I need your help or advising in solving a theoretical problem and it’s application in Dynare.
Specifically, I have my Log-linearized (Uhlig method) NK model with fiscal and monetary policy according with some fiscal rules.
My household’s utility function has Consumption, Labour and Pubblic spending as arguments.
I have now to write down my fiscal optimal policy but I’m trying to understand when I have to use LQA approach or simple Ramsey Optimal Policy approach.
What is the difference from an economic point of view and in Dynare results ?
with LQA i mean Linear-Quadratic Approximation Problem.
I’m trying to understand why some author use this approach and others simple Ramsey Policy (as a simple maximization problem of the Central Planner) and specifically how to implement in Dynare.
I have read the Dynare manual about differences between Optimal Simple Rules and Ramsey Problem but now I have a little confusion about the different results by an economic point of view.
Ramsey solves the maximization problem of a planner in a decentralized economy. Ramsey assumes full commitment, implements a fully state-contingent planner policy and is therefore optimal, and allows approximating the FOCs at order>1.
LQA usually does exactly the same, but the approximation of the planner objective is restricted to quadratic and the private sector FOCs to linear. This will result correct welfare rankings only in special cases.
OSR is different in that it still assumes commitment, but instead of a fully state-contingent policy, the planner policy is restricted to simple parametric rules instead of fully state-contingent planner policies.
Can I ask you in which particular cases the quadratic form is better in ranking welfare with respect to Ramsey? Expecially in Dynare.
In research papers, I have often found it in cases about distorted steady-state (e.g: precence of intermediate sector monopolistic competition, etc…) but never found in Dynare an example of LQA approach of the Policy function (instead the most famous "planner_objective" and “ramsey_policy” commands)
LQA is never better in terms of accuracy. It is only computationally easier to do. Dynare will approximate both the planner objective and the private sector FOCs, but at a consistent order, not in a linear-quadratic way.