Appendices for:
“Efficiency Costs of Increased U.S. Biofuels Mandates”
2/22/2010
(for reference only; not for publication)
Contents
1. Households................................................................................................................................... 3
1.1. Representative Agent ............................................................................................................ 3
Calibration................................................................................................................................ 3
1.2. VMT Decision ...................................................................................................................... 3
Data .......................................................................................................................................... 3
Calibration................................................................................................................................ 4
2. Landowner’s Land Allocation Sub-problem................................................................................ 4
Data .......................................................................................................................................... 4
Calibration.............................................................................................................................. 17
3. Ethanol Production..................................................................................................................... 20
Data ........................................................................................................................................ 20
4. Regular Gasoline Production ..................................................................................................... 25
Data ........................................................................................................................................ 25
Calibration.............................................................................................................................. 25
5. Fuel Blenders ............................................................................................................................. 25
Data ........................................................................................................................................ 25
6. Natural Gas Production .............................................................................................................. 25
Data ........................................................................................................................................ 25
Calibration.............................................................................................................................. 26
7. Food Producers .......................................................................................................................... 26
Data ........................................................................................................................................ 26
Calibration.............................................................................................................................. 26
8. Other Intermediate Sectors ........................................................................................................ 27
8.1. Numeraire Good.................................................................................................................. 27
Data ........................................................................................................................................ 27
Calibration.............................................................................................................................. 27
8.2. Fertilizer .............................................................................................................................. 27
Data ........................................................................................................................................ 27
9. Rest-of-World Import and Export Markets ................................................................................ 27
9.1. Agricultural Products .......................................................................................................... 27
1
Calibration.............................................................................................................................. 27
9.2. Crude Oil............................................................................................................................. 28
Data ........................................................................................................................................ 28
Calibration.............................................................................................................................. 28
10. Government ............................................................................................................................. 28
Data ........................................................................................................................................ 28
11. Baseline Prices ......................................................................................................................... 29
12. Description of Data Sources .................................................................................................... 29
13. Additional Data Tables ............................................................................................................ 32
14. References ................................................................................................................................ 34
2
1. Households
1.1. Representative Agent
Calibration
Elasticities
The elasticity of substitution between miles and non-mile expenditures (𝜎𝑈1 ) from equation 1.1.1
and its nested partner (𝜎𝑈2 ), the elasticity of substitution between food expenditures and the numeraire,
from equation 1.1.3, were jointly specified to validate an own price elasticity of demand for miles of 0.13, and an own price elasticity of demand for food of -0.08.
Estimates of the elasticity of miles with respect to the price of miles (or the negative of the
‘rebound effect’ divided by 100) vary considerably, from zero to -0.90. Disaggregate studies that rely on
cross-sectional and temporal variation tend to suggest consistent long-run estimates of -0.20 to -0.25. De
Jong and Gunn (2001), Graham and Glaister (2002), and Goodwin et al. (2004) each summarize results
across the literature with means for short-run estimates between -0.10 and -0.26 and long-run estimates of
-0.26 and -0.31.
West (2004), using single-year data for 1997, estimate a short-run elasticity of -0.87 on average,
whereas Pickrell and Schimek (1997), using single-year data for 1995 find a value of just -0.04. Using a
multi-year dataset (1984-1990), Goldberg (1998) provides a joint short-run/long-run estimate of -0.20.
Greene et al.(1999) use a multiyear dataset (1979-1994) and find an average estimate of -0.23, with a
range of -0.17 to -0.28.
Using a pooled cross section of U.S. states for 1966-2001, Small and Van Dender (2007) estimate
a short-run VMT elasticity in the range of -0.022 and -0.085. They report a central value of -0.045 when
evaluating at the sample average and -0.022 when evaluating at the 1997-2001 average. Their long-run
estimates fall in the range of -0.11 and -0.34, with a central value of -0.22 when evaluating at the sample
average and -0.11 when evaluating at the 1997-2001 average.
Seale et al. (2003) estimate the own price elasticity for a broad consumption group, “Food,
Beverages and Tobacco” in the range of -0.075 (for the Frisch elasticity) to -0.098 (for the Cournot
elasticity) using data from the International Comparisons Project.
The choice of a CES functional form for the representative agent’s utility function implies an
expenditure elasticity of VMT demand of unity. This is on the high end of empirical estimates as Pickrell
and Schimek (1997) report estimates between 0.35 and 0.8 and Parry and Small (2005) use a central value
of 0.6.
Expenditure Shares
Our estimate for total GDP of $7,667 billion in 2003 represents the sum of compensation to
employees plus the consumption of fixed capital, taken from the Bureau of Economic Analysis’ National
Income and Product Accounts (NIPA) dataset (BEA 2009).
We treat the consumption of fixed capital as the after tax consumption of capital and compute an
implied value of our capital endowment of $2,108.52 billion after re-adding the tax component.
Subtracting the initial value of land ($22.80 billion) and the implied capital endowment from the above
estimate of GDP provides an estimate for the value of the labor endowment in 2003 of $5,490.20 billion.
The share of food expenditures to total consumption expenditure was computed using Table 2.4.5
of the BEA’s NIPA dataset. This share is 0.14. The share of VMT expenditures to total consumption
expenditures is 0.065. This is an adjusted figure that was calculated using total VMT and fuel quantities,
the fuel price, and the ratio of fuel costs per mile of driving to the total cost per mile of driving. The
expenditure share on the numeraire good (0.80) represents all non-food and non-VMT expenditures.
1.2. VMT Decision
Data
Total vehicle miles traveled (VMT) was computed using data from the Federal Highway
Administration’s (FHWA) Highway Statistics Dataset (FHWA 2003). This involved taking the annual
3
total fuel consumption for ‘passenger cars and other two-axle, four-tire vehicles’ (PC24) and dividing by
the average miles traveled per gallon of fuel for PC24 vehicles in 2003. This calculation yielded a
benchmark quantity of 2.66 trillion VMT.
Our initial fuel economy for the calibration year was 20.3 miles per gallon (FHWA 2003). Parry
and Small (2005) report a value of 20 miles per gallon.
Calibration
Blended Fuel Own-Price Demand Elasticity
The elasticity of substitution between fuel and non-fuel expenditures on driving, 𝜎𝑀 from
equation 1.2.2 was selected to validate and own-price elasticity of demand for fuel of -0.47.
Pre-1990 estimates of the long-run elasticity of fuel demand with respect to the price of fuel vary
between -0.50 and -1.10 (Dahl and Sterner (1991), Goodwin (1992), Espey (1996), Espey (1998), Graham
and Glaister (2002)). Later studies, however, find values about half as large. U.S. DOE (1996) propose a
best estimate of -0.38, which is also the 3 stage least squares result that Small and Van Dender (2007)
report when evaluating their data from 1966-2001 at the sample average. In addition, they find that by the
late 1990’s that this value has declined even further, with estimates ranging between -0.31 and -0.34 when
evaluating their model at the 1997-2007 average. The value adopted by Parry and Small (2005) is -0.55.
Ratio of Fuel Cost to Total Cost of Driving
The ratio of fuel costs of to total cost per mile of driving is commonly computed by taking the
ratio of the long-run elasticity of vehicle miles traveled with respect to the price of fuel and the long-run
elasticity of fuel demand with respect to the price of fuel.
