Transcript Chapter 16 - Cengage Learning

Macroeconomics
Chamberlin and Yueh
Chapter 16
Lecture slides
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Models of Long-run Growth
• Neoclassical Model of Growth
•
The Solow Model
•
The Solow Model with Technology
•
Long-run Growth in the Solow model
•
The Convergence Hypothesis
• Growth Models with Human Capital
• Endogenous Growth Theories
•
The AK Model
•
The Romer Model
•
Evidence of Growth
•
Evaluation of Endogenous Growth Theory
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Learning objectives
• Understanding the drivers of long-term growth
• Using the neoclassical model of growth to assess
changes in growth rates
• Introducing human capital into growth models
• Assessing the contribution of endogenous growth
theories
• Gaining perspective into why countries grow at
different rates
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Economic growth
• Economic growth is the change in GDP on an
annual basis.
• A rule of thumb is that a country growing at g
percent per year will double its per capita GDP
every 70/g years.
• To see this, let Y(t) be per capita GDP at time t and
let Y0 be the initial value of per capita GDP. Then,
Therefore,
per capital GDP will double when
Y t   Y0 e gt .
Yt=2Y0.
• The rule of thumb can be worked out as follows.
First, 2Y0=Y0egt. Then, solving for t, t=log 2/g. We
get the rule of thumb by noting: log 20.7.
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Economic growth
• Therefore, if the U.S. grew at 3% per annum for
the past 30 years while China grew at 8% per
annum, then GDP per capita will double
approximately every 23 years in the U.S. and every
9 years in China.
• Within a generation, the average American will be
three times as rich as his grandparents, while a
Chinese person would be more than 18 times
richer.
• Over a fairly short period of time, small differences
in compound growth rates can lead to large
differences in per capita incomes.
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Long-run economic growth
• The rate of growth that is consistent with an
economy’s natural rate of output and the position
of the long-run aggregate supply curve seen in
earlier chapters.
• Therefore, when policymakers are interested in
improving the long-run potential of an economy
and economists are attempting to understand why
countries grow at different rates, these are the
models that are relevant.
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Neoclassical Model of Growth:
The Solow Model
• The neoclassical framework for long-run growth is the
Solow model.
• The Solow model is comprised of a production function and
a capital accumulation function.
• The production function refers to the inputs of capital (K)
and labour (L) necessary to produce output (Y).
• It is assumed to have the Cobb-Douglas form and is given
by:
(16.1)
Y  F K , L  K L
 1
,
where α is a number between 0 and 1.
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Production function
• This production function exhibits constant returns to scale,
so that if all inputs are doubled, then output will double.
• We are interested in finding output per worker or per capita
output, so we write the production in terms of output per
worker and capital per worker, which are given respectively
by: yY/L, k=K/L, which gives y=kα.
• With more capital per worker, firms produce more output
per worker. But, there are diminishing returns to capital
worker, so each additional unit of capital increases the
output per worker by less than the previous unit of capital.
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Capital accumulation equation
• The second equation of the Solow model is an equation that explains
how capital is accumulated in the economy.
• The capital accumulation equation is given by:
(16.2)
K  sY  dK.
• According to (16.2), the change in the capital stock, K , is equal to the
gross investment, sY, minus depreciation, dK. The change in capital
stock is given by the variable differentiated with respect to time, so
dK

