Taylor Rule Formula | Calculator (Example with Excel Template)

Taylor Rule Formula (Table of Contents)

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What is the Taylor Rule Formula?

The term “Taylor Rule” refers to the monetary policy guideline that helps the central banks in estimating the target short-term interest rate when the expected inflation rate and GDP growth differs from the target inflation rate and long-term GDP growth rate. In other words, Taylor rule is a general rule of thumb that is used by the central banks in predicting how the short-term interest rates will be move as a response to the changes in the economy.

The method was named after John Taylor, professor of economics at Stanford University, who articulated the formula based on his empirical study on the Federal Reserve’s monetary policy between 1987 and 1992. The formula for the Taylor rule can be used to derive the newer short-term interest rate by adding up the existing short-term interest rates to the average of the deviation in GDP growth rate and inflation rate from the target. Mathematically, it is represented as,

Formula,

Target Rate = Neutral Rate + 0.5 * (GDP_e – GDP_t) + 0.5 * (I_e – I_t)

Where,

Target Rate: Short-term interest rate after the change
Neutral Rate: Short-term interest rate that currently prevails
GDP_e: Expected GDP Growth Rate
GDP_t: Long-Term GDP Growth Rate
I_e: Expected Inflation Rate
I_t: Target Inflation Rate

Example of Taylor Rule Formula (With Excel Template)

Let’s take an example to understand the calculation of the Taylor Rule Formula in a better manner.

You can download this Taylor Rule Formula Excel Template here – Taylor Rule Formula Excel Template

Taylor Rule Formula – Example #1

Let us take a simple example where the long-term GDP growth rate is 7.0% while the target inflation rate is 4.5%. The short-term interest rate in the economy is currently fixed at 8.0%. However, the inflation rate is expected to increase to 5.0% while the GDP growth is expected to be 7.5%. Calculate the new short-term interest rate based on the given information.

Solution:

Target Rate is calculated using the Taylor Rule formula given below

Target Rate = Neutral Rate + 0.5 * (GDP_e – GDP_t) + 0.5 * (I_e – I_t)

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Target Rate = 8.0% + 0.5 × (7.5% − 7.0%) + 0.5 × (5.0% − 4.5%)
Target Rate = 8.50%

Therefore, the new short-term interest rate in the economy should be increased to 8.50%.

Taylor Rule Formula – Example #2

Let us take the example of a central bank that is engaged in formulating the short-term interest rate while incorporating the changes in the economy. In July 2019, the economy was growing at its long-term GDP growth rate of 3.0% while the inflation rate was at its target of 1.5%. The current short-term interest rate targeted by the central bank is 4.0%. Today is 25 September 2019, and the central bank committee will be get together soon to decide whether or not to change the short-term interest rate. Determine whether the short-term interest rate will be changed if the expected GDP growth is 3.5% and the expected inflation rate is 2.5%.

Solution:

Target Rate is calculated using the Taylor Rule formula given below

Target Rate = Neutral Rate + 0.5 * (GDP_e – GDP_t) + 0.5 * (I_e – I_t)

Target Rate = 4.0% + 0.5 × (3.5% − 3.0%) + 0.5 × (2.5% − 1.5%)
Target Rate = 4.75%

Based on the given information, it seems that the central bank will revise the short-term interest rate upwards by 0.75% to a new target rate of 4.75%. The rate increase resulted due to expected increase in inflation rate and GDP growth in the near term.

Explanation

The Taylor Rule Formula can be computed by using the following steps:

Step 1: Firstly, determine the neutral rate which is the short-term interest rate that the central banks want to continue with if there is no deviation in inflation rate and GDP growth rate in the near term.

Step 2: Next, figure out the expected GDP growth rate and it is denoted by GDP_e.

Step 3: Next, determine the long-term GDP growth rate achieved in the given period and it is denoted by GDP_t.

Step 4: Next, calculate the deviation in the GDP growth rate, which is the difference between the expected GDP growth rate and the long-term growth rate, i.e., (GDP_e − GDP_t).

Step 5: Next, figure out the expected inflation rate and it is denoted by I_e.

Step 6: Next, determine the actual inflation rate during the given period and it is denoted by I_e.

Step 7: Next, calculate the deviation in the inflation rate, which is the difference between the expected inflation rate and the target inflation rate, i.e., (I_e − I_t).

Step 8: Finally, the formula for the Taylor rule is derived by adding up the neutral rate (step 1) to the average of the deviation in GDP growth rate (step 4) and inflation rate (step 7) as shown below.

Target Rate = Neutral Rate + 0.5 * (GDP_e – GDP_t) + 0.5 * (I_e – I_t)

Relevance and Use of Taylor Rule Formula

From the economic and banking point of view, it is important to understand the concept of how the Taylor rule is used to maneuver the short-term interest rate in order to stabilize the economy. For instance, the Taylor rule will suggest an expansionary monetary policy if the expected inflation rate is below the target or the production is expected to be lower than the potential. On the other hand, the Taylor rule will suggest a contractionary approach if the inflation rate is expected to increase or the national production is expected to increase.

The below graph shows how the Fed rate and interest rate based on Taylor’s rule have moved in tandem historically.

Source Link: FRED