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Empirical assessment of bifurcation regions within New Keynesian models

机译:新凯恩斯模型内分叉区域的经验评估

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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 parameters’ 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 (Physica A 387(15):3817–3825, 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.
机译:正如系统理论中众所周知的那样,大多数动态模型的参数空间被分为多个子集,每个子​​集都支持不同类型的动态解决方案。由于我们不确定地了解这些参数,因此了解分叉边界的位置至关重要。如果不知道这些边界的位置,就无法知道关于参数点估计的置信区域是否可能被一个或多个这样的边界所跨越。如果分叉边界和置信区域之间存在交集,则仅通过常规模拟在点估计处生成此类动态推断时,置信区域的分层结果会破坏有关动态的推断鲁棒性。最近,在某些领域,人们对政策的兴趣已经转移到新凯恩斯主义模型上,该模型已在货币政策制定中变得普遍。结果,我们探索了新凯恩斯模型中的分叉。我们研究了新凯恩斯主义功能结构内货币政策规则的不同规范。在该领域的初步研究中,Barnett和Duzhak(Physica A 387(15):3817–3825,2008)发现了新的凯恩斯霍普夫分叉边界,其政策参数的设置会影响分叉边界的存在和位置。 Hopf分叉是在经济模型中最常遇到的分叉边界类型,因为Hopf分叉边界的存在伴随着分叉边界附近的规则振动。现在,在对参数空间进行更广泛和系统的搜索之后,我们还发现了模型类别中周期倍增(翻转)分支的边界的存在。这项研究的主要结果是我们在每种考虑的情况下关于Hopf分叉边界的存在和位置的定理。我们还用数值方法求解了“周期加倍”分支边界的位置和属性及其对策略规则参数设置的依赖性。

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