el. This derivation of the PPP is called the Relative Purchasing Power Parity: Where S is the exchange rate and P is the domestic price level, P* the foreign price level and r is a constant parameter known as the real exchange rate. The real exchange rate being constant is a fundamental tenet of the PPP hypothesis and is quite easy to evaluate. In order to do so I must first collect the necessary data. Statistics Canada offers a rather extensive collection of data sets through its CANSIM database. There, I collected the consumer price indices for Canada and the US as well as the spot exchange rate. Then, I logged the variables so that I can test, using an ordinary least squares estimation method, the value of a, b1 and b2 in the equation:Where s, p and p* are the respective logs of the exchange rate, the domestic price level, and the foreign price level. For the Relative Purchasing Power Parity hypothesis to hold I must find that b1=b2=1. In order to test this I execute an F-test with two restrictions, b1=1 and b2=1.That the Relative Purchasing Power hypothesis does not hold is no surprise. In fact it would have been surprising to find that it was true. There are two types are reasons for this, one relating to the inadequacy of my test, and the other to the validity of hypothesis in general. The test I executed was inherently flawed since I used consumer price indices that are not necessarily the same as general price indices. CPIs only reflect the prices that typical consumers pay, this excludes the prices of high volume goods such as manufacturing inputs that may be more responsive to the exchange rates. Moreover, my sample size is small, only 42 data points, as well as being spread over a relatively short period of time, ten years. However more elaborate models of relative PPP were found that the real exchange rate tends exhibit mean reversion in the long term.(Isard p65) In other words, that the deviations from the exp...
