Transcript Endogenous Growth

Chapter 16
Endogenous Growth
Theory
Introduction
• The neoclassical growth model was constructed
in the 1950s to accommodate some stylized
facts about the U.S. economy.
• Now, data on most countries that extends back
to 1960 is available.
• It is found that a number of predictions of the
simplest version of the neoclassical model are
inconsistent with the evidence.
2
Introduction
• Both the neoclassical and endogenous growth
theories make the simplifying assumption that
each country in the world produces the same
homogenous commodity – no international
trade in commodities.
• However, both of the models allow for trade in
capital as countries borrow from and lend to
each other.
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Introduction
• Endogenous and exogenous growth theories
explain growth as increases in the efficiency of
labor, Q.
• The neoclassical model assumes that Q is
exogenous, but endogenous growth theory
explains why Q increases from one year to the
next.
• As the economy builds more complicated
machines and workers learn to operate new
machines, they acquire knowledge which
accumulates over time and contributes to the
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growth process.
The Neoclassical Model and the
International Economy
• The major motive for international trade is the
diversity in the abilities of different countries
to produces the goods and services.
• The neoclassical growth model excludes the
trade in commodities because the model deals
with a world in which there is only one good.
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The Neoclassical Model and the
International Economy
• A second kind of trade is intertemporal trade
-- trade between different points in time.
• Intertemporal trade occurs when one country’s
consumption plus investment is greater than its
GDP.
• Possible reasons :
1. People in one country might be more patient
than those in another which implies a higher
saving rate.
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The Neoclassical Model and the
International Economy
• Possible reasons :
2. One country may have a higher rate of growth
rate of population than another. The highpopulation-growth country needs to invest at a
faster rate in order to maintain a fixed capitallabor ratio.
3. One country is richer than the others.
4. Different countries may use different
production function. (This is not the case.)
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The Neoclassical Model and the
International Economy
•
In this chapter, we model the world as a
collection of countries, each of which
produces the same homogenous commodity
using the same production function.
• Countries differ for only three reasons :
1. Different saving rates;
2. Different rate of population growth;
3. Different initial stocks of capital.
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Modeling World Trade
• Two ways :
1. Assume that world capital markets are
completely open.
2. Assume that world capital markets are closed.
•
Reality is somewhere in between the two
extremes but difficult to model.
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The Neoclassical Growth Model with
Open Markets
• The first task in amending the neoclassical
model is to allow for the fact that countries can
borrow and lend internationally.
SS I I
World saving equals world investment.
f
f
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The Neoclassical Growth Model with
Open Markets
SSf I If
• Figure 16.1 shows that domestic saving in each
of these countries is very close to domestic
investment.
• The neoclassical model cannot explain.
• This gives us to question the assumptions of the
theory.
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The Neoclassical Growth Model with
Open Markets
• A second implication of the neoclassical model
is that investment in a perfect capital market
should flow freely between countries to
equalize the interest.
• If one country has a higher interest rate, capital
should flow to the high-rate country as the
MPK is higher.
• As capital flows into a country, the MPK will
fall and the rates of return are equalized.
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The Neoclassical Growth Model with
Open Markets
• For the neoclassical production function, the
rate of return depends only on the ratio of
capital to labor.
• If the rate of return is equal in different
countries, the capital-labor ratio must also be
equal.
 1
 K 
MPK   A 

NQ


 1
 K 
 MPK   A  f 
N Q
f
f
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The Neoclassical Growth Model with
Open Markets
• How to test whether the marginal product of
capital is equalized across countries ?
• Equalization of capital-labor ratios implies
equalization of GDP per person :

1
 K   QN 
Y
 A
 

QN
 QN   QN 

 K 
 A

 QN 
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The Neoclassical Growth Model with
Open Markets

