Rt is not a forward looking variable but it is affected by contemporaneous values of pi and y. The usual method to deal with such “static” variables that I’ve encountered is to just solve for them in terms of states and jump variables. However this does not seem possible because Rt is not just a linear combination of jump and state variables, but also contains lagged values of itself. It also doesn’t seem to be merely a state variable since it is affected by the jump variables.

I’ve been using this method described by Eric Sims which seemed close to the method that we discussed in our meeting on friday. I’ve gotten as far as finding the policy function for yt and pit in terms of the interest rate, zt, and gt, but cannot solve for Rt since it is also affected by y and pi.

I’m at a loss as to how to proceed from this point, and any help would be appreciated greatly.

If I have a backward looking inflation \pi_{t-1} in my NKPC, will this be interpreted as state now as explained in this one? The “Cogley, T. and Sbordone, A. M. (2008). Trend inflation, indexation, and inflation persistence in the new keynesian phillips curve. American Economic Review, 98(5):2101–26” has a partial indexation of inflation which makes the NK an AR(2) process.

I have a model with habit formation (internal or external should not matter for this question). So c_{t-1} is state, c_{t} and c_{t+1} are control variables is it?

I also have partial indexation in my model. So \pi_{t-1} is a state and \pi_{t} and \pi_{t+1} is a control?

Again, everything dated t-1 is a state variable. That applied to any variable appearing with a lag due to propagation mechanisms like indexing or habits.