Observation equation in THE IACOVIELLO-NERI MODEL

US_data_65Q106Q4.m (36.3 KB)Hi,
I am trying to replicate the IACOVIELLO-NERI MODEL attached here. However, I could not understand the observation equations starting from the line 360. Taking consumption for example, I understand when they stationarise the model, they detrended the model by taking out the deterministic trend from the variables with balanced growth path and leaving stationary component in the model. For example, C_tilde=C/(1+TRENDY)^t, where C is the original level consumption, C_tilde is the stationarised variables that used in the other model equations, and TRENDY is equal to the TRENDC. Therefore, when linking the data with variables in the observation equation and ignoring the steady states, should we have ln(DATA_C)=ln(C_tilde)+tln(1+TRENDY)=ln(C_tilde)+tTRENDY instead of ln(DATA_C)=ln(C_tilde)+TRENDY? My confusion is the terms of TRENDY, I think it should multiply it by the time t. The consumption data attached is the log form of raw consumption data.
I am not sure if I have made any mistake here. I would greatly appreciate it if anyone can help me to solve my confusion.

Best regards,
jules1.mod (18 KB)

At the time of this writing, there is a problem with backward compatibility on this model, because the observation_trends-command does not work as expected all the time (see github.com/DynareTeam/dynare/issues/679).

In general you are right that you should have t*TRENDY, but Dynare cannot handle trending model variables. The

block therefore instructs Dynare to detrend the data at the specified rate before matching it to the data. Due to Dynare’s handling of this detrending in version 4.0.4 used, there was one times the trend coefficient left, which is taken care of manually here (which explains the TRENDY).
If you aim at working with this model, you might want to stick with with Dynare 4.0.4 for the moment.

Many thanks for your help. I have got another question regarding the steady states in the observation equation. I notice that in the line 360, ln(DATA_C)=ln(C_tilde)-CC_SS+TRENDY. The right-hand side is the model log-deviation from the steady states. In order to match the data with this specification, do I need to take out the steady state from the log data and how to do it? I notice the data starts from zero. Does it mean the log data needs to minus the value in the first observation?

Best regards