot be rejected and PPP is accepted both in the Bretton Woods period and in the post Bretton Woods period.
However, beyond the late 1970s, specifically since 1978, the estimation by monetary model started to deteriorate as Frankel (1983) concludes that the monetary model has provided a poor fit and sometimes even generates empirical results with opposite signs against reality from what are indicated by the model, which shows the collapse of the monetary approach. Jeffrey A. Frankel (1982) argues especially for the German mark/U.S. dollar exchange rate, the coefficient of monetary model sometimes shows a reverse relationship between money supply and the exchange rate. Frankel (1982, 1983) lists some possible explanations for the breakdown of the monetary model, which include the econometric misspecification or the model is too simplistic to capture the wealth effects.
For the reasons mentioned above, Frenkel (1981) suggests that one should test the real exchange rate instead of nominal exchange rate in order to verify whether PPP holds continuously in practice.
Mean Reversion and Unit Root Test
The failure to verify continuous PPP using nominal exchange rates leads to the emergence of new tests for PPP using real exchange rates since the end of 1970s. The formula for real exchange rate is:
𝑄 = 𝐸𝑃∗ 𝑃 Where,
Q denotes the real exchange rate expressed in terms of real domestic goods versus real foreign goods,
E denotes the nominal exchange rate,
P* denotes the price index for the foreign country, P denotes the price index for the domestic country.
The real exchange rate is without a unit. It is the ratio of the number of units of domestic currency required to buy a foreign basket of goods to the number of units of domestic currency required to buy a domestic basket of goods (Erlat and arslaner, 1997). If the Absolute PPP formula, which states E=P/P*, is plugged
into the real exchange rate formula above, the real exchange rate will be equal to 1. This means when Absolute PPP is true, the real exchange is the price of foreign goods expressed in domestic currency should always be equal to 1. However, as Taylor et al. (2004) demonstrate，because of the potential problems related with Absolute PPP mentioned in Part Two, real exchange rates may deviate from 1 in practice. The way to test whether these problems are true is to test whether the real exchange rate is equal to 1, or if not, whether it is converging to 1.
However, Stein (1990) observed the real exchange rate of U.S. dollar against currencies of the G-‐10 countries for the period 1973-‐1988 and has found the real exchange rates are volatile in the short run. Rudiger Dornbusch (1976) develops a framework on how monetary expansion influence the exchange rates movement in order to explain the observed volatility. In his paper, he argues in the short run, there is an initial overshooting effect of the exchange rate that arises from the different speeds of adjustments within the market such as the slow adjustment of price level, and it will gradually adjust to an equilibrium level only in a long term. Therefore, he suggests only long-‐run real exchange rates should be employed to test PPP. Taylor (1988) concludes that the key difference between the monetary model of the exchange rate and the sticky-‐price model such as the one developed by Dornbusch is that the latter allows short-‐run volatility of real exchange rates and focuses on the long run.
Since the late 1970s, the empirical tests for PPP in the long run have been conducted by testing whether the real exchanging rate presents a mean reversion in the long run. One crucial position underlying the method is that a positive result is only a necessary condition to verify PPP in the long run because convergence to a certain level for long-‐run PPP does not necessarily mean it is converging to the level that is in line with what PPP indicates. However, when the exchange rate does not converge to any specific mean level in the long run, that is if it follows a random walk, PPP even in the long run must not hold.
One way to test whether long-‐run PPP follows a random walk is to test whether it contains a unit root. If it does, it does not converge to any specific level in the long run and thus, PPP does not hold. Dickey and Fuller (1979) first develop the unit root test to test whether a time series variable sticks to a stationary level in its evolvement. Thus, as Assaf (2006) indicates, if one can prove the real exchange rate carries a unit root in its process of evolvement, it is sufficient to reject Absolute PPP.
