IDEAS home Printed from https://ideas.repec.org/a/kap/jeczfn/v125y2018i3d10.1007_s00712-018-0604-6.html
   My bibliography  Save this article

Stochastic accumulation of human capital and welfare in the Uzawa–Lucas model: an analytical characterization

Author

Listed:
  • Mizuki Tsuboi

    (University of Hyogo)

Abstract

Stochastic growth models are often solved numerically, because they are not tractable in general. However, recent several studies find the closed-form solution to the stochastic Uzawa–Lucas model in which technological progress or population dynamics follow a Brownian motion process with one or two parameter restriction(s). However, they assume that the return on the accumulation of human capital is deterministic, which is inconsistent with empirical evidence. Therefore, I develop the Uzawa–Lucas model in which the accumulation of human capital follows a mixture of a Brownian motion process and many Poisson jump processes, and obtain the closed-form solution. Moreover, I use it to examine the nexus between human capital uncertainty, technological progress, expected growth rate of human capital, and welfare.

Suggested Citation

  • Mizuki Tsuboi, 2018. "Stochastic accumulation of human capital and welfare in the Uzawa–Lucas model: an analytical characterization," Journal of Economics, Springer, vol. 125(3), pages 239-261, November.
    • Handle: RePEc:kap:jeczfn:v:125:y:2018:i:3:d:10.1007_s00712-018-0604-6
    DOI: 10.1007/s00712-018-0604-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00712-018-0604-6
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s00712-018-0604-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Markus K. Brunnermeier & Yuliy Sannikov, 2014. "A Macroeconomic Model with a Financial Sector," American Economic Review, American Economic Association, vol. 104(2), pages 379-421, February.
    2. Bilkic, N. & Gries, T. & Pilichowski, M., 2012. "Stay in school or start working? — The human capital investment decision under uncertainty and irreversibility," Labour Economics, Elsevier, vol. 19(5), pages 706-717.
    3. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947.
    4. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-351, March.
    5. Jakob B. Madsen, 2014. "Human Capital and the World Technology Frontier," The Review of Economics and Statistics, MIT Press, vol. 96(4), pages 676-692, October.
    6. Sennewald, Ken, 2007. "Controlled stochastic differential equations under Poisson uncertainty and with unbounded utility," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1106-1131, April.
    7. Stephen J. Turnovsky, 1997. "International Macroeconomic Dynamics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262201119, December.
    8. Shiro Kuwahara, 2017. "Multiple steady states and indeterminacy in the Uzawa–Lucas model with educational externalities," Journal of Economics, Springer, vol. 122(2), pages 173-190, October.
    9. Brent Neiman, 2014. "The Global Decline of the Labor Share," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(1), pages 61-103.
    10. Hiraguchi, Ryoji, 2009. "A note on the closed-form solution to the Lucas-Uzawa model with externality," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1757-1760, October.
    11. Eichenbaum, Martin & Parker, Jonathan A. (ed.), . "NBER Macroeconomics Annual 2017," National Bureau of Economic Research Books, University of Chicago Press, number 9780226577838, July.
    12. Benjamin Moll, 2014. "Productivity Losses from Financial Frictions: Can Self-Financing Undo Capital Misallocation?," American Economic Review, American Economic Association, vol. 104(10), pages 3186-3221, October.
    13. Lester, Robert & Pries, Michael & Sims, Eric, 2014. "Volatility and welfare," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 17-36.
    14. Jonathan Eaton, 1981. "Fiscal Policy, Inflation and the Accumulation of Risky Capital," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(3), pages 435-445.
    15. Simone Marsiglio & Davide La Torre, 2012. "A note on demographic shocks in a multi-sector growth model," Economics Bulletin, AccessEcon, vol. 32(3), pages 2293-2299.
