Table of contentsIntroductionShort-term PPPEmpirical progressRandom walkCointegration sectionIntroductionThe theory behind purchasing power parity (PPP) has attracted many economists and researchers over the decades. Although simplistic in theory, the PPP literature has required extensive empirical research and has produced many different results which will be discussed in this literature review. Say no to plagiarism. Get a tailor-made essay on “Why Violent Video Games Should Not Be Banned”? Get an original essay While previous PPP literature has sampled a range of datasets and the results have been drawn from intriguing methods, the objective of this article is to investigate whether PPP is valid in Canada and at its 10 main trading partners: United States, China, Mexico, United Kingdom, Japan, Germany, South Korea, Hong Kong, Netherlands and France. This study will use Johansen's cointegration approach, while the aim of this literature review is to discuss notable previous studies that employ econometric techniques applicable to our empirical process. Our cointegration approach will use data from consumer price indices (CPI), wholesale price indices. (WPI) and nominal exchange rates between Canada and its top 10 trading partners to determine whether the PPP holds. The CPI is a measure that represents national price levels, while the PPI is used as a measure of weighted producer price levels. Nominal exchange rates are generally interesting to study in the PPP area; where studies such as (Lothian, JR 2016) investigated whether inflation rates eventually adjust to changes in nominal exchange rates. If this is the case, PPP is said to be valid. A similar approach will be implemented in this study. The law of one price provides an underlying theoretical framework for determining whether or not the PPP hypothesis is true. The PPP is an aggregation of the LOP, where, in theory, national prices should be equal when their respective values ​​are converted into a common currency. PPP, whose theoretical origin is based on LOP, suggests that a basket of goods should have the same price when converted into a common currency. This phenomenon is shaped by the effects of market forces that often contribute to conflicting research findings. Short-term PPP (Lothian, JR 2016) explains PPP as a theory for understanding the equilibrium behavior between price levels and exchange rates in the long term. Researchers and economists agree that PPP does not hold in the short term between two nominal exchange rates. At the same time, whether or not PPPs hold up in the long run has often been contested. In a study aimed at analyzing how asset markets adjust quickly while price adjustments are slow to follow, Dornbush (1976) studied the equilibrium of short- and long-term price levels by employing a model of excess in their study. The behavior of asset markets and the price adjustments that occur at different rates are what allow exchange rates to initially overshoot. However, the study lacks theoretical foundation to further explain this phenomenon (Dornbush 1979). Dornbush (1979) also discovered how monetary and financial shocks upset the nominal exchange rate and have an effect on real exchange rates, thereby leading them to change their exchange rates. in the short term. Considering that such shocks are theoretically temporary (to the extent that these shocks and price adjustments will eventually adjust), all things being equalelsewhere, it would be fair to expect PPPs to move toward uniformity even in the short term. Rogoff (1996) conducted a study, which partly challenged Dornbush's (1979) earlier findings on short-term PPPs. Building on Dornbush's overshoot model, the study found that previous results were primarily due to the sticky nature of nominal prices (and among other factors). This study provided empirical evidence that coincides with most studies that PPPs are not valid in the short term. Maintaining PPPs in the long term and not the short term may also be due to economies experiencing temporary monetary and financial shocks that disrupt real exchange rates. The literature offers an empirical solution consisting of taking into account structural breaks when using a cointegration model. As we will see later in this literature review, previous conventional cointegration tests, which did not take into account structural breaks, often failed to prove the validity of PPPs. The theory comes from understanding how financial and monetary shocks affect exchange rates and, when sampling a long period of data, it is essential to account for structural breaks. Although such shocks tend to cause short-term deviations, a common consensus to reject short-term PPPs has led to a recent consensus. The literature focuses on whether or not real exchange rates stabilize at an equilibrium level in the long run. Furthermore, real exchange rates must move around a constant or temporal trend for PPP to be maintained; therefore, PPP can still be valid in the long run provided that any short-term deterministic trend or deviation from the mean is only short-lived (Wu, J., Bahmani-Oskooee, M. & Chang, T. 2018)Empirical progressOn the other hand, the PPP literature has produced a large number of studies demonstrating the sustainability of PPPs in the long term. Theoretically, this means that the evolution of nominal exchange rates is moving towards long-term parity levels. In order to empirically test this theory, researchers used various methods, which will be discussed in this literature review, to reveal why previous tests failed to validate PPP theory over the long term. Like Frankel (1985) and Edison, Hali J (1987) often used time series analysis to prove that PPP was violated. The apparent cause was the observation that the PPPs in their samples had properties embedded in real exchange rates that follow a random walk and do not revert to the mean. A study by Taylor (1996) found that previous studies testing PPPs, around the floating exchange rate period, were carried out with tests of low statistical power, using data sets consisting of short periods, and the use of standard unit root tests has now been shown to have another technical weakness. This opened the way for researchers to make empirical progress using tests with higher statistical power techniques and data sets spanning longer time periods. Kim (1990) conducted a study to test whether PPP was sustained in the long run using a cointegration approach developed by Engle. and Granger (1987). In tests to analyze the relationship between exchange rates and prices between the United States and five other G7 countries (Canada, France, Italy, Japan and the United Kingdom), they use WPI data from 1900 to 1987 and CPI data from 1914 to 1987. The studyfound that PPP held