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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 $\bar{n}\bar{Y}$

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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 ($m > 0, n < 0$)

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