Dr Corrado Di Guilmi

Di Guilmi, C. 2008, The Generation of Business Fluctuations: Financial Fragility and Mean-Field Interactions, 1st, Peter Lang, USA.
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The limits imposed on economic modeling by the representative agent hypothesis have prevented dynamic analysis from fully exploring the links between the micro and macro level of the economic system. This book presents developments and applications of the innovative techniques of dynamic stochastic aggregation, first proposed by Masanao Aoki, through an implementation in a New Keynesian financial fragility framework. The introduction in macroeconomics of statistical mechanics tools, such as mean-field interaction, statistical entropy and master equation, constitutes a step toward a new definition of microfoundation and allows an integrated modeling of the relationships between micro financial variables and aggregate indicators.

Chiarella, C. & Di Guilmi, C. 2013, 'A reconsideration of the formal Minskyan analysis: Microfoundations, endogenous money and the public sector' in Gian Italo Bischi, Carl Chiarella and Iryna Sushko (eds), Global analysis of dynamic models in economics and finance: Essays in honour of Laura Gardini, Springer, Germany, pp. 63-81.

Di Guilmi, C., Gallegati, M. & Landini, S. 2010, 'Financial fragility, mean-field interaction and macroeconomic dynamics: A stochastic model' in Salvadori, N (eds), Institutional and Social Dynamics of Growth and Distribution, Edward Elgar, UK, pp. 322-350.
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In recent decades, a considerable stream of research, following the complexity approach (Rosser, 2004), has developed a series of models that import concepts and tools from hard sciences to economics. They represent an attempt to identify an alternative framework to the representative agent hypothesis and to its underlying simplified solution to the aggregation problem (Kirman, 1992). Theoretical research has moved in two main directions: first, the development of agent-based models, solved by means of computer simulations (Axtell et al., 1996; Axelrod, 1997); second, formulations of stochastic frameworks for the aggregation of micro-variables (Aoki, 1996, 2002; Aoki and Yoshikawa, 2006).

Delli Gatti, D., Di Guilmi, C., Gaffeo, E., Gallegati, M., Giulioni, G. & Palestrini, A. 2005, 'Firms' size distribution and growth rates as determinants of business fluctuations' in A. Kirman and M. Salzano (eds), Economics: Complex Windows, Springer, US, pp. 181-186.
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Chiarella, C. & Di Guilmi, C. 2012, 'The fiscal cost of financial instalbility', Studies in NonLinear Dynamics and Econometrics, vol. 16, no. 4, pp. 1-27.
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This paper presents an agent based model that investigates the possible outcomes of different fiscal and regulatory policies in a financially fragile economy. We analyse the consequences of the attempt by the government to counteract a downturn when it ignores the debt dynamics as modelled by Fisher and Minsky. In particular, we formulate an educated guess about the burden that the government and the taxpayer must bear when a bubble bursts, and its relationship with the extent of government intervention and the taxation system. We also evaluate the outcomes of possible alternatives or complementary regulatory policies. We model four different scenarios treating separately a tax on profits and a tax on private wealth and, for both of them, we specify two cases depending on whether the financial system is able to autonomously generate liquidity. Therefore, we can assess the effect of endogenous money and endogenous credit on the different stabilization policies.

Gaffeo, E., Di Guilmi, C., Gallegati, M. & Russo, A. 2012, 'On The Mean/variance Relationship Of The Firm Size Distribution: Evidence And Some Theory', Ecological Complexity, vol. 11, no. NA, pp. 109-117.
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Firm-level data fora small sample of European countries are used to provide evidence of a positive linear relationship between the mean and the variance of firms' size at a sectoral level, an empirical regularity known in mathematical biology and ecology

Chiarella, C. & Di Guilmi, C. 2011, 'The financial instability hypothesis: A stochastic microfoundation framework', Journal of Economic Dynamics and Control, vol. 35, no. 8, pp. 1151-1171.
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This paperexaminesthedynamicsoffinancialdistressandinparticularthemechanism of transmissionofshocksfromthefinancialsectortotherealeconomy.Theanalysisis performedbyrepresentingthelinkagesbetweenmicroeconomicfinancialvariablesand the aggregateperformanceoftheeconomybymeansofamicrofoundedmodelwith firms thathaveheterogeneouscapitalstructures.Themodelissolvedbothnumerically and analytically,bymeansofastochasticapproximationthatisabletoreplicatequite well thenumericalsolution.Thesemethodologies,byovercomingtherestrictions imposedbythetraditionalmicrofoundedapproach,enableustoprovidesomeinsights into thestabilizationpolicieswhichmaybeeffectiveinafinanciallyfragilesystem.

