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Supporting Online Material (SOM):
A. Overview of the Index Decomposition Analysis Method
We employ an index decomposition analysis (IDA) method to allocate changes in corn use for
ethanol in the U.S. to the contributing processes, including changes in domestic corn uses, net
exports, corn yield, and land use. IDA is a comparative statics technique to estimate the
contribution of individual factors or groups of factors to the change in an aggregate variable if all
other factors are held constant (Albrecht et al., 2002)*.1 IDA analysis can be performed either in
additive or multiplicative form. In the additive form, the aggregate variable change is the sum of
the component contributions. Under the multiplicative form, it is the product of the contributions.
The additive approach is often used in decomposition studies because its results are easier to
interpret than with the multiplicative form, and was therefore adopted in the current study.
The basics of the additive index decomposition approach can be outlined for a general function of
n contributing factors, x1, x2... xn, of the general form (Lenzen, 2006): 2
y(x1, x2, ... xn) = x1*x2* ...*xn =
.
(A.1)
The additive decomposition of Equation (A.1) is based on its total differential:
.
(A.2)
For discrete changes, ∆y, Equation (A.2) can be applied in two ways depending on how the
infinitesimal changes dy are integrated (Lenzen, 2006).2 The first form, referred to as the
Laspeyres family, gives the discrete change in y, ∆yL, as:
∆yL =
.
(A.3)
The second form, known as the Divisia family, gives the discrete change in y, ∆yD, as:
∆yD =
,
(A.4)
where i and j = 1, ..., n are the number of factors contributing to the aggregate variable.
In applications, Equations (A.3) and (A.4) require a choice of integral paths to generate the value
of the product terms as xi changes from t0 to t1.
The choice between the Laspeyres and Divisia techniques depends on the exact relationship being
analyzed (Lenzen, 2006).2 We analyze a relationship that closely matches Equation (1) for which
the Divisia family is more appropriate. In this case, the decomposition equation takes the form:
*
The IDA is closely related to another decomposition methodology known as Structural Decomposition Analysis
(SDA) and differs mainly in the type of data for which it is appropriate. The SDA approach is useful for decomposing
changes based on economic input-output tables, while the IDA approach is applicable to more aggregate time series
(Chunbo and Stern, 2008).3 The underlying computations are essentially the same.
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∆yD =
,
(A.5)
where wi is a weight function and the continuous growth rate, dxi/xi, is approximated by the
logarithmic growth rate function. The exact form of the weight function determines the specific
type of the Divisia IDA.
Different potential formulations of the IDA technique are judged by a number of criteria derived
from index number theory. These criteria include factor reversal, time reversal, proportionality,
aggregation, and zero/negative value robustness. For the additive decomposition approach used in
this study, these criteria can be summarized as follows. Factor reversal implies that the sum of
contributions over all factors equals the total change in the aggregate data (i.e., there are no
residuals). Time reversal means that the contribution of a given factor changes sign, but not
magnitude, if the time sequence is reversed. Aggregation implies that the sum of contributions
from a factor in a decomposition involving sub-aggregates equals the factor contribution in
decomposition without the sub-aggregates. Proportionality means that the decomposition
specification is homogenous of degree one (i.e., if the contributions of all factors are increased by
1 percent, the aggregate value also increases by 1 percent). No decomposition method passes all
these tests, but the factor-reversal and zero-value-robustness criteria are very desirable attributes
(Ang et al., 2004; Ang and Zhang, 2000).4,5 On the basis of an extensive review of IDA
techniques, Ang (2004)6 recommended the Type I Logarithmic Mean Divisia Index (LMDI I)
formulation for IDA. For an aggregate variable y with a multiplicative relationship to n
contributing factors x1, x2, ..., xn of the general form:
∆yD =
=
,
(A.6)
where gxi and gy are the logarithmic growth rate of xi and y, respectively.
