The RATS Software Forum

Dear Tom,

Consider a SVAR of the following form: Cy_t = A(L)y_(t)+e_t , with the lag polynominal A(L) = A1*L + A2*L^2+...+AnL^n and e_t ~ N(0,I), where I is the identity matrix. Then the redurced form VAR can be estimated by Bayesian methods, for example a Gibbs sampler with indepenent Normal-Wishart distribution.
Then the reduced form shocks v_t= C^(-1)*e_t have the covariance matrix S=C^(-1)C^(-1)'.
Consider I have restrictions on C, such that the model is exactly identified, then theoretically it should be possible to take the non-linear system of equations S=C^(-1)C^(-1)' and solve it for the free parameters of the C matrix. Is there a solver for that in RATS?

Basicly what I want to do is to draw the reduced form coefficients of the VAR within a Gibbs sampler and then for every draw solve S=C^(-1)C^(-1)', to get a draw of C, which has as many restrictions as is needed to have an exaclty identified VAR and then calculate the IRFs to get a draw of those.

Thank you in advance

Best Jules

That's what CVMODEL does. There are only a handful of structural models where the solution can be computed algebraically, so anything else requires some type of non-linear optimization. Maximizing the likelihood on a just-identified model is equivalent to solving the implicit equation.

Thank you very much Tom