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Production Technologies in Stochastic Continuous Time Models

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  • Klaus Wälde

Abstract

Properties of dynamic stochastic general equilibrium models can be revealed by either using numerical solutions or qualitative analysis. Very precise and intuition-building results are obtained by working with models which provide closed-form solutions. Closed-form solutions are known for a large class of models some of which, however, have some undesirable features. This paper offers closed-form solutions for models which are just as tractable but do not suffer from these shortcomings.

Suggested Citation

  • Klaus Wälde, 2009. "Production Technologies in Stochastic Continuous Time Models," CESifo Working Paper Series 2831, CESifo.
  • Handle: RePEc:ces:ceswps:_2831
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    1. Turnovsky, Stephen J. & Bianconi, Marcelo, 2005. "Welfare Gains From Stabilization In A Stochastically Growing Economy With Idiosyncratic Shocks And Flexible Labor Supply," Macroeconomic Dynamics, Cambridge University Press, vol. 9(3), pages 321-357, June.
    2. Santanu Chatterjee & Paola Giuliano & Stephen J. Turnovsky, 2004. "Capital Income Taxes and Growth in a Stochastic Economy: A Numerical Analysis of the Role of Risk Aversion and Intertemporal Substitution," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 6(2), pages 277-310, May.
    3. Grinols, Earl L. & Turnovsky, Stephen J., 1993. "Risk, the financial market, and macroeconomic equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 1-36.
    4. Gong, Liutang & Zou, Heng-fu, 2002. "Direct preferences for wealth, the risk premium puzzle, growth, and policy effectiveness," Journal of Economic Dynamics and Control, Elsevier, vol. 26(2), pages 247-270, February.
    5. Koethenbuerger, Marko & Lockwood, Ben, 2010. "Does tax competition really promote growth?," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 191-206, February.
    6. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947, May.
    7. Stephen J. Turnovsky, 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, October.
    8. 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.
    9. Ken Sennewald & Klaus Wälde, 2006. "“Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View," Journal of Economics, Springer, vol. 89(1), pages 1-36, October.
    10. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," Review of Economic Studies, Oxford University Press, vol. 42(3), pages 375-393.
    11. 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.
    12. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    13. Anne Epaulard & Aude Pommeret, 2003. "Recursive Utility, Endogenous Growth, and the Welfare Cost of Volatility," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(3), pages 672-684, July.
    14. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    15. Grinols, Earl L & Turnovsky, Stephen J, 1998. "Consequences of Debt Policy in a Stochastically Growing Monetary Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(2), pages 495-521, May.
    16. Turnovsky, Stephen J., 1999. "Productive Government Expenditure In A Stochastically Growing Economy," Macroeconomic Dynamics, Cambridge University Press, vol. 3(4), pages 544-570, December.
    17. Rebelo, Sergio & Xie, Danyang, 1999. "On the optimality of interest rate smoothing," Journal of Monetary Economics, Elsevier, vol. 43(2), pages 263-282, April.
    18. Garcia-Penalosa, Cecilia & Turnovsky, Stephen J., 2005. "Production risk and the functional distribution of income in a developing economy: tradeoffs and policy responses," Journal of Development Economics, Elsevier, vol. 76(1), pages 175-208, February.
    19. Turnovsky, Stephen J, 1993. "Macroeconomic Policies, Growth, and Welfare in a Stochastic Economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(4), pages 953-981, November.
    20. 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.
    21. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    22. Jonathan Eaton, 1981. "Fiscal Policy, Inflation and the Accumulation of Risky Capital," Review of Economic Studies, Oxford University Press, vol. 48(3), pages 435-445.
    23. Philippe Monfort & Aude Pommeret, 2002. "Fiscal Harmonization and Portfolio Choice," Cahiers de Recherches Economiques du Département d'économie 02.16, Université de Lausanne, Faculté des HEC, Département d’économie.
    24. Turnovsky, Stephen J., 1999. "On the role of government in a stochastically growing open economy," Journal of Economic Dynamics and Control, Elsevier, vol. 23(5-6), pages 873-908, April.
    25. Pommeret, Aude & Smith, William T., 2005. "Fertility, volatility, and growth," Economics Letters, Elsevier, vol. 87(3), pages 347-353, June.
    26. Asea, Patrick K. & Turnovsky, Stephen J., 1998. "Capital income taxation and risk-taking in a small open economy," Journal of Public Economics, Elsevier, vol. 68(1), pages 55-90, April.
    27. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    28. Gokan, Yoichi, 2002. "Alternative government financing and stochastic endogenous growth," Journal of Economic Dynamics and Control, Elsevier, vol. 26(4), pages 681-706, April.
    29. Grinols, Earl L. & Turnovsky, Stephen J., 1994. "Exchange rate determination and asset prices in a stochastic small open economy," Journal of International Economics, Elsevier, vol. 36(1-2), pages 75-97, February.
    30. 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.
    31. Gertler, Mark & Grinols, Earl, 1982. "Monetary randomness and investment," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 239-258.
    32. Klaus Wälde, 2005. "Endogenous Growth Cycles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(3), pages 867-894, August.
    33. Gong, Liutang & Zou, Heng-fu, 2003. "Military spending and stochastic growth," Journal of Economic Dynamics and Control, Elsevier, vol. 28(1), pages 153-170, October.
    34. 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.
    35. Grinols, Earl L & Turnovsky, Stephen J, 1998. "Risk, Optimal Government Finance and Monetary Policies in a Growing Economy," Economica, London School of Economics and Political Science, vol. 65(259), pages 401-427, August.
    36. Smith, William T., 1996. "Taxes, uncertainty, and long-term growth," European Economic Review, Elsevier, vol. 40(8), pages 1647-1664, November.
    37. Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March.
    38. 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.
    39. Clemens, Christiane & Soretz, Susanne, 2004. "Optimal fiscal policy, uncertainty, and growth," Journal of Macroeconomics, Elsevier, vol. 26(4), pages 679-697, December.
    40. Evans, Lynne & Kenc, Turalay, 2003. "Welfare Cost Of Monetary And Fiscal Policy Shocks," Macroeconomic Dynamics, Cambridge University Press, vol. 7(2), pages 212-238, April.
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    Cited by:

