Advanced and Contemporary Topics in Macroeconomics I ... 3 NewGrowth_Alema… · Advanced and...
Transcript of Advanced and Contemporary Topics in Macroeconomics I ... 3 NewGrowth_Alema… · Advanced and...
Advanced and Contemporary Topics in
Macroeconomics I
Alemayehu Geda
[email protected] (Teaching Assistant: Addis Yimer)
Department of Economics, Addis Ababa University
PhD Program, 2014
Based on: David Romer (2009/2012), Validez (1999) Heidjra
(2009/2012) & Aghiwo and Howitt (2009)
Class Lecture Note 3 _ Chapter 3
New Growth Theory: Endogenous growth
models
Chapter 3
New Growth Theory: Endogenous
Growth Theory/ models
Introduction: Evolution of the Literature
Part A: Models with R&D
Part B: Models with human capital
Lecture Content
Introduction: Evolution of the Endogenous
Growth Literature
Part A: A two-sector model with R&D
I. Framework and Assumptions
• Overview
• Specifics
II.The dynamics of knowledge accumulation
• The model without capital:
III.The General Case: The model with capital:
The dynamics of knowledge and capital
A: Capital
B: Knowledge
Lecture Content…cont’d
IV. The Nature of Knowledge and the Allocation
of Resources to R&D (The AK Model) The Nature of Knowledge
The Determinants of the Allocation of resources to R&D
V. Endogenous growth theory and the central
questions of growth theory
Lecture Content…cont’d
Part B: Models with human capita(The
Lucas, 1988 Model) I.Overview
II.The Solow model with human capital
Human capital
The dynamics of the economy
Increased level of education
Implications for cross-country income differences
Testing growth theories: Growth Accounting
Cross-country differences in growth rates
Unconditional and conditional convergence
An Overview of the Lecture This lecture follows two approaches:
I. I will show the broad evolution of the literature
from its early formulation of the Harrod-Domar
(1940s) and Frankel (1962) to Its modern variant
such as Romer (1990), Lucas (1988) and others in
a chronological order- this part is aimed at
offering you a perspective.
II. I will then move to a thematic generalization of
this literature as provided in Romer‟s (2012)
„Advanced Macroeconomics‟ Text book – this
time we go to detail and specifics
Introduction: The Literature
Overview of the Endogenous Growth Literature
Incorporating endogenous technology into grwoth theory forces as to
work on increasing returns and the associate market structure -
imperfect competition.
In SS/RCK model owing to CRS in the PF, Euler equations tells us
that it takes all the economy output to pay K and L their MP – so there
is no resource left to improve technology [or pay for A].
This implies the theory of endogenous technology [or theory about
A] can not be based on competitive equilibrium
OR Technology has, thus, to come from externality to develop a
growth model on neoclassical setup [that way u don‟t pay fro A]
Various solutions are suggested – the first one being what is now
called the AK model [or the linear in K model ie., Y=f(K)=AK, „A‟
being a constant &alpha being 1 – note the linearity, as opposed to
convexity/diminishing return of the PF in SS/RCK].
Note: The idea/concept of the AK model • The idea of the AK model is to say Y, output is a linear (A) [ not
diminishing or convex/power [alpha=1 now] function of capital (K); so that as capital increase Y grows linearly [ ie Y=AK]
The Learning –by-Doing and Knowledge Spillover Hypothesis
• The Hypothesis of “Learning-by-Doing”: Romer/Frankel starts from Arrow‟s hypothesis that accumulation of knowledge is largely the result of mechanization. Why?
Because each new machine is capable of modifying the production environment in such away that learning (&often innovation) receives continuous stimuli.
Eg: Suppose a firm has 20 workers and 2 machineries and a new machine is brought in(thus raising the firm‟s level of mechanization, i.e., higher Κ/L ratio).
The idea/concept of the AK model
This may lead to – as workers work on the new machine, they progressively
accustomed to it better; learn how to get the best out of it .(learn the new technique by actually using it/ doing it)
– In the process of adopting the new devise, new forms of organization of production and/or find new ideas to improve on the equipment itself (say change in structure of its components)
This process is known as “learning-by-doing” or more accurately “learning-and-inventing by inventing-and-doing”
Hence higher level of mechanization(↑ K/L ) and increase in the stock of knowledge are two faces of the process of capital formation [note then Y is linear in K or[K/L] – an AK model.
