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Resilience, Leverage and Credit Network in an Agent Based Model - - PowerPoint PPT Presentation

Aug 26, 2023 121 likes •364 views

Resilience, Leverage and Credit Network in an Agent Based Model Ermanno Catullo, Mauro Gallegati and Antonio Palestrini DiSES, Universit Politecnica delle Marche WEHIA Winter meeting Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19,

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SLIDE 1

Resilience, Leverage and Credit Network in an Agent Based Model

Ermanno Catullo, Mauro Gallegati and Antonio Palestrini

DiSES, Universit Politecnica delle Marche

WEHIA Winter meeting

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 1 / 23

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SLIDE 2

Cats in St.Louis, 1987

Should we take seriously the ABM approach?

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 2 / 23

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SLIDE 3

Microfoundations

Microfoundations in Macroeconomic Models

Microfoundation

Mainstream ABM RA Models DSGE mark I HNIA DSGE mark II ACE T esfatsion Judd, 2006 Gintis 2007 ASHIA Statistical physics Foley 1994, Aoki 1996 Learning and strategic behaviours Landini, Stiglitz et al 2012 Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 3 / 23

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SLIDE 4

Vulnerability of Leveraged and Interlinked Credit Market: an Agent Based Model

Aims

  • Resilience of credit network
  • Dynamics of output and networks via balance sheet (leverage)
  • Early warning indicator

Methodology Agent based modeling:

  • Bottom-up methodology
  • ABM within a network: Agents as nodes, links as financial relationship
  • Interaction of many HA, which produces a statistical equilibrium
  • Emergence: models with HIA where the resulting aggregate dynamics

and empirical regularities are not deducible from individual behavior

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 4 / 23

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SLIDE 5

The Drama

Heterogeneous firms and banks

  • Firms and banks have a leverage target, they choose among a limited

set of leverage levels (different level of risk)

  • Firms are hit by idiosyncratic shocks
  • The number of banks and firms is fixed, there are (endogenous) links

(credit) between them The credit network

  • Both firms and banks can have multiple credit relationships
  • Two period loans contracts
  • Banks credit supply and is constrained by minimum net-worth

requirements

  • The credit network evolve endogenously following individual demand

and supply of credit dynamics

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 5 / 23

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SLIDE 6

The Model

Credit relationships depend on leverage and on market

  • The network evolves through credit leverage’s conditions

Credit amounts depend on learning

  • Basic reinforcement learning algorithm from Tesfatsion 2005: choices

derive from past experience but with also small probability of random exploration of the action space

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 6 / 23

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SLIDE 7

The Model

Firms Firms production function: capital employed is given by equities (Eit) and loans (Lit): Yit = ρKit, (1) where Yit depend on πit ´ a la Hommes 2012, Kit = Lit + Eit The interest on loans depends on the target leverage (Γit): Γit = (Litd + 1 φLi(t−1))/Eit (2) rit = αΓit + r (3) leading to a trade off between profit opportunities and loans costs in presence of differences among effective and targeted leverage levels (r is the discount rate)

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 7 / 23

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SLIDE 8

The model

Firms Profits depend on the difference between idiosyncratic revenues and debt commitments: πit = uitYit − rEit − ritLit − 1 φri(t−1)Li(t−1) − F (4) (5) where F are fixed costs, uit is a normally distributed idiosyncratic shock on profit. Individual leverage increases production but aggregate leverage depresses it: leverage acts as an externality.

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 8 / 23

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SLIDE 9

The Model

Banks Credit supply Lzts = Ezt ηzt −

  • Iz(t−1)

1 φLiz(t−1) (6) ηzt is updated through reinforcement learning (Tesfatsion 2005). Banks’ profit is given by the sum of interest on lending minus interest payments on borrowing minus bad debts πzt =

  • Izt

riztLizt +

  • Iz(t−1)

riz(t−1)Liz(t−1)−BDzt −BDz(t−1)−r(Ezt +Dzt)−F (7) where Izt is the set of borrowing firms

