Perfect foresight solver with linear approximation


Currently, I am working on simulating the deterministic path of a model written in non-linear form.

If I use the option perfect_foresight_solver(linear_approximation), what is Dynare doing in the background? I would like to further understand the steps that Dynare is following, but I was not able to find much detail about this option in the manual.

Thanks in advance.

Dynare will linearly approximate the model about the steady state using a first order Taylor approximation. Then it will solve this linear equation system.

Thank you for your answer. I have two follow up questions.

First, if I feed in an initval block and an endval block, which one is the steady state used for the approximation?

Second, if it is a first order approximation, does this mean we have to interpret the simulated path as deviations from the steady state? If so, is it percentage deviations or absolute deviations?

Thank you in advance.

From the manual on linear_approximation:

Solves the linearized version of the perfect foresight model. The model must be stationary and a steady state needs to be provided. Linearization is conducted about the last defined steady state, which can derive from initval, endval or a subsequent steady. Only available with option stack_solve_algo==0 or stack_solve_algo==7.

No, the linear approximation does not remove the mean, so it’s not in deviations from steady state.