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Purchasing Power Parity (PPP) | FIN9026M

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University of Lincoln

   

Added on  2020-03-13

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Purchasing power parity (PPP) is a balance condition that is frequently accepted in both hypothetical and useful monetary examinations. This paper endeavors to accommodate the wide utilization of purchasing power equality and the Experimental  Confirmation, by utilizing more proper Techniques to test the speculation, inside multivariate and multi-nation settings for the European region, the United Kingdom, and the UnitedStates in the period 1988-2010

Purchasing Power Parity (PPP) | FIN9026M

   

University of Lincoln

   Added on 2020-03-13

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Test for Long-run Purchasing Power Parity (PPP)NameUniversity22nd August 2017
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INTRODUCTIONPurchasing power parity (PPP) is a balance condition that is frequently accepted in bothhypothetical and useful monetary examination. Observational testing of PPP has not, however,gave clear proof that legitimizes its expansive application - despite what might be expected,various examinations have achieved negative conclusions with respect to its validity. This paperendeavors to accommodate the wide utilization of purchasing power equality and theexperimental confirmation, by utilizing more proper techniques to test the speculation, inside amultivariate and multi-nation setting for European region, United Kingdom, and the UnitedStates in the period 1988-2010. In its supreme rendition, the theory of purchasing power parity builds up that the value levels oftwo nations ought to be equivalent when expressed in a similar currency. In this manner,P=SP¿Where S is the nominal exchange rate of the currency of country A expressed in terms of thecurrency of country B, and P and P* the price levels of countries A and B, respectively. Thisversion of PPP implies, therefore, that the logarithm of the real exchange rate is constant andequal to zero.The theory of long-run purchasing power parity (PPP) states that monetary standards of variousnations have a similar buying power within the sight of universal arbitrage. Testing thehypothesis for the long-run PPP gives a valuable understanding into whether the country'scompetitiveness and its trading partners, based on the real exchange rate, fluctuates or remainssteady after some time. Previous studies heavily depended upon standard econometric techniqueswhen it came to testing the long-run PPP. The disappointment experienced from theseprocedures especially to consider the economic time series non-stationary behavior brings aboutwhat has turned out to be known as "spurious regressions."Modeling techniques such as co-integration have been able to detect the presence of long-runequilibrium associations that exist between non-stationary variables, with this, the long-run PPPtheory has therefore been getting restored consideration. Notwithstanding whether the theory of long-run PPP remains constant or not, the examiner'sdecision of the co-integration approach, regardless of whether it is the Granger and Engle twostage strategy or the Juselius and Johansen multivariate procedure, ought not have anynoteworthy effect upon the result of the hypothesis test. Notwithstanding, in one of the recentstudies, Huan and Yang (1996) concluded that when the Granger and Engle technique rejects thelong-run PPP theory the Juseliusand Johansen technique has a tendency to acknowledgeit.Through Monte Carlo simulations utilizing data from France, Canada, Switzerland, Germany,the U.S.A., and the U.K., Huan and Yang found that the Juselius and Johansen co-integration
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strategy is one-sided toward supporting the long-run PPP under conditions in which thepresumption of ordinarily as well as autonomously and indistinguishably appropriatedaggravation term is violated.This paper applies the two co-integration strategies to consumer price index (CPI) and exchangerate data from three developed regions to test for the long-run PPP speculation. In particular, ittests whether Huan and Yang's claim, that the two co-integration systems yield contradictingoutcomes, remains constant with regards to developed regions. The two co-integrationapproaches are applied to a time series data spanning from 1988 to 2010. The paper utilizeseffective exchange rate as the measure of exchange rate. Most countries have more than oneexchanging partner, the effective exchange rate is the suitable measure of exchange rate (Officer(1980)).The early experimental has grounded for a long time to look at the purchasing power parity(PPP) exchange rates proved by statistical estimations and discovering versatility coefficients onresidential and foreign costs. Frankel (1978) conducted a study on relative and absolute PPPconvention amid the adaptable exchange rates. His