<p>You are making a mistake because what you have in your question is not <strong>the</strong> Taylor rule. It is <strong>a</strong> Taylor rule, to be more specific the version you present is some very simplified version of Taylor rule.</p>
<p>More complete version of  Taylor rule that you will find in PhD level textbooks is given by;
<span class="math-container">$${\displaystyle i_{t}=\pi _{t}+r_{t}^{*}+a_{\pi }(\pi _{t}-\pi _{t}^{*})+a_{y}(y_{t}-{\bar {y}}_{t}).}
$$</span></p>
<p>In this equation, <span class="math-container">$i$</span> is nominal interest, <span class="math-container">$\pi$</span> inflation, <span class="math-container">$r^*$</span> natural rate of interest, <span class="math-container">$\pi^*$</span> inflation expectation, <span class="math-container">$y$</span> output and <span class="math-container">$\bar{y}$</span> natural rate of output.</p>
<p>As you can see, the Taylor rule does not say that when there is no output gap interest rate is constant. It actually allows for the natural rate of interest to change over time. In your case you are just using a simplified version of Taylor rule, which is simplified for undergraduate students.  So the cheeky answer to your question is that the reason why the answers are different is that typical economics undergraduate does not have solid math skills.</p>
<p>Also, there are multiple possible specifications of Taylor rule, so researchers often talk about <a href="https://link.springer.com/referenceworkentry/10.1057/978-1-349-95121-5_2411-1" rel="nofollow noreferrer">Taylor rule<strong>s</strong></a>, but the advanced versions do allow for natural rate to vary as in the example I gave.</p>

CC BY-SA 4.0
2024-10-31T12:05:01.810Z
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
User2956
CC BY-SA 4.0
2024-11-05T22:04:35.233Z
@User2956 $i_t=r_t^*$ would mean that the inflation is zero, and there is no output gap. Yes, that is why they raise the interest rate, but central bank does not control $r$ directly. It brings $r=r^*$ by closing output and inflation gap
Lorenzo Pozzi
CC BY-SA 4.0
2024-11-06T06:41:07.570Z
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 =∗ by closing output and inflation gap" wouldn't it be the other way around? Through setting $i$ they close the output gap
User2956
CC BY-SA 4.0
2024-10-31T09:11:30.103Z
2024-10-31T09:18:38.320Z
2024-10-31T09:18:38.320Z
Lorenzo Pozzi
<p>No the natural rate of interest is not constant, it is determined by the amount of consumer savings vs the demand to borrow money.</p>

CC BY-SA 4.0
2024-11-07T07:11:24.253Z
2024-11-07T07:11:24.253Z
Zak Young
<p>Former Fed chair Ben Bernanke explains in his textbook, that the reason the Fed adjusts its target interest rate is because there are IS shocks that change the equilibrium interest rate or the interest rate that corresponds to potential output</p>
<p><a href="https://i.sstatic.net/9QZHTUNK.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/9QZHTUNK.png" alt="enter image description here" /></a></p>
<p>However, according to Taylor's rule:</p>
<p><a href="https://i.sstatic.net/FygNIHLVm.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FygNIHLVm.png" alt="enter image description here" /></a></p>
<p>At potential output, the interest rate is a sum of constants. In other words, there is a fixed interest rate at which output is equal to the potential output</p>
<p>1- Why are the two analysis suggesting different answers?</p>
<p>2- What are we attempting to do through gradually raising interest rates in response to inflation if not reach the new IS-FE intersection?</p>

CC BY-SA 4.0
2024-10-29T16:16:51.837Z
If the aim of the Fed is steady low inflation and full employment, then when there is an output gap it may be able to have lower real interest rates than when there is not without accelerating inflation.  If there is an upward IS shock then the Fed may need to raise real interest rates either now or after higher inflation occurs, and at least some now might be better than waiting.  The Taylor rule is a rule of thumb:  for example it is not obvious why $\pi$ should be the recent inflation rate rather than the prospective inflation rate.
Henry
<macroeconomics>
Is the neutral interest rate a constant?
User2956
# Is the neutral interest rate a constant?

(Asked by: username_0 on 2024-10-29)

Former Fed chair Ben Bernanke explains in his textbook, that the reason the Fed adjusts its target interest rate is because there are IS shocks that change the equilibrium interest rate or the interest rate that corresponds to potential output

[![enter image description here](https://i.sstatic.net/9QZHTUNK.png)](https://i.sstatic.net/9QZHTUNK.png)

However, according to Taylor's rule:

[![enter image description here](https://i.sstatic.net/FygNIHLVm.png)](https://i.sstatic.net/FygNIHLVm.png)

At potential output, the interest rate is a sum of constants. In other words, there is a fixed interest rate at which output is equal to the potential output

1- Why are the two analysis suggesting different answers?

2- What are we attempting to do through gradually raising interest rates in response to inflation if not reach the new IS-FE intersection?

**Tags:** macroeconomics
> **Comments:**
> **username_1**: If the aim of the Fed is steady low inflation and full employment, then when there is an output gap it may be able to have lower real interest rates than when there is not without accelerating inflation.  If there is an upward IS shock then the Fed may need to raise real interest rates either now or after higher inflation occurs, and at least some now might be better than waiting.  The Taylor rule is a rule of thumb:  for example it is not obvious why $\pi$ should be the recent inflation rate rather than the prospective inflation rate.  

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## 2 answers

### Answer by username_2 on 2024-10-31. Score: 1

You are making a mistake because what you have in your question is not **the** Taylor rule. It is **a** Taylor rule, to be more specific the version you present is some very simplified version of Taylor rule.

More complete version of Taylor rule that you will find in PhD level textbooks is given by;
$${\displaystyle i\_{t}=\pi \_{t}+r\_{t}^{\*}+a\_{\pi }(\pi \_{t}-\pi \_{t}^{\*})+a\_{y}(y\_{t}-{\bar {y}}\_{t}).}
$$

In this equation, $i$ is nominal interest, $\pi$ inflation, $r^\*$ natural rate of interest, $\pi^\*$ inflation expectation, $y$ output and $\bar{y}$ natural rate of output.

As you can see, the Taylor rule does not say that when there is no output gap interest rate is constant. It actually allows for the natural rate of interest to change over time. In your case you are just using a simplified version of Taylor rule, which is simplified for undergraduate students. So the cheeky answer to your question is that the reason why the answers are different is that typical economics undergraduate does not have solid math skills.

Also, there are multiple possible specifications of Taylor rule, so researchers often talk about [Taylor rule**s**](https://link.springer.com/referenceworkentry/10.1057/978-1-349-95121-5_2411-1), but the advanced versions do allow for natural rate to vary as in the example I gave.

> **Comments:**
> **username_0**: 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  
> **username_2**: @User2956 $i_t=r_t^*$ would mean that the inflation is zero, and there is no output gap. Yes, that is why they raise the interest rate, but central bank does not control $r$ directly. It brings $r=r^*$ by closing output and inflation gap  
> **username_0**: 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 =∗ by closing output and inflation gap" wouldn't it be the other way around? Through setting $i$ they close the output gap  

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### Answer by username_3 on 2024-11-07. Score: 0

No the natural rate of interest is not constant, it is determined by the amount of consumer savings vs the demand to borrow money.


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