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Existence, Stability and Computation of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem

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Author Info

  • Takashi Kamihigashi

    (Research Institute for Economics & Business Administration (RIEB), Kobe University, Japan)

  • John Stachurski

    (Research School of Economics, Australian National University, Canberra, Australia)

Abstract

This paper strengthens the Hopenhayn and Prescott stability theorem for monotone economies. We extend the theorem to a larger class of applications, and develop new perspectives on the nature and causes of stability and instability. In addition, we show that models satisfying the Hopenhayn-Prescott theorem are ergodic, in the sense that sample averages of time series converge with probability one to their corresponding expectations under the stationary distribution, independent of initial conditions.

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File URL: http://www.rieb.kobe-u.ac.jp/academic/ra/dp/English/DP2011-32.pdf
File Function: First version, 2011
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Bibliographic Info

Paper provided by Research Institute for Economics & Business Administration, Kobe University in its series Discussion Paper Series with number DP2011-32.

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Length: 42 pages
Date of creation: Dec 2011
Date of revision:
Handle: RePEc:kob:dpaper:dp2011-32

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  1. 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.
  2. Kiminori Matsuyama, 2004. "Financial Market Globalization, Symmetry-Breaking, and Endogenous Inequality of Nations," Econometrica, Econometric Society, vol. 72(3), pages 853-884, 05.
  3. 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.
  4. Olson, Lars J., 1989. "Stochastic growth with irreversible investment," Journal of Economic Theory, Elsevier, vol. 47(1), pages 101-129, February.
  5. 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 915-38, October.
  6. Lloyd-Ellis, Huw & Bernhardt, Dan, 2000. "Enterprise, Inequality and Economic Development," Review of Economic Studies, Wiley Blackwell, vol. 67(1), pages 147-68, January.
  7. 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.
  8. 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.
  9. Josep Pijoan-Mas, 2003. "Precautionary Savings Or Working Longer Hours?," Working Papers wp2003_0311, CEMFI.
  10. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2006. "Testing For Stochasticmonotonicity," STICERD - Econometrics Paper Series /2006/504, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  11. António Antunes & Tiago Cavalcanti & Anne Villamil, 2006. "Computing General Equilibrium Models with Occupational Choice and Financial Frictions," SCAPE Policy Research Working Paper Series 0611, National University of Singapore, Department of Economics, SCAPE.
  12. Olson, Lars J. & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics.
  13. 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.
  14. 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.
  15. Lloyd-Ellis, Huw, 2000. "Public Education, Occupational Choice, and the Growth-Inequality Relationship," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(1), pages 171-201, February.
  16. Takashi Kamihigashi, 2006. "Stochastic Optimal Growth with Bounded or Unbounded Utility and with Bounded or Unbounded Shocks," Discussion Paper Series 189, Research Institute for Economics & Business Administration, Kobe University.
  17. 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.
  18. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
  19. Takashi Kamihigashi & John Stachurski, 2011. "An Order-Theoretic Mixing Condition for Monotone Markov Chains," ANU Working Papers in Economics and Econometrics 2011-559, Australian National University, College of Business and Economics, School of Economics.
  20. 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.
  21. 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.
  22. Liutang Gong & Xiaojun Zhao & Heng-fu Zou, 2010. "Stochastic Growth with the Social-Status Concern: The Existence of a Unique Stable Distribution," CEMA Working Papers 408, China Economics and Management Academy, Central University of Finance and Economics.
  23. 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.
  24. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," MPRA Paper 23107, University Library of Munich, Germany.
  25. 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.
  26. Nishimura, Kazuo & Stachurski, John, 2005. "Stability of stochastic optimal growth models: a new approach," Journal of Economic Theory, Elsevier, vol. 122(1), pages 100-118, May.
  27. 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.
  28. Kevin Reffett & Manjira Datta & Leonard Mirman & Olivier Morand, . "Monotone Methods for Markovian Equilibrium in Dynamic Economies," Working Papers 2133476, Department of Economics, W. P. Carey School of Business, Arizona State University.
  29. 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.
  30. Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
  31. Stachurski, J., 2001. "Stochastic Optimal Growth with Unbounded Shock," Department of Economics - Working Papers Series 777, The University of Melbourne.
  32. 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.
  33. Huggett, Mark, 1993. "The risk-free rate in heterogeneous-agent incomplete-insurance economies," Journal of Economic Dynamics and Control, Elsevier, vol. 17(5-6), pages 953-969.
  34. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-406, November.
  35. San Vicente Portes, Luis, 2009. "On the distributional effects of trade policy: Dynamics of household saving and asset prices," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(3), pages 944-970, August.
  36. 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.
  37. Morand, O.F., 2005. "Erratum to "Inequality, mobility and the transmission of ability" [Journal of Macroeconomics 26 (3) 533-545]," Journal of Macroeconomics, Elsevier, vol. 27(2), pages 363-363, June.
  38. Morand, O.F., 2005. "Corrigendum to "Inequality, mobility, and the transmission of ability" [Journal of Macroeconomics 26 (4) 747]," Journal of Macroeconomics, Elsevier, vol. 27(1), pages 169-169, March.
  39. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
  40. Mitra, Tapan & Roy, Santanu, 2003. "Optimal Exploitation of Renewable Resources under Uncertainty and the Extinction of Species," Working Papers 03-10, Cornell University, Center for Analytic Economics.
  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, 05.
  42. Piketty, Thomas, 1997. "The Dynamics of the Wealth Distribution and the Interest Rate with Credit Rationing," Review of Economic Studies, Wiley Blackwell, vol. 64(2), pages 173-89, April.
  43. Das, Satya P., 2006. "Trade, skill acquisition and distribution," Journal of Development Economics, Elsevier, vol. 81(1), pages 118-141, October.
  44. 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.
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Citations

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Cited by:
  1. Takashi Kamihigashi, 2012. "Elementary Results on Solutions to the Bellman Equation of Dynamic Programming: Existence, Uniqueness, and Convergence," Discussion Paper Series DP2012-31, Research Institute for Economics & Business Administration, Kobe University.
  2. Cai, Yiyong & Kamihigashi, Takashi & Stachurski, John, 2014. "Stochastic optimal growth with risky labor supply," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 167-176.
  3. Takashi Kamihigashi & John Stachurski, 2010. "Stochastic Stability in Monotone Economies," Discussion Paper Series DP2010-12, Research Institute for Economics & Business Administration, Kobe University.
  4. Takashi Kamihigashi & John Stachurski, 2012. "Existence, Uniqueness and Stability of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem," Discussion Paper Series DP2012-27, Research Institute for Economics & Business Administration, Kobe University.

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