Dear all,
I would like to know how Dynare deals with indeterminacy and overidentification problems of a dgse model.
Say that we are trying to estimate a DGSE with bayesian estimation, and for some parts of the parameter space there will be overidentification (or indeterminacy), in these draws of the prior, will dynare just drop it, and go on with another draw of the prior, or will it cancel all the computation?
Best, Joan
I am not sure what you mean with “overidentification (or indeterminacy)”. The term “Indeterminacy” usually denotes not having a unique solution to the model in terms of the endogenous variables. Overidentification is usually not a concept used in connection to full information estimation techniques.
Dear Johannes,
Let me use and example to ilustrate better my inquieries.
Following Sims(2001) we can rewritte a lineal rational expectation model into a canonical form:
Gamm0*X_t=Gamma1X_t-1+PsiZ_t+PiEta_t, where X_t is the vector of states variables, Z_t of fundamental shocks and Eta of endogenous shocks (or forecast errors). To have a bounded solution we need that the number of the general eigenvalues ratio between Gamma1 and Gamma0 that are larger than 1,p, is lower or equal tan the number of expectational variables,m, of the model. If p=m then we will have a unique bounded solution (the model is determined), if p<m we will have multiple bounded solutions (indeterminacy). If we are in the case of p>m we will have no solution.
Now, let’s try to estimate the simple new keynesian model with bayesian estimation. Let’s say that if psi_pi<1 we have indeterminacy and if psi_pi>1 (for sake of simplicity) deteminacy. Then, if we make a prior that has positive probability in both regions of psi_pi, we will make draws, for which our simple model has determinate and inderterminate solutins. My question was if Dynare just do not take into acount the output when the draw creates indeterminacy, and goes on with another draw of the prior.
And the same for Overidentification, as far as I know, if we follow Farmer, Nicolo, Kramov method, we can identify a unique bounded solution for cases where psi_pi is lower than 1. Nevertheless, if we make draws of psi_pi larger than one we will face overidentification, and hence, no bounded solution (the number of general eigenvalues ratio larger than one is two, but the number of expectational variables under this specification is 1)
So in summary, whar Dynare does when parameter draws creates a problem on determinacy of LRE.
So your question is what happens if at a parameter draw the Blanchard Kahn conditions for having a unique bounded solution are not satisfied. Unless you use tricks as in Bianchi/Nicolo those parameter draws are discarded, i.e. their prior density is set to 0.
1 Like