IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_2831.html
   My bibliography  Save this paper

Production Technologies in Stochastic Continuous Time Models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp2831.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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, November.
    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," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 375-393.
    11. Marco Cagetti & Lars Peter Hansen & Thomas Sargent & Noah Williams, 2002. "Robustness and Pricing with Uncertain Growth," The 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," The Review of Economic Studies, Review of Economic Studies Ltd, 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. repec:bla:econom:v:65:y:1998:i:259:p:401-27 is not listed on IDEAS
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Darong Dai, 2014. "A Golden Formula in Neoclassical-Growth Models with Brownian-Motion Shocks," Scottish Journal of Political Economy, Scottish Economic Society, vol. 61(2), pages 211-228, May.
    3. Posch, Olaf, 2011. "Risk premia in general equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1557-1576, September.
    4. Liao, Zhong-Wei & Shao, Jinghai, 2024. "Stability and mean growth rate of stochastic Solow model driven by jump–diffusion process," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    5. Matthias Birkner & Niklas Scheuer & Klaus Wälde, 2023. "The dynamics of Pareto distributed wealth in a small open economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 607-644, August.
    6. 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.
    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. Giorgio Ferrari & Torben Koch, 2019. "On a strategic model of pollution control," Annals of Operations Research, Springer, vol. 275(2), pages 297-319, April.
    9. 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.
    10. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
    11. 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.
    12. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    13. Tsuboi, Mizuki, 2019. "Consumption, welfare, and stochastic population dynamics when technology shocks are (Un)tied," Economic Modelling, Elsevier, vol. 79(C), pages 74-85.
    14. 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.
    15. Kalamov, Zarko Y. & Zimmermann, Karl J., 2023. "GDP-linked bonds and economic growth," Journal of International Money and Finance, Elsevier, vol. 137(C).
    16. Andrea Modena & Luca Regis, 2024. "Capital risk, fiscal policy, and the distribution of wealth," Mathematics and Financial Economics, Springer, volume 18, number 8, February.
    17. Tsuboi, Mizuki, 2020. "Growth, R&D, and uncertainty," Economic Modelling, Elsevier, vol. 87(C), pages 394-400.
    18. Darong Dai, 2018. "Fiscal policy under a minimum‐time objective," Scottish Journal of Political Economy, Scottish Economic Society, vol. 65(3), pages 293-314, July.
    19. 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.
    20. 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.
    21. 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, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Posch, Olaf, 2011. "Risk premia in general equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 35(9), pages 1557-1576, September.
    2. Pommeret, Aude & Smith, William T., 2005. "Fertility, volatility, and growth," Economics Letters, Elsevier, vol. 87(3), pages 347-353, June.
    3. Liao, Zhong-Wei & Shao, Jinghai, 2024. "Stability and mean growth rate of stochastic Solow model driven by jump–diffusion process," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    4. 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.
    5. Clemens Christiane, 2009. "Stochastic Growth and Factor Income Risk," German Economic Review, De Gruyter, vol. 10(4), pages 422-447, December.
    6. 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.
    7. Christian Bayer & Klaus Waelde, 2011. "Existence, Uniqueness and Stability of Invariant Distributions in Continuous-Time Stochastic Models," Working Papers 1111, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 21 Jul 2011.
    8. 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.
    9. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    10. 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.
    11. Giuliano, Paola & Turnovsky, Stephen J., 2003. "Intertemporal substitution, risk aversion, and economic performance in a stochastically growing open economy," Journal of International Money and Finance, Elsevier, vol. 22(4), pages 529-556, August.
    12. Turnovsky, Stephen J. & Chattopadhyay, Pradip, 2003. "Volatility and growth in developing economies: some numerical results and empirical evidence," Journal of International Economics, Elsevier, vol. 59(2), pages 267-295, March.
    13. Smith, William T., 1999. "Risk, the Spirit of Capitalism and Growth: The Implications of a Preference for Capital," Journal of Macroeconomics, Elsevier, vol. 21(2), pages 241-262, April.
    14. Dibooglu, Sel & Kenc, Turalay, 2009. "Welfare cost of inflation in a stochastic balanced growth model," Economic Modelling, Elsevier, vol. 26(3), pages 650-658, May.
    15. Evans, Lynne & Kenc, Turalay, 2004. "FOREX risk premia and policy uncertainty: a recursive utility analysis," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 14(1), pages 1-24, February.
    16. Clemens, Christiane & Soretz, Susanne, 2004. "Optimal fiscal policy, uncertainty, and growth," Journal of Macroeconomics, Elsevier, vol. 26(4), pages 679-697, December.
    17. Erauskin, Iñaki, 2015. "The net foreign asset position and government size," International Review of Economics & Finance, Elsevier, vol. 35(C), pages 130-148.
    18. Ott, Ingrid & Soretz, Susanne, 2002. "Optimal Taxation in a Stochastic Endogenous Growth Model with Congestion," Hannover Economic Papers (HEP) dp-253, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    19. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    20. Ingrid Ott & Susanne Soretz, 2004. "Growth and Welfare Effects of Tax Cuts: The Case of a Productive Public Input with Technological Risk," Economic Change and Restructuring, Springer, vol. 31(2), pages 117-135, June.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ces:ceswps:_2831. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.