How does one proceed to solve a rational expectations model by guessing. Could someone illustrate a very simple case, or guide me to a resource on this? I am guessing this is somewhat similar to the method of undetermined coefficients, but I have been unable to find something on this online so far.
For example, if I have an endogenous variable $y_t = a_0 + a_1E_{t-1}[y_t] + a_2E_{t-1}[y_{t+1}] + r_t$, where r is exogenous and mean zero, how would I proceed guessing the solution and finding parameters that solve this model.
I have tried to think about this and I think I need to guess a solution, iterate that and take expectations. I think that would eliminate exogenous variable x since its mean on average is zero and you are rational. But I need to somehow incorporate that guess into my original equation and compare coefficients. Could someone point me in the right direction, possibly a similar example, or some textbooks that introduce this method.
