Is it possible for the Taylor Rule to suggest a target federal...

Question

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%.

Accepted Answer

Alright. Let's see what you did here. 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%. Of 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. So if current inflation is 0%, current inflation is 0%, equilibrium federal fund rate is 2%, and our inflation gap. What's gonna be our inflation gap in this case? Inflation gap is equal to current minus target, right? Target inflation. So our current inflation is 0% and our target inflation is 2%. We're going to get an inflation gap of 2 negative 2%. Right? 0 minus 2 is negative 2%. So we're going to have half times negative 2% for our inflation gap. And our output gap, they didn't really tell us anything about this, but we can make up some numbers here in a second. Let's go ahead and fill out what we know so far. So our target federal funds and let's add up the numbers we have. We've got 0 +2 is 2 and half of negative 2. So this is gonna equal negative 1 in this case, right? Or excuse me, 2 minus 1 gets us to 1% plus half of the output gap. Half times output gap. Right? This is 2. This right here in this was a negative one. So 0 plus 2 minuteus 1 gives us 1% plus half of the output gap. So how do we get this to be negative? Remember, the question is asking us, can the Taylor rule suggest a funds rate to be negative? So the idea is how what what could we have as our output gap that could suggest a negative number? So let's say we had our target federal funds rate, let's assume would be negative 1%. Right? We're looking for a negative number for our target federal funds rate. What would the output gap have to be in this case? So we could do a little algebra, subtract 1% from both sides and we'll get negative 2% equals half of the output gap. Multiply both sides by 2, multiply by 2, multiply by 2, and this gets us negative 4% equals the output gap. So if the output gap is negative, it is potent there is potential for this to happen. Right? Notice we've got a negative inflation gap and a negative output gap can lead to a situation where we would have a negative tech target federal funds rate. So what this is telling us is that the target federal funds rate would be negative 1% if our current inflation is 0%, our equilibrium federal fund rate is 2%. Our output gap is negative 1%. And our or excuse me, our inflation gap is negative 1% and our output gap, half of it is negative 2%. Right? So that gets us to our target Federal Funds Rate of negative 1%. I'll just label those. Target equals current inflation plus equilibrium federal funds, half inflation gap and half output gap. Alright. So it is possible for the Taylor rule to come up with a negative number in a very certain situation like this where we've got our inflation is below the target and our potential GDP is below as well. Okay? So let's go ahead and pause here. Now that we've seen how the Taylor rule works, let's go ahead and move to another.

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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%.

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