Macro chapter 9 summary

The macro model of R&D-based endogenous growth studied in this chapter had the following
features:
• Final goods are produced from the inputs of capital, labour and (labour-augmenting)
technology, A,, according to a standard Cobb- Douglas production function.
• New technology is produced in the R&D sector from the inputs of labour and existing
technology according to a production function with constant returns to labour at the firm
level but possibly diminishing returns at the aggregate level, because firms in the R&D
sector may be 'stepping on each other's toes' by working on the same ideas. There is a
specific elasticity, ¢,of the output of new technology, A,. 1 - Au with respect to the input
of existing technology, A,.
• The labour force can be used in either production of final goods or in production of new
technology, whereas existing technology can be used in both sectors. reflecting that ideas
are non-rival. The fraction of labour used in the R&D sector is an exogenous parameter
called the research (or R&D) share.
• In other respects the model is standard: capital accumulates from savings and investment
(minus depreciation), and the labour force grows at an exogenous rate.
2. If¢ is equal to 1, a constant input of labour in the R&D sector creates a constant and positive
growth rate of technology, (A ,. 1 - A,)/A,. If¢ is less than 1, reflecting that it becomes harder
to generate new ideas as the more obvious ideas have already been discovered, a constant
labour input in research will imply that the absolute production of technology, At+ 1 -A 1,
increases and goes to infinity over time, but the growth rate, (A,. 1 -A1)/A 1, goes to 0. To
maintain a positive, constant growth rate of technology requires a positive, constant growth
rate of the labour input into the research sector (when ¢ < 1 ).
In the case 0 < 4> < 1, the model implies conver~ence to a steady state where capital and
output per worker both grow at the same constant rate as technology, and the growth rate of
technology depends positively on the rate of growth of the labour force (or population) in such
a way that there can only be economic growth if there is population growth. The reason is that
given a constant research share, the labour input in the research sector can only grow at a
constant rate if population grows at a constant rate. The semi-endogenous growth arising in
this case suggests that a policy to promote economic growth should be one that stimulates
population growth.
4. In the alternative case where ¢ = 1, a constant labour force and a constant research share
imply a constant positive growth rate of technology that depends positively, and in a simple
way, on the size of the research share. The fu ll model gives convergence to a steady state
where capital and income per worker both grow at the same rate as technology. A growthpromoting
structural policy is one that increases the research share, but the model is tacit
about how th is can be achieved since the research share is exogenous. The model of truly
endogenous growth arising when 4> = 1 implies a highly implausible scale effect: a larger
labour force should imply a higher rate of growth of GDP per worker, and if the labour force
incrco.scs at o. consto.nt ro.tc, the growth ro.tc of income per worker should explode.
5. Mainly because of empirical evidence concerning the links between population growth and
economic growth, it can be hard to believe that the observed long-lasting economic growth in
Western countries should be understood as either purely semi-endogenous growth (where
growth in the labour force is needed for economic growth because the research share is
constant, and ¢ < 1) or as truly endogenous growth (where economic growth can occur for a
constant labour force because 4> = 1, but an increasing labour force would imply increasing
economic growth).
6. According to the model studied in th is chapter there could be an in-between explanation of
economic growth during the last 200 years. Hemi-endogenous growth, as we called it, is
closely related to semi-endogenous growth (assuming 4> < 1 ), but explains the required
growth of the labour input in R&D as the result, not of population growth given the research
share, but of a gradually increasing research share possibly for a constant labour force. We
showed that under reasonable parameter specifications, a realistic slow and gradual increase
in the research share could, according to our model, explain annual growth rates of GDP per
capita in the range 1.5-2 per cent over periods of 200 years and more. This makes the hemiendogenous
growth interpretation look plausible. Of course, the research share cannot grow
at a constant rate forever, so one day hemi-endogenous growth is over. When the research
share reaches its maximum, increased labour input in the R&D sector (required for economic
growth when 4> < 1) can only be achieved by increases in the labour force.

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