<p>As you mentioned before, $\bar{n}$ is the sensitivity parameter of the interest rate to changes in short run output in a monetary policy rule. What is the relationship of $\bar{m}$ and $\bar{n}$ within the Taylor rule? It heavily depends on the given economic climate.</p>

<p>Assuming the basic <em>Canonical New Keynesian DSGE Model</em> the equations of our economy are the following:</p>

<p>IS (investment/saving) curve:
$$   y_t = E_t [y_{t+1}] - \theta r_t +u_t^{y} $$
AD (aggregate demand) curve:
$$ \pi_t = \beta E_t [\pi_{t+1}] +\kappa y_t + u_t^{\pi}$$
Taylor rule:
$$   r_t = m E_t [\pi_{t+1}] + n E_t [y_{t+1}] +  u_t^{r} $$</p>

<p>If you estimate the Taylor rule empirically with some kind of economic techniques, there should be considered 4 scenarios (shocks) .</p>

<ol>
<li><p>Demand shock ($m, n &gt; 0$)</p></li>
<li><p>Supply shock ($m &gt; 0, n &lt; 0$)</p></li>
<li><p>Monetary policy shock ($m, n &lt; 0$)</p></li>
<li><p>Technology shock ($m &gt; 0, n &lt; 0$)</p></li>
</ol>

CC BY-SA 3.0
2017-05-27T10:08:46.407Z
2017-05-27T10:08:46.407Z
Übel Yildmar
<blockquote>
  <p>I was asked what the relationship of $\bar m$ and $\bar n$ are with the taylor rule. </p>
</blockquote>

<p>Using $\bar m$'s definition which is the sensitivity of real interest rate to inflation in a market's monetary policy rule. I said $\bar n$ is the sensitivity of the interest rate to changes in short run output in a monetary policy rule.</p>

<p>To answer the question, i said the parameters  $\bar m$ and $\bar n$ indicate the sensitivity of the taylor rule towards changes inflation and short-run output.</p>

<p>The taylor rule being
$$R_t-\bar r  = \bar m (\pi_t -\bar \pi)+ \bar{n}\bar{Y}   \quad \bar m&gt;0, \, \bar n&gt;0$$</p>

<p>And the resulting new AD curve being
 $$Y^t_t = \bar a - \bar{b} \bar m (\pi_t -\bar \pi)-\bar{b} \bar{n}\bar{Y}$$ </p>

<p>$$ Y^t_t = \frac{\bar a}{(1+\bar{b}\bar{n})} - \frac{\bar{b}\bar m}{(1+\bar{b}\bar{n})} (\pi_t -\bar \pi) $$</p>

<p>As in the addition $\bar{n}\bar{Y}$ </p>

<macroeconomics>
What does n stand for in the taylor rule?
Ivan
# What does n stand for in the taylor rule?

(Asked by: username_0 on 2015-10-08)

> I was asked what the relationship of $\bar m$ and $\bar n$ are with the taylor rule.

Using $\bar m$'s definition which is the sensitivity of real interest rate to inflation in a market's monetary policy rule. I said $\bar n$ is the sensitivity of the interest rate to changes in short run output in a monetary policy rule.

To answer the question, i said the parameters $\bar m$ and $\bar n$ indicate the sensitivity of the taylor rule towards changes inflation and short-run output.

The taylor rule being
$$R\_t-\bar r = \bar m (\pi\_t -\bar \pi)+ \bar{n}\bar{Y} \quad \bar m>0, \, \bar n>0$$

And the resulting new AD curve being
$$Y^t\_t = \bar a - \bar{b} \bar m (\pi\_t -\bar \pi)-\bar{b} \bar{n}\bar{Y}$$

$$ Y^t\_t = \frac{\bar a}{(1+\bar{b}\bar{n})} - \frac{\bar{b}\bar m}{(1+\bar{b}\bar{n})} (\pi\_t -\bar \pi) $$

As in the addition $\bar{n}\bar{Y}$

**Tags:** macroeconomics

---

## 1 answers

### Answer by username_1 on 2017-05-27. Score: 1

As you mentioned before, $\bar{n}$ is the sensitivity parameter of the interest rate to changes in short run output in a monetary policy rule. What is the relationship of $\bar{m}$ and $\bar{n}$ within the Taylor rule? It heavily depends on the given economic climate.

Assuming the basic *Canonical New Keynesian DSGE Model* the equations of our economy are the following:

IS (investment/saving) curve:
$$ y\_t = E\_t [y\_{t+1}] - \theta r\_t +u\_t^{y} $$
AD (aggregate demand) curve:
$$ \pi\_t = \beta E\_t [\pi\_{t+1}] +\kappa y\_t + u\_t^{\pi}$$
Taylor rule:
$$ r\_t = m E\_t [\pi\_{t+1}] + n E\_t [y\_{t+1}] + u\_t^{r} $$

If you estimate the Taylor rule empirically with some kind of economic techniques, there should be considered 4 scenarios (shocks) .

1. Demand shock ($m, n > 0$)
2. Supply shock ($m > 0, n < 0$)
3. Monetary policy shock ($m, n < 0$)
4. Technology shock ($m > 0, n < 0$)


---

