Hi everyone
I estimated the model from Lubik and Schorfheide (2007) using the observable equation:
obs_{}pi_t=4 \pi_t
This transformation aligns the model’s quarterly inflation rate (\pi_t) with the annualized inflation rate observed in the data. Now, I want to compare the theoretical moments (e.g., standard deviation) of the model with those from the data. Specifically, should I multiply the (theoretical) standard deviation of the model variable \pi_t by 4 to align it with the observed data?
I bring this up because, while most theoretical moments align closely with the values suggested by the data, inflation is an exception. The model implies significantly higher volatility for inflation—around four times greater than what is observed in the data.
Thanks in advance for any insights or suggestions!