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A 3-region new economic geography model in discrete time

A 3-region new economic geography model in discrete time. Pasquale Commendatore Ingrid Kubin Iryna Sushko. NEG - Central question. Long- run spatial distribution of industry. equally distributed. a gglomerated in one region. unevenly distributed. NEG – Basic structure.

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A 3-region new economic geography model in discrete time

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  1. A 3-region new economicgeography model in discrete time Pasquale Commendatore Ingrid Kubin IrynaSushko

  2. NEG - Central question • Long-runspatialdistribution of industry equallydistributed agglomerated in oneregion unevenlydistributed

  3. NEG – Basic structure • Givenamountofproductivefactors • Distributed acrosstwoidenticalregions • Allowedtomovefreelybetweenregionsaccordingtofactorrewards (dynamiclaw) • Output sold in home regionaswellas in otherregions (tradecost) • Decisive for location decision: Costforcommoditytradebetweenregions

  4. Where do dynamicprocesses play a role? • Goods and labourmarkets: istantaneousequilibrium • Shipping of goods: istantaneous • Factormobility: gradual over time, adaptiveprocess • Analytical core: One-dimensionaldifferentialequation

  5. Continuous Vs discrete time • 2-R NEG in continuous time (1-D bimodal flow): Multiple equilibria; catastrophic agglomeration; hysteresis; ‘regular’ local stability properties which holds within well-defined basins of attraction • 2-R NEG in discrete time (1-D bimodalmap): Multiple equilibria; catastrophic agglomeration; hysteresis; multiple attractors of any periodicity; chaotic dynamics; agglomeration via volatility

  6. ContinuousVs discrete time • NEG models in discrete time: • CP (Currie&Kubin; JEBO, 2006) [CK, 2006] • FE (Commendatore, Currie&Kubin; SEA, 2008) [CCK, 2008] • FC (Commendatore, Currie&Kubin;NDPLS, 2007) [CCK, 2007] • FE 3-R (Commendatore&Kubin, 2012) – Local stabilityanalysis • FE 3-R (Commendatore, Kubin & Sushko, current) – Global stabilityanalysis

  7. Footloose Entrepreneur (FE)(Forslid & Ottaviano, 2003, JEG) • Factors of production - unskilled workers (immobile, variable costs) - entrepreneurs (mobile, fixed cost) • Agglomeration and dispersionforces are allat work • Self-reinforcingagglomerationprocessespreserved • Entrepreneurs migrate in response to differences in realprofits

  8. 3-R Footloose Entrepreneur model • 3symmetricRegions (1, 2, 3) • 2 Sectors (agriculture, manufacturing) • 2 Factors of production (unskilledworkers, entrepreneurs)

  9. Manufacturing sector Agriculturalsector Undifferentiatedgood Producedwith: 1 unitofunskilledlabour Constantaveragecosts Perfect competition MR = MC No transportcost (perfecttradefreeness) • Differentiatedgoods • Producedwith: 1 entrepreneur unitsofunskilledlabour • Decreasingaveragecosts • Monopolisticcompetition: • Price: mark-up over marginalcost • Iceberg transportcost, T

  10. 3 1 2 3 equidistant regions Tradefreeness

  11. Number of firms = number of entrepreneursN • number of firmslocated in regionr: • Share of entrepreneurs (firms) located in regionr:

  12. Istantaneous Short-runequilibriumin regionr Price index: Operating profit: σ : CES – taste for variety regional expenditure share µ : share of expenditureallocated to manufacturing

  13. Real profit in regionr Operating profit per variety in regionr Price index in regionr

  14. Central dynamicequation: non-linear, two-dimensional in Replicator dynamics : migrationspeed butbounduaryconditions 14

  15. Central dynamicequation: non-linear, two-dimensional in 15

  16. Core-Peripheryequilibria 1 0.5 0 1 0.5

  17. 3-Region symmetricequilibrium 1 0.5 0 1 0.5

  18. 3-Region asymmetricequilibria 1 0.5 0 1 0.5

  19. 2-Region ‘symmetric’ equilibria 1 0.5 0 1 0.5

  20. 2-R asymmetricequilibria ( 1 0.5 0 1 0.5

  21. 3-Region Tomahawkdiagrams

  22. Local stabilityresults

  23. Global dynamicspreliminaryresults

  24. Global dynamicspreliminaryresults

  25. Global dynamicspreliminaryresults

  26. Finalremarks • 2-Dimensional nonlinearmap: Multiple equilibria; catastrophic agglomeration; hysteresis; 2-R and 3-R stationaryequilibria, possible 2-R asymmetricstableequilibria periodic and quasi-periodic multiple attractors; chaotic dynamics; strange attractors, complex basins of attraction • Simple extensions: slightincrease in the number of regions; asymmetrictradecosts • Lesssimpleextensions: largerincrease in the number of regions, endogenoustrasportcosts, network structure

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