Tipping Points in Macroeconomic Agent-Based Models

The aim of this work is to explore the possible types of phenomena that simple macroeconomic Agent-Based models (ABM) can reproduce. We propose a methodology, inspired by statistical physics, that characterizes a model through its "phase diagram'' in the space of parameters. Our first motivation is to understand the large macro-economic fluctuations observed in the "Mark I'' ABM devised by D. Delli Gatti and collaborators. In this regard, our major finding is the generic existence of a phase transition between a "good economy'' where unemployment is low, and a "bad economy'' where unemployment is high. We then introduce a simpler framework that allows us to show that this transition is robust against many modifications of the model, and is generically induced by an asymmetry between the rate of hiring and the rate of firing of the firms. The unemployment level remains small until a tipping point, beyond which the economy suddenly collapses. If the parameters are such that the system is close to this transition, any small fluctuation is amplified as the system jumps between the two equilibria. We have explored several natural extensions of the model. One is to introduce a bankruptcy threshold, limiting the firms maximum level of debt-to-sales ratio. This leads to a rich phase diagram with, in particular, a region where acute endogenous crises occur, during which the unemployment rate shoots up before the economy can recover. We also introduce simple wage policies. This leads to inflation (in the "good'' phase) or deflation (in the "bad'' phase), but leaves the overall phase diagram of the model essentially unchanged. We have also explored the effect of simple monetary policies that attempt to contain rising unemployment and defang crises. We end the paper with general comments on the usefulness of ABMs to model macroeconomic phenomena, in particular in view of the time needed to reach a steady state that raises the issue of ergodicity in these models