K
.
dt
• The notation simply denotes the change in capital stock per period, so it
is the continuous time version of Kt+1-Kt.
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Capital accumulation equation
• Assumes that workers save a constant fraction, s, of their combined
wage and rental income.
• Because the economy is closed, savings equals investment and
investment is used solely to accumulate capital.
• The other assumption relates to the depreciation of the capital stock that
occurs during production, which is a constant fraction, d, of the capital
stock. Depreciation happens every period regardless of how much
output is produced.
• Now, we have the capital accumulation equation in per worker terms:
k  sy  n  d k.
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Capital accumulation equation
• This equation says that capital per worker in each period is
determined by three factors.
• The first is that investment per worker, sy, increases capital,
k, while depreciation per worker, dk, reduces k. There is
also a reduction in k because of population growth, the nk
term.
• Each period there are nL new workers since the model
assumes a constant growth rate of n in the population,
which is also assumed to have a 100% labour force
participation rate.
• So, if there were no new investment and no depreciation,
capital per worker would decline because of the increase in
the labour force. Because k is known as capital per worker,
it is also referred to as the capital-labour ratio.
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Solving the Solow Model
• To solve the Solow model, we take the production function
and capital accumulation equation together.
• The production function in terms of output per worker is
given by:
y  k .
• The capital accumulation function in terms of capital per
worker is:
k  sy  n  d k.
• The equilibrium is found where the two curves meet. To
find this point which is the steady state of the economy.
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The Solow Diagram
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Equilibrium in the Solow Model
• The Solow diagram consists of two curves, which are
functions of k, capital per person or the capital-labour ratio.
• The first depicts the amount of investment per person:
sy  sk  .
• The curve has the same shape as the production function but
is translated in terms of the function s.
• The second curve is the amount of new investment per
person required to keep the amount of capital per worker
constant: (n+d)k. Population growth and depreciation will
both reduce the amount of capital per person, which is
captured here.
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Disequilibrium in the Solow Model
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Capital deepening/widening
• When the economy is below k* and say capital per worker
is increasing, then capital deepening occurs. Below k*, the
amount of investment per worker exceeds the amount
needed to keep capital per worker constant, so k increases
over time. Capital deepening will continue until the
economy has reached a steady state.
• If the economy, on the other hand, began with a capital
stock per worker that was larger than k*, then we would be
to the right of k*. The amount of investment per worker
provided by the economy is less than the amount needed to
keep the capital-labour ratio constant. The amount of
capital per worker will decline. This decline will cease
when the amount of capital per worker falls to k*. This is
known as capital widening.
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Solving for the steady state
• We now add the production function to find the steady-state value of
output per worker.
• At k*, the steady state output of the economy is at is at y*. If different
countries have different values of y*, then some will be richer and some
will be poorer.
• So, we need to do one more thing which is to solve the model and find
out what determines y*. We can do this by finding the steady-state
quantities of capital per worker and output per worker.
• Recall that the steady-state quantity of capital per worker is determined
by the condition:
k  0.
• This means that there is no change in the capital-labour ratio over time
so that the economy is at its steady state.
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Solving for the steady state
• We also need the two key equations of the Solow model, the production
function and capital accumulation function.
• The first equation is output per worker which is given by
y  k .
• The second is capital per worker which is given by
k  sy  n  d k.
• Substitute the first equation into the second and we get
k  sk   n  d k.
• Setting this equation to zero yields the steady-state quantity of capital
1
per worker, as follows:
 s  1
(16.3)
k*  

nd 
.
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Solving for the steady state
• We now need to find the steady-state output per worker, which is found
by substituting (16.3) into the production function (16.1). So, y* is
given by:
(16.4)
 s 
y*  

nd 
1
1
.
• Therefore, y* is now written in terms of the parameters of the model
and we have a solution.
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Steady state in the Solow Model
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Different steady states
• Countries which have higher savings and investment rates
will tend to be richer than those who do not. These
countries accumulate more capital per worker and thus
more output per worker.
• In contrast, countries which have high population growth
will be poorer. And, in these countries, a larger portion of
savings will be required to keep the capital-labour ratio
constant. The tendency for capital widening will make
capital deepening more difficult and these countries will
tend to accumulate less capital per worker.
• However, when the economy is in steady state, it can still
experience “shocks” along these lines where key parameters
like savings rates and population change.
• This explains and fits the empirical fact that countries have
different levels of per capita income.
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Increase in investment
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Increase in population growth rate
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Rate of economic growth
• In the simple version of the Solow model, there is no per
capita growth when the economy is at its steady state.
• In the simple Solow model, this means that economies will
grow until they reach their steady state and eventually
growth will stop altogether!
• Although the outcome of the Solow model fits the empirical
observation that countries have different per capita incomes,
it does not explain why economies grow persistently over
long periods of time. To generate sustained growth in per
capita income, we have to introduce technological
progress.
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Solow Model with Technology
• Thus, we include a technology variable, A, to the production
function:
1

