Asking for the derivation in Gali(2003)

Dear Admin
I am trying to practise Dynare with Gali(2003), The new Perspectives on Monetary Policy,Inflation ,and the Business Cycle.

However, after trying derivation of equation 27 page 16 Topic 4.1.2 The Presence (or Lack Thereof) of a Liquidity Effect. I am stuck. Do you have any guidance regarding this issue?
What I have done is…

  1. Difference m-p=y-eta*i
  2. Combine it with the stationary process of money supply growth.
  3. Combine 2.) with the output gap equation 20.
  4. Stuck
    So, do you have any guideline or any further recommendations on this? Please.
    All the best
    The Beginner!

Please try to outline the steps you are taking and where you get stuck in a PDF-file. That makes it easier to track. Did you impose the assumptions outlined at the beginning of 4.1 that make the natural parts drop out, because they are 0? You also need to plug in the definition of the output gap first. Once you have that in imposed that y_t=0 (and rr_t from (14) with a=g=0), you should be able to derive (27). The last trick is that (27) was solve forward. That is, after plugging in the things I mentioned before, you can solve for r_t as a function of other variables. That one is most probably going to involve r_t+1. You now need to plug in the derived equation for r_t shifted by one period for r_t+1. That introduces r_t+2 into the equation. Now plug in for r_t+2 as before for r_t+1. Repeat until you spot the pattern and get (27)

Thank you! I will outline my derivation and show it to you…I have a question regarding rr_t
If i follow the assumption that at gt =0, rr_t will be collapsed to rr_t=rho. So,Can I assume that rho =0? If yes, is there any intuition behind this?
Thank you very much

My guess is that Gali simply leaves the constant term out of equation (27). Because without growth, the RHS of (27) would be 0, but in steady state, r_t=rho.