Taylor Rule - Online Tutor, Practice Problems & Exam Prep

The Taylor rule is a formula that connects the Federal Funds Rate to economic variables like current inflation and the equilibrium real federal funds rate, typically set at 2%. The target Federal Funds Rate is calculated as the sum of the current inflation rate and the equilibrium rate, adjusted for the inflation gap (current inflation minus target) and the output gap (current GDP minus potential GDP). This rule serves as a guideline for monetary policy, although the Federal Reserve does not strictly use it in practice.

Taylor Rule

Now let's discuss a calculation used when studying monetary policy. It's called the Taylor rule. So the Taylor rule, I want to make a note real quick. This is something you generally deal with more in higher-level economic classes, but sometimes they like to mention it here and a lot of times it's just knowing what it is. You might not even have to do these calculations, so I would suggest double-checking with your professor. But let's go through it just in case you need to know it. The Taylor rule links the Federal target the Fed's target for the Federal Funds Rate to several economic variables. Okay? So we're thinking about what is the Federal Funds Rate that the Fed wants to set and this goes back to that money market, right? What is that equilibrium interest rate that the Fed wants? So remember that the federal fund rate is the interest rate banks give to other banks on overnight loans. So this is generally when they need to meet reserve requirements. They need a certain amount of reserves for their level of deposits and they get a short-term loan just to meet these requirements. And those loans are given at this interest rate, the federal funds rate. So the Fed is regularly making decisions to get to the correct, in quotations, Federal Funds Rate, right? They want to set the Federal Funds Rate where they think is best for the economy. Now, I want to make a note about the Taylor rule is that the Fed does not use the Taylor rule. This is an approximation that this smart dude, John Taylor made. He made this mathematical approximation of how the Fed sets their target funds rate the target federal funds rate. Okay? So let's get into the calculation now. So the target Federal Funds Rate is going to be composed of these variables here. First, it's the current inflation rate. What is the inflation rate currently in the economy? Plus the equilibrium real federal funds rate. So this is also going to be basically the equilibrium real federal funds rate is adjusted for inflation. So the current inflation rate is equal to actual inflation and here we've got equilibrium real. And this is generally given to you in the problems. It's going to have to be given and it's generally set as 2% is the target that the Fed has for this number. So equilibrium real federal funds rate and notice, this might look complicated but they're going to have to give you all of this information in the problem. There's really not so much math that goes on. So the sum of the first two terms is where the federal funds rate would be at long-run equilibrium. That's where they want it to be, and it's generally 4%. They generally target for 2% in inflation and 2% in equilibrium there as well. Now, the last two terms make it look a little complicated, but it's not that bad. The inflation gap, it's the difference between the current inflation and the target and the Fed usually sets the target at 2%. The target is generally 2% for inflation. So the inflation gap equals current inflation minus target. So you can get a negative number here. You can get a negative current minus target for the inflation gap and you can also get a negative number for the output gap as well. So the output gap deals with GDP. So we've got the inflation gap and then the output gap which is the difference. It equals the current GDP minus the potential GDP. The potential GDP of the economy, right? What is the total GDP that they could have?

Taylor Rule

Alright. Let's try this example for the Taylor rule. Use the Taylor rule to estimate the target federal funds rate. The current inflation rate in the economy is 4% and the equilibrium real federal funds rate is 2%. The target inflation is 2%. Real GDP is currently above potential GDP by 1%. There are a lot of numbers there, but it's just asking if you can apply this formula. So, the target federal funds rate is calculated as follows: the target federal funds rate is equal to the current inflation plus the equilibrium real federal funds rate, which they have also given to us. They have given us all these numbers, plus half of the inflation gap. I'll put IG plus half of the output gap, OG, as well. Okay? So they have given us information about all these numbers. We just have to figure out what they are and put them in the correct place. They told us the current inflation rate is 4%, right? 4% for the current inflation rate plus the equilibrium real federal funds rate is 2%. So, they have given us these numbers already. Now, we need to think about the inflation gap and the output gap. So, remember, the inflation gap is equal to the current inflation minus the target inflation, which we have information about both. They told us the current inflation is 4%, and the target inflation right here is given to us as 2%. So our inflation gap is equal to 2% right there. 2% is going to be our inflation gap. So over here, we'll have 0.5 times 2% for our inflation gap. And finally, we need our output gap and they told us straightforwardly. They told us that the output, real GDP, is currently above potential GDP by 1%. So if real GDP is above potential GDP, our output gap, remember, our output gap is current minus potential. So, right now, they told us that the current is above potential by 1%. So the output gap is equal to that 1% that we are above potential. They didn't tell us both numbers in that case; they just told us what the difference is, the 1%. So, this would be 0.5 times the output gap of 1%, and we just have to wrap this up here. So the target federal funds rate is going to equal, I'll do it over here, 4% plus 2% plus 0.5 times 2% plus 0.5 times 1%, this comes out to 7.5% as the target federal funds rate in this example.

So, what's happening here is we've got high inflation and our economy is hot, we're producing past our potential GDP, so they want to set a high interest rate to de-incentivize investment and de-incentivize aggregate demand and bring that spending down to a more reasonable level. 7.5% would be the rate approximate for the target federal funds rate.

