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Endogenous Growth
Endogenous Growth
• Beginning with the 1970’s, US and other
developed economies went through a 20
year period of relatively low productivity
growth.
• Economists began looking for models
which could explain productivity growth as
function of fundamentals.
AK Models
• A simple way to develop endogenous growth
is to assume that capital intensity equals 1 and
technology is constant. (i.e. α=1)
y k
Yt  AKt  yt  Akt  
y k
• Assume constant savings rate, then growth
rate of capital is equal to the growth rate of
output
kt 1  kt
yt
k y
kt
s
kt
 (n   )  sA  (n   ) 
k

y
Growth in AK Models
• Q: Why do we have constant growth as a
function of investment levels, when that is not
the case in the neo-classical model?
• A: Marginal productivity of capital, A, is constant.
Because the effect of capital on output does not
diminish, capital accumulation can persistently
cause output to increase.
Endogenous Growth
• A large body of work has explored channels to
explain why labor productivity continues to grow
and why productivity differs across countries.
• Theories that explain long-term growth as an
outcome of the decisions of economic agents
are called endogenous growth theories.
• Capital accumulation cannot be the source of
long-term growth because capital has
diminishing returns.
• We must find an engine of growth which does
not have diminishing returns.
Two Strands: Brains vs. Ideas
1. Brains: Human capital is the source of
long-term growth. Human capital can be
used to produce future human capital
without diminishing returns.
2. Ideas: Research and development
explains long term growth. If you invent a
new idea, other inventors can use your
ideas to invent even newer ideas.
Example: Human Capital
Accumulation
• Total labor input is a function of total
hours worked and worker quality.
L  Lt  Ht
*
t
• Assume that hours worked and
technology remain constant, A = 1.
 *1
Yt  Kt Lt

1
 Kt (Lt Ht )
Model
• Let 1-u be the fraction of human capital
which is used to teach new workers.
• Let u be the fraction of human capital used
to produce goods.
Yt
 ( Kt
yt 
Yt
Lt

1


)  (uH )
t
 (kt )  (uHt )1
Human Capital Accumulation
• Human capital accumulation is done with
human capital.
Ht 1  Ht H
Ht 1  Ht  b  (1  ut )  Ht 
  b  (1  ut )
Ht
H
• If ut is converges to a steady-state level
that is above zero, human capital will grow
at a constant rate. {Economics of selection
of u is beyond the scope of this clas.}
Production
• Along the balanced growth path, if human
capital grows at a constant rate, then
output per hour and capital per hour will
also converge to the same growth rate.
y
k
H
k
   (1   )    (1   ) b  (1  u)
y
k
H
k
Convergence
gk
gy
b(1-u)
Y
K
Technological Advance
Sources of Growth
• Techniques for producing goods can be
deliberately increased through research
and development.
• Ideas developed through R&D have a
property unlike physical or human capital.
• A rival good, if used by one user, cannot be
used by others.
• Ideas are non-rival. Once the ideas are
produced they can be used by multiple
producers at the same time.
Fixed Costs of Research and
Development
• Production of Ideas: Each unit of
technology requires 1 B units of labor to
t
produce. Thereafter ideas can be used for
free.
• Accumulation of ideas is through research
work.
A
At 1  At  Bt  Lt
Technology Growth
• Assume that a constant share of labor is
devoted to goods production and R & D.
L  L  Lt  L  s Lt
A
t
•
Y
t
A
t
RD
L  (1  s ) Lt
Y
t
RD
Yt  K t  ( At (1  s RD ) Lt )1
At 1  At
A
RD Lt
 gt  Bs 
At
At
Balanced Growth Path
• Along the balanced growth path, labor
productivity, capital-labor ratio and
technology all grow at the same rate.
• If technology is constant, the numerator
must grow at the same rate at the
denominator.
gA  n
People are the source of new
ideas.
• Ideas have diminishing returns. If the stock
of ideas gets to be high relative to the
number of researchers, the growth rate of
innovation will start to slow down.
• As the population grows, the number of
researchers will grow generating growth in
ideas.
People per Idea and Growth of
Technology
gA
Ss`
n
Lt
At
Research & Development
• Increasing the share of workers in R&D will not
affect productivity growth in the long-run.
– More researchers will generate more new ideas each
period. But in % terms these extra new ideas will shrink
relative to the growing technology level.
– This will be mitigated by the knowledge spillovers
generated by the new ideas. But new ideas have
decreasing returns in creating new knowledge. As
these new ideas accumulate, the marginal impact of
extra research will diminish.
• However, R&D shares will affect the level of
technology along the BGP!
Increase in sRD
gA
B∙sRD
n
Lt
At
Increase in sRD
gA
n
time
Increase in sRD
A
time
Standing on the shoulders of giants
• Technology is non-rival in two ways.
• It can be used freely in producing goods

