In the classical monetary model described by Gali (2008), in chapter 1, on page 28 it is written that:

$$ \pi_t=-\frac{\sigma \psi_{y a}\left(1-\rho_a\right)}{\phi_\pi-\rho_a} a_t $$

The author states that it is possible to obtain this equation by substituting

$$ \widehat{r}_t=-\sigma \psi_{y a}\left(1-\rho_a\right) a_t $$


$$ \pi_t=\sum_{k=0}^{\infty} \phi_\pi^{-(k+1)} E_t\left\{\widehat{r}_{t+k}\right\} $$

Could someone explain to me how I can do this?



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