Mathematical models for credit dynamics in macroeconomics

宏观经济学中信用动态的数学模型

• 批准号: RGPIN-2014-03591
• 负责人: Grasselli, Matheus
• 金额: $ 1.68万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635725
• 关键词: Mathematical; models; credit; dynamics; macroeconomics

The 2007-08 financial crisis was a wake-up call to many mathematicians working in the area of quantitative finance. Because the financial instruments that relied on sophisticated mathematics were at the very centre of the crisis, many decided to look for general models that likewise would put finance at the core of economic activity. Surprisingly, mainstream macroeconomic models, for example the Dynamic Stochastic General Equilibrium (DSGE) models routinely adopted by central banks, had no fundamental role for banks, or financial markets for that matter, other than that of passive intermediaries. One alternative are stock-flow consistent models (SFC), where aggregate transactions between sectors - firms, banks, households, government, etc - are modelled together with the corresponding flows of funds and changes in financial balances. Another are agent-based computational models, where the financial interactions between individual firms, banks, depositors, etc, are modelled directly and the resulting aggregate behaviour is obtained without recourse to fictitious auctioneers and the like. The objectives of the proposed research program are to use both SFC and agent-based models to understand the role of credit dynamics in macroeconomics. On the one hand, I propose to analyze the systems of equations obtained in several alternative specifications of SFC models using the tools of modern dynamical systems theory, including bifurcations, global estimates, and topological properties. In recent work, my collaborators and I performed a detailed analysis of a model proposed in Keen (1995), including the characterization of two types of locally stable equilibria, one with finite and the other with infinite private-debt ratios, and found that under precise conditions, government intervention can prevent the latter and guarantee employment persistence. The following are among the many possible extensions of these models: financing of firm activities both by debt and equity issuance; independent central bank and the effects of monetary policy implementation, including quantitative easing (QE); consumer credit and the shadow banking system. All of these features are bound to increase the complexity of early models, but are necessary for a fully integrated approach to the role of credit in economics. Apart from rigorous mathematical analysis of the effects of each modification, I propose to guide the development of the project by carefully testing the implications of the models using databases of the OECD, IMF, World Bank, Federal Reserve, etc. On the other hand, I propose to use the tools of network science to continue my work on agent-based computational model for the emergence of banks and interbank lending. Many recent papers characterize the empirical properties of financial networks (degree distribution, connectivity, centrality, etc), while other focus on stability, for example by investigating the effects of removal of nodes due to default, but with limited emphasis on the behaviour of individual agents. I propose to extend these models by introducing agents endowed with bounded rationality, realistic objective functions and computational capabilities, explicit interactions and inductive learning. Ultimately, the two strands of the project come together through the notion of time scales, with the network of fast-interacting agents creating the structural relationships that govern the long-term dynamics of the aggregate flows between sectors. This innovative way of macroeconomic modelling has just begun and has the potential to be a paradigm shifting development that, together with complementary work on incomplete knowledge economics and radical uncertainty, can redefine the role of mathematics in economic theory.

2007 - 08年的金融危机是对许多在定量金融领域工作的数学家的警钟。由于依靠复杂数学的金融工具处于危机的中心，因此许多人决定寻找同样将财务构成经济活动核心的通用模型。令人惊讶的是，主流宏观经济模型，例如中央银行通常采用的动态随机通用平衡（DSGE）模型，对银行或金融市场没有基本作用，除了被动中间人之外。一种替代方案是股票流量一致的模型（SFC），其中企业，银行，家庭，政府，政府等部门之间的总交易与相应的资金流和财务余额变化一起建模。另一个是基于代理的计算模型，在该模型中，直接对单个公司，银行，存款人等之间的财务互动进行建模，并在没有求助于虚拟的拍卖者等的情况下获得了由此产生的总体行为。拟议的研究计划的目标是使用SFC和基于代理的模型来了解信用动态在宏观经济学中的作用。一方面，我建议使用现代动力学系统理论的工具，包括分叉，全球估计和拓扑特性，分析在SFC模型的几种替代规范中获得的方程系统。在最近的工作中，我和我的合作者对Keen（1995）提出的模型进行了详细的分析，包括表征两种类型的本地稳定平衡，一个具有有限的私人私人DEBT比例，并发现在精确的条件下，政府的干预可以防止后者并保证雇佣持久性。以下是这些模型的许多可能扩展之一：债务和股权发行的公司活动融资；独立中央银行以及货币政策实施的影响，包括量化宽松（QE）；消费者信贷和影子银行系统。所有这些特征必将增加早期模型的复杂性，但对于信贷在经济学中的作用进行完全整合的方法是必不可少的。除了对每次修改的效果进行严格的数学分析外，我建议通过使用OECD，IMF，世界银行，联邦储备等数据库仔细测试模型的含义来指导项目的开发。另一方面，我建议使用网络科学工具来继续我的工作对基于代理的计算模型的工作，以实现银行和Interbank Lendend的基于代理的计算模型。许多最近的论文表征了金融网络（程度分布，连通性，中心性等）的经验特性，而其他重点是稳定性，例如，通过研究由于默认值而导致的消除节点的影响，但重点有限，对各个代理的行为的重视程度有限。我建议通过引入具有有限的理性，现实的目标功能和计算能力，明确的相互作用和归纳学习的代理来扩展这些模型。最终，该项目的两个链通过时间尺度的概念汇集在一起​​，快速相互作用的代理的网络创建了结构关系，该结构关系控制了扇区之间总体流动的长期动态。这种创新的宏观经济建模方式才刚刚开始，并有可能成为改变范式发展的发展，与不完整的知识经济学和根本性不确定性的互补工作一起，可以重新定义数学在经济理论中的作用。