Stationarity and IRF problem

Dynare help (legacy posts)
1

Dear all,

I am working with a New Keynesian model featuring the financial accelerator mechanism as in BGG1999 (a summary of the model and its solution is attached). I am working with the model in levels, and productivity is assumed to follow an AR process. So, to make the model stationary, I make a replacement for the variables that should be trending: output (y), consumption ©, investment (i), capital (k), entrepreneurs’ net worth (n), and wages (w). I divide all these variables by the technology shock (A) and make the adjustments to the model equations consistent with this transformation (I took Fernandez-Villaverde’s (2006) paper for the NK_baseline model as example).

First, as you can see from the IRFs, with a first order approximation, most of the variables do not tend to return to the steady state even after a long time (say, 50 quarters). What could be the reason for this? Could also the investment specific shock be playing a role here (eq. 22 of the code)? Also, the theoretical moments are rather weird: investment has a very low standard deviation, while the one for net worth is huge. Comments on this are very welcome.

Second, the IRF for the interest rate shows that a positive shock to the taylor rule actually triggers a decrease of the interest rate. Since the shock enters directly in the taylor rule (eq. 16 of the code), I find this very weird. Any possible explanation?

Thanks a lot in advance!
appendix.pdf (262 KB)
CD08_nonlinear_ss3.mod (6.45 KB)

2
  1. 50 periods is not long. 1000 periods is. Check whether there is a unit root that should not be there (use the check command to see the eigenvalues). If not the parameters and shock processes simply imply a huge persistence
  2. Regarding moments, if you use the attached files, you are computing absolute deviations instead of log deviations. As investment is a small share of GDP, the absolute deviations can be smaller. Define auxiliary variables like

and compare them.
3. For the rise in the nominal interest rate, see [Monetary Shock)

3

Dear Johannes,
thank you for the answers. You were right about the first issue. The model parameters implied a really big persistency. In particular, adjusting the curvature parameter of the external risk premium allows to obtaining a more reasonable persistency. And thanks a lot for the tips in points 2. and 3. Problems solved!