Complex roots

Dear all,

I am working on relatively big dsge model (18 endogenous variables: 8 state, 10 others). I used the 1st order Taylor approximation for solving the model. One root (eigenvalue), I obtained, is a unit root. Several roots are complex numbers, but imaginary part is very small (e.g., +o.ooooi or -0.007i).

I would like to ask what implications this has for the model? Can i still implement the Bayesian estimation in this case?

Thank you in advance for your help.


Complex roots are a perfectly normal outcome. They don’t create any problem for simulation and estimation.

The unit root is more problematic. At first, you may want to detrend your model to remove the stochastic trend and estimate on stationarized data. When that is working, you can go back to estimate on non stationary data. Look at the example in fs2000



Dear Mr. Michel Juillard,

Thank you for your quick reply.

I think that unit root “comes” from the net foreign assets position:

foreign_borrowing(t-1)*int._rate(t-1) =foreign_borrowing(t)+ nominal_export(t)-nominal_import(t) , i.e.

foreign borrowing in used to finance foreign trade deficit.
In the steady state: foreign_borrowing=0.

In the previous version of the model where there is no foreign borrowing (nominal import=nominal export), there is no unit root.

Therefore, maybe I should not pay attention to this unit root and simply proceed with Bayesian estimation.