Policy function & Second order Approximation

Dear All,

I am new to Dynare and looking for some help regarding the following questions:

1. As we know that the solution of DSGE is a state/transition equation and a policy/observation equation. However, when all variables defined under -var- block are included in the state variable vector (as per dynare manual), then what are the policy variables ?

2. Dynare output under “Policy and Transition Function” exhibits a table of endogenous variables as a function of its own and other variables lags , does this suggests that policy variables are the state variables but at time t (today) ?

Thank you very much,

1. You can always combine both equations into a single one by substituting in the observation equation for the contemporaneous states using the state transition equation. That’s mathematically equivalent to the representation you have in mind.
2. Yes, all variables that can be chosen at time t are policy variables, while everything dated t-1 is predetermined and, therefore, a state variable you need to take as given.

Now its crystal clear to me, Thanks a lot. One last thing that I missed to address in the last question:

A second order approximation solution of DSGE using perturbation methods invokes the parameter σ (sigma: standard deviation of distribution of the error term) into the transition equation as shown by Schmitt-Grohe and Uribe (2004) to account for uncertainty. However, solution presented by dynare does include sigma terms, Why ?

Regards and thank you

At second order, you get the ghs2-term, at third order, the g_{x\sigma\sigma}-term is folded into ghx.

Thank you