Is it Worth Refining Linear Approximations to Non-Linear Rational Expectations Models?

We characterize the balanced growth path of the basic neoclassical growth economy using standard, almost linear numerical solution methods, as well as the parameterized expectations approach, which preserves the nonlinearity in the model. We also apply the same methods after adding indivisible labor to the basic model, and to a monetary version of that economy, subject to a cash-in-advance constraint. In a unified framework we tackle the question of how much of the nonlinear structure of the original problem is useful to maintain when using an “almost” linear method. We show that it is possible to find an almost linear method to solve these models as accurately as by parameterizing expectations. Our results show the importance of performing log-linear approximations, as well as the convenience of refining a linear solution method by mixing some structure of the original non-linear problem with structure of the approximated system.Linear-quadratic approximation, numerical accuracy, simulation,numerical methods.

About gauge invariance in compactified extra dimensions

Gauge theories formulated in a space-time manifold that includes compact extra dimensions can show a nontrivial gauge structure. Depending on whether the gauge parameters propagate or not in the extra dimensions, two different Kaluza--Klein theories can arise when the extra dimensions are compactified. A comparison between these two possibilities, in the context of a five dimensional theory, is presented from both the theoretical and phenomenological viewpoints. The phenomenological implications of these theories are contrasted by discussing the one--loop decay of the Higgs boson into two photons. It is shown that the amplitude for this decay differs substantially from one approach to the other and that such a difference is intimately related to gauge invariance.Comment: 5 pages, 1 figur