Stoch_simull(order=1) and news shocks

Stochastic simulations
1

Dear all,

I have a stupid and embarrassing question to ask. I let dynare solve my DSGE model by choosing a first order Taylor approximation (i.e. stoch_simull(order=1,…) ). However, we know that 1st order linearizations yield the certainty equivalence property. Since my model contains news shocks, is there a conflict regarding the approximation number? As we know it is quite complicated to introduce news shocks into perfect foresight models.

Many thanks in advance for your help.

Best

Robert

2

At first order, there is no difference. See github.com/DynareTeam/dynare/blob/master/tests/forecast/Hansen_exo_det_forecast.mod for an example showing the equivalence between a perfect foresight shock and a news shock. Only at order>1 would it matter.

3

Great, many thanks! Sorry, I just wanted to ask you two quick questions regarding the simulation of endog. variables and comparing them with the actual data:

  1. I usually have used stoch_simul(period=xxx) endog. variable to simulate model variables. What is the difference between simult_ and stoch_simul? Im a bit confused, is it just the simulation approach?

  2. Let’s say I estimate my model on a dataset, which contains GDP. I then simulate the model at the estimated posterior means and let dynare produce data for GDP. Shouldn’t actual and simulated GDP be very close (or even identical) to each other, due the fact that GDP was used as an observable?

Many thanks for your help!

4

1.) stoch_simul is Dynare’s function to produce moments, IRFs, and decision rules. Internally, it relies on

simult_.m

to simulate the model. You can use that function to conduct simulations were you specify the exact shock sequence you want to have, i.e. it gives you full control over the simulations
2.) Due to different shocks being simulated, the series will not be close in terms of realizations. Rather the series should have similar stochastic properties (second moments). If you were to simulate the model with the smoothed shocks, you should be getting the actual observed output series.

5

Thanks a lot Johannes!