Delli Gatti, D., Di Guilmi, C., Gallegati, M., Gaffeo, E., Giulioni, G. & Palestrini, A. 2008, 'Scaling laws in the macroeconomy', Advances in Complex Systems, vol. 11, no. 1, pp. 131-138.
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The practice of detecting power laws and scaling behaviors in economics and finance has gained momentum in the last few years, due to the increased use of concepts and methods first developed in statistical physics. Some disappointment has emerged in the economic profession, however, as regards the models proposed so far to theoretically explain these phenomena. In this paper we aim to address this criticism, showing that scaling behaviors can naturally emerge in a multiagent system with optimizing interacting units characterized by financial fragility

Di Guilmi, C., Clementi, F., Di Matteo, T. & Gallegati, M. 2008, 'Social networks and labor productivity in Europe: An empirical investigation', Journal of Economic Interaction and Coordination, vol. 3, no. 1, pp. 43-57.
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This paper uses firm-level data recorded in the Amadeus database to investigate the distribution of labour productivity in different European countries. We find that the upper tail of the empirical productivity distributions follows a decaying power-law, whose exponent ? is obtained by a semi-parametric estimation technique recently developed by Clementi et al. [Physica A 370(1):49+53, 2006]. The emergence of +fat tails+ in productivity distribution has already been detected in Di Matteo et al. [Eur Phys J B 47(3):459+466, 2005] and explained by means of a model of social network. Here we show that this model is tested on a broader sample of countries having different patterns of social network structure. These different social attitudes, measured using a social capital indicator, reflect in the power-law exponent estimates, verifying in this way the existence of linkages among firms+ productivity performance and social network.

Delli Gatti, D., Di Guilmi, C., Gallegati, M. & Giulioni, G. 2007, 'Financial Fragility, Industrial Dynamics and Business Fluctuations in an Agent Based Model', Macroeconomic Dynamics, vol. 11, no. S1, pp. 62-79.
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n the 1990s a large body of literature--sometimes referred to as the financial accelerator hypothesis, broad credit view, or balance sheet channel--focused on the role of financial factors in business fluctuations and in the transmission of monetary shocks [Bernanke and Gertler (1989, 1990, 1995), Bernanke et al. (1996, 1999), Greenwald and Stiglitz (1988, 1990, 1993), Stiglitz and Greenwald (2003)]. Insightful new additions to the literature, albeit along different lines, have been provided by Kiyotaki and Moore (1997, 2002) and Cooley and Quadrini (2001). In these models, in principle, agents are heterogeneous, and sometimes it is also recognized that heterogeneity is a necessary ingredient of important business cycle features (such as composition effects), but the nature and consequences of heterogeneity are not thoroughly explored. At a certain point of the analysis, the representative agent pops up and heterogeneity gets lost or is simply neglected. The temptation to keep the analysis simple by resorting to the representative agent is understandable. After all, the representative agent framework has been one of the most successful tools in economics [Hartley (1997); Stoker (1993)] and is still the cornerstone of standard macroeconomics. This modeling strategy, however, is justified if heterogeneity is temporary, that is, if the population of different households/firms converges over time to a stationary distribution in which agents are identical. This condition is generally not fulfilled empirically. In real economies heterogeneity is not bound to disappear and the evolution over time of the distribution of heterogeneous agents affects the dynamics of the macrovariables. If macroeconomic modeling relies on the representative agent, therefore, the analysis of business fluctuations and of the transmission mechanism of monetary policy will be too simple and sometimes even simplistic.

Delli Gatti, D., Di Guilmi, C., Gaffeo, E., Giulioni, G., Gallegati, M. & Palestrini, A. 2005, 'A New Approach to Business Fluctuations: Heterogeneous Interacting Agents, Scaling Laws and Financial Fragility', Journal of Economic Behavior and Organization, vol. 56, no. 4, pp. 489-512.
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In this paper, we discuss a scaling approach to business fluctuations. Our starting point consists in recognizing that concepts and methods derived from physics have allowed economists to (re)discover a set of stylized facts which have to be satisfactorily accounted for in their models. Standard macroeconomics, based on a reductionist approach centered on the representative agent, is definitely badly equipped for this task. On the contrary, we show that a simple financial fragility agent-based model, based on complex interactions of heterogeneous agents, is able to replicate a large number of scaling type stylized facts with a remarkable high degree of statistical precision.

Di Guilmi, C., Gaffeo, E., Gallegati, M. & Palestrini, A. 2005, 'International evidence on business cycle magnitude dependence', International Journal of Applied Econometrics and Quantitative Studies, vol. 2, no. 1, pp. 5-16.
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Are expansions and recessions more likely to end as their magnitude increases? In this paper we apply parametric hazard models to investigate this issue in a sample of 16 countries from 1881 to 2000. For the total sample we find evidence of positive magnitude dependence for recessions, while for expansions we are not able to reject the null of magnitude independence. This last result is likely due to a structural change in the mechanism guiding expansions before and after the second World War. In particular, upturns show negative magnitude dependence in the post-World War II sub-sample, meaning that in this period expansions become less likely to end as their magnitude increases.

