Research program
FINANCIAL FRAGILITY AND TECHNICAL PROGRESS WITH HETEROGENEOUS AGENTS AND SOCIAL INTERACTION: MODELS, SIMULATIONS, EMPIRICAL ANALYSIS
University Co-ordinator
Università Politecnica delle MARCHE -
ECONOMIA - ANCONA(AN)
Research Unit Leader
Mauro GALLEGATI
Description
The main objective of this research unit is to investigate the relationship between aggregate dynamics, financial fragility and the conditions under which economic scaling laws may arise. Work hypothesis (supported by work already begun in this direction by other members of this operative unit [6, 10, 11]) consists in investigating whether the interplay between random multiplicative growth and complex financial structures that link economic units can generate complex dynamics that reproduce the real ones. The project is divided in 2 parts: (i) the construction of an agent based model which illustrates the interaction between heterogeneous agents; (ii) the empirical investigation of stylized facts regarding industrial dynamic and the business cycle, and the econometric estimation of model simulation.In this project, we intend to model a prototype agent-based artificial economy (along the lines of [6,10,11]) in which heterogeneous agents (firms, banks and households) interact in a situation characterized by asymmetric information giving rise to complex dynamics and to emergent behaviors as a result of local or mean-field behavioral rules (see [1, 2, 4]). Mauro Gallegati will coordinate this research phase. Agents' heterogeneity will be modeled according to the balance sheets conditions (leverage ratios) and to their dimension (total capital, total labor employed and wealth). The model will be written at the level of the individual economic units (bottom-up approach) and aggregate them up [3]. By this way, we adopt a micro foundation process alternative to classic paradigm: we shall not use the representative agent hypothesis, but rather to interaction between heterogeneous agents, which has a bounded rationality and learn by the experience.Our artificial economy will be characterized by the coexistence of agents with different financial positions. A purpose of the research will be the individuation of the link between this kind of heterogeneity and the interaction investigating the evolution of it. The interaction (stocastic/deterministic e local/global) will be modelled among the 3 kinds of agents (goods, credit and deposit markets) e intra-agents (inter-bank market).In the goods market, from the firm’s side, it is easy to determine the aggregate investment. So, the demand modelization will require the microfoundation of the aggregate consumption function. As a first step we will assume that consumption is simply a share of the agent income (given by income and wealth), and then we will introduce an intertemporal utility function trying to identify the Euler equation in our setting.As regards deposits market, it seems plausible to imagine that consumer behavior for what concerns funds withdrawal, it depends on their income level ad on their wealth stock. If income distribution would be uniform, it would be easy for the banks to statistically foresee the aggregate demand for liquidity, since individual shocks tend to be compensate in aggregate. But it is well known that income distribution follows a Pareto-Levy distribution[15]. Under these conditions, individual shocks are not compensated in aggregate, thus making is difficult to forecast bank cash flow. The assets requirements of the banks would be greater than expected and the probability of creating a domino effect cannot be excluded. One of the distinctive character of financial accelerator model is the presence of a risk premium on sources of external finance. Investigation of this aspect will be carried out by explicitly modeling banks’ behavior, credit offer and the consequent endogenous dynamic of interest rate. Regarding this aspect, demand for credit will be derived from the profit maximization. In particular we determine firstly the investment decision; the demand for credit will be proportional to the investment being the part of investment that are not financed by internal funds. Because investment is negatively related to the interest rate even the demand for credit is a decreasing function of the rate of interest. From the demand side we use a simple rule. The bank determines the aggregate supply of credit using risk ratio, so the supply is a multiple of the banks equity base: the total amount of credit supply is shared among the firm according to their capital that is used as a proxy of collateral. In this way each firm have a vertical credit supply. Using credit supply and demand we can determine the equilibrium level of the rate of interest rate.The interaction between banks takes place mainly on interbanking deposit market. The introduction of such a market opens two direction of study. On the one hand, On the one hand we will have to model the firms’procedure of choosing a bank, highlighting how the relative weight of contacts with clients compared to the mere considerations of economic convenience inluences the distribution of financial positions and of the firms’ size and, through these, the aggregate result. On the other hand, the presence of many banks makes it possible to interact between banks and to investigate the effects, microeconomically, the