Various forms of unit root tests were used in the existing literatures since 1980s, among which Meese and Singleton developed one of the earliest papers. Meese and Singleton (1982) test the weekly Swiss franc/U.S. dollar, German mark/U.S. dollar and Canadian dollar/U.S. dollar exchange rates for the period 7th of January 1976 to the 8th of July, 24th of June 1981 and 2nd of July for Switzerland, Germany and Canada respectively by using:
𝑦! = 𝛽!+ 𝛽!𝑡 + 𝛽!𝑦!!!+ 𝛽!∆𝑦!!!+ 𝜖! Where,
𝑡 denotes time and 𝑡 = 1, 2, . . . . , 𝑇, 𝜇 ∈ 𝑅,
∆ denotes the different operator, and ∆𝑦! ≡ 𝑦!− 𝑦!!!,
𝜖! is a sequence of independently and normally distributed random variables with mean zero and variance 𝜎! (Dickey and Fuller, 1981).
Under the null hypothesis of a unit root, 𝛽! equals 1.
The result shows that a unit root could not be rejected for all three exchange rates at the 5% significance level for the testing period. Thus there is no evidence that PPP is valid.
Thereafter, more papers aiming to test unit root in exchange rates have come forth. Some researches could not reject a unit root in while others could.
Corbae and Oularis (1988) used the following model to test the monthly real exchange rate data for Canadian dollar, French franc, German mark, Italian lira, Japanese yen and U.K. pound against U.S. dollar during the post Bretton Woods period from July 1973 to September 1986:
𝑦!= 𝜇 + 𝛼𝑦!!!+ 𝑢! where,
𝑦! denotes the natural logarithm of real exchange rate at time t, 𝑡 denotes time and 𝑡 = 1, 2, . . . . , 𝑇, 𝜇 ∈ 𝑅,
𝑢! is a sequence of independently and normally distributed random variables with mean zero and variance 𝜎! (Dickey and Fuller, 1981).
Under the null hypothesis of a unit root, 𝛼 equals 1. The result shows that except for Japanese yen, a unit root could not be rejected for all the other exchange rates at the 5% significance level for the testing period, which does not give enough empirical evidence for long-‐run PPP.
However, more recent studies started to find out empirical evidence of PPP. Lean and Russell (2007) tested the natural logarithm of monthly real exchange rates against U.S. dollar for 15 Asian countries during the period from January 1990 to July 2005 by using the following model:
Δy! = Κ + αy!!!+ βt + ! d!Δy!!!+ ε!
!!! ,
Where,
y! denotes the natural logarithm of the real exchange rate, Δ is the first difference operator, and ∆𝑦! ≡ 𝑦!− 𝑦!!!, 𝑡 denotes time and 𝑡 = 1, 2, . . . . , 𝑇, 𝜇 ∈ 𝑅,
ε! is a noise disturbance term independently and normally distributed with mean zero and variance 𝜎! (Dickey and Fuller, 1981),
Δy!!! allows for serial correlation and ensures the disturbance term is white noise.
Κ denotes the lag length.
Under the null hypothesis of a unit root, 𝛼 = 0 because here the dependent variable is Δy!.
Part of the results has shown support for PPP. Among the 15 countries concerned, the null hypothesis of a unit root for Philippines and Myanmar could
be rejected at 1% significance level. For India, the null hypothesis of a unit root could be rejected at a 5% level. For Pakistan and Thailand, it could be rejected at 10%. For the rest of the countries, namely Vietnam, Sri Lanka, Singapore, P.R. China, Malaysia, Lao PDR, Korea, Indonesia, Cambodia and Bangladesh, the null hypothesis of a unit root could not be rejected. Thus, for one-‐third of the countries involved, PPP applied during the period.
Not only for Asian countries, Maican and Sweeney (2013) have found that for EU countries, recent studies have also conveyed a supportive result for PPP. For Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Slovakia, Slovenia, Bulgaria and Romania, nine of them have presented evidence of a mean reversion in their exchange rates against EUR from January 1993 to December 2005 before some of the countries mentioned above have joined Eurozone later. Only for Poland, a unit root cannot be rejected during the period.