outcome discovered causality relationship ofexchange rate on cost in the sense of granger. Most traditional econometric estimations such asleast square approach (GLS) in view of non-stationary time series results to spurious regressionand statistics may essentially show only correlated trends as opposed to a genuine relationship(Granger and Newbold, 1974). Augmented Dickey-Fuller (1981) and Philips and Perron, (1988)tests can help maintain a strategic distance from false outcomes through stationary tests of timesseries.Based on this, a number of observational studies present progression in the estimated equation ofPPP. Abuaf and Jorian (1990), conducted a unit-root test for non-stationary time series data.Their results do not bolster PPP in long-run of the significant monetary forms. Taylor (1988)utilized a co-integration of Johansen approach (1988) to conclude that there is a no connectionamongst costs and exchange rate. Patel (1990) utilized Engel-granger co-integration strategy toaffirm purchasing power parity prove. They pointed in their outcomes unfavorable proof to PPPhypothesis amid the 1971-period assessed as ridiculing period after the Nixon (1993) inspectedlong-run purchasing power parity utilizing a partial co-integration examination for the period1914 - 1989. Their results upheld PPP as a long-run approach.Johnson (1990) identified a solid and long-run U.S. - Canada data PPP idea. Philip (2001)affirmed the confirmation of PPP in small-sample from yearly data spreading over 1973 through1997 Nominal exchange rates for France, Canada, Japan, Italy, U.K and Switzerland are relativeto the U.S. dollar. Rogoff (1996)found out that PPP hypothesis did not hold amongst developingand developed countries. Haug and Besher (2007) established a sort of mixed outcomes for non–linear and linear co-integration in the PPP model utilizing monthly data from the post-BrettonWoods period for G-10 nations. Ozdemir (2008), established bolster for PPP either over the longrun. Hyrina and Serletis (2010) looked at various econometric strategies utilized in earlier and
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later studies to verify PPP idea, where early experimental techniques failed to recognize PPPpresence contrasted with current investigations.Hussein (2015) analyzed the long run development between US dollar and Canadian dollarexchange rates upon month to month data for the period 1995 to 2008 utilizing the Engle-Granger co-integration test. In his paper, he doesn't give the validity of PPP between US dollarand Canadian dollar trade rates. Pedroni (2001) showed blended proof of PPP in view of panelunit root tests. He showed the presence of weak PPP and rejected solid PPP idea. Robertson et al(2014) utilized panel co-integration approach of month to month data from 1982 through to 2010to explore the Purchasing Power Parity (PPP) between the Mexico and US.The rest of the paper is organized in the following way. The literature review on the theory oflong-run PPP is presented in section II. Section III introduces the methodology used whichincludes the approaches, philosophies, strategies and justification of the approaches used. SectionIV presents the empirical findings based on the analysis of data. Section V provides discussion ofthe findings and interpretation of the results. Lastly, section VI provides the conclusions,limitations of the study and a brief summary of the entire paper.METHODOLOGYThis chapter presents the methodologies as well as testable hypothesis regarding the purchasingpower parity (PPP). Three stages as outlined by Froot and Rogoff (1995) have been employed.The first step involves regression testing using the following equation model;st=α+β(pt+pt¿)+εtWhere st represents the logarithm of the nominal exchange rate, α represents the constant, pt andpt¿ represents the logarithms of domestic and foreign price levels and εt is the error term. Thefirst step will mainly test whether β is close to one. The next step would involve putting more emphasis on the properties of the logarithm of the realexchange rate rx:rx=st(ptpt¿)Here an assumption is made that PPP holds so long as the logarithm of the real exchange rate rxis stationary. In the third step, the focus is on both multivariate and univariate co-integration tests of PPP. Themodel applied checks for stationarity in any of the constants μ¿ and μst(μpt+μ¿pt¿)
