Optimal Policy & Bayesian Estimation

[family_eigenvalues]

Hello all,

For those familiar with it, I seek to reproduce the work done in Matthes (2015)'s Figuring Out the Fed. This is 4-equation optimal policy NK model with an IS curve, a Phillips Curve, and their respective AR(1) error terms, which serves as a constraint in the optimization of a (matrix-form) quadratic loss function. This can be represented in state-space form, with predetermineds on top, forwards on the bottom, and i_t as the instrument.

Matthes uses St Louis Fed data from 1960-2005, and looks at commitment vs. discretion. There is a learning algorithm wherein private agents update beliefs on which regime is generating the interest rates they observe. For now, however, I would just like to solve the model and estimate its parameters. I know the priors I would like to test. I am curious if this can be done in dynare, and particularly, if somebody knew of an example that was along these lines? I was told that dynare may not be able to handle some specifics of the paper---namely, that the normal dynare likelihood function wouldn't work since, in the paper, agents use the observed shocks to update Lagrange multipliers, which are used to calculate optimal interest rates. Being a mere masters student, I can perhaps forget this problem momentarily while I try to understand the estimation procedure.

Anywho, thank you very much for your help. A simple link to an similar example would be very welcome!

[jpfeifer]

I haven't read the paper so you will need to provide more details. In principle, you should be able to do this in Dynare, but it will pretty surely require much programming effort on your side. So do not embark on this if you are time-constrained by e.g. a thesis deadline. In general, I would not recommend this below the PhD-level.

Particularly implementing the learning algorithm might be hard. I am unable to infer whether you want to do the learning, or whether you just want to estimate the model under optimal policy. The latter is in principle possible, but a user-friendly way of doing this is not yet available, see https://github.com/DynareTeam/dynare/issues/1173

[family_eigenvalues]

With my fears for the programming burden of the learning algorithm all but confirmed, I will for now stick to a simple estimation of the model---first by ML, and perhaps incorporating priors next.

Thank you for your help, and sorry for my vagueness.