I know this is a stupid question, nevertheless it has been haunting me since I first learned about BK conditions because it seemed to me that just counting the number of eigenvalues was too weak to be sufficient.
Assume a trivial model, with one predetermined variable and one forward looking variable, written with Dynare timing convention :
k = rhok(-1) + eps
c(+1) = thetac + mu
It is already written in BK form E(X) = A X(-1) + F, with A already diagonal. Of course, if rho <1 and theta > 1, then it is saddle-path stable.
But if we switch the two parameter values(rho >1 and theta < 1), then we still have the “right” number of eigenvalues higher that 1, but obviously this model has to stable solution. I don’t see which assumption in BK’s original paper excludes this case.
I put it in a Dynare code, Dynare counts the number of eigenvalues but still says that the rank condition is not verified (which it is, all my matrices are invertible). What does Dynare do in that case?
test.mod (212 Bytes)