Leonardo Bargigli

Statistical ensembles for money and debt

We build a statistical ensemble representation of two economic models describing respectively, in simplified terms, a payment system and a credit market. To this purpose we adopt the Boltzmann–Gibbs distribution where the role of the Hamiltonian is taken by the total money supply (i.e. including money created from debt) of a set of interacting economic agents. As a result, we can read the main thermodynamic quantities in terms of monetary ones. In particular, we define for the credit market model a work term which is related to the impact of monetary policy on credit creation. Furthermore, with our formalism we recover and extend some results concerning the temperature of an economic system, previously presented in the literature by considering only the monetary base as a conserved quantity. Finally, we study the statistical ensemble for the Pareto distribution.

Econometric Methods for Agent-Based Models

Abstract In this chapter, I review the recent developments of the Agent-Based literature with respect to empirical estimation. The methods employed in the literature include Bayesian estimation, simulated minimum distance, simulated maximum likelihood. In the second part, I focus on two distinct problems. The first one is parameter calibration. This approach is indeed useful since Agent-Based Models (ABMs) have typically a large parameter space. The second one regards the possibility of replacing ABMs with a metamodel, that is, a statistical model linking the value of parameters to a set of moments of the simulated data. The metamodels provide the conditional expectation of the moments, which might be used for a variety of purposes, including estimation. In particular, I focus on sensitivity analysis and on the problem of parameter identification.

Interbank Markets and Multiplex Networks: Centrality Measures and Statistical Null Models

The interbank market is considered one of the most important channels of financial contagion. Its network representation, where banks and claims/obligations are represented by nodes and links (respectively), has received a lot of attention in the recent theoretical and empirical literature, for assessing systemic risk and identifying systemically important financial institutions. Different types of links, for example in terms of maturity and collateralization of the claim/obligation, can be established between financial institutions. Therefore a natural representation of the interbank structure which takes into account more features of the market, is a multiplex, where each layer is associated with a type of link. In this paper we review the empirical structure of the multiplex and the theoretical consequences of this representation. We also investigate the betweenness and eigenvector centrality of a bank in the network, comparing its centrality properties across different layers and with Maximum Entropy null models.

A Simple Model of Business Fluctuations with Heterogeneous Interacting Agents and Credit Networks

In what follows we firstly describe and then implement and simulate a very simple model, that is a simplified version of Riccetti et al. (2013), by using R. In the original paper, a multitude of heterogeneous firms and banks interact in the credit market. Firms want to produce and sell a homogeneous commodity in the goods market and, in order to finance production, they need credit from banks. Firms look at a random subset of potential partners (due to imperfect information) and then choose the most convenient bank (i.e. the bank charging the lowest interest rate); as a consequence, an endogenous network of credit interlinkages evolves over time. The model shows the emergence of business fluctuations and highlights both the role of financial fragility and network structure in shaping economic dynamics.

A Statistical Test of Walrasian Equilibrium by Means of Complex Networks Theory

We represent an exchange economy in terms of statistical ensembles for complex networks by introducing the concept of market configuration. This is defined as a sequence of nonnegative discrete random variables

Job insecurity and successful re-employment: Examples from Italy

\{w_{ij}\}

The Multiplex Structure of Interbank Networks

{wij} describing the flow of a given commodity from agent i to agent j. This sequence can be arranged in a nonnegative matrix W which we can regard as the representation of a weighted and directed network or digraph G. Our main result consists in showing that general equilibrium theory imposes highly restrictive conditions upon market configurations, which are in most cases not fulfilled by real markets. An explicit example with reference to the e-MID interbank credit market is provided.

Random digraphs with given expected degree sequences: A model for economic networks

Real markets can be naturally represented as networks, and they share with other social networks the fundamental property of sparsity, whereby agents are connected by l = O (n) relationships. The exponential networks model introduced by Park and Newman can be extended in order to deal with this property. When compared with alternative statistical models of a given real network, this extended model provides a better statistical justification for the observed network values. Consequently, it provides more reliable maximum entropy estimates of partially known networks than previously known ME techniques.