# Purchasing Power Parity (PPP) Theory of Exchange Rate

Purchasing Power Parity Theory (PPP) holds that the exchange rate between two currencies is determined by the relative purchasing power as reflected in the price levels expressed in domestic currencies in the two countries concerned. Changes in the exchange rate are explained by relative changes in the purchasing power of the currencies caused by inflation in the respective countries. The concept of Purchasing power parity theory (PPP) is traced to David Ricardo, but the credit for stating the law in an orderly manner is given to the Swedish economist Gustav Cassel who proposed it in 1918 as a basis for resumption for normal trade relations at the end of First World War.

The Purchasing Power Parity Theory is stated in two versions :

1. The stronger absolute version of Purchasing Power Parity, and
2. The diluted relative version of Purchasing Power Parity.

Absolute Version of Purchasing Power Parity

The absolute version of Purchasing Power Parity is based on the law of one price. This law states that under conditions of free market with the absence of transportation costs, tariffs and other frictions to free trade, the price for identical goods should be the same at any market when measured in terms of a common currency. To give an example, suppose a particular quality of coffee seeds cost Rs 100 a kg in India and the same commodity costs 2\$ in USA. The exchange rate between US dollar and Indian rupee in the market will be Rs 50 so that when the dollar price of coffee is converted into rupees will be the same Rs 100 as prevailing in the domestic market. If the exchange rate in the market is anything other than Rs 50 it will lead to arbitraging opportunities. The arbitraging operations will ultimately lead the exchange rate to the equilibrium level.

To explain how arbitraging operations will restore the exchange rate to Rs 50 per dollar, let us suppose that the market rate for dollar is Rs 45. In the absence of transaction costs, traders in India will find that coffee is priced low in terms of dollars as compared to its rupee price. They will find it advantageous to buy coffee in USA and sell in the domestic market. Suppose a trader imports 1000 kgs of coffee. He will pay Rs 90,000 to acquire the required 2,000\$ from the market. He can sell 1000 kgs of coffee in the domestic market at Rs 100 a kg and earn Rs 1,00,000. This results in a profit of Rs 10,000 to the trader.

Similar operations will be done by all the traders in India. The  combined effect of the operations of  all the traders in India is that the demand for dollars increases in the foreign exchange market, pushing its prices in terms of rupees. With successive deals the dollar keep as appreciating. The arbitrating profit is reduced with the appreciation of dollar. For example if dollar moves to Rs 47, the net profit is reduced to Rs 3 a kg from Rs 5 a kg available earlier. The appreciation of dollar will continue until the arbitrating profit is totally eliminated. That is the level where price of coffee is same when measured in terms of either rupees or dollar.

If the ruling exchange rate is Rs 54 per dollar, traders in India will find it advantageous to sell coffee in USA to get higher rupee realization. For instance, a trader can buy 1000 kgs of coffee for Rs 100,000 and sell them for 2,000\$ in the US market. By selling the dollars in the foreign exchange market at Rs 54, he will realize Rs 1,08,000 and thus gain Rs 8000. Similar operations by all traders will increase the supply of dollars in the market exerting a downward pressure on its price in terms of rupee. The exchange rate will move to a level where arbitrating is no more possible.

While the law of one price relates to a single product, PPP theory does not confine to a single product. Instead of a single commodity we may consider a basket comprising a variety of products. If a basket of commodities costs Rs 10,000 in India and the same set of commodities costs 200\$ in USA , the dollar will be quoted at Rs 50 in the foreign exchange market.

The absolute version of PPP can be stated symbolically as

e =  Pd/Pf

where,

• e = exchange rate for the foreign currency in terms of the domestic currency.
• Pd = Price in domestic currency.
• Pf = Price in foreign currency.

If the price in the domestic market rises relative to the price level in the foreign market, the domestic currency will depreciate proportionately against the foreign currency. In the above example, if the cost of the basket increases to Rs 11,000 in India, while the price does not change in USA, the dollar will now be traded at Rs 55 to maintain the price parity (indicating depreciation of rupee or equivalently appreciation of dollar).

Relative Version of Purchasing Power Parity

The absolute version of Purchasing Power Parity is based on unrealistic assumptions of free trade, no transportation costs and identical commodities. Transportation costs are a big hurdle in benefiting from lower prices in another market. Movement of goods and services are not free. The commodities in any basket are not identical and they may differ in quality. Further, there are certain goods which do not enter international trade. Examples of non-traded goods are housing and personal services like health and haircut.

