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Stability of Stationary Distributions in Monotone Economies

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  • Takashi Kamihigashi
  • John Stachurski

Abstract

This paper generalizes the sufficient conditions for stability of monotone economies and time series models due to Hopenhayn and Prescott (Econometrica, 60, p. 1387–1406, 1992). We introduce a new order-theoretic mixing condition and characterize stability for monotone economies satisfying this condition. We also provide a range of results that can be used to verify our mixing condition in applications, as well as the other components of our main stability theorem. Through this approach, we extend Hopenhayn and Prescott’s method to a significantly larger class of problems, and develop new perspectives on the causes of instability and stability.

Suggested Citation

  • Takashi Kamihigashi & John Stachurski, 2011. "Stability of Stationary Distributions in Monotone Economies," ANU Working Papers in Economics and Econometrics 2011-561, Australian National University, College of Business and Economics, School of Economics.
    • Handle: RePEc:acb:cbeeco:2011-561
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    File URL: https://www.cbe.anu.edu.au/researchpapers/econ/wp561.pdf
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    1. Gong, Liutang & Zhao, Xiaojun & Yang, Yunhong & Hengfu, Zou, 2010. "Stochastic growth with social-status concern: The existence of a unique stable distribution," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 505-518, July.
    2. Chatterjee, Partha & Shukayev, Malik, 2012. "A stochastic dynamic model of trade and growth: Convergence and diversification," Journal of Economic Dynamics and Control, Elsevier, vol. 36(3), pages 416-432.
    3. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    4. Kamihigashi, Takashi & Stachurski, John, 2012. "An order-theoretic mixing condition for monotone Markov chains," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 262-267.
    5. Marcet, Albert & Obiols-Homs, Francesc & Weil, Philippe, 2007. "Incomplete markets, labor supply and capital accumulation," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2621-2635, November.
    6. Samaniego, Roberto M., 2008. "Can technical change exacerbate the effects of labor market sclerosis," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 497-528, February.
    7. Hidalgo Cabrillana, Ana, 2009. "Endogenous capital market imperfections, human capital, and intergenerational mobility," Journal of Development Economics, Elsevier, vol. 90(2), pages 285-298, November.
    8. Kamihigashi, Takashi, 2007. "Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 477-500, April.
    9. Diaz, Antonia & Pijoan-Mas, Josep & Rios-Rull, Jose-Victor, 2003. "Precautionary savings and wealth distribution under habit formation preferences," Journal of Monetary Economics, Elsevier, vol. 50(6), pages 1257-1291, September.
    10. Kiminori Matsuyama, 2000. "Endogenous Inequality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(4), pages 743-759.
    11. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
    12. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    13. Josep Pijoan-Mas, 2006. "Precautionary Savings or Working Longer Hours?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(2), pages 326-352, April.
    14. Mukul Majumdar & Tapan Mitra & Yaw Nyarko, 1989. "Dynamic Optimization Under Uncertainty: Non-convex Feasible Set," Palgrave Macmillan Books, in: George R. Feiwel (ed.), Joan Robinson and Modern Economic Theory, chapter 19, pages 545-590, Palgrave Macmillan.
    15. W. Davis Dechert & Kazuo Nishimura, 2012. "A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 237-257, Springer.
    16. Olivier F. Morand & Kevin L. Reffett, 2005. "Stationary Markovian Equilibrium in Overlapping Generation Models with Stochastic Nonclassical Production," Working papers 2005-52, University of Connecticut, Department of Economics.
    17. Huw Lloyd-Ellis & Dan Bernhardt, 2000. "Enterprise, Inequality and Economic Development," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 147-168.
    18. Antunes, Antonio R. & Cavalcanti, Tiago V. de V., 2007. "Start up costs, limited enforcement, and the hidden economy," European Economic Review, Elsevier, vol. 51(1), pages 203-224, January.
    19. Owen, Ann L. & Weil, David N., 1998. "Intergenerational earnings mobility, inequality and growth," Journal of Monetary Economics, Elsevier, vol. 41(1), pages 71-104, February.
    20. Hopenhayn, Hugo & Rogerson, Richard, 1993. "Job Turnover and Policy Evaluation: A General Equilibrium Analysis," Journal of Political Economy, University of Chicago Press, vol. 101(5), pages 915-938, October.
    21. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
    22. Lars J. Olson & Santanu Roy, 2006. "Theory of Stochastic Optimal Economic Growth," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 11, pages 297-335, Springer.
    23. Couch, K.A. & Morand, O.F., 2005. "Inequality, mobility, and the transmission of ability," Journal of Macroeconomics, Elsevier, vol. 27(2), pages 365-377, June.
    24. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
    25. Antunes, António & Cavalcanti, Tiago & Villamil, Anne, 2008. "Computing general equilibrium models with occupational choice and financial frictions," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 553-568, July.