Introduction: The Literature
Overview of the Endogenous Growth Literature…cont’d
The AK model goes back to Harrod (1939) and Domar
(1946) who assumed aggregate production function with
fixed coefficient [no substitutability / Kinked PF which is
not diminishing as Y is f(K) through ICOR linearly]
Frankel (1962) developed the first AK model with
substitutable factors and knowledge externality to
reconcile the long run positive growth result of the HD
model with factor substitutability and market clearing
features of the neoclassical model
This idea of knowledge externality and hence the
reconciliation with neoclassical model is facilitated by
Arrow‟s (1962) concept of „learning by doing‟ noted
Overview of the Endogenous Growth Literature .. cont’d
• Based on the works of Arrow (1962) and Frankel (1962) Romer (1986) further developed the AK model which Romer first developed it in his PhD dissertation (1983)
• First, Romer‟s understanding of “technical progress” is central for his theory. By this he meant
In S-S model technical progress is anything that raises labor efficiency
For Romer it is more Specific: stock of Knowledge (i.e., with a new knowledge how to produce more efficiently)
This includes
a) Scientific discoveries &(plus)
b) Know-how to use them in production
New discoveries came from R & D and job-practice and know-how results from job-practice and formal training or education (to be discussed)
• The second most important thing he did is that he developed an AK model in an “intertemporal consumer maximization setup (in RCK setup)
Overview of the Endogenous Growth Literature…Cont’d
• Lucas (1988/90) then developed an AK model where the
creation and transformation of knowledge occurs through
human capital (not physical capital as in Romer) formation
– the Lucas/Lucas-Uzawa Model.
• Lucas‟s model is based on Uzawa (1965) who developed the basic
idea 2 decades earlier – hence the Uzawa-Lucas model
– Rebelo (1990) used the AK model to explain how grwoth differ
across countries; saying it could be the result of differences in
government policies
– King and Rebelo (1991) used the AK model to analyze the effect
of fiscal policy on grwoth.
– Jones, Manuelli and Stacchetti (2000) used the AK model to study
the effect of macroeconomic volatility on growth
– Acemoglu and Ventura (2002) used the AK model to analyze the
effect of terms of trade on growth.
Overview of the Endogenous Growth Literature..cont’d
Further advances by Romer (1990,1994,1995),
Aghion and Howitt’s (1992), Jones (1995),
Grossman and Helpman (1991) among
others
• Dissatisfaction with the AK model in explaining
long-run growth led to innovation based
theories of growth (R&D models). This models
have two branches:
– (1) Product variety/Horizontal innovation model of
Romer (1990) & Jones (1995) [innovation creates
new, not necessarily improved, verities of products]
The Endogenous Growth Literature .. End
– (2) Aghion and Howitt‟s (1992) Schumpeterian/or
Vertical innovation theory of growth – named so
„cause it focuses on quality–improving innovation
that make old products obsolete/ „creative
destruction‟
– [similar model is also given by Grossman and
Helpman (1991)]
• In these models
– out put is not CRS function but IRS/Scale economy
– Romer (1990) for instance framed the product
variety model in an imperfect competition modeling
framework introduced by Dixit and Stiglitz (1977)
which was further developed by Ethier (1982).
Time for Specifics!
Part A: Models with Research and
Development Sector (R&D) –
hence a 2 sector model
Part B: Models with Human Capital
Part A: A two-sector model with R&D
I. Framework and Assumptions
An additional sector that only do R&D.
• Models the production of new technologies –
technological progress is endogenous
• The allocation of resources between the conventional
goods-producing sector and the sector producing R&D is
exogenous.
