Index IntroductionPPP in the Short RunEmpirical AdvancesRandom WalkCointegration SectionIntroductionThe theory behind purchasing power parity (PPP) has fascinated many economists and researchers over the decades. Although simplistic in theory, the literature on PPP has required extensive empirical research and has produced many different findings that will be discussed in this literature review. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an Original Essay While past literature on PPP has sampled a number of datasets and the results have been drawn from intriguing methods, the goal of this article is to investigate whether PPP is viable in Canada and among its 10 major partners commercial: United States, China, Mexico, United Kingdom, Japan, Germany, South Korea, Hong Kong, the Netherlands and France. This study will use the Johansen cointegration approach, while the purpose of this literature review is to discuss previous noteworthy 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 10 major trading partners to investigate the validity of the PPP. 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 commonly interesting to study in the context of PPP; where studies such as (Lothian, JR 2016) have sought to discover whether inflation rates eventually adjust to changes in nominal exchange rates. If so, then the PPP is valid. A similar approach will be implemented in this study. The law of one price provides an underlying theoretical framework for determining whether the PPP hypothesis is valid or not. PPP is an aggregation of 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 the effects of market-level forces that often contribute to conflicting research findings. Short-run PPP (Lothian, JR 2016) explains PPP as a theory for understanding the equilibrium behavior between price levels and exchange rates in the long run. Researchers and economists commonly agree that the PPP is not valid in the short run between two nominal exchange rates. Meanwhile, whether or not PPP is worth it in the long run has often been the subject of discussion. In a study aimed at analyzing how asset markets adjust rapidly while price adjustments are slow to follow, Dornbush (1976) studied short-run and long-run price level equilibrium using an overshooting model approach in the their study. The behavior of financial markets and price adjustments that occur at different rates are what allow for an initial overshoot of exchange rates. However, the study provides a lack of theoretical support to further explain this phenomenon (Dornbush 1979). Dornbush (1979) also found how monetary and financial shocks shake the nominal exchange rate and cause an effect on real exchange rates, thus leading them to alter in the short run. If one considers that such shocks are theoretically temporary (since such shocks and price adjustments would eventually adjust), all other things being equal, it would be fair to expect the PPP to shifttowards uniformity even in the short term. Rogoff (1996) conducted a study, which partly questioned Dornbush's (1979) earlier findings on short-term PPP. Extending Dornbush's overshooting model, the study found that previous results were mainly due to the sticky nature of nominal prices (and other factors). This study provided empirical evidence that coincides with most of the literature that PPP does not hold in the short run. The holding of the PPP in the long run and not in the short run may also be due to economies experiencing temporary monetary and financial shocks that shake real exchange rates. The literature has indicated an empirical solution taking into account structural breaks when employing a cointegration model. As will be discussed later in this literature review, past conventional cointegration tests that did not consider structural breaks have often failed to demonstrate the validity of PPP. The theory comes from understanding how financial and monetary shocks affect exchange rates, and when sampling a long period of data, structural breaks are key to consider. Although such shocks tend to cause short-run deviations, a common consensus in rejecting short-run PPP has led recent literature to focus on whether or not real exchange rates settle at an equilibrium level in the long run. Furthermore, for the PPP to hold, real exchange rates must evolve around a constant or temporal trend; therefore, PPP can still hold in the long run provided that any deterministic short-run trend or deviation from the mean is only short-lived (Wu, J., Bahmani-Oskooee, M. & Chang, T. 2018)Empirical ProgressOn D On the other hand, the literature on PPP has produced a large number of studies that provide evidence of the maintenance of PPP in the long term. Theoretically this means that the movement of nominal exchange rates will move towards parity levels in the long run. 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 validity of the PPP theory in the long run. Studies following the floating exchange rate period, such as since Frankel (1985) and Edison, Hali J, (1987) have often used time series analysis to provide evidence that the PPP has failed to hold. The apparent cause was the observation that the PPP in their samples had properties built into real exchange rates that follow a random path and do not revert to the mean. A study conducted by Taylor (1996) found that previous studies testing PPP, around the time of the floating exchange rate period, were performed with tests of low statistical power, using data sets consisting of short-duration intervals, and it was now discovered that the use of standard unit root tests had a further technical weakness. This has paved the way for researchers to make empirical progress in using tests with techniques of higher statistical power and datasets that span longer time intervals. Kim (1990) conducted a study to test whether PPP was valid in the long run using a cointegration approach developed by Engle and Granger (1987). In tests to analyze the exchange rate price relationship 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 study found that the PPP is