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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
    DOI: 10.2202/1935-1690.1524
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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. 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.
    3. Simone Marsiglio, 2016. "Uncertainty, Crowding Aversion and Tourism Aversion in Tourism Destinations," Tourism Economics, , vol. 22(1), pages 111-123, February.
    4. 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.
    5. Marsiglio, Simone, 2014. "Reassessing Edgeworth’s conjecture when population dynamics is stochastic," Journal of Macroeconomics, Elsevier, vol. 42(C), pages 130-140.
    6. 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.
    7. 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.
    8. Olaf POSCH & Klaus WALDE, 2009. "On the non-causal link between volatility and growth," LIDAM Discussion Papers IRES 2009025, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
    14. 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.
    15. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    16. Tsuboi, Mizuki, 2019. "Consumption, welfare, and stochastic population dynamics when technology shocks are (Un)tied," Economic Modelling, Elsevier, vol. 79(C), pages 74-85.
    17. 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.
    18. Olaf Posch & Klaus Wälde, 2011. "On the link between volatility and growth," Journal of Economic Growth, Springer, vol. 16(4), pages 285-308, December.
    19. 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.
    20. Wälde, Klaus, 2011. "Production technologies in stochastic continuous time models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 616-622, April.
    21. 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.
    22. Simone Marsiglio & Davide Torre, 2018. "Economic growth and abatement activities in a stochastic environment: a multi-objective approach," Annals of Operations Research, Springer, vol. 267(1), pages 321-334, August.
    23. 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.
    24. 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.
    25. 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.

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