Optimal education in times of ageing: The dependency ratio in the Uzawa-Lucas growth model
Anne Edle von Gaessler & Thomas Ziesemer
#2015-020
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 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 an age-independent dependency ratio into a
discrete-time Uzawa-Lucas model with international capital movements,
human capital externalities and decreasing returns to labour in
education. 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.
Key Words: Demographic Change, Education, Endogenous Growth, Human
Capital Development
JEL Classification: O15, J11