Overview
We‟ll model technology as the output of a
research and development industry
• So the economy produces two things:
consumption goods and ideas
Major simplification
• We‟re going to go back to the idea that the
saving rate is constant, and not optimally
determined
The model is set in continuous time
Specifics
Like the previous models same four endogenous variables: K, L, A and Y
• For simplicity, there is no depreciation
Two sectors
• Goods producing sector - where output is produced
• R &D/Ideas sector - where additions to the stock of knowledge are made
Labor and capital are split between the two sectors
• You can only work in one sector
Technology is not split
• Ideas can be used anywhere
Specifics…Cont’d
Returns-to-scale restrictions are made to capture
scalability of production processes
– Constant-returns-to-scale makes sense for most
physical processes, so we impose it for the
goods production function
– It isn‟t clear what makes sense for the
production of ideas
• Later, we spend a lot of time discussing what
seems plausible
Specifics…Cont’d
The key to understanding the model is the similarities
and differences between output, capital and technology
• New output is produced every period, but it is all
consumed in that period (its “depreciation” = 100%)
• New technology is produced every period, but it
never depreciates, so it accumulates like capital
• Capital is output diverted from consumption
• Technology is produced instead of consumption
Specifics…Cont’d
The model assumes that the economy‟s labour force and capital
stock are divided between one goods-producing sector and one
sector conducting R&D:
• Fraction of labour and capital in R&D sector =
• Fraction of labour and capital in goods-producing sector =
The production function in the goods-producing sector takes the
form (CRS; homogenous of degree 1: doubling inputs doubles
output)
KL aa ,
KL aa 1,1
[1] 10,)(1)()(1)(1
tLatAtKatY LK
Specifics…Cont’d
Technological advances depend on the amount of labour and capital devoted to R&D and the current level of technology:
– The restrictions of the coefficients do not imply CRS!
– Note that this is production of new ideas (old ideas do
not have to be replaced)
– This function allows for decreasing, constant or
increasing returns to scale
– The value of can be both positive or negative as it reflects the effect of existing knowledge stock on the success of R&D.
,0,0,0
[2] ,)()()((t)A
B
tAtLatKaB LK
Specifics…Cont’d
Like in the Solow model ,the saving rate is assumed to
be exogenous and constant
For Simplicity depreciation is set to zero
The labour force is assumed to grow at rate n
Still, the model has two stock variables that are
endogenously determined: K & A ,Hence it is more
complicated to analyze than the Solow model.
- We therefore begin by considering the model
without capital; that is ,we set α and β to zero. We
then turn to the general case
[3] )()( tsYtK
[4] 0 ),()( ntnLtL
II. The model without capital
The dynamics of knowledge accumulation
Where there is no capital, the production function for the goods sector becomes:
Output is proportional to A – hence the dynamics of A is of particular interest.
[5] )()1)(()( tLatAtY L
[7] )()()(
)()(
[6] )()()(
1
tAtLBatA
tAtg
tAtLaBtA
LA
L
Taking logs of both sides and differentiate w.r.t. to time gives
us the growth rate of the growth rate of A (the growth in
technological progress):**
The initial values of A and L determines the initial value of
, which determines the value but all depends on θ
[9] )()1()()(
[8] )()1()(
)(
2tgtngtg
tgntg
tg
AAA
A
A
A
Ag )(tg A
The behaviour of A (how does the grwoth rate of
A, , behaves?): Three cases
Case 1:
When , is positive for small values of
and negative for large values:
1
1 Ag Ag
*Ag Ag
Ag
c
0
Ag
There is a unique value of the growth rate of A, , where :i.e., the steady state is where
• Regardless of the economy‟s initial conditions converges
to [eg if the parameter values and the initial value of L and A imply (0)< , is positive; ie is rising ]
• The long-run growth rate of output per worker, , is an increasing function of the population growth.
• An increase in the fraction of the labor force devoted to R&D, and when θ<1, has a level effect (influences , Eqn 7) but no growth effect on the long run path of A [ie aL is not found in [eqn 10] but on Eqn 7].
*Ag
0Ag
[10] 1
01
0)1()(
*
*
2
ng
gn
ggndt
dg
A
A
AAA
Ag*Ag
*Ag
Ag
*AgAg
Ag Ag
.