However, there are some potential problems related with unit root test testing long-‐run real exchange rates as Frankel (1990) argues that the post Bretton Wood period time period used to test real exchange rates is not long enough to reject a unit root even in the case that a unit root is not preset. Thus, the unit root test may suffer from a low power.
Part Four: Test of PPP in the 21st Century
In Part Two, I have reviewed the main reasons why PPP might not hold in reality. Some of these reasons, however, might not be valid in the 21st Century, especially for the following reasons.
The 21st Century is featured as globalization. Due to the improvement on information technology in the 21st Century, people nowadays have more access to foreign life styles and foreign goods, and thus there is a potential trend of convergence in people’s tastes of consumption throughout the economically developed world. For example, Statistics Canada (2015) publishes over the last century, the Canadian CPI basket of Canada did continuously evolve so as to reflect the altered consumer spending habits resulted from the expanded range of services and goods available to people. In addition, enhanced international cooperation all over the world could also lead to similarity in people’s consuming pattern through increased international trades as Miskiewicz (2010) tested 20 industrialized countries and finds out that the increasing amount of interaction between them has resulted in more similar CPI baskets since the introduction of Euro. All of the reasons mentioned above contribute to a convergence of CPI basket construction around the world.
Moreover, the transaction costs in the new Century may also lessen. Dettmer (2014) indicates the innovation information technology and telecommunication technology have shortened the geographical distance on merchandise trade because physical interactions between trading partners are not as important as before.
arbitrage. Therefore, I conduct a new test for PPP for the period January 2000 to December 2014.
Data
I test the monthly U.S. dollar/U.K. pound, Canadian dollar/U.S. dollar and Japanese yen/U.S. dollar real exchange rate data for the period January 2000 to December 2014. Following the previous literatures, all the data being tested are in natural logarithm.
The reason I choose these three exchange rates to test is because they are the representatives that have been tested most frequently in the existing literatures. Moreover, U.S., U.K. and Japan have been the world top five economies in the world and Canada the eleventh since the 21st Century and thus they have more trades with other countries.
I conduct the logarithm of the monthly real exchange rate data in the same way as Caporale and Cerrato (2006) did:
𝑞 = 𝑒 + 𝑝∗− 𝑝 Where,
q is the natural logarithm of the real exchange rate,
e is the natural logarithm of the nominal spot exchange rate (here it represents units of domestic currency per unit of foreign currency),
p is the logarithm of the domestic price index, 𝑝∗ is the logarithm of the foreign price index.
I obtain the nominal U.S. dollar/U.K. pound, Canadian dollar/U.S. dollar and Japanese yen/U.S. dollar spot exchange rate data for the period January 2000 to December 2014 from the Exchange Rate Data section of International Monetary Fund, as was done by Cheung and Lai (1998), as well as Chou and Chao (2001). Each monthly nominal exchange rate is calculated by taking the average of the daily exchange rates for that month, as is done by most database websites.
For the U.S. CPI, I obtained the monthly data (U.S. city average, all items, base period 1982-‐84=100) from the official website of Bureau of Labor Statistics. For the U.K. CPI, I obtained the monthly data (base period 2005=100) from the official website of Office for National Statistics.
For the Canadian CPI, I obtained the monthly data (base period 2002=100) from the official website of Bank of Canada.
For the Japanese CPI, I obtained the monthly data (all items, base period 2010=100) from the website of Economic Research Federal Reserve Bank of ST. Louis.
Because the base periods of the four series of CPI data are different, I have standardized the CPI data of the U.S., Canada and Japan being 100 for June in 2005 in order to match them with that of UK.
The following Table 1, Table 2 and Table 3 are the summaries of the data I have obtained of the natural logarithm of the monthly U.S. dollar/U.K. pound, Canadian dollar/U.S. dollar and Japanese yen/U.S. dollar real exchange rate respectively for the period January 2000 to December 2014.
