Empirical Assessment of Bifurcation Regions within New Keynesian Models

As is well known in systems theory, the parameter space of most dynamic models is stratified into subsets, each of which supports a different kind of dynamic solution. Since we do not know the parameters with certainty, knowledge of the location of the bifurcation boundaries is of fundamental importance. Without knowledge of the location of such boundaries, there is no way to know whether the confidence region about the parametersí point estimates might be crossed by one or more such boundaries. If there are intersections between bifurcation boundaries and a confidence region, the resulting stratification of the confidence region damages inference robustness about dynamics, when such dynamical inferences are produced by the usual simulations at the point estimates only. Recently, interest in policy in some circles has moved to New Keynesian models, which have become common in monetary policy formulations. As a result, we explore bifurcations within the class of New Keynesian models. We study different specifications of monetary policy rules within the New Keynesian functional structure. In initial research in this area, Barnett and Duzhak (2008) found a New Keynesian Hopf bifurcation boundary, with the setting of the policy parameters influencing the existence and location of the bifurcation boundary. Hopf bifurcation is the most commonly encountered type of bifurcation boundary found among economic models, since the existence of a Hopf bifurcation boundary is accompanied by regular oscillations within a neighborhood of the bifurcation boundary. Now, following a more extensive and systematic search of the parameter space, we also find the existence of Period Doubling (flip) bifurcation boundaries in the class of models. Central results in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the considered cases. We also solve numerically for the location and properties of the Period Doubling bifurcation boundaries and their dependence upon policy-rule parameter settings.