Question

The following table shows the evolution of an index of \(\$ / £\) nominal exchange rate, and the behaviour of prices in each of two countries. In the initial years, monetary policy is very different; in the last three years both countries succeed in achieving inflation targeting at a low level. For simplicity, we assume that the inflation target is zero. (a) Calculate the evolution of the implied real exchange rate, setting the index initially at 100 . (b) Graph the nominal and real exchange rates. (c) What happens to the correlation between nominal and real exchange rates once inflation convergence is achieved?

Short answer

Calculate and graph nominal and real exchange rates, and observe convergence effects on correlation after inflation targets are met.

Step-by-step solution

Understanding Nominal Exchange Rate

The nominal exchange rate is given in units of one currency relative to another, denoted as $/£. This rate reflects how much one dollar can be exchanged for in British Pounds.

Inflation Impact Analysis

Inflation affects the real exchange rate, which accounts for price level differences between the two countries. The real exchange rate formula is: \( RER = \frac{E \times P^*}{P} \), where \( E \) is the nominal exchange rate, \( P^* \) and \( P \) are foreign and domestic price levels respectively.

Initial Real Exchange Rate Calculation

Set the initial real exchange rate to 100, which represents the base index value for calculating changes in future periods.

Real Exchange Rate Evolution

Using the formula \( RER = \frac{E \times P^*}{P} \), calculate the real exchange rate for each year given nominal exchange rates and domestic/foreign price indices. Adjust calculations as inflation changes or stabilizes.

Graphing Nominal and Real Exchange Rates

Graph the nominal and real exchange rates over time using the calculated data points. Plot each rate on the same graph to visually compare their evolution and trends.

Correlation Analysis between Exchange Rates

After plotting, analyze the correlation between nominal and real exchange rates yearly. Post-inflation convergence, the correlation reflects less deviation as inflation stabilizes, potentially indicating a stronger correlation.

Key concepts

Inflation Targeting

Inflation targeting is a monetary policy strategy used by central banks to keep inflation rates within a specified range. The goal is to create a stable economic environment by controlling inflation, which in turn helps stabilize prices and promotes economic growth. When inflation targeting is successful, the economy benefits from predictable changes in the purchasing power of a currency. This stability often leads to better economic planning for households and businesses.

In the context of our exercise, inflation targeting is set with an assumed target of zero inflation. This means both countries aim to maintain the price levels at a constant, eliminating year-over-year inflation. By achieving this zero inflation target, the variability or unpredictability caused by fluctuating prices is minimized. This stability can enhance the effectiveness of other economic components such as exchange rates.

• It helps central banks anchor inflation expectations.
• Focuses on retaining economic confidence.
• Provides a clear rule for monetary policy actions.

As monetary policy succeeds in achieving these targets, it contributes to a more predictable economic landscape and allows analysts to better gauge future trends and align economic indicators with actual performance.

Nominal Exchange Rate

The nominal exchange rate plays a crucial role in international trade and finance. It is the rate at which one currency can be exchanged for another. In simpler terms, it tells us how much of one currency you need to give up to get a unit of another currency. For instance, if the nominal exchange rate between the US dollar and the British pound is 1.3, it means that $1.30 is needed to purchase £1.

It's important to remember that the nominal exchange rate is heavily influenced by various factors, including differences in interest rates between countries, economic policies, and current geopolitical events. The exchange rates can fluctuate daily based on market demands and supply.

Nominal rates do not adjust for inflation; thus, they merely show the "face value" of the trade between currencies. Hence, they may not fully capture the true purchasing power between the currencies. Despite this limitation, nominal exchange rates provide the base for more comprehensive analyses.

Real Exchange Rate

The real exchange rate provides a more complex picture than the nominal exchange rate because it takes inflation differences between countries into account. It reflects the purchasing power parity (PPP) of a currency by adjusting the nominal exchange rate for the relative price levels in two countries.

The formula for calculating the real exchange rate (RER) is:\[RER = \frac{E \times P^*}{P}\]where \(E\) represents the nominal exchange rate, \(P^*\) is the price index of the foreign country, and \(P\) is the price index of the domestic country.

By using this formula, you can gauge how much of domestic goods a foreign currency can actually buy. It's an essential tool for understanding true costs in international markets. Changes in RER indicate shifts in competitiveness; if the RER rises, domestic goods become more expensive relative to foreign goods, impacting exports and imports.

In scenarios where inflation targeting is effective, changes in real exchange rates are more likely due to currency movements rather than inflation differentials.

Correlation Analysis

Correlation analysis is a statistical method used to understand the strength and direction of a linear relationship between two quantitative variables. In this context, we are interested in the correlation between nominal and real exchange rates over time. As economic variables, these exchange rates can, at times, display varying relationships depending on monetary policy frameworks, especially during transitions to stable inflation targeting.

The correlation coefficient ranges from -1 to 1. A correlation close to 1 implies a strong positive linear relationship, where both variables move together. A correlation close to -1 implies a strong negative linear relationship, while a correlation around 0 indicates no linear relationship at all.

Post-inflation convergence, as seen in the exercise, a stable inflation environment can lead to less divergence between nominal and real exchange rates. This could result in a higher positive correlation because both rates may stabilize and reflect fewer inflation-induced discrepancies. This means they move more closely together, suggesting an alignment in economic conditions or successful inflation targeting.

• Helps understand economic stability impacts on exchange rates.
• Assists in forecasting future trends and economic conditions.
• Indicates how various monetary policies may affect currency valuation.

By studying this relationship, policymakers and economists can derive insights into the efficacy of inflation targeting and its broader impact on economic activities.