I am estimating a standard RE model. In the example below I estimate coefficients a11,a12,a13,a21,a22,a23.
I can write the model in two versions
x(1) = a11x + a12y(-1) + a13eps;
y = a21x + a22y(-1) + a23eta;
y = b11y(-1) + b12eta + b13 eps;
x = b21y(-1) + b22*eta + b23 *eps;
In the version 2 I use a matlab subroutine that solves the RE model (performing say Blanchard-Kahn decomposition, or, more generally qz decomposition).
I wonder why the estimates differ SUBSTANTIALLY, both and posteriors of coefficients and marginal data densities? I would have thought that the Dynare translates version 1 into version 2 before the estimation. Am I wrong? (The BK decomposition I use is standard and correct - I cannot see how it can be wrong.)
PS. I work witn Dynare 3 as Dynare 4 does not eat the line # [b11,b12,b13,b21,b22,b23]=BK(a11,a12,a13,a21,a22,a23); I will be also grateful if one explains how to call Matlab routines inside the model block.