Dynamic aggregation in a model with heterogeneous interacting agents in a self evolving network
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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. Objectives.

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

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Dynamic aggregation in a model with heterogeneous interacting agents in a self evolving network

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


Objectives

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

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

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

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

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


Results1

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

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 approach1

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

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?


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