Purchasing Power Parity

Introduction

The theory behind the purchasing power parity (PPP) has appealed to many economists and researchers over the decades. Though simplistic in theory, literature on PPP has demanded extensive empirical research and has produced many different results which will be discussed in this literature review.

While past PPP literature has sampled an array of data sets, and results have been drawn from intriguing methods, the objective of this paper is to investigate if PPP holds within the Canada and it’s top 10 trading partners: US, China, Mexico, UK, Japan, Germany, South Korea, Hong Kong, Netherlands, and France. This study will employ Johansen’s cointegration approach, while the aim of this literature review is to discuss previous noteworthy studies which employ econometric techniques that are applicable for our empirical process.

Our cointegration approach will use data of Consumer Price Indices (CPI), Wholesale Price Indices (WPI), and nominal exchange rates among Canada and it’s top 10 trading partners to investigate whether PPP holds. CPI is a measurement that represents national price levels, while PPI is used as a measurement of weighted producer price levels. Nominal exchange rates are commonly of interest to study within the realm of PPP; where studies such as (Lothian, J.R. 2016) have sought to find if inflation rates eventually adjust for changes in nominal exchange rates. If so then PPP is said to hold. A similar approach will be implemented in this study.

The law of one price provides an underlying theoretical framework to whether the PPP hypothesis does or does not holds. PPP is an aggregation of the LOP, where theoretically speaking, national prices should be equal when their respective values are converted into a common currency. PPP with its theoretical origin based on the LOP, suggests that a basket of goods must have the same price when converted into a common currency. This phenomenon is shaped by effects of market wide forces which often contributes to conflicting results in research.

Ppp in the short run

(Lothian, J.R. 2016) explains PPP as a theory to understand equilibrium behavior between price levels and exchange rates in the long run. Researchers and economist commonly agree that PPP does not hold in the short-run between two nominal exchange rates. Meanwhile, whether or not PPP holds in the long run has often been disputed.

In a study to analyse how asset markets adjust rapidly while price adjustments are slow to follow, Dornbush (1976) investigated short run and long run price level equilibrium by employing an overshooting model in their study. The behavior of asset markets and price adjustments occuring at differing rates is what allows for an initial overshooting of exchange rates. However, the study provides a lack theoretical support to further explain this phenomenon (Dornbush 1979).

Dornbush (1979) also found how monetary and financial shocks jolt the nominal exchange rate and cause an effect on the real exchange rates, thus leading them to alter in the short-run. When considering such shocks are theoretically temporary (as such shocks, and price adjustments, would eventually adjust), all other things equal, it would be fair to expect PPP would move towards uniformity even in the short run.

Rogoff (1996) conducted a study, which in part challenged earlier short run PPP findings of Dornbush (1979). Extending on Dornbush’s overshooting model, the study found that earlier results were predominantly due to the sticky nature of nominal prices (and amongst other factors). This study provided empirical evidence that coincides with most literature that PPP does not hold in the short run.

PPP holding in the long run and not in the short, can also be due to economies experiencing temporary monetary and financial shocks which jolt real exchange rates. Literature has pointed to an empirical solution by accounting for structural breaks when employing a cointegration model. As will be discussed later on in this literature review, past conventional cointegration tests which have not considered structural breaks, have oftentimes failed to prove PPP holds. The theory comes from understanding how financial and monetary shocks affect exchange rates and when sampling a long span of data, structural breaks are key to consider.

While such shocks tend to cause short run deviations, a common consensus to reject short run PPP has led recent literature to focus on whether or not real exchange rates settle to an equilibrium level in the long run. Furthermore, real exchange rates must evolve around a constant or a time trend in order for PPP to hold; therefore, PPP can still hold in the long run on the condition that any short run deterministic trend or deviation from the mean are only short lived (Wu, J., Bahmani-Oskooee, M. & Chang, T. 2018)

Empirical advancements

On the other hand, PPP literature has produced a vast amount of studies providing evidence for PPP holding in the long run. Theoretically this means that the movement in nominal exchange rates move toward parity levels in the long run. In order to empirically test this theory, researchers have employed various methods, which will be discussed in this literature review, to reveal why previous tests have failed to validate the PPP theory holding in the long run.

Studies following the floating exchange rate period, such as Frankel (1985) and Edison, Hali J, (1987) often employed time-series analysis to provide evidence that PPP failed to hold. The apparent cause was from observing that PPP in their samples had properties embedded in real exchange rates that follow a random walk and do not revert back to the mean.

