IDEAS home Printed from https://ideas.repec.org/p/drm/wpaper/2025-46.html

Endogenous Innovation in a Growth Model à la Solow

Author

Listed:
  • Ngoc-Sang Pham
  • Thi Kim Cuong Pham
  • Trong Tin Nguyen
  • Cuong Le Van

Abstract

We develop a dynamic endogenous-growth model with an R&D sector in which the elasticity of innovation with respect to existing knowledge can be negative. We prove the existence and uniqueness of a balanced growth path (BGP) and derive closed-form growth factors, showing that productivity and output growth are semi-endogenous and population-driven. We also establish the global stability under general production function. Under testable parameter restrictions, the economy converges to the BGP. When the knowledge elasticity is sufficiently low, a Jacobian-based condition implies instability, and an N-period innovation cycle can emerge. Comparative statics are conducted to show the role of several factors, including research efficiency, elasticity of inputs and population growth. Calibrated simulations map out transitions and mark the points at which stability is lost. They make clear when innovation frictions endanger balanced growth and provide practical guidance for R&D and demographic policy.

Suggested Citation

  • Ngoc-Sang Pham & Thi Kim Cuong Pham & Trong Tin Nguyen & Cuong Le Van, 2025. "Endogenous Innovation in a Growth Model à la Solow," EconomiX Working Papers 2025-46, University of Paris Nanterre, EconomiX.
    • Handle: RePEc:drm:wpaper:2025-46
    as

    Download full text from publisher

    File URL: https://economix.fr/pdf/dt/2025/WP_EcoX_2025-46.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Romer, Paul M, 1986. "Increasing Returns and Long-run Growth," Journal of Political Economy, University of Chicago Press, vol. 94(5), pages 1002-1037, October.
    2. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    3. Romer, Paul M, 1990. "Endogenous Technological Change," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 71-102, October.
    4. Nicholas Bloom & Charles I. Jones & John Van Reenen & Michael Webb, 2020. "Are Ideas Getting Harder to Find?," American Economic Review, American Economic Association, vol. 110(4), pages 1104-1144, April.
    5. Segerstrom, Paul S, 1998. "Endogenous Growth without Scale Effects," American Economic Review, American Economic Association, vol. 88(5), pages 1290-1310, December.
    6. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-784, August.
    7. K. J. Arrow, 1971. "The Economic Implications of Learning by Doing," Palgrave Macmillan Books, in: F. H. Hahn (ed.), Readings in the Theory of Growth, chapter 11, pages 131-149, Palgrave Macmillan.
    8. Aghion, Philippe & Howitt, Peter, 1992. "A Model of Growth through Creative Destruction," Econometrica, Econometric Society, vol. 60(2), pages 323-351, March.
    9. Tor Jakob Klette & Samuel Kortum, 2004. "Innovating Firms and Aggregate Innovation," Journal of Political Economy, University of Chicago Press, vol. 112(5), pages 986-1018, October.
    10. Benhabib, Jess & Spiegel, Mark M., 1994. "The role of human capital in economic development evidence from aggregate cross-country data," Journal of Monetary Economics, Elsevier, vol. 34(2), pages 143-173, October.
    11. He, Sicheng, 2022. "Growing through endogenous innovation cycles," Journal of Macroeconomics, Elsevier, vol. 71(C).
    12. Rachel Griffith & Stephen Redding & John Van Reenen, 2004. "Mapping the Two Faces of R&D: Productivity Growth in a Panel of OECD Industries," The Review of Economics and Statistics, MIT Press, vol. 86(4), pages 883-895, November.
    Full references (including those not matched with items on IDEAS)

