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Complete Closed-form Solution to a Stochastic Growth Model and Corresponding Speed of Economic Recovery preliminary

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  • Robert Feicht
  • Wolfgang Stummer
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    Abstract

    We consider a continuous-time neoclassical one-sector stochastic growth model of Ramsey-type with CRRA utility and Cobb-Douglas technology, where each of the following components are exposed to exogeneous uncertainties (shocks): capital stock K, effectiveness of labor A, and labor force L; the corresponding dynamics is modelled by a system of three interrelated stochastic differential equations. For this framework, we solve completely explicitly the problem of a social planner who seeks to maximize expected lifetime utility of consumption. In particular, for any (e.g. short-term) time-horizon t > 0 we obtain in closed form the sample paths of the economy values Kt, At, Lt and the optimal consumption copt(Kt, At, Lt) as well as the non-equilibrium sample paths of the per capita effective capital stock kt = Kt/At Lt. Moreover, we also deduce explicitly the limiting long-term behaviour of kt expressed by the corresponding steady-state equilibrium distribution. As illustration, we present some Monte Carlo simulations where the abovementioned economy is considerably disturbed (out of equilibrium) by a sudden crash but recovers well within a realistic-size time-period.

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    Bibliographic Info

    Paper provided by DEGIT, Dynamics, Economic Growth, and International Trade in its series DEGIT Conference Papers with number c015_041.

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    Length: 29 pages JEL Classification:
    Date of creation: Sep 2010
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    Handle: RePEc:deg:conpap:c015_041

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    Related research

    Keywords: stochastic Ramsey-type growth; utility maximization; stochastic differential equations; explicit closed-form sample path dynamics; economic recovery; Monte Carlo simulations; steady-state.;

