By Yuriy Smirnov Ph.D.

## Definition

The theory of purchasing power parity or PPP claims that the currency exchange rate between two countries adjusts to changes in the price of a basket of the same goods and services in both countries. In turn, the theory derives from the low of one price that states that two identical goods must have the same price in any country, and any change in price results in an adjustment in the exchange rate.

For example, the price of wheat in United States is \$209.81 U.S. per metric ton, and in France it costs 175.27 Euro per metric ton. Under the law of one price, the current spot exchange rate should be 0.8354 as a direct quote and 1.1971 as an indirect quote.

 Spot exchange rate as USD/EUR = 175.27 = 0.8354 209.81
 Spot exchange rate as EUR/USD = 209.81 = 1.1971 175.27

Let’s suppose the price of wheat in France increases to 183.51 Euro per metric ton. Profit-seeking importers from France will convert Euros for U.S. dollars at the current spot exchange rate to buy wheat in the United States and then sell it in France. Thus, they will have an arbitrage profit of 8.24 Euro per metric ton (183.51-175.27) from an imbalance in the price of wheat between the two markets. However, the growing demand for U.S. dollars from French importers will cause its appreciation against the Euro. After some time, the market will reach equilibrium, and the arbitrage opportunity will disappear. The new spot exchange rate will be 0.8354 as a direct quote and 1.1971 as an indirect quote.

 Spot exchange rate as USD/EUR = 183.51 = 0.8746 209.81
 Spot exchange rate as EUR/USD = 209.81 = 1.1433 183.51

Purchasing power parity works the same way as the law of one price, but instead of the price of a single good, the exchange rate adjusts to the change in price of a basket of goods and services.

## Assumptions

The theory of purchasing power parity believes that the following assumptions are met:

1. There are no transportation costs. In other words, any good may be moved from one country to another country at no cost.
2. There are no trade barriers. This means no trade restrictions, such as import or export tariffs, duties, and special taxes.
3. Perfect information. Any market participant has perfect information about the prices of goods and services in any country. If this condition is met, markets are in equilibrium, and there is no arbitrage opportunity.
4. Goods and services are perfectly interchangeable. There is an identical basket of goods and services in both countries.

## Formula

If we consider two identical baskets of goods and services in two countries, the purchasing power parity exchange rate can be expressed as follows:

 Exchange Rate = Price of Basket in Country A Price of Basket in Country B

Please note that the price of each basket is given in its national currency!

Thus, any change in the basket’s price will result in an adjustment of the exchange rate. For example, if the price of a basket in Country A increases and the price of an identical basket in Country B remains the same, the exchange rate will grow. In other words, the national currency in Country B appreciates against the national currency in Country A.

### Purchasing power parity and inflation

If we know the expected inflation rate in both countries, the expected exchange rate under the theory of purchasing power parity may be calculated as follows:

 Expected Exchange Rate = Price of Basket in Country A × (1 + rA) Price of Basket in Country B × (1 + rB)

or

 Expected Exchange Rate = Exchange Rate × 1 + rA 1 + rB

where rA and rB are expected inflation rates in Country A and Country B respectively.

In other words, we can state that the exchange rate between two countries adjusts to the inflation rate differential.

## Examples

### Example I: The law of one price

Let’s suppose that the price of a consumer basket in the United States is \$1,457, and the identical basket in Germany is priced at 1,279 Euro. As mentioned before, the basket of goods and services in one country should have the same price as an identical basket in another country. Therefore, the exchange rate between U.S. dollars and the Euro under purchasing power parity should be 0.8778 as a direct quote and 1.1392 as an indirect quote.

 USD/EUR = 1,279 = 0.8778 1,457
 EUR/USD = 1,457 = 1.1392 1,279

### Example II: PPP and inflation rate differential

The expected annual inflation rate in the United States is 1.551% and 1.818% in Great Britain. What should be the expected exchange rate in one year under PPP theory if the current spot exchange rate is USD/GBP = 0.7865?

To answer this question, we should use the formula of expected exchange rate from above.

 Expected exchange rate as USD/GBP = 0.7865 × 1 + 0.01818 = 0.7886 1 + 0.01551

We can also express the expected exchange rate as an indirect quote (GBP/USD).

 Spot exchange rate as GBP/USD = 1 = 1.2715 0.7865
 Expected exchange rate as GBP/USD = 1.2715 × 1 + 0.01551 = 1.2682 1 + 0.01818

## Criticism

Critics of the purchasing power parity theory indicate that some assumptions are unrealistic.

1. Transportation costs. Despite the theory’s assumption, transportation costs do exist in the real world, and sometimes they have a great effect on the price of a good. For example, the price of a particular good in an exporting country is always lower than the price in an importing country due to transportation costs.
2. Trade restriction. Such trade restrictions as import/export tariffs, duties, and special taxes increase the price of a given good for an importing country.
3. Perfect information. Price information is not perfectly and immediately available to every market participant. Therefore, some price discrepancies do exist and cannot be eliminated by the arbitrage process.
4. Effect of nontraded costs. In the real world, there are some nontraded inputs, e.g., land and labor, that affect the price of a good but cannot be traded. For example, the rent fee in downtown can be much higher than in the suburbs. Therefore, the price of identical foods in a grocery store downtown will be higher than in the suburbs because higher prices are needed to compensate for higher rent fees. Thus, we can say that purchasing power parity does not even hold up within a single city.

## The bottom line

It should be noted that even critics of purchasing power parity do not reject the theory completely because it can be used as a tool for forecasting exchange rates. It works best for long-term forecasting when price levels between two countries differ significantly, but the accuracy of an exchange rate forecast depends on the accuracy of an inflation rate forecast.

The purchasing power parity model can be applied to forecast the expected exchange rate in the long term, which is usually from one to five years, but it is not recommended for short-term forecasting, i.e., for a time range of less than one year. Short-term forecasts may have a significant error because of a time lag between price changes and the adjustment of exchange rates to these changes as well as intraannual, seasonal, and market fluctuations.