Global Stability: Subsystem Approaches

Abstract

In the preceding chapter we have seen that local asymptotic stability and thus convergence back to the steady state may apply when adjustment speed parameters are — broadly speaking — sufficiently small and shocks out of the balanced growth position not too large such that the economy is pushed out of its stability basin. However, the size of the parameters and the shocks that will allow for such outcomes is not really known and can basically only be obtained from numerical simulations of the considered dynamics Furthermore, there is some indication that actual parameter sizes may be such that the steady state is locally repelling and possibly also globally. However the Hopf bifurcations that occur when stability gets lost are either subcritical or — if supercritical — too local in nature to really find application from the economic point of view (where broader parameter ranges need to be considered).