thank you for the clarifications. very helpful. Just to be totally clear what if the auxiliary variables were (C is consumption at time t)
Z1=C(+1)^-(rho); in dynare Z1= E_t { (C_(t+1)^-(rho))}
Z2=Z1*Z1(+1);
in dynare still the same logic holds?
1-) Z2= E_t { (C_(t+1)^-(rho))(C_(t+2)^-(rho)) }
2-) Z2(+1)= E_t { (C_(t+2)^-(rho))(C_(t+3)^-(rho)) }
or in my previous example Z1=C^-(rho); the E_t { } cancels ( as explained in Dynare timing and redefinition) hence
Z1=C(+1)^-(rho);
Z1(+1)=C(+2)^-(rho),
Z1(+2)=C(+3)^-(rho)… holds in every period without expectations so i can put Z1(+1) inside exceptions of another long complicated equation with endogenous variables without worrying about Jensen and concavity.
Regards