Interacting Agents Produce Endogenous Inequality
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Interacting Agents Produce Endogenous Inequality

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Here is a talk delivered at the Eastern Economic Association Meetings, Feb 26--March 1, 2009.

Here is a talk delivered at the Eastern Economic Association Meetings, Feb 26--March 1, 2009.

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    Interacting Agents Produce Endogenous Inequality Interacting Agents Produce Endogenous Inequality Presentation Transcript

    • Introduction The Model Results Conclusion Endogeneous Inequality Stephen Kinsella, Edward J. Nell, Matthias Greiff Annual Meeting of the Eastern Economic Association February/March 2009, New York City February 21, 2009 Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Distributions of Income Results Econophysics Conclusion Income Distributions and Econophysics 1 Distributions of Income Econophysics The Model 2 Behavioral Rules Structure of the Model Results 3 Model without bank Introducing debt Mobility Conclusion 4 Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Distributions of Income Results Econophysics Conclusion Income Distribution Vilfredo Pareto, “Ecrits sur la courbe de la repartition de la richesse”, ch. 2, Librairie Droz, Geneve, (1896) 1965. David G. Champernowne, “A model of income distribution”, EJ, 1953. Benoit Mandelbrot, “The Pareto-Levy Law and the Distribution of Income”, IER, 1960. John Angle (1983-. . . ), The Inequality Process. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Distributions of Income Results Econophysics Conclusion Conservation Principle Conservation Law Idea from physics: conservation of energy. In econophysics: conservation of money. We cannot keep track of all goods consumed. A simple econophysics model n agents, each agent has m Dollars total amount of money M = n × m ¯ each period two agents are drawn and a random amount of money is transferred from one agent to the other nonnegativity constraint, mi ≥ 0 Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Distributions of Income Results Econophysics Conclusion Distribution of Money distribution of money converges to a Boltzmann-Gibbs exponential distribution (entropy increases) thermodynamic equilibrium P(m) = c × e −m/m ¯ m: money temparature, c: normalizing constant ¯ Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • nential Boltzmann- the Web page [35].Introduction The final distribution is universal despiteof Income rules The Model Distributions different Results Econophysics for ∆m. To amplify this point further, Ref. [25] also con- Conclusion . (7) sidered a toy model, where ∆m was taken to be a ran- Distribution of Money dom fraction of the average amount of money of the two d Tm is the “money agents: ∆m = ν(mi + mj )/2. This model produced the average amount of where M is the total ts. 5 5 N=500, M=5*10 , time=4*10 . 5] performed agent- 18 y transfers between 16 n the same amount !mquot;, T of agents (i, j) was 14 3 as transferred from 12 Probability, P(m) was repeated many log P(m) 2 ility distribution of 10 animation videos at 1 8 itory period, money 0 6 nary form shown in 0 1000 2000 3000 Money, m n is very well fitted 4 2 e considered in Ref. amount was fixed 0 0 1000 2000 3000 4000 5000 6000 cally, it means that Money, m s for the same price shows that the ini- FIG. 1 Histogram and points: Stationary probability distri- dens toFigure: Boltzmann-Gibbs P (m) obtained in agent-based computer sim- bution of money exponential distribution for money a symmet- (Source: ulations. Solid curves: Fits to the Boltzmann-Gibbs law (7). r a diffusion process. p around the m = 0 2008). lines: The initial distribution of money. (Reproduced Yakovenko Vertical from Ref. [25]) e boundary, because Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Distributions of Income Results Econophysics Conclusion Critique & Modifications Critique Model is attractive in its simplicity but represents a rather primitive picture of the market. Agents are characterized by their amount of money. Modifications Heterogeneous agents (in terms of money, abilities, opportunities, and savings rates). Ability changes as agents spend money on education. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Behavioral Rules Results Structure of the Model Conclusion The Question How is inequality of incomes and wealth generated? Simple four sector model. Conservation law should be fulfilled. Model should produce exponential and power-law distributions of income. Model should be more realistic but not too complex. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Behavioral Rules Results Structure of the Model Conclusion Characteristics of the Model no representative agent no utility function no production function no rational expectations large number of heterogeneous agents individual behavior is unpredictable individuals follow simple rules indeterminacy at the micro level (random selection from a given distribution) Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Behavioral Rules Results Structure of the Model Conclusion Four Sectors In the simplest version of our model we have three sectors. Workers... search for work. work for a wage or get dole. spend money on consumption (demand). Firms... hire workers. pay wages. receive revenue from selling output. Government: collects taxes and provides dole. Add banking sector later. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Behavioral Rules Results Structure of the Model Conclusion Wage Bargaining Each agents’ reservation wage is given by: w (m, a, o) : R3 → R+ Hiring rule: Every unemployed worker is matched with a randomly chosen firm. Provided that the firm has enough money to pay the wage, wF W they sign a wage contract with probability p = min w W , w F . w Firing rule: If a firm has not enough money to pay all its employees, layoff workers until the firm can pay the wagebill for the remaining workers. Wage payment rule: Employees get their wages. Dole payment rule: Unemployed workers get a dole-income which is a fraction of their reservation wage. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Behavioral Rules Results Structure of the Model Conclusion Demand Each agent (workers and firms) spends money on average once a month. Agents save a fraction of their money sm, (s ∈ [0, 1]). The agent (=buyer) spends a random fraction u (u ∈ U [0, 1]) of his remaining money (1 − s)m on consumption, ∆m = u(1 − s)m. A fraction t∆m goes to the government as tax income (t = tax rate). The remaining part (1 − t)∆m is transferred to seller. The seller is a firm. The probability that a particular firm is choosen is proportional to the sum of its employees’ abilities. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Behavioral Rules Results Structure of the Model Conclusion Ability & Education Modelled in a rather crude way. Assume that a fraction of money is spend on education. Ability increases by η = U [0, o] ∆m. But more sophisticated versions are possible... Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Behavioral Rules Results Structure of the Model Conclusion Government Government is passive (no government spending besides dole). Spend money on dole. Collect taxes on consumption. Increase tax rate if government deficit, decrease if surplus. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Behavioral Rules Results Structure of the Model Conclusion Structure of the Model Each month the following happens: Wage bargaining. Demand. At the end of each year we collect data on income distribution (and other data). Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction Model without bank The Model Introducing debt Results Mobility Conclusion Income Distribution 0.14 0.12 0.10 0.08 0.06 0.04 0.02 5 10 15 20 25 30 Figure: Probability density function for 95% of incomes and exponential distribution. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction Model without bank The Model Introducing debt Results Mobility Conclusion Banks: zero interest rate debt is permitted (negative money) unlimited borrowing has to be precluded total amount of debt is limited by minimum reserve requirement for banks, M = M0 r maximal debt of any agent is limited by, mi > −md ∀i ¯ debt: increase in money temparature Money supply ’increases’ (money multiplier) but conservation law is still fulfilled! Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction Model without bank The Model Introducing debt Results Mobility Conclusion Bond Market Introduce a market for one-year bonds. Agents can save (buy bonds) or get a loan (sell bonds). Higher interest rate r increases supply and reduces demand. Trading at disequilibrium. Interest rate r adjusts. r increases if excess demand for bonds. r decreases if excess supply for bonds. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction Model without bank The Model Introducing debt Results Mobility Conclusion Interest Rate Adjustment r r supply supply r2 r1 r1 demand demand t t+1 Figure: Excess demand in the bond market. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction Model without bank The Model Introducing debt Results Mobility Conclusion Measuring Mobility N 1 0 − log mi1 | i=1 | log mi Mb = N Two time period framework. Money at time t: m0 = (m1 , m2 , . . . , mN ) . 0 0 0 Money at time t + 10: m1 = (m1 , m2 , . . . , mN ) . 1 1 1 Source: G.S. Fields & E.A. Ok, “Measuring Movement of Income”, Economica (1999). Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction Model without bank The Model Introducing debt Results Mobility Conclusion Mobility mobility 1.5 1.4 1.3 1.2 1.1 1.0 0.9 spending 0.2 0.4 0.6 0.8 Figure: Absolute mobility and spending. Higher savings → lower mobility. Higher mobility if debt is allowed for. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Results Conclusion Conclusion summarize main results from our model Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Results Conclusion Problems Workers income is now wage income plus interest earned / paid (on bonds). Income can get negative if interest payment > wage income. A possible solution: Restrict borrowing and introduce a minimum wage such that income from minimum wage is sufficiently high to pay interest. Or: Allow for agents to get bankrupt. (Interest rate on borrowing > interest rate on lending.) Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Results Conclusion Further research and possible extensions Further research: Allow for more than one bank. Look at firm size distribution. Fit model to actual data. Possible Extensions: Add production technology and growth. Introduce central bank. Look at the effects of policy. Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality
    • Introduction The Model Results Conclusion Conclusion http://www.stephenkinsella.net http://matthiasgreiff.wordpress.com http://www.newschool.edu/... Stephen Kinsella, Edward J. Nell, Matthias Greiff Endogeneous Inequality