Long-run estimates of the elasticity of vehicle miles traveled with respect to the price of fuel fall
between -0.1 to -0.3, but sometimes larger (Goodwin (1992); Greene et al. (1999); and U.S. DOE (1996).
Following Parry and Small (2005), we adopt a ratio of per mile fuel costs to total per mile cost of driving
of 0.40. This value is close to the recommendations of Johansson and Schipper (1997) and U.S. DOE
(1996).
2. Landowner’s Land Allocation Sub-problem
Data
The agricultural dataset consists of input use, cost of production, and baseline acres, average
yields and baseline prices for 5 main commodities (corn, soybeans, hay, wheat and cotton). Where
applicable, four tillage systems (conventional, reduced, mulch, no-till) have been considered. The
Agricultural Resource Management Survey (ARMS) provides the estimates for input use and baseline
acreage data for the years 1996-2005 (ERS 2008a)1 and is the basis for the tillage level cost of production
estimates. The ARMS data was supplemented with data from the USDA’s Commodity Cost and Return
(CCR) dataset (ERS 2009), the Regional Environment and Agricultural Programming Model (REAP)
dataset (R. Johansson, Peters, and House 2007) and a number of academic studies and extension reports.
Baseline yield data was derived from the Agricultural Statistics Database (ASD) (NASS 2009).
The agricultural dataset also includes the baseline acreage and the average rental payment for
land held in the Conservation Reserve Program (CRP). This data was collected from various U.S.
Department of Agriculture reports which are discussed below.
Crops and Tillage Systems Considered
Acreage data for field crops was collected for each crop and tillage combination from the ARMS.
We consider five major U.S. crops: corn, soybeans, hay, wheat and cotton. These crops make up the
majority of U.S. agriculture, both in terms of area and economic value.2 In each year since 1980, these
1
There is a more extensive discussion of the ARMS dataset in the Agricultural Resource Management Survey (ARMS) section.
Our wheat category represents the sum of the three wheat categories reported in the ARMS (spring, winter and durum). In
constructing the input use dataset the weighted average of these three categories was used.
2
4
five crops have made up at least 80% of total principal crops harvested and made up 91% of principal
crops harvested in 2003 (Table 1). In 2003, the value of corn and soybean production was $24.5 billion
and $18.0 billion respectively. In the same year, the value of hay, wheat and cotton production was $12.0
billion, $7.9 billion and $5.5 billion respectively (NASS 2003). Together, these five crops represent
82.7% of the total value of field crop production ($68.06 of $82.3 billion) in 2003 (NASS 2003).
Table 1. Historic Crop Trends (Million Harvested Acres)
Crops Considered
Total
Year
Corn
Soybeans
Hay
Wheat
Cotton
Model
Principal Crops
Share
1980
82.8
67.8
58.9
71.1
13.2
293.8
340.1
86%
1985
82.7
61.6
60.5
64.7
10.2
279.7
330.3
85%
1990
73.1
56.5
61.0
69.1
11.7
271.4
307.8
88%
1995
70.5
61.5
59.8
61.0
16.0
268.8
301.3
89%
2000
78.5
72.4
60.4
53.1
13.1
277.5
308.0
90%
2003
77.5
72.5
63.4
53.1
12.0
278.5
307.4
91%
The ‘Principal Crops’ column is NASS (2003) data and include: corn, sorghum, oats, barley, wheat, rice, rye,
soybeans, flaxseed, peanuts, popcorn, cotton, hay, dry beans, dry peas, potatoes, sweet potatoes, tobacco, sugarcane
and sugarbeets
The ARMS tabulates acres according to the USDA’s standard definitions (Table 2) of five tillage
systems, conventional (CT), reduced (RT), mulch (MT), no-till (NT), ridge tillage along with a ‘tillage
practice not determined’ category. The only modifications we make to the USDA’s classification system
are to combine ridge tillage into mulch tillage and to add any acres with an undetermined tillage practice
into conventional tillage. This aggregation does not bias our dataset as the share of ridge tillage to total
acres in all crops is very small and in most surveys the acreage and input data for the ‘tillage practice not
determined’ category are not reported3. The input data for the ridge tillage and ‘tillage practice not
determined’ categories was ignored due to the number of missing data points. For example, the reported
acres in ridge tillage were added to the mulch tillage category and were assumed to have identical input
data as that reported for mulch tillage. The resulting tillage shares vary substantially by crop and are
reported in Table 3.
Table 2. Tillage Definitions
Tillage Category
Conventional
Residue
Less than 15%
Reduced
15-30%
Mulch
Greater than 30%
No-till
Greater than 30%
Other
Typically involves plowing or other intensive tillage.
Some combination of cultivation and herbicides is
used for weed control.
Weed control is accomplished with some combination
of herbicides and cultivation
The soil is disturbed prior to planting although less
intensive tillage tools are used. Weed control is
accomplished with herbicides and cultivation. This
category also includes land that the USDA classifies as
ridge tillage.
The soil is left undisturbed from harvest to planting
except for nutrient injection. Planting occurs is a
narrow seedbed and weed control is accomplished
primarily with herbicides. Some cultivation may be
used for emergency weed control
3
Corn under ridge tillage makes up at most 3% of total corn acres for the surveyed years, while soybeans under ridge tillage
make up at most 1% of total soybean acres for all surveyed years. For wheat, ridge tillage data is not reported in the ARMS,
either due to lack of observations or poor statistical quality (which is likely due to a lack of observations).
5
Base Acreage
Crops
The ARMS data represents a surveyed quantity of land and does not equal the total area devoted
to a given crop within the U.S. The ARMS acreages are used to compute the share of land in each crop
and tillage system combination relative to the total acreage of land in each crop. These shares are then
multiplied by total acres in a given crop from the NASS (2009). The ARMS data reports ‘Planted Acres’
while the NASS data used is ‘Harvested Acres’. Therefore our baseline matches the total harvested acres
of corn, soybeans, hay, wheat and cotton in 2003, with tillage shares matching the planted acres reported
in ARMS. As the ARMS data does not cover hay production, it is assumed that the tillage shares for hay
are the same as the tillage shares for wheat. The tillage shares for each crop are reported in Table 3.
Table 3. 2003 Crop Acreage (Million Acres) and Tillage Shares
Corn
Soybean
Hay
Wheat
Cotton
Total
77.53
72.48
63.38
53.06
12.00
Convention
31.5%
al
15.4%
39.4%
36.5%
87.9%
Reduced
27.5%
18.2%
26.2%
24.7%
1.8%
Mulch
21.6%
34.4%
20.2%
17.6%
4.6%
No-till
19.4%
32.1%
14.2%
21.2%
5.7%
Conservation Reserve Program
The Conservation Reserve Program (CRP) is the largest environmental program administered by
the USDA. This program pays farmers to address environmental concerns by converting marginal or
highly erodible crop land to native grasses, trees, filter strips or riparian buffers. In exchange for taking
land out of production, the farmers receive a payment that is based on the average rental rate of similar
agricultural land. Typically contracts of approximately 10 years are signed. There are a number of
different CRP programs. The primary programs are discussed below.
In the general sign-up, landowners and operators with eligible lands compete nationally for
acceptance based on an environmental benefits index (EBI) during specified enrollment periods.