two levels of interaction. The macroeconomic result would not depend only on firms’ financial position distribution, but also on that of the bank. The explicit modelization of interbanks market will allow us to verify the existence of domino effect due to liquidity crises of the banks and to evacuate their importance. The presence of interbanks links is usually considered as the origin of the sharp propagation of a single bank cris, but this link introduces also some stability factors. On this hand, our aim is to verify how, and in which measure, heterogeneity among banks affects stability or instability effects, originated by the introduction of interbanks market.In the analysis of our computational model we will use some specifical softwares and of skills of Giulioni and Russo. Some preliminary results will be obtained using Laboratory for Simulation Development software, which, trough simple functions, let us perform quickly the work. A deeper insight will be carried out by writing a code in C language which uses the very reliable SWARM libraries. The robustness of the results will be further tested by using recently released JAS (Java Agent-based Simulation library) which (besides to possess all SWARM characteristics) allow us to easily and quickly use genetic algorithms, classificatory systems and neural networks. Even if the analysis of an agent based model is mainly done by computer simulations we want to investigate if some analytical conclusion can be drawn. Modeling the statistical features of markets, mainly using a framework derived from statistical physics, will help in understanding: (i) the relationship between the financial position of firms and the market concentration in order to explain situations when small perturbations can dramatically influence the behavior of large-scale, generally robust and reliable economic systems; (ii) how can arise time joint distribution conditions sufficient to produce power-law type unconditional marginal distribution of macro-variables [2].For what regards the second object of the research (which involves T.Terasvirta, C.Di Guilmi and Marco Gallegati), a particular attention will be pay to business cycle analysis (cycle of the financial fragility ratio, defined as the ratio between equity base and total capital employed; steepness, asymmetry, variability e scaling); to firm sizes distribution and to Laplace distributed growth rates. The empirical analysis will study both the unconditional and conditional (on financial position variables) distribution of European firms. For our purposes we need a dataset that collect information on firms' industrial dynamics (entry, exit, bankruptcies) and on firms' financial position; these information would cover companies of all the EU member states and, at least, the most important emerging countries. A data source, which meets these two basic requirements reasonably well, is the Amadeus database. In its most concise version, it contains detailed reports on the 200.000 largest European companies. Each company report contains descriptive information and up to 10 years of historical consolidated and unconsolidated annual accounts, presented in a standard format of 44 lines and 20 ratios that cover the major items of profit and loss and balance sheet accounts. The data are compiled from national firm-level sources.The first part of the work is the construction of the unbalanced panel needed for the analysis described above (a number of selection criteria will be applied to the initial sample of firms to avoid the outliers problem) and second the analysis will be based on dynamic panel data estimation of selected company account dataset matched with firms' industrial dynamics to analyze the financial-real part of the economic system relationship when conditioning on firm’s size, business cycles and to investigate the existence of regularities in joint and marginal distributions. Then tests for the goodness of fit for a power law distribution will be conducted to verify the property of scale invariance, which states that, independently of the size of an event, say C, the proportion of events larger than C responds to an invariant scaling law accordingly to the slope coefficient. Often, when applied to real world data, Zipf plots present a downward curvature, so that linear fitting in log-log space tends to overestimate the tails of the distribution. These departures from a scale invariant distribution may appear because of finite size effect, or due to scaling breakdown, meaning that the events are actually originated by different probabilistic laws. In economics, for example, a recent work [14] showed that duration distribution of recessions displayed a breakdown of scaling due to different behaviors of agents in the cases of severe or mild downturns. The alternative possibility is that the lack of fit in the tails could signal the need for exploring other probability distributions exhibiting linearity over their central range and concavity in the tails, when plotted in a log-log space [7, 8]. From this viewpoint, one of the most flexible and general distribution law is the Weibull distribution. Its form depends on two or three parameters, according to the kind of probability density functions adopted. Among these, the shape parameters reveals, if equal to 1, the usual exponential distribution and the