Therefore it is granted that the exchange rate in the market may differ from the absolute PPP. For instance , when the cost of a basket of commodities is Rs 10,000 in India and 200\$ in the USA, the market may quote Rs 45 per dollar. What is expected is that the exchange rate will move along with the relative changes in prices in the two countries. If the price of the basket of commodities increases to Rs 11000 in India and the basket is now costing 212\$ in USA, the rupee will suffer a depreciation in relation to dollar. The extent to which the rupee will depreciate is the difference in the inflation rates in the two countries during the period. In the given example the inflation was 10%  in India and 6% in USA. The rupee will depreciate approximately by 4% to quote about Rs 46.80.

In order to main the PPP, the change in the exchange rate should be proportionate to the change in the relative purchasing power of the currencies concerned. Therefore,

New exchange rate/ Old exchange rate = Proportionate change in domestic price/ Proportionate change in foreign price

Symbolically this can be stated as

et = e * (1+Id)/(1+If)

where,

• et = expected exchange rate after period t.
• Id = rate of domestic inflation during period t.
• If = rate of foreign inflation during period t.

et = 45* (1.1/1.06)= Rs 46.70

In practice , in the place of a basket of goods, price indices are used to compute the Purchasing Power Parity. To begin with, suppose the price index in India and USA  are 100 and the exchange rate is Rs 45 a dollar. At the end of the period, the price index in India is 115 and in USA is 108. The exchange rate will move to Rs 47.92 as computed ,

Et/45 =(115/100)/(108/100)

Et= Rs 47.92

Nominal Exchange Rate and Real Exchange Rate

The exchange rate as quoted in the foreign exchange market are nominal exchange rates. For instance, if dollar earlier in the market at Rs 45.00 is now quoted at Rs 45.40, the dollar has appreciated by 40 paise in nominal terms. When the inflation rate in two countries differs, the change in the nominal exchange rate is expected. The PPP will hold if the change in nominal terms equals the inflation differential between the two countries. In the earlier example, when the inflation differential was 4% and the nominal exchange rate moved from Rs 45 to Rs 46.70 , the PPP between the dollar and rupee was maintained. A change in the nominal exchange rate does not alter the export competitiveness of the countries , so long as the movement is in accordance with the inflation differential and the PPP is not changed.

Real exchange rate is the nominal exchange rate as adjusted for inflation. For computing the real exchange rate there should be a base period exchange rate. Current nominal exchange rate is discounted for the inflation differential to arrive at the real exchange rate. If the inflation adjusted exchange rate is same as the base period exchange rate, there is no change in the real exchange rate during the period. If the inflation adjusted exchange rate is higher than the base period exchange rate, there is depreciation of the home currency in real terms. If the inflation adjusted exchange rate is lower than the base period exchange rate, the home currency has depreciated in real terms against the foreign currency.

Changes in the real exchange rates can be seen as deviations from PPP. In the given example, against dollar the rupee deviated from PPP by 40 paise. This is same as the real exchange rate changes, allowing for the difference due to different bases. It may be understood that it is the real exchange rate that affects the competitiveness of a country and not the nominal exchange rate changes.

Empirically it is found that PPP holds only in a very long period. During short term and over medium term, the exchange rate in the market differs significantly from the PPP. The reasons for this deviation are :

1. Price Indices: There are different price indices like wholesale price index and consumer price index with different constituents. Even if we use the same index in the two countries concerned, each country follows its own composition and assigns its own weights. Therefore there are no identical indices based on which the inflation differential can be calculated accurately.
2. Inclusion of non-traded goods: The price indices are based on the changes in prices of traded as well as non-traded goods. The exchange rates in the market are affected only by changes in the prices of traded goods. It is common knowledge that during a given period, in any country, all the goods do not undergo price changes to the same extent. A price index which includes both traded and non-traded goods is influenced by price changes in both types of goods. To the extent the weights assigned to each type differs between the indices, the effect of changes in the price of traded goods on the price index varies. The actual PPP tends to be different from that suggested by the price indices by the inclusion of non-traded goods in the index.
3. Stickiness of the price of goods price: In many cases the prices of goods are determined by the manufacturers on the basis of various factors, other than the cost of production.
4. Government interference: Govt. interference in the form of tariffs and other hindrances to free flow of international trade does not permit the arbitrageurs to take advantage of the price differences in two markets.
5. Liberalization of markets: With the liberalization of markets, the cross border movement of cash for capital transactions and speculative activities have gained greater importance. The exchange rate is now determined not only by movement of goods and services.
6. Price discrimination by MNCs : Multinational firms adopt the policy of price discrimination by market segmentation leading to the same product being priced differently in different markets.

Source: Slideshare.net