Producers may submit offers below soil-specific maximum rental rates to increase their EBI ranking.
In the continuous (Non-CREP) sign-up, landowners and operators with eligible lands may enroll
certain high priority conservation practices, such as filter strips and riparian buffers, at any time during
the year without competition. In addition to annual soil rental payment and cost-share assistance, many
practices are eligible for additional annual and one-time up-front financial incentives.
The Conservation Reserve Enhancement Program (CREP) was initiated by the Federal
Agriculture Improvement and Reform Act of 1996. Under federal-state cooperative conservation efforts,
landowners and operators implement projects designed to address specific environmental objectives
through targeted CRP enrollments. Sign-up is held on a continuous basis, general sign-up practices may
be included, and additional financial incentives are generally provided.
The Farmable Wetland Program (FWP) was initiated by the FY 2001 Agriculture Appropriations
Act. Landowners and operators enroll small non-flood plain wetlands under modified continuous sign-up
provisions.
We assume that only general sign-up and continuous non-CREP CRP land will be available for
conversion to cropland. In 2003, the acres in general sign-up totaled 31.63 million acres, and the acres in
non-CREP continuous signup totaled 1.89 million acres (FSA 2004). Our estimate of total CRP land in
2003 is therefore 33.52 million acres. The acres enrolled in the CREP or FWP were not included as these
acres are unlikely to be converted to cropland. The CREP and FWP target lands with specific
environmental benefits, and have higher rental payments, making this land less likely to be converted.
These assumptions do not bias our baseline, as the CREP and FWP contain very few acres compared to
the general sign-up with only 0.50 and 0.85 million acres respectively.
6
Sources of Input Data
The ARMS is our main source for agricultural production practice data. While the ARMS
collects data on a wide variety of production practices (see Agricultural Resource Management Survey
(ARMS) section below), we focus on a small subset of the categories. Specifically we utilize the
application rates of nitrogen (N), phosphorous (P) and potassium (K) fertilizers, pesticide use and seeding
rates. In the case of fertilizer and pesticides, the application rates (lbs/acre) are multiplied by the percent
of surveyed acres receiving a given treatment. The production practice data from the ARMS has been
supplemented with other sources. Specifically, hay input data is constructed using extension
recommendations and energy use data is constructed based on literature sources.
Hay Input Data
The ARMS does not survey hay producers. Therefore nutrient application rates have been
derived from extension reports and recommendations. The assumptions used to construct the hay data are
summarized in Table 4. For all other values, such as the percent of planted acres with N, P and K applied
and pesticide use, data from continuous wheat is used. The USDA reports that hay is made up of about
37% alfalfa (NASS 2003), and we assume that remaining share is split evenly between legume hays and
grass hays. This split is important because grass hays will require nitrogen, while alfalfa and legume hays
will not. N, P and K application rates are taken from various extensions sources which are listed below.
The extension data is taken to represent average values for hay, regardless of tillage system, and tillage
specific values are constructed so that the variation in application rates across tillage systems match those
of wheat (in terms of deviation from the mean).
The N, P and K application recommendations have been collected from extension sources located
in major hay producing areas, including: North Dakota State, University of Wisconsin, Kansas State
University, South Dakota State University, Pennsylvania State University, Auburn University, and
Louisiana State University. From each source, a central value for each nutrient application rate is
collected and our final application rates are simple averages across the sources. In general, P and K
recommendations are based on soil test levels of P and K, and expected yields. We collected
recommendations assuming an optimal soil test, sometimes referred to as “medium” or “maintenance”
level, for both P and K.4 It is also assumed that expected yields are slightly higher (rounding up to the
nearest ton/acre) than the average yield used in the model for 2003 (Table 10).
Table 4. Hay Input Requirements
Alfalfa
Other Legumes
Grasses
Average
Share
37%
31.5%
31.5%
N
0
0
100
31.5
P
50
50
40
46.85
K
100
80
80
87.4
Other legumes includes clover and vetch
The grasses category includes brome, bermuda, orchard, reed and
canary grasses, as well as fescue and small grains hay.
Energy Use Data
Energy use is a major contributor to agricultural production costs and varies significantly with
tillage intensity. However the potential to derive detailed energy use data from the ARMS is limited.
Therefore, energy use is constructed from literature sources, with five primary energy types considered.
The estimated use of gasoline, natural gas (NG), liquefied petroleum gas (LPG) and electricity varies at
4
More specifically, we have assumed a Bray-I of 11-15 or Olsen of 8-11 for P and a Bray-I of 80-120 for K.
7
the crop level, while estimated diesel use is specified at the tillage level. While this is a simplification, it
is not without justification.5
NG and LPG are primarily used to run crop dryers, electricity is used to run irrigation equipment
and to light, heat and cool barns and houses, while gasoline powers the smaller farm vehicles, cars and
light trucks, and equipment. These operations are independent of tillage choice, but highly dependent on
the choice of crop (Schenpf 2004). The values for gasoline, NG, LPG and electricity represent estimates
from literature that assesses the lifecycle energy use of corn, soybeans and wheat (Table 5).
Table 5. Energy Requirements by Crop (mBTU/acre)
Gasoline
Natural Gas
LPG
Electricity
Corn
0.49
0.26
0.29
0.31
Soybeans
0.15
0.05
0.03
0.10
Wheat
0.12
0.00
0.03
0.05
Hay is assumed to have the same energy requirements as wheat
Source
Farrell et al. (2006)
Hill et al. (2006)
Piringer and Steinberg (2006)
Diesel fuel is used in farm equipment (tractors, combines, balers etc) as well as large trucks used
for the transportation of input factors and final products. The use of large farm equipment is highly
dependent on the choice of tillage practice as this equipment is used to prepare fields, plant and harvest
crops and apply chemicals. For example, a conventional tillage system requires running a moldboard
plow over the entire field. This has higher energy requirement not only because a tractor is driven across
the field, but the increased drag of the plow increases per acre energy use of the tractor. Under a no-till
system the moldboard plow is not used, and other operations (such as a disc or cultivation operations) are
avoided. Therefore the diesel fuel requirements of a no-till system are significantly lower than those of a
conventional tillage operation.
Our diesel use data has been derived from literature that attempts to calculate the full greenhouse
gas consequences of altering tillage practices (West and Marland 2002). These estimates are based on
assumptions for field operations used in specific tillage systems and the energy requirements of each
operation (Table 6). For plowing, disking, planting and cultivation operations, the energy requirements
are based on whether that crop-tillage combination will require a given operation. For example, a typical
field producing conventionally tilled corn would be cultivated, while a field producing no-till corn would
not. Therefore a fixed energy requirement for cultivation is added to the energy requirements of the
conventional system but not the no-till system.
The application of fertilizers and pesticide also requires diesel fuel, but not every acre has
fertilizer or pesticide applied. As a result, for each crop-tillage combination, the diesel energy required to
apply fertilizer (or pesticide) to an acre of land is multiplied by the average number of acres receiving
fertilizer (or pesticide).6
5
Due to a lack of literature sources, the energy requirements for hay are assumed to be the same as wheat and we assume that
energy expenditures for cotton do not vary by tillage system (this is justified below).
6 The ARMS data provides data on the percent of acres receiving N, P and K separately so the maximum percentage reported for
the three nutrients is used.