Delli Gatti, D., Di Guilmi, C., Gaffeo, E. & Gallegati, M. 2004, 'Bankruptcy as an Exit Mechanism for Systems with a Variable Number of Components', Physica A: Statistical Mechanics and its Applications, vol. 344, no. 1-2, pp. 8-13.
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Dynamical systems with components whose sizes evolve according to multiplicative stochastic rules have been recently combined with entry and exit processes. We show that the assumptions usually made in modeling exits are at odds with the available evidence. We discuss a recently proposed macroeconomic model with random multiplicative shocks and a mechanism for exit based on bankruptcy, which displays several observed stylized facts for firms' dynamics, like power law distributions for firms' sizes and Laplace distributions for firms' growth rates

Delli Gatti, D., Di Guilmi, C., Gaffeo, E., Gallegati, M., Giulioni, G. & Palestrini, A. 2004, 'Business Cycle Fluctuations and Firms - Size Distribution Dynamics', Advances in Complex Systems, vol. 7, no. 2, pp. 223-240.
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Power law behavior is an emerging property of many economic models. In this paper we emphasize the fact that power law distributions are persistent but not time invariant. In fact, the scale and shape of the firms' size distribution fluctuate over time. In particular, on a log+log space, both the intercept and the slope of the power law distribution of firms' size change over the cycle: during expansions (recessions) the straight line representing the distribution shifts up and becomes less steep (steeper). We show that the empirical distributions generated by simulations of the model presented in Ref. 11 mimic real empirical distributions remarkably well.

Di Guilmi, C., Gaffeo, E. & Gallegati, M. 2004, 'Empirical Results on the Size Distribution of Business Cycle Phases', Physica A: Statistical Mechanics and its Applications, vol. 333, pp. 325-334.
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We study the size distribution of business cycles phases, that is expansions and contractions, for a sample of 16 industrialized countries over 120 years. We find that the best-fitting distribution for both expansions and contractions is Weibull, meaning that business cycles possess a characteristic scale. Furthermore, we discuss how parameters+ estimates can be used to make inference on the probability a typical episode ends, that is on what economists call turning points.

Di Guilmi, C., Gallegati, M. & Ormerod, P. 2004, 'Scaling Invariant Distributions of Firms' Exits in OECD Countries', Physica A: Statistical Mechanics and its Applications, vol. 334, no. 1-2, pp. 267-273.
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Self-similar models are largely used to describe the extinction rate of biological species. In this paper we analyse the extinction rate of firms in eight OECD countries. Firms are classified by industrial sectors and sizes. We find that while a power-law distribution with exponent close to 2 fits the extinction rate very well by sector, a Weibull distribution is more appropriate if one analyses the firms+ size.

Fujiwara, Y., Di Guilmi, C., Aoyama, H., Gallegati, M. & Souma, W. 2004, 'Do Pareto-Zipf and Gibrat Law Hold True? An Analysis with European Firms', Physica A: Statistical Mechanics and its Applications, vol. 335, no. 1-2, pp. 197-216.
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By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto+Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find that detailed balance holds in the large-size region for periods we investigated; the empirical probability for a firm to change its size from a value to another is statistically the same as that for its reverse process. We prove several relationships among Pareto+Zipf's law, Gibrat's law and the condition of detailed balance. As a consequence, we show that the distribution of growth rate possesses a non-trivial relation between the positive side of the distribution and the negative side, through the value of Pareto index, as is confirmed empirically.

Fujiwara, Y., Aoyama, H., Di Guilmi, C., Souma, W. & Gallegati, M. 2004, 'Gibrat and Pareto-Zipf revisited with European firms', Physica A: Statistical Mechanics and its Applications, vol. 344, no. 1-2, pp. 112-116.
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A firms growth and failure are the two sides of the same coin. This paper reports new phenomenological findings for firm size distribution and growth, and bankruptcy. This paper is based on [Y. Fujiwara et al., Physica A 335 (2004) 197] and on [Y. Fujiwara, Physica A 337 (2004) 219]. See also these proceedings for kinematical relationship between Pareto´+¢Zipf and Gibrat's laws.

Di Guilmi, C., Gaffeo, E. & Gallegati, M. 2003, 'Power Law Scaling in World Income Distribution', Economics Bulletin, vol. 15, no. 6, pp. 1-7.
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We show that over the period 1960-1997, the range comprised between the 30th and the 85th percentiles of the world income distribution expressed in terms of GDP per capita invariably scales down as a Pareto distribution. Furthermore, the time path of the power law exponent displays a negatively sloped trend. Our findings suggest that the cross-country average growth process appears to be scale invariant but for countries in the tails of the world income distribution, and that the relative volatility of smaller countries' growth processes have increased over time.