I am currently working on an small open economy DSGE model where as usual their is a combination of home and imported goods (usually investment and consumption). For policy purposes headline inflation is divided into three components:
- Core Inflation (where this home and foreing goods are included)
- Food Inflation
- Energy Inflation (or regulated inflation)
This is important because some times food and regulated prices can affect drastically headline inflation (for example during a climate phenomena like el niño). Due to the nature of food inflation and regulated inflation this variables are asume to be AR(1) processes that converges to their steady state value. In the model we asume that food and regulated inflations steady state are the same as the headline inflation and the inflation target. This is usually done. For example see the relative prices restriction in RAMSES II model:
However, the problem is that in the data this inflations are very different from the inflation target of 3%, so the AR(1) processes structure would result in large forecast errors for this variables (even just only taking into account the mean of the process).
Is their any way of modeling different steady state values for this inflation components given the relative prices restrictions usually imposed in this models?