Dear dynare team,
I have a simple question regading the idea behing efficiency policy frontier. From what I understand, is it really necessary to compute the optimal policy for the model one uses? Isn’t it simply varying the coefficients of the Taylor rule, compute the unconditional variances of both output and inflation for many combinations and plot all points on a graph? Then we can hopefully derive the Taylor curve? Or I’m completely wrong about that.
Those are two different things.
- You have in mind fixing a simple rule, changing the parameters in the rule, and then plotting the resulting variances for output and inflation.
2, That is different from formulating an objective function with weights on output and inflation, varying those weights, and then computing the optimal policy for those weights, before plotting the resulting variances at the optimum.
In case 1 you very the weights in the instrument, while in 2 you vary the weights in the objective.
Thanks a lot for your reply. So let’s take the very basic NK model as an example. Then the welfare loss function is derived by means of a 2nd order approximation around the utility function whereby the weights on the output gap and inflation are also derived and functions of the model’s deep parameters.
L=0.5*( (sig + (varphi+alppha)/(1-alppha))*varygap + (eps/lam)*varpi ) (which of course you’re pretty familiar with)
If I’d like to get a Taylor curve for this very basic NK model, then all I need to do is to set up a grid for the coefficients of both inflaton and output in the Taylor rule (i.e. phi_pi and phi_y), find those combinations that produce the smallest value of the loss function and for that value plot var(yhat) against var(pi), am I right?
That exercise would not be well-defined. For a given loss function, there is a (often unique) Taylor rule defining the optimal policy. As I said, you can either vary the loss-function (thus not using the one defining the agents’ preferences in the economy) and then compute the optimal policy or the coefficients of the Taylor rule given the loss function (thus not doing optimal policy)
Yes, tried it, so I’ll stick to varying the coefficients of the Taylor rule Thanks a lot for your help.