Technological Change and Timing Reductions in Greenhouse Gas Emissions

Rolf FäreOregon State University

Shawna GrosskopfOregon State University

Dimitris MargaritisAUT

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 + x2 + x3 ≤ 3

x1 + x2 + x3 ≤ 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 (30-70%) 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 (yRM+)

• undesirable outputs (bRJ+)

• inputs (xRN+).

• Time substitution model-Technological change affects the timing of production. Färe, Grosskopf, and Margaritis (2009)

( ) {( , ) : can produce ( , )}P x y b x y b

Technology represented by the output possibility set

. (0) (0,0) Scarcityi P . if ( , ) ( ) and 0 then 0 Null-jointnessii y b P x b y

. if ( , ) ( ) then for 0 1, ( , ) ( )

Weak disposability of undesirable outputs

iv y b P x y b P x

. if ( , ) ( ) then for ' , ( ', ) ( )

Strong disposability of desirable outputs

iii y b P x y y y b P x

Strong disposability of yy

b

Weak Disposability of y and b

Best-Practice Frontier

y=desirable output

b=undesirableoutput

P1(x)

P2(x)

1

1

1

( ) {( , ) : , 1,..., ,

, 1,..., ,

, 1,..., ,

0, 1,..., DMUs,

1,..., periods}.

Kt t t t

o m k kmk

Kt t ton k kn

k

Kt t

j k kjk

tk

P x y b y z y m M

x z x n N

b z b j J

z k K

t T

• Given a binding regulatory constraint, when should production begin, 0, and when should production end, T0?

, 1,...,T

toj j

t

b b j J

2 2 3 6

5

15

13

8.66

y

b

y

b

t=1 t=2

CC

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. 1 2 8b b b

1 2

1 1 1 1 2 2 2 2

1 2

max . .

( , ) ( ), ( , ) ( ),

8

y y s t

y b P x y b P x

b b b

Solution: y1=9, y2=13 b1=5, b2=3

0 0

10

65

9

The Optimization Problem-Single Desirable output

0 0

0 00

0 0

0

, , ,

1 1

1

0

max subject to

, , 1,..., ,

, 1,..., , , 1,...,

0, 1,..., , ( , ) ( 1,..., )}

T

T b y

K K

o k k on k knk k

K T

oj k kj oj jk

k

y

y z y x z x n N

b z b j J b b j J

z k K T t 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/Do

t(xt,yt,bt) Where Do

t(xt,yt,bt)=max{λ: (y/λ , b) ε P(x)}Average efficiency=0.90Average technical change=0.7% per year

See Jeon and Sickles (2004) for bootstrappedEstimates of Malmquist/Luenberger productivity for OECD and Asian countries. 

Mean Std. dev. Min. Max.

co2 119869.1 275301.8 513 1593086

realgdp 1.01E+12 1.96E+12 6.4E+09 1.27E+13

labor 18559171 27968210 139863.4 1.52E+08

capital 2.78E+12 5.05E+12 2.27E+10 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

0

2E+11

4E+11

6E+11

8E+11

1E+12

1.2E+12

1.4E+12

110000 112000 114000 116000 118000 120000 122000 124000 126000 128000

CO2 Emissions

Rea

l GD

P

Figure 2. Actual and Restricted CO2 Emissions for a 5% reduction

0

20000

40000

60000

80000

100000

120000

140000

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

Actual Emissions 95% CO2 Emissions

Figure 3. Optimal Real GDP with 5% Emissions Cuts and Frontier Real GDP

0

2E+11

4E+11

6E+11

8E+11

1E+12

1.2E+12

1.4E+12

1.6E+12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Optimal Real GDP Frontier Real GDP

Figure 4. Cumulative % of Total Cuts Made By All 28 Countries

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

%

50% of total cuts made

Proportion of Cuts Made by Year

-1

-0.5

0

0.5

1

1.5

2

2.5

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

Austria

Australia

Belgium

Canada

Czechoslovakia

Denmark

Spain

Finland

France

UK

Germany

Greece

Hungary

Ireland

Proportion of Total Cuts Made by Year

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

Israel

Italy

Japan

Korea

Luxembourg

Mexico

Netherlands

Norw ay

New Zealand

Poland

Portugal

Sw eden

Turkey

US

• 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.

Conclusions