Is it possible for the Taylor Rule to suggest a target federal funds rate to be negative? Assume the current inflation rate is 0%, the equilibrium real federal funds rate is 2%, and the target inflation rate is 2%.

Is it possible for the Taylor rule to suggest a target Federal funds rate to be negative? Assume the current inflation rate is 0%, the equilibrium real federal funds rate is 2%, and target inflation is 2%. Alright. So let's think about target federal funds. Let's think about our Taylor rule. We've got our current inflation plus equilibrium federal funds rate plus half of the output gap, excuse me, half of the inflation gap plus half of the output gap. Okay? So let's think about all these numbers, what they've given us, and what could potentially make this work for us. If the current inflation is 0%, and the equilibrium federal fund rate is 2%, what will our inflation gap be? The inflation gap is the difference between the current and target inflation: the current inflation is 0%, and our target inflation is 2%. Therefore, the inflation gap is -2%, calculated as 0%-2%. This gives us a contribution of -22 or -1% to the target federal funds rate calculation. Combining that with the equilibrium federal fund rate, we get 2%-1% or 1% plus half of the output gap. To determine how the output gap affects the rate, and to find if it could lead to a negative rate, assume the target federal funds rate needs to be -1%. Using algebra, setting 1%+halfoutputgap=-1% and solving for the output gap gives -2%=halfoutputgap. Multiplying both sides by 2 gives -4% for the output gap. Thus, if the output gap is -4%, the target federal funds rate would be -1%. Therefore, it is indeed possible for the Taylor rule to suggest a negative federal funds rate under specific conditions such as when both inflation and output gaps are negative enough.

Here’s what students ask on this topic:

What is the Taylor Rule in economics?

The Taylor Rule is a formula that links the Federal Funds Rate to key economic variables such as the current inflation rate and the equilibrium real federal funds rate. It is used as a guideline for setting monetary policy. The formula is:

$\mathrm{Target} \mathrm{Federal} \mathrm{Funds} \mathrm{Rate}= \mathrm{Current} \mathrm{Inflation} + \mathrm{Equilibrium} \mathrm{Real} \mathrm{Federal} \mathrm{Funds} \mathrm{Rate} + 0.5 \times \mathrm{Inflation} \mathrm{Gap} + 0.5 \times \mathrm{Output} \mathrm{Gap}$

Although the Federal Reserve does not strictly use the Taylor Rule, it provides a useful approximation for understanding how the Fed might set its target rate based on economic conditions.

How is the Taylor Rule calculated?

The Taylor Rule is calculated using the following formula:

$\mathrm{Target} \mathrm{Federal} \mathrm{Funds} \mathrm{Rate}= \mathrm{Current} \mathrm{Inflation} + \mathrm{Equilibrium} \mathrm{Real} \mathrm{Federal} \mathrm{Funds} \mathrm{Rate} + 0.5 \times \mathrm{Inflation} \mathrm{Gap} + 0.5 \times \mathrm{Output} \mathrm{Gap}$

Where:

• Current Inflation is the current inflation rate in the economy.
• Equilibrium Real Federal Funds Rate is typically set at 2%.
• Inflation Gap is the difference between current inflation and the target inflation rate (usually 2%).
• Output Gap is the difference between current GDP and potential GDP.

This formula helps approximate the Federal Funds Rate that would be appropriate given current economic conditions.

What are the components of the Taylor Rule?

The Taylor Rule consists of several key components:

• Current Inflation Rate: The current rate of inflation in the economy.
• Equilibrium Real Federal Funds Rate: Typically set at 2%, this is the rate adjusted for inflation.
• Inflation Gap: The difference between the current inflation rate and the target inflation rate (usually 2%).
• Output Gap: The difference between the current GDP and the potential GDP of the economy.

These components are combined in the Taylor Rule formula to estimate the target Federal Funds Rate:

$\mathrm{Target} \mathrm{Federal} \mathrm{Funds} \mathrm{Rate}= \mathrm{Current} \mathrm{Inflation} + \mathrm{Equilibrium} \mathrm{Real} \mathrm{Federal} \mathrm{Funds} \mathrm{Rate} + 0.5 \times \mathrm{Inflation} \mathrm{Gap} + 0.5 \times \mathrm{Output} \mathrm{Gap}$

Why does the Federal Reserve not strictly use the Taylor Rule?

The Federal Reserve does not strictly use the Taylor Rule because it is a simplified approximation and does not account for all the complexities of the economy. While the Taylor Rule provides a useful guideline, the Fed considers a broader range of factors, including financial market conditions, global economic developments, and other economic indicators. Additionally, the Fed's decision-making process involves judgment and discretion, which cannot be fully captured by a single formula. Therefore, while the Taylor Rule is a valuable tool for understanding monetary policy, it is not the sole determinant of the Federal Funds Rate.

What is the significance of the equilibrium real federal funds rate in the Taylor Rule?

The equilibrium real federal funds rate is a crucial component of the Taylor Rule. It represents the interest rate adjusted for inflation that is consistent with full employment and stable inflation in the long run. Typically set at 2%, this rate serves as a benchmark for the Federal Reserve's target rate. By incorporating the equilibrium real federal funds rate, the Taylor Rule helps ensure that the target Federal Funds Rate aligns with the economy's long-term potential, promoting sustainable economic growth and price stability.