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 into 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 funds rate is the bank the interest rate banks gives 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 their 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 uh 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 it's gonna have to be given and it's generally set as 2% is the target that the The Fed has for this number. So equilibrium real federal funds rate and notice this. This might look complicated, but they're gonna have to give you all of this information in the problem. There's really not so much math that goes on. So the some of the for 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% inflation and 2% in equal in the 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 uh 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 G. D. P. So we've got the inflation gap and then the output gap which is the difference it equals the current G. D. P minus the potential GDP the potential GDP of the economy. Right, what is the total GDP that they could have uh necessarily. So let's go ahead and pause here and let's apply these rules of the target federal funds rate and the taylor rule in a couple examples.
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example
Taylor Rule
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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 is the in the economy is 4% and the equilibrium real federal funds rate is 2%. Target inflation is 2% Real GDP is currently above potential GDP by 1%. A lot of numbers there. But it's just can you apply this formula? So the target federal funds rate oops federal funds, the target federal funds is equal to the current inflation plus equilibrium real federal funds which they also gave it to us. Right? They give us all of these numbers plus half of the inflation gap. I'll put I. G. Plus half uh half times the output gap. O. G. As well. Okay, so they've given us information about all these numbers. We just have to figure out what they are And put them in the correct place. So 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've given us these numbers already Now we gotta think about the inflation gap and the output gap. So remember that the inflation gap is equal to current inflation minus the target inflation, Which we have information about both of those right? They told us current inflation is 4% minus target inflation right here is given to us target inflation rate of 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 half times 2% for our inflation gap. And finally, we need our output gap. And they told us this straight up, they told us 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 it told us that the current Is currently above by 1%. So the output gap is equal to that 1% that were above the potential. Okay, so, they didn't tell us both numbers in that case. They just told us what is the difference? The 1%. So this would be half times the output gap of 1%. And we just have to wrap this up here. So, the target federal funds rate is gonna equal, I'll do it over here. 4% plus 2% is 6% half of 2%. It's another 1.5 of this. So four plus two plus one plus half comes out to 7.5% as the target federal funds rate in this example. Okay, so what's happening here is we've got high inflation, we've got um, we're hot in our economy where we're producing past our potential GDP. So they want to set a high inflation rate. Excuse me. A high interest rate to basically de incentivize investment and de incentivize aggregate demand and bring that spending down a little bit uh to a more reasonable sustainable level. Okay, so 7.5% would be the approximate, uh, for the target federal funds rate. All right, let's go ahead and try another.
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Problem
Problem
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%.
