Hi everybody,
I am trying to compute the steady state of an E-DSGE which builds on Carattini et al. (2023). Here you find attacched the mod. file. I provide an initval, but the steady state is not computed as residuals of static equations are not always zero. In particular, I can’t get why residual of mg.utility with external habit is so high, even with a standard calibration of the CRRA parameter (ie. = 2).
Thank for the support
edsge_ss.mod (6.2 KB)
Check your model and your initial values and then focus on the big residuals. I fixed the Taylor rule to have exp(epsa_r) as otherwise the RHS would always be 0 in steady state. Also note that your model contains the price level. In New Keynesian models it usually has a unit root. Thus, there may be infinitely many steady states, which can cause root finders to fail.
Thank. My concern is the fact that the equation delivering the highest residual is mg. utility including external habi which is indeed right (ie \lambda_{t}=\left(C_{t}-h\bar{C}_{t-1}\right)^{-\sigma_{c}}). As for the price level, how can I detect the presence of a unit root if I do not have a closed form expression for P_{t} but just the non-linear FOC of the monopolistic retailer who faces quadratic adjustment costs?
R_ss was also wrong. Start from
edsge_ss.mod (6.2 KB)
Regarding the price level: typically, the model is only formulated in terms of inflation rates and relative prices. There is no way to pin down the price level endogenously from the model.