The LMDI I formulation has a number of advantages over other decomposition techniques. First,
LMDI I satisfies the most important IDA criteria, such as factor and time reversal, as well as
aggregation. The approach is also easy to apply to functions involving more than two factors
because the specification remains the same as the number of factors increase. There is also a direct
and simple relationship between the additive and multiplicative forms of the LMDI I. In addition,
IDA methods of the form in Equation A.5 that leave a residual have been shown to reduce to the
LMDI I if the residual term is proportionally distributed to the individual factor contributions and
if the weight functions wi are the same for each factor (Ang et al., 2010).7 Approaches for dealing
with negative and zero data value issues caused by the presence of logarithms in the LMDI I
formulation have also been demonstrated (Ang and Liu, 2007).8
The LMDI I approach is exact for a wide range of functional forms often used in the analysis of
discrete data (Muller, 2010). 9 This feature is related to the fact that LMDI I approximates the
continuous growth rates in Equation A.4 by the logarithm growth function, which is generally a
close approximation. As Ang and Zhang (2000) pointed out,5 the logarithm weight function was
mentioned by Tornqvist in 1935, and Sato in 1976 found it to generate an ideal index when used to
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discretize the integral of the Divisia index formulae. Also, there is a simple relationship between
the LMDI I in Equation A.6 and the total differential in Equation A.2 when using the logarithmic
growth function approximation. From an equation of the form (1), the total differential in (2)
implies that
.
(A.7)
As a result, Equation A.6 can be interpreted as an allocation of the aggregate change, ∆y, in
proportion to the growth rates of its contributing factors.† Although LMDI I is a recent addition to
the IDA literature, it has become a preferred method in recent years because of the advantages
described above. It has been adopted for energy decomposition analysis by governmental agencies
in New Zealand, United States, and Canada as well as by the Asia Pacific Energy Research Center
and World Energy Council (Liu and Ang, 2007).10 Other recent applications include application of
the LMDI I to decompose the change in China's energy intensity from 1980 to 2003 (Ma and
Stern, 2008)11 and the structural decomposition of Australia's greenhouse-gas emissions between
1974 and 2005 (Wood, 2009).12 Although not as common as applications to energy-related issues, the
IDA and related SDA method have also been applied to agricultural and other non-energy issues.13−16
†
The case analyzed in this paper can be seen as a special case because the decomposition does not involve sub-sectors
or sub-aggregates of corn use for ethanol and is thus relatively straightforward. In the energy-analysis literature, for
example, total energy use may be decomposed into the effects of total industrial production, distribution of sectoral
production across sectors, and sector energy intensities, among other possible factors. However, Equation A.6
continues to apply at each level of aggregation.
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B. Supply and Allocation Relationship for the Decomposition of U.S. Corn Used for Ethanol
Production
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The LMDI I technique was used to decompose changes in corn use for ethanol production based on a
chained relationship that captures the main processes in corn supply and allocation. This relationship is
illustrated by Figure B.1 which represents the supply and distribution of corn as a hierarchical or nested
process. This structure is similar to the modeling of crop supply and distribution in economic models. This
approach improves the flexibility of models by separating variables into branches of the tree nest, while
preserving the role of the variables in a consistent aggregation framework. It provides a similar advantage in
the current paper because it preserves the physical/logical relationship among supply, export, and domestic
uses of corn, while allowing for the specification of a multiplicative relationship suitable for index
decomposition analysis.
Corn
Production
Corn
Imports
Corn
Exports
All Harvested
Cropland
Beginning
Stocks
Ending
Stocks
Harvested Grain
& Oil Seeds Land
Harvested Other
Crops Land
Total Corn Supply
Harvested All
Grains Land
Domestic Corn
Consumption
Harvested Coarse
Grains Land
Food, Fuel, Seed
and Industrial Uses
Corn Use for Ethanol
Production
Feed and
Residual Uses
Other Food, Seed and
Industrial Use
(a) Corn Supply and Distribution
Other Coarse
Grains
Corn
Yield
Oilseeds
Land
Harvested Other
Grains Land
Harvested Corn
Area
Corn
Production
(b) Corn Land Use
Figure B.1: Hierachical Description of Corn Supply and Distribution and Cropland Use
Panel (a) of Figure B.1 illustrates the USDA definition of total corn supply as the combination of beginning
stock, production, and imports. Corn imports by the U.S. are small, but are included here for completeness.
Figure B.1 also showed that total supply can be allocated to exports, ending stocks, and domestic
consumption. In turn, the domestic consumption portion can be distributed to a food, fuel, seed, and
industrial uses (FFSI) aggregate and a feed and residual aggregate. The portion of corn used for ethanol
production is part of the FFSI category, as shown in the lowest nest of Panel (a). Panel (b) further
disaggregates corn production into yield and land variables. The land variable is, in turn, related to intercrop transfers and to increases in total cropland. A multiplicative relationship for the IDA is generated
based on Figure B.1:
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Qce =
and
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(B.1)
Qprd=
,
(B.2)
where
Qce = Annual corn use for ethanol production (million tons);
Qffsi = Annual corn use for food, fuel, seed and industrial purposes (million tons)
Qdom = Annual total domestic corn consumption (million tons)
Qprd = Annual total corn production (million tons)
Qsup = Annual total corn supply (i.e., production + imports + beginning stock (million tons)
Ycorn = Annual corn yield defined as U.S. production divided by harvested area (tons/ha)
Acorn = Annual corn harvested area (million ha)
Acgrn = Annual coarse grain harvested area (million ha)
Agrn = Annual all-grain harvested area‡ (million ha)
Agn+oilsd = Annual all-grain plus oilseed harvested area (million ha)
Aall = Annual total harvested cropland area§ (million ha)
Equation (B.2) was substituted into (B.1) for the computations. These equations can be seen as tracing the
source of corn used for ethanol production through the corn distribution and supply chain, including corn
production. This path follows the solid arrow at each nest of panels (a) and (b), with the dashed arrow being
the complement(s). As mentioned above, corn imports by the U.S. are small, and the net withdrawal from
stocks was relatively small between 2001 and 2009. Thus, these variables were not included on a separate
level of the nest. The resulting relationship is an apt description of the corn supply and distribution market
specifications in models that have been used to evaluate the indirect effects of corn ethanol production.
Note that the consistency-in-aggregation property of the LMDI I method allows the calculation of the effect
of aggregates derived by folding the branches of the nests in panels (a) and (b). For example, the net
contribution of land-use change to corn production can be derived by folding the land branches of the nests.
This is represented by evaluating Equation (B.2) backwards from the Aall term to the (Acorn/Acgrn) term. The
factors in the decomposition analysis are represented by the multiplicative terms in equations (3a) and (3b)
which are described below:
Qce/Qffsi: This factor captures changes in the distribution of a given level of corn used for FFSI
between corn ethanol and other FFSI uses. If corn use for ethanol production expanded more
rapidly than other FFSI uses, then the contribution of this factor would be expected to increase,
and vice versa.
Qffsi/Qdom: This factor is similar to the above one in that it captures changes in the distribution of
domestic corn consumption between FFSI and other domestic uses, namely food and residual
uses. If FFSI expanded faster than food and residual uses, the contribution of this factor to corn
used for ethanol would increase, and vice versa.
Qdom/Qsup: This factor represents the share of domestic consumption in total U.S. corn supply and
is the main measure of corn diversion from export markets for ethanol purposes in this study.
‡
Grains include corn, barley, oats, rye and sorghum (coarse grains), wheat, and milled rice (other
grains).
§
Oilseeds include soybean, cottonseed, peanut, rapeseed, and sunflower seed.
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The contribution of this factor to corn ethanol production would be expected to increase, and
judged to divert exports to domestic markets, under two conditions: (1) if corn exports were
reduced while corn used for ethanol production increased and (2) if corn used for ethanol
production were met by increased supply but exports did not grow at the same rate as supply.
