AR(1) Questions

Hi everyone,

I have a Gali-Monacelli (2005) model with 2 small open economies (that are symmetrical in every way except for different productivity AR(1) processes) and 1 large, exogenous economy. I want to research the benefits of policy coordination in the face of world output shocks. I have 2 questions:

  1. For the different productivity processes, I want them to have the same variance and persistency, but I want them to have different means. Is there a way to do that inn a log-linearised model? I unfortunately whether or not my variance should be in percentage terms relative to the mean or in absolute terms.

  2. How would I simulate a recession in the large economy’s output? Would simply introducing a 1 standard deviation shock do it or would I need to do something else?

If it makes things clearer, I am trying to stick as close as possible to Gali and Monacelli (2005).

Thank you very much for your time in advance!

  1. If you are working in logs, then
    \ln(y_t)=(1-\rho)\ln(y)+\rho \ln(y_{t-1})+\varepsilon_t
    allows you to set the mean y to any arbitrary value. The shock will be in percentage terms due to using logs. If you want it to be in absolute terms, use
    y_t=(1-\rho)y+\rho y_{t-1}+\varepsilon_t
  2. Yes, using an output shock should be sufficient. But without knowing the particular economic experiment, it is impossible to tell