8
Table 6. Diesel Requirements by Tillage (mBTU/acre)
CT
RT
MT
NT
Operation
mBTU/acre Corn Other
Corn Other
Corn Other
Corn Other
Moldboard Plow
0.43
0.43 0.43
Disk
0.13
0.26 0.26
0.26 0.26
0.26 0.26
Planting
0.10
0.10 0.10
0.10 0.10
0.10 0.10
0.10 0.10
Cultivation
0.06
0.06
0.06
0.06
Harvest Combine
0.19
0.19 0.19
0.19 0.19
0.19 0.19
0.19 0.19
Fertilizer Application
0.22
based on ARMS values
Pesticide Application
0.02
based on ARMS values
Total
1.05 0.99
0.62 0.56
0.62 0.56
0.29 0.29
Data is derived from West and Marland (2002)
Diesel requirements for fertilizer (and pesticide) application are calculated for each crop-tillage combination
using ARMS data for the percent of acres receiving any fertilizer (or pesticide).
Other crops include soybeans, wheat and hay
Disking is counted twice to represent two passes over the field
As conventional tillage was used for nearly 90% of cotton production (Table 3) and because there
are no reliable studies regarding the disaggregated energy use for US cotton production, we do not impose
tillage variability in cotton energy expenditures.7 Instead, the energy expenditure for each cotton tillage
practice is taken to be the average energy expenditure for cotton from the USDA’s Commodity Cost and
Returns (ERS 2009).
Economic Variables
It is assumed that crops are produced with labor, capital, energy and fertilizer using fixed
Leontief technology. To parameterize these production functions, we estimate the units of each factor
required to produce one acre of a given crop in a given tillage. The crop and tillage specific input
requirements are represented by parameters 𝜆𝑘,𝑡,𝐿 , 𝜆𝑘,𝑡,𝐾 , 𝜆𝑘,𝑡,𝑁 and 𝜆𝑘,𝑡,𝐽 in equations 2.3.1-2.3.20. For
each factor, the total number of unites required to produce an acre of crops is calculated by first
estimating total per acre expenditure for each category, and then dividing by the relevant price. Labor,
capital and energy have standard definitions, but the fertilizer category includes a variety of variable
factors of production. The input categories are described below with details on how each is calculated,
and the final dataset is presented in Table 23.
Labor
Expenditure on labor was obtained at the crop level for 2003, from the USDA’s Commodity
Costs and Returns data, and includes wages paid to workers, and the opportunity costs of unpaid workers
(Table 21). While labor expenditure data from the CCR dataset is aggregated to the crop level, there is
likely to be a decrease in labor costs as tillage intensity decreases. As tillage intensity decreases, the
number of passes over the field is reduced, as plowing and cultivation is avoided. With fewer passes over
the field, fewer operator hours are required and thus labor expenditures would be lowered. In the absence
of data on the variation of labor requirements for different tillage practices, labor costs are allowed to vary
across tillage practices with the same relationships as energy. The relationship between energy and labor
costs is clear. As the variation in energy costs is driven totally by the amount of diesel fuel required for
passes over the field, labor costs would be expected to follow the same pattern.
To implement this variation, the percent deviation in energy expenditure from the crop mean is
calculated for each tillage practice, and this percent deviation is imposed on the crop level labor
Nelson et al. (2009) provide estimates for energy use by crop and tillage based on the University of Tennessee’s Agricultural
Budget System, but do not report specific energy types used only aggregate levels. Lifecycle analyses for cotton production have
been conducted but either do not report energy use by type (Matlock et al. 2008) or are not US specific (Yilmaz, Akcaoz, and
Ozkan 2005).
7
9
expenditure data. This procedure was not conducted for cotton as we do not consider energy variation by
tillage system for this crop. To calculate the number of units of labor used per acre, the total expenditure
on labor is divided by the 2003 wage rate of hired farm labor (Table 20).
Capital
Expenditures on capital are taken directly from the CCR data (Table 21) and are the sum of the
interest on operating capital and the capital recovery of machinery and equipment. The CCR data is
reported at the crop level, but capital costs should decrease with reduced tillage intensity. The equipment
requirements for conservation tillage practices are lower because equipment purchases can be avoided
and because the equipment required could be cheaper (a smaller or less powerful tractor). For example,
conventional tillage uses a moldboard plow, but other practices do not. In addition to not purchasing a
moldboard plow, the other tillage practices may be able to use a cheaper tractor because the power
required to pull a moldboard plow are higher than other field operations.
Variation in capital expenditure follows the REAP dataset. For each region/crop combination,
with the necessary observations8, the deviation from no-till for capital costs was calculated. It is evident
that the variation is consistent across regions and crops so a simple rule was used for all crops. Compared
to no-till, capital costs for mulch tillage are 5% higher, reduced tillage are 10% higher and conventional
tillage are 20% higher. Capital expenditures for each tillage practice are calculated as the crop level
capital expenditures, scaled by the expected tillage relationships. This variation was not imposed on the
cotton data. To calculate the units of capital used per acre, the total expenditure on capital is divided by
the real 2003 interest rate on long-run T-bills plus one (Table 20).
Energy
Energy use data for all crops except cotton is constructed at the tillage level (described above in
Table 5 and Table 6) for five energy sources. To calculate total energy expenditures, total energy use for
a given source is multiplied by the relevant 2003 price (Table 22). After estimating total expenditure on
energy for each crop and tillage combination, these estimates are scaled at the crop level so that the
average expenditure at the crop level matches national averages reported in Commodity Cost and Returns
data. To calculate the units of energy used, total expenditure is divided by the 2003 price of natural gas
(Table 20). For cotton, expenditure on energy is the reported value for ‘fuel, lube and electricity’ from
the USDA’s Commodity Cost and Returns.
Fertilizer
The Commodity Cost and Returns data provides an aggregate variable at the crop level that
includes all expenditures on nutrients, soil conditioners and manure. This variable is not ideal for our
purposes as fertilizer expenditures will vary with tillage practices. Therefore a fertilizer variable as has
been constructed using ARMS data and national prices. In our model’s specification, the fertilizer
category includes other variable costs that are not included in the labor, capital or energy categories.
While most of these other categories vary only at the crop level, expenditures on seed and chemicals are
allowed to vary with tillage intensity. To calculate the units of fertilizer used per acre, the total
expenditure on nutrients, seed, chemicals, and other variable inputs is divided by the 2003 price of
anhydrous ammonia (Table 22).
Nutrients
Expenditures on nutrients are calculated using national estimates for crop and tillage system input
use data, from the ARMS, and national price data from the Agricultural Prices Summary (NASS 2006).
For each nutrient, the average application rate is multiplied by the national average price.
8
In the REAP dataset, not every crop/region combination has data for each tillage system. For example there are no observations
in any region for soybeans in a moldboard tillage or no-tillage system.