(16.5)
Y  F K , AL  K  AL .
• The technology variable is viewed as “labour-augmenting”
in this formulation. Alternatively, it could take the form of
“capital-augmenting.”
• This means that a unit of labour is more productive when
the level of technology is higher.
• However, technology in this model is exogenous. It is an
important assumption of the model, but one that has been
viewed as akin to “manna from heaven.” Somehow
technology comes into the economy from the outside
regardless of what is happening within the economy.
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Solow Model with Technology
~
• Rewriting the production function in terms of k ,
~
(16.6) ~
y k ,
Y
y
where ~y 
 .
AL
A
y as the output-technology ratio or
• We will now refer to ~
“output per effective unit of labour.”
• We also need to rewrite the capital accumulation function:
~
~
~
k  sy  n  g  d k .
• Combining the new versions of the production function and
capital accumulation function, we have the Solow diagram
with technological progress.
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Solow Model with Technology
• The economy is in steady state and grows at the rate of
technological progress, g.
• Capital, output, consumption and population are growing at
constant rates as a result, and so the economy is said to be
growing along a balanced growth path.
• Solving for for the steady state in the Solow model with
technology, first recall that the steady-state output per
effective unit of labour is determined by the production
function and the condition that
~
k  0.
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Solow Model with Technology
• First, similar to the simple Solow model, we
find that
1
 1
~ 
s
(16.7) k *  

.
n g d 
• Substituting into the production function
yields


 1
s
~

.
(16.8) y *  
n g d 
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Solow Model with Technology
• In terms of output per worker, we rewrite the above as
(16.9)


s

y * t   At 
n g d 

1
.
• What is notable and different here is that output y* and A
both depend on time, so an economy can grow at the rate of
technological progress.
• So, output per worker is determined by technology, the
investment rate, and population growth rate.
• Now, if g=0, then the result would be identical to the Solow
model without technology.
• And, changes in the investment rate and population growth
rate affect the long-run level of output per worker but not
the long-run growth rate of output per worker!
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Solow diagram with technological
progress
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Changing the long-run level of
output per worker
• Suppose that there is a permanent increase in the saving rate
from s to s’.
• The result is very similar to the Solow model with no
technological progress. At the initial capital-technology
ratio, investment exceeds the amount needed to keep the
capital-technology ratio constant. An upward shift in the s
curve, therefore, speeds up the rate of growth temporarily
until the new steady state is reached.
• Fundamentally, however, g has not been affected and thus
the rate of economic growth remains the same as before.
• Therefore, policies that say permanently increase the rate of
investment will push the economy to a higher steady state
level of income, but it will not increase its long-run rate of
growth.
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Permanent increase in the saving rate
in the Solow model
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Long-run growth in the Solow model
• The Solow model shows that sustained economic
growth occurs only in the presence of technological
progress.
• Without technological progress, capital
accumulation will encounter diminishing returns.
• However, if there was improvement in technology,
then labour productivity will grow and capital
accumulation will also increase because it slows
down the diminishing returns to capital.
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Technological progress in the Solow
model
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Technological progress in the Solow
model
• Technological progress has allowed the existing inputs to be
used more efficiently, so the production function has shifted
upward.
• At the initial capital-technology ratio there is now a higher
level of steady state output.
• Part of this increase in output is due to productivity
advancement or total factor productivity (TFP), and the
other part is ensuing capital accumulation.
• Global Applications 16.1 The Solow residual
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Annual Growth Rates of Output per Capita
and of Technological Progress, 1950-87
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Technological progress in the Solow
model
• There is a clear association between periods of high
output growth and high technological progress.
• These developed nations follow similar
experiences with much better performance over
1950-73 than 1974-87, implying that all the most
significant developed economies are subject to
similar technology shocks.
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The convergence hypothesis
• Consider the key equation from the Solow model again:
~
~
k
y