A study conducted by Taylor (1996) found that earlier studies testing for PPP, around the time of the floating exchange rate period, were performed with tests of low statistical power, using data sets which consisted of small duration spans, and the use of standard unit root tests were by now found to have a further technical weakness. This paved the way for researchers to make empirical advances in using tests with higher statistical power techniques and data sets spanning over longer time spans.

Kim (1990) conducted a study to test if PPP held in the long run using a cointegration approach developed by Engle and Granger (1987). In testing to analyze the exchange rate price relationship between the U.S and five other countries within the G7 (Canada, France, Italy, Japan, and the United Kingdom), they use WPI data from 1900 - 1987 and CPI data from 1914 - 1987. The study found PPP to hold for the most part, with the exception of Canada, where all other exchange rates tested positive for cointegration with both WPI and CPI ratios. This study provides solid empirical evidence supporting PPP to hold in the long run, however, other studies using a cointegration approach have produced varying results when using data containing the floating exchange rate period.

Chang, T., Lee, C., Chou, P. & Tang, D. (2011) investigated properties of asymmetric adjustments on long-run PPP in the G7 countries using monthly data from 1994 to 2010. The study employed an advanced threshold cointegration technique by Enders and Skilos (2001) and gave strong evidence of long-run PPP for six out of the seven countries (PPP did not hold for Canada). The study provided an insightful analysis that nominal exchange rates are main mechanisms in price adjustments which caused the long run equilibrium in G7 countries.

Random walk

Literature on long run PPP between the 1970’s - 1980’s, commonly encountered a technical dilemmas when testing if PPP holds in the long run. When seeking to reject the random walk hypothesis, most studies were unsuccessful in doing so when using data from real exchange rates of major world currencies (under floating exchange rate regimes). Often times the theory would imply that shocks on real exchange rates are not reversed; in which vast empirical evidence suggests otherwise.

A study conducted by Froot and Rogoff (1994) distinguish PPP into three different stages while investigating determinants of long run PPP. While some convergence of long run PPP was found, the most compelling evidence of real exchange rate stationarity was driven by using fixed-rate data sets. On the other hand, studies have produced interesting results with data from the floating-rate period when employing unit root tests to analyze real exchange rates. Furthermore, cointegration tests have commonly been employed to test for PPP with respect to price levels and nominal exchange rates.

A noteworthy study by Darby (1980) provided a stochastic framework and employed an ARIMA process to investigate alternative conceptual problems that may have led previous researchers to mishandle the unit root problem. The study sampled the UK, Canada, France, Germany, Italy, Japan, and Netherlands with data from 1971 - 1978. The study used the purchasing power ratio (domestic price levels over exchange rate when converted to foreign price levels), to test for stationarity.

The results found that in all currencies the PPR was non stationary and that PPP did not hold in the long run. Darby (1980) explains that such results may be driven by more complicated processes with such theoretical reasons including a “random walk with an overlaid self-reversing moving average process” and “the possibility that it may be due to a stationary process if few assumptions are relaxed” Darby (1980). Despite an interesting approach to solve a persistent PPP problem, the study arguably included an low duration of data to be able to validate it’s claims.

The duration of data required to properly test PPP has been a common issue. Lothian and Taylor (1996) ensured to avoid data duration criticism by using two centuries of real exchange rate annual data from 1791 - 1990. The data sampled the US, the UK and France with their respective currencies. The study split the sample before applying the standard Dickey-Fuller and a nonparametric test to investigate the unit root. Their results were interesting and was successful in rejecting the unit root hypothesis for the data sample of 1791 - 1900. However, the study unsuccessful in rejecting the unit root hypothesis for the same of data from 1946 - 1990.

The ability to reject the random walk in the former sub sample and not the latter, has grabbed the attention of many researchers and started out by blaming lack of power tests have for investigating nonstationarity properties of real exchange rates during floating rate periods. Meanwhile researchers such as Wallace (2013) suggest the unit root problem may be by not making nonlinear adjustments to PPP.

