Simulation under optimal policy


Hello everyone,
I want to compute the optimal simple rule for a certain period. Basically, I estimate a model I take the parameters estimated values and computed the osr for a model calibrated with this parameters. Nevertheless, what I want to get is the welfare losses and the dynamics asociated with this optimal rule for this specifc period, with the shocks of the estimated model, not shocks that are simulated.

How can I do it?

Thank you very much in advance


You need to explain this in more detail. What do you mean with

Does that mean you want conditional welfare measure based on the state in the particular period?


First thank you for the answer and i apologyze for the poor explanation.

What I want to get is the dynamics of the variables (for example, the dynamic of output generated by the model given some values for the structural and shock parameters) under the optimal simple rule and the estimated shocks. Nevertheless, if I calibrate the model (and therefore the variance of the shocks) dynare generates a simulation from this calibration and compute the optimal response for this simulation. But the dynamics of the variables are driven by these simulated shocks and I want to get the dynamics considering the actual realization of the shocks (the estimated shocks, not simulated).

I hope now it is understandable


That is a simple simulation. You need to use the simult_-function after solving the model under optimal policy and select the smoothed shocks you want, starting from the initial condition. It should be similar to


Thank you very much for the link.

Now that I have done the simulation I want to compute the Welfare associated with the OSR (the objective function of the CB is the variances of inflation and output gap) in order to compare it with the Welfare of the estimated Taylor rule. Can I just apply exp( ) and plug the simulated consumption and hours worked in the utility function and make the discounted sum?

Is it correct? Because I have been reading the forum and I get that many people use second order approximation when they are doing something related with welfare but I do not understand why. Therefore, I do not know if my results would be trustable since my model is a first order approximation.

Thank you very much in advance


Generally, you need a second order approximation (unless your steady state is efficient). See e.g. Born/Pfeifer (2018): “The New Keynesian Wage Phillips Curve: Calvo vs. Rotemberg” for an explanation and references.