How to Calculate The Change in Real Dollar Exchange Rate

The real exchange rate measures the value of one currency relative to another, adjusting for price differences between countries. This guide explains how to calculate the change in real exchange rate between two periods.

What is a Real Exchange Rate?

The real exchange rate accounts for price differences between countries by comparing the nominal exchange rate with inflation rates. A nominal exchange rate shows how much of one currency is needed to buy another, while the real exchange rate adjusts for purchasing power parity.

Key points about real exchange rates:

Higher real exchange rate means your currency is stronger relative to foreign goods
Lower real exchange rate means foreign goods are cheaper in your currency
Used to analyze international trade and economic conditions
Different from nominal exchange rates which don't account for inflation

Formula for Calculating Change in Real Exchange Rate

The change in real exchange rate between two periods can be calculated using the following formula:

ΔRER = (E2 / E1) × (P1 / P2) - 1 Where: ΔRER = Change in real exchange rate E1 = Nominal exchange rate at time 1 E2 = Nominal exchange rate at time 2 P1 = Price level at time 1 (usually CPI) P2 = Price level at time 2 (usually CPI)

This formula adjusts the nominal exchange rate change by the inflation differential between the two periods.

Step-by-Step Calculation

Determine the nominal exchange rates for both periods (e.g., 1 USD = 1.20 EUR in 2020, 1 USD = 1.10 EUR in 2023)
Find the consumer price indices (CPI) for both periods (e.g., CPI in 2020 = 100, CPI in 2023 = 120)
Calculate the ratio of the second nominal exchange rate to the first: 1.10 / 1.20 = 0.9167
Calculate the ratio of the first CPI to the second CPI: 100 / 120 = 0.8333
Multiply these two ratios: 0.9167 × 0.8333 = 0.7667
Subtract 1 from this product to get the change in real exchange rate: 0.7667 - 1 = -0.2333 or -23.33%

Worked Example

Let's calculate the change in real exchange rate between 2020 and 2023 for the USD/EUR pair.

Year	Nominal Exchange Rate (USD/EUR)	CPI (Base 2020=100)
2020	1.20	100
2023	1.10	120

Using the formula:

ΔRER = (1.10 / 1.20) × (100 / 120) - 1 ΔRER = (0.9167) × (0.8333) - 1 ΔRER = 0.7667 - 1 ΔRER = -0.2333 or -23.33%

This means the real value of the euro decreased by 23.33% between 2020 and 2023.

Interpreting Results

Interpreting the change in real exchange rate requires understanding several factors:

Positive change indicates your currency is gaining relative purchasing power
Negative change indicates your currency is losing relative purchasing power
Large changes may indicate economic shifts or policy changes
Compare with nominal exchange rate changes to understand inflation effects

Note: Real exchange rate changes should be analyzed alongside other economic indicators for a complete picture.

Frequently Asked Questions

What is the difference between nominal and real exchange rates?

Nominal exchange rates show the direct conversion between currencies without accounting for price differences. Real exchange rates adjust for inflation, showing the true purchasing power of one currency relative to another.

Why is the real exchange rate important?

The real exchange rate helps businesses and economists understand the true cost of importing goods, analyze international trade, and assess economic conditions between countries.

How often should real exchange rates be calculated?

Real exchange rates are typically calculated quarterly or annually using official inflation data and exchange rate reports from central banks.

What factors affect real exchange rates?

Key factors include domestic and foreign inflation rates, interest rate differentials, trade policies, and economic growth between countries.