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# 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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### Endogeneous Inequality

1. 1. Introduction The Model Results Conclusion Interacting Heterogeneous Agents Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ February 27, 2009 Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
2. 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 Greiﬀ Interacting Heterogeneous Agents
3. 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 Greiﬀ Interacting Heterogeneous Agents
4. 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 Greiﬀ Interacting Heterogeneous Agents
5. 5. of money conserva- same stationary distribution (7), as in the ﬁrst 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 ﬁnal distribution is universal despite diﬀerent 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 = 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- (Source: bution of money exponential distribution for money a symmet- ulations. Solid curves: Fits to the Boltzmann-Gibbs law (7). r a diﬀusion process. Yakovenko 2008). p around the m =Kinsella, Edward lines: The initial distribution of money. (Reproduced Vertical 0 Stephen J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents from Ref. [25])
6. 6. Introduction The Model Econophysics Results Conclusion Critique & Modiﬁcations 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. 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 Interacting Heterogeneous Agents
7. 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 fulﬁlled. 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 Greiﬀ Interacting Heterogeneous Agents
8. 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 Greiﬀ Interacting Heterogeneous Agents
9. 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 Greiﬀ Interacting Heterogeneous Agents
10. 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, θ, o) : R3 → R+ . Every unemployed worker is matched with a randomly chosen ﬁrm. If the ﬁrm’s res. wage exceeds the worker’s res. wage, they sign a wage contract. 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. Unemployed workers get a dole-income which is a fraction of their reservation wage. Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
11. 11. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model Ability & Education Workers can be of ﬁve 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, θiw . Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
12. 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 θt+1 = f (θt , me , o) Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
13. 13. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model Production & 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 θw < θf worker performs inadequately (accidents, slowdowns). A ﬁrm produces its highest potential output if θw ≥ θf for all employees. min θw , θf output= Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
14. 14. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model 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 its output. Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
15. 15. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model 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 Interacting Heterogeneous Agents
16. 16. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model Banks 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 . rr Maximum 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 Interacting Heterogeneous Agents
17. 17. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model 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 Interacting Heterogeneous Agents
18. 18. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model 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 Interacting Heterogeneous Agents
19. 19. Labor Market Introduction Education The Model Production Results Demand Conclusion Banks Structure of the Model Structure of the Model At the beginning of the year agents buy or sell one-year bonds. Workers die and get born. Each month the following happens: Wage bargaining, hiring and ﬁring. Eﬀective Demand. Education. At the end of each year we collect data on income distribution (and other data). Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
20. 20. Introduction The Model Mobility Results Income Distribution 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 Interacting Heterogeneous Agents
21. 21. Introduction The Model Mobility Results Income Distribution 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. Positive interest rate reduces mobility. Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
22. 22. Introduction The Model Mobility Results Income Distribution Conclusion Income Distribution by Education 0.15 0.10 0.05 5 10 15 20 25 Figure: Income distribution for diﬀerent levels of education. Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
23. 23. Introduction The Model Results Conclusion Conclusion Workers are heterogeneous with respect to wealth, ability, and opportunities. Almost no restrictions on agents behavior. Markets generate surpluses that go to the successful, gains are carried forward through time. Labor Market Education Diﬀerences in wealth, ability, and opportunity translate into income inequality within and between classes. Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
24. 24. Introduction The Model Results Conclusion Problems Workers income is 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 go bankrupt. (Interest rate on borrowing > interest rate on lending.) Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
25. 25. 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 (Irland 2000-2006). Possible Extensions: Introduce central bank. Look at the eﬀects of policy. Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents
26. 26. Introduction The Model Results Conclusion Stephen Kinsella stephen.kinsella@ul.ie http://www.stephenkinsella.net Edward J. Nell ejnell@aol.com Matthias Greiﬀ greiﬀ@uni-bremen.de http://matthiasgreiﬀ.wordpress.com Stephen Kinsella, Edward J. Nell, Matthias Greiﬀ Interacting Heterogeneous Agents