The theory of Purchasing Power Parity (PPP) is not new to economics. It was first introduced by Cassel in 1918, but it was presented by himself three years before using an equivalent term “theoretical rate of exchange”(Economics Discussion, 2015). In this paper, we analyzed this theory based on U.S.A, Canada, Denmark and Norway from 1978 until 2015. Throughout the paper, Purchasing Power Parity will be tested by using the United States as the domestic country, and Canada, Denmark and Norway as foreign countries. To specify, the producer price index for manufacturing (PPI) and consumer price index for all items (CPI) will be compared amongst the countries, after converting each country's currency to the US dollar. After running various tests using the Eviews software, one is able to determine that there is no long run relationship.