This is a model of endogenous growth
• Output growth occurs because of technological growth
• Technology grows because new ideas are created and old
ideas don‟t depreciate
It‟s kind of odd that the growth of technology depends
on population growth
• This seems truer at larger scales, but not at smaller ones (ie
larger population larger chance of innovation)
Technological growth does not depend on the proportion of
people working in research and development
Although Eqn 7 says increase in aL immediately increase gA
owing to the limited contribution of the additional knowledge to
the production of new knowledge, this increase in the growth
rate of knowledge is not sustained (like saving rate in SS model,
shown in the next figure/slide)
Aln
t.
The impact of a rise in the share of the labor force employed in the
R&D sector when θ<1 .
0t
• So, an increase in the share of the population
working in R&D can produce a level effect on
technology and output
– But, no growth effect
• For example, the R&D in a war effort might
boost your output permanently, but would only
produce a transitory effect on its growth rate
– This sounds a lot like the U.S. in World War II
Case 2: 1
Ag
Ag
2)()1()()( tgtngtg AAA
When , is positive for all values of , implying that the
economy is characterized by ever-increasing growth rather than
convergence.
The impact of an increase in the share of the labor force employed
in the R&D sector is substantial through its impact on which in
turn affect as shown in the diagram above. .
1 Ag Ag
AgAg
• In this case, there is no steady-state growth
rate of technology
– The growth rate accelerates
• This implies that the overall economy never
reaches a steady-state either
– This is implausible, but shouldn‟t be completely
dismissed. Growth rates of developed countries
have been inching up over the decades.
• This is one type of fully endogenous model of growth
Case 3: When θ=1, the model simplifies to:
• Growth of ideas depends on population
• Growth of ideas depends on the proportion of the population working in research and development [see Eqn 8]
• Growth of ideas is accelerating when population growth is positive, and has no steady state.
• Growth of ideas stops when population growth stops
These models are simple and plausible • In this models given Eqn 11, and using it in Eqn 5 implies the
growth rate of knowledge, output and output per worker are all equal to ; thus aL affects the long run grwoth of the economy [aL could be taken as saving as it is used to produce knowledge which in turn produce goods in the future]
• Sometimes such model are called AK models or linear growth models
[11] )( tLBag LA
[12] )()( tngtgdt
dgAA
A
1
LBaL
.
)()( tngtg AA Ag
Ag
When existing knowledge is just productive enough in
generating new knowledge that the production of new knowledge
is proportional to the stock.
the rate of knowledge growth is a linear function of the
population growth and the knowledge growth is a linear
function of the labour force and the fraction of it devoted to
R&D.
1
Since the output good in this economy has no use other than in
consumption, we can think of the resources devoted to R&D as
resources withdrawn from consumption, i.e. a form of saving.
resources devoted to R&D are useful in increasing future
consumptions rather than current consumption.
With this interpretation of as saving, as noted earlier the
model provides an example of a case where the saving rate may
affect long-run growth.
La
The Importance of Returns to Scale to Produced Factors:
The reason that these three cases have such different
implication is that whether θ is less than, greater than or
equal to 1, it determines whether there are decreasing
,increasing, or constant returns to scale to produced factors
of production.
The growth of labor is exogenous, and we have eliminated
capital from the model; thus
• knowledge is the only produced factor.
