Nonlinear moving average ( Lan/Meyer-Gohde)

General DSGE Modeling
1

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

2

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.

3

First order approximation: They evaluate first order approximation of the policy around the deterministic steady state image of the form given below:
image
In the end First order approx. for policy function as below:
image
Certainty equivalence holds as above equation is independent of image

Second order policy function is of the form

image
image.png697×90 6.18 KB

Now, they say in compare to first order it depends on image with term image now as image goes to 1. we move from the deterministic SS image to Second order stochastic SS image

Would you please explain again. Hope, I correctly understood first two points.

  1. usual perturbation evaluate the policy function around the deterministic steady state using state space method

  2. Lan/Meyer-Gohde do not use state space rather they develop Euler equation error method.

  3. Lan/Meyer-Gohde at First order holds Certainty equivalence

  4. Higher order 2 or more, They move from DSS to SSS.

Thanks!