Ramsey optimal policy yields zero approximated value of welfare

Optimal Policy
1

I am studying Ramsey optimal policy problem using mod.file from professor Pfeifer’s GitHub. It generates IRF well but consistently yields zero approximated welfare(for both conditional and unconditional). I experienced similar results from Willi Mutschler sample code file.
example.mod (7.2 KB)

It seems the problem comes from the below warning but I cannot exactly figure out why welfare estimates are zero.
Warning: Some of the parameters have no value (Omega, lambda, kappa, vartheta) when using stoch_simul. If these parameters are not initialized
in a steadystate file or a steady_state_model-block, Dynare may not be able to solve the model. Note that simul, perfect_foresight_setup, and
perfect_foresight_solver do not automatically call the steady state file.

How can I get exact welfare estimate by modifying above mod file?

2

Welfare is a stochastic object that depends on higher order properties of the model. In linear models, average welfare deviations from steady state are trivially zero.

3

In this youtube video, however, approximated planner objective value is not zero.(see 40:19).

Since the planner objective is a quadratic function of inflation and the output gap, 0 approximated value of unconditional welfare means that ramsey policy can achieve divine coincidence(i.e inflation=ouput gap = 0). This is also somewhat weird since under the existence of cost-push shock there exists trade-off between stabilizing inflation and stabilizing output gap.

4

My mistake. You want a second order approximation (order=2). At first order, you end up in steady state.