• There are constant returns to knowledge in goods production
→ Thus whether there are on the whole increasing, decreasing,
or constant returns to knowledge in this economy is
determined by the returns to scale to Knowledge in
knowledge production-that is , by θ
III. The General Case: The model with capital
The dynamics of knowledge (A) and capital (K)
A: Capital
Now there 2 endogenous stock variables, A &K in the model
Substituting the production function [Eqn 1] into the
expression for capital growth [Eqn 3] yields:
[14] )(
)()()1()1(
)(
)()(
[13] )()()()1()1()(
1
1
111
tK
tLtAaas
tK
tKtg
tLtAtKaastK
KC
LKK
LK
The growth rate of capital, , is always positive and is
increasing if
decreasing if
is zero if
[15] )()()1()(
)(tgntg
tg
tgKA
K
K
0)()( tgntg KA
0)()( tgntg KA
Taking logs of both sides and differentiate w.r.t. time results
in an expression giving the growth rate of the growth rate of
capital: **
)()( tgntg AK
Kg
B: Knowledge
The growth rate of knowledge is expressed by:
implying that the growth rate of the knowledge accumulation is:
Implying that the growth rate of capital when knowledge grows
at a constant rate is:
In 17, gA is rising if is positive, falling if it is
negative and constant if it is zero (this is show in the next figure,
drown for a case θ <1
[16] )()()()(
)()(
,)()()((t)A
1
tAtLatKaBtA
tAtg
tAtLatKaB
LKA
LK
** 1AK g
ng
[17] )()1()()(
)(tgntg
tg
tgAK
A
A
AK gng )1(
• The production function for output [Equation 1] exhibits
constant returns to scale in the two produced factors of
production (K and A).
• Whether there are on net increasing, decreasing or constant
returns to scale to the produced factors depends on their
returns to scale in the production function for knowledge.
• The key information about the returns to scale to K and A
as can be read from Equation 2 is given by the sum of the
parameters
• Increasing both K and A by a factor of X increases by a
factor of
• The key determinants of the economy‟s behavior is now not
how θ compares with 1 but how compares with 1.
X
A
• Case 1:
• if , is greater than 1 -the locus of points
where gA=0 [the previous figure] is steeper than the locus where
gK=0 [the one before the last one]: see in the diagram below
• The behavior of the growth rates of knowledge and capital when
implies that regardless of the initial level, these growth
rates converge to E in the diagram next - a level where they both
remain constant:
1
- In this equilibrium and are 0/ satisfy the equations
*Ag *
Kg
[18] 0 **** ngggng AKKA
[19] 0)1( ** AK gng
** 1AK g
ng
1 /1
1
Kg
Ag
0Ag
0Kg
0Ag
Case 1: The dynamics of the growth rates of knowledge and
capital when (n is positive):
n
Slope = 1/1
1
0Kg
0Ag
Slope = 1
0Kg
*Ag
*Kg
n
• Rewritings [18] for and substituting into [19] yields
• Combining these conditions give an expression for :
• In equilibrium (when A&K are growing at =n+ : – Then output will grow at rate [see Eqn1 &CRS assumption]
– Output per worker will grow at rate
– Long run growth is an increasing function of population
growth [from 21]
– The fractions of the labor force and capital stock devoted to
R&D hove no long-run effect on growth rates, but a level
effect [are not in 21 but are there on 16]
– The saving rate do not affect long-run growth rate but has a
level effect [again via aL]
*Ag
[21] )(1
* ng A
*Ag
*
Kg
[20] 0)1()( ** AA gg
*
Kg
*
Kg *Ag
Case 2: The dynamics of the growth rates of
knowledge and capital when
–In this case the loci gA and gK are constant and diverge as
shows in the next figure.
–Regardless of where economy starts it eventually enters the
region between the two loci
–Once this occurs the growth rate of both A and K and hence
output grwoth rate increases continuously.
–This case is analogous to the case when θ exceeds 1 in the
simple model with no capital
1
0Ag
Kg
Ag
Regardless of where the
economy begins it converges
to a between the loci.
0,1 2 nCase
0Kg
0
n
n
Case 3: The dynamics of the growth rates of
knowledge and capital when
–In this case (1-θ)/β equals 1 and hence the loci gA and gK have
the same slope (see next figure)
–In n is postive the gK.=0 line lies above gA =0 line and the
dynamics of the economy is similar to those when (θ+β) >1
(shown in panel a figure)
–When n is 0 on the other hand the two loci lie on to of each
other (shown in panel b of the figure next)
–The figure (panel b) shows regardless of where the economy
begins it converges to the balanced growth path
–As in the model with θ =1 and n=0 in the model without capital,
panel b doesn‟t tell us what balanced growth path the economy
converges to. (the model, however has a unique balance growh
path) –Romer (1990) model is good example (Nxt slide)
1
0Ag
Kg
Ag
Regardless of where the
economy begins it converges
to a point between the loci.
