Oh okay, so they're essentially over/undershooting what they think is $r_n+\pi$ to move the economy there faster, and as it begins moving in that direction they bring the interest rates towards $r_n+\pi$. The advanced book you're referring to here is the Woodford one or Mankiw?

But Blanchard's description of this is essentially that the central bank, through setting $i=r_n+\pi$ sets the real interest rate to $r_n$, which closes the output and inflation gap. You said "only if there is no inflation gap and no output gap. Otherwise no"

Could you please recommend an article or book at the introductory level that covers this topic well. This way I can have another look at the topic. I feel like I'm missing something here

But we know that expected inflation $\pi$ = 2% and that expectations are well-anchored in developed countries. So isn't it right to then set $i = r_n+2$ to set the real interest rate to $r_n$

My bad, I meant setting the real rate of interest $r=r^*$ or equivalently, $i_t = r^* + \pi_e$. Since $\pi_e$ is known to be 2%, why can't they close the output gap through setting $i_t = r^* + 2%$. You mention they "bring 𝑟=𝑟∗ by closing output and inflation gap" wouldn't it be the other way around? Through setting $i$ they close the output gap

But when there is an output gap and inflation gap, shouldn't the central bank set $i = r_n+\pi$. The section I linked in Blanchard suggests that output and inflation gaps are the result of the real interest rate not being equal to $r_n$, which is what the central bank is attempting to do through gradually raising interest rates

Okay, so the first point is clarified. But the second point that Blanchard is making is there's an output gap and inflation above target when the real interest rate $r$ isn't $r_n$ and what the central bank is attempting to return the $r$ to $r_n$. This is what seems inconsistent with Taylor's rule. Instead of setting $r = r_n$ it recommends setting it to $r_n$ + $a$ inflation gap + $b$ output gap

Ah, I think I understood why there's confusion. I was talking about setting the real rate of interest equal to $r_n$, which is the terms in which Blanchard is describing things. Clearly, this would mean a nominal interest rate $i = r_n + \pi$. Also, for the second point, Blanchard seems to be implying that the reason there's an output gap and inflation above target is that the real interest rate is not $r_n$ and the whole section I linked talks about the central bank adjusting $r$ to bring it to $r_n$ to close the output gap and bring the economy to its medium run equilibrium

Sure, Blanchard p. 181 Macroeconomics 8e. I have taken screenshots of the entire relevant section and numbered the images in order so you can easily have a look imgur.com/a/4zKyO3H

Also, as far as point 1 is concerned, you're saying inflation equals expected inflation at $i=r+\pi_e$. According to Blanchard, at $i=r_n$ inflation equals expected inflation and there's a zero output gap

Okay. So my previous understanding, which is what is presented in my textbook (Blanchard) is when there's a positive output gap at a given interest rate, it means we're not at $r_n$. Since the central bank does not precisely know $r_n$ it may slowly increase interest rates until it finds $r_n$, at which point the output gap will close. This seems to be incorrect, and suggests that output gaps are the result of $r_n$ changing, or in other words IS shifts. Could you recommend me an article or textbook at the beginner level that explains what we're doing with monetary policy.

1. When the output gap is zero and interest rate = $r_n$, isn't inflation equal to expected inflation, which would be $pi_e = 2%$ rather than zero? This is what is written in Blanchard's macroeconomics. 2. Isn't $r_n$ by definition the interest rate that brings the output gap to 0 and brings inflation = expected inflation. So if there is a positive output gap and inflation exceeding expected inflation, that would imply the prevailing interest rate isn't $r_n$

I guess what I'm confused about is, since we want to bring output to potential output, and this corresponds to $r_n$, why doesn't the central bank set the interest rate to what it thinks is $r_n$ rather than $r_n$ + $a$ inflation gap + $b$ output gap

Well, when inflation and output are above target, isn't the hike in interest rates to find the new natural rate of interest. Why isn't $i_t = r_t^*$. The reasoning presented by Mr. Bernanke seems to suggest that the reason you hike interest rates in response to inflation is to find the new $r_t^*$ which is what the Taylor rule is helping you do

What I don't understand though is, suppose inflation and output is above target and I start increasing interest rates, hoping to find the interest rate at which the economy is at potential output. As the fed approaches this rate and the gap is closing, it seems like interest rates suddenly take a nose-dive and drop. I can understand stopping the hikes or even some downward correction, but why don't they stay in some vicinity of the rate that is giving them an output close to potential output