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Optimal education in times of ageing: The dependency ratio in the Uzawa–Lucas growth model


  • von Gaessler, Anne Edle
  • Ziesemer, Thomas


The increasing share of retirees puts pressure on the shrinking working generation which will need to produce more output per worker to ensure a constant standard of living. We investigate the influence of a changing dependency ratio has on the time individuals spend in education and production. Longer education will increase productivity in the future, but will lower production in the short run, whereas an increase in labour input at the cost of education will provide more production immediately. We introduce a dependency ratio into a discrete-time Uzawa–Lucas model with international capital movements, human capital externalities and decreasing returns to labour in human capital formation. The dependency ratio is defined as the fraction between inactive and active individuals in regard to work or education. By calibration of the model, we find multiple steady states indicated by a u-shaped relation between education time-shares and the growth rate of the dependency ratio. Near the stable, high-level steady state, the optimal response to higher growth of the dependency ratio is more education to enhance productivity. We find evidence for this relation for 16 OECD countries. As a model extension, a debt-dependent interest rate has been introduced and estimated.

Suggested Citation

  • von Gaessler, Anne Edle & Ziesemer, Thomas, 2016. "Optimal education in times of ageing: The dependency ratio in the Uzawa–Lucas growth model," The Journal of the Economics of Ageing, Elsevier, vol. 7(C), pages 125-142.
  • Handle: RePEc:eee:joecag:v:7:y:2016:i:c:p:125-142 DOI: 10.1016/j.jeoa.2016.03.001

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    Cited by:

    1. Ziesemer, Thomas, 2018. "The serendipity theorem for an endogenous open economy growth model," MERIT Working Papers 001, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    2. Ziesemer, Thomas, 2017. "Testing linear growth rate formulas of non-scale endogenous growth models," MERIT Working Papers 036, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    3. repec:aes:amfeco:v:46:y:2017:i:19:p:654 is not listed on IDEAS

    More about this item


    Demographic change; Education; Endogenous growth; Human capital development;

    JEL classification:

    • O15 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Economic Development: Human Resources; Human Development; Income Distribution; Migration
    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts


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