10
The calculation of U.S. average prices requires some discussion. Fertilizer is sold in a variety of
forms each of which has a different combination of N, P and K with prices reported in material tons.9 The
U.S. average nutrient prices have been calculated using the shares (ERS 2008b), prices (NASS 2006), and
chemical make-up (Mitchell 2008) of the most common fertilizer materials. Calculating the average
prices of nutrient nitrogen and potassium is straight forward (Table 7 and Table 8). For each material
type, the price per pound nutrient is calculated by dividing the price per material ton by the pounds of
nutrient in a ton of material. The national average is a weighted average of these nutrient prices, based on
U.S. consumption of the various materials in 2003. The N fertilizers considered are anhydrous ammonia,
aqua ammonia, ammonium nitrate, ammonium sulfate, nitrogen solutions, sodium nitrate and urea.
Potassium chloride is the only K fertilizer considered.
Table 7. Baseline Nitrogen Nutrient Prices
Anhydrous
Aqua
Ammonium
Ammonium
Nitrogen
Sodium
Ammonia
Ammonia
Nitrate
Sulfate
Solutions
nitrate
2003 Shares
17.6%
1.8%
7.0%
5.2%
43.8%
0.1%
$/material ton
373
130
243
195
161
278
%N
82%
20%
34%
21%
30%
16%
$/lb N
0.23
0.33
0.36
0.46
0.27
0.87
Average $/lb N
0.28
The shares of material used is based on the fertilizers for which price and use data is available
Urea
24.6%
261
45%
0.29
Table 8. Baseline Potassium Nutrient Prices
2003 Shares
$/material ton
%K
Average $/lb K
Potassium Chloride
100%
165
60%
0.14
Isolating the price of phosphorous fertilizer is more complicated as the most used P fertilizer
materials are combined with nitrogen (Table 9). For example, diammonium phosphate (DAP), which
makes up 60% of total phosphorous materials applied in the U.S., contains 18% N and 46% P by weight.
For mixed fertilizers, the prices are lowered by the nutrient value of the nutrients not being isolated.
Continuing the example, the average price of DAP was 250 $/material ton in 2003. Each material ton of
DAP contains 360 lbs of nutrient N, which has a total value of 360lbs*.284 $/lb N = $102. Therefore the
price of nutrient P from DAP is ($250-$102)/(.46*2000) = 0.16 $/lb.
9
A material ton (or lb) refers to a quantity of a fertilizer material, while a nutrient ton (or lb) refers to a quantity of a specific
nutrient (N, P, K). To convert to nutrient tons, the specific makeup of the material fertilizer must be known. For example, a
material ton of anhydrous ammonia, which is 82% N by weight, has only .82 nutrient tons of N.
11
Table 9. Baseline Phosphorous Nutrient Prices
Triple
Diammonium
Monoammonium
superphosphate
phosphate
phosphate
2003 Shares
6.0%
61.0%
33.0%
$/material ton
243
250
266
%N
0%
18%
11%
value of N ($)
0.00
102.24
62.48
%P
44%
46%
48%
$/lb P
0.28
0.16
0.21
Average $/lb P
0.18
The shares of material used is based on the fertilizers for which price and
use data is available
Nitrogen costs based on the 2003 average N price ($/lb)
Seed
Calculating the expenditure on seed is straight forward. For corn and soybeans, expenditure is
calculated using seeding rates from the ARMS and U.S. national seed prices (NASS 2006). The seed
prices used are the weighted U.S. average price of biotech and non-biotech seeds and are reported in
Table 22. There is no seed data in the ARMS for wheat, so total expenditure on seed from the CCR data
is used. As a result, there is no tillage variation for wheat seed expenditure. Seed expenditure for cotton
production is derived from the Commodity Costs and Returns dataset.
Chemicals
The average expenditures on chemicals for each crop match the CCR data (Table 21). As it is
likely that chemicals expenditures change with tillage intensity, tillage variability is incorporated using
pesticide application rate data from the ARMS. It may be possible to disaggregate chemical use into its
various components, down to the chemical used and then calculate chemical expenditures from the
bottom up. The ARMS reports data on pesticide application rates, broken down by chemical (although
the quality and coverage of this data has not been checked) and the USDA Agricultural Price Summaries
(NASS 2006) have U.S. average costs for many chemicals. The benefits from going to this level are
questionable as chemicals are a relatively small share of total expenditure.
Other Inputs
Other variable costs that do not fall in the labor, capital or energy categories are included in the
fertilizer variable. Each of these categories is taken from the Commodity Costs and Returns dataset and
varies only by crop. The categories included are: soil conditioners, manure, custom operations10, repairs,
purchased irrigation water, taxes and insurance and general farm overhead (Table 21).
Yields
Our yield data comes from the NASS Agricultural Statistics Database. From this dataset the
average annual production of corn as grain, corn as silage, soybeans, hay (dry), cotton and all varieties of
wheat (all varieties) was collected. For wheat and hay total US production was divided by total acreage
in each crop. The calculation of corn, soybean and cotton yields requires more discussion.
Since corn harvested for grain or silage, to determine the total corn acreage harvested we added
together the harvested acres for corn as grain and the harvested acres for corn as silage. To determine an
average yield for this new quantity, it is necessary to convert the tons of corn as silage produced into
equivalent bushels of corn grain. We assume a conversion factor of 8.0 bushels corn grain per ton corn
10
Custom operations are farm operations that are performed by a contracted operator. These operations can include any standard
job including plowing, spraying, hauling, fencing etc.
12
silage for this calculation11. To calculate the average yield, the total quantity of corn grain plus corn grain
equivalents is divided by total acreage.
For soybeans and cotton, the 5-year average yield between 2001 and 2005 is used. This
adjustment was made because 2003 yields for soybeans and cotton where well below expected levels.
For example, the reported soybean yield of 33.9 bu/acre was 11% and 24% below reported yield levels in
2002 and 2004 respectively.
Table 10. Average U.S. yields - 2003
Corn
Soybeans
Hay
Wheat
Cotton
141.2
39.3
2.5
44.2
757.2
bushels/acre
bushels/acre
tons/acre
bushels/acre
pounds/acre
CRP Rental Rate
The CRP rental rate is 46.35 $/acre. This value is calculated as the weighted average annual
rental payment to CRP in 2003 (FSA 2004). The average payment to general sign-up and non-CREP
continuous sign-up CRP were 43.70 $/acre and 90.57 $/acre respectively, with general sign-up making up
94% of total CRP land. These payments include the annual soil rental payments, maintenance allowances
and annual incentive payments.
Crop Prices
The US average prices from the USDA (NASS 2006) serve as our benchmark crop prices (𝑝𝑘 in
equation 2.1.1). For cotton, the price represents the average price between 2001 and 2005. For each
other crop, the price represents the reported value for 2003. These prices are reported in Table 11.
Table 11. 2003 Crop Prices
Corn
Soybeans
Hay
Wheat
Cotton
2.42
7.34
85.50
3.23
0.47
$/bushel
$/bushel
$/ton
$/bushel
$/pound
Farm Support Program Payments
Farm policy changed during the years under consideration. Between 2003 and 2008 the
legislation that determined government payments to the agricultural sector was the 2002 Farm Bill. For
the years 2008 to 2012, this payment regime was superseded by the 2008 Farm Bill. As such our
calculations of average government payments per unit yield are different under the various policy regime
and we assume that the 2008 Farm Bill covers the years between 2013 and 2015. The calculations and
data sources used to calculate the average government payments are described here.
