Financial Fragility, Heterogeneous Agents' Interaction, and Aggregate Dynamics
Mauro Gallegati, Domenico Delli Gatti, Gianfranco Giulioni, Antonio Palestrini


     According to the traditional views on economic fluctuations, large fluctuations arise because of some impulses propagate through the entire economy (the so-called Slutsky-Frish approach) or because of some endogenous properties of the system (the deterministic approach). Despite their different attitudes, and a different methodological approach, they share a common analytical tool: the "representative agent" hypothesis. In the last few years, this tool has been under the attack of a growing criticism, beginning with Kirman, 1992. As well known, very restrictive analytical (and empirically implausible) conditions are requested to have exact aggregation. Recent empirical works show that heterogeneity can explain aggregate dynamics: idiosyncratic shocks affect the rate of change of macroeconomic quantity (Davis et al. 1996, Davis and Haltinwanger 1996, Caballero et al. 1997). Theoretical research and applied investigation demonstrate that macroeconomics is not equivalent to the simply "summation and averaging" process of individual agents. Since the aggregate can be (and under very general conditions it is) different from the sum of its component, to analyse the behaviour of a representative agent as it were representing the whole economy is misleading. The failure of the law of the large numbers can be blamed for such a result. In fact, it holds only if non-linearities are not at work (Allen, 1982) or if non-market interactions are ruled out (Brock and Durlauf, 2000).
     One of the puzzles the equilibrium theory of fluctuations has to face is why large fluctuations arise without any large shocks. Idiosyncratic shocks are natural candidates for small shocks but we still need an amplification mechanism able to produce large movements. Unfortunately, if the system is linear, small shocks may produce only small effect. In this paper we analyse a model in which interaction and financial fragility are the source of non-linearities. As we said before, there is an immediate consequence regarding the law of large numbers whose validity does not hold any more. Moreover, when a system is non-linear, its dynamics can generate endogenous business cycles (in out context they are coupled with stochastic elements). The presence of non-linearities and interaction, and the presence of exogenous components, make the economic system to be a "complex" one (Rosser, 1999), in the sense that there is not a long run
definite dynamics.
    A not negligible branch of literature claims that, because of informational imperfections, financial factors play an important role in output fluctuation. In the "old" Keynesian literature, financial fragility is "systemic" (Minsky, 1982) and it can endogenously cause the business cycle. In the "new" Keynesian literature financial fragility represents an amplification mechanism in the spirit of the impulse-propagation approach (Bernanke and Gertler 1989, 1990; Greenwald and Stiglitz 1988, 1990, 1993; and Kiyotaki and Moore, 1997) where informational imperfections make the system deviate from the first best solution. The presence of informational imperfections involves a setting where agents are heterogeneous and evolve dynamically. Moreover, because of heterogeneity, agents can interact outside the market possibly identifying a self-reinforcing mechanism. In our modelling strategy both old and new Keynesian aspects of financial fragility are at work. Each firm sells its output at a random price, which can be assumed as an idiosyncratic shock. Rather than annulling, each other (the law of large number does not apply in our context), their effect on aggregate activity is amplified by the financial position of each firm. A fast growing research on empirical evidence shows that the firms' birth-death process drives employment fluctuations. Following this insight, Delli Gatti et al., 2001, consider the entry-exit process as the main factor affecting the distribution (and aggregate dynamics). Note that, since the amplification mechanism is a function of financial fragility, and this last modifies during the business cycle, our model predicts fluctuations to be "state dependent": the economy reacts differently to the same shock being the propagation mechanism sensitive to the state of financial robustness. This paper argues for two dynamical causal links. The first one runs from financial fragility to investment at a micro level: firm's investment spending is determined by the availability of internal finance. The other one identifies investment activity as the main determinant of internal finance. Differently from the first one, aggregate elements affect this link via interest rate changes. Moreover, attention should also be paid to  the cash flow-debt commitments ratio. Differently from the mainstream literature, this paper explicitly models firms' turnover and the behaviour of firms and banks and their interaction through the dynamics of the interest rate (whose changes are affected by a proxy of the financial fragility) using an agent based framework (an economist' version of SWARM we developed). We represent the economy as a continuum of square lattices; each one is filled with many firms and one bank. Firms sell a homogeneous good at a given stochastic price. This stochasticity is the source of uncertainty in the model, which is the ultimate cause of bankruptcies. When a firm goes bankrupt, it leaves its site. Empty sites are filled in a stochastic way; in particular the probability of a new-firm birth is higher the better credit conditions are (as proxies by the mean financial position of the zone). Again, financial factors affect firms' geographical and equity distribution, the turnover rate and, at the end, aggregate dynamics. (A similar approach, albeit in a different context, can be found in Campbell, (1997), who considers embodied technology instead of financial market imperfections. Emphasis on the relations between financial heterogeneity and industrial dynamics can be found in a series of recent papers by Cooley and Quadrini (1998,1999).) The paper is organised as follow. In sections 2 we describe the model: after having exposed the theory of the firm (2.1), we discuss the bank behaviour as stemming from agents' interactions (2.2). Section 3 presents the simulation's results, while the following section estimates the model by using UK longitudinal panel data between 1984-1999. Section 5 concludes.