Mathematical models for credit dynamics in macroeconomics

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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.