In summary reports of the Commodity Credit Corporation (CCC), the FSA (2009) provides total
gross government payments by crop, as well as total government payments by program type. However
this source does not provide total government payments by crop and program. This data will be referred
to as ‘CCC net’ from here forward. Unfortunately reconciling the CCC net data with the formulas found
within the FSA Handbook 1-DCP - Direct and Counter-Cyclical Program is not possible. Instead, this
data set serves as a comparison point for our calculations. The FSA does provide several tables with
payments broken down by program type, crop and year for the most significant, in terms of net payments,
government support programs administered by the CCC. The programs that are most relevant for the
11
This value assumes corn silage at 60% moisture and assumes that the acreage of corn planted for silage would otherwise have
produced 100 bushels (a mid-range) per acre corn grain (Lauer 2005).
13
years 2003-2008 are: the CCC Direct Payments, the CCC Counter-Cyclical Payments, the CCC
Marketing Loan Write-Offs and the CCC Loan Deficiency Payments. These four programs will be
referred to as the ‘Major Programs’ from here forward. Table 12 provides a comparison of the
government payments from these four programs to the total payments from the CCC net data.
Table 12. Government Support Payments to Agriculture 2003-2008 (Billion $)
Corn, ‘CCC net’
Corn, ‘Major Programs’
% Difference
Soybeans, ‘CCC net’
Soybeans, ‘Major Programs’
% Difference
Wheat, ‘CCC net’
Wheat, ‘Major Programs’
% Difference
Cotton, ‘CCC net’
Cotton, ‘Major Programs’
% Difference
2003
$1.42
$1.43
1.11%
$0.91
$0.90
-0.22%
$1.12
$0.85
-23.85%
$2.89
$1.95
-32.39%
2004
$2.50
$2.59
3.31%
$0.60
$0.61
1.92%
$1.17
$1.18
0.75%
$1.37
$0.87
-36.42%
2005
$6.24
$6.10
-2.22%
$1.14
$0.89
-22.03%
$1.23
$1.19
-3.68%
$4.25
$2.42
-42.92%
2006
$8.80
$8.73
-0.84%
$0.59
$0.60
1.17%
$1.08
$1.09
1.18%
$3.98
$2.24
-43.72%
2007
$3.20
$3.22
0.84%
$0.34
$0.49
46.50%
$0.73
$0.85
16.66%
$2.59
$1.85
-28.71%
2008
$1.86
$1.95
5.08%
$0.45
$0.55
22.45%
$0.87
$1.03
18.74%
$1.60
$0.84
-47.58%
Trends in the Major Government Support Programs
For corn, the four major government support programs provide the bulk of total government
support to corn, and the percent difference between the two totals is no more than 5% for a given year.
For soybeans and wheat the story is less clear. However, the major programs match soybean total
payments well in 2003, 2004 and 2006, and wheat totals match well for the years 2003, 2007, and 2008.
The major programs account for a much smaller share of the government support for cotton. For cotton,
the major programs account for at best 71% (2003) and at worst only 52% (2008) of total government
support.12
Table 13 summarizes government support payments to agriculture by major program between
2003 and 2008. Between 2003 and 2008, direct payments to corn producers provided the largest share of
total support, in all years except 2005 and 2006. Between 2004 and 2007, countercyclical payments for
corn production were positive and these payments were particularly large in 2006 and 2007. Marketing
loan write-offs were positive in all years except 2008, but are small relative to the total amount of
government support provided to corn. Loan deficiency payments were especially significant in 2005 and
2008, making up more than 45% of total government support to corn producers in these years.
With the exception of the year 2005, direct payments accounted for the bulk (greater than 90%)
of total government support for soybeans. Counter-cyclical payments for soybeans were positive only in
2005, making up 28% of government support. Also in 2005, loan deficiency payments to soybean
producers accounted for 28% of total government support. In the other years, these two programs
contributed less than 10% of total support for soybean production. Marketing loan write-offs for
soybeans were positive between 2005 and 2007 but were insignificant overall.
Wheat support follows a similar pattern to soybean support, with direct payments making up at
least 85% of government payments to wheat. Likewise, wheat countercyclical payments were virtually
zero for all years between 2003 and 2008, but more significant in 2005 than the other years. Marketing
loan write-offs and loan deficiency payments were insignificant for wheat.
12
Attempts to find an explanation as to the missing government support program proved unsuccessful. One explanation would
be that if severe weather affected cotton production in unusual ways, disaster relief may be a large contributor to cotton support.
We have ruled out this explanation as cotton abandonment exceeded 10% of planted acres only for the years 2003 and 2008.
14
Unlike the other three crops, direct payments to cotton producers were not the largest source of
government support to cotton producers. These payments made roughly 25% of total support for each
year except 2004 and 2008. Counter cyclical payments for cotton producers were in general large than
the direct payments. With the exception of 2004 and 2008 countercyclical payments made up around
65% of government payments to cotton. As with the other crops marketing loan write-offs and loan
deficiency payments were insignificant relative to direct and countercyclical payments for cotton.
Table 13. Government Support Payments to Agriculture by Major Program, 2003-2008 (Billion $)
Corn Total
Direct Payments
Counter-Cyclical Payments
Marketing Loan Write-Offs
Loan Deficiency Payments
Soybeans Total
Direct Payments
Counter-Cyclical Payments
Marketing Loan Write-Offs
Loan Deficiency Payments
Wheat Total
Direct Payments
Counter-Cyclical Payments
Marketing Loan Write-Offs
Loan Deficiency Payments
Cotton Total
Direct Payments
Counter-Cyclical Payments
Marketing Loan Write-Offs
Loan Deficiency Payments
2003
1.43
1.41
0.00
0.01
0.01
0.90
0.89
0.00
0.00
0.02
0.85
0.8
0.0
0.0
0.1
1.95
0.5
1.3
0.0
0.2
2004
2.59
2.12
0.34
0.03
0.11
0.61
0.60
0.00
0.00
0.00
1.18
1.1
0.0
0.0
0.0
0.87
0.6
0.2
0.0
0.0
2005
6.10
2.10
0.91
0.23
2.87
1.04
0.60
0.00
0.01
0.29
1.33
1.1
0.1
0.0
0.0
2.42
0.6
1.4
0.0
0.4
2006
8.73
1.99
2.51
0.18
4.04
0.45
0.56
0.00
0.01
0.02
0.96
1.1
-0.1
0.0
0.0
2.24
0.6
1.4
0.0
0.3
2007
3.22
1.59
1.63
0.00
0.00
0.49
0.45
0.00
0.00
0.05
0.85
0.9
0.0
0.0
0.0
1.85
0.5
1.3
0.0
0.1
2008
1.95
1.95
0.00
0.00
0.00
0.55
0.55
0.00
0.00
0.00
1.03
1.0
0.0
0.0
0.0
0.84
0.6
0.3
0.0
0.0
Calculation of Government Support Payments to Agriculture
Given the above discussion it is clear that simply taking an average of total government payments
for a particular crop across several years is inadequate to capture the high variability in government
payments, especially for corn and cotton. As such, in what follows we model government support for
each crop across two broad categories: non-price adjusting support payments, and price adjusting support
payments.
Non-price support payments include direct payments. Direct payments remain relatively fixed
within the particular policy regime (the 2002 and 2008 Farm Bill), although the payment per unit of
(actual) yield of crop k actually harvested in a given year will vary within the simulation as direct
payments are pegged to base acres, and since the yields used to calculate direct payments differ from
actual yields.