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    1. Conesa, Juan Carlos & Kitao, Sagiri & Krueger, Dirk, 2006. "Taxing capital? Not a bad idea after all!," CFS Working Paper Series 2006/21, Center for Financial Studies (CFS).
    2. Marco Cagetti & Lars Peter Hansen & Thomas Sargent & Noah Williams, 2002. "Robustness and Pricing with Uncertain Growth," Review of Financial Studies, Society for Financial Studies, vol. 15(2), pages 363-404, March.
    3. Marco Cagetti & Mariacristina De Nardi, 2007. "Estate taxation, entrepreneurship, and wealth," Working Paper Series WP-07-08, Federal Reserve Bank of Chicago.
    4. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    5. Clemens Christiane, 2005. "Income Taxation, Productive Government Expenditure and Stochastic Growth: On Conditions for an Optimal Policy and the Role of the Risk Premium," The B.E. Journal of Macroeconomics, De Gruyter, vol. 5(1), pages 1-42, June.
    6. Turnovsky, Stephen J. & Smith, William T., 2006. "Equilibrium consumption and precautionary savings in a stochastically growing economy," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 243-278, February.
    7. Bjarne Jensen & Mogens Larsen, 2005. "General equilibrium dynamics of multi-sector growth models," Journal of Economics, Springer, vol. 10(1), pages 17-56, December.
    8. Daron Acemoglu & Veronica Guerrieri, 2006. "Capital Deepening and Non-Balanced Economic Growth," NBER Working Papers 12475, National Bureau of Economic Research, Inc.
    9. Roche, Herve, 2003. "Stochastic growth: a duality approach," Journal of Economic Theory, Elsevier, vol. 113(1), pages 131-143, November.
    10. Stummer, Wolfgang & Vajda, Igor, 2007. "Optimal statistical decisions about some alternative financial models," Journal of Econometrics, Elsevier, vol. 137(2), pages 441-471, April.
    11. BOUCEKKINE, Raouf & RUIZ-TAMARIT, Ramon, 2004. "Imbalance effects in the Lucas model: an analytical exploration," CORE Discussion Papers 2004008, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Barro, R.J. & Mankiw, N.G. & Sala-i-Martin, X., 1992. "Capital Mobility in Neoclassical Models of Growth," Papers 655, Yale - Economic Growth Center.
    13. 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.
    14. Olaf Posch, 2008. "Explaining output volatility: The case of taxation," CREATES Research Papers 2008-04, School of Economics and Management, University of Aarhus.
    15. Merton, Robert C., 1973. "An asymptotic theory of growth under uncertainty," Working papers 673-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    16. Robert E. Hall, 1999. "The Stock Market and Capital Accumulation," NBER Working Papers 7180, National Bureau of Economic Research, Inc.
    17. repec:cor:louvrp:2003 is not listed on IDEAS
    18. Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March.
    19. Caselli, Francesco & Coleman II, Wilbur John, 2000. "The World Technology Frontier," CEPR Discussion Papers 2584, C.E.P.R. Discussion Papers.
    20. Chang, Fwu-Ranq, 1988. "The Inverse Optimal Problem: A Dynamic Programming Approach," Econometrica, Econometric Society, vol. 56(1), pages 147-72, January.
    21. Olaf Posch & Klaus Wälde, 2010. "On the Non-Causal Link between Volatility and Growth," Working Papers 1002, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 08 Mar 2010.
    22. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    23. Jones, Larry E. & Manuelli, Rodolfo E., 2005. "Neoclassical Models of Endogenous Growth: The Effects of Fiscal Policy, Innovation and Fluctuations," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 1, pages 13-65 Elsevier.
    24. Kenc, Turalay, 2004. "Taxation, risk-taking and growth: a continuous-time stochastic general equilibrium analysis with labor-leisure choice," Journal of Economic Dynamics and Control, Elsevier, vol. 28(8), pages 1511-1539, June.
    25. Noah Williams, 2003. "Small Noise Asymptotics for a Stochastic Growth Model," NBER Working Papers 10194, National Bureau of Economic Research, Inc.
    26. P.M. Hartley & L.C.G. Rogers, 2005. "Two-Sector Stochastic Growth Models ," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 322-351, December.
    27. Xie, Danyang, 1991. "Increasing Returns and Increasing Rates of Growth," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 429-35, April.
    28. Jensen, Bjarne S & Wang, Chunyan, 1999. "Basic Stochastic Dynamic Systems of Growth and Trade," Review of International Economics, Wiley Blackwell, vol. 7(3), pages 378-402, August.
    29. Pindyck, Robert S., 1998. "Irreversibilities and the timing of environmental policy," Working papers WP 4047-98., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    30. BOUCEKKINE, Raouf & RUIZ-TAMARIT, José Ramon, . "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," CORE Discussion Papers RP -2003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    31. Pindyck, Robert S. & Solimano, Andres, 1993. "Economic instability and aggregate investment," Policy Research Working Paper Series 1148, The World Bank.
    32. Orazio Attanasio & James Banks & Costas Meghir & Guglielmo Weber, 1995. "Humps and bumps in lifetime consumption," IFS Working Papers W95/14, Institute for Fiscal Studies.
    33. Bjarne S. Jensen & Mogens E. Larsen, 2005. "General Equilibrium Dynamics of Multi-Sector Growth Models," DEGIT Conference Papers c010_003, DEGIT, Dynamics, Economic Growth, and International Trade.
    34. King, R.G. & Rebelo, S.T., 1989. "Transitional Dynamics And Economic Growth In The Neoclassical Model," RCER Working Papers 206, University of Rochester - Center for Economic Research (RCER).
    35. Corsetti, Giancarlo, 1997. "A portfolio approach to endogenous growth: equilibrium and optimal policy," Journal of Economic Dynamics and Control, Elsevier, vol. 21(10), pages 1627-1644, August.
    36. Jensen, Bjarne S, et al, 2001. "Saving Rates, Trade, Technology, and Stochastic Dynamics," Review of Development Economics, Wiley Blackwell, vol. 5(2), pages 182-204, June.
    37. Bourguignon, Francois, 1974. "A particular class of continuous-time stochastic growth models," Journal of Economic Theory, Elsevier, vol. 9(2), pages 141-158, October.
    38. Kwamie Dunbar, 2009. "Stochastic Business Cycle Volatilities, Capital Accumulation and Economic Growth: Lessons from the Global Credit Market Crisis," Working papers 2009-36, University of Connecticut, Department of Economics.
    39. Douglas Gollin & Steven Parente & Richard Rogerson, 2003. "Structural Transformation and Cross-Country Income Differences," Levine's Working Paper Archive 506439000000000259, David K. Levine.
    40. Stephen J. Turnovsky, 2000. "Methods of Macroeconomic Dynamics, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262201232, December.
    41. Romuald Elie & Nizar Touzi, 2008. "Optimal lifetime consumption and investment under a drawdown constraint," Finance and Stochastics, Springer, vol. 12(3), pages 299-330, July.
    42. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    43. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947, October.
    44. Turnovsky, Stephen J, 2000. " Government Policy in a Stochastic Growth Model with Elastic Labor Supply," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 2(4), pages 389-433.
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    Cited by:
    1. Herbst, Anthony F. & Wu, Joseph S.K. & Ho, Chi Pui, 2012. "Relationship between risk attitude and economic recovery in optimal growth theory," Global Finance Journal, Elsevier, vol. 23(3), pages 141-150.

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