What do you understand by Purchasing Power Parity and Interest Rate Parity? Discuss the reasons for their deviations.

 Q. What do you understand by Purchasing Power Parity and Interest Rate Parity? Discuss the reasons for their deviations.

Purchasing Power Parity (PPP) and Interest Rate Parity (IRP) are two foundational concepts in international finance and economics that aim to explain and predict the relationships between exchange rates, inflation, and interest rates across countries. Although both are rooted in economic theory, they are based on different assumptions and focus on different aspects of economic activity. The two concepts provide important insights into how international markets function and how the variables within them interact. However, both PPP and IRP are often subject to deviations in practice, due to various factors that undermine their predictive power. This deviation from theory has been a topic of significant interest and research in the field of economics.

Purchasing Power Parity (PPP)

Purchasing Power Parity (PPP) is an economic theory that suggests that in the absence of transportation costs and other trade barriers, the exchange rate between two currencies should equalize the price of a basket of goods and services in both countries. In other words, the theory asserts that the same basket of goods should have the same price when expressed in a common currency, regardless of the country in which it is sold. The essence of PPP is that the relative value of two currencies is determined by their purchasing power, and the exchange rate should adjust to reflect the difference in price levels between two countries.

The theory of PPP is based on the Law of One Price, which states that in a perfectly competitive market, identical goods should sell for the same price when expressed in a common currency. If this does not occur, arbitrage opportunities will arise, and market participants will exploit the price difference until the price parity is achieved. For instance, if a specific good is cheaper in one country than in another when the price is converted into a common currency, traders will buy the cheaper good and sell it in the more expensive market. This process will eventually lead to an adjustment in prices and exchange rates to reflect parity.

There are two versions of PPP:

1.     Absolute PPP: This version assumes that a basket of goods in one country should cost exactly the same as the same basket in another country when expressed in the common currency. Mathematically, this can be represented as:

$$S = \frac{P_1}{P_2}$$

Where:

$$$$

$S$

$$

$P_1$

${}_{}$

$P_2$

According to Absolute PPP, the exchange rate should adjust so that the purchasing power of a given currency is the same across countries.

2.     Relative PPP: This version is more widely accepted and more commonly used in practice. Relative PPP suggests that the rate of change in the exchange rate between two currencies is proportional to the difference in inflation rates between the two countries. It holds that:

${}_{}$

$$\frac{S_1}{S_0} = \frac{(1 + \pi_1)}{(1 + \pi_2)}$$

Where:

$$\frac{{}_{}}{}$$

$S_1$

${}_{}$

$S_0$

${}_{}$

$\pi_1$

${}_{}$

$\pi_2$

This version of PPP focuses on how inflation differentials between countries lead to changes in exchange rates over time.

Interest Rate Parity (IRP)

Interest Rate Parity (IRP) is another fundamental concept in international finance, specifically relating to the relationship between interest rates and exchange rates. IRP theory asserts that the difference in interest rates between two countries is equal to the expected change in the exchange rate between their currencies. In other words, the expected return on an investment in a foreign country, when adjusted for exchange rate changes, should be the same as the expected return on a domestic investment.

The central idea behind IRP is that arbitrage opportunities will prevent deviations from this parity. If investors can borrow in one currency, convert it to another, and invest at a higher interest rate, they will engage in currency speculation until the return on the foreign investment equals the return on the domestic investment. The IRP condition can be expressed mathematically as:

${}_{}$

$$1 + i_1 = (1 + i_2) \times \frac{E(S_1)}{S_0}$$

Where:

$$\mathrm{}$$

• $i_1$

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