The ME introduced in Chapter 3 is applied to a financial fragility ABM with heterogeneous and interacting firms. The ABM is considered as the DGP of macro-variables: by using the ME technique, the impact of micro-variables is analytically assessed by means of an inferential method. The whole dynamics of the economy is described by a system of dynamic equations that well mimics the evolution of a numerical simulation with the same features.

The identification of the ME requires the specification of the transition rates, which are obtained from the ABM by following the lines developed in Appendix C. The solution of the ME provides the solution to the ABM-DGP and requires some methodological tools that are presented in Appendixes B and C.

This chapter has the following structure: Section 4.1 briefly introduces the chapter and frames the contribution within the existing literature on financial fragility; Section 4.2 presents the behavioural assumptions of the ABM; Section 4.3 details the inference process through which the ME provides an analytical representation of the ABM; Section 4.4 illustrates the results of the Monte Carlo simulations and Section 4.5 concludes.

Introduction

This chapter develops a model of financial fragility along the lines of Delli Gatti et al. (2010, 2012); Di Guilmi (2008); Di Guilmi et al. (2010). The degree of financial soundness of firms is modelled à la Greenwald and Stiglitz (1993) (GS henceforth) and it is assumed as a clustering criterion to qualify firms on a state space (see Chapter 2) of financial states.

Algebraic aggregation of the simulation outcomes provides the state of the world, that is, the macrostate of the system. Analytic inference is specified by means of the ME technique.

The specification of the ME requires modelling the transition rates, which implement the mean-field interaction among subsystems of robust (RB) and fragile (FR) firms. Transition rates refer to the switching of firms between the two financial states. The solution to the ME yields the dynamic estimator of the expected trend of the number of firms that are RB and FR together with endogenous fluctuations. Since the evolution of the macroeconomy depends on the proportion of firms in the two conditions, the solution will also identify the trend and cycle components of the macroeconomic time-series. It is worth remarking that these aggregate functional forms will embody the transition rates and, consequently, firm-level variables.