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This study will focus more on properties of the real exchange rates (using multivariate andunivariate approaches) as well as co-integration methods given that the series of the logarithmsof nominal exchange rates and consumer price index are normally non-stationary.In testing for the unit root especially for the real exchange rates and consumer price index (CPI),Augmented Dickey Fuller (ADF) tests is applied. The following equation models are used;yt=βyt1+αiyti+1+εtyt=c0+βyt1+αiyti+1+εtyt=c0+βyt1+c1t+αiyti+1+εtThe final equation model is;yt=δyt1+i=1kδiyti+εtWhere yt is basically regressed on the lagged independent variable yt1 and on ytiso that itcould account for any possible autocorrelation of say order k that may occur in the error term εt.Rejecting the null hypothesis H0: δ=0 in favor of the alternative hypothesis HA: δ<0 wouldimply that the given series is stationary. For the case of Dickey-Fuller (1979), he suggested three different regression equations models tobe used in testing the presence or the absence of a unit root;yt=βyt1+εtyt=c0+βyt1+εtyt=c0+βyt1+c1t+εtThe difference in the three regressions is based on the presence of the two deterministic elementsc0, c1t. The first deterministic element (c0) presents a pure random walk model, while the secondone simply adds an intercept, and the last deterministic element includes both intercept and lineartime trend. The main concept behindDickey –Fuller test is the fact that the t-test normallybecomes inappropriate so long as the process is non-stationary, thus starting from yt=kyt1+εtand if we subtract yt1from both the RHS and the LHS we obtain;yt=βyt1+εtIn this case, testing whether β equals to 0 is similar to testing whether k equals to 1. This impliesthat the parameter of interest in all the three regression equations is β, as such if β=0 then theseriesythas a unit root. OLS is used to estimate the above equations so as the value of β can be
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obtained as well as associated standard error. The t-statistic associated with testing for the nullhypothesis β=0 is gotten by dividing the estimated β value by its corresponding standard error (β/StandardError). A smaller critical value compared to the absolute t-statistic value implies thattest is significant hence the null hypothesis is rejected. The Philips-Perron test supports the Dickey-Fuller test where it assumes that the errors aresignificantly independent and that they follow homogeneity. The test is a generalization of theDickey-Fuller approach which permits for lighter assumptions regarding the error distributions.The following regression equations are related to the Philips-Perron test;yt=γ0+γ1yt1+μtyt=λ0+λ1yt1+λ2(tT2)+μtIn the above equations, T denotes the number of observations while μt is the disturbance termsuch that E(μt)=0. The disturbance term need not to be homogeneous or serially uncorrelated.Unlike the Dickey-Fuller test where the homogeneity and independence assumptions take acenter-stage, the Philips-Perron test gives room for disturbance term to be non-homogenouslydistributed and weakly dependent.
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Results and DiscussionIn this section, the test results for the PPP hypothesis are presented. The absolute version of PPP,highlights that the nominal exchange rate computed between two currencies is the same as theratio of the general price levels that exists between two countries and this is formulated asfollows;et=ptpt¿Wherept, pt¿ is the logarithm forms of the price levels for the three countries (United states,United Kingdom and European Union) at time t respectively, and etis the logarithm of thecurrency price for a unit of foreign currency observed at time t. The real exchange rate denotes aprice adjusted nominal exchange rate which is given as:rt=et(ptpt¿)Therefore, in this paper, PPP hypothesis is being tested by evaluating the time series propertiesof {rt} series. With this in mind, if {rt} series is stationary, then it can be said that would expectthe PPP to also hold; however, if {rt} series is non-stationary, for instance, if the series has unitroot then PPP does not hold.Descriptive statisticsFor the analysis purpose the time series data for inflation and the exchange rate was collected forthe three different region namely United States, United Kingdom and the European Union.Descriptive results for the selected variable have been discussed below:Percentiles Smallest 1% 64.59 64.25 5% 66.79 64.4210% 70.14 64.59 Obs 27625% 79.185 64.76 Sum of Wgt. 27650% 87.905 Mean 88.79076
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Largest Std. Dev. 12.9643475% 99.535 110.1990% 107.88 110.52 Variance 168.074195% 108.54 110.62 Skewness -.071535599% 110.52 111.29 Kurtosis 2.022907Table 1 Descriptive statistics for inflation in United StatesResults from the descriptive statistics in shows that average CPI European Union countries is88.8. Similarly the standard deviation is 12.96. As per the probability distribution, if the datafollows the normal distribution then 68 % of the values lies within mean ± SD. As the histogramin figure below indicates that cpieuro is normally distributed so 68 % of the values lies between75.83 and 101.75. Apart from the mean results also shows the percentile wise distribution of thedata and the Skewness and Kurtosis values. 0.01.02.03.04Density60708090100110cpieuroFigure 1 Histogram for CpieuroSimilarly the descriptive statistics for remaining 5 variables has also been shown the followingtable. Histogram for other variable is shown in the appendix.
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