Macro chapter 8 summary
Productive externalities and Endogenous Growth
1. In endogenous growth theory the growth rate of technology, which underlies the long-run
growth in GOP per worker, is endogenous: it depends on basic behavioural model parameters
and therefore on structural policies that affect these parameters.
2. According to the replication argument, the individual firm's production function should exhibit
constant returns to the inputs of capital and labour at any given technological level. If there are
productive externalities from the aggregate stock of capital (or from aggregate production) to
labour productivity or total factor productivity in the individual firm, then there can be constant
returns to capital and labour at the firm level and increasing returns to capital and labour at the
aggregate level. With productive externalities one can therefore maintain the convenient
assumption of perfect competition and the associated theory of income distribution, and at
the same time have a potential source of endogenous growth in the model.
3. There are theoretical as well as empirical motivations for productive externalities and aggregate
increasing returns. The theoretical arguments are associated with learning by doing: by being
involved w1th (new) capital, or with production in general, workers obtain better skills. Empirical
motivations come, for instance, from attempts at estimating aggregate Cobb- Douglas
production functions where the sum of exponents is often found to be considerably above one
4. Building on the idea of productive externalities, we formulated in this chapter a base model
with the following features:
• The representative firm was assumed to produce output (GOP) from the inputs of labour
and capital according to a usual Cobb-Douglas production function with constant returns
to capital and labour and a labour-augmenting productivity variable A1
•
• The labour productivity variable of the representative firm depended on the aggregate
stock of capital as given by a function, A1 = Kf, ¢;;. 0. Since the firm should be thought of
as small relative to the entire economy, it took Ku and hence Au as given.
• Capital accumulated from savings the usual way, and the (gross) savings or investment
rate was a given constant. The labour force was assumed to grow at a given rate, n.
• The real prices of capital and labour were determined by the marginal products, computed
for a given level of the productivity variable.
5. It makes a qualitative difference in this model if the strength of the external effects is below,
equal to, or above 1 : ¢ < 1 leads to semi-endogenous growth, ¢ = 1 leads to (truly) endogenous
growth. and ¢> 1 (a case we did not consider in the chapter, but which is considered
in an exercise) leads to explosive growth and basically an ill-behaved model.
6. In the case¢< 1, the model implies convergence of capital per effective worker and of output
per effective worker to well-defined steady state levels. In steady state there was a common
constant growth rate for output per worker and for technology. This growth rate depended in
a specific way on ¢ and n, and it was strictly positive if and only if both of¢ and n were strictly
positive. The feature that growth in the labour force is required for economic growth motivates
the term 'semi' in semi-endogenous growth. The intuition is that the increasing returns driving
the (semi-)endogenous growth can only be exploited if some input increases by itself. Given
that the labour force grows, the capital stock will grow by a rate higher than n.
7. For the policy implications of the model of semi-endogenous growth it is important that both
the level of, and the growth rate along, the growth path for output (and consumption) per
worker depend on behavioural model parameters. The levels of these paths are positively
influenced by the rate of saving and investment and negatively influenced by the population
growth rate. Th s speaks for policies to raise investment rates and dampen population growth.
On the other hand, the growth rate along the steady state growth path was positively influenced
by population growth, speaking for policies to promote population growth, since in the
long run the positive growth effect will outweigh the negative level effect.
8. Empirically it seems hard to find a clear positive association between population growth and
growth in income per capita, although there are both pros and cons in the debate over
whether growth in the labour force really promotes growth in output per worker. Given that
this issue is unsettled, one would be cautious recommending policies to promote population
growth, since it seems relatively certain that higher population growth will erode the stock of
capital per worker and increase the pressure on scarce natural resources, thereby lowering
the level of the basic growth path, whereas the positive effect on the growth rate along this
path seems doubtful.
9. The negative association between population growth and economic growth found in the data
does not contradict the model of semi-endogenous growth per se since, if convergence to
steady state is very slow, the negative level effect of higher population growth will dominate the positive growth effect for a long time. In this case, however, the steady state itself will not
be very descriptive of the economy, rather the convergence process will be the relevant
thing to study. The empirical evidence therefore suggests looking at the model with very slow
convergence, which obtains as if> tends to 1.
10. We took this idea to the extreme and assumed if>= 1, at the same time assuming a constant
labour force. This gave us the so-called AK model. This model has constant returns to the
reproducible factor, capital. It therefore implies a common and constant positive growth rate
of capital per worker and output per worker, without any assumption of exogenous technological
progress and without growth in the labour force being required. This is why the
model's growth is called 'truly' endogenous. The everlasting balanced growth described by
the model can be seen as approximating the very long lasting transitory growth that would
result if </> were smaller than, but close to 1. Importantly the endogenous growth rate
depended positively on the rate of saving and investment.
11. The main policy implication of the AK model was therefore that policies to promote saving and
investment become even more attractive, now not only because of their level effects, but also
for their permanent (or very long lasting) effect on economic growth.
12. Empirically one finds across countries a rather strong positive relationship between, on the
one hand, investment rates and, on the other hand, long-run growth rates in output per worker
and in estimates of the productivity variable A,. This is in very nice accordance with models of
(truly) endogenous growth. On the other hand these models are plagued by an empirically
implausible scale effect: according to endogenous growth models, a larger labour force gives
higher economic growth and a growing labour force gives explosive economic growth. These
features are highly counterfactual.
13. We closed this chapter by discussing the arguments for and against the theories of exogenous,
semi-endogenous and endogenous growth. The scale effect implied by truly
endogenous growth models speak against these models and in favour of models of semiendogenous
growth. Compared to endogenous growth models, models of exogenous growth
seem easier to reconcile with the empirical evidence on convergence and on the relationship
between population growth and economic growth. Nevertheless, endogenous growth models
have made an interesting and promising contribution to the theory of economic growth,
because of their ability to account for the observed positive relationship between investment
rates and productivity growth, and because they have forced growth theorists to think harder
about the forces underlying technological change.
1. In endogenous growth theory the growth rate of technology, which underlies the long-run
growth in GOP per worker, is endogenous: it depends on basic behavioural model parameters
and therefore on structural policies that affect these parameters.
2. According to the replication argument, the individual firm's production function should exhibit
constant returns to the inputs of capital and labour at any given technological level. If there are
productive externalities from the aggregate stock of capital (or from aggregate production) to
labour productivity or total factor productivity in the individual firm, then there can be constant
returns to capital and labour at the firm level and increasing returns to capital and labour at the
aggregate level. With productive externalities one can therefore maintain the convenient
assumption of perfect competition and the associated theory of income distribution, and at
the same time have a potential source of endogenous growth in the model.
3. There are theoretical as well as empirical motivations for productive externalities and aggregate
increasing returns. The theoretical arguments are associated with learning by doing: by being
involved w1th (new) capital, or with production in general, workers obtain better skills. Empirical
motivations come, for instance, from attempts at estimating aggregate Cobb- Douglas
production functions where the sum of exponents is often found to be considerably above one
4. Building on the idea of productive externalities, we formulated in this chapter a base model
with the following features:
• The representative firm was assumed to produce output (GOP) from the inputs of labour
and capital according to a usual Cobb-Douglas production function with constant returns
to capital and labour and a labour-augmenting productivity variable A1
•
• The labour productivity variable of the representative firm depended on the aggregate
stock of capital as given by a function, A1 = Kf, ¢;;. 0. Since the firm should be thought of
as small relative to the entire economy, it took Ku and hence Au as given.
• Capital accumulated from savings the usual way, and the (gross) savings or investment
rate was a given constant. The labour force was assumed to grow at a given rate, n.
• The real prices of capital and labour were determined by the marginal products, computed
for a given level of the productivity variable.
5. It makes a qualitative difference in this model if the strength of the external effects is below,
equal to, or above 1 : ¢ < 1 leads to semi-endogenous growth, ¢ = 1 leads to (truly) endogenous
growth. and ¢> 1 (a case we did not consider in the chapter, but which is considered
in an exercise) leads to explosive growth and basically an ill-behaved model.
6. In the case¢< 1, the model implies convergence of capital per effective worker and of output
per effective worker to well-defined steady state levels. In steady state there was a common
constant growth rate for output per worker and for technology. This growth rate depended in
a specific way on ¢ and n, and it was strictly positive if and only if both of¢ and n were strictly
positive. The feature that growth in the labour force is required for economic growth motivates
the term 'semi' in semi-endogenous growth. The intuition is that the increasing returns driving
the (semi-)endogenous growth can only be exploited if some input increases by itself. Given
that the labour force grows, the capital stock will grow by a rate higher than n.
7. For the policy implications of the model of semi-endogenous growth it is important that both
the level of, and the growth rate along, the growth path for output (and consumption) per
worker depend on behavioural model parameters. The levels of these paths are positively
influenced by the rate of saving and investment and negatively influenced by the population
growth rate. Th s speaks for policies to raise investment rates and dampen population growth.
On the other hand, the growth rate along the steady state growth path was positively influenced
by population growth, speaking for policies to promote population growth, since in the
long run the positive growth effect will outweigh the negative level effect.
8. Empirically it seems hard to find a clear positive association between population growth and
growth in income per capita, although there are both pros and cons in the debate over
whether growth in the labour force really promotes growth in output per worker. Given that
this issue is unsettled, one would be cautious recommending policies to promote population
growth, since it seems relatively certain that higher population growth will erode the stock of
capital per worker and increase the pressure on scarce natural resources, thereby lowering
the level of the basic growth path, whereas the positive effect on the growth rate along this
path seems doubtful.
9. The negative association between population growth and economic growth found in the data
does not contradict the model of semi-endogenous growth per se since, if convergence to
steady state is very slow, the negative level effect of higher population growth will dominate the positive growth effect for a long time. In this case, however, the steady state itself will not
be very descriptive of the economy, rather the convergence process will be the relevant
thing to study. The empirical evidence therefore suggests looking at the model with very slow
convergence, which obtains as if> tends to 1.
10. We took this idea to the extreme and assumed if>= 1, at the same time assuming a constant
labour force. This gave us the so-called AK model. This model has constant returns to the
reproducible factor, capital. It therefore implies a common and constant positive growth rate
of capital per worker and output per worker, without any assumption of exogenous technological
progress and without growth in the labour force being required. This is why the
model's growth is called 'truly' endogenous. The everlasting balanced growth described by
the model can be seen as approximating the very long lasting transitory growth that would
result if </> were smaller than, but close to 1. Importantly the endogenous growth rate
depended positively on the rate of saving and investment.
11. The main policy implication of the AK model was therefore that policies to promote saving and
investment become even more attractive, now not only because of their level effects, but also
for their permanent (or very long lasting) effect on economic growth.
12. Empirically one finds across countries a rather strong positive relationship between, on the
one hand, investment rates and, on the other hand, long-run growth rates in output per worker
and in estimates of the productivity variable A,. This is in very nice accordance with models of
(truly) endogenous growth. On the other hand these models are plagued by an empirically
implausible scale effect: according to endogenous growth models, a larger labour force gives
higher economic growth and a growing labour force gives explosive economic growth. These
features are highly counterfactual.
13. We closed this chapter by discussing the arguments for and against the theories of exogenous,
semi-endogenous and endogenous growth. The scale effect implied by truly
endogenous growth models speak against these models and in favour of models of semiendogenous
growth. Compared to endogenous growth models, models of exogenous growth
seem easier to reconcile with the empirical evidence on convergence and on the relationship
between population growth and economic growth. Nevertheless, endogenous growth models
have made an interesting and promising contribution to the theory of economic growth,
because of their ability to account for the observed positive relationship between investment
rates and productivity growth, and because they have forced growth theorists to think harder
about the forces underlying technological change.
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