 K 
Y
 A

QN
QN


• Figure 16.2 presents evidence from five
countries : the U.S., the U.K., Mexico, Turkey,
and India.
• In reality, we see that poor countries, like India,
tend to stay poor, and rich countries, like the
U.S. tend to stay rich.
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GDP Per Person Relative to U.S. GDP Per
Person for a Selection of Five Countries
Figure 16.2
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The Neoclassical Growth Model with
Closed Capital Markets
• Evidence suggests that capital does not flow
freely between countries. Can a different
version of the neoclassical model, zero capital
mobility, explain the facts ?
• Consider two countries that are different in only
one aspect -- the saving rate, s.
sYt  sAK t  Qt N t 

Saving
1
 K t 1  1    K t
Investment
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The Neoclassical Growth Model with
Closed Capital Markets
• If we let gE represent the growth rate of labor in
efficiency units, the steady state value of capital
per efficiency unit of labor is
K  sA 


QN  g E   
1
1
which depends on the four factors, the saving
rate, the depreciation rate, the growth rate of
labor in efficiency unit and the capital elasticity
of output.
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The Neoclassical Growth Model with
Closed Capital Markets
K  sA 


QN  g E   
1
1
• For the same production function, the
depreciation rate and the capital elasticity are
ruled out as possible factors that differ across
countries.
• Two factors left : the saving rate and the growth
rate of labor in efficiency unit.
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The Neoclassical Growth Model with
Closed Capital Markets
1/(1 )
 sA 
K


QN  g E   
• This equation predicts that countries saving
more will accumulate more capital per unit of
labor in the steady state and have higher level
of GDP per person.
 sA 
Y
 A

QN
 gE   

1
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The Neoclassical Growth Model with
Closed Capital Markets
 sA
Y
 A
QN
 gE  
 

1 
• If country A has a higher saving rate than
country B, (with the same level of Q)
YA YB
 B
A
N
N
Steady state level of GDP per person
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The Neoclassical Growth Model with
Closed Capital Markets
s 
 Y 
Y
 or 

N
 NQ 
• As a test of this prediction, panel A of BOX
16.1 plots average GDP per person from 1960
to 1998 against the average investment-GDP
ratio for 17 countries.
• Panel B corrects for population growth rate.
• In fact, there is little or no correlation between
them !!
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FOCUS ON THE FACTS
Investment and GDP Per Person
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FOCUS ON THE FACTS
Investment and GDP Per Person
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The Neoclassical Growth Model with
Closed Capital Markets
• The neoclassical model predicts that GDP per
person should be correlated with saving rates,
but the data does not supports this.
• The model also falls short in its predictions
about growth rates of GDP per person.
• The model maintains that the growth rates of
GDP per person should be the same because the
model states that all growth is ultimately due to
exogenous technical progress.
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The Neoclassical Growth Model with
Closed Capital Markets
• Consider two countries A and B that have
different saving rates and growth rates of
population growth, then the output per unit of
labor are
YA
YA
N AQ
 y A,
N BQ
 yB ,
• and the growth rate of GDP per person are
 YA / N A  Q  YB / N B  Q

,

.
YA / N A  Q YB / N B  Q
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The Neoclassical Growth Model with
Closed Capital Markets
 YA / N A  Q  YB / N B  Q