    26. Kazuo Nishimura & John Stachurski, 2012. "Stability of Stochastic Optimal Growth Models: A New Approach," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 289-307, Springer.
    27. Gilles Joseph & Thomas Weitzenblum, 2003. "Optimal Unemployment Insurance: Transitional Dynamics vs. Steady State," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 869-884, October.
    28. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    29. Tapan Mitra & Santanu Roy, 2006. "Optimal exploitation of renewable resources under uncertainty and the extinction of species," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(1), pages 1-23, May.
    30. repec:hal:spmain:info:hdl:2441/8623 is not listed on IDEAS
    31. Manjira Datta & Leonard Mirman & Olivier Morand & Kevin Reffett, 2002. "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Annals of Operations Research, Springer, vol. 114(1), pages 117-144, August.
    32. H. Lloyd-Ellis, 1995. "Occupational Choice and the Growth-Inequality Relationship," Working Papers lloydell-95-02, University of Toronto, Department of Economics.
    33. Philippe Aghion & Patrick Bolton, 1997. "A Theory of Trickle-Down Growth and Development," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(2), pages 151-172.
    34. Kiminori Matsuyama, 2004. "Financial Market Globalization, Symmetry-Breaking, and Endogenous Inequality of Nations," Econometrica, Econometric Society, vol. 72(3), pages 853-884, May.
    35. Olson, Lars J., 1989. "Stochastic growth with irreversible investment," Journal of Economic Theory, Elsevier, vol. 47(1), pages 101-129, February.
    36. Rabah Amir, 2002. "Complementarity and Diagonal Dominance in Discounted Stochastic Games," Annals of Operations Research, Springer, vol. 114(1), pages 39-56, August.
    37. Leonard Mirman & Olivier Morand & Kevin Reffett, "undated". "A Qualitative Theory of Markovian Equilibrium in Infinite Horizon Economies with Capital," Working Papers 2133376, Department of Economics, W. P. Carey School of Business, Arizona State University.
    38. Olson, Lars J. & Roy, Santanu, 2000. "Dynamic Efficiency of Conservation of Renewable Resources under Uncertainty," Journal of Economic Theory, Elsevier, vol. 95(2), pages 186-214, December.
    39. William A. Brock & Leonard J. Mirman, 2001. "Optimal Economic Growth And Uncertainty: The Discounted Case," Chapters, in: W. D. Dechert (ed.), Growth Theory, Nonlinear Dynamics and Economic Modelling, chapter 1, pages 3-37, Edward Elgar Publishing.
    40. repec:hal:wpspec:info:hdl:2441/8623 is not listed on IDEAS
    41. Buly A. Cardak, 2004. "Ability, Education, and Income Inequality," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 6(2), pages 239-276, May.
    42. Bhattacharya, Rabi & Majumdar, Mukul, 2001. "On a Class of Stable Random Dynamical Systems: Theory and Applications," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 208-229, January.
    43. Razin, Assaf & Yahav, Joseph A, 1979. "On Stochastic Models of Economic Growth," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(3), pages 599-604, October.
    44. Samaniego, Roberto M., 2006. "Industrial subsidies and technology adoption in general equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1589-1614.
    45. Chatterjee, Partha & Shukayev, Malik, 2008. "Note on positive lower bound of capital in the stochastic growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2137-2147, July.
    46. Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), 2006. "Handbook on Optimal Growth 1," Springer Books, Springer, number 978-3-540-32310-5, June.
    47. Thomas Piketty, 1997. "The Dynamics of the Wealth Distribution and the Interest Rate with Credit Rationing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(2), pages 173-189.
    48. Ranjan, Priya, 2001. "Dynamic evolution of income distribution and credit-constrained human capital investment in open economies," Journal of International Economics, Elsevier, vol. 55(2), pages 329-358, December.
    49. Cabrales, Antonio & Hopenhayn, Hugo A., 1997. "Labor-market flexibility and aggregate employment volatility," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 46(1), pages 189-228, June.
    50. de Hek, Paul A, 1999. "On Endogenous Growth under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 727-744, August.
    51. Diaz, Antonia & Pijoan-Mas, Josep & Rios-Rull, Jose-Victor, 2003. "Precautionary savings and wealth distribution under habit formation preferences," Journal of Monetary Economics, Elsevier, vol. 50(6), pages 1257-1291, September.
    52. Das, Satya P., 2006. "Trade, skill acquisition and distribution," Journal of Development Economics, Elsevier, vol. 81(1), pages 118-141, October.
    53. Balbus, Łukasz & Reffett, Kevin & Woźny, Łukasz, 2012. "Stationary Markovian equilibrium in altruistic stochastic OLG models with limited commitment," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 115-132.
    54. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    55. Morand, Olivier F. & Reffett, Kevin L., 2007. "Stationary Markovian equilibrium in overlapping generation models with stochastic nonclassical production and Markov shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 501-522, April.
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