Table 1
Summary of 𝑞! for U.S./U.K.
Observation Mean Std. Dev. Minimum Maximum
180 0.5233 0.0849 0.3539 0.7049 Table 2
Summary of 𝑞! for Canada/U.S.
Observation Mean Std. Dev. Minimum Maximum
180 0.1895 0.1442 0.0114 0.4684
Table 3
Summary of 𝑞! for Japan/U.S.
Observation Mean Std. Dev. Minimum Maximum
180 4.6836 0.1039 4.4892 4.9406
Methodology
I use the simplest form of unit root test as was adopted by Corbae and Oularis (1988) as well as Taylor et al. (2004),
𝑞! = 𝛼 + 𝛽𝑞!!!+ 𝜀! Where,
𝑞! denotes the natural logarithm of the real exchange rate at time t, 𝑡 denotes time and 𝑡 = 1, 2, . . . . , 𝑇, 𝜇 ∈ 𝑅,
𝜀! denotes a noise disturbance term normally and independently distributed with mean zero and variance of 𝜎! (Dickey and Fuller, 1981).
I conduct the ordinary least squares estimates as Dickey and Fuller (1981) did in their illustrative example.
The reason I do not choose to use the more sophisticated models is because as a bachelor student, I do not understand the econometric meanings for the additional items involved.
Result
The OLS estimate results of 𝛼 and 𝛽 for the three exchange rates are shown in Table 4 with the standard errors for each estimate in the brackets. I have also conducted a hypothesis test for each estimated 𝛽 to test whether they are significantly different from 1. The resulting p-‐values are shown in table 5. However, whether the hypothesis is rejected or not depends on the chosen significance level. As we can see, at a conventional 5% significance level, the hypothesis 𝛽 = 1 is not rejected for all the three real exchange rates being tested. Only in the case of a 10% significance level, the hypothesis 𝛽 = 1 is rejected for the U.S. dollar/U.K. pound real exchange rate, but not for the other
two. Since I have 180 samples for each real exchange rate, I choose 5% as the significance level. Thus, for the period 2000 to 2014 period, there is not enough evidence that PPP holds.
Table 4
Unit Root Test Result
Variable U.S./U.K. Canada/U.S. Japan/U.S.
𝛼 0.0159 (0.0098) 0.0014 (0.0023) 0.1116 (0.0826) 𝛽 0.9692 (0.0184) 0.9867 (0.0096) 0.9767 (0.0176) Table 5
Result of the hypothesis test
Variable p-‐value
𝛽 for U.S./U.K. 0.0959
𝛽 for Canada/U.S. 0.1693
𝛽 for Japan/U.S. 0.1887
One possible reason for the observed result is due to the existence of real shocks during the period, as McNown and Wallace (1989) and Phylaktis (1992) argue that real shock in the economy is the dominant reason for deviations from long-‐run PPP. Thus I have conducted graphs for each real exchange rate (in logarithm) being tested during the period in order to have a better view of their evolvement.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Ja n-‐0 0 D ec -‐0 0 N ov -‐0 1 O ct -‐0 2 Se p-‐0 3 Au g-‐0 4 Ju l-‐0 5 Ju n-‐0 6 M ay -‐0 7 Ap r-‐0 8 M ar -‐0 9 Fe b-‐1 0 Ja n-‐1 1 D ec -‐1 1 N ov -‐1 2 O ct -‐1 3 Se p-‐1 4
U.S./U.K.
U.S./U.K. -‐0.1 0 0.1 0.2 0.3 0.4 0.5 Ja n-‐0 0 Ja n-‐0 1 Ja n-‐0 2 Ja n-‐0 3 Ja n-‐0 4 Ja n-‐0 5 Ja n-‐0 6 Ja n-‐0 7 Ja n-‐0 8 Ja n-‐0 9 Ja n-‐1 0 Ja n-‐1 1 Ja n-‐1 2 Ja n-‐1 3 Ja n-‐1 4Canada/U.S.