s
~
~  n  g  d .
k
k
• Output per effective unit of labour will decline as capital
stock rises because of diminishing returns to capital.
Therefore, if an economy has low levels of capital stock,
then it should realise higher returns to its capital than a
country which is developed.
• If these economies have the same levels of technology,
investment rate, and population growth, then the developing
country will grow faster. The output per worker gap
between these countries will narrow over time as both
economies approach the steady state.
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The Evolution of Output per Capita
in Five Rich Countries Since 1950
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Per Capita Real GDP
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Empirical Evidence
• In terms of annual growth rates, it is clear that Japan, which
started at a much lower level of development at the start of
this period, grew faster than other more developed
economies.
• Several observations can be made. Firstly, growth rates
were much higher between 1950-1973 than 1974-2000.
Secondly, the ratio of real per capita output between 2000
and 1950 shows that in the space of 50 years the size of
these economies has increased substantially from 2.6 times
for the U.S. economy to 11.4 times for Japan. It is true over
a longer period of time.
• It is clear from these tables that even slight differences in
growth performance, when compounded over a long time,
can result in remarkably different levels of output.
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Empirical Evidence
• If there is convergence,
then there should be an
inverse relationship
between a nation’s
starting level of
income and subsequent
growth.
• Evidence from 18801973
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Empirical Evidence
• However, if we look at a
more recent period (19601995) there is no clear
relationship.
• DeLong (1988) argued that
results found by Baumol
(1986) relied too much on
the countries which were
industrialised and therefore
had data which was
available from the earlier
period.
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Conditional convergence
• Another inference that can be drawn from the
Solow model is that countries will converge in
growth rates conditioned on differences in steady
states.
• This means that countries are converging to their
own steady states. This is known as conditional
convergence or sigma convergence.
• This concept tests for convergence by looking at
the actual distribution of world income levels. If
convergence is to be observed, then the variance of
income levels should be falling over time.
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Per Capita GNP and Annual Growth
Rates
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Conditional convergence
• Some poor and middle income countries (particularly China
and Korea) have a tendency to grow faster, and catch up
with the richer nations, whereas there are many other poor
countries that actually record growth rates that are lower
than those in the OECD.
• In terms of the world income distribution this implies that
instead of seeing convergence, you may actually observe
polarization between rich and poor nations.
• The negative relationship in the following figure looks like
there is conditional convergence among these nations, the
world’s richest countries in this later as well as earlier
period.
• Global Applications 16.2 Feldstein-Horioka Puzzle
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Growth rates and initial income
levels, OECD countries, 1960-1995
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Growth Models with Human Capital
• The simple assumptions surrounding labour in the Solow
model can be revised to include human capital, that is,
workers with skills and education, so growth could be
driven by human capital instead of ‘manna from heaven.’
• In 1988, Lucas extended the neoclassical model by
assuming that individuals spend time accumulating skills,
such as by going to school. Mankiw, Romer and Weil
(1992) thought of human capital accumulation in the same
way as physical capital accumulation by forgoing
consumption.
• We will now incorporate human capital into the Solow
model by introducing a concept of labour that includes
human capital.
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Growth Models with Human Capital
• Output, Y, is produced by physical capital, K, labour, L, and
h which is human capital per person, in a Cobb-Douglas
production function. This can be seen as:
1
(16.10)
Y  K  hL .
• Technology is still assumed to grow exogenously at rate, g.
However, individuals in this economy accumulate human
capital by spending time learning new skills instead of
working.
• So, if an individual devotes 1-μ fraction of time learning
(and μ amount of time working), then
(16.11)
h  1   h.
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Growth Models with Human Capital
• An increase in time spent accumulating
human capital will increase the growth rate
of human capital, as seen as follows:
(16.12)
h
 1  .
h
• The inference to be drawn here is that h is
very similar to A in the labour-augmenting
version of the simple Solow model.
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Growth Models with Human Capital
• The solution to the neoclassical model with human capital
in steady state is virtually identical to the simple version of
the Solow model.
• We start by writing the production function in terms of
output per worker:
1

y  k hl .
(16.13)
• The parameter 1-μ is assumed to be constant and
exogenously determined, so individuals accumulate human
capital at a constant rate. Since it is constant, the equation
should look very similar to the Solow model from before.
• So, y and k will grow at the constant rate, g, the rate of
technological progress, which is now determined by human
capital accumulation, so that g=1-μ.
 