    16. Xu, Shaofeng, 2017. "Volatility risk and economic welfare," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 17-33.
    17. Stephen J. Turnovsky, 2000. "Methods of Macroeconomic Dynamics, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262201232, December.
    18. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 407-437.
    19. Hiraguchi, Ryoji, 2014. "A Note On The Analytical Solution To The Neoclassical Growth Model With Leisure," Macroeconomic Dynamics, Cambridge University Press, vol. 18(2), pages 473-479, March.
    20. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    21. Duffie, Darrel & Lions, Pierre-Louis, 1992. "PDE solutions of stochastic differential utility," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 577-606.
    22. Smith William T, 2007. "Inspecting the Mechanism Exactly: A Closed-form Solution to a Stochastic Growth Model," The B.E. Journal of Macroeconomics, De Gruyter, vol. 7(1), pages 1-33, August.
    23. 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.
    24. Levhari, David & Weiss, Yoram, 1974. "The Effect of Risk on the Investment in Human Capital," American Economic Review, American Economic Association, vol. 64(6), pages 950-963, December.
    25. Antonio Ladrón-de-Guevara & Salvador Ortigueira & Manuel S. Santos, 1999. "A Two-Sector Model of Endogenous Growth with Leisure," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 609-631.
    26. Caballe, Jordi & Santos, Manuel S, 1993. "On Endogenous Growth with Physical and Human Capital," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1042-1067, December.
    27. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    28. Hojo, Masakazu, 2003. "An indirect effect of education on growth," Economics Letters, Elsevier, vol. 80(1), pages 31-34, July.
    29. SeHyoun Ahn & Greg Kaplan & Benjamin Moll & Thomas Winberry & Christian Wolf, 2018. "When Inequality Matters for Macro and Macro Matters for Inequality," NBER Macroeconomics Annual, University of Chicago Press, vol. 32(1), pages 1-75.
    30. Xie, Danyang, 1991. "Increasing Returns and Increasing Rates of Growth," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 429-435, April.
    31. Robert E. Lucas Jr., 2003. "Macroeconomic Priorities," American Economic Review, American Economic Association, vol. 93(1), pages 1-14, March.
    32. Francesco Cinnirella & Jochen Streb, 2017. "The role of human capital and innovation in economic development: evidence from post-Malthusian Prussia," Journal of Economic Growth, Springer, vol. 22(2), pages 193-227, June.
    33. Joop Hartog & Hans Van Ophem & Simona Maria Bajdechi, 2007. "Simulating the Risk of Investment in Human Capital," Education Economics, Taylor & Francis Journals, vol. 15(3), pages 259-275.
    34. Jang-Ok Cho & Thomas Cooley & Hyung Seok Kim, 2015. "Business Cycle Uncertainty and Economic Welfare," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(2), pages 185-200, April.
    35. Lee, Jong-Wha & Lee, Hanol, 2016. "Human capital in the long run," Journal of Development Economics, Elsevier, vol. 122(C), pages 147-169.
    36. Rebelo, Sergio & Xie, Danyang, 1999. "On the optimality of interest rate smoothing," Journal of Monetary Economics, Elsevier, vol. 43(2), pages 263-282, April.
    37. Tom Krebs, 2003. "Human Capital Risk and Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(2), pages 709-744.
    38. A. Bucci & C. Colapinto & M. Forster & D. La Torre, 2011. "Stochastic technology shocks in an extended Uzawa–Lucas model: closed-form solution and long-run dynamics," Journal of Economics, Springer, vol. 103(1), pages 83-99, May.
    39. Marsiglio, Simone & La Torre, Davide, 2012. "Population dynamics and utilitarian criteria in the Lucas–Uzawa Model," Economic Modelling, Elsevier, vol. 29(4), pages 1197-1204.
    40. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    41. Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March.
    42. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kazuyuki SASAKURA, 2023. "Optimal Schooling for Economic Growth," Working Papers 2302, Waseda University, Faculty of Political Science and Economics.