for most, with the exception of Canada, where all other exchange rates tested positive for cointegration with the WPI and CPI ratios. This study provides strong empirical evidence supporting the maintenance of long-term PPPs. However, other studies using a cointegration approach have produced varying results using data containing the floating exchange rate period. Chang, T., Lee, C., Chou, P. & Tang, D. (2011) studied the properties of asymmetric long-term PPP adjustments in G7 countries using monthly data from 1994 to 2010. L he study used an advanced threshold cointegration technique by Enders and Skilos (2001) and provided strong evidence. long-term PPP for six of the seven countries (PPP was not valid for Canada). The study provided an insightful analysis that nominal exchange rates are the main price adjustment mechanisms that brought about long-term equilibrium in the G7 countries. long term. In seeking to reject the random walk hypothesis, most studies have failed to do so using real exchange rate data for major world currencies (under floating exchange rate regimes). Often, the theory implies that shocks to real exchange rates are not reversed; in which much empirical evidence suggests otherwise. A study conducted by Froot and Rogoff (1994) distinguishes PPPs into three different stages while studying the determinants of long-term PPPs. Although some convergence of long-run PPPs has been found, the most convincing evidence of real exchange rate stationarity has been provided by the use of fixed rate data sets. On the other hand, studies have produced interesting results with data from the floating rate period when they used unit root tests to analyze real exchange rates. Additionally, cointegration tests have been commonly used to test PPPs with respect to price levels and nominal exchange rates. A notable study by Darby (1980) provided a stochastic framework and used an ARIMA process to investigate other conceptual issues that might have led previous researchers to mishandle the root of unity problem. The study sampled the United Kingdom, Canada, France, Germany, Italy, Japan and the Netherlands with data from 1971 to 1978. The study used the power ratio of purchase (domestic price levels relative to the exchange rate when converted to foreign price levels), to test stationarity. The results showed that in all currencies, PPP was not stationary and that PPP did not hold over the long term. Darby (1980) explains that such results may be driven by more complex processes, for theoretical reasons such as a "random walk with a superimposed self-reversing moving average process" and "the possibility that this may be due to a stationary process if few hypotheses are made. are relaxed” Darby (1980). Despite an interesting approach to solving a persistent PPP problem, the study arguably included a short duration of data to validate its claims. A common problem is the length of data needed to properly test PPP. Lothian and Taylor (1996) were careful to avoid criticism of the length of the data by using two centuries of annual real exchange rate data from 1791 to 1990. The data sampled the United States, the United Kingdom and the France with their respective currencies. The study split the sample before applying the Dickey-Fuller standard and a nonparametric test to study the unit root. Their results were interesting and managed to rejectthe unit root hypothesis for the sample data from 1791 to 1900. However, the study failed to reject the unit root hypothesis for the same data from 1946 to 1990. The possibility of rejecting the walk random in the first subsample and not in the second, attracted the attention of many researchers and initially blamed the lack of power of the tests to study the nonstationarity properties of real exchange rates during rate periods floating exchange rates. Meanwhile, researchers such as Wallace (2013) suggest that the unit root problem may arise from not making nonlinear adjustments to PPPs. Bahmani-Oskooee et al. (2008) argued that standard ADF tests do not provide much support for PPP. They conducted a study to compare the results of tests using the standard or linear version of the ADF, with tests using the non-linear version of the ADF test, namely the KSS test. They studied, on their sample, a classic unit root test with the null of non-stationarity, and compared tests on the same sample, a non-linear adjustment of the ADF test with an alternative hypothesis of non-linear stationarity. They used ESTAR and KSS procedures on monthly data from 1980 to 2005 of 88 developing countries and their real effective exchange rates. Comparing the results, they found that PPP held across a larger number of countries (31 out of 88) for the non-linear version of the FAD. while the ADF's standard tests provided evidence of PPP between 12 of 88 countries. These results suggest that linear testing procedures may have inference bias if PPP is verified with nonlinear fits. Due to conventional cointegration methods assuming a unit root as the null hypothesis (as well as a linear fit under the alternative hypothesis), such procedures should be avoided when testing PPP. Abuaf, N. & Jorion, P. (1990) conducted a study to challenge previous research, such as Roll (1979) and Alder and Lehmann (1983) which failed to reject the random walk hypothesis real exchange rates. Using annual data from 1900 to 1972, then monthly data from 1973 to 1987 (flexible exchange rate period data) from Canada, France, Germany, Italy, Japan, Netherlands, Switzerland and Great Britain. The study argues that the previous findings of Roll (1979) and Alder and Lehmann (1983) were made using low-power tests; therefore, as an alternative hypothesis, (Abuaf, N. & Jorion, P. 1990) introduced more power into their tests by employing a Dickey and Fuller (1979) test with first order autoregression in levels. This was different from previous studies which used the Dickey and Fuller (1979) test for first differences. (Abuaf, N. & Jorion, P. 1990) explain that when an alternative hypothesis to a random walk is possible with a stable walk or close to the random walk model, whose first difference regressions offer low power. The results successfully rejected the random walk hypothesis in six of the eight countries in the sample. Furthermore, employing a first-order autoregressive process, which appears to capture real exchange rates well, the root of this process is slightly less than unity, implying that long-run PPP does indeed hold, PPA being reduced to a half-life in three years on average. As the discussion above shows, the duration of the data in different exchange rate regimes should be taken into account when testing the unit root, but the method and econometric techniques used should also be addressed with.