    1. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
    2. 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.
    3. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    4. Parra-Alvarez, Juan Carlos, 2018. "A Comparison Of Numerical Methods For The Solution Of Continuous-Time Dsge Models," Macroeconomic Dynamics, Cambridge University Press, vol. 22(6), pages 1555-1583, September.
    5. Jetter, Michael & Nikolsko-Rzhevskyy, Alex & Smith, William T., 2013. "The effects of wage volatility on growth," Journal of Macroeconomics, Elsevier, vol. 37(C), pages 93-109.
    6. Parra-Alvarez, Juan Carlos & Polattimur, Hamza & Posch, Olaf, 2021. "Risk matters: Breaking certainty equivalence in linear approximations," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    7. Dai, Darong & Tian, Guoqiang, 2021. "Toward longer investment: Is an inclusive regime always better than an authoritarian one?," Economic Modelling, Elsevier, vol. 98(C), pages 41-68.
    8. Posch, Olaf, 2011. "Risk premia in general equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1557-1576, September.
    9. Tsuboi, Mizuki, 2019. "Consumption, welfare, and stochastic population dynamics when technology shocks are (Un)tied," Economic Modelling, Elsevier, vol. 79(C), pages 74-85.
    10. 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.
    11. Dirk Bethmann & Markus Reiß, 2012. "Simplifying numerical analyses of Hamilton–Jacobi–Bellman equations," Journal of Economics, Springer, vol. 107(2), pages 101-128, October.
    12. 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.
    13. Giorgio Ferrari & Torben Koch, 2019. "On a strategic model of pollution control," Annals of Operations Research, Springer, vol. 275(2), pages 297-319, April.
    14. Tsuboi, Mizuki, 2020. "Growth, R&D, and uncertainty," Economic Modelling, Elsevier, vol. 87(C), pages 394-400.
    15. Dai, Darong, 2012. "Comparative Studies on Cooperative Stochastic Differential Game and Dynamic Sequential Game of Economic Maturity," MPRA Paper 44339, University Library of Munich, Germany.
    16. 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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    More about this item

    Keywords

    dynamic stochastic general equilibrium models; closed-form solution; continuous time; jump diffusion;
    All these keywords.

    JEL classification:

    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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