Price adjusting support payments include: counter-cyclical payments, write-off gains from
marketing loans, and loan deficiency payments. Effectively for crop prices above a certain threshold,
these values will be zero and below that threshold these payments will be positive.
Non-Price Support Payments
Here we consider only direct payments (DP). These are a quantity decoupled payment, which
means that payments are made relative to some base acreage and yields pre-specified by legislation, not
relative to the actual acreage planted and yields in a given year.
In general we have:
𝐷𝑃_𝑦𝑖𝑒𝑙𝑑𝑘
𝐸𝑥𝑝_𝐷𝑃𝑘 = (𝐷𝑃_𝑟𝑎𝑡𝑒𝑘 ) (
) (𝜑𝑘 )
𝑌𝑖𝑒𝑙𝑑𝑘
15
where 𝐸𝑥𝑝_𝐷𝑃𝑘 is expected non-price support payment per unit yield received by crop 𝑘, 𝐷𝑃_𝑟𝑎𝑡𝑒𝑘 is the
direct payment rate per unit yield received by crop 𝑘, 𝐷𝑃_𝑦𝑖𝑒𝑙𝑑𝑘 is the direct payment yield for crop k,
𝑌𝑖𝑒𝑙𝑑𝑘 is the actual yield for crop 𝑘 in a given year, and 𝜑𝑘 is given as:
(𝐵𝐴𝑦𝑘 ∗ 𝐵𝐴_𝑠ℎ𝑎𝑟𝑒𝑦 )
,
𝜑𝑘 = {
𝐸{𝐴𝑘 }
1,
𝐸{𝐴𝑘 } ≤ (𝐵𝐴𝑦𝑘 ∗ 𝐵𝐴_𝑠ℎ𝑎𝑟𝑒𝑦 )
𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
where 𝐵𝐴𝑦𝑘 are base acres determined by the 2002 and 2008 Farm Bills, 𝐵𝐴_𝑠ℎ𝑎𝑟𝑒𝑦 is the share of base
acres receiving government support for a given Farm Bill 𝑦, 𝐸{𝐴𝑘 } is the acreage expected to be planted
to crop 𝑘. For the years between 2003 and 2008, 𝐵𝐴_𝑠ℎ𝑎𝑟𝑒𝑦 is set to 0.85 and 𝐵𝐴𝑦𝑘 are the base acres
set by the 2002 Farm Bill, while in all subsequent years 𝐵𝐴_𝑠ℎ𝑎𝑟𝑒𝑦 is set to 0.83 while 𝐵𝐴𝑦𝑘 remains the
base acres set by the 2002 Farm Bill.
For these calculations the values for 𝐷𝑃_𝑟𝑎𝑡𝑒𝑘 and 𝐷𝑃_𝑦𝑖𝑒𝑙𝑑𝑘 were collected from the FSA’s
website (2008), and 𝐵𝐴𝑦𝑘 is an aggregation of county level base acres from the same source (Table 14).
Price Support Payments
There are two main price support payments to agriculture. The first are counter-cyclical
payments. Like direct payments described above, these are also quantity decoupled to the same base
acreage used to determine direct payments. The second are loan deficiency payments and marketing loan
write-off gains. These are not quantity decoupled.
Countercyclical payment (CCP) rates are calculated as:
𝑞 𝑇 − [max{𝑞𝑘𝐿𝑅 , 𝑞𝑘 } + 𝐷𝑃_𝑟𝑎𝑡𝑒𝑘 ],
𝐶𝐶𝑃_𝑟𝑎𝑡𝑒𝑘 = { 𝑘
0,
𝑞𝑘𝐿𝑅 < [max{𝑞𝑘𝐿𝑅 , 𝑞𝑘 } + 𝐷𝑃_𝑟𝑎𝑡𝑒𝑘 ]
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
where 𝑞𝑘𝑇 is the CCP target price, 𝑞𝑘 is the market year average price (which is the same price that our
model reports), 𝑞𝑘𝐿𝑅 is the national loan rate.
To calculate the expected countercyclical payment per unit yield of crop 𝑘 (𝐸𝑥𝑝_𝐶𝐶𝑃𝑘 ) we have:
𝐶𝐶𝑃_𝑦𝑖𝑒𝑙𝑑𝑘
𝐸𝑥𝑝_𝐶𝐶𝑃𝑘 = (𝐶𝐶𝑃_𝑟𝑎𝑡𝑒𝑘 ) (
) 𝜑𝑘
𝑌𝑖𝑒𝑙𝑑𝑘
where 𝐶𝐶𝑃_𝑟𝑎𝑡𝑒𝑘 is the CCP rate per unit yield received by crop 𝑘, 𝐶𝐶𝑃_𝑦𝑖𝑒𝑙𝑑𝑘 is the CCP yield for
crop.13 The values for 𝑞𝑘𝐿𝑅 , 𝐶𝐶𝑃_𝑟𝑎𝑡𝑒𝑘 and 𝐶𝐶𝑃_𝑦𝑖𝑒𝑙𝑑𝑘 are taken from the FSA’s website (FSA 2008).
Marketing loan write-off gains are gains resulting from CCC marketing loans. A producer is
eligible to make these write-off gains if their repayment rate for a given marketing loan falls below a CCC
determined loan rate. Loan deficiency payments (LDP) are payments made to producers who, although
eligible to obtain a CCC marketing loan, agree to forgo the loan in return for a payment on the eligible
commodity. Effectively, with the LDP program, a producer is able to claim the marketing loan write-off
gain despite never having taken out a marketing loan in the first place. Since these programs are very
similar, we model them similarly and when refer to the combination of these programs as LDPs. The
expected loan deficiency payment per unit yield of crop 𝑘 (𝑒𝑥𝑝_𝐿𝐷𝑃𝑘 ) is given as:
13
In all years, 𝐶𝐶𝑃_𝑦𝑖𝑒𝑙𝑑𝑘 and 𝐷𝑃_𝑦𝑖𝑒𝑙𝑑𝑘 are less than actual and projected yields, 𝑌𝑖𝑒𝑙𝑑𝑘 . As a consequence, for the
calculations for DP and CCP above, the yield ratios in both are less than one, and thus to simplify the exposition we do not
include a similar 𝜑𝑘 on the yield ratio when we model this yield decoupling.
16
𝐸𝑥𝑝_𝐿𝐷𝑃𝑘 = {
𝐿𝑜𝑎𝑛_𝑅𝑎𝑡𝑒𝑘 − 𝑞𝑘 ,
0,
𝐿𝑜𝑎𝑛_𝑅𝑎𝑡𝑒𝑘 > 𝑞𝑘
𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
where 𝐿𝑜𝑎𝑛_𝑅𝑎𝑡𝑒𝑘 are the CCC’s published loan rates (Table 14) and 𝑞𝑘 are prices of the given crops.
Finally, the average government payment per unit yield for crop 𝑘, 𝐺𝑃𝑘 , is:
𝐺𝑃𝑘 = 𝐸𝑥𝑝_𝐷𝑃𝑘 + 𝐸𝑥𝑝_𝐶𝐶𝑃𝑘 + 𝐸𝑥𝑝_𝐿𝐷𝑃𝑘 .
