Transcript technological progress

Economic Growth and the
Convergence in Carbon
Emissions Across Countries
M. Scott Taylor
Department of Economics, Calgary
Institute for Advanced Policy Research, Calgary
National Bureau of Economic Research,
Cambridge MA
The Environment and Growth
• Is continuing economic growth compatible
with an improving environment?
• What determines cross country differences
in environmental quality?
Problem
• Continual growth with environmental
improvement requires falling emissions
per unit of output.
• But lowering emissions per unit of output
comes at increasing cost, because of
Diminishing Returns.
Implication
• Pollution abatement costs should rise
precipitously
• This lowers the return to investment
• This should choke off growth
Potential Solution
• Technological progress holds costs down
• The return to capital accumulation is not
choked off
• Growth with environmental improvement is
possible
Is it possible?
• Maybe
The Solow Model
• One Aggregate Good produced via capital
equipment and labor
• Aggregate output can be consumed or
invested
• Capital accumulates over time via
investment
• Technological progress makes inputs to
goods production more efficient over time.
Y CI
Y  F ( K , BL )
I  sY
dK
 sF ( K , BL )  K
dt
dB
 Bg g  0
dt
dL
 Ln n  0
dt
K (0)  K0 B(0)  B0 L(0)  L0
Rewrite in Different Units
Define : k  K / BL , y  Y / BL , etc.
Manipulate to find :
dk
 sf (k )  [  g  n]k
dt
k (0) given and
f (k )  F ( K / BL ,1)
The Solow Model
f(k)
y*
sf(k)
i*
Output
Savings
Investment
(n+g+δ)k
k(0)
k*
Capital per
effective worker
BGP Predictions
• Technological progress determines an
economy’s long run growth.
• k* is constant along the BGP, but this
means:
• Capital per worker, K/L grows at rate g
• Income per capita Y/L grows at rate g
• Aggregate output grows at rate g+n
Transition Path Predictions
Rates of
Change
dk / dt sf (k )

 [  g  n]
k
k
dk / dt
k
(n+g+δ)
sf(k)/k
k(0)
k*
Capital per
effective worker
Unconditional Convergence
Poor Countries Should grow faster
than Rich ones
Transition Path Predictions
Rates of
Change
dk / dt
k
(n’+g+δ)
(n+g+δ)
sf(k)/k
s’f(k)/k
k*’
k*
Capital per
effective worker
Conditional Convergence
Correct for SS differences
The Green Solow Model
• Technological progress makes inputs used
in both goods production and abatement
more efficient over time.
• Environmental standards rise slowly over
time
Emissions produced
are proportionate to
output flow
Emissions can be abated but
at some cost
E  [ F  A( F ,  )]
d
  g A where g A  0
dt
(0)   0
Manipulate to Obtain

dE / dt
k
   [g  n  g A ]
E
k
Emissions Growth along BGP
Transitional Growth Component
Defined as GE=g+n-gA
Two Time Frames
• Along the BGP we again have dk/dt = 0
• Emissions fall or rise over time
• If GE > 0 we say growth is unsustainable
• If GE< 0 we say growth is sustainable
Sustainable Growth: GE <0
Rates of
Change
[dE/dt]/E
[dk/dt]/k
α(n+g+δ)-GE
α(n+g+δ)
αsf(k)/k
kT
k*
Capital per
effective worker
0.7
0.01
0.6
0.5
0.001
Log (E/Y)
Emissions
0.4
0.3
0.0001
0.2
0.1
0
0.00001
0
25
50
Emissions
75
E/Y
10
Empirical Implications
Declining Emissions to GDP ratios
Tons of Emissions//Dollar
1940=100
100
SO
NOx
VOCs
PM10
CO
10
1
1950
1955
1960
1965
1970
1975
Years
1980
1985
1990
1995
Pollution Abatement costs/GDP
are virtually constant
U.S. Real Pollution Abatem ent and Control Expenditure GDP ratio
2.0000%
1.8000%
1.6000%
1.2000%
1.0000%
ratio
0.8000%
0.6000%
0.4000%
0.2000%
Year
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
0.0000%
1972
real expenditure/GDP
1.4000%
Sulfur Dioxide Emissions, 1940-1998
Carbon Monoxide Emissions, 1940-1998
Nitrogen Oxide Emissions, 1940-1998
Volatile Organic Compounds 1940-1998
Particulate Matter PM10, 1940-1998
What if Growth is Unsustainable?
UnSustainable Growth: GE>0
Rates of
Change
[dE/dt]/E
α(n+g+δ)
α(n+g+δ)-GE
αsf(k)/k
k*
kT
Capital per
effective worker
Unconditional Convergence
Average Log changes 1999-1960
1.25E-01
7.50E-02
2.50E-02
2
3
4
5
6
7
-2.50E-02
-7.50E-02
Log Lbs/capita 1960
8
9
10
11
12
Conditional Convergence
0.06
0.05
Average Log Changes 1998-1960
0.04
0.03
0.02
0.01
0
7
7.5
8
8.5
9
9.5
-0.01
-0.02
-0.03
Log Lbs/capita 1960
10
10.5
11
11.5
12
Convergence in OECD
45
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
Greece
Iceland
Ireland
Italy
Japan
Luxembourg
Netherlands
New Zealand
Norway
Portugal
Spain
Sweden
Switzerland
United Kingdom
United States
40
35
metric tons/capita
30
25
20
15
10
5
0
19
60
19
62
64
19
66
19
68
19
70
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
9
19
6
98
19
Estimated Rate of Convergence
Rate of convergence is 2% per year.
This implies:
• 35 years to halve the gap between current
position and steady state
• Observation of positive emission growth for a
very long period is consistent with
“sustainable” growth.
• Could Carbon be like sulfur, nitrogen oxides,
particulates, etc?
Conclusions
• Green Solow model offers a consistent
explanation for observed data on emission
levels, emission intensities, and
environmental control costs.
• Predicts conditional convergence in
emissions per person. Estimated rate of
convergence is very slow. 2% per year.
• Predicts eventually rising environmental
quality if technological progress is
sufficiently rapid
• Left to do: Other pollutants and European
countries; rest of the world and Carbon
emissions; other estimation strategies.