Qsup/Qprd: This factor measures the relative contribution of new production to the total supply of
corn and therefore captures the role of beginning stock and imports (the latter is quite
negligible in the case of the U.S. at less than 0.5 million tons).
Ycorn: This factor represents the contribution of corn yield to corn used for ethanol through the
change in corn production.
Acorn/Acgrn: This factor represents the ratio of corn harvested area to total coarse grains harvested
area and captures the effect of land transfers among coarse grains in corn used for ethanol
through the change in corn production
Acgrn/Agrn: This factor captures the effect of land competition between coarse grains and other
grains in corn used for ethanol through the change in corn production
Agrn/Agrn+oilsd: This factor captures the effect of land competition between grains and oilseeds in
corn used for ethanol through the change in corn production
Aall/Agrn+oilsd: This factor captures the effect of land competition between aggregate grains/oilseeds
area and other crops in corn used for ethanol through the change in corn production
Aall: This factor reflects the role of total cropland harvested in corn used for ethanol through the
change in corn production.
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C. Additional Tables of Decomposition-Analysis Results
Table C.1. Decomposition-Analysis Results of Contributions from Supply and Distribution
Factors to Changes in Corn Used for Ethanol Production: 1981 to 2009 (million tons)
Factor Contributions
Qce/Qffsi
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2001–2009
6
1.14
0.94
0.19
1.15
0.50
0.00
-0.38
-0.05
0.45
0.37
0.56
0.54
0.43
1.12
-2.87
0.30
0.74
0.84
0.52
1.23
1.23
4.48
2.16
2.14
3.26
5.71
8.77
5.60
5.79
39.15
Qffsi/Qdom
0.13
0.19
0.79
0.31
0.39
-0.32
-0.07
1.30
-0.31
-0.07
0.24
-0.61
1.29
-0.88
0.87
-0.52
0.12
0.24
0.00
-0.09
0.52
2.89
0.77
-0.07
2.65
7.67
6.66
11.19
2.21
34.49
Qdom/Qsup
-0.11
-0.11
0.82
-0.22
-1.13
-0.28
0.33
0.89
0.51
0.57
0.73
-0.92
1.62
-1.53
0.80
0.27
-0.02
-1.14
0.31
-0.10
0.57
1.60
-0.10
-2.30
-0.11
2.37
-0.78
2.99
0.01
4.26
Total
Qsup/Qprd
-0.16
0.31
1.31
-2.41
0.30
1.63
0.88
0.73
-3.05
-0.61
0.29
-0.80
2.02
-2.61
1.30
-1.53
0.53
0.45
0.66
-0.22
0.38
-0.38
-1.69
-0.78
3.56
-0.12
-4.90
2.58
-0.66
-2.02
Qprd
0.29
0.04
-2.59
3.00
0.93
-0.54
-1.03
-2.66
3.28
0.44
-0.57
2.48
-4.51
5.79
-3.58
2.32
-0.03
0.74
-0.47
0.76
-0.72
-1.24
3.23
4.97
-2.24
-2.52
13.86
-6.42
8.49
17.41
1.30
1.37
0.51
1.83
0.99
0.48
-0.28
0.21
0.86
0.70
1.25
0.69
0.83
1.89
-3.48
0.84
1.33
1.14
1.02
1.57
1.99
7.36
4.37
3.95
7.12
13.11
23.62
15.94
15.83
93.28
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4
Table C.2. Decomposition-Analysis Results of Yield and Harvested-Area Components of the
Production Contribution to Corn Used for Ethanol Production: 1981 to 2009
Factor Contributions
Total
Ycorn
