Endogeneous Inequality

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Presentation by Steve Kinsella, Ed Nell and Matthias Greiff, at the Agent-Based Modeling Session at the Annual Meeting of the Eastern Economic Association, February 2009

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<ul><li> 1. Introduction The Model Results Conclusion Interacting Heterogeneous Agents Stephen Kinsella, Edward J. Nell, Matthias Grei February 27, 2009 Stephen Kinsella, Edward J. Nell, Matthias Grei Interacting Heterogeneous Agents </li> <li> 2. Introduction The Model Econophysics Results Conclusion Income Distributions and Econophysics 1 Econophysics The Model 2 Labor Market Education Production Demand Banks Structure of the Model Results 3 Mobility Income Distribution Conclusion 4 Stephen Kinsella, Edward J. Nell, Matthias Grei Interacting Heterogeneous Agents </li> <li> 3. Introduction The Model Econophysics Results 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 initially 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 Grei Interacting Heterogeneous Agents </li> <li> 4. Introduction The Model Econophysics Results 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 Grei Interacting Heterogeneous Agents </li> <li> 5. of money conserva- same stationary distribution (7), as in the rst model. nary distribution of Computer animation for this model is also available on Introduction nential Boltzmann- the Web page [35]. Model The Econophysics Results The nal distribution is universal despite dierent rules Conclusion for m. To amplify this point further, Ref. [25] also con- . (7) sidered a toy model, where m was taken to be a ran- d T Distribution of Money dom fraction of the average amount of money of the two is the money m agents: m = (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 tted 4 2 e considered in Ref. amount was xed 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- (Source: bution of money exponential distribution for money a symmet- ulations. Solid curves: Fits to the Boltzmann-Gibbs law (7). r a diusion process. Yakovenko 2008). p around the m =Kinsella, Edward lines: The initial distribution of money. (Reproduced Vertical 0 Stephen J. Nell, Matthias Grei Interacting Heterogeneous Agents from Ref. [25]) </li> <li> 6. Introduction The Model Econophysics Results Conclusion Critique &amp; Modications Critique Model is attractive in its simplicity but represents a rather primitive picture of the market. Agents are characterized only by their amount of money. Data on wealth is rarely available, but data on income is. Modications 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 Grei Interacting Heterogeneous Agents </li> <li> 7. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model The Question How is inequality of incomes generated? Simple four sector model. Conservation law should be fullled. Model should produce exponential (or gamma) and power-law distributions of income. Inequality of income between and within classes should be explained. Stephen Kinsella, Edward J. Nell, Matthias Grei Interacting Heterogeneous Agents </li> <li> 8. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model Characteristics of the Model no representative agent no utility 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 Grei Interacting Heterogeneous Agents </li> <li> 9. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model 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. spend money on education. 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 Grei Interacting Heterogeneous Agents </li> <li> 10. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model Wage Bargaining Hiring rule: Each agents reservation wage is given by: w (m, , o) : R3 R+ . Every unemployed worker is matched with a randomly chosen rm. If the rms res. wage exceeds the workers res. wage, they sign a wage contract. If a rm has not enough money to pay all its employees, layo workers until the rm can pay the wagebill for the remaining workers. Unemployed workers get a dole-income which is a fraction of their reservation wage. Stephen Kinsella, Edward J. Nell, Matthias Grei Interacting Heterogeneous Agents </li> <li> 11. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model Ability &amp; Education Workers can be of ve types. no degree college degree BA degree MA degree PhD Workers are born with innate abilities which they can augment by further training and education. The workers skills can be summed up in a measure of the workers productivity, iw . Stephen Kinsella, Edward J. Nell, Matthias Grei Interacting Heterogeneous Agents </li> <li> 12. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model Education Levels PhD MA innate ability, productivity BA College a0' a0 = innate ability a0 me = money spend on education me t+1 = f (t , me , o) Stephen Kinsella, Edward J. Nell, Matthias Grei Interacting Heterogeneous Agents </li> <li> 13. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model Production &amp; Capacity Utilization Think of the production sector as a vertically integrated linear production model (neo-Ricardian). In each market there will be winners and loosers, the higher earnings of the successful are exactly balanced by the lower earnings of the less successful. If w &lt; f worker performs inadequately (accidents, slowdowns). A rm produces its highest potential output if w f for all employees. min w , f output= Stephen Kinsella, Edward J. Nell, Matthias Grei Interacting Heterogeneous Agents </li> <li> 14. Labor Market...</li></ul>