Bahmani-Oskooee et al. (2008) claimed that standard ADF tests do not give much support for PPP. They conducted a study to compare results from tests using standard or linear version of the ADF, with tests using nonlinear version of the ADF test namely the KSS test. They investigated, on their sample, a conventional unit root test with the null of nonstationarity, and compared tests on the same sample, a nonlinear adjustment of the ADF test with an alternative hypothesis of nonlinear stationarity. They employed both ESTAR and KSS procedures on monthly data from 1980 - 2005 of 88 developing countries and their real effective exchange rates.

When comparing results, they found PPP to hold between more countries (31 out of the 88) for nonlinear version of the ADF test whereas standard ADF tests provided evidence of PPP between 12 out of the 88 countries. These results suggest that linear testing procedures may have an inference bias if PPP holds with nonlinear adjustments. Due to conventional cointegration methods assuming a unit root as a null hypothesis (as well as a linear adjustment under the alternative hypothesis), such procedures should be avoided when testing for PPP.

Abuaf, N. & Jorion, P. (1990) conducted a study to challenge the earlier research, such as Roll (1979) and Alder and Lehmann (1983) who were unsuccessful in rejecting the random walk hypothesis of real exchange rates. Using annual data from 1900 - 1972 and then monthly data from 1973 - 1987 (data from flexible exchange rate period) from Canada, France, Germany, Italy, Japan, Netherlands, Switzerland, and Britain.

The study argues that previous findings by Roll (1979) and Alder and Lehmann (1983) were performed using tests with low power; therefore as an alternative hypothesis, (Abuaf, N. & Jorion, P. 1990) introduced more power to their tests by employing a Dickey and Fuller (1979) test with first-order autoregression in levels. This was different to earlier studies which were using the Dickey and Fuller (1979) test in first differences.

(Abuaf, N. & Jorion, P. 1990) explain that when an alternative hypothesis to a random walk is possible with either a stable or near to random walk model, that having regressions in first difference offer low power. The results were successful in rejecting the random walk hypothesis in six of the eight countries in the sample. Furthermore, that by employing a first-order autoregressive process, which seemed to capture real exchange rates well, the root of this process is slightly below unity implying that long-run PPP does hold with PPP deviations reducing to half life in three years on average.

As we can see from the discussion above, both duration of data across different exchange rate regimes should be considered when testing for a unit root, but also the method and econometric techniques used should be approached with consideration. By designing and employing more powerful unit root tests, researchers have outlined advances in econometric techniques to understand why PPP has been rejected in the past. For example, recent studies have found interesting approaches to overcome a previous obstacle when using the random walk model. Various approaches were used such as cointegration, variance ratio, and error-correction models.

Cointegration section

Sarno (2000) conducted a study using both monthly and quarterly real exchange rate data from 1973 - 1996. By employing nonlinear methods to test PPP between the G5 countries (the US, the UK, Germany, France and Japan), their evidence found PPP to hold within the sample. Furthermore, while real exchange rates could be driven by a stochastic process, data from the floating exchange rate period was outlined well by nonlinear stationary models: “nonlinear modeling techniques developed by Haggan and Ozaki (1981), Granger and Teräsvirta (1993) and Teräsvirta (1994)”. This study provides further insight into the behaviour of real exchange rates properties and how aggregation causes an affect and was well presented with both quarterly and monthly data.

Narayan (2006) used data from 1960 - 2000 from India and 16 trading partner countries. They compared the stationarity of India’s real exchange rate to others in the sample, by converting nominal bilateral exchange rates to real bilateral exchange rates. They also analyzed how accounting for structural breaks could determine the results of PPP holding between India and the other sampling countries. This was observed by employing the Lagrange multiplier unit root test which was found to provided more robust results than those driven from ADF type structural break tests.

Accounting for structural breaks is particularly important when employing data sets spanning over long time periods where structural changes in the economy must be considered in an econometric model. Perron (1989) explains that the use of a long data set is advantageous when investigating the presence of a unit root against stationary fluctuations around a deterministic trend. Their study found that ignoring structural breaks in the sample will lessen the power to reject a unit root, thus providing spurious results. While including a longer data set will naturally mean including events that cause financial or monetary shocks, Perron (1989) found that such shocks had little-to-no effect over the long run.

Choji, N.M (2017) conducted a study testing PPP in the long run in ASEAN-5 countries by using monthly data from 1996 - 2016. Using a threshold cointegration method with asymmetric adjustments, the study found PPP to hold between Philippines and Thailand, however not for the remaining countries in the sample who were found to have symmetric adjustment processes.