I am a bachelor student (with limited experience of DSGE models) trying to replicate Galí 2013 Monetary Policy and Rational Asset Price Bubbles. I did some research on how this class of models are solved but a course on dynamic programming would be necessary to gain a thorough understanding. Thus, I am not sure if the equations I implemented fully determine the evolution of the variables. Overall, I seek to analyze how various monetary policy rules alter the evolution of variables and affect the convergence to the steady state.
So far, I have implemented the euler function (5), the determination of the market value of bubble assets (6), the optimal price setting rule (8), the aggregate goods condition (10) and the monetary policy (9). However, I am confused about the role of the optimal price P*_t as i do not see any relevance for the price index P_t. What am I missing? There is an error that says that p (price index) cannot take any arguments.
1 = beta*(1+i)c1/c2(+1)p/p(+1) // (5)
qb = (1-delta)betac1/c2(+1)qb(+1); // (6)
betac1(-1)/c2y(mp/p-psilonw)=0; // (8)
y = c1 + c2; // (10)
1 + i = R*(pi(+1)/pit)^phii*(qb/qbt)^phib; // (9)
Also, I am also wondering if I should work with the log-versions or not. If i do not re-write the variables to growth variables, e.g. v-v(-1), there will appear numerous logs of parameters. Galí does that only for the derivation of the stochastic equilibria (for which a closed form solution exist since it is an OLG model).
I hope you can give me some directions how to approach my target. I am also happy to get reading tips which will help me understand the system.
Sorry for these starters questions - as I said I am new to this.