IDEAS home Printed from https://ideas.repec.org/p/aim/wpaimx/1454.html
   My bibliography  Save this paper

Stochastic Stability of Endogenous Growth: The AK Case

Author

Abstract

This note studies the stochastic stability of the standard AK growth model under uncertain output technology. Capital accumulation follows a stochastic linear homogenous differential equation. It's shown that exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncertainty. Precisely, it's demonstrated that the economy almost surely collapses at exponential speed even though productivity is initially arbitrarily high.

Suggested Citation

  • Raouf Boucekkine & Benteng Zou, 2014. "Stochastic Stability of Endogenous Growth: The AK Case," AMSE Working Papers 1454, Aix-Marseille School of Economics, France.
    • Handle: RePEc:aim:wpaimx:1454
    as

    Download full text from publisher

    File URL: http://www.amse-aixmarseille.fr/sites/default/files/_dt/2012/wp_2014_-_nr_54.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Boucekkine, R. & Fabbri, G. & Pintus, P., 2014. "Growth and financial liberalization under capital collateral constraints: The striking case of the stochastic AK model with CARA preferences," Economics Letters, Elsevier, vol. 122(2), pages 303-307.
    2. anonymous, 1995. "Does the bouncing ball lead to economic growth?," Regional Update, Federal Reserve Bank of Atlanta, issue Jul, pages 1-2,4-6.
    3. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
    4. 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.
    5. 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.
    6. Xavier Sala-I-Martin, 1997. "Transfers, Social Safety Nets, and Economic Growth," IMF Staff Papers, Palgrave Macmillan, vol. 44(1), pages 81-102, March.
    7. Steger, Thomas M., 2005. "Stochastic growth under Wiener and Poisson uncertainty," Economics Letters, Elsevier, vol. 86(3), pages 311-316, March.
    8. 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.
    9. de Hek, Paul A, 1999. "On Endogenous Growth under Uncertainty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(3), pages 727-744, August.
    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. Raouf Boucekkine & Fabien Prieur & Benteng Zou, 2015. "Symmetric vs Asymmetric Equilibria and Stochastic Stability in a Dynamic Game of Legislative Lobbying," AMSE Working Papers 1531, Aix-Marseille School of Economics, France, revised Jan 2018.
    2. Anne Epaulard & Aude Pommeret, 2016. "Financial Integration, Growth and Volatility," Pacific Economic Review, Wiley Blackwell, vol. 21(3), pages 330-357, August.
    3. Patrick Pintus, 2015. "Risk-Taking, Global Diversification and Growth: Comment," AMSE Working Papers 1504, Aix-Marseille School of Economics, France.
    4. Raouf Boucekkine & Fabien Prieur & Benteng Zou, 2015. "Institutional dynamics under revenue volatility and revenue-dependent lobbying power: A stochastic differential game approach," DEM Discussion Paper Series 15-08, Department of Economics at the University of Luxembourg.

