Transcript University of New Mexico Talk on Time Substitution

Technological Change and Timing Reductions
in Greenhouse Gas Emissions
Rolf Färe
Oregon State University
Shawna Grosskopf
Oregon State University
Dimitris Margaritis
AUT
William L. Weber
Southeast Missouri State University
The problem of time substitution
• Firms have some finite amount of input (x)
that they can allocate over periods
t=1,…,T.
• The constraint: x1+x2+…xT ≤ x
• Single output (y)
• Maximize y1+ y2 +… + yT
subject to x1 + x2 +…+ xT ≤ x
• Production begins at τo and continues for To
periods.
• t
τo
τo +To
T
• t
τo
τo+To T
• t τo
τo +To
T
x1 + x 2 + x 3 ≤ 3
x1 + x 2 + x 3 ≤ 3
Applications
• Education-To maximize student achievement how
should we allocate the fixed budget equal across K-12?
Should more be spent in early (late) years? Or equally?
• Financial institutions-Collect deposits. When should
those deposits be transformed into loans?
• Advertising-Do short intensive ad campaigns (early or
late) increase revenues (votes) more than ad campaigns
that are spread out evenly over more periods?
• Inputs can be used to produce desirable
outputs or to reduce undesirable outputs
(pollution). If firms (countries) face an
upper bound on pollution, when should
resources be used to reduce pollution?
• Kyoto Protocol-Proposed that industrial
nations cut greenhouse gas emissions by
5.2% from 1990 levels by 2008 to 2012.
• US—CO2 equivalent emissions increased
by 17% from 1992-2007.
• European Union members-by 2004,
emissions had been reduced by only 0.9%
of targeted 8% emissions cuts targeted by
Kyoto Protocol .
• Nicholas Stern (2007)-global GDP will shrink by
5-20% unless immediate cuts in emissions (3070%) are made in next 20 years.
• Nordhaus (2007)-Stern Review uses a discount
rate that is too low and a coefficient of risk
aversion between generations that is too low
relative to market based estimates.
• Weitzman (2007)-gradual reduction in emissions
with a ramping up over time.
• Nordhaus (2007) -“the central questions about
global-warming policy-how much, how fast, and
how costly-remain open.”
• Production model-Färe, Grosskopf, Noh,
and Weber (2005), Rogers and Weber
(2004, 2011)
• desirable outputs (yRM+)
• undesirable outputs (bRJ+)
• inputs (xRN+).
• Time substitution model-Technological
change affects the timing of production.
Färe, Grosskopf, and Margaritis (2009)
Technology represented by the output possibility set
P( x)  {( y, b) : x can produce ( y, b)}
i. P(0)  (0,0) Scarcity
ii. if ( y, b)  P( x) and b  0 then y  0 Null-jointness
iii. if (y, b)  P( x) then for y '  y, ( y ', b)  P( x)
Strong disposability of desirable outputs
iv. if ( y, b)  P( x) then for 0    1, ( y, b)  P( x)
Weak disposability of undesirable outputs
Best-Practice Frontier
y
Strong disposability of y
b
Weak Disposability of y and b
y=desirable output
P2(x)
P1(x)
b=undesirable
output
P ( x )  {( y, b) :
t
t
o
K
t
t
z
y
 k km ,
ym 
t
on
x
m  1,..., M ,
k 1

K
t
t
z
x
 k kn ,
k 1
bj 
zkt  0,
n  1,..., N ,
K
t
t
z
b
 k kj ,
j  1,..., J ,
k 1
k  1,..., K DMUs,
t  1,..., T periods}.
• Given a binding regulatory constraint,
when should production begin, 0, and
when should production end, T0?
T
b
t
oj
t
 bj ,
j  1,..., J
t=1
y
10
9
C
t=2
15
13
C
8.66
5
0
y
2
5 6
b
0
2 3
6
b
Country C-produces 10+15 units of y and 6+6=12 units of b in the two periods
Regulation requires cuts of 4 units of b.
max
y1  y 2
s.t.
( y1 , b1 )  P1 ( x1 ), ( y 2 , b 2 )  P 2 ( x 2 ),
b1  b 2  b  8
b1  b 2  b  8
Solution: y1=9, y2=13
b1=5, b2=3
The Optimization Problem-Single
Desirable output
 0 T 0