Y 1
t t
Yt  Kt ( A L )
• but also makes it even easier to produce
goods in the future.
Bt  BAt
Endogenous Growth
• In the long run, research and development
has an effect of long-run growth rates only
in one case: γ = 1
• When technology spillovers have no
diminishing returns, then sRD will directly
impact long term growth rate.
At 1  At
 gtA  Bs RD  Lt
At
Scale Problem
• Long run growth is a function of the scale
of the economy.
• As the economy increases in size (i.e.
population) the number of researchers will
increase.
• The growth rate of technology should
accelerate.
Microeconomics
• Production of ideas is done with increasing
returns to scale. Once idea is developed it can
be used over and over again at zero marginal
cost.
• Average cost of production is greater than
marginal cost.
• If the good were sold under perfect competitive
conditions (i.e. with price below marginal cost),
any firm that invested in R&D would make loss.
Production Function
• Output is produced with labor and At
different types of capital goods:


Y 1
Yt    xi ,t   ( Lt )
 i 1

At
• Constant returns to scale, but diminishing
returns to each type of capital good.
• Each type of capital good is rented to the
production firm by its inventor.
Rent capital
• If the rental price of each capital good is the
same, the production firms will rent the
same number of each type of intermediate
good.
– Due to diminishing returns, get high marginal
product from using more of an underused type
of capital.
• Aggregate capital stock is divided evenly
among each good.
xi ,t  x
xAt  K t  x 
Kt
At
Returns to Variety
• Examine production function
 At i
Yt    xt
 i 1
 

 Y 1

Y 1
(
L
)

A
x
(
L


t
t
t )
 t



K t  Y 1
Y 1

 At 
(
L
)

K
(
A
L
 t t t )

t
A
t 

• Number of types of goods is analogous to
technology level. Economy benefits by having
more types of goods in which to allocate their
capital – Diminishing returns.
Investment in R & D
• Inventors have a monopoly on producing
the good of their type. They rent their
capital at a rate higher than their marginal
cost - earning profits.
• Inventors invest in research up to that
point that the present value of future
profits equals the fixed costs of R&D
investment.
Demand for Invention
• The producers decide how much of invention
i, they want to rent in any time period.
 At i
Yt    xt
 i 1
 
 
 x
1
t


 Y 1
 ( Lt )

Y 1
t
 (L )
 
 x
2
t

Y 1
t
 (L )
 
 x
3
t

 ( LYt )1  ....
• Profit maximizing level of xi sets marginal
product equal to the real cost. Assume that
the producer rents the invention from
inventor for ROYt
Demand Curve for Inventions
• Profit Maximization
Y
  xti
xi
 
 1
 ( LYt )1
Y
P
 ROYt   xti
x
 
 1
 Zt Z t  Pt  ( LYt )1
Inventor
• The inventor rents capital at rate R and
uses the blueprint to transform it into at a
1-for-1 transformation.
• Profits: Roy*x- R*x
• Inventor is a monopolist. The amount of x
they produce determines ROY
 
  x
i
t
 1
 Zt  xti  R  xti
MR  MC
P
x  P  MC   2 xti
x
 
 1
 Z t  R   ROY  R  ROY 
1

*R
Policy Issues
• Markets fail in a number of ways
– Inventors don’t take knowledge spillovers into
account
– Monopolists produce an inefficiently low level
of the capital good.
– Inventors will diminish the effect of previous
inventions.
Estimating Cross-country
Technology Differences
• It is easy to think of a number of factors
which might cause the efficient allocation of
resources to be different across countries.
• These are sometimes estimated through
multivariate regression analysis.
Estimate TFP level:

1
 Yt   Yt 
TFPt     
 Kt   Lt 
Examples of X
• Variables which might affect technology
growth include inflation, openness to
trade, capital controls, tariffs, marginal tax
rates, education levels, income
distribution, political instability, weather,
colonial history, type of government etc.
Discussion of
The Myth of the Asian Miracle
Reference Points
• Growth Accounting
– We can calculate the share of output growth
attributed to a variety of sources
• Neo-classical growth model
– Capital accumulation cannot be the long-term
engine of growth because it has diminishing
returns.
– Advances in technology & TFP can be a
source of permanent growth.
Analogy between East Asia and
Soviet Union
• Krugman compares East Asian Tigers with
Soviet Union
• In 1994, East Asian tigers were thought of
as “Miracle” economies. USSR was
thought of as the miracle economy of the
1950’s with very high GDP growth.
• In both cases, high GDP growth was due
to rapid accumulation of resources.
Factors
• Output growth in East Asia was
substantially higher than the USA.
• Labor productivity growth was also higher,
but difference not as stark. Large growth in
E.A. workforce during this time period.
• Capital Productivity Fell Dramatically as
Capital Stock increased much faster than
output levels.
Data from
• Allwyn Young, 1995, “The Tyranny of
Numbers: Confronting the Statistical
Realities of the East Asian Growth
Experience,” Quarterly Journal of
Economics 110, 641-680.
Growth in East Asia
Output
0.12
0.1
0.08
0.06
.
0.04
0.02
0
Hong Kong
Singapore
South Korea
Taiwan
USA
Capital Growth
Capital
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Hong Kong
Singapore
South Korea
Taiwan
USA
Labor
Labor
0.06
0.05
0.04
0.03
0.02
0.01
0
Hong Kong
Singapore
South Korea
Taiwan
USA
Labor Productivity
0.12
0.1
0.08
0.06
0.04
0.02
0
Hong Kong
Singapore
South Korea
Output
Labor Productivity
Taiwan
USA
Capital Productivity
Capital Productivity
0
Hong Kong
-0.005
-0.01
-0.015
-0.02
-0.025
-0.03
Singapore
South Korea
Taiwan
USA
TFP
• Combination of high but less fantastic than
originally though labor productivity growth
and diminishing capital productivity implies
slow or mild TFP growth.
• This has been especially pronounced in
Singapore which has had very strong
capital growth.
TFP Growth
TFP Growth
0.03
0.025
0.02
0.015
0.01
0.005
0
Hong Kong
Singapore
South Korea
Taiwan
USA
Questions
• Why has TFP growth been much higher in
HK than in Singapore?
• What is your prediction for further growth?
Does Asia have existing opportunities to
push
– Young’s answer: Singapore tried to push its
way up the manufacturing chain to fast.
Implications
• Implications: Less than 30% of
outstanding output growth in East Asia is
due to TFP growth.
• Since capital accumulation has
diminishing returns and labor forces reach
saturation, East Asia is likely to slow in
growth.
Complaints about Young’s
methodology
• Young calculates TFP growth using labor shares
of income to estimate labor and capital intensity.
• But Young’s estimates generally attribute 50% of
income to labor. But EA national accounts may
not do a good job of calculating labor income,
especially of the self-employed.
• How does TFP growth look if we use numbers
for α = 1/3 as in developed world.
 ln TFP   ln Y  13  ln K  2 3  ln L
Bosworth and Collins
• Measure labor quality increase
– φ = .07
Capital income shares
– α = .35
Increase in Labor Participation
3.5
3
2.5
2
%
Growth in Population
Growth in Labor Force
1.5
1
0.5
Am
er
ica
In
du
st
ria
l
La
tin
Ch
i
na
In
do
ne
sia
Ko
re
a
M
al
a
Ph ysia
ilip
pi
ne
Si
s
ng
ap
or
Th e
ai
la
nd
Ta
iw
an
0
Education per Worker
East Asian expansion in
Education came from
broadening primary and
secondary education.
China
Indonesia
Korea
Malaysia
Philippines
Singapore
Thailand
Taiwan
1960
1.66
1.11
3.23
2.34
3.78
2.99
3.45
3.24
1994
5.33
4.95
9.67
6.95
7.35
6.11
7.47
8.17
Latin America
Industrial
2.97
7.26
5.53
9.92
3.67
3.84
6.44
4.61
3.57
3.12
4.02
4.93
0
2.56
2.66
Spectacular East Asian growth
performance due mostly to increase
in k
• East Asian TFP
growth strong relative
to USA and
developing world.
• Average relative to
most industrial
countries.
Growth in
y
China
4.5
Indonesia
3.4
Korea
5.7
Malaysia
3.8
Philippines
1.3
Singapore
5.4
Thailand
5
Taiwan
5.8
Latin America
1.5
Non US Industria 2.9
USA
1.1
Growth due to
Growth in
k
H
1.5
2.1
3.3
2.3
1.2
3.4
2.7
3.1
0.9
1.5
0.4
A
0.4
0.5
0.8
0.5
0.5
0.4
0.4
0.6
2.6
0.8
1.5
0.9
-0.4
1.5
1.8
2
0.4
0.4
0.4
0.2
1.1
0.3
Productivity Differences
• McKinsey Global Institute conducts a
number of studies of labor and capital
productivity at aggregate level in a
number of countries.
• Results in “The Power of Productivity:
Wealth, Poverty, and the Threat to Global
Stability” U. of Chicago Press 2004.
Some Conclusions
•
•
•
•
“An evaluation of economic performance requires an
analysis at the level of individual industries, such as
automotive, steel, banking, and retailing.”
An economy’s productivity is determined by “the way it
organizes and deploys both its labor and its capital”
Policies governing competition in product markets are
as important as macroeconomic policies. …One factor
that was profoundly underestimated was the importance
of a level playing field..””
“Direct investments by the more productive companies
from the rich countries would raise the poor countries’
productivity and growth…”
Points
• Korea’s TFP and GDP per Capita are about
50% of the U.S. level, but capital productivity
and capital returns are lower than U.S. levels.
• Korean education levels are similar (slightly
less) than U.S. levels.
• Korea has many advanced technological
industries (Samsung, Hynix)
Korea digital connectivity much better than USA.
Sectoral Approach
• Manufacturing
– Pohang Steel, Worlds most productive integrated
steel producer, exceptional success story.
– Most manufacturing (automotive, semi-conductor) are
dominated by uncompetitive conglomerates chaebols
protected from international competition and have not
adopted best practice manufacturing techniques.
– Semiconductors have lagged technological leaders
and sell commodity chips and low prices.
• Retailing
– Until recently, government regulations
prevented large stores and shopping centers
from developing. Labor productivity in retailing
sector is 1/3 of US..
• Construction
– Reasonably strong productivity in apartment
construction, but needs rezoning of outlying
areas to develop new single family dwellings.