0Kg
0
n
n
0,1 3(a) nCase
0 AK gg Kg
Ag
Regardless of where the
economy begins it converges
to a balanced growth path
where the growth rates of
capital and labour is
constant.
0,1 3(b) nCase
Case 3: The dynamics ... when …Cont‟d
– The Romer (1990) model of “endogenous technological
change” fits into this framework (ie. Figure panel b above).
–As in this model, the Romer (1990) model has no population
grwoth (n=0); the PF is CRS: R&D uses only labour and the
existing stock of knowledge (no physical capital); thus all
physical capital is used for production of goods (Eqn 23).
–Thus the PF for knew knowledge (see Eqn 2) is
1
[23] )()()1()()(
[22] ),()((t)A
1
tAtLatKtY
tAtLBa
L
L
The Romer (1990) model.. Cont‟d
– Our usual assumption of a constant saving rate, .
completes the model.
–This is the case we have been considering with
–To see the implication of this model note that Eqn 22 implies
that A grows steadily at .
–This means the model is identical to the Solow model when
n=δ=0 and with the rate of technological progress
–Thus the grwoth rate of output and capital on the balanced
growth path are
–This model provides a situation where long run growth is
endogenous (and depends on parameters other than population
growth) but is not affected by the saving rate.
)()( tsYtK
)()(
)()()((t)A tLBa
tA
tAtAtLBa LL
1..,1,0 and
)(tLBaL
)(tLBaL
IV. The Nature of Knowledge and the Allocation
of Resources to R&D [Romer 1990 Model]
A. The Nature of Knowledge
Knowledge comes in many forms, from highly abstract
scientific results to highly applied every-day solutions found
by each and every individual.
Knowledge in all its forms between basic scientific research
to product specific development plays a fundamental role in
economic activity.
There is, however, no reason to believe that the
accumulation process of different types of knowledge to be
the same.
Still, all types of knowledge share on essential feature:
non-rivalry
The Nature of Knowledge: Non-rivalry
The use of a specific item in one activity does not prevent its simultaneous use in any other activity.
This feature of knowledge has two important implications:
1. The production and allocation of knowledge cannot be completely governed by competitive market forces:
– since the marginal cost of supplying knowledge to an additional user is zero the rental price of knowledge in a competitive market is also zero, implying that the creation of knowledge would not be motivated by private economic incentives.
2. Returns to scale:
– If a non-rival input has productive value, then output cannot be a constant-returns-to-scale function of all its inputs taken together.
– The standard replication argument used to justify homogeneity of degree one does not apply because it is not necessary to replicate non-rival inputs.
The Nature of Knowledge : Excludability
A good is excludable if it is possible to prevent others from using it.
Although all knowledge is non-rival the possibility to exclude others
from using it varies with the type of knowledge:
– Complex knowledge has a lower propensity to „leak‟
– Different type of knowledge is protected by different types of property rights.
The degree of excludability are likely to have strong influences on
how the production and allocation of knowledge depart from a
competitive market equilibrium:
– With no excludability – private returns are small
– With strong excludability – private returns are large due to monopoly rents.
B. The Determinants of the Allocation of resources to R&D
What determines the fraction of inputs devoted to R&D, i.e. the
exogenously parameters and ?
– Support for basic scientific research by governments and
charities
• Done by research centers/universities
• Available freely and thus need to be subsidized
– Private incentives for R&D and innovation
• Intellectual property rights allows for temporary monopolies
– Positive externality: New knowledge are created that will become
available for others after some time
– Positive externality: Consumers consume qualitatively upgraded goods
– Negative externality: Some producers of old technologies are driven out
of business.
– The production of new knowledge has a positive effect on production of
additional knowledge, i.e. stimulates further technological progress
La Ka
- Alternative Opportunities for talented individuals
• Baumol (1990) and Murphy, Shleifer and Vishny (1991) observe that major innovations and technology advances are often results of the work of extremely talented individuals.
• Talented individuals have many opportunities to choose from and historically such individuals have made careers in rent-seeking rather than socially productive activities.
• The probability that talented individuals choose socially productive careers is largely dependent on the opportunities to gain private economic returns to these activities.
B. The Determinants of the Allocation to R&D..... Cont’d
B. The Determinants of the Allocation to R&D..... Cont’d
– Learning-by-doing (The AK-Model)
• When learning-by-doing is the source of
technological progress the rate of knowledge
accumulation depends not on the fraction of the
economy‟s resources devoted to R&D but on how
much new knowledge is generated by the
conventional economic activity.
• This idea requires a model where all factors are used
in goods production:
1)()()()( tLtAtKtY
B. The Determinants of the Allocation to R&D..... Cont’d
– The simplest case of learning-by-doing is when
learning occurs as a side effect of the production of
new capital (& hence technology is labour-
augmenting).
– In this case knowledge accumulation is a function of
the increase in capital or capital/Labour ratio:
1)1(1 )()()()(
)()(
tLtKBtKtY
tBKtA
Thus in Eqn 6, the key determinants of how the economy evolves
is how the θ parameter compares with 1; her it is how [which is
equivalent to ] compares to 1.
if long-run growth is a function of n,
if long-run growth is explosive,
if long-run growth is explosive if n is positive and
constant if n = 0.
Since capital grows according to , the
dynamics of the capital stock is given by
-*Nb that this is similar to Eqn [6] and the dynamics are the same
1)1(1 )()()()( tLtKtKsBtK
)()( tsYtK
)1(
,1
,1
,1
When and n = 0 the production function becomes
,1
)()( tbKtY
Capital accumulation is then given by )()( tsbKtK
• Both output and capital is growing at constant rate (sb)
• Long-run growth depend on the saving rate
The contribution of capital extends beyond its conventional
contribution to the economy in the goods production since
capital also contributes to the development of new ideas.
Read the Implication of such Endogenous grwoth models when
framed in a Ramsey (endogenous saving) set up. Romer, 2001,
2nd edn, P. 122.
V. Endogenous growth theory and the
central questions of growth theory
What do models of R&D and knowledge accumulation
say about the issues of economic growth over time and
across countries?
Worldwide growth over time
• The growth of knowledge appear to be the central
reason that output and living standards are
significantly higher today than a century ago
• Results of empirical growth accounting points to the
importance of the „Solow residual‟ which may reflect
technological progress.
Endogenous growth theory and the central
questions of growth theory (cont.)
• Cross-country differences in real income
– The relevance of endogenous growth models are less obvious
• If income differences are attributed to lags in technological diffusion, the lags in the diffusion of knowledge from rich to poor countries that are needed to account for observed income differentials are extremely long, more than 100 years.
• Since technology and knowledge are largely non-rival it is difficult to explain why poor countries should not have access to the same technology as rich countries.
• It seems like it is the lack of ability to adopt advanced technologies rather than poor access to them that differ between poor and rich countries (see the Nelson and Phelp‟s (1966) model)
• Poverty and prosperity is related to whatever factors that allow some countries (and individuals) to take better advantage of advanced technologies [Institution! Politics!Vision! etc see PE Lecture).
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I.Overview
In this section we investigate the role of human capital
in economic growth.
Investments in human capital, and hence growth in
human capital, has been seen in the literature as an
endogenous engine of growth.
Human capital investment in this framework typically
includes not only schooling but also on the job
training.
We start by incorporating human capital in the Solow
model.
II. The Solow model with human capital
We have already discussed in Lecture 1, the Augmented
Solow-Swan model – the Solow model with human capital.
That model can also be taken as a variety of endogenous
grwoth model (so refer Lecture 1)
It had to be recall that that model is based on the classic works
of Mankiw, Romer and Weil(1992).
Recall also further that the Mankiw et al (1992) „Augmented
Solow-Swan model” has helped to solve the puzzle of high
share of capital from the model (about 68%) which doesn‟t
tally with the reality of capital share (about 33%) using a
“Growth Accounting Exercise”.
In the rest of the lecture, thus, we will focus on another
human capital-based endogenous growth model attributed to
Uzawa (1961) and Lucas (1988) – the Uzawa-Lucas Model