valid for most, except Canada, where all other exchange rateswere positive for cointegration with both WPI and CPI ratios. This study provides solid empirical evidence supporting the validity of PPP in the long run, however, other studies using a cointegration approach have produced different results when using data containing the floating exchange rate period. Chang, T., Lee, C., Chou, P . & Tang, D. (2011) studied the properties of asymmetric adjustments on long-run PPP in G7 countries using monthly data from 1994 to 2010. The study used an advanced threshold cointegration technique of Enders and Skilos (2001) and provided strong evidence of long-run PPP for six of the seven countries (PPP is not valid for Canada). The study provided an in-depth analysis that nominal exchange rates are the main price adjustment mechanisms that caused long-run equilibrium in G7 countries. Random walkThe literature on long-run PPP between the 1970s and 1980s commonly encountered technical dilemmas when testing whether PPP is valid in the long run. When attempting to reject the random walk hypothesis, most studies have been unsuccessful in doing so using data on real exchange rates of major world currencies (under a floating exchange rate regime). Often the theory would imply that real exchange rate shocks are not reversed; where extensive empirical evidence suggests otherwise. A study conducted by Froot and Rogoff (1994) distinguishes PPP into three different phases while studying the determinants of long-term PPP. Although some long-run PPP convergence has been found, the most convincing evidence of real exchange rate stationarity has been provided using fixed rate data sets. On the other hand, studies have produced interesting results with data from the floating rate period when using unit root tests to analyze real exchange rates. Furthermore, cointegration tests have been commonly employed to test PPP 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 alternative conceptual problems that may have led previous researchers to mishandle the unit root 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 ratio of purchasing power (domestic price levels to the exchange rate when converted to foreign price levels), to test stationarity. The results found that across all currencies the PPR was not stationary and that the PPP did not hold up 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 a superimposed self-reversing moving average process” and “the possibility that it may be due to a stationary process if few hypotheses are relax” Darby (1980). Despite an interesting approach to solving a persistent PPP problem, the study likely included low data duration in order to validate its claims. The length of data required to adequately test PPP has been a common issue. Lothian and Taylor (1996) made sure to avoid criticisms 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, United Kingdom, and France with their respective currencies. The study split the sample before applying the Dickey-Fuller standard and a nonparametric test to investigate the unit root. Their results were interesting and they succeededreject the unit root hypothesis for the data sample from 1791-1900. However, the study failed to reject the unit root hypothesis for the same data from 1946 to 1990. The ability to reject the random walk in the first subsample, and not in the second, attracted the attention of many researchers and began blaming the lack of power of the tests in investigating the non-stationarity properties of real exchange rates during periods of floating rate. Meanwhile, researchers such as Wallace (2013) suggest that the unit root problem may be due to not making nonlinear adjustments to PPP. Bahmani-Oskooee et al. (2008) stated that standard ADF tests do not provide much support for PPP. They conducted a study to compare test results using the standard or linear version of the ADF, with tests using the nonlinear version of the ADF test, i.e. the KSS test. They studied, on their sample, a conventional unit root test with the null value 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 both the 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 holds across multiple countries (31 out of 88) for the nonlinear version of the ADF while standard ADF tests provided evidence of PPP in 12 out of 88 countries. These results suggest that the Linear tests may have an inference bias if the PPP is valid with nonlinear adjustments. Due to conventional cointegration methods that assume a unit root as the 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 previous research, such as Roll (1979) and Alder and Lehmann (1983) who failed to reject the random walk hypothesis of real exchange rates . Using annual data from 1900 to 1972 and then monthly data from 1973 to 1987 (data from the flexible exchange rate period) from Canada, France, Germany, Italy, Japan, the Netherlands, Switzerland and Great Britain. The study argues that previous results by Roll (1979) and Alder and Lehmann (1983) were performed 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 across levels. This was different from previous studies that 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 method or close to the random walk model, that having regressions in the first difference offers low power. The results succeeded in rejecting the random walk hypothesis in six of the eight countries in the sample. Furthermore, employing a first-order autoregressive process, which appeared to capture real exchange rates well, the root of this process is slightly less than unity, implying that the long-run PPP holds with the deviations of the PPP decreasing to the half-life averaged over three years As we can see from the previous discussion, when testing a unit root both the duration of the data between different exchange rate regimes should be considered, but the method and econometric techniques used should also be approached with consideration. By designing and employing more powerful unit root tests, researchers have outlined advances in econometric techniques for understanding.