# Optimal Simple Rule Question

Does dynare solve the model once fixing all the parameters and pick the policy rule coefficients that minimizes the loss function

OR

Does Dynare fix the non-policy rule parameters and then solves the model (each time it picks a new set of policy rule coefficients) for different policy rule coefficients and then pick the one that minimizes the loss function?

In other words is the optimal simple rule calculated by dynare subject to Lucas critique or not subject to the Lucas critique.

Best,
Abhishek

Dear Abhishek,

Dynare minimizes the declared loss function with respect to the policy parameters (for instance the parameters of a Taylor rule) given the (calibrated) deep parameters. So obviously the results will depend on the calibration of the deep parameters. Optimal simple rules are described here.

I have never heard of a Lucas critique…

Best,
Stéphane.

Dear Stephane,

Thanks for the quick response. Let me state how I understand the optimal simple rule being calculated by Dynare and you can then tell me if I understand correctly.

Dynare minimizes the loss function w.r.t the policy rule parameters. In doing so in minimizes the unconditional variance of the variables specified in the loss function. Since the unconditional variance is dependent on the deep parameters (which also include some of the policy rule parameters), when dynare picks a new draw of policy rule parameters and calculates the loss function for them then it is not subject to the Lucas critique since changing the policy rule parameters changes the associated unconditional variance. Dynare continues to search for new policy parameters until it minimizes the loss function and the termination of this search process is defined by the critical value of improvement to the loss function given by 10*e-7 in Dynare.

By Lucas critique I mean for instance, if Dynare were to solve for the reduced form solution based on the initial value of policy rule parameters and then use that same reduced form solution to calculate the unconditional variance in its search for the policy rule parameter that minimize the loss function. This approach would be subject to the lucas critique since changing the policy rule parameters each time would change the reduced form parameters and calculating the loss function based on initial reduced form solution would not be optimal.

Thanks and Best Regards,

Abhishek.