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Fully Endogenous Vertical and Horizontal Growth in R&D-Based Models: Escaping Population-Growth Restriction

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  • Ohki, Kazuyoshi

Abstract

This paper provides benchmark R&D-based growth models in which both vertical and horizontal growth rates are fully endogenous. In traditional models with both vertical and horizontal innovation, horizontal growth or a weighted average of vertical and horizontal growth is often constrained by population growth along the balanced growth path. This paper shows that this restriction arises from balanced-growth requirements imposed by market-clearing conditions and that it can be removed by appropriately specifying R&D externalities. The result is robust across models that differ in the input used in R&D and in the structure of vertical innovation. The reconstructed models also show that innovation policies affect not only the level of growth but also the composition of growth between vertical and horizontal innovation. The proposed formulation therefore provides a tractable building block for richer R&D-based growth models.

Suggested Citation

  • Ohki, Kazuyoshi, 2026. "Fully Endogenous Vertical and Horizontal Growth in R&D-Based Models: Escaping Population-Growth Restriction," MPRA Paper 130110, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:130110
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    References listed on IDEAS

    as
    1. Segerstrom, Paul S, 2000. "The Long-Run Growth Effects of R&D Subsidies," Journal of Economic Growth, Springer, vol. 5(3), pages 277-305, September.
    2. Peretto, Pietro F, 1998. "Technological Change and Population Growth," Journal of Economic Growth, Springer, vol. 3(4), pages 283-311, December.
    3. Ohki, Kazuyoshi, 2023. "Disruptive innovation by heterogeneous incumbents and economic growth: When do incumbents switch to new technology?," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    4. Peretto, Pietro F., 2007. "Corporate taxes, growth and welfare in a Schumpeterian economy," Journal of Economic Theory, Elsevier, vol. 137(1), pages 353-382, November.
    5. Alwyn Young, 1998. "Growth without Scale Effects," Journal of Political Economy, University of Chicago Press, vol. 106(1), pages 41-63, February.
    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. Peter Howitt, 1999. "Steady Endogenous Growth with Population and R & D Inputs Growing," Journal of Political Economy, University of Chicago Press, vol. 107(4), pages 715-730, August.
    8. Ohki, Kazuyoshi, 2025. "Incremental Innovation by Heterogeneous Incumbents and Economic Growth: relationship between two sources of growth," MPRA Paper 124304, University Library of Munich, Germany.
    9. Dinopoulos, Elias & Thompson, Peter, 1998. "Schumpeterian Growth without Scale Effects," Journal of Economic Growth, Springer, vol. 3(4), pages 313-335, December.
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    Keywords

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    JEL classification:

    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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