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Inspecting the Mechanism Exactly: A Closed-form Solution to a Stochastic Growth Model

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  • Smith William T

    () (University of Memphis)

Abstract

This paper considers the canonical stochastic growth model with CRRA utility and Cobb-Douglas technology. It obtains a closed-form solution for the case where capital's share is equal to the reciprocal of the intertemporal elasticity of substitution. This provides a useful benchmark that illuminates the transmission mechanism under uncertainty. In particular, it highlights the complicated ways in which risk and nonlinearities interact, via Jensen's inequality, to affect the steady state capital stock.

Suggested Citation

  • 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.
  • Handle: RePEc:bpj:bejmac:v:7:y:2007:i:1:n:30
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    Citations

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    Cited by:

    1. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    2. Alberto BUCCI & Cinzia COLAPINTO & Martin FORSTER & Davide LA TORRE, 2008. "On human capital and economic growth with random technology shocks," Departmental Working Papers 2008-36, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    3. Marsiglio, Simone, 2014. "Reassessing Edgeworth’s conjecture when population dynamics is stochastic," Journal of Macroeconomics, Elsevier, vol. 42(C), pages 130-140.
    4. 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.
    5. 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.
    6. Ruiz-Tamarit, J.R. & Ventura-Marco, M., 2011. "Solution to nonlinear MHDS arising from optimal growth problems," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 86-96, March.
    7. 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.
    8. Md. Azizul Baten & Anton Abdulbasah Kamil, 2013. "Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-8, March.
    9. Olaf Posch, 2009. "Explaining Output Volatility: The Case of Taxation," CESifo Working Paper Series 2751, CESifo Group Munich.
    10. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
    11. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    12. Tsuboi, Mizuki, 2019. "Consumption, welfare, and stochastic population dynamics when technology shocks are (Un)tied," Economic Modelling, Elsevier, vol. 79(C), pages 74-85.
    13. Erauskin, Iñaki & Turnovsky, Stephen J., 2019. "International financial integration and income inequality in a stochastically growing economy," Journal of International Economics, Elsevier, vol. 119(C), pages 55-74.
    14. Olaf Posch & Klaus Wälde, 2011. "On the link between volatility and growth," Journal of Economic Growth, Springer, vol. 16(4), pages 285-308, December.
    15. Miguel Palacios, 2010. "Human Capital as an Asset Class: Implications from a General Equilibrium Model," Working Papers 2011-016, Human Capital and Economic Opportunity Working Group.
    16. Klaus Wälde, 2009. "Production Technologies in Stochastic Continuous Time Models," CESifo Working Paper Series 2831, CESifo Group Munich.
    17. repec:kap:jeczfn:v:125:y:2018:i:3:d:10.1007_s00712-018-0604-6 is not listed on IDEAS
    18. Wälde, Klaus, 2011. "Production technologies in stochastic continuous time models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 616-622, April.
    19. repec:spr:annopr:v:267:y:2018:i:1:d:10.1007_s10479-016-2357-3 is not listed on IDEAS
    20. Guerrini, Luca, 2010. "A closed-form solution to the Ramsey model with logistic population growth," Economic Modelling, Elsevier, vol. 27(5), pages 1178-1182, September.
    21. Johnson Kakeu, 2017. "Environmentally conscious investors and portfolio choice decisions," Journal of Sustainable Finance & Investment, Taylor & Francis Journals, vol. 7(4), pages 360-378, October.

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