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2001–2009
5
6
7
0.26
0.11
-1.27
1.35
0.64
0.08
0.03
-2.50
2.45
0.16
-0.83
2.00
-2.99
4.01
-2.34
1.19
-0.04
0.76
-0.07
0.34
0.16
-1.42
2.60
3.79
-2.98
0.37
0.69
1.79
7.14
12.14
Acorn/Acgrn
Acgrn/Agrn
Agrn/Agrn+oilsd
Agrn+oilsd/Aall
-0.04
-0.06
-0.27
0.20
0.08
0.05
0.06
0.40
-0.12
0.44
0.01
0.04
0.17
0.39
0.01
-0.18
0.38
0.24
0.05
0.14
-0.05
0.40
-0.38
1.08
0.75
0.42
-0.09
-1.67
2.91
3.37
-0.05
0.04
-0.05
0.41
0.17
-0.08
-0.22
-0.11
-0.07
-0.44
0.79
-0.18
-0.69
0.63
-0.45
0.45
-0.18
0.20
0.28
0.23
0.20
0.36
-1.02
0.66
-0.05
0.08
2.97
-5.21
3.35
1.32
0.04
-0.02
-0.15
0.19
0.15
-0.01
-0.29
-0.23
0.35
0.11
-0.33
0.32
-0.39
-0.02
-0.45
0.41
-0.40
-0.15
-0.55
0.07
-0.50
0.01
0.87
-0.48
0.10
-1.56
7.43
-3.43
-2.18
0.26
0.04
-0.01
-0.21
0.18
-0.06
-0.19
-0.07
-0.07
0.17
0.06
-0.08
0.33
-0.32
0.24
-0.05
0.05
-0.05
-0.06
-0.23
0.07
-0.37
-0.31
0.40
0.24
-0.27
-0.20
1.05
1.02
-0.31
1.25
Aall
0.04
-0.03
-0.63
0.67
-0.06
-0.39
-0.55
-0.15
0.50
0.11
-0.12
-0.03
-0.30
0.54
-0.31
0.41
0.25
-0.24
0.04
-0.10
-0.16
-0.28
0.76
-0.33
0.20
-1.63
1.82
1.09
-2.41
-0.94
0.29
0.04
-2.59
3.00
0.93
-0.54
-1.03
-2.66
3.28
0.44
-0.57
2.48
-4.51
5.79
-3.58
2.32
-0.03
0.74
-0.47
0.76
-0.72
-1.24
3.23
4.97
-2.24
-2.52
13.86
-6.42
8.49
17.41
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
33%
1981
9%
1980
42%
13% 4% 1989
60
40
million tons
16%
14%
19%
24%
31%
12%
11%
11%
50%
46%
44%
19%
15%
19%
12%
13% 12%
55%
58%
19%
17%
14% 11%
13% 11%
14% 6%
14% 7%
57%
60%
60%
59%
20%
14% 6%
14% 6%
19%
60%
13% 5%
15% 6%
13% 6%
14% 5%
15% 5%
15% 5%
20%
62%
59%
17%
55%
60%
58%
20%
26%
62%
62%
23%
20%
17%
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
54%
13% 4% 1987
14% 4% 1988
14% 5%
54%
13% 4% 1986
61%
29%
62%
20%
28%
63%
14% 4% 1990
22%
59%
20%
12% 3% 1984
14% 4% 1985
59%
63%
26%
19%
10%2% 1982
12%2% 1983
9%0% 1980
9%1% 1981
Net Stock Withdrawal
NetExports
18%
30%
21%
60%
17%
70%
22%
20%
Net Exports
Feed and Residual Use
Other Food,Seed and Industrial Use
Fuel Use
58%
58%
0%
63%
50%
28%
80%
61%
10%
25%
33%
40%
29%
90%
Domestic Consumption
Production
Figure D.2. Supply and Uses of All Grain Crops (Except Corn) in the United States: 1980 to
2009
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9
10
11
12
13
Figure D.1. Percentage Allocation of Corn Supply in the United States to Different Uses:
1980 to 2009
3
4
5
6
7
D. Additional Figures Illustrating the Empirical Data
1
2
100%
140
120
100
80
20
0
-20
-40
120
100
million tons
80
60
40
20
0
1
2
3
4
5
6
Production
Domestic Consumption
NetExports
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
-20
Net Stock Withdrawal
Figure D.3. Supply and Uses of All Oilseed Crops in the United States: 1980 to 2009
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2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
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39
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