    2. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    3. Tsuboi, Mizuki, 2019. "Consumption, welfare, and stochastic population dynamics when technology shocks are (Un)tied," Economic Modelling, Elsevier, vol. 79(C), pages 74-85.
    4. Giovanni Bella & Paolo Mattana & Beatrice Venturi, 2022. "Existence and implications of a pitchfork-Hopf bifurcation in a continuous-time two-sector growth model," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 259-285, January.
    5. Kazuyuki Sasakura, 2020. "The Education Sector and Economic Growth: A First Study of the Uzawa Model," Working Papers 2013, Waseda University, Faculty of Political Science and Economics.
    6. Tsuboi, Mizuki, 2020. "Growth, R&D, and uncertainty," Economic Modelling, Elsevier, vol. 87(C), pages 394-400.
    7. Motoh Tsujimura & Hidekazu Yoshioka, 2023. "A robust consumption model when the intensity of technological progress is ambiguous," Mathematics and Financial Economics, Springer, volume 17, number 2, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    2. Tsuboi, Mizuki, 2019. "Consumption, welfare, and stochastic population dynamics when technology shocks are (Un)tied," Economic Modelling, Elsevier, vol. 79(C), pages 74-85.
    3. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    4. Motoh Tsujimura & Hidekazu Yoshioka, 2023. "A robust consumption model when the intensity of technological progress is ambiguous," Mathematics and Financial Economics, Springer, volume 17, number 2, June.
    5. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    6. Matthias Birkner & Niklas Scheuer & Klaus Wälde, 2023. "The dynamics of Pareto distributed wealth in a small open economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 607-644, August.
    7. Long, N.V. & Wong, K.Y., 1996. "Endogenous Growth and International Trade: A Survey," Working Papers 96-07, University of Washington, Department of Economics.
    8. Wälde, Klaus, 2011. "Production technologies in stochastic continuous time models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 616-622, April.
    9. Tsuboi, Mizuki, 2020. "Growth, R&D, and uncertainty," Economic Modelling, Elsevier, vol. 87(C), pages 394-400.
    10. Robert Feicht & Wolfgang Stummer, 2010. "Complete Closed-form Solution to a Stochastic Growth Model and Corresponding Speed of Economic Recovery preliminary," DEGIT Conference Papers c015_041, DEGIT, Dynamics, Economic Growth, and International Trade.
    11. Olaf Posch & Timo Trimborn, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Economics Working Papers 2010-08, Department of Economics and Business Economics, Aarhus University.
    12. Antony, Jürgen & Klarl, Torben, 2022. "Poverty and sustainable development around the world during transition periods," Energy Economics, Elsevier, vol. 110(C).
    13. Jones, C.I., 2016. "The Facts of Economic Growth," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 3-69, Elsevier.
    14. Jesús Fernández‐Villaverde & Samuel Hurtado & Galo Nuño, 2023. "Financial Frictions and the Wealth Distribution," Econometrica, Econometric Society, vol. 91(3), pages 869-901, May.
    15. Pommeret, Aude & Smith, William T., 2005. "Fertility, volatility, and growth," Economics Letters, Elsevier, vol. 87(3), pages 347-353, June.
    16. Etro, Federico, 2017. "Research in economics and macroeconomics," Research in Economics, Elsevier, vol. 71(3), pages 373-383.
    17. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
    18. Johnson Kakeu, 2023. "Concerns for Long-Run Risks and Natural Resource Policy," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 84(4), pages 1051-1093, April.
    19. Ryoji Hiraguchi, 2013. "On a closed-form solution to the stochastic Lucas–Uzawa model," Journal of Economics, Springer, vol. 108(2), pages 131-144, March.
    20. Olaf Posch & Klaus Wälde, 2011. "On the link between volatility and growth," Journal of Economic Growth, Springer, vol. 16(4), pages 285-308, December.

    More about this item

    Keywords

    Human capital; Welfare; Endogenous growth; Uncertainty;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:jeczfn:v:125:y:2018:i:3:d:10.1007_s00712-018-0604-6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.