    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. Raouf Boucekkine & Patrick Pintus & Benteng Zou, 2015. "Stochastic Stability of Endogenous Growth: Theory and Applications," AMSE Working Papers 1532, Aix-Marseille School of Economics, France.
    2. Boucekkine, Raouf & Pintus, Patrick A. & Zou, Benteng, 2018. "Mean growth and stochastic stability in endogenous growth models," Economics Letters, Elsevier, vol. 166(C), pages 18-24.
    3. Clemens Christiane, 2009. "Stochastic Growth and Factor Income Risk," German Economic Review, De Gruyter, vol. 10(4), pages 422-447, December.
    4. Wälde, Klaus, 1999. "A Poisson-Ramsey growth model: Creative destruction, endogenous cycles and growth," Technical Reports 1999,32, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. Wälde, Klaus, 2011. "Production technologies in stochastic continuous time models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 616-622, April.
    6. repec:zbw:rwidps:0030 is not listed on IDEAS
    7. Kristinn Hermannsson & Patrizio Lecca, 2016. "Human Capital in Economic Development: From Labour Productivity to Macroeconomic Impact," Economic Papers, The Economic Society of Australia, vol. 35(1), pages 24-36, March.
    8. Yew-Kwang Ng & Xiaokai Yang, 2005. "Specialization, Information, And Growth: A Sequential Equilibrium Analysis," World Scientific Book Chapters, in: An Inframarginal Approach To Trade Theory, chapter 20, pages 447-474, World Scientific Publishing Co. Pte. Ltd..
    9. Naddeo, Andreina, 2014. "How crime affects the economy: evidence from Italy," MPRA Paper 65419, University Library of Munich, Germany.
    10. Auffret, Philippe, 2001. "An alternative unifying measure of welfare gains from risk-sharing," Policy Research Working Paper Series 2676, The World Bank.
    11. G rkemli Kazar & Altu Kazar, 2015. "Is Harmonious Development Valid for European Union Regions?," International Journal of Economics and Financial Issues, Econjournals, vol. 5(4), pages 954-967.
    12. Глазьев С.Ю. & Горидько Н.П. & Нижегородцев Р.М., 2016. "Критика Формулы Ирвинга Фишера И Иллюзии Современной Монетарной Политики," Журнал Экономика и математические методы (ЭММ), Центральный Экономико-Математический Институт (ЦЭМИ), vol. 52(4), pages 3-23, октябрь.
    13. David de la CROIX, 2014. "Economic Growth," LIDAM Discussion Papers IRES 2014019, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    14. Wei-Bin Zhang, 2015. "A Portfolio Equilibrium Model of Gold and Capital in an Integrated Walrasian General Equilibrium and Neoclassical Growth Theory," International Journal of Economics and Empirical Research (IJEER), The Economics and Social Development Organization (TESDO), vol. 3(12), pages 616-627, December.
    15. Kevin S. Nell & Maria M. De Mello, 2015. "Testing Capital Accumulation-Driven Growth Models in a Multiple-Regime Framework: Evidence from South Africa," CEF.UP Working Papers 1501, Universidade do Porto, Faculdade de Economia do Porto.
    16. Albert J.F. Yang & William N. Trumbull & Chin Wei Yang & Bwo‐Nung Huang, 2011. "On The Relationship Between Military Expenditure, Threat, And Economic Growth: A Nonlinear Approach," Defence and Peace Economics, Taylor & Francis Journals, vol. 22(4), pages 449-457, April.
    17. Claude DIEBOLT & Jamel TRABELSI, 2009. "Human Capital and French Macroeconomic Growth in the Long Run," Economies et Sociétés (Serie 'Histoire Economique Quantitative'), Association Française de Cliométrie (AFC), issue 40, pages 901-917, May.
    18. Valerija Botric, 2013. "Output Convergence between Western Balkans and EU-15," Research in Economics and Business: Central and Eastern Europe, Tallinn School of Economics and Business Administration, Tallinn University of Technology, vol. 5(1).
    19. Ravallion, Martin, 2019. "Global inequality when unequal countries create unequal people," European Economic Review, Elsevier, vol. 111(C), pages 85-97.
    20. Amal MATALLAH & Amal MATALLAH, 2017. "Does fiscal policy spur economic growth? Empirical evidence from Algeria," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(3(612), A), pages 125-146, Autumn.
    21. Ranjit Singh Ghuman & Indervir Singh, 2013. "Providing Affordable Higher Education to Rural Girls in Indian Punjab: A Case Study of Baba Aya Singh Riarki College," Annals of the University of Petrosani, Economics, University of Petrosani, Romania, vol. 13(2), pages 61-84.

    More about this item

    Keywords

    optimal growth; AK model; Ito stochastic differential equation; balanced growth paths; stochastic stability;
    All these keywords.

    JEL classification:

    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:aim:wpaimx:1454. 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: Gregory Cornu (email available below). General contact details of provider: https://edirc.repec.org/data/amseafr.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.