# Deriving Sufficient Conditions For Existence of Unique Non-Explosive Equilibrium In DSGE Model With Hybrid New Keynesian Phillips Curve

Consider the following New Keynesian DSGE Model with standard notation:

$$\pi_t = \kappa y_t + \gamma_f \mathbb{E}_t[\pi_{t+1}] + \gamma_b \pi_{t-1},$$

$$y_t = \mathbb{E}_t[y_{t+1}] - \frac{1}{\sigma}(i_t - \mathbb{E}_t[\pi_{t+1}] - r_t^n),$$

$$i_t = \rho + \phi_{\pi}\pi_t + \phi_y y_t + v_t.$$

How would one go about deriving sufficient conditions for the existence of a unique non-explosive equilibrium under rational expectations? I'm familiar with a method for doing this when $$\gamma_b=0$$ (such that the Phillips curve is non-hybrid), but I have been unable to find any litterature on the case of a hybrid Phiilips curve.

Any input is appreciated very much, thanks!