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Notes: A new approach to business
fluctuations: heterogeneous interacting
agents, scaling laws and financial fragility
(JEBO...
Introduction: Main Points

◮

The paper: (Gatti D D, Guilmi C D, Gaffeo E, et al. 2005): A
new approach to business fluctuat...
Introduction: Agent-based Methodology

◮

Model the economy from ‘bottom-up’.

◮

Agents are heterogeneous, interacting wi...
Empirical Observations

◮

(Axtell 2001) and (Gaffeo et al. 2003) have shown the
distribution of firms size follows a Zipf o...
Firms’ size: Power law Vs. Lognormal distribution
Model: the economy

◮

Economy with goods market and credit markets, in discrete
time periods t = 1, 2, . . ..

◮

Nt firms...
Firm i = 1, . . . , N: I
◮

Use capital Kit to produce goods, under a linear production
technology: Yit = φKit .

◮

Firm ...
Firm i = 1, . . . , N: II
◮

Firm’s net worth: Ait = Ait−1 + πit .

◮

Firm goes bankrupt when Ait < 0, the threshold of fi...
Firm i = 1, . . . , N: III

◮

◮

d
To keep optimal capital stock, firm invests Iit = Kit − Kit−1 .
Iit is either from profi...
The Banking Sector: I

◮

◮

◮

The total credit supply from the banking sector is:
Ls = Et + Dt = Et−1 /v .
t
K

A

Credi...
The Banking Sector: II
◮

The banking sector’s profit is:
B
πt =

rit Ls − rt [(1 − ω)Dt−1 + Et−1 ],
it
i ∈Nt

where the re...
Entry-Exit Mechanism
◮

Firm i goes bankrupt if Ait < 0.

◮

Number of new entry firms is:
entry
Nt
= NPr (entry ) =

N
,
1...
Simulation: Setup

◮

Simulation with 10, 000 firms for 1, 000 periods.
Simulation Result: Aggregate Output
Simulation Result: Growth Rates of Aggregate Output
Simulation Result: Firm Size
Simulation Result: Growth Rate Distribution
Open Topics

◮

Micro foundation of Macroeconomic models.

◮

Representative Agents (RA) or Heterogenous Interactive
Agent...
References
◮

◮

◮

◮

◮

(Gatti et al. 2005): Gatti D D, Guilmi C D, Gaffeo E, et al. A
new approach to business fluctuatio...
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Seminar talk: A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility

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Seminar talk: A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility

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Seminar talk: A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility

  1. 1. Notes: A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility (JEBO 2005) Li Xihao Polytechnic University of Marche, Ancona, Italy xihao.li@gmail.com 2013. 03. 25
  2. 2. Introduction: Main Points ◮ The paper: (Gatti D D, Guilmi C D, Gaffeo E, et al. 2005): A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility. Journal of Economic behavior & organization, 2005, 56(4): 489-512. ◮ The idea: By agent-based modeling and simulation, the interaction of heterogeneous financially fragile firms and a banking sector replicates business fluctuation.
  3. 3. Introduction: Agent-based Methodology ◮ Model the economy from ‘bottom-up’. ◮ Agents are heterogeneous, interacting with each other. ◮ Networks to capture the interrelationship among agents. ◮ interaction among agents in ‘micro-foundation’ produces the economic phenomenon in ‘macro-level’.
  4. 4. Empirical Observations ◮ (Axtell 2001) and (Gaffeo et al. 2003) have shown the distribution of firms size follows a Zipf or power law. ◮ (Stanley et al. 1996) and (Amaral et al. 1997) have found the growth rate of firms output follows a Laplace distribution.
  5. 5. Firms’ size: Power law Vs. Lognormal distribution
  6. 6. Model: the economy ◮ Economy with goods market and credit markets, in discrete time periods t = 1, 2, . . .. ◮ Nt firms and one banking sector.
  7. 7. Firm i = 1, . . . , N: I ◮ Use capital Kit to produce goods, under a linear production technology: Yit = φKit . ◮ Firm receives a selling price Pit fluctuating around the average market price Pt , with Pit = uit Pt , E(uit ) = 1. ◮ Firm get loans Lit from the banking sector under the interest rate rit . Firm’s financial cost is rit (Lit + Ait ) = rit Kit . ◮ Firm’s profit: πit = uit Yit − grit Kit = (uit φ − grit )Kit , g > 1. Firm’s expected profit: E(πit ) = (φ − grit )Kit . ◮ Firm’s net worth: Ait = Ait−1 + πit . ◮ Firm goes bankrupt when Ait < 0, the threshold of firm’s bankruptcy is: 1 Ait−1 uit ≡ (grit − ). φ Kit
  8. 8. Firm i = 1, . . . , N: II ◮ Firm’s net worth: Ait = Ait−1 + πit . ◮ Firm goes bankrupt when Ait < 0, the threshold of firm’s bankruptcy is: Ait−1 1 ). uit ≡ (grit − φ Kit ◮ 2 Firm faces bankruptcy cost C f when uit < uit : C f = cYit . ◮ Firm maximizes its expected profit, with its objective function: Γit = E(πit ) − E(C f ) = (φ − grit )Kit − ◮ φc 2 (grit Kit − Ait−1 Kit ). 2 The optimal capital stock is: d Kit = Ait−1 φ − grit + . cφgrit 2grit
  9. 9. Firm i = 1, . . . , N: III ◮ ◮ d To keep optimal capital stock, firm invests Iit = Kit − Kit−1 . Iit is either from profits or by loan in the credit market, i.e. Iit = πit−1 + ∆Lit = πit−1 + (Lit − Lit−1 ) The demand for credit is: Ld = it 1 − 2grit φ − grit − πit−1 + ( )Ait−1 . cφgrit 2grit
  10. 10. The Banking Sector: I ◮ ◮ ◮ The total credit supply from the banking sector is: Ls = Et + Dt = Et−1 /v . t K A Credit for firm i is: Ls = λLs Kit−1 + (1 − λ)Ls Ait−1 , with t t−1 t t−1 it Kt−1 = i Kit−1 and At−1 = i Ait−1 . K Denote κit−1 = Kit−1 and αit−1 = t−1 interest rate for firm i is: rit = Ait−1 At−1 , the equilibrium 2 + Ait−1 . 2cg ((1/φc) + πit−1 + Ait−1 ) + 2cgLs [λκit−1 + (1 − λ)αit−1 ] t
  11. 11. The Banking Sector: II ◮ The banking sector’s profit is: B πt = rit Ls − rt [(1 − ω)Dt−1 + Et−1 ], it i ∈Nt where the return rate of the bank’s equity is rt , the average of 1 lending interest rate; and (1−ω) rt is the borrowing rate of the deposits Dt−1 . ◮ When a firm goes bankrupt, the banking sector bears the bad debt loss: Bit = Lit − Kit . ◮ The banking sector’s equity evolves: B Et = πt + Et−1 − Bit−1 . i ∈Ωt−1
  12. 12. Entry-Exit Mechanism ◮ Firm i goes bankrupt if Ait < 0. ◮ Number of new entry firms is: entry Nt = NPr (entry ) = N , 1 + exp[d(rt−1 − e)] with d, e, and N > 1 are constants. ◮ New entry firm j has initial capital stock Kj0 randomly drawn from a uniform distribution with the mode of the size distribution of surviving firms. ◮ New entry firm j endows with an equity ratio aj0 = Aj0 /Kj0 equal to the mode of the equity base distribution of surviving firms.
  13. 13. Simulation: Setup ◮ Simulation with 10, 000 firms for 1, 000 periods.
  14. 14. Simulation Result: Aggregate Output
  15. 15. Simulation Result: Growth Rates of Aggregate Output
  16. 16. Simulation Result: Firm Size
  17. 17. Simulation Result: Growth Rate Distribution
  18. 18. Open Topics ◮ Micro foundation of Macroeconomic models. ◮ Representative Agents (RA) or Heterogenous Interactive Agents (HIA).
  19. 19. References ◮ ◮ ◮ ◮ ◮ (Gatti et al. 2005): Gatti D D, Guilmi C D, Gaffeo E, et al. A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility. Journal of Economic behavior & organization, 2005, 56(4): 489-512. (Axtell 2001): Axtell, R., 2001. Zipf distribution of U.S. firm sizes. Science 293, 1818C1820. (Gaffeo et al. 2003): Gaffeo, E., Gallegati, M., Palestrini, A., 2003. On the size distribution of firms. Additional evidence from the G7 countries. Physica A 324, 117C123. (Stanley et al. 1996): Stanley, M., Amaral, L., Buldyrev, S., Havlin, S., Leschorn, H., Maas, P., Salinger, M., Stanley, E., 1996. Scaling behavior in the growth of companies. Nature 379, 804C806. (Amaral et al. 1997): Amaral, L., Buldyrev, S., Havlin, S., Leschhorn, H., Maas, P., Salinger,M., Stanley, E., Stanley, M., 1997. Scaling behavior in Economics: I. Empirical results for company growth. Journal de Physique 7, 621C633.

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