ABSTRACT
The partial derivatives in this equation (which are matrices, in general, since y, u, 17, 0 and d are vectors) are evaluated on the anticipated trajectory (Uk = UZ,Yk = rk, 17k = 17Z, Ok = oZ, dk = dZ), and consequently depend on the period k, even if the function fk is itself independent of k (i.e. even if fo = f1 = f2 = ... ). However, for the purposes of policy design we shall make the further approximation that these partial derivatives do not depend on k, so that (7) becomes a constant-coefficient, linear difference equation
(8)
These approximations may seem reckless, but it should be remembered that any policy that is designed on the basis of these approximations can and should be tested on the original model. We re-emphasise that the results presented in Chapter VIII were obtained with the full non-linear model described in Appendix A.
