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


  • Smith William T

    () (University of Memphis)


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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    References listed on IDEAS

    1. Nicoletta Batini & Paul Levine & Joseph Pearlman, 2003. "Indeterminacy with inflation-forecast-cased rules in a two-bloc model," Proceedings, Board of Governors of the Federal Reserve System (U.S.).
    2. Ignazio Angeloni & Gunter Coenen & Frank Smets, 2003. "Persistence, The Transmission Mechanism And Robust Monetary Policy," Scottish Journal of Political Economy, Scottish Economic Society, vol. 50(5), pages 527-549, November.
    3. Angeloni,Ignazio & Kashyap,Anil K. & Mojon,Benoît (ed.), 2003. "Monetary Policy Transmission in the Euro Area," Cambridge Books, Cambridge University Press, number 9780521828642, March.
    4. Backé, Peter & Kashyap, Anil K. & Mojon, Benoît & Terlizzese, Daniele, 2003. "The output composition puzzle: a difference in the monetary transmission mechanism in the euro area and U.S," Working Paper Series 268, European Central Bank.
    5. Benigno, Pierpaolo & Lopez-Salido, J. David, 2006. "Inflation Persistence and Optimal Monetary Policy in the Euro Area," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 38(3), pages 587-614, April.
    6. Tamim Bayoumi & Barry Eichengreen, 1992. "Shocking Aspects of European Monetary Unification," NBER Working Papers 3949, National Bureau of Economic Research, Inc.
    7. Ignazio Angeloni & Anil K. Kashyap & Benoit Mojon & Daniele Terlizzese, 2003. "Monetary Transmission in the Euro Area: Does the Interest Rate Channel Explain it All?," NBER Working Papers 9984, National Bureau of Economic Research, Inc.
    8. Javier Andrés & Eva Ortega & Javier Vallés, 2003. "Market structure and inflation differentials in the European Monetary Union," Working Papers 0301, Banco de España;Working Papers Homepage.
    9. Benigno, Pierpaolo, 2004. "Optimal monetary policy in a currency area," Journal of International Economics, Elsevier, vol. 63(2), pages 293-320, July.
    10. Michael Ehrmann & Marcel Fratzscher, 2005. "Equal Size, Equal Role? Interest Rate Interdependence Between the Euro Area and the United States," Economic Journal, Royal Economic Society, vol. 115(506), pages 928-948, October.
    11. Batini, Nicoletta & Nelson, Edward, 2001. "Optimal horizons for inflation targeting," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 891-910, June.
    12. Michael Ehrmann & Marcel Fratzscher, 2003. "Interdependence between the Euro area and the U.S.: what role for EMU?," Proceedings, Board of Governors of the Federal Reserve System (U.S.).
    13. Bergin, Paul R., 2003. "A model of relative national price levels under pricing to market," European Economic Review, Elsevier, vol. 47(3), pages 569-586, June.
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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. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
    9. Olaf Posch & Klaus Wälde, 2011. "On the link between volatility and growth," Journal of Economic Growth, Springer, vol. 16(4), pages 285-308, December.
    10. 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.
    11. Wälde, Klaus, 2011. "Production technologies in stochastic continuous time models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 616-622, April.
    12. 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.

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