Conditions for Asymptotic Stability in OLG and Growth Models

长期以来，经济学家一直使用代际重叠和新古典增长模型来探索公共财政、发展、国际贸易、储蓄和货币政策等领域的重要实证和理论问题。最近，一些研究人员对这些模型描述经济长期趋势的方式进行了抨击。该项目将研究经济学家用来编纂和应用这些模型的数学方程，并研究经验确定的参数与模型的相应长期属性之间的关系。由于将模型的假设编入公式的方程在实际使用时可能导致奇怪的行为，因此这些模型可能会对经济行为做出误导性的预测。通过应用最先进的计算机编程技术，将开发出表征感兴趣的参数的合理范围的公式。由Laitner和Anderson- Moore提出的确定性概念将被应用于识别具有稳定性的不动点环和极限环，这些稳定性意味着从附近点的唯一收敛轨迹。该项目将侧重于离散时间模型。当一般公式无法获得时，将开发特定效用函数和生产函数的解析表达式。这些模型的渐近稳定性将在经验相关的模型参数范围内进行研究，以表征面对现实世界数据时潜在复杂渐近行为的合理性和相关性。该项目将开始研究这些模型的全局收敛特性，目的是开发“高阶”收费公路定理，以表征保证收敛到给定周期的极限环的条件。

Economists have long used overlapping generations and neoclassical growth models to explore important empirical and theoretical issues in public finance, development, international trade, savings and monetary policy. Recently, some researchers have attacked the way these models characterize the long run tendency of the economy. This project will study the mathematical equations which economists use to codify and apply these models and investigate the relationship between the empirically determined parameters and the corresponding long run properties of the models. Since the equations which codify the assumptions of the models can lead to bizarre behavior when these models are used in practice, the models could give misleading forecasts of the behavior of the economy. By applying state of the art computer programming techniques, formulae for characterizing the plausible ranges of parameters of interest will be developed. The concept of determinacy developed by Laitner and Anderson- Moore will be applied to identify fixed-point and limit cycles which possess stability properties that imply unique convergent trajectories from nearby points. The project will focus on discrete time models. Analytic expressions for specific utility and production functions will be developed when general formulae are unattainable. The asymptotic stability of these models will be investigated for empirically relevant ranges of model parameters in order to characterize the plausibility and relevance of the potentially complex asymptotic behavior when confronting real world data. The project will begin an investigation of the global convergence properties of these models with the objective of developing "higher order" turnpike theorems characterizing conditions guaranteeing convergence to limit cycles of a given periodicity.