Analyzing non-stationary and unbalanced growth economic models

这个项目将开发一种分析经济数学模型的新方法。新方法的主要特点是，它将为经济学家提供新的工具来建立和分析模型，这些模型不仅包括随时间变化的模型(动态模型)以及偶然性在这种变化中发挥作用的可能性(随机动态模型)，而且还包括变化的概率本身随时间变化的模型(非平稳随机动态模型)。该项目显然有潜力改进经济学家目前用来回答需要这些非平稳随机动态模型的研究问题的方法。此外，该项目具有变革的潜力；新的方法可能意味着经济学家将能够解决用以前的方法无法回答的新研究问题。如果这个项目完全成功，美国的经济政策制定者将受益于就他们的决策对美国经济的影响提供更好的科学建议。总体目标是开发扩展功能路径(EFP)方法，用于校准、求解、模拟和估计非平稳和不平衡增长的动态随机经济模型。EFT的关键特征是半马尔可夫过程的概念，其中转移密度函数是时间相关的，同时对于导致当前状态的特定历史也是无记忆的。PI团队计划将EFP应用到一组不允许传统的平稳马尔可夫解的例子中。在这些例子中有两个研究项目。第一种方法分析了1963至2012年间美国经济的不平衡增长模式。第二个项目将试图在新凯恩斯模型的背景下解释最近的经济危机，该模型具有名义利率的泰勒规则和政府政策可能的非马尔科夫变化。

This project will develop a new method for the analysis of mathematical models of the economy. The key feature of the new method is that it will give economists new tools to build and analyze models that include not just changes over time (dynamic models) and the possibility that chance plays a role in this changes (stochastic dynamic models) but models in which the probability of a change can itself vary over time (nonstationary stochastic dynamic models). The project has clear potential to improve the methods economists currently use to answer research questions calling for these nonstationary stochastic dynamic models. In addition, the project has transformative potential; the new methods may mean that economists will be able to tackle new research problems that were impossible to answer with previous methods. If this project is fully successful, economic policymakers in the US will benefit from better scientific advice about the effects of their decisions on the US economy.The overall goal is to develop the extended function path (EFP) method for calibrating, solving, simulating and estimating non-stationary and unbalanced growth dynamic stochastic economic models. The key feature of EFT is the notion of semi-Markov processes in which transition density functions are time dependent while also memoryless with respect to the specific history that leads to a current state. The PI team plans to apply EFP to a collection of examples that do not admit conventional stationary Markov solutions. Among these examples are two research projects. The first uses the method to analyze unbalanced growth patterns in the U.S. economy between 1963 and 2012. The second project will attempt to explain the recent economic crisis in the context of a new Keynesian model with a Taylor rule for nominal interest rates and possible non-Markov changes in government policies.