Purchasing power parity dates back several centuries but was actually introduced after World War 1. Before the war, gold standards were used but after the war it was difficult to continue this way because speculators were afraid countries would ask for high revenues after devaluing their currencies. Therefore, Cassel developed Purchasing Power Parity during the international policy debate when they were discussing about the nominal exchange rates and what the appropriate level would be.
Gustav Cassel has created the modern definition of purchasing power parity; ‘When measured in the same unit, the monies of different countries should have the same purchasing power and command the same basket of goods.’ In simpler terms it means, that in its absolute version, when expressed in a common currency the price levels should be equal worldwide. The theory is developed from the law of one price. The law of one price is the main building block of purchasing power parity. ‘The law states that once converted to a common currency, the same good should sell for the same price in different countries’ (Mkenda 2001 pg 6). That is for any good:
P* = SP**
Where; P* is the domestic price of the good P** is the foreign price for the good S is the domestic nominal exchange rate.
(Mkenda 2001 pg 6-7).
Under the law of one price it assumes that the there is perfect competition, hence no transportation costs, trade barriers or tariffs. Purely free trade, which makes the price of goods in any country equal therefore no arbitrage opportunities exist (Shapiro pg 135). In both the countries there has to be competitive markets for the goods and lastly it only applies to tradable goods.
The Big- Mac index demonstrates the law of one price and absolute purchasing power parity. It is developed by the Economist; it compares all the prices of a Big Mac around the world. ‘The Big Mac PPP is the exchange rate that would leave hamburgers costing the same overseas as in the US’ (Shapiro pg 135). However, in the real world non tariff barriers, taxes, tariffs and transportation costs do exist and this causes differences in prices between the different countries. Also Engel and Rogers, in one of their researches, said that the greater the distance between the cities the higher the volatility of the price differential. They also said that countries do not produce perfect substituted goods but differentiated ones which lead to deviations in the prices of the goods (Taylor et al pg 137). So the law cannot exactly be held. In the case of the Big Mac index, there are price differences due to non tradable inputs such as labor and location. (Emeraldinsight.com, 2013)
The table shows that the Big Mac prices vary across countries with the most expensive being in the UK at 1.81 pounds and the cheapest in Australia at 0.87 pounds.
Absolute purchasing power parity ignores free trade, therefore absolute purchasing power Parity does not hold for the same reasons as the law of one price.(Mkenda pg 7) and (Shapiro pg 135)
Due to this relative purchasing power parity was introduced. This states that the ‘exchange rate between the home currency and any foreign currency will adjust to reflect changes in the price levels of the two countries’ (Shapiro pg 135).
Isard has stated ‘in the assumed absence of transportation costs and trade restrictions, perfect commodity arbitrage insures that each good is uniformly priced (in common currency units) throughout the world- the law of one price prevails’. This statement is one where a lot of debates have been undertaken and also empirical tests have been held as to whether this holds.
A lot of empirical tests have been carried out on the Law of one Price and many of them have rejected it. Research has constantly found that the prices depend on the exchange rates which the law of one price does not abide by. (Knetter, 1997 pg 5). Exchange rates are very volatile compared to relative nominal prices. Isard undertook research on highly tradable goods such as clothes on the US, German, Canadian and Japanese markets. He found out the Law of one Price only reflected nominal exchange movements. Alberto Giovannini compared prices for the US and Japan commodity goods in the manufacturing sector, i.e. screws and nuts etc. He ultimately found out that the change in the Law of one price is ‘highly correlated with the exchange rate movements’ (Rogoff pg 652). Therefore, prices really do rely on the exchange rates and this is not what the law of one price states hence resulting in empirical tests rejecting the law of one price.
Other potential reasons for rejecting the law of one price could be that the costs of the local inputs such as labor are very important for prices. Also due to location, goods in different areas have different prices. Lastly, the law of one price says that there are no transport costs for identical goods however transport costs are generally really high and hence no equal prices and no perfect commodity arbitrage. A test was done on duty free outlets, where the same product was sold in the same location, but had two different currencies. It was found that ‘the duty – free outlets allow deviations from law of one price of up to 7-10 percent’ ((Asplund and Friberg, 2001, pp. 1). Any changes below this can last for up to a decade and be continual.
Purchasing power parity is very attractive because of its simplicity. However, empirical tests have a mixed view on this. I will briefly mention the purchasing power tests undertaken and then discuss in detail about the theories behind it.
There are four classes of approaches undertaken; firstly, a test on the absolute purchasing powers parity and the relative purchasing power parity. Secondly, exchange rates fluctuate more than the price levels, therefore purchasing power parity cannot hold at any particular time.
Third, is the co integration analysis (used to determine if there is a long term equilibrium relationship between the variables). This produces a mixture of results when testing for purchasing power parity, when a sample data which are large are used, for example Kim (1990) did research on the purchasing power parity in the long run using this approach, and the purchasing power parity was supported. However on smaller samples the results have not been that good. Lastly is the panel data analysis, which allows the researcher to make use of information from both variables. (\Vz\Vd\'Arek, 2010). It involves time series and cross-sectional observations. This increases the sample size and therefore the younger nations like Botswana, Kenya and other African countries can be combined to produce a large sample. (Mkenda. 2001. Pg 12). A lot of studies have been carried out that support purchasing power parity, for example; Holmes (2000), MacDonald (1996), Wu (1996) who ‘ pooled data on real exchange rates between the United States and eighteen OECD countries as a panel’ (Wu, 1996, pp. 54-63).
It is important to remember that there are two types of exchange rates;
1. Nominal exchange rate – ‘the number of units of the domestic currency that can purchase a unit of a given foreign currency’ (Cnb.cz, 2014).
2. Real exchange rate - ‘the ratio of the domestic price level and the price level abroad’ (Cnb.cz, 2014). i.e. the price of one countries goods in terms of another countries goods.
The empirical evidence for purchasing power parity has mixed results. It is dependent on the amount of time, the countries under consideration, the methods being used and the productivity differences across nations. (Sephton, 2008, pp. 55--57)
Purchasing power parity is extremely important in international finance because a lot of models of exchange rate determination are developed from the assumption that purchasing power parity holds. ( Wu 1996 pg 54). However, empirical evidence has shown that Purchasing power parity does not determine exchange rates in the short term. In the short run exchange rates are determined using interest rate changes, news driven information and many other factors. However, purchasing power parity is supported in the long run by empirical studies.

Figure 1a shows data on the UK and US Consumer Price Indices from 1820 – 2001. Figure 1b shows data for the US and UK producer price indices from 1791 - 1991. (Taylor pg 138). Taylor and Taylor raised three points from these graphs; firstly there are short run changes from the purchasing power parity, in both cases the correlation between the two lines is not perfect. Secondly, the national price levels for both the countries did move together over the long period. Thirdly, producer price gives a much greater correlation than the consumer prices. (Tayloe et al. pg 138).