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 9 / 23

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SLIDE 10

Japanese credit network

credit market dataset

  • a survey of firms and banks

quoted in the Japanese stock-exchange markets

  • reporting annual data from 1980

to 2012

  • on average 226.18 banks and

2218 firms

year 2000

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 10 / 23

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SLIDE 11

Network Analysis

How to measure network resilience

  • Banks loans structure and leverage determine shocks diffusion and

amplification

  • According to Palestrini (2013) ‘Deriving Aggregate Network Effects in

Macroeconomic Models’, it is possible to infer the system effects of idiosyncratic shocks from weighted outdegrees

  • The adjusted degree (adeg) is the mean of the banks normalized

degree times the total amount of loan they provide times leverage (adeg = deg· loan· lev)

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 11 / 23

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SLIDE 12

Credit networks

Empirical and simulated data

  • Output growth standard

deviation is similar

  • Growth rate is autocorrelated
  • The adjusted degree (adeg)

growth anticipates output growth

  • The adjusted degree growth is

positively correlated to output growth in simulations

1 2 3 4 5 −0.4 0.0 0.4 0.8 Lag ACF

acf output

1 2 3 4 5 −0.4 0.0 0.4 0.8

acf output

lag ccf

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 12 / 23

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SLIDE 13

Credit networks

Empirical and simulated data

  • Output growth is Laplacian
  • Firms’ and Banks’ size distribution has fat tails
  • The aggregate leverage anticipates downturn, while recovery comes

after deleveraging

  • Inequality in come distribution is counter-cyclical
  • Expansions and recessions are asymmetric (duration, phases,

steepness end deepness)

  • Connectivity is pro-cyclical

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 13 / 23

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SLIDE 14

Calibration: IRFs

VAR with one lag log differences variables: output (out), bank leverage (lev) and the mean adjusted degree (adeg) IRF on empirical data

2 4 6 8 10 0.00 0.02 0.04 0.06 lag
  • ut−>out
2 4 6 8 10 −0.04 0.00 0.02 0.04 lag
  • ut−>lev
2 4 6 8 10 −0.05 0.00 0.05 0.10 lag
  • ut−>adeg
2 4 6 8 10 −0.04 −0.02 0.00 0.01 lag lev−>out 2 4 6 8 10 0.00 0.05 0.10 0.15 lag lev−>lev 2 4 6 8 10 −0.10 0.00 0.10 0.20 lag lev−>adeg 2 4 6 8 10 −0.015 −0.005 0.005 lag adeg−>out 2 4 6 8 10 −0.02 −0.01 0.00 0.01 lag adeg−>lev 2 4 6 8 10 −0.05 0.00 0.05 0.10 lag adeg−>adeg

IRFs on simulated data

2 4 6 8 10 0.00 0.02 0.04 0.06 lag
  • ut−>out
2 4 6 8 10 −0.005 0.005 0.015 0.025 lag
  • ut−>lev
2 4 6 8 10 0.00 0.05 0.10 0.15 lag
  • ut−>adeg
2 4 6 8 10 −0.020 −0.010 0.000 lag lev−>out 2 4 6 8 10 −0.01 0.01 0.03 lag lev−>lev 2 4 6 8 10 −0.10 0.00 0.10 lag lev−>adeg 2 4 6 8 10 −0.020 −0.010 0.000 lag adeg−>out 2 4 6 8 10 −0.010 −0.005 0.000 0.005 lag adeg−>lev 2 4 6 8 10 0.0 0.1 0.2 0.3 lag adeg−>adeg
  • If leverage and connectivity increase (endogenously and because of

shocks) then system vulnerability rises leading to successive output contractions

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 14 / 23

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SLIDE 15

Simulated economy dynamics

From the interaction of individual agents behaviors emerge aggregate dynamic patterns (Minsky, 1975, 1982) interaction produces emergence

  • Safe expansion (SE): output growth

with low leverage

  • Fragile expansion (FE): output growth

with increasing leverage

  • Fragile contraction (FC): output

decrease with high leverage

  • Safe contraction (SC): output decrease

with low leverage

  • utput

leverage SE ↑ ↓ FE ↑ ↑ FC ↓ ↑ SC ↓ ↓ leverage dynamics

−20 −10 10 20 −0.15 −0.05 0.05 0.15

Ccf Output and Firm Leverage

lag ccf −20 −10 10 20 −0.05 0.00 0.05 0.10

Ccf Output and Excess Credit Demand

lag ccf

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 15 / 23

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SLIDE 16

Systemic risk indicator

Network before the crisis

cycle 400

Network after the crisis

cycle 410

Before the crisis high levels of the risk indicator:

  • Leverage of both banks and firms is increasing
  • The credit network is strongly connected (prone to domino’s effect)

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 16 / 23

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SLIDE 17

Systemic risk indicator

k-indicator: adjusted degree concentration

  • The systemic risk represents a synthetic measure of the concentration
  • f leverage, credit capabilities and connectivity of banks

kt =

  • z∈10d adegz
  • z adegz

(8)

  • We define a crisis as an output drop above 15% in 5 consecutive

years. Hit ratio represents the capacity of predicting future crisis when the indicator is activated Hitting ratio = n. crises predicted

  • n. crises

False alarm ratio represents the propensity of the indicator to be activated without a crisis will successively occur False allarm ratio = n. indicator activations−n. crises predicted

  • n. observation−n. crises

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 17 / 23

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SLIDE 18

Systemic risk indicator

Risk indicator one year before the crisis

  • 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Risk indicator

False allarm ratio Hit ratio

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Risk indicator five years before the crisis

  • 0.0

0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0

Risk indicator

False allarm ratio Hit ratio

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
  • This systemic risk indicator may be conceived as an early warning

indicator

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 18 / 23

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SLIDE 19

Systemic risk indicator

False Positives and Leverage Level

1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.0 0.2 0.4 0.6 0.8 1.0 Firm Leverage Hit and False Allarm k=0.80 Firm Leverage Density Hit mean Hit median False Positive mean False Positive median 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.0 0.2 0.4 0.6 0.8 1.0 Firm Leverage Hit and False Allarm k=0.85 Firm Leverage Density Hit mean Hit median False Positive mean False Positive median 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.0 0.2 0.4 0.6 0.8 1.0 Firm Leverage Hit and False Allarm k=0.90 Firm Leverage Density Hit mean Hit median False Positive mean False Positive median 1.5 2.0 2.5 3.0 3.5 4.0 4.5 0.0 0.2 0.4 0.6 0.8 1.0 Firm Leverage Hit and False Allarm k=0.95 Firm Leverage Density Hit mean Hit median False Positive mean False Positive median
  • False positive are related to lower aggregate leverage: the higher the

risk indicator the greater the leverage level difference between false positives and hits

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 19 / 23

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SLIDE 20

Systemic risk indicator

Risk indicator and output in the Japanese sample

1980 1985 1990 1995 2000 2005 2010 −0.15 0.00 0.15

Output growth rate and k−indicator

time g g k 0.86 0.90 0.94 0.98

kind

  • Increase of connectivity concentration since the late eighties bubble
  • High connectivity concentration associated with low growth and
  • utput drops

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 20 / 23

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SLIDE 21

Concluding Remarks and Perspectives

Remarks

  • The model replicates several endogenous aspects of the Japanese

credit network dynamics

  • Idiosyncratic shocks to firms may be amplified by leverage of firms

and banks

  • Leverage choices and accumulation processes shape the credit

network and influences system vulnerability

  • The credit network configuration determines the diffusion of

idiosyncratic shocks and, thus, the systemic vulnerability

  • The predictive alarm warning indicator for crisis foresees fluctuations

too Perspectives

  • Improving calibration and validation of the model
  • Counterfactual experiments for policy measures through simulations

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 21 / 23

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SLIDE 22

Concluding remarks: economy as a complex adaptive system

  • Their interaction leads to empirical regularities, which emerge from

the system as a whole and cannot be identified by looking at any single agent in isolation these emerging properties are the main distinguishing feature of a complex system

  • The focus on interaction allows us to abandon the heroic and

unrealistic RA framework, in favor of the science of complexity.

  • ABM (and complexity) approach is a tough line of research whose

results are very promising (despite me)

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 22 / 23

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SLIDE 23

Merci!

Catullo, Gallegati, Palestrini (UPM, DiSES) November 18-19, 2013 Singapore 23 / 23