Purchasingpower parity is used in international finance to compareinternational incomes and expenditures. The principle provides thatthere is for a one on one relationship between the exchange rates andinflation levels of different countries. Consequently, it argues thatthe prices of various identical goods are the same in differentcountries. The effect of one price results from the differential inthe exchange rates between the two countries. The theory argues thatthe difference in inflation rates between two countries causes achange in the exchange rates. Countries with high inflation rateshave a high exchange rates compared to countries that prices are low.
Thispaper investigates the existence of purchasing power parity betweenCanada and the United States of America for a period of ten yearsfrom 2005 to 2015. The exchange rates and consumer price indicesduring the period of interest are used to conduct a regressionanalysis.
Thestudy identified that the law of one price does not apply between theUnited States and Canada. The regression analysis indicated that theline was not a straight line and it did not pass through the origin.
Thestudy obtained historical exchange rates and consumer price indicesfor both countries. The 2005 -2015 consumer price indices wereobtained from the website of the Federal Reserve Bank of ST. Louis oneconomic research. The 2005 – 2015 data on nominal exchange rates wasobtained from the international financial statistics of theInternational Monetary Fund (IMF). The home country was Canada andthe United States served as the foreign currency. The nominal ratewas obtained in the form of US/Canada .The inverse was conducted totransform it into the Canada / USA form.
Theone on one relationship between exchange rates and the price levelsis indicated as follows: qt = Et x Pt* / Pt. Where qt-real exchange rate, Et –Nominal exchange rate (home currency perunit foreign currency) Pt*-Priceindex of foreign country, and Pt.Priceindex of home country. According to the principle, the change in the real rate is unitary,as it does not change.
Consequently,the equation becomes Et=Pt /Pt*.Itindicates that any change in the nominal exchange is equal to thedifference between the percentage change in domestic and foreignprice level : %∆Et=%∆P t- %∆P t* .
Consequently,the paper shall estimate % ∆E= β0+ β1(%∆P– %∆P*) + u . Similar to the linear equation Y= bx +c, β0 and β1 are the yintercept and the gradient of the line respectively. U is a residualterm. At Ceteris Paribus, there should be a one-for-one relationship. A unit change in the inflation rates (price index) causes a unitchange in the nominal exchange rate. Consequently, the value of β0should be equal to 0 and β1 should be equal to 1. This shouldindicate a straight line that passes through the origin at point (X,Y)= (0, 0) and with a gradient of one (1) .
Thedata on the exchange rates and the price level difference between theUnited States and Canada for the period between 2005 and 2015 wasarranged in excel. The data was arranged in terms of months. Excelwas used to obtain the difference in the price levels and theexchange rates over the years. The difference in the price levels wasexpressed in percentage form. The analysis was conducted usingregression analysis in excel. The percentage change in the exchangerates was entered as the depended variable on the Y axis. Theindependent variable was the differentia in the interest rates thatwas entered in the X axis. The results are discussed below.
Research findings and conclusions
Regressionanalysis revealed that the coefficient for the equations are Et=0.065061β0 + 0.0571974 β1 (Pt-Pt*)+u. The coefficient β0 does not equate to 0 while β1 does not equateto one. There is lack of one on one relationship in the exchangerates and the price level differences between Canada and the UnitedStates. Consequently, the line is not a straight line and it does notpass through the origin. The absence of one on one relationshipbetween the exchange rates of Canada and price levels of the UnitedStates signifies that there was no purchasing power parity betweenthe United States and Canada during the period 2005 to 2015.Regression analysis verified that the data was not scientificallysignificant as indicated by F = 0.087641, that is above 0.05. The Rsquare results at the summary of output indicated that the data wasnot a very good fit at 0.0006896.
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