Canada/U.S. 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 Ja n-‐0 0 Ja n-‐0 1 Ja n-‐0 2 Ja n-‐0 3 Ja n-‐0 4 Ja n-‐0 5 Ja n-‐0 6 Ja n-‐0 7 Ja n-‐0 8 Ja n-‐0 9 Ja n-‐1 0 Ja n-‐1 1 Ja n-‐1 2 Ja n-‐1 3 Ja n-‐1 4Japan/U.S.
Japan/U.S.
As we can see from the graphs, during the financial crisis from 2007-‐2008, the real U.S. dollar/U.K. pound exchange rate dropped significantly. The same situation happened for the real Canadian dollar/U.S. dollar as it rose significantly during the crisis. These situations fit the problem I mentioned in Part Two that exogenous factors in the real economies can also result in a change of the equilibrium exchange rate between them.
Also we can see that for all the three real exchange rates, there is no obvious trend that they are converging to any mean level. Instead, they are changing into different directions frequently. For example, the Japanese yen/U.S. dollar exchange rate was generally rising before 2002. However, it dropped in the next three years. From 2005, it started to rise again and in the middle of 2007, it dropped again even more sharply until the middle of 2012, when it rose again quickly. The same type of problem also applies to the other two real exchange rates. As mentioned earlier, Stein (1990) has also found the real exchange rate of U.S. dollar against currencies of the G-‐10 countries for the period 1973-‐1988 volatile in the short run.
Thus another reason why I could not reject a unit root could be my data period is not long enough. To compare with the literatures I mentioned in Part Three, Meese and Singleton (1982) tested a roughly 6-‐year-‐long period of data and rejected PPP for all the four tested real exchange rate. Corbae and Oularis (1988) tested a longer period, which is 14 years, and could not reject a unit root for 5 out of 6 real exchange rates. For Lean and Russell (2007), they tested a period more than 16 years and a half and rejected PPP for 13 out of 15 real exchange rates. The only literature I mentioned which has rejected a unit root in a majority of the sample real exchange rates is by Maican and Sweeney (2013). However, most of these countries have a fixed exchange rate regime to some other currencies (Hsing, 2013). Thus, I suggest an even longer period is required to test whether PPP holds in reality.
Conclusion
This paper introduced the concept and two different forms of Purchasing Power Parity in determining exchange rates and the basic idea underlying it. Despite its conciseness and explicitness, Purchasing Power Parity has suffered from its overly idealized assumptions, both for the Absolute PPP and Relative PPP although some of the problems may not be true or they are not true anymore in the 21st Century. This leads to plenty of researches trying to test the validity of PPP especially in the post-‐Bretton Wood period, as well as my test of PPP for the 21st Century in this paper. Several different approaches were adopted in order to test PPP, especially the monetary approach and the unit root test. Both approaches have led to acceptance of PPP as well as rejection of PPP and I did a brief review of some of the key literatures about these two approaches. Since 1987, the unit root test has gradually dominated the research on PPP because of the failure of the monetary approach and the increasing focus on the real
exchange rate. Although the early studies on PPP using the unit root test were not successful in accepting the validity of PPP in practice, the recent studies tend to find more supportive evidence for it because of the potential globalization effect in the 21st Century. Therefore, I tested the first 14 years’ monthly U.S. dollar/U.K. pound, Canadian dollar/U.S. dollar and Japanese yen/U.S. dollar real exchange data by using unit root test in order to find evidence for PPP. The result is I cannot reject a unit root in all the three real exchange rates for the testing period. Have concluded two main reasons for it, which are the real shocks and the length of the testing period is not long enough. My suggestion is a longer period of data should be tested in order to see if PPP holds in reality in the future.
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