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: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=565964
• 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年至2008年的金融危机给许多从事定量金融领域工作的数学家敲响了警钟。由于依赖于复杂数学的金融工具是危机的核心，许多人决定寻找同样将金融置于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，例如央行经常采用的动态随机一般均衡（DSGE）模型，除了被动中介机构之外，对银行或金融市场没有根本性作用。一种替代方法是存量-流量一致性模型（SFC），其中将企业、银行、家庭、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。另一种是基于代理人的计算模型，在这种模型中，个体公司、银行、储户等之间的金融互动被直接建模，由此产生的总体行为是在不求助于虚构的拍卖人等的情况下获得的。拟议的研究计划的目标是使用SFC和基于代理的模型，以了解信贷动态在宏观经济中的作用。一方面，我建议使用现代动力系统理论的工具，包括分叉，全局估计和拓扑性质，来分析在几种替代规格的SFC模型中获得的方程组。在最近的工作中，我和我的合作者对Keen（1995）提出的一个模型进行了详细的分析，包括两种局部稳定均衡的特征，一种是有限的，另一种是无限的私人债务比率，并发现在精确的条件下，政府干预可以防止后者并保证就业持续性。以下是这些模型的许多可能的扩展：通过债务和股票发行为公司活动融资;独立的中央银行和货币政策实施的影响，包括量化宽松（QE）;消费信贷和影子银行系统。所有这些特征必然会增加早期模型的复杂性，但对于全面综合地研究信贷在经济学中的作用来说，这些特征是必要的。除了严格的数学分析的影响，每一个修改，我建议指导该项目的发展，仔细测试的影响模型使用数据库的经合组织，国际货币基金组织，世界银行，联邦储备等另一方面，我建议使用网络科学的工具，继续我的工作，基于代理的计算模型的出现银行和银行间拆借。最近的许多论文描述了金融网络的经验性质（度分布、连通性、中心性等），而其他论文则侧重于稳定性，例如通过研究因违约而移除节点的影响，但对个体代理的行为强调有限。我建议通过引入具有有限理性、现实目标函数和计算能力、显式交互和归纳学习的代理来扩展这些模型。最终，项目的两个部分通过时间尺度的概念结合在一起，快速互动的代理人网络创建了管理部门之间总流量长期动态的结构关系。这种宏观经济建模的创新方式才刚刚开始，有可能成为一种范式转变的发展，再加上对不完整知识经济学和根本不确定性的补充工作，可以重新定义数学在经济理论中的作用。