Dynamic Aggregation in a Model with Heterogeneous Interacting Agents in a Self-Evolving Network

1. 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 Association February, 2011

2. 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

3. 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

4. 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)

5. 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)

6. 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

7. 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

8. 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

9. 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”

10. 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?