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Growth Models with Human Capital
• Since 1-μ is constant, the output per worker
equation is still given by:
~
~
(6.14) y  k .
• The capital accumulation equation can be
similarly written as:
(6.15) k~  s~y  n  g  d k~.
~
k 0
• To finish the
~ solution, we first set
k
s
.
• And find ~ 
y
n g d
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Growth Models with Human Capital
• Substituting this condition into the output per worker
equation gives the steady-state value of output:


s
~

y *  
n g d 
(16.6)

1
.
• Rewriting this in terms of output per worker:


 1
s
(16.7)

y t   
ht .
n g d 
• This shows that y* should grow at the same rate as 1-μ.
*
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Growth Models with Human Capital
• The extended Solow model sheds some additional
light on why some countries are rich and others are
poor.
• Some countries do well because they have high
investment rates in physical capital, low population
growth, high levels of technology and spend a large
fraction of time accumulating human capital.
• In steady state, though, this extended Solow model
still predicts that per capita output grows at the rate
of technological progress, g, as in the simple
model.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Endogenous Growth Theories
• It is clear, therefore, that the main determinant of
long-run growth is technological progress. Yet,
this is the one variable that is determined outside of
the neoclassical models.
• A newer strand of models, known as endogenous
growth theory, attempts to incorporate the
determinants of the main engine of growth,
technology, into the framework.
• If we can understand what determines A, then we
can explain the growth rate of y*.
• This is what endogenous growth theories try to do.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The AK Model
• The simplest version of this strand of theories is the AK
Model.
• Let us start with a modified Solow-type production function
where =1.
• The production function is now given by: Y=AK (16.8)
• A is a positive constant and K is broad capital. Broad
capital represents physical capital, but also human capital.
• Though it is a notion of broad capital, we simplify the
analysis to say that capital is accumulated as individuals
save in the economy rather than consume.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The AK Model
• Capital accumulation equation:
(16.9)
K  sY  dK,
where s is the investment rate and d is the rate of depreciation,
both are assumed to be constant.
• We assume that no population growth and treat these as per
capita variables for simplicity.
• There are two curves in the following diagram, where the
dK line represents the amount of investment needed to
replace the depreciation of the capital stock. The sY curve
is the total investment in the economy as a function of the
capital stock. Because Y is a linear function of K, this is a
straight line.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The AK Model
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The AK Model
• When we assume that total investment is larger
than depreciation, the capital stock will grow. This
is the key feature of the AK model. If the economy
starts at point K0. At every point to the right of K0,
the investment exceeds depreciation so the
economy continues to grow. In fact, the capital
stock is always growing and growth never stops in
this model!
• The key difference between the AK model and the
Solow model is that this model assumes constant
returns to capital, while the Solow model assumed
diminishing returns so that each unit of capital was
less productive than the previous unit.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The AK Model
• The marginal product in the AK model, in contrast, is
always A. This means that growth can continue perpetually.
And, it means that the growth rate of output is equal to the
growth rate of capital because A is constant. This implies
that the growth rate of the economy is an increasing
function of the investment rate.
• However, the AK model does not provide an intuition as to
why constant returns to scale is achievable with broad
capital. For instance, if the capital had positive spillover
effects so that it made other capital productive, then we
might not expect diminishing returns to set in. This
intuition is provided by the next set of models.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Romer model
• The endogenous growth model developed by
Romer endogenises technological progress by
introducing researchers who invent new ideas and
spur technological advancement.
• In these types of models, technological progress is
driven by R&D (research and development) and
can explain why rich countries experience
persistent growth.
• It also goes to show why technology transfer is so
important for developing countries and why poor
countries have lower levels of technology if they
do not have much R&D.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Romer model
• Similar to the Solow model, the Romer model has two main
elements representing the production function and a set of
equations explaining how the inputs into production evolve
over time.
• The key point is that technology can be thought of as ideas,
which are generated by researchers.
• So, similar to the neoclassical models, for a given level of
technology, A, the production function exhibits constant
returns to scale.
• But, because ideas are also an input into production, the
production function exhibits increasing returns with respect
to technology. This derives from the non-rivalrous nature
of ideas!