    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. Thi Kim Cuong Pham & Ngoc-Sang Pham & Cuong Le Van & Tin Nguyen-Trong, 2025. "Endogenous Innovation in a Growth Model à la Solow," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-05388671, HAL.
    2. Capolupo, Rosa, 2009. "The New Growth Theories and Their Empirics after Twenty Years," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy, vol. 3, pages 1-72.
    3. Adriana Di Liberto, 2007. "Convergence and Divergence in Neoclassical Growth Models with Human Capital," Economia politica, Società editrice il Mulino, issue 2, pages 289-322.
    4. Volker Grossmann & Thomas Steger, 2007. "Growth, Development, and Technological Change," CESifo Working Paper Series 1913, CESifo.
    5. Cem Ertur & Wilfried Koch, 2007. "Growth, technological interdependence and spatial externalities: theory and evidence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(6), pages 1033-1062.
    6. Amavilah, Voxi Heinrich, 2014. "Knowledge = Technology + Human Capital and the Lucas and Romer Production Functions," MPRA Paper 58847, University Library of Munich, Germany.
    7. Bayraktar-Sağlam, Bahar & Yetkiner, Hakan, 2014. "A Romerian contribution to the empirics of economic growth," Journal of Policy Modeling, Elsevier, vol. 36(2), pages 257-272.
    8. Raquel Ortega-Argilés, 2013. "R&D, knowledge, economic growth and the transatlantic productivity gap," Chapters, in: Frank Giarratani & Geoffrey J.D. Hewings & Philip McCann (ed.), Handbook of Industry Studies and Economic Geography, chapter 11, pages 271-302, Edward Elgar Publishing.
    9. T. Gries & R. Grundmann & I. Palnau & M. Redlin, 2017. "Innovations, growth and participation in advanced economies - a review of major concepts and findings," International Economics and Economic Policy, Springer, vol. 14(2), pages 293-351, April.
    10. Pozzolo, Alberto Franco, 2004. "Endogenous Growth in Open Economies - A Survey of Major Results," Economics & Statistics Discussion Papers esdp04020, University of Molise, Department of Economics.
    11. Jeon, Heesang, 2015. "Knowledge and Contemporary Capitalism in Light of Marx's Value Theory," Thesis Commons g5njk, Center for Open Science.
    12. repec:spo:wpmain:info:hdl:2441/4cufqrm9749dbol0m0bsfeopka is not listed on IDEAS
    13. Martin Zagler & Georg Dürnecker, 2003. "Fiscal Policy and Economic Growth," Journal of Economic Surveys, Wiley Blackwell, vol. 17(3), pages 397-418, July.
    14. Gomes, Orlando, 2007. "Externalities in R&D: a route to endogenous fluctuations," MPRA Paper 2850, University Library of Munich, Germany.
    15. Lutz Arnold, 2007. "A generalized multi-country endogenous growth model," International Economics and Economic Policy, Springer, vol. 4(1), pages 61-100, April.
    16. MARTINS, Ana Paula, 2015. "Increasing Returns And Endogenous Growth: Market Size And Taste For Variety," Academica Science Journal, Economica Series, Dimitrie Cantemir University, Faculty of Economical Science, vol. 1(5), pages 3-33, June.
    17. repec:ebl:ecbull:v:15:y:2007:i:8:p:1-7 is not listed on IDEAS
    18. Callaghan, Christian William, 2021. "Growth contributions of technological change: Is there a burden of knowledge effect?," Technological Forecasting and Social Change, Elsevier, vol. 172(C).
    19. Arkadiusz Kijek & Tomasz Kijek, 2020. "Nonlinear Effects of Human Capital and R&D on TFP: Evidence from European Regions," Sustainability, MDPI, vol. 12(5), pages 1-14, February.
    20. Harashima, Taiji, 2010. "An Asymptotically Non-Scale Endogenous Growth Model," MPRA Paper 26025, University Library of Munich, Germany.
    21. Thomas Ziesemer, 2018. "Testing the Growth Links of Emerging Economies: Croatia in a Growing World Economy," Bulletin of Applied Economics, Risk Market Journals, vol. 5(1), pages 1-27.
    22. Long, N.V. & Wong, K.Y., 1996. "Endogenous Growth and International Trade: A Survey," Discussion Papers in Economics at the University of Washington 96-07, Department of Economics at the University of Washington.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    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:drm:wpaper:2025-46. 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: Valerie Mignon The email address of this maintainer does not seem to be valid anymore. Please ask Valerie Mignon to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/modemfr.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.