Heterogeneity in New Keynesian Model

Macro

Model

The main equations for the heterogeneous one is super similar to the normal New Keynesian Model. But we add a Wage Phillips Curve.

The four equations:

1. New Keynesian Phillips Curve

${\pi }_t={\kappa }_p{\tilde{y}}_t+\Lambda {\tilde{\omega }}_t+\beta {\mathbb{E}}_t({\pi }_{t+1})$

2. Dynamic IS Equation

${\tilde{y}}_t={\mathbb{E}}_t\left({\tilde{y}}_{t+1}\right)-\frac{1}{\sigma }\left(i_t-{\mathbb{E}}_t\left({\pi }_{t+1}\right)-r_t^n\right)$ 3. Wage Phillips Curve

${\pi }_t^w=\beta {\mathbb{E}}_t\left({\pi }_{t+1}^w\right)-{\kappa }_w\phi {\hat{u}}_t^w$

4. Monetary Policy Rule

$i_t=\rho +{\varphi }_{\pi }{\pi }_t+{\varphi }_y{\tilde{y}}_t+v_t$