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Romer model
• The accumulation equations for capital and labour are
identical to the Solow model in the Romer model. The only
difference is the treatment of technological progress, which
is now not assumed to be driven by factors outside of the
model.
• Instead, Romer introduces a production function for ideas.
The Romer model offers A(t) as the stock of knowledge or
ideas that have been invented through history up to time t.
• Then, A is the number of new ideas produced at any given
time. So, it is equal to the number of people inventing new
ideas, LA, multiplied by the rate at which they discover
these new ideas,  .
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Romer model
• The production function for A is thus given by:
(16.20)
A   LA ,
where the discovery rate,  , could be constant or could be an
increasing or decreasing function of A.
• There are essentially three possibilities.
– Non-changing rate of invention, so it is simply a constant stream of
inventions.
– The second is a “standing on shoulders of giants” notion so  is an
increasing function of A.
– Conversely, a third possibility is a “crowding out” effect where  is
a decreasing function of A.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Romer model
• This framework also suggests that there are two types of
workers in this model, those who produce LY and those who
invent LA, so LY+LA=L.
• The set up is similar to the Solow model except that there
are two types of workers and there is an ideas equation.
• Except that in this model, the rate of technological progress
is generated by workers, LA, and does not rely on exogenous
shocks.
• So long as inventive activities continue, the economy will
grow and A is now determined within the model.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Evidence of growth
• Since 1950, the fraction of the labour force that
consists of scientists and engineers engaged in
R&D had increased three-fold. However, average
growth rates in the U.S. are no higher today than
they were from 1870 to 1929.
• Investment rates in the U.S. also increased greatly
since 1950 without similar evidence of an increase
in growth rates.
• Finally, the U.S., Bolivia and Malawi all grew at
around the same rate despite significant differences
in the level of human capital, investment and also
R&D personnel.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
International Comparisons
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Technology
• Endogenous growth theory says that technology is
determined within the model and produced by having
researchers. If poorer countries do not have investment
funds for R&D facilities and personnel, then they will have
a lower level of technology than rich countries.
• This main driver of growth is not exogenously given but
very much related to the factors within the model, such as
the level of development, capital stock, human capital, etc.
• These theories also suggest that developing countries can
catch up by imitating the technology in developed countries
rather than re-invent the wheel. But the “catch up” process
is probably both more costly and complex than the models
indicate.
• Global Applications 16.3 Does the “New Economy” measure up to
the inventions of the past?
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The importance of Threshold Effects and
General Purpose Technologies
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Evaluation of endogenous growth
theories
• Crucially, the driver of growth in this type of model is a
constant rate of invention that may vary positively or
negatively with the number of researchers in the economy.
• The rate of invention and innovation appear to be
exogenous to the model. So, although endogenous growth
models go further than neoclassical models in trying to
explain how technological progress, the driver of long-run
growth, occurs, it still leaves many questions unanswered.
• New growth theories, moreover, emphasise institutions,
infrastructure, health, social capital, legal contracting
regimes, political instability, conflict and war, among many
others.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• We have covered the main models of long-run economic
growth.
• We started with neoclassical growth models, namely the
Solow model.
• We also considered an extended version of the Solow model
that included human capital, known as the Lucas
formulation.
• After discussing the limitations of the Solow model, we
moved to consider endogenous growth theories or new
growth theories.
• The simplest formulation of an endogenous growth model
was the AK model, which could explain persistent growth
by modifying the assumption of constant returns in the
neoclassical framework.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• Then, we considered the Romer model which
introduced a new production equation for ideas into
the mix. Ideas and inventions can generate
increasing returns, thus providing for persistent
growth of an economy.
• We also examined the notion of technology
transfers in versions of the convergence hypothesis.
• We concluded with an assessment of endogenous
growth theories and how they still leave key
factors, such as what drives innovation,
unanswered.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• We also looked briefly at new growth
theories more widely which attempt to
understand why some countries seem to
persistently lag behind. The evidence
suggests that there are numerous factors,
such as institutions, political stability, which
seem to contribute to developing countries
falling further behind.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning