Writting expectations regarding inflation and output gap

[huleaadriana]

Hello!

I intend to estimate a non-linear DSGE model for the Romanian economy using the Simulated Method of Moments. The model I have choosen is the one presented in "Animal Spirits and monetary policy" by Paul de Grauwe and used by Jang and Sacht (2012) in their article Identification of Animal Spirits in a Bounded Rationality model. In this article the authors consider that people are not rational. Instead they have bounded rationality. The authors try to emphasis the effect of people's heterogeneous beliefs about the output gap and inflation. Regrading output gap, some people believe that it will be positive and equal to g(t) and are presented like optimists(opt) and the others believe that it will be negative and equal to -g(t) and are presented like pessimists(pes) . In what concerns the inflation gap, some people believe that the target will be reached and the inflation gap will equal 0 and they are considered targeters(tar), while the others consider that inflation(t+1)=inflation(t-1) and are considered extrapolators(ext).

In order to estimate the model I need to write it in Dynare. I would really appreciate your opinion regarding the way i can write in Dynare the equations that exist in the attached file, especially those that are related to the expectations formation process regarding the output gap y and the inflation gap represented by the greek letter phi. Where and how can I write in Dynare the fact that the exogeneous shocks are normally distributed with mean 0 and variance sigma_epsilon?

Thank you very much in advance!