Dynamic Aggregation in a Model with Heterogeneous Interacting

Agents in a Self-Evolving Network

C. Di Guilmi, M. Gallegati, S. Landini, and J. E. Stiglitz

Eastern Economic AssociationFebruary, 2011

Objectives

• To construct a model with Heteregeneous Interacting Agents (HIA) taking into account constraints/behavior resulting from asymmetric information

• Focusing on networks created endogenously as firms get linked with banks

• Examining the structure and stability of those networks—looking at macro-economic consequences

• Using both simulation models and analytic techniques

The Model

• Based on Greenwald-Stiglitz (1993) where asymmetries of information lead to constraints in financial markets so that– Firm borrowing is limited by net worth– Costly to raise additional equity– Random outcomes (prices received) of

individual firms lead to random evolution of firm net worth

Bank/firm relationship

• Banks are modeled as firms (as in Greenwald-Stiglitz (New Paradigm for Monetary Economics, 2003) whose willingness and ability to lend is affected by their net worth

• Each non-self-financing (NSF) firm borrows from a single bank

• Based on based offer received in a random search• Offers based on firm and bank’s economic situation• Net worth of bank evolves as firms repay loans and/or go

into default• When banks default, firms have to find new lender • If firm net worth becomes large enough, it becomes self-

financing (SF)

Linkages and networks

• Firms that are dependent on same bank are linked together – Failure of bank affects all of them– Forced to look for another bank—pay higher interest rate– Failure of one firm in the network worsens bank’s financial

position, forces bank to increase interest rate, increases probability of other firms in network going bankrupt

– Interdependence created through “supply” side (net worth, financial constraints). Future work will model further interdependence through demand side (demand for labor, profits, affected by evolution of net worth)

Results

• Model exhibits macro-fluctuations• Downturns associated with avalanches of failures of

banks– Consistent with, generalization of, Greenwald-Stiglitz (2003),

where credit networks let to avalanches of failures of firms– In downturns more firms become NSF

• Positive correlation of production with lagged debt suggests a mechanism that is reminiscent of Minksy’s Financial Instability Hypothesis– Firms take on debt to the point where probability of bankruptcy

goes up for weakest firms, setting off downturn, through tightening credit conditions, bank and firm defaults

Results

• Credit networks are “right skewed”—a few large banks connected with many firms– More concentrated in peak of cycle– Successful banks recruit more customers– Other research (Haldane) suggests that such

networks, while they may be more robust against small shocks, are more likely to experience large crashes (see also Stiglitz, 2010)

• Network structure and macro-fluctuations are endogenous

Analytic approach

• Simulation results are consistent with analytic approach

• Which focuses on the evolution of the degree of the network k—focusing on the probability of two firms having the same bank

• Taking into account the flow of firms into and out of the pool of borrowing (NSF) firms– Firms leave when they go bankrupt or when they

become so wealthy, that they no longer borrow– New firms enter as “borrowers” (NSF) firms or as SF

firms that lose capital

Analytic approach

• Can derive simple equation describing variations of the probability of observing N1 firms that are NSF– By splitting into two components– Drift– Aggregate fluctuations around the drift– Can derive asymptotic solutions– Analytic results show that the amplitude of the

fluctuations is dependent on the level of concentration in the system

• The more concentration, the higher the fluctuation in degree, and particularly, on the relative size of the biggest “clique”

Future Research

• Explore other avenues of interdependence (demand side)

• Refinements of credit markets—if banks and firms understood the structure, would they behave differently, e.g. make interest rates they charge depend on certain macro-economic variables that predict systemic risk, and would that lead to increased stability?– What are consequences of a few highly competitive

firms not acting fully rationally?• What regulations (restrictions on banks) would

enhance systemic stability?