Hello Professor Johannes,
I would to like confirm that,
non-linear moving average method( Lan/Meyer-Gohde) evaluate the policy function at the ergodic mean or stochastic steady state while usuall perturbation evaluate the policy function around the deterministic steady state using state space method. And Lan/Meyer-Gohde do not use state space rather they develop Euler equation error method.
Their NLMA add in(link given below) for dynare do evaluation of policy function around ergodic mean not the stochastic steady state
My understanding is that this is not the case. A true approximation at a point that is not the deterministic steady state would lead to effects of uncertainty already at first order. But they still need to perform a third order approximation to capture the effect of uncertainty shocks.
First order approximation: They evaluate first order approximation of the policy around the deterministic steady state of the form given below:
In the end First order approx. for policy function as below:
Certainty equivalence holds as above equation is independent of
Second order policy function is of the form
Now, they say in compare to first order it depends on
goes to 1. we move from the deterministic SS
to Second order stochastic SS
Would you please explain again. Hope, I correctly understood first two points.
usual perturbation evaluate the policy function around the deterministic steady state using state space method
Lan/Meyer-Gohde do not use state space rather they develop Euler equation error method.
Lan/Meyer-Gohde at First order holds Certainty equivalence
Higher order 2 or more, They move from DSS to SSS.