Transcript The Neoclassical Growth Model

Chapter 15
Neoclassical Growth
Theory
Introduction
Growth theorists concentrated on
documenting the sources of growth
- population
- capital stock
- new discoveries and innovations
- others (human capital, R&D, …)
Robert Solow and T.W. Swan
- the leading contributors (1950s)
2
Introduction
Robert Solow and T.W. Swan
- Investment in new capital and the growth
of population cannot lead to continued
growth in per capita income.
- They attributed growth to the invention of
new technologies.
- The source of these innovations was
unexplained in their models.
(exogenous growth theory)
3
Introduction
From the 1950s until the late 1980s, the
theory of economic growth was a stagnant
area for economic research.
All of this changed for two reasons:
1. The Penn World Table.
2. A comprehensive source of data.
4
Introduction
Two theoretical papers were instrumental
in the resurgence of growth theory.
Romer (1986) & Lucas (1988)
- they searched for an explanation of the
sources of technological progress.
- one of the main ideas is human capital,
accumulation of knowledge.
- endogenous growth theory.
5
The Sources of Economic Growth
• Growth theory begins with the assumption that
GDP is related to aggregate capital and labor
through a production function.
• For simplicity, suppose the output is produced
from a single (compound) input.
Ex. k = K/L.
• Figure 15.1
-- input and output person for the U.S. economy
from 1929 through 1995.
-- more input leads to more output.
6
Inputs and Outputs in the United States,
1929–1999
Figure 15.1
7
©2002 South-Western College Publishing
Exogenous v.s Exogenous Growth Theory
• Ex. growth theory
-- the state of technology does not remain
constant over time.
-- the production function satisfies CRS.
-- The slope is a measure of productivity.
-- because the points in Figure 15.1 do not lie on a
straight line through the origin, the slope of the
production function must have changed from
one year to the next.
8
Exogenous v.s Exogenous Growth Theory
• Ex. growth theory (cont.)
-- Because early work in growth theory did not try
to explain the influence of invention and
innovation, productivity was left exogenous.
• Endogenous theory
-- rejects the assumption – CRS.
-- allows for the possibility that the points in
Figure 15.1 may all come from the same
production function.
9
Production Function and Returns to Scale
• Frequently used production function :
 is a parameter that measures
the relative importance of capital
Q measures increases in
the productivity of labor
and labor.
due to new inventions.
Y
Y is GDP.
 AK

A is a constant.
 L Q
1
K is capital.
L is labor.
10
Production Function and Returns to Scale
Y
 AK

 L Q
1
• Constant Returns to Scale (CRS)
-- if all the inputs are increased by a fixed
multiple, than output should increase by the
same multiple.
-- in the Cobb-Douglas production fun., CRS
means that the exponents on capital and labor
add up to 1.
11
The Neoclassical Theory of Distribution
• How the output is distributed to the owners of
the factors of production, labor and capital.
• The theory asserts that factors are paid their
marginal products. ( Euler Theorem )
• We can measure how much labor and capital
contribute to growth by observing how much
they are paid.
12
The Theory of Distribution and the
Cobb-Douglas Function
• The representative firm maximize

=
AK

 LQ 
1
M

L  rK
P
• F.O.C. yields
MPL  L
wL
 1  
(labor share),
Y
PY
MPK  K
rK
 
(capital share).
Y
Y
13
The Theory of Distribution and the
Cobb-Douglas Function
MPL  L
wL
 1  
Y
PY
• 1-α (α) measures the percentage increase in
output that will be gained by a given
percentage increase in labor (capital) input,
and is so called the labor (capital) elasticity.
• 1-α (α) can be estimated to calculate how
much of the growth in GDP per person is due
to growth in labor and capital per person.
14
Labor’s Share of National Income
15
©2002 South-Western College Publishing
Growth Accounting
Yt
Nt
1/ 3
 Kt 
  
 Nt 
Output per person
 Lt 
 
 Nt 
Input per person
2/3
2/3
Q
 t A
Total factor productivity
(slope of the production
function)
• Output per person equals input per person
multiplied by a term called “total factor
productivity”.
16
Growth Accounting
Yt
Nt
1/ 3
 Kt 
  
 Nt 
 Lt 
 
 Nt 
2/3
2/3
Q
 t A
• If we construct the aggregate input as
described by this equation, the graph of the
production function is a straight line through
the origin.
• On this graph, GDP per person is plotted
against input per person, and total factor
productivity corresponds to the slope.
17
Growth Accounting
• In figure 15.1, we found that if we plot points
on the production function for different years,
these points do not follow the same straight
line through the origin.
• Solow took this as evidence of the fact that
productivity has increased, i.e. the slope of the
production function has been increasing over
time.
18
Inputs and Outputs in the United States,
1929–1999
Figure 15.1
19
©2002 South-Western College Publishing
Growth Accounting
• Growth in labor and capital would be
represented as a movement along the
production function.
• Part of GDP growth per person must be due to
changes in total factor productivity as
measured be increases in the slope of the
production function.
• Economists call total factor productivity the
“Solow residual”.
20
The Solow Residual in the United States
Figure 15.3
21
©2002 South-Western College Publishing
Growth Accounting
1/ 3
2/3
 K t   Lt 
2/3
    
Q
A

t
 Nt   Nt 
 Yt  1  K t  2  Lt 
 ln    ln    ln    ln Qt2 / 3 A
 Nt  3  Nt  3  Nt 
Yt
Nt
• Suppose growth rates of GDP per person,
capital per person and labor per person are
10%, 5%, 3% respectively, then growth in the
Solow residual is
10%-1/3*6%-2/3*3%=6%.
22
The Sources of Growth in GDP per Person
Figure 15.4
23
©2002 South-Western College Publishing
The Neoclassical Growth Model
• We have described the factors that account for
growth in GDP per person and one of these
factors is the growth in capital per person
which can be increased by increasing
investment.
• Can we increase growth by investing more as
a nation?
• Neolcassical spells out the link between
investment and growth.
24
The Neoclassical Growth Model
• Increases in productivity are necessary if a
nation is to experience sustained growth in its
standard of living.
• The neoclassical growth model shows that an
economy with a fixed production that is
subject to constant returns to scale cannot
grow forever. ( due to diminishing returns to
capital )
25
Three Stylized Facts
•
The neoclassical growth model begins with
three stylized facts that characterize the U.S.
data to a first approximation.
1. GDP per person has grown at an average rate
of 1.89% over the past century.
2. The share of consumption in GDP have
remained approximately constant.
3. The labor’s share of income have remained
approximately constant.
26
Three Facts Used To Construct
the Neoclassical Growth Model
Figure 15.5A
27
©2002 South-Western College Publishing
Three Facts Used To Construct
the Neoclassical Growth Model
Figure 15.5B
28
©2002 South-Western College Publishing
Three Facts Used To Construct
the Neoclassical Growth Model
Figure 15.5C
29
©2002 South-Western College Publishing
Three Stylized Facts
•
The neoclassical model builds these
constants into an economic model based on a
competitive theory of production and
distribution.
•
It uses this model to explain the per capita
GDP growth rate.
30
Assumptions
St
 It ,
K t 1  (1   ) K t  I t ,
These two eqs. are accounting identies.
St
Yt
 s,
This eq assume that the saving rate is constant,
based on one of the three stylized facts.
31
Assumptions
Yt  A ( K t )
1/ 3
(Qt Lt )
2/3
This is the equation of the Cobb-Douglas
production function.
It combines the neoclassical theory of distribution
and the stylized fact that labor's share of income
is constant.
32
Simplifying the Model
•
We make three assumptions that are not
strictly necessary, but that will simplify the
exposition.
1. Each person in the economy supplies exactly
one unit of labor to the market.
2. The population is constant. (N)
3. There are no changes in the efficiency of
labor, i.e. Q is constant over time.
33
Diminishing Marginal Product
• Divide both sides of the production function
by population, N.
This is defined to be y.
Y
N
This is defined to be k.
1/ 3

K
A 
N
L
 
N
2/3
L / N  1 by assumption.
• This leads to the per capita production
function, which expresses the relationship
between output per person and capital per
person.
1/ 3
y

Ak
34
Diminishing Marginal Product
y

Ak
1/ 3
• Diminishing marginal product of capital
means that if capital changes by a fixed
percentage, holding the input of labor
constant, then output will change by a smaller
percentage as k increases.
y 1 2 / 3
MPk 
 Ak
 0,
k 3
MPk
2 5/ 3
  Ak
 0.
k
9
35
The Per Capita Production Function
Figure 15.6
36
©2002 South-Western College Publishing
Three Steps to the Neoclassical
Growth Equation
Step 1
kt 1  kt (1   )  it
This is the investment indentity.
It defines how capital accumulates.
Step 2
kt 1  kt (1   )  syt
This step assumes that investment (=s t )
to saving) is proportional to output.
Step 3
kt 1  kt (1   )  sAk
Replace output with the production function
to generate the neoclassical growth equation.
37
Steady State
kt 1  1    kt  Ask
1/ 3
t
• Let kt 1  kt  k ,
k  1    k  Ask ,
1/ 3
 sA 
 k  
 
3/ 2
.
38
Convergence When the Economy
Begins with Too Little Capital
Figure 15.7
39
©2002 South-Western College Publishing
Convergence When the Economy
Begins with Too Much Capital
Figure 15.8
40
©2002 South-Western College Publishing
Dynamics
kt 1  1    kt  Ask
kt  kt 1  kt  Ask
1/ 3
t
1/ 3
t
  kt
if 0  k  k , kt  0;
if k  k , kt  0.
41
Steady State
k   sA /  
3/ 2
1. An economy with a very high saving rate
should also have very high levels of
capital and GDP per person.
2. The economy always grows to the point at
which new investment is just sufficient to
replace worn-out capital.
3. Higher depreciation will tend to lower the
steady state stock of capital and per capita
GDP.
42
The Effects of Productivity Growth
• We have learned that per capita output cannot
grow forever.
• A key to understanding growth is in being able
to explain how the input of labor per person
can grow.
• The neoclassical growth model explains how
labor can grow by distinguishing labor supply
measured in hours from labor supply measured
in efficiency units.
43
Measuring Labor in Efficiency Units
E  N Q
• E is equal to the number of people, N, each of
whom supplies one unit of time, multiplied by
their efficiency, Q.
• Although we have assumed that the population
is constant and each person supplies a fixed
number of hours, it will still be possible for the
labor supplied by each person to increase as
long as we measure labor in efficiency units.
44
Table 15.1
45
©2002 South-Western College Publishing
The Neoclassical Growth Equation
K t 1  (1   ) K t  I t ,
K t 1
K t Qt N t
It
Qt N t

 (1   )

,
Qt 1 N t 1
Qt N t Qt 1 N t 1 Qt N t Qt 1 N t 1
(1   )
i
 kt 1 
kt 
.
1  gE
1  gE
Yt  AK t
1/ 3
Qt N t 
2/3
1/ 3
,
 K t   Qt N t 
Yt

 A
 

Qt N t
 Qt N t   Qt N t 
 yt  Akt1/ 3 .
2/3
46
The Neoclassical Growth Equation
(1   )
i
(1   )
syt
kt 1 
kt 

kt 
1  gE
1  gE
1  gE
1  gE
(1   )
sAkt1/ 3

kt 
.
1  gE
1  gE
 sA 
k 

 g  
3/ 2
.
47
The Neoclassical Growth Equation
 sA 
k 

 g  
y  Ak
1/ 3
3/ 2
 Kt

 Nt
 Yt

 Nt
 1
 ,
 Qt
 1
 .
 Qt
 Kt 
 Yt 
When steady state is achieved,   and  
 Nt 
 Nt 
must be growing at the same rate as Qt .
48
Homework
Question 6, 7, 11
49
END