distribution will become a stretched exponential in the case the parameter is included in the open interval (0,1). A second aspect regards the verifying whether firms distributions, conditioned and not conditioned, are subject to changes with time and how they are modified by contingent events. In other words, we want to test if the straight line which fits data on log-log plane (dimension-frequency, extinctions-frequency, etc…) is subject to translation and which are the causes of these distributions movements (as well as co movements between countries). The next problem will be if, given a determinated power law, points movements (groups of firms with a certain dimension) along the line are or not able to origin macroeconomic effects and to investigate the nature of such effects. In terms of size distribution of firms, this means that we want to study the effects of the disappearing of a remarkable number of firms against the entry of a great one. These consideration lead us to consider another interesting point on which we will duel on our research: the entry and exit processes. The high volatility of individual phenomena, makes the extremely uncertain the firm's life. In every period it is possible to observe a high number of firms exiting the market. Our model is particularly friendly to introduce this feature because the burder of debt make it possible the firm's bankrupt. This open the possibility to analyze the relation between the number of bankrupt and the aggregate variable during the business cycle phase. We want to point our attention to the empirical analysis to establish the exit process characteristics. In this investigation we will use the Amadeus dataset the reason of the disappearance of the firm from the sample allowing to distinguish among genuine bankruptcy, merger or acquisition. Our goal is again to verify if the statistical distribution of the number of bankruptcies in distributed in a not normal way as some recent works [5, 9] seem to state. Further we want to investigate using defaulted firms' balance sheet the relevance of the financial factor in the firms' shutdown.In our model the financial position of the firms plays a central role. From this variable depends the probability of default. We think this variable is playing an important role even in the firm's development and growth. So we want to investigate the relation between the financial position and the growth rate of the firm. We are clearly on the Gibrat's law field. We want in particular to see if Gibrat's law holds once we condition the growth rate to the financial fragility.Finally, an important part of the project will be the econometric analysis of model simulations. Since we know the data generation process we can connect both the statistical features observed in the simulations (both conditional and unconditional) and the results of dynamic panel data estimation to the economic features of the model. Furthermore, the econometric results of the artificial economy will give us a deep contribution in interpreting the econometric analysis of the Amadeus dataset under the hypothesis leading the model apart from data truncation or censuring that may handled with the recent social interaction econometric literature [4]. This part of the project regarding the microsimulations will be performed together with the University of Pisa [1] Aoki, M. (1996), New Approaches to Macroeconomic Modelling, Cambridge University Press, Cambridge.[2] Aoki. M. (2002), Modelling Aggregate Behaviour and Fluctuation in Economics, Cambridge University Press, Cambridge.[3] Axtell, R., Epstein, J. (1996), Growing Artificial Societies. Social Science From the Bottom Up, Brookings Institution Press MIT Press.[4] Brock W.A. and Durlauf S. (2000), Interaction-Based Models, In J. Heckman and E. Leamer, editors, Handbook of Econometrics (Vol. 5). North-Holland, Amsterdam.[5] Cook, W., Ormerod, P. (2002), Power Law Distribution of the Frequency of Demises of U.S. Firms, Volterra Consulting.[6] Delli Gatti D., Di Guilmi C., Gaffeo E., Gallegati M., Giulioni G. and Palestrini A. (2004), A New Approach to Business Fluctuations, forthcoming, Journal of Economic Behavior and Organization. [7] Di Guilmi, C., Gaffeo, E., Gallegati, M. (2003), Power Law Scaling in the World Income Distribution, Economic Bullettin.[8] Di Guilmi, C., Gaffeo, E., Gallegati, M. (2003), Empirical Results on the Size Distribution of Business Cycle Phases, Physica A.[9] Di Guilmi, C., Gallegati, M., Ormerod, P. (2003), Scaling Invariant Distributions of Firms’ Exit in OECD countries, Physica A.[10] Gallegati, M., Giulioni, G., Kichiji N. (2003), Complex Dynamics and Financial Fragility in an Agent Based Model, Complex Systems. [11] Gallegati, M., Delli Gatti, D., Gaffeo E., Palestrini A., Giulioni G. (2004) Aggregate Fluctuations and Financial Fragility with Heterogeneus Interacting Agents, Macroeconomic Dynamics.[12] Gallegati M., Kirman, A. (1999) Beyond the Representative Agent, Elgar.[13] Greenwald, B.C., Stiglitz J.E. (1993), Financial Markets Imperfections and the Business Cycle, Quarterly Journal of Economics. [14] Ormerod. P., Mounfield, C. (2001), Power Law Distribution of the Duration and Magnitude of Recessions in Capitalist Economies, Physica A.[15] Pareto, V. (1896), Course d’Economie Politique, Geneva.
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