The parameter 𝑠𝑘 in equation 2.1.1, is calculated by multiplying 𝐺𝑃𝑘 by reported yields. The government
payment rates, yields, target prices and base acres for 2003 are presented in Table 14. The sources for
this data are described in the text above.
Table 14. Government Support Programs Data 2003
Unit Yield
Direct Payment Rate ($/unit)
Direct Payment Yields (units/acre)
Countercyclical Target Price ($/unit)
Countercyclical Payment Yields (units/acre)
Loan Deficiency Rates ($/unit)
2002 Farm Bill Base Acres (million)
Corn
bushels
0.28
102.30
2.60
114.30
1.98
87.75
Soybeans
bushels
0.44
30.80
5.80
34.10
5.00
53.45
Wheat
bushels
0.52
34.50
3.86
36.10
2.80
76.13
Cotton
pounds
0.07
604.30
0.72
638.90
0.52
18.86
Calibration
Crop Supply Elasticities
We calibrate the parameters 𝛿𝑘 , 𝜎𝑘 , 𝜎𝑘𝑝 in equations 2.1.1 and 2.1.3-2.1.23 such that our ownprice elasticity of corn acreage supply is 0.4, and so the cross price acreage elasticities with respect to the
price of corn for the other crops match the values in Table 15. The calibration procedure that utilizes
these target elasticities is discussed below.
Table 15. Target Crop Acreage Supply Elasticities for Calibration
Corn
Soybeans
Hay
Wheat
Cotton
CRP
Elasticity
0.4
-0.2
-0.04
-0.1
-0.2
-0.06
Type
Own Price
Corn Price
Corn Price
Corn Price
Corn Price
Corn Price
Gardner (2007) reports a corn supply elasticity of 0.23, while DeGorter and Just (2009) use a
value for the corn supply elasticity of 0.40. Lin et al. (2000) report several estimates of acreage response.
They report weighted national averages of own and cross price elasticities for corn covering the years
1991-1995 and calculate an own-price elasticity of corn of 0.29. They also report a cross-price elasticity
of soybeans with respect to the price of corn of -0.23 and a cross price elasticity of wheat with respect to
the price of corn of -0.046. Also discussed are elasticity projections following the 1996 Farm Bill using
the POLYSYS model. Again, the own-price elasticity of corn supply is 0.29. However, the cross-price
elasticity of soybeans with respect to the price of corn decreases to -0.15 and the cross-price elasticity of
wheat with respect to the price of corn increases to -0.065.
17
Our implied wheat acreage elasticity may be higher than the estimate suggested by Lin et al.
(2000). This is at least partly results from the spatial aggregation of our agricultural production dataset.
Lin et al. (2000) use a regional model to generate their estimates, whereas we consider a model that
collapses these regions. Since wheat is produced predominately in regions that are not large producers of
corn and soybeans, their elasticity estimates are smaller than ours. In effect, by aggregating across
regions, we may smooth the response to a level greater than what is reported in Lin et al (2000).
CRP Cross-Price Elasticity
The agricultural parameters are chosen so that the cross-price elasticity of CRP with respect to
corn is -0.03 (discussed below). Featherstone and Goodwin (1993) use a 2 stage least squares Tobit
model to estimate conservation investment as a function various attributes. One attribute, crop efficiency,
is defined in the paper as: value of crop production/total variable costs. They find an elasticity of
conservation investment with respect to crop efficiency of -0.95 for a total change and elasticity of -0.13
for a ‘change above the limit’. Since the share of CRP investment relative to the USDA’s total
investment in conservation is 41.2% (Claassen 2006), these elasticity values become -0.39 and -0.055
respectively. We believe that the CRP cross-price elasticity might be lower than -0.06.
Parameter Search
We calibrate the response of the agricultural sector for a given year y by searching for a vector of
parameters, denoted 𝛿𝑦 = [𝛿𝑘,𝑦 , 𝛿𝐶𝑅𝑃,𝑦 ] which are in equation 2.1.1, such that the implied elasticities
resulting from a full model equilibrium, for year 𝑦, match those in Table 15. We assume these elasticities
to be the same for each year. Note that for each year, 𝑦, we are searching for a vector, 𝛿𝑦 , unique to that
year.
Specifically, we attempt to minimize the loss function:
𝐽
2
𝑓(𝛿𝑦 ) = ∑(𝜀𝑗 (𝛿𝑦 ) − ε̅𝑗 )
𝑗=1
where 𝑦 ∈ 𝑌 = {2009, … , 2015} and 𝐽={corn, soybeans, hay, wheat, cotton, CRP}, where 𝜀𝑗 (𝛿𝑦 ) is the
estimated acreage elasticity of crop/land-use j with respect to the price of corn implied by the model for a
price shock in year 𝑦 (the difference between the benchmark and policy equilibrium prices) conditional
on the parameter vector 𝛿𝑦 , and 𝜀̅𝑗 are the literature estimates of acreage elasticity of crop/land-use 𝑗 with
respect to the price of corn (Table 15).
One should note that 𝜀𝑗 (𝛿𝑦 ) is estimated by computing the general equilibrium model through
year 𝑦, starting with the year 2009. We search for the optimal 𝛿𝑦 That is, we search for 𝛿𝑦 such that the
loss function in 2009 is minimized, and then iterate forward over the set Y, storing the optimal vectors for
each year. It should also be noted that despite the storing of the prior year optimal parameters, each year
is independent in that 𝜀𝑗 (𝛿𝑦 ) only depends upon benchmark data and dynamical assumptions for the
current year.
Algorithms Used
We use three methods for this search: a scaling descent algorithm, the Dividing Rectangles
(DIRECT) algorithm (D. R. Jones, Perttunen, and Stuckman 1993) and a simple descent approach. Each
of these methods is discussed below. The algorithm that converged most rapidly, with the fewest
anomalies was the scaling descent algorithm.
Scaling Descent
The logic of the scaling descent algorithm is straight forward: first perturb the starting parameter
using scaling perturbations (reducing the size of the perturbation if no or little improvement is made) until
no further improvement can be made in minimizing the loss function. A sketch of this procedure is
18
described in Table 16. Note that 𝑓(𝛿𝑦 ) is the loss function evaluated at 𝛿𝑦 and 𝛿̅ is a starting vector of
parameters.
Table 16. Framework of Scaling Descent Algorithm
Initialize
Set: 𝛿 = [𝛿2009 = 𝛿̅, … , 𝛿2015 = 𝛿̅] and 𝑅 ∈ (0,1)
For y = 2009 to 2015
Set: 𝑓0 = 1 × 109 and 𝑇 = 1
Until: (𝑓𝑇 − 𝑓𝑇−1 )
Create local search grid: 𝛿𝑦𝐿𝑜𝑐𝑎𝑙 = [𝛿𝑦,𝑗,𝑙+ , 𝛿𝑦,𝑗,𝑙− , ∀ 𝑗], where
𝛿𝑦,𝑗,𝑙+ = [(1 + 𝑅)𝛿𝑦,𝑗 , 𝛿𝑦,~𝑗 ] and 𝛿𝑦,𝑗,𝑙− = [(1 − 𝑅)𝛿𝑦,𝑗 , 𝛿𝑦,~𝑗 ]
For: each 𝛿𝑦,𝑗,𝑙