,

.
YA / N A  Q YB / N B  Q
• This equation shows that in the steady state,
output per person will grow at the same rate in
each country because countries that have the
same production function should experience the
same increases in the efficiency of labor.
• Figure 16.3 : the prediction of the simple
neoclassical model does not do a good job!
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Convergence
• Some economists note that the prediction that
countries will grow at the same rate, only holds
if all the countries in the world have attained
their steady state.
• With the same saving rate and population
growth rate, countries with lower capital stock
should grow faster.
• Evidence : Japan, Germany and Italy grew
rapidly in the postwar period.
• This idea is called reconstruction hypothesis.
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Convergence
• A second way : test whether countries with low
levels of GDP per person grow faster.
• This is called convergence hypothesis.
• Most studies conclude that this hypothesis does
not hold across all of the countries in the world.
• Conditional convergence : if we include
variables such as education, political stability
and etc., we can explain some of the differences
in growth rates.
• However, the convergence occurs at a much
slower rate than the simplest model predicts.
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The Model of Learning by Doing
• The neoclassical theory attributes growth to
increases in labor efficiency which are not
explained by other economic variables and is so
called exogenous growth theory.
• More recently, economists have begun to study
alternative approach that assumes workers
acquire skill, human capital, as they learn a
new technology.
• The accumulation of human capital is
responsible for growth in GDP per person.
(Endogenous Growth Theory)
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Endogenous and Exogenous Theories
of Growth
• The acquisition of human capital allows a
worker to operate complicated machinery or
join a team of other skilled workers.
• Human capital can be accumulated in the same
way that physical capital is accumulated by
devoting resources to the act of investment.
Physical capital : building factories and machines
Human capital : acquiring knowledge (skills)
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Endogenous and Exogenous Theories
of Growth
• Human capital is acquired through
-- the active pursuit of learning (or education)
-- the act of production itself (learning by doing)
• Learning by Doing :
-- The cost of production declines as companies
learn the best way to produce.
-- Workers acquire this knowledge through their
experiences in the workplace.
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The Technology of Endogenous Growth
• Endogenous grow theory makes a relative
minor change to the neoclassical production
function.
• It assumes that the aggregate (social)
production function is described by a C-D
technology :
Y  AK  L1
 1
 AK
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The Technology of Endogenous Growth
Y  AK
• If the capital elasticity of output is equal to 1
(rather than 1/3), this means that the economy is
no longer subject to a diminishing marginal
product of capital.
MPK  A ( a constant )
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The Technology of Endogenous Growth
Y  AK
• In the neoclassical theory, the capital elasticity,
α=1/3, is proposed to be consistent with the
evidence.
• How does endogenous growth theory explain
this alternative value, α=1, can be made
consistent with the fact ? (constant returns to
capital )
--- This is the social technology !!
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Social and Private Technology
• The acquisition of human capital is a social
process whose effects go beyond the
individual’s own productivity. (Externality)
-- As one firm produces a idea, another firm
copies it.
-- As one individual learns a quick and easy way
of solving a problem, another individual can
duplicate it.
-- The technological progress, Q, is a function of
the level of industrialization of the society.
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Social and Private Technology
• Suppose an economy consists of M firms and
each firm produces output using a private
technology that is identical that in the
neoclassical growth mode.
• Let Y, K, L be the aggregate GDP, capital and
labor, respectively, the private production
function is given by

1
Y
 K   LQ 
 A  

M
M  M 
 Y  AK

 LQ 
1
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Social and Private Technology
• The new element in the theory of learning by
doing is what determines Q !!
-- The aggregate level of industrialization.
-- The aggregate stock of capital per worker, K/N,
is a good proxy.
-- Q is assumed to be proportional to K/N.
For simplicity, we assume
K
Q  , the knowledge function.
N
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Social and Private Technology
• The accumulation of capital has two effects :
1. The private effect that gives rise to the term
Kα in the social production function.
2. The second effect is called “externality”
which gives rise to the term K1-α.
Y  AK
The private effect

L Q
1
Externality (Spillover Effect)
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Externality
• As workers learn to use the new technology in
one firm, they acquire skills that can transferred
to another firm.
• The learning was acquired from the workers’
exposure to ideas over the course of their work
history.
• The degree of exposure grows with the social
acquisition of capital.
• It’s almost free.
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The Social Production Function
QK/N
1
 L 
Y  A K Q   N 
 N 

L
 1 (for simplicity)
N
Aggregate
GDP

1
Y  AK K  A K
The Social Technology
Aggregate
Capital
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The Private Production Functions
Y  AK

 LQ 
1
MPK 
Figure 16.4B
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The Social and Private Production
Functions Compared
Y  AK
MPK  A (constant)
Figure 16.4A
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Social and Private Technology
• The economic meaning :
1. When an individual firm expands its use
of capital, it captures only the private
impact of this additional capital.
2. As the firm trains its workers in the use of
new equipment, most of this benefit is lost
when the worker leave to take new jobs.
Their new skills are widely disseminated
to friends and colleagues who work at
other firms.
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Social and Private Technology
•
An important implication
A firm will be more productive if it is part of a
society with a high level of capital.
Contrast this with the neoclassical model,
which assumes that if a firm were transported
from the U.S. to Ghana, it would still employ
the same technology.
Learning by doing argues that the firm would
be less productive because the skills of the
Ghanaian workforce are lower.
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Learning by Doing and Endogenous
Growth
• Because evidence suggests that there is
relatively little international borrowing and
lending, we examine the extreme case that the
capital market is closed.
It

