I am working on some consumption based asset pricing models. I am modelling consumption growth in several different ways. An obvious one is to model consumption growth as an AR(1) process:
$g_{t+1} = \phi_0 + \phi_1 g_t +\epsilon_{t+1 }$
Where $g_{t+1}$ is consumption growth. What are the implications of having $\phi_1=0$? What about $\phi_1=1$?
In which case is consumption growth iid?