max
0 0 
 ,T , b , y
K
y
subject to
  0
K
y   z y , x   z x , n  1,..., N ,

o
k 1
K

k

k
boj   zk bkj ,
k 1

on
k 1
 
k kn
j  1,..., J ,
 0 T 0

boj  b j ,
j  1,..., J
0
zk  0, k  1,..., K , ( ,  T 0 )  (t  1,..., T )}
• Simulation of 28 OECD countries, 1991-2006.
• Simulation-countries are restricted to 95% of
total emissions during 1991-2006 period.
• Countries produce real GDP (y) and CO2
equivalent emissions (b) using labor (x1) and
capital (x2).
• Penn World Tables (y, x1, x2).
• Carbon Dioxide Information Analysis Center (b).
• 0 can take 15 values-1991, 1992,…,2005.
• T0 can take 15 values, with production ending in
1992, 1993,…,2006.
• Must solve (15+14+13+…+1)=120 LP problems
for each country.
To isolate time substitution from efficiency changes
And technical change we inflate desirable outputs
by the output distance function.
ykt/Dot(xt,yt,bt)
Where Dot(xt,yt,bt)=max{λ: (y/λ , b) ε P(x)}
Average efficiency=0.90
Average technical change=0.7% per year
See Jeon and Sickles (2004) for bootstrapped
Estimates of Malmquist/Luenberger productivity for
OECD and Asian countries.
•
•
•
•
Mean
Std. dev.
Min.
Max.
co2
119869.1
275301.8
513
1593086
realgdp
labor
capital
1.01E+12
18559171
2.78E+12
1.96E+12
27968210
5.05E+12
6.4E+09
139863.4
2.27E+10
1.27E+13
1.52E+08
3.26E+13
Average annual real GDP growth=2.7%
Average annual emissions growth=0.8%
US-average real GDP growth=3.4%
US-average emissions growth = 1.1%
Figure 1. Annual Mean CO2 Emissions and Real GDP
1.4E+12
1.2E+12
Real GDP
1E+12
8E+11
6E+11
4E+11
2E+11
0
110000
112000
114000
116000
118000
120000
CO2 Emissions
122000
124000
126000
128000
Figure 2. Actual and Restricted CO2 Emissions for a 5% reduction
140000
120000
100000
80000
60000
40000
20000
0
1991
1992
1993
1994
1995
1996
1997
1998
Actual Emissions
1999
2000
2001
95% CO2 Emissions
2002
2003
2004
2005
2006
Figure 3. Optimal Real GDP with 5% Emissions Cuts and Frontier Real GDP
1.6E+12
1.4E+12
1.2E+12
1E+12
8E+11
6E+11
4E+11
2E+11
0
1
2
3
4
5
6
7
8
Optimal Real GDP
9
10
11
Frontier Real GDP
12
13
14
15
16
Figure 4. Cumulative % of Total Cuts Made By All 28
Countries
1
0.9
%
0.8
0.7
0.6
0.5
0.4
0.3
50% of total cuts made
0.2
0.1
0
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Proportion of Cuts Made by Year
2.5
Austria
2
Australia
Belgium
1.5
Canada
Czechoslovakia
Denmark
1
Spain
Finland
0.5
France
UK
Germany
0
1991
-0.5
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Greece
Hungary
Ireland
-1
Proportion of Total Cuts Made by Year
2.5
Israel
2
Italy
1.5
Japan
Korea
1
Luxembourg
Mexico
0.5
Netherlands
Norw ay
0
1991
-0.5
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
New Zealand
Poland
Portugal
-1
Sw eden
Turkey
-1.5
-2
US
Conclusions
• Nordhaus (2007) -“the central questions about
global-warming policy-how much, how fast, and
how costly-remain open.”
• Our results-How fast? 50% of total emissions
cuts would not come until 2001-2002.
• Some countries (Japan) would cut emissions in
early part of period (sell permits), while other
countries (US, New Zealand) would defer cuts
until later in the period.
• How costly? An optimal inter-temporal
reallocation would hold costs down to about
1.4% of real GDP for the US.