What is the Fisher Equation?
The Fisher Equation illustrates the relationship between nominal interest rates and real interest rates, where the difference is attributable to inflation.
How to Calculate the Fisher Equation in Economics
The Fisher equation is a concept from the field of macroeconomics that establishes the relationship between the nominal interest rate and the real interest rate.
The equation and supporting theory originated from Irving Fisher, an economist most well-known for his contributions to the quantity theory of money (QTM).
According to Fisher, the link between the nominal and the real interest rate is related to the effects of inflation.
The list below briefly describes the three inputs to the Fisher equation.
- Nominal Inflation Rate → The stated interest rate denoted in terms of dollars and remains fixed irrespective of inflation.
- Inflation Rate → The inflation rate is the percentage change in prices over a specified period and is broadly intended to capture the rise or decline in the cost of living in a given country.
- Real Interest Rate → The interest rate adjusted for the effects of inflation (and therefore reflects the rate of change in purchasing power).
The most common measure of inflation is the consumer price index (CPI) despite the criticism surrounding the methodology by which the index is calculated.
Fisher distinguished between the nominal interest rate and the real interest rate, as it was the real interest rate – rather than the nominal interest rate – which is far more influential on consumer behavior and the more accurate indicator of an economy’s financial state.
Fisher Equation Formula
The Fisher equation is as follows:
Where:
- i = Nominal Interest Rate
- π = Expected Inflation Rate
- r = Real Interest Rate
But assuming that the nominal interest rate and expected inflation rate are within reason and in line with historical figures, the following equation tends to function as a close approximation.
While unrealistic, if the expected inflation rate was zero, the nominal and real interest rate would be equal to each other.
But since inflation is an inherent risk to all countries (e.g. the Fed, the central bank of the U.S., sets specific targets for inflation) and is most often a positive figure, the real interest rate is typically lower than the nominal interest rate in most cases, barring unusual circumstances.
In order to adjust the nominal interest rate for inflation, we can rearrange the formula from above to estimate the real interest rate.
The only step here is to subtract the inflation rate from the nominal interest rate, resulting in the formula for calculating the real interest rate.
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As a quick example, suppose that a loan was issued at a 10.0% nominal interest rate and the expected inflation rate is 6.0%.
Q. Given those assumptions, what is the real interest rate?
If we subtract the inflation rate from the nominal interest rate, the real interest return comes out to 4.0%, which is the yield that the lender is expected to earn from the financing agreement.
But more importantly, the takeaway from our scenario is that even if the lender were to receive all interest payments on time and the original principal on the date of maturity, the actual return is still lower than that of the nominal interest rate due to the effects of inflation.
The risk of inflation is among one of the risks considered by lenders when determining the pricing terms on a debt issuance.
The more concerning matter for lenders is not inflation by itself, but inflation that exceeds their expectations.
On the date that a financing arrangement is finalized, the inflation rate that will occur in the future is an unknown variable. Hence, the lenders in the market (and the borrowers) must use sound judgment to set expectations for future inflation to determine appropriate interest rate pricing.
How the Fisher Effect Impacts Fiscal Policy?
The Fisher Effect describes how the real interest rate and the expected rate of inflation move in tandem.
The practical application here is that if an economy’s actual inflation rate exceeds expectations, the beneficiary is the borrowers at the expense of the lenders.
Thus, unexpected inflation benefits debtors, while reducing the real returns received by creditors.
Given a high interest rate environment, borrowers pay lower real interest rates on their borrowings such as loans and pay them back using less valuable dollars, i.e. the dollar has lost value because of rising inflation.
On the other side, the lenders such as commercial banks earn lower yields in terms of real interest rates. The inflation caused their investments to erode in value, which reduces their real returns.
Fisher Equation Calculator
We’ll now move to a modeling exercise, which you can access by filling out the form below.
Fisher Equation Calculation Example
Suppose a consumer has taken out a loan with an 8.00% fixed interest rate from a commercial bank.
On the initial date of the borrowing, the expected inflation rate was 4.00%.
- Nominal Interest Rate (i) = 8.00%
- Inflation Rate, Expected (πe) = 4.00%
To calculate the estimated real return, we’ll enter our assumptions into the following formula in Excel.
- Real Interest Rate, Estimate = (1 + i) / (1 + πe) – 1
- Real Interest Rate, Estimate (re) = 3.85%
If we used the alternate formula, the expected inflation rate would be 4.00%, reflecting how the difference is relatively marginal.
Next, we’ll assume that the actual inflation data comes out to be 6.00%, meaning that the initial expectations were exceeded by 2.00%.
- Inflation Rate, Actual (πa) = 6.00%
Originally, the lender had expected to earn a real interest rate of around 3.85%. Yet, the higher-than-anticipated inflation rate caused the real interest rate to decline to 1.89%, instead.
- Real Interest Rate, Actual = (1 + i) / (1 + πa) – 1
- Real Interest Rate, Actual = 1.89%
- Actual vs. Estimate Differential = (1.96%)