St
domestic investment equals domestic saving
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Learning by Doing and Endogenous
Growth
• Saving is assumed to be a fixed fraction of GDP
St  sYt
• Capital is accumulated with the identity :
K t  I t 1  (1   )K t 1
• The social production function :
Yt  AK t
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Learning by Doing and Endogenous
Growth
K t 1  I t  (1   ) K t
 sYt  (1   ) K t
 sAK t  (1   ) K t
 (1    sA) K t
• In a learning by doing economy, the solution to
the growth equation is a straight line.
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Learning by Doing and Endogenous
Growth
Yt 1  AK t 1  A(1    sA)K t
 (1    sA)Yt
• Notice that because the population is assumed
to be constant, the dynamics of Y (or K) and y (
or k) are almost the same.
kt 1  (1    sA)kt
yt 1  (1    sA) yt
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Endogenous Growth
unstable steady state
Figure 16.5
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Predictions of Comparative Growth
Rates
• Consider two economies that have the same
saving rates, country A and B, but country A
begins with an higher initial level of capital
lower than that of country B.
The learning-by-doing model predicts that
country B will always remain ahead of country
A, but both countries’ capital will grow at the
same rate.
This explain why countries like India, U.K.,
Mexico, which have similar saving rates, grow
at about the same rate.
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Two Economies with the Same Growth
Rate But Different Initial Conditions
Figure 16.6
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Predictions of Comparative Growth
Rates
• A second piece of evidence concerns two
countries with different saving rates.
• Consider two economies begin with the same
initial capital stock, but have different saving
A
rates.
K  (1    s A) K ,
t 1
t
K t 1  (1    s B A) K t ,
s A  sB ,
A
B
 K t 1   K t 1 

 
 .
 Kt   Kt 
53
Two Economies with the Same Initial Condition
But Different Savings Rates
Figure 16.7
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Investment and Growth
Figure 16.8
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Endogenous Growth and Economic Policy
• One issue that concerns contemporary
policymakers is the fact that GDP growth per
capita was a little slower in the 1970s than it was
in the immediate postwar period.
-- If the neoclassical growth theory is correct, not
much can be done about this.
-- The learning-by-doing suggests that growth is
related to investment- both public and private.
56
Endogenous Growth and Economic Policy
• Q=K/N is indeed a too simplified assumption!!
• In the real world, a poor country can just invest
and copy the technologies from the other
countries to raise the level Q.
• However, for a rich country like the U.S., Q is
extreme high, and can only be raised through
new invention or more education of workers.
(the growth rate of Q may be smaller than the
growth of capital per person)
57
Endogenous Growth and Economic Policy
• Policy :
-- Investment in human capital can have great
public benefits.
-- Research & Development (R&D)
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Modified Theories of Learning by Doing
• Although economists agree that the neoclassical
model does not do a good job of explaining the
cross-country evidence, they do not accept the
extreme from of the learning-by-doing hypothesis.
• They believe as a country gets close to the frontier
of world knowledge, part of its investment will
spillover over and improve growth in other world
countries.
 the externalities can cross international
boundaries.
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Modified Theories of Learning by Doing
• A weaker form of the learning-by-doing
hypothesis argues that the knowledge function for
each country may display decreasing returns.
Ex. Q   K / N  ,0    1.

 y  Ak    (1 )
• This leads to a model behaves much like the NGT.
• GDP per capital is predicted to converge across
countries, but the speed at which it converges is
much slower.
kt 1  1    kt  sAk    (1 )
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Homework
Question 8, 11, 14
In question 14, the production function is
corrected to be
Y   aK  (1  a ) N


 1/ 
.
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END