Endogenous Economic Resilience, Loss of Resilience, Persistent Cycles, Multiple Attractors, and Disruptive Contractions

This paper presents a dynamic model of complex system dynamics vulnerable to loss of resilience, cycles, and contractions. We use a limit cycle model built upon Koçkesen & Semmler (2017) to evaluate Brunnermeirs’s theory of Resilience in the light of complex system dynamics and discuss the issue of loss of stability, corridor stability, multiple attractors, and trapping dynamics. Empirically, using the Semmler & Sieveking (1993) and the Koçkesen & Semmler (2017) model we show the existence of cyclical solution paths and demonstrate that the empirics of financial/real forces indeed can exhibit multiple features such as corridor-stability and endogenous resilience. Corridor stability pertains to small shocks with no lasting effects, but large enough shocks can lead to limit cycles and contractions. We refer to the Bautin-Bifurcation theorem, to establish corridor stability for the interaction of real and financial variables where the trajectories can be stable or unstable in the vicinity of the equilibrium. Moreover, we employ a macrodynamic model of regime change by transforming our continuous-time form into an estimable discrete- time form employing the discrete-time Smooth Transition Regression (STR) methodology. Our estimation procedure is applied to U.S. time-series data, where we find essential nonlinearities and regime changes in the data where however the equilibrium is unstable, but global resilience (limit cycles) can arise, representing a Hopf bifurcation type dynamic. As a result, we explore locally unstable but globally bounded fluctuations and detect asymmetric responses to shocks. Some extensions are indicated where the dynamics with multiple equilibria and disruptive contractions are sketched