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Endogenous growth
Convergence
New Growth Theories
Bill Gibson
UVM 1 Mar 2010
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Summary of Solow with Technical Change
=
L(t ) =
A(t ) =
ke =
ye =
k˙e =
Y
ke∗
ye∗
K α (AL)1−α
L(0)e nt
A(0)e πt
K /AL
Y /AL
skeα − (n + π + δ)ke
1
s
) 1− α
= (
n+π+δ
α
s
= (
) 1− α
n+π+δ
Estimated by Mankiw, Romer and Weil (1992)
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Empirics of the Solow model
Solow model gives simple testable predictions
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Empirics of the Solow model
Solow model gives simple testable predictions
Higher the rate of savings the richer the country
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Empirics of the Solow model
Solow model gives simple testable predictions
Higher the rate of savings the richer the country
Higher the rate of population growth the poorer the country
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Empirics of the Solow model
Solow model gives simple testable predictions
Higher the rate of savings the richer the country
Higher the rate of population growth the poorer the country
To a first approximation, results are true
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Empirics of the Solow model
Solow model gives simple testable predictions
Higher the rate of savings the richer the country
Higher the rate of population growth the poorer the country
To a first approximation, results are true
Savings and pop growth affect income in the way Solow
predicts
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Empirics of the Solow model
Solow model gives simple testable predictions
Higher the rate of savings the richer the country
Higher the rate of population growth the poorer the country
To a first approximation, results are true
Savings and pop growth affect income in the way Solow
predicts
More than half the cross country variation in per capita
income can be explained by these results
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Empirics of the Solow model
Solow model gives simple testable predictions
Higher the rate of savings the richer the country
Higher the rate of population growth the poorer the country
To a first approximation, results are true
Savings and pop growth affect income in the way Solow
predicts
More than half the cross country variation in per capita
income can be explained by these results
Example
Why might this model be unrealistic?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Empirics of the Solow model
Solow model gives simple testable predictions
Higher the rate of savings the richer the country
Higher the rate of population growth the poorer the country
To a first approximation, results are true
Savings and pop growth affect income in the way Solow
predicts
More than half the cross country variation in per capita
income can be explained by these results
Example
Why might this model be unrealistic?
Answer: Exogenous rate of technical change and no human
capital
Bill Gibson
University of Vermont
Endogenous growth
Convergence
The estimated equation
ye
ln ye
α
s
) 1− α
n+π+δ
α
α
ln s −
ln(n + π + δ)
1−α
1−α
α
α
ln s −
ln(n + π + δ)
1−α
1−α
α
α
ln s −
ln(n + π + δ)
1−α
1−α
α
ln A(0) + πt +
ln s
1−α
α
−
ln(n + π + δ)
1−α
= (
=
ln Y − ln(AL) =
ln Y − ln(L) − ln A(0)e πt
=
ln y
=
or: ln y = β 0 + β 1 t + β 2 ln s + β 3 ln(n + π + δ)
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Results
414
QUARTERLY JOURNAL OF ECONOMICS
TABLE I
ESTIMATION
OF THETEXTBOOK
SOLOWMODEL
Dependent variable: log GDP per working-age person in 1985
Sample:
Observations:
CONSTANT
ln(I/GDP)
ln(n + g + 8)
H2
s.e.e.
Restricted regression:
CONSTANT
ln(I/GDP) - ln(n + g + 8)
1?2
s.e.e.
Test of restriction:
p-value
Implied a
Non-oil
98
5.48
(1.59)
1.42
(0.14)
-1.97
(0.56)
0.59
0.69
Intermediate
75
5.36
(1.55)
1.31
(0.17)
-2.01
(0.53)
0.59
0.61
OECD
22
7.97
(2.48)
0.50
(0.43)
-0.76
(0.84)
0.01
0.38
6.87
(0.12)
1.48
(0.12)
0.59
0.69
7.10
(0.15)
1.43
(0.14)
0.59
0.61
8.62
(0.53)
0.56
(0.36)
0.06
0.37
0.38
0.60
(0.02)
0.26
0.59
(0.02)
0.79
0.36
(0.15)
Note. Standard errors are in parentheses. The investment and population growth rates are averages for the
period 1960-1985. (g + 8) is assumed to be 0.05.
Three aspects of the results support the Solow model. First,
the coefficients on saving and population growth have the predicted
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Regression
More than half the world wide variation in per capita GDP
can be explained by the two variables s and n.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Regression
More than half the world wide variation in per capita GDP
can be explained by the two variables s and n.
Growth highly correlated with both
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Regression
More than half the world wide variation in per capita GDP
can be explained by the two variables s and n.
Growth highly correlated with both
Both highly significant and wide variation in both
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Regression
More than half the world wide variation in per capita GDP
can be explained by the two variables s and n.
Growth highly correlated with both
Both highly significant and wide variation in both
Coefficients are large (1.42 and -1.97).
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Regression
More than half the world wide variation in per capita GDP
can be explained by the two variables s and n.
Growth highly correlated with both
Both highly significant and wide variation in both
Coefficients are large (1.42 and -1.97).
Not same magnitude (close)
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Regression
More than half the world wide variation in per capita GDP
can be explained by the two variables s and n.
Growth highly correlated with both
Both highly significant and wide variation in both
Coefficients are large (1.42 and -1.97).
Not same magnitude (close)
Not equal to 1/2
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Regression
More than half the world wide variation in per capita GDP
can be explained by the two variables s and n.
Growth highly correlated with both
Both highly significant and wide variation in both
Coefficients are large (1.42 and -1.97).
Not same magnitude (close)
Not equal to 1/2
Population seems to have stronger effect on per capita
incomes than savings
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
Developing countries have shortage of skilled and excess
supply of unskilled
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
Developing countries have shortage of skilled and excess
supply of unskilled
Must augment growth model so that individuals can save in
two forms, physical and human capital
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
Developing countries have shortage of skilled and excess
supply of unskilled
Must augment growth model so that individuals can save in
two forms, physical and human capital
y = k α h1−α all per capita terms
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
Developing countries have shortage of skilled and excess
supply of unskilled
Must augment growth model so that individuals can save in
two forms, physical and human capital
y = k α h1−α all per capita terms
k (t + 1) − k (t ) = sy (t )
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
Developing countries have shortage of skilled and excess
supply of unskilled
Must augment growth model so that individuals can save in
two forms, physical and human capital
y = k α h1−α all per capita terms
k (t + 1) − k (t ) = sy (t )
h (t + 1) − h (t ) = qy (t ) with q the amount spent on
education
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
Developing countries have shortage of skilled and excess
supply of unskilled
Must augment growth model so that individuals can save in
two forms, physical and human capital
y = k α h1−α all per capita terms
k (t + 1) − k (t ) = sy (t )
h (t + 1) − h (t ) = qy (t ) with q the amount spent on
education
This model will reach a steady state as well
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
Developing countries have shortage of skilled and excess
supply of unskilled
Must augment growth model so that individuals can save in
two forms, physical and human capital
y = k α h1−α all per capita terms
k (t + 1) − k (t ) = sy (t )
h (t + 1) − h (t ) = qy (t ) with q the amount spent on
education
This model will reach a steady state as well
Example
Compute the rate of growth of k if the ratio of human to physical
capital is r
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
Developing countries have shortage of skilled and excess
supply of unskilled
Must augment growth model so that individuals can save in
two forms, physical and human capital
y = k α h1−α all per capita terms
k (t + 1) − k (t ) = sy (t )
h (t + 1) − h (t ) = qy (t ) with q the amount spent on
education
This model will reach a steady state as well
Example
Compute the rate of growth of k if the ratio of human to physical
capital is r
Answer:
k (t +1)−k (t )t )
k (t )
= sr 1−α
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
If both growth at the same rate r = q/s
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
If both growth at the same rate r = q/s
k (t +1)−k (t )
k (t )
= sr 1−α
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
If both growth at the same rate r = q/s
k (t +1)−k (t )
k (t )
= sr 1−α
k (t +1)−k (t )
k (t )
= s (q/s )1−α
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
If both growth at the same rate r = q/s
k (t +1)−k (t )
k (t )
= sr 1−α
k (t +1)−k (t )
= s (q/s )1−α
k (t )
k̂ = ĥ = s α q 1−α
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
If both growth at the same rate r = q/s
k (t +1)−k (t )
k (t )
= sr 1−α
k (t +1)−k (t )
= s (q/s )1−α
k (t )
k̂ = ĥ = s α q 1−α
Example
Let α = 0.4 The propensity to save in the form of physical capital
is s = 0.2 while that of human capital is 0.35. What is the steady
state rate of growth of income per capita?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Human capital
If both growth at the same rate r = q/s
k (t +1)−k (t )
k (t )
= sr 1−α
k (t +1)−k (t )
= s (q/s )1−α
k (t )
k̂ = ĥ = s α q 1−α
Example
Let α = 0.4 The propensity to save in the form of physical capital
is s = 0.2 while that of human capital is 0.35. What is the steady
state rate of growth of income per capita?
Answer:k̂ = ĥ = 0.20.4 (0.35).6 = 0.28 So that ŷ = 0.28
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Possible for there to be diminishing returns to capital (both
kinds) and still no convergence
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Possible for there to be diminishing returns to capital (both
kinds) and still no convergence
If they have similar savings and technological parameters they
grow at the same rate
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Possible for there to be diminishing returns to capital (both
kinds) and still no convergence
If they have similar savings and technological parameters they
grow at the same rate
Might be relatively constant returns to physical and human
capital combined.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Possible for there to be diminishing returns to capital (both
kinds) and still no convergence
If they have similar savings and technological parameters they
grow at the same rate
Might be relatively constant returns to physical and human
capital combined.
World behaves as if there were constant returns to scale as in
HD
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Possible for there to be diminishing returns to capital (both
kinds) and still no convergence
If they have similar savings and technological parameters they
grow at the same rate
Might be relatively constant returns to physical and human
capital combined.
World behaves as if there were constant returns to scale as in
HD
Both rates of savings now have obvious connections to savings
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Possible for there to be diminishing returns to capital (both
kinds) and still no convergence
If they have similar savings and technological parameters they
grow at the same rate
Might be relatively constant returns to physical and human
capital combined.
World behaves as if there were constant returns to scale as in
HD
Both rates of savings now have obvious connections to savings
Even in the steady-state!
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Solves empirical problem?
Recall that coefficients on savings and population growth
higher than they should be
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Solves empirical problem?
Recall that coefficients on savings and population growth
higher than they should be
Upwardly biased since increase in income causes more income
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Solves empirical problem?
Recall that coefficients on savings and population growth
higher than they should be
Upwardly biased since increase in income causes more income
More income causes more investment in human capital
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Solves empirical problem?
Recall that coefficients on savings and population growth
higher than they should be
Upwardly biased since increase in income causes more income
More income causes more investment in human capital
This biases the coefficient on savings in an upward direction
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Solves empirical problem?
Recall that coefficients on savings and population growth
higher than they should be
Upwardly biased since increase in income causes more income
More income causes more investment in human capital
This biases the coefficient on savings in an upward direction
Population coef also biased upward since rise in population
reduces
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Solves empirical problem?
Recall that coefficients on savings and population growth
higher than they should be
Upwardly biased since increase in income causes more income
More income causes more investment in human capital
This biases the coefficient on savings in an upward direction
Population coef also biased upward since rise in population
reduces
per capita income and thus savings in both forms
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Solves empirical problem?
Recall that coefficients on savings and population growth
higher than they should be
Upwardly biased since increase in income causes more income
More income causes more investment in human capital
This biases the coefficient on savings in an upward direction
Population coef also biased upward since rise in population
reduces
per capita income and thus savings in both forms
Example
Which regression coefficient is likely to be larger?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Solves empirical problem?
Recall that coefficients on savings and population growth
higher than they should be
Upwardly biased since increase in income causes more income
More income causes more investment in human capital
This biases the coefficient on savings in an upward direction
Population coef also biased upward since rise in population
reduces
per capita income and thus savings in both forms
Example
Which regression coefficient is likely to be larger?
Answer: An increase in physical savings is only an increase in
one of two kinds of savings while an increase in population
decreases two kinds of capital
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Summary of Solow with human capital
=
L(t ) =
A(t ) =
ke =
ye =
k˙e =
h˙e =
Y
K α H β (AL)1−α− β
L(0)e nt
A(0)e πt
K /AL
Y /AL
sye − (n + π + δ)ke
qye − (n + π + δ)he
s 1− β q β 1−α1−β
)
n+π+δ
ss 1− β q 1−α 1−αα−β
= (
)
n+π+δ
ke∗ = (
he∗
Bill Gibson
University of Vermont
Endogenous growth
Convergence
The estimated equation-HC
ln y
= ln A(0) + πt +
+
−
α
ln s
1−α−β
β
ln q
1−α−β
α
ln(n + π + δ)
1−α
ln y = β 0 + β 1 t + β 2 ln s + β 3 ln(n + π + δ) + β 4 ln q
Bill Gibson
University of Vermont
between SCHOOL and the population growth rate is -0.38. Thus,
Endogenous
growth
accumulation could alter substantially
human-capital
including
Convergence
of physical-capital accumulation and populathe estimated impact
tion growth on income per capita.
Results
C. Results
Table II presents regressions of the log of income per capita on
the log of the investment rate, the log of n + g + 8, and the log of
the percentage of the population in secondary school. The humancapital measure enters significantly in all three samples. It also
TABLE II
OF THEAUGMENTED
SOLOWMODEL
ESTIMATION
Dependent variable: log GDP per working-age person in 1985
Sample:
Observations:
CONSTANT
ln(I/GDP)
ln(n + g +5)
ln(SCHOOL)
R2
s.e.e.
Restricted regression:
CONSTANT
ln(I/GDP) - ln(n + g + 5)
ln(SCHOOL) - ln(n + g + 5)
R2
s.e.e.
Test of restriction:
p-value
Implied a
Implied ,
Non-oil
98
6.89
(1.17)
0.69
(0.13)
-1.73
(0.41)
0.66
(0.07)
0.78
0.51
Intermediate
75
7.81
(1.19)
0.70
(0.15)
-1.50
(0.40)
0.73
(0.10)
0.77
0.45
OECD
22
8.63
(2.19)
0.28
(0.39)
-1.07
(0.75)
0.76
(0.29)
0.24
0.33
7.86
(0.14)
0.73
(0.12)
0.67
(0.07)
0.78
0.51
7.97
(0.15)
0.71
(0.14)
0.74
(0.09)
0.77
0.45
8.71
(0.47)
0.29
(0.33)
0.76
(0.28)
0.28
0.32
0.41
0.31
(0.04)
0.28
(0.03)
0.89
0.29
(0.05)
0.30
(0.04)
0.97
0.14
(0.15)
0.37
(0.12)
Note. Standard errors are in parentheses. The investment and population growth rates are averages for the
period 1960-1985. (g + 8) is assumed to be 0.05. SCHOOL is the average percentage of the working-age
population in secondary school for the period 1960-1985.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Comparing rich and poor countries
In DCs there is a shortage of unskilled labor
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Comparing rich and poor countries
In DCs there is a shortage of unskilled labor
This lowers the rate of return to physical capital
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Comparing rich and poor countries
In DCs there is a shortage of unskilled labor
This lowers the rate of return to physical capital
But large supplies of human capital also increase the rate of
return on capital
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Comparing rich and poor countries
In DCs there is a shortage of unskilled labor
This lowers the rate of return to physical capital
But large supplies of human capital also increase the rate of
return on capital
Hence rate of return affected in two opposite ways
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Comparing rich and poor countries
In DCs there is a shortage of unskilled labor
This lowers the rate of return to physical capital
But large supplies of human capital also increase the rate of
return on capital
Hence rate of return affected in two opposite ways
Net effect might be small
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Comparing rich and poor countries
In DCs there is a shortage of unskilled labor
This lowers the rate of return to physical capital
But large supplies of human capital also increase the rate of
return on capital
Hence rate of return affected in two opposite ways
Net effect might be small
Diminishing returns to each individual input still exists
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Comparing rich and poor countries
In DCs there is a shortage of unskilled labor
This lowers the rate of return to physical capital
But large supplies of human capital also increase the rate of
return on capital
Hence rate of return affected in two opposite ways
Net effect might be small
Diminishing returns to each individual input still exists
Conditional convergence after controlling for human capital,
poor countries tend to grow faster
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Comparing rich and poor countries
In DCs there is a shortage of unskilled labor
This lowers the rate of return to physical capital
But large supplies of human capital also increase the rate of
return on capital
Hence rate of return affected in two opposite ways
Net effect might be small
Diminishing returns to each individual input still exists
Conditional convergence after controlling for human capital,
poor countries tend to grow faster
Conditional divergence after controlling for initial levels of per
capital income.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Unconditional convergence
Two countries with same savings, depreciation and technical
progress rates
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Unconditional convergence
Two countries with same savings, depreciation and technical
progress rates
If population growth rate also the same: will converge to the
same level of y
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Unconditional convergence
Two countries with same savings, depreciation and technical
progress rates
If population growth rate also the same: will converge to the
same level of y
No remanence or hysteresis: path dependency
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Unconditional convergence
Two countries with same savings, depreciation and technical
progress rates
If population growth rate also the same: will converge to the
same level of y
No remanence or hysteresis: path dependency
Just divide up the time path: start one country a line 1 and
the next at 100
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Unconditional convergence
Two countries with same savings, depreciation and technical
progress rates
If population growth rate also the same: will converge to the
same level of y
No remanence or hysteresis: path dependency
Just divide up the time path: start one country a line 1 and
the next at 100
Both will converge to the same income per capita
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Unconditional convergence
Two countries with same savings, depreciation and technical
progress rates
If population growth rate also the same: will converge to the
same level of y
No remanence or hysteresis: path dependency
Just divide up the time path: start one country a line 1 and
the next at 100
Both will converge to the same income per capita
Shorter time for the richer country
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Unconditional convergence
Two countries with same savings, depreciation and technical
progress rates
If population growth rate also the same: will converge to the
same level of y
No remanence or hysteresis: path dependency
Just divide up the time path: start one country a line 1 and
the next at 100
Both will converge to the same income per capita
Shorter time for the richer country
This will happen independent of their starting values–history
doesn’t matter
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Data on convergence
Should have a strong negative correlation between growth and
starting income per capita
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Data on convergence
Should have a strong negative correlation between growth and
starting income per capita
Poorer countries should in 1870 should grow faster
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Data on convergence
Should have a strong negative correlation between growth and
starting income per capita
Poorer countries should in 1870 should grow faster
Convergence says countries should all go to their steady states
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Data on convergence
Should have a strong negative correlation between growth and
starting income per capita
Poorer countries should in 1870 should grow faster
Convergence says countries should all go to their steady states
Steady states should be approximately the same!
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Data on convergence
Should have a strong negative correlation between growth and
starting income per capita
Poorer countries should in 1870 should grow faster
Convergence says countries should all go to their steady states
Steady states should be approximately the same!
Baumol looked at 16 countries: got negative relationship
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Data on convergence
Should have a strong negative correlation between growth and
starting income per capita
Poorer countries should in 1870 should grow faster
Convergence says countries should all go to their steady states
Steady states should be approximately the same!
Baumol looked at 16 countries: got negative relationship
Selection bias Japan, Finland, Sweden, Norway, Germany,
Italy, Austria, France Canada Denmark, US, Netherlands,
Switzerland, Belgium, UK Australia
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Data on convergence
Should have a strong negative correlation between growth and
starting income per capita
Poorer countries should in 1870 should grow faster
Convergence says countries should all go to their steady states
Steady states should be approximately the same!
Baumol looked at 16 countries: got negative relationship
Selection bias Japan, Finland, Sweden, Norway, Germany,
Italy, Austria, France Canada Denmark, US, Netherlands,
Switzerland, Belgium, UK Australia
Did not include countries like Argentina, Chile, Spain,
Portugal...also did not weight by population
Bill Gibson
University of Vermont
Endogenous growth
Convergence
DeLong’s study
Early measurement error bolstered case for convergence
Bill Gibson
University of Vermont
Endogenous growth
Convergence
DeLong’s study
Early measurement error bolstered case for convergence
Case for absolute converge not supported.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
DeLong’s study
Early measurement error bolstered case for convergence
Case for absolute converge not supported.
Or is it: have break out countries: first four Tigers: South
Korea, Singapore, Taiwan, Hong
Bill Gibson
University of Vermont
Endogenous growth
Convergence
DeLong’s study
Early measurement error bolstered case for convergence
Case for absolute converge not supported.
Or is it: have break out countries: first four Tigers: South
Korea, Singapore, Taiwan, Hong
Ray: “Disparity in relative incomes has remained the same,
because the poorest countries have grown at the same rate as
the richest”
Bill Gibson
University of Vermont
Endogenous growth
Convergence
DeLong’s study
Early measurement error bolstered case for convergence
Case for absolute converge not supported.
Or is it: have break out countries: first four Tigers: South
Korea, Singapore, Taiwan, Hong
Ray: “Disparity in relative incomes has remained the same,
because the poorest countries have grown at the same rate as
the richest”
Wrong! China has changed that
Bill Gibson
University of Vermont
Endogenous growth
Convergence
DeLong’s study
Early measurement error bolstered case for convergence
Case for absolute converge not supported.
Or is it: have break out countries: first four Tigers: South
Korea, Singapore, Taiwan, Hong
Ray: “Disparity in relative incomes has remained the same,
because the poorest countries have grown at the same rate as
the richest”
Wrong! China has changed that
Do relative growth rates matter?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Unconditional
THE EMPIRICS OF ECONOMICGROWTH
A.
co 66
Unconditional
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427
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Log output per working age adult:1960
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Bill Gibson
D
0
University of Vermont
10.5
0
Oo0
Endogenous
00 growth
Convergence
-~0
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5,5
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6,5
8,5
Conditional
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9.5
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Log output per working age adult:1960
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7, 5
8.5
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10,5
Log output per working age adult:1960
LO
C.Conditionalon saving, populationgrowthand humancapital
6
0~~~~~~
?
2 0~~~~~~
0
?
O??b 9
Bill Gibson
0
lb8
University of Vermont
o
020
Endogenous growth
Convergence
0
Conditional 5on
and7, 5pop growth
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6.5
8.5
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Log output per working age adult:1960
LO
C.Conditionalon saving, populationgrowthand humancapital
6
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lb8
-2
5.5
6.5
7.5
8.5
9.5
Log output per working age adult:1960
FIGUREI
Unconditional
versusConditional
Convergence
Bill Gibson
University of Vermont
10.5
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Rate of savings and rate of investment in human capital have
growth rate effects, not just level effects.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Rate of savings and rate of investment in human capital have
growth rate effects, not just level effects.
Pace of growth determined within the model
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Rate of savings and rate of investment in human capital have
growth rate effects, not just level effects.
Pace of growth determined within the model
If we have unskilled labor, constant returns disappears
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Rate of savings and rate of investment in human capital have
growth rate effects, not just level effects.
Pace of growth determined within the model
If we have unskilled labor, constant returns disappears
Example
Why is the coefficient on labor so much larger than on savings in
MRW regressions?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Rate of savings and rate of investment in human capital have
growth rate effects, not just level effects.
Pace of growth determined within the model
If we have unskilled labor, constant returns disappears
Example
Why is the coefficient on labor so much larger than on savings in
MRW regressions?
Answer: Savings does not account for HC accumultion!
Increase in s only affects one kind of capital. Population
growth lowers per capital income and therefore affects both
forms of accumulation
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Rate of savings and rate of investment in human capital have
growth rate effects, not just level effects.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Rate of savings and rate of investment in human capital have
growth rate effects, not just level effects.
Pace of growth determined within the model
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Rate of savings and rate of investment in human capital have
growth rate effects, not just level effects.
Pace of growth determined within the model
If we have unskilled labor, constant returns disappears
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Rate of savings and rate of investment in human capital have
growth rate effects, not just level effects.
Pace of growth determined within the model
If we have unskilled labor, constant returns disappears
Example
Why is the coefficient on labor so much larger than on savings in
MRW regressions?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Perfectly possible for there to be diminishing returns to
physical capital but no covergence.
Rate of savings and rate of investment in human capital have
growth rate effects, not just level effects.
Pace of growth determined within the model
If we have unskilled labor, constant returns disappears
Example
Why is the coefficient on labor so much larger than on savings in
MRW regressions?
Answer: Savings does not account for HC accumultion!
Increase in s only affects one kind of capital. Population
growth lowers per capital income and therefore affects both
forms of accumulation
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Human capital also explains why rates of return to physical
capital may not be as high in LDCs as in DCs.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Human capital also explains why rates of return to physical
capital may not be as high in LDCs as in DCs.
Rich countries as a result can grow faster
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Human capital also explains why rates of return to physical
capital may not be as high in LDCs as in DCs.
Rich countries as a result can grow faster
Diminishing returns to capital offset by accumulating human
capital
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Human capital also explains why rates of return to physical
capital may not be as high in LDCs as in DCs.
Rich countries as a result can grow faster
Diminishing returns to capital offset by accumulating human
capital
Rate of growth of the economy is s α q 1−α
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Human capital also explains why rates of return to physical
capital may not be as high in LDCs as in DCs.
Rich countries as a result can grow faster
Diminishing returns to capital offset by accumulating human
capital
Rate of growth of the economy is s α q 1−α
Model predicts no tendency to unconditional convergence
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Human capital also explains why rates of return to physical
capital may not be as high in LDCs as in DCs.
Rich countries as a result can grow faster
Diminishing returns to capital offset by accumulating human
capital
Rate of growth of the economy is s α q 1−α
Model predicts no tendency to unconditional convergence
Convergence conditional on human capital possible
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Human capital also explains why rates of return to physical
capital may not be as high in LDCs as in DCs.
Rich countries as a result can grow faster
Diminishing returns to capital offset by accumulating human
capital
Rate of growth of the economy is s α q 1−α
Model predicts no tendency to unconditional convergence
Convergence conditional on human capital possible
Example
How do we know that the human capital augmented Solow model
is correct?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Conclusions
Human capital also explains why rates of return to physical
capital may not be as high in LDCs as in DCs.
Rich countries as a result can grow faster
Diminishing returns to capital offset by accumulating human
capital
Rate of growth of the economy is s α q 1−α
Model predicts no tendency to unconditional convergence
Convergence conditional on human capital possible
Example
How do we know that the human capital augmented Solow model
is correct?
Answer: China! (Also S. Korea, Taiwan, Singapore, Hong
Kong)
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Barro’s regression
Used Summers-Heston data set
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Barro’s regression
Used Summers-Heston data set
haty = β 0 + β 1 GDP1965 + β 2 S + β z Z
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Barro’s regression
Used Summers-Heston data set
haty = β 0 + β 1 GDP1965 + β 2 S + β z Z
β 1 < 0 and significant (t − score > 2)
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Barro’s regression
Used Summers-Heston data set
haty = β 0 + β 1 GDP1965 + β 2 S + β z Z
β 1 < 0 and significant (t − score > 2)
β 2 > 0 and significant
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Barro’s regression
Used Summers-Heston data set
haty = β 0 + β 1 GDP1965 + β 2 S + β z Z
β 1 < 0 and significant (t − score > 2)
β 2 > 0 and significant
High income per capita in themselves slow growth rates
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Barro’s regression
Used Summers-Heston data set
haty = β 0 + β 1 GDP1965 + β 2 S + β z Z
β 1 < 0 and significant (t − score > 2)
β 2 > 0 and significant
High income per capita in themselves slow growth rates
Higher endowments of human capital speed growth up
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Barro’s regression
Used Summers-Heston data set
haty = β 0 + β 1 GDP1965 + β 2 S + β z Z
β 1 < 0 and significant (t − score > 2)
β 2 > 0 and significant
High income per capita in themselves slow growth rates
Higher endowments of human capital speed growth up
Little statistical leverage however since high income per capita
countries also have high human capital levels
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Internal and External Technological Change
Internal: Gains from knowledge that are created by deliberate
diversion of resources
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Internal and External Technological Change
Internal: Gains from knowledge that are created by deliberate
diversion of resources
New products or innovation in production technologies
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Internal and External Technological Change
Internal: Gains from knowledge that are created by deliberate
diversion of resources
New products or innovation in production technologies
Classic trade off of less today for more tomorrow
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Internal and External Technological Change
Internal: Gains from knowledge that are created by deliberate
diversion of resources
New products or innovation in production technologies
Classic trade off of less today for more tomorrow
Returns are captured in form of higher profits
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Internal and External Technological Change
Internal: Gains from knowledge that are created by deliberate
diversion of resources
New products or innovation in production technologies
Classic trade off of less today for more tomorrow
Returns are captured in form of higher profits
External Technology diffused from other countries-
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Internal and External Technological Change
Internal: Gains from knowledge that are created by deliberate
diversion of resources
New products or innovation in production technologies
Classic trade off of less today for more tomorrow
Returns are captured in form of higher profits
External Technology diffused from other countriesComplicated: might slow down internal (appropriate
technolgy) tech change
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Internal and External Technological Change
Internal: Gains from knowledge that are created by deliberate
diversion of resources
New products or innovation in production technologies
Classic trade off of less today for more tomorrow
Returns are captured in form of higher profits
External Technology diffused from other countriesComplicated: might slow down internal (appropriate
technolgy) tech change
Or: process of diffusion might spur tech change
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Internal and External Technological Change
Internal: Gains from knowledge that are created by deliberate
diversion of resources
New products or innovation in production technologies
Classic trade off of less today for more tomorrow
Returns are captured in form of higher profits
External Technology diffused from other countriesComplicated: might slow down internal (appropriate
technolgy) tech change
Or: process of diffusion might spur tech change
Example
What is the principal means of technical change in your country:
internal or external
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Internal and External Technological Change
Internal: Gains from knowledge that are created by deliberate
diversion of resources
New products or innovation in production technologies
Classic trade off of less today for more tomorrow
Returns are captured in form of higher profits
External Technology diffused from other countriesComplicated: might slow down internal (appropriate
technolgy) tech change
Or: process of diffusion might spur tech change
Example
What is the principal means of technical change in your country:
internal or external
Answer: It varies from country to country
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Deliberate Technical Change
Technological frontier already exists in Platonic form as
“blueprints”
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Deliberate Technical Change
Technological frontier already exists in Platonic form as
“blueprints”
Y (t ) = E (t )γ K (t )α (uH )1−α
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Deliberate Technical Change
Technological frontier already exists in Platonic form as
“blueprints”
Y (t ) = E (t )γ K (t )α (uH )1−α
where E = rate of technical change and given by
E (t + 1) − E (t )
= a (1 − u )H
E (t )
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Deliberate Technical Change
Technological frontier already exists in Platonic form as
“blueprints”
Y (t ) = E (t )γ K (t )α (uH )1−α
where E = rate of technical change and given by
E (t + 1) − E (t )
= a (1 − u )H
E (t )
Where a is a positive constant. Physical capital grow
according to Solow
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Deliberate Technical Change
Technological frontier already exists in Platonic form as
“blueprints”
Y (t ) = E (t )γ K (t )α (uH )1−α
where E = rate of technical change and given by
E (t + 1) − E (t )
= a (1 − u )H
E (t )
Where a is a positive constant. Physical capital grow
according to Solow
Example
How could the growth rate be maximized?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Deliberate Technical Change
Technological frontier already exists in Platonic form as
“blueprints”
Y (t ) = E (t )γ K (t )α (uH )1−α
where E = rate of technical change and given by
E (t + 1) − E (t )
= a (1 − u )H
E (t )
Where a is a positive constant. Physical capital grow
according to Solow
Example
How could the growth rate be maximized?
Answer: Market will not do it...need a benevolent planner
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Externalities
Externality: trade between A and B affects C.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Externalities
Externality: trade between A and B affects C.
Railroad example: plus towns with train stations −towns
without
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Externalities
Externality: trade between A and B affects C.
Railroad example: plus towns with train stations −towns
without
Are technological advances externalities?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Externalities
Externality: trade between A and B affects C.
Railroad example: plus towns with train stations −towns
without
Are technological advances externalities?
Not in the standard model: technology is part of the
endowment
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Externalities
Externality: trade between A and B affects C.
Railroad example: plus towns with train stations −towns
without
Are technological advances externalities?
Not in the standard model: technology is part of the
endowment
Externalities have no impact on firms: only on consumers
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Externalities
Externality: trade between A and B affects C.
Railroad example: plus towns with train stations −towns
without
Are technological advances externalities?
Not in the standard model: technology is part of the
endowment
Externalities have no impact on firms: only on consumers
Discovery that “wipes out existing patent and inflicts losses
on patent holders”
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Externalities
Externality: trade between A and B affects C.
Railroad example: plus towns with train stations −towns
without
Are technological advances externalities?
Not in the standard model: technology is part of the
endowment
Externalities have no impact on firms: only on consumers
Discovery that “wipes out existing patent and inflicts losses
on patent holders”
Private and social marginal benefits and costs diverge
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Externalities
Externality: trade between A and B affects C.
Railroad example: plus towns with train stations −towns
without
Are technological advances externalities?
Not in the standard model: technology is part of the
endowment
Externalities have no impact on firms: only on consumers
Discovery that “wipes out existing patent and inflicts losses
on patent holders”
Private and social marginal benefits and costs diverge
Example
Where does technological change come from in economic theory?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Externalities
Externality: trade between A and B affects C.
Railroad example: plus towns with train stations −towns
without
Are technological advances externalities?
Not in the standard model: technology is part of the
endowment
Externalities have no impact on firms: only on consumers
Discovery that “wipes out existing patent and inflicts losses
on patent holders”
Private and social marginal benefits and costs diverge
Example
Where does technological change come from in economic theory?
Answer: Economics largely silent on the issue.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Romer Model
Let E = rate of technical change and given by
Y (t ) = E (t )K (t )α L1−α
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Romer Model
Let E = rate of technical change and given by
Y (t ) = E (t )K (t )α L1−α
K ∗ is average capital stock
E (t ) = aK ∗ (t ) β
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Romer Model
Let E = rate of technical change and given by
Y (t ) = E (t )K (t )α L1−α
K ∗ is average capital stock
E (t ) = aK ∗ (t ) β
Example
How can we use this model to show that there is underinvestment
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Romer Model
Let E = rate of technical change and given by
Y (t ) = E (t )K (t )α L1−α
K ∗ is average capital stock
E (t ) = aK ∗ (t ) β
Example
How can we use this model to show that there is underinvestment
Answer: A benevolent planner would invest more if she knew
that TC in one of her industries would spillover to the rest
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Constant returns to scale can exist at level of firm
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Constant returns to scale can exist at level of firm
Increasing returns at the level of the economy as a whole
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Constant returns to scale can exist at level of firm
Increasing returns at the level of the economy as a whole
Consider case where all production functions are similar
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Constant returns to scale can exist at level of firm
Increasing returns at the level of the economy as a whole
Consider case where all production functions are similar
We then have IRS
Y (t ) = aK (t )α+ β L1−α
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Constant returns to scale can exist at level of firm
Increasing returns at the level of the economy as a whole
Consider case where all production functions are similar
We then have IRS
Y (t ) = aK (t )α+ β L1−α
Example
With IRS diminishing returns are impossible?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Implications
Constant returns to scale can exist at level of firm
Increasing returns at the level of the economy as a whole
Consider case where all production functions are similar
We then have IRS
Y (t ) = aK (t )α+ β L1−α
Example
With IRS diminishing returns are impossible?
Answer: No IRS simply means that doubling inputs more than
doubles outputs
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Complementarities
If firm is planning investment must forecast future productivity
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Complementarities
If firm is planning investment must forecast future productivity
In Roemer model ρ depends on future path of average capital
accumulation
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Complementarities
If firm is planning investment must forecast future productivity
In Roemer model ρ depends on future path of average capital
accumulation
Example
Write down the payoff matrix in a coordination game
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Complementarities
If firm is planning investment must forecast future productivity
In Roemer model ρ depends on future path of average capital
accumulation
Example
Write down the payoff matrix in a coordination game
Answer:

I=
I
∼I
Bill Gibson
I
∼I
1, 1 −1, 0
0, −1
0, 0
University of Vermont


Endogenous growth
Convergence
Complementarities
Question for policy: how to induce the I , I Nash equilibrium
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Complementarities
Question for policy: how to induce the I , I Nash equilibrium
Think of each firm as choosing its own savings rate, s
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Complementarities
Question for policy: how to induce the I , I Nash equilibrium
Think of each firm as choosing its own savings rate, s
Average rate of investment then is not exogenous
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Complementarities
Question for policy: how to induce the I , I Nash equilibrium
Think of each firm as choosing its own savings rate, s
Average rate of investment then is not exogenous
Outcome of all individual choices
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Complementarities
Question for policy: how to induce the I , I Nash equilibrium
Think of each firm as choosing its own savings rate, s
Average rate of investment then is not exogenous
Outcome of all individual choices
Gives rise to multiple equilibria
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Complementarities
Question for policy: how to induce the I , I Nash equilibrium
Think of each firm as choosing its own savings rate, s
Average rate of investment then is not exogenous
Outcome of all individual choices
Gives rise to multiple equilibria
Example
Are complementarities the same as externalities?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Complementarities
Question for policy: how to induce the I , I Nash equilibrium
Think of each firm as choosing its own savings rate, s
Average rate of investment then is not exogenous
Outcome of all individual choices
Gives rise to multiple equilibria
Example
Are complementarities the same as externalities?
Answer: No! The former induces behavior on the part of the
agent that experiences the externality
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Savings rate of the ith firm
12
10
8
6
4
2
2
4
6
8
Economywide anticipated investment rates
Bill Gibson
University of Vermont
10
Endogenous growth
Convergence
Multiple equilibria
Not just an equilibrium of action, but an equilibrium of beliefs
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Multiple equilibria
Not just an equilibrium of action, but an equilibrium of beliefs
At first intersection firms are pessimistic about other firms
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Multiple equilibria
Not just an equilibrium of action, but an equilibrium of beliefs
At first intersection firms are pessimistic about other firms
The low investment on the part of firm as result of belief is
justified
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Multiple equilibria
Not just an equilibrium of action, but an equilibrium of beliefs
At first intersection firms are pessimistic about other firms
The low investment on the part of firm as result of belief is
justified
In general complementarities give rise to multiple equilibria
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Multiple equilibria
Not just an equilibrium of action, but an equilibrium of beliefs
At first intersection firms are pessimistic about other firms
The low investment on the part of firm as result of belief is
justified
In general complementarities give rise to multiple equilibria
An economy and its clone can give rise to two different
growth rates
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Multiple equilibria
Not just an equilibrium of action, but an equilibrium of beliefs
At first intersection firms are pessimistic about other firms
The low investment on the part of firm as result of belief is
justified
In general complementarities give rise to multiple equilibria
An economy and its clone can give rise to two different
growth rates
Example
What is economic theory of this example?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Multiple equilibria
Not just an equilibrium of action, but an equilibrium of beliefs
At first intersection firms are pessimistic about other firms
The low investment on the part of firm as result of belief is
justified
In general complementarities give rise to multiple equilibria
An economy and its clone can give rise to two different
growth rates
Example
What is economic theory of this example?
Answer: Self-fulfilling prophesy
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Take production function
Y = f (K , L)
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Take production function
Y = f (K , L)
Take total differential
dY =
Bill Gibson
∂f
∂f
dK + dL
∂K
∂L
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Take production function
Y = f (K , L)
Take total differential
∂f
∂f
dK + dL
∂K
∂L
Note that MPK = r and MPL = w
dY =
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Take production function
Y = f (K , L)
Take total differential
∂f
∂f
dK + dL
∂K
∂L
Note that MPK = r and MPL = w
Divide by Y
dY
dK K
dL L
=r
+r
Y
K Y
L Y
dY =
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Take production function
Y = f (K , L)
Take total differential
∂f
∂f
dK + dL
∂K
∂L
Note that MPK = r and MPL = w
Divide by Y
dY
dK K
dL L
=r
+r
Y
K Y
L Y
dY =
In share terms
Ŷ = αK̂ + (1 − α)L̂
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Now fit this equation to data
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Now fit this equation to data
Shares are 30-60 percent for wages Marquetti’s data
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Now fit this equation to data
Shares are 30-60 percent for wages Marquetti’s data
In most countries
Ŷ > αK̂ + (1 − α)L̂
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Now fit this equation to data
Shares are 30-60 percent for wages Marquetti’s data
In most countries
Ŷ > αK̂ + (1 − α)L̂
Therefore have to
Ŷ = αK̂ + (1 − α)L̂ + T
where T = total factor productivity growth
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Now fit this equation to data
Shares are 30-60 percent for wages Marquetti’s data
In most countries
Ŷ > αK̂ + (1 − α)L̂
Therefore have to
Ŷ = αK̂ + (1 − α)L̂ + T
where T = total factor productivity growth
Have to be careful with population growth as a proxy for labor
force growth
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Now fit this equation to data
Shares are 30-60 percent for wages Marquetti’s data
In most countries
Ŷ > αK̂ + (1 − α)L̂
Therefore have to
Ŷ = αK̂ + (1 − α)L̂ + T
where T = total factor productivity growth
Have to be careful with population growth as a proxy for labor
force growth
Must also correct for labor force quality human capital and
aggregating capital growing at different rates is always tricky
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Now fit this equation to data
Shares are 30-60 percent for wages Marquetti’s data
In most countries
Ŷ > αK̂ + (1 − α)L̂
Therefore have to
Ŷ = αK̂ + (1 − α)L̂ + T
where T = total factor productivity growth
Have to be careful with population growth as a proxy for labor
force growth
Must also correct for labor force quality human capital and
aggregating capital growing at different rates is always tricky
Factors must be paid the marginal products
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Example
Growth rate of the labor force is 1.5 percent. Depreciation is 3
percent. The capital-output ratio, is about 2.3. The share of
investment from the SAM, is 19 percent. Share of profit 0.40.
Output growth has been about 4.5 percent over the past decade.
Compute TFPG.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Example
Growth rate of the labor force is 1.5 percent. Depreciation is 3
percent. The capital-output ratio, is about 2.3. The share of
investment from the SAM, is 19 percent. Share of profit 0.40.
Output growth has been about 4.5 percent over the past decade.
Compute TFPG.
Answer:
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Example
Growth rate of the labor force is 1.5 percent. Depreciation is 3
percent. The capital-output ratio, is about 2.3. The share of
investment from the SAM, is 19 percent. Share of profit 0.40.
Output growth has been about 4.5 percent over the past decade.
Compute TFPG.
Answer:
step 1: dK /K = I /K − δ = (I /Y )(Y /K ) − δ =
0.19(1/2.3) − 0.03 = 0.526
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Total Factor Productivity
Example
Growth rate of the labor force is 1.5 percent. Depreciation is 3
percent. The capital-output ratio, is about 2.3. The share of
investment from the SAM, is 19 percent. Share of profit 0.40.
Output growth has been about 4.5 percent over the past decade.
Compute TFPG.
Answer:
step 1: dK /K = I /K − δ = (I /Y )(Y /K ) − δ =
0.19(1/2.3) − 0.03 = 0.526
step 2: 4.5 = 0.4(5.26) + 0.6(1.5) + T → T = 1.5
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of Growth
East Asia over the 1965-90 period grew faster than any other
region in history of world
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of Growth
East Asia over the 1965-90 period grew faster than any other
region in history of world
Includes: Japan, Hong Kong, S. Korea, Taiwan, Signapore,
Indonesia, Thailand and Malaysia
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of Growth
East Asia over the 1965-90 period grew faster than any other
region in history of world
Includes: Japan, Hong Kong, S. Korea, Taiwan, Signapore,
Indonesia, Thailand and Malaysia
Eclipsed now by China
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of Growth
East Asia over the 1965-90 period grew faster than any other
region in history of world
Includes: Japan, Hong Kong, S. Korea, Taiwan, Signapore,
Indonesia, Thailand and Malaysia
Eclipsed now by China
Very high savings rates (LA + 20)
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of Growth
East Asia over the 1965-90 period grew faster than any other
region in history of world
Includes: Japan, Hong Kong, S. Korea, Taiwan, Signapore,
Indonesia, Thailand and Malaysia
Eclipsed now by China
Very high savings rates (LA + 20)
All but Thailand had primary school enrollments rates higher
than for other countries of their income class.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of Growth
East Asia over the 1965-90 period grew faster than any other
region in history of world
Includes: Japan, Hong Kong, S. Korea, Taiwan, Signapore,
Indonesia, Thailand and Malaysia
Eclipsed now by China
Very high savings rates (LA + 20)
All but Thailand had primary school enrollments rates higher
than for other countries of their income class.
Was TFP a major factor in their growth
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of Growth
East Asia over the 1965-90 period grew faster than any other
region in history of world
Includes: Japan, Hong Kong, S. Korea, Taiwan, Signapore,
Indonesia, Thailand and Malaysia
Eclipsed now by China
Very high savings rates (LA + 20)
All but Thailand had primary school enrollments rates higher
than for other countries of their income class.
Was TFP a major factor in their growth
World Bank: Yes! Called it “productivity based catching up”
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of Growth
East Asia over the 1965-90 period grew faster than any other
region in history of world
Includes: Japan, Hong Kong, S. Korea, Taiwan, Signapore,
Indonesia, Thailand and Malaysia
Eclipsed now by China
Very high savings rates (LA + 20)
All but Thailand had primary school enrollments rates higher
than for other countries of their income class.
Was TFP a major factor in their growth
World Bank: Yes! Called it “productivity based catching up”
Example
Is the World Bank right about your country?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of Growth
East Asia over the 1965-90 period grew faster than any other
region in history of world
Includes: Japan, Hong Kong, S. Korea, Taiwan, Signapore,
Indonesia, Thailand and Malaysia
Eclipsed now by China
Very high savings rates (LA + 20)
All but Thailand had primary school enrollments rates higher
than for other countries of their income class.
Was TFP a major factor in their growth
World Bank: Yes! Called it “productivity based catching up”
Example
Is the World Bank right about your country?
Answer: It depends on the data!
Bill Gibson
University of Vermont
Endogenous growth
Convergence
The East Asian Miracle
Most explanations of the link between TFP growth and exports
emphasize such static factors as economies of scale and capacity
utilization. While these may account for an initial surge of
productivity soon after the start of an export push, they are
insufficient to explain continuing high TFP growth rates.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
The East Asian Miracle
Rather, the relationship between exports and productivity growth
may arise from exports’ role in helping economies adopt
best-practice technologies. High levels of labor force cognitive skills
permit better firm-level adoption, adaptation and mastery of
technology. Thus exports and human capital interact to provide a
particularly rapid phase of productivity-based catching up.
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of growth essential to know
How did this happen in so many countries at once
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of growth essential to know
How did this happen in so many countries at once
Is it good “old fashioned” accumulation of human and
physical capital?
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of growth essential to know
How did this happen in so many countries at once
Is it good “old fashioned” accumulation of human and
physical capital?
Do exports play an essential role
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of growth essential to know
How did this happen in so many countries at once
Is it good “old fashioned” accumulation of human and
physical capital?
Do exports play an essential role
shows that 2/3 of this super growth can be attributed to
human and physical capital
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of growth essential to know
How did this happen in so many countries at once
Is it good “old fashioned” accumulation of human and
physical capital?
Do exports play an essential role
shows that 2/3 of this super growth can be attributed to
human and physical capital
1/3 from TFP-says WB
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of growth essential to know
How did this happen in so many countries at once
Is it good “old fashioned” accumulation of human and
physical capital?
Do exports play an essential role
shows that 2/3 of this super growth can be attributed to
human and physical capital
1/3 from TFP-says WB
Excellent study by Young (1995) reduced the estimates
considerably!
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Sources of growth essential to know
How did this happen in so many countries at once
Is it good “old fashioned” accumulation of human and
physical capital?
Do exports play an essential role
shows that 2/3 of this super growth can be attributed to
human and physical capital
1/3 from TFP-says WB
Excellent study by Young (1995) reduced the estimates
considerably!
Numbers are not high but well above the rest of the world
Bill Gibson
University of Vermont
Endogenous growth
Convergence
Ferreira, de Abreu Pessoa and Veloso
Full Sample
GDP-hat
1.68%
Excluding disasters
2.24%
East Asian Miracles
5.68%
Miracles
4.57%
Fast Growth
2.60%
Medium Growth
1.65%
Slow Growth
0.69%
Disasters
-1.09%
Capital
1%
68%
1%
60%
3%
49%
2%
49%
2%
58%
1%
63%
1%
123%
0%
-17%
Labor
1%
42%
1%
32%
1%
14%
1%
17%
1%
26%
1%
41%
1%
108%
1%
-54%
China
Bill Gibson
University of Vermont
TFP
-0.17%
-10.00%
0.18%
8.00%
2.09%
37.00%
1.55%
34.00%
0.43%
16.00%
-0.06%
-4.00%
-0.90%
-130.00%
-1.86%
171.00%
2.26-4%
Endogenous growth
Convergence
Countries
East Asian Miracles
Fast
Taiwan
Barbados
Hong Kong
Ireland
S Korea
Portugal
Singapore
Pakistan
Italy
Miracles
Malaysia
Botswana
Finland
Taiwan
Austria
Korea
Spain
Singapore
Greece
Hong Kong
Syria
Thailand
Turkey
Indonesia
Brazil
Cyprus
Paraguay
Medium
Netherlands
Ecuador
Nepal
Israel
USA
Tunisia
Guatemala
France
Panama
Lesotho
Iceland
Belgium
Sweden
Mauritius
Jordan
Norway
Australia
Zimbabwe
Malawi
Dominican
South Africa
Republic
Philippines
United KingdomCanada
Kingdom
Denmark
Germany
Kenya
Fiji
Bangladesh
Uruguay
Bill Gibson
Slow
New Zealand
Switzerland Bolivia
Trinidad & Tobago
El Salvador
Mexico
Senegal
Cameroon
Honduras
Disasters
Chile
Zambia
Costa Rica
Central African Republic
Uganda
Peru
Tanzania
Guyana
Papua New Guinea
Mozambique
Togo
Niger
Iran
Venezuela
Ghana
Nicaragua
Argentina
Congo
Jamaica
University of Vermont