Behavioral Equations NK3E

Step Equations

1. Central Bank Slope

Compute the monetary policy reaction slope a3 from structural parameters.

\begin{align} a_3 = \frac{1}{a_1\left(\frac{1}{a_2 b} + a_2\right)} \end{align}

2. Is Curve Output

IS curve: output as a function of demand shifter and lagged real rate.

\begin{align} y_t = A - a_1 r_{t-1} \end{align}

3. Monetary Policy Rate

Monetary policy rule: real rate reacts to inflation deviations.

\begin{align} r_t = r_s + a_3 (\pi_t - \pi^T) \end{align}

4. Phillips Curve Inflation

Phillips curve: inflation responds to the output gap.

\begin{align} \pi_t = \pi_{t-1} + a_2 (y_t - y_e) \end{align}

5. Stabilizing Real Rate

Compute the stabilizing real rate r_s consistent with output at potential.

\begin{align} r_s = \frac{A - y_e}{a_1} \end{align}