Download The Lucas Model

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1. Theories of Economic Growth
1.2- Endogenous Growth
1.2.2- The Lucas Model (Basic Ideas)
1.2.3- The Stokey Model (Basic Ideas)
2. Economic Integration, Technology Transfer…
2.1- The Grossman & Helpman Model
2.1- The Rivera-Batiz & Romer Model
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• Rivera-Batiz, Luis and Paul Romer (1988), “Economic Integration
and Endogenous Growth”, Quarterly Journal of Economics,
106(2), 531-55.
• Stokey, Nancy (1991), “Human Capital, Product Quality, and
Growth”, Quarterly Journal of Economics, 106(2) ,587-616.
• Grossman, Gene and Elhanan Helpman (1991), “Quality Ladders
and Product Cycles”, Quarterly Journal of Economics, 106(2) ,55786.
• Lucas, Robert (1988), “On the Mechanics of Economic
Development”, Journal of Monetary Economics, 22, 3-42.
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• In its 1988 paper, Nobel laureate Robert Lucas
presented a model in which the ultimate goal is to
endogenise economic growth. In that model, the
‘engine’ of growth is
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, as human capital
accumulation raises the productivity of both labour and
physical capital. This is the main feature of the model.
• In spite of having been much upgraded by other
contributors, the importance of the Lucas model resides
in the fact that he provided the first human capital
approach to endogenous growth.
• The basic idea of the model is that people divide their
time between work and training. So, there is a trade-off,
since when taking on training people give up part of
their work income, but raise their future productivity,
and therefore their future wages.
• In essence, this trade-off is just like the typical one
appearing in physical capital accumulation: it is a
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question of postponing income today (and hence
consumption) for income tomorrow. Thus, the decisions
concerning the accumulation of human depend on the
dynamic features of the economy, which makes it
endogenous. Since human capital accumulation is the
‘engine’ of growth, growth will itself be endogenous as
well.
• This model has two types of capital: physical and
human capital. The fundamental equation of the model,
which is a portfolio equilibrium equation, states that in
steady-state the marginal product of the two types of
capital must be the same. This implies that the
dynamics of accumulation of the two types of capital
are interlinked. This prediction of the model seems to
make sense in the ‘real world’.
• The model is quite simplistic in the sense that its
assumptions are quite reductive. The basic assumptions
of the model are:
- The
consumers
welfare
is
given
by
an
intertemporal constant-elasticity of substitution
utility function.
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- The ‘effectiveness’ of training, that is, the rate at
which productivity is risen by one additional unit
of training is exogenous.
• The main results of the model can be summarised as
follows.
- The higher the productivity of training, the higher
will be the increase in the marginal product labour
that follows training and hence the higher the
future wage rate. This means that the incentives to
training are greater and so will be the growth rate
of the economy.
- The lower is the rate of ‘impatience’, that is the
less consumers privilege present relative to future
consumption, the more will workers be willing to
forsake
present
consumption
to
dedicate
themselves to training. Therefore, the higher will
be the rate of economic growth.
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• In her 1991 paper, Nancy Stokey (Robert Lucas’ wife),
devises a model aimed at explaining growth phenomena
such as that experienced by some successful new
industrialised countries in East Asia, where rapid
economic growth has been accompanied by high volume
of exports, rapid growth in education and rapid changes in
the composition of output.
• Labour is heterogeneous and differentiated by the level of
human capital.
• The technology for human capital accumulation used in
the model is one that distinguishes between the private
human capital of individuals and the stock of knowledge
of the society as a whole.
• An individual accumulates human capital by investing,
that is, going to school. His level of human capital upon
leaving school and entering the labour force depends:
- On the
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of his investment period, which he
chooses.
- On the
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of the time spent, which is
determined by the social stock of knowledge.
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• The level of human capital of an individual upon entering
the work force determines his wage over the rest of his
life, which he spends working. Thus, his choice about the
length of the investment period is made by balancing the
opportunity cost of later entry into the work force against
higher wage rate paid to more skilled labour.
• Private investment in schooling also has an external effect
(externality): it causes growth in the social stock of
knowledge, which increases the effectiveness of time spent
in school. Since it is assumed that individuals are finite
lived, this external effect is the only source of steady-state
growth.
• In much of the related literature in which labour of
different skill levels is assumed to be perfectly
substitutable in production, that is, 1 unit of labour with
human capital ok K is perfectly substitutable by K units of
labour with human capital of unity. In contrast, in Stokey’s
model human capital is not perfectly substitutable.
• This
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among different types of
labour is modelled by allowing higher-quality labour to
perform more highly-valued services.
• In the model, goods are differentiated in terms of quality.
In this setting, as aggregate human capital grows, output
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consists of dropping lower-quality goods from production
and adding higher-quality goods. This is the most
distinctive feature of the model and one that seems
extremely important in the ‘real world’.
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• In this model, economic growth is
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, since, as
in Lucas model, growth is driven by the individuals
investment in human capital which depends on variables
internal to the model, such as the rate of ‘impatience’.
• The fact that it is the external effect that is driving
economic growth means that the growth rate under ODLVVHU
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will be generally lower than the social one, so that
the equilibrium is
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. The reason is that, since the
decision to invest in human capital by any individual is
made in such a way as to optimise its private earnings
profile, the externalities are not taken into account and
investment will be sub-optimal.
• The model has another important finding. In an openeconomy setting, in which economies are assumed to trade
among themselves, the model shows that for economies
that are sufficiently backward relatively to the rest of the
world, the optimal investment rate will be generally lower
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than in the rest of the world. The reason is that, since highskilled labour is relatively abundant in the rest of the
world, international trade will push the prices of highquality goods downwards, reducing the incentive of
individuals to invest in human capital.
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• This model seems to hold some important implications for
a country like Portugal:
- It seems consensual that economic development in
a country like Portugal means moving away from
the
actual
base
of
production,
which
is
characterised by essentially low value-added
goods.
- Also, since the rate at which people invest in
human capital is rather low in Portugal, maybe
because of the externality identified in the model,
some policies like subsidies to education, effective
child labour laws and incentives to R&D might be
particularly useful.
- Finally, if the predictions of the model are right,
the fact that Portugal is submerged in a
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community of more developed countries may
imply that Portugal is condemned to grow at lower
rates than its EU partners. The argument is that of
a relatively backward economy under free trade.
The fact that Portuguese people and businesses
have access to the higher-quality goods from
abroad, constitutes a negative incentive to upgrade
out productive system into a higher value-added
production base.
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•
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products.
entails the creation of new processes and
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is one means by which new ideas
spread through the economy. Together, these two features
account for much of what we call ‘technological progress’.
• In spite of the fact that innovation and imitation are
interlinked, economists now little about how they interact.
We would like to know whether imitation, by shortening
the length of time the innovator can enjoy monopoly rents,
reduces the incentives to innovation and so economic
growth.
• The model developed by Grossman an Helpman (1991)
deals with this issues and goes further by typifying the
model according to the world’s economic geography. That
is, in the model it is assumed that the ’North’ has a
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comparative advantage in R&D and so makes the bulk of
innovation, whereas the ‘South’ has a factor cost
advantage that makes that region to hold a comparative
advantage in manufacturing and so in imitating.
• There are many goods in this economy and so the model
can be seen as a model of ‘patent races’ in which firms in
the ‘North’ try to go up in the products
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by
devoting resources to R&D. In the ‘South’, firms also
devote resources to research, but with the aim of being
able to reproduce the technology embodied in the latest
patent.
• It is assumed that the holder of the latest patent of each
product (the
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) has an informational advantage in
discovering the next quality upgrade when production has
already been displaced to the ‘South’, i.e. after some
Southern firm has been able to imitate.
• The model is one of endogenous growth, since the
decisions to invest in learning (R&D in the ‘North and
imitation in the ‘South’) involve a comparison of potential
profits and research costs. Economic growth is assumed to
be equal to the aggregate rate of innovation.
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• It is assumed that successful innovators in the ‘North’ earn
monopoly profits for a while, because their new products
are superior to those available from other suppliers.
• Successful imitators in the ‘South’ earn rents because their
manufacturing costs are lower than those of competitors in
the ‘North’. In this sense, the G&H model can be seen as a
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model, as like in Aghion and Howitt,
firms that are successful in innovating or imitating reap the
whole market share from the incumbent.
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• The SS is characterised by permanent product upgrading
and by product cycles (i.e., migration in the location of
production for a particular type of good from the ‘North’
to the ‘South’ and back again). Each product may exhibit a
complex
life
history,
with
alternating
periods
of
technological stagnation, rapid growth, etc., but the
aggregate rates of innovation and imitation are constant,
and so is the rate of economic growth in SS.
• This result of the SS equilibrium in the model has some
resemblance to what happens in the ‘real world’ in which
waves of technological advances in some industries are
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followed by waves of imitation that spread the technology
worldwide.
• For example, the beginning of the history of the PC had
such a pattern. IBM introduced its original PC based on
the 8088 processor in the early 80s. It amassed an
enormous market share until firms in Taiwan and South
Korea were able to offer competitively priced ‘clones’.
Then the ‘South’ began to export massive amounts of PCs
to the ‘North’. However, much of the production reverted
to the ‘North’ when IBM and others successfully
developed the higher quality machines based on the 80286
processor.
• Another result consists of the effects of government
incentives to innovation, in the ‘North’, and to imitation in
the ‘South’.
• Subsidies to Northern industries R&D accelerate the pace
of innovations and so accelerates the SS rate at which
goods flow from ‘North’ to ‘South’. With the same
reasoning, subsidies to imitation have a detrimental effect
on the rate at which goods climb the quality ladder, as the
incentives to innovation in the ‘North’ gets reduced
(EXVLQHVVVWHDOLQJHIIHFW).
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• Many economists believe that increased economic
integration among developed economies has had a positive
impact on long run growth. This belief is underpinned by
some empirical evidence according to which the creation
and transmission of ideas has been important in
establishing the modern standards of living.
• Conventional attempts to quantify the effects of integration
using the neoclassical growth models often suggest that
the gains from integration are small, as this type of models
only identifies OHYHOHIIHFWV and not JURZWKHIIHFWV.
• In dealing with economic integration, the authors use a
broad definition of integration. One that includes the
exchange of goods as well as of ‘ideas’.
• The model used in this paper is basically the Romer’s
model we have dealt with in previous lectures. (At this
stage, you should revise the main ideas of that model).
• Recalling the comparative static exercise we did for the
Romer’s model, an increase in
+
, the level of human
capital, would shift both the Romer and the Ramsey line,
yielding higher growth rate and interest rate.
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• In this context, assuming that full economic integration
implies a merge of two economies, we see that
+
would
double and so growth would be permanently higher as the
growth rate of the ‘production’ of designs would also
double.
• However, we want to analyse the dynamic behaviour of
the economy when there is economic integration. We will
do that sequentially, by first considering the impact of
goods trade liberalisation and only then will we evaluate
the impact of trade liberalisation of goods and ideas.
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• The first point is that because there is only one (aggregate)
consumption good that is assumed similar for the two
economies, trade will only occur in the intermediate,
capital input sector.
• The second point is that opening trade in goods has no
permanent effect on the rate of growth. In balanced growth
the rate of growth of output is equal to the growth rate of
, $
$
$
capital,
= δ+ , which is determined by the split of human
$
+
=
+
$
++
<
between the consumption good
sector and the research sector.
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• It is straightforward to show that such split does not
change in balanced growth after trade in goods has been
opened, because opening trade has two offsetting effects
on the wages of human capital in these two sectors.
• In what concerns the consumption good sector, when trade
is opened, the machine producers, in order to avoid
redundancy and so competition specialise and so the
number of machines available for the production of the
consumption good doubles. This has the effect of doubling
the marginal product (MP) and so the wage rate of +.
• In the research sector, opening of trade implies that the
market for new designs is twice as large as before. This
doubles the prices of patents and doubles the MP of human
capital in research. However, since the foreign stock of
knowledge is not available for use in research because
only goods can be traded, the productivity of human
capital remains the same.
• It turns out that the wage of human capital doubles in both
sectors and so the allocation of
+
between the two sectors
does not change. Consequently, the growth rate of the
stock of knowledge and so of the economy’s output, does
not change in SS. However, there is a growth effect that
results from the fact that at any moment the number of
machines in use is twice as much as in autarky.
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• As we have seen, trade liberalisation entails specialisation
in the types of machines produced, so that after a while the
stocks of knowledge of the two economies are completely
distinct, and so the ‘area-wide’ stock is twice what was for
each economy in isolation.
• If flows of ideas is allowed between the two economies
then the research sectors of each country have twice as big
a stock of ideas to use in creating new designs. In this
model, this means that the growth rate of designs jumps
from $ = δ+
$
$
to $ = δ+
$
2
$
+ $* .
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• Thus, even if the share of human capital allocated to the
research sector does not change, the growth rate of
$
and
so the output’s growth rate would double permanently in
balanced growth.
• However, the increase in $ has the effect of increasing the
productivity of human capital in the research sector and no
effect on the productivity of
+
in the output sector. This
change in relative productivity raises the wage of human
capital in the research sector relative to the output sector.
• The consequence is a migration of human capital from the
output sector to the research sector, which reinforces the
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growth effect of the liberalisation of the flow of ideas. So
the growth rate in SS more than doubles compared to a
situation in which the flow of ideas is not permitted.
• From the G&H and R-B&R models we had a flavour of
the implications of exchange of goods and ideas to
economic growth. In this context, we can summarise some
of the most conclusions:
- The exchange of goods stimulates the economy if
only for the fact that it extends the scope of capital
inputs that can be used in production of the final
good
and
also
for
creating
incentives
to
specialisation and so for higher efficiency.
- The exchange of ideas, allows countries to share
knowledge and ideas, which naturally amplifies their
technological possibilities, but also provide more
inputs to the creative process. This creativeness is, as
we
know,
the
most
important
factor
of
competitiveness in modern economies.
• The next step is to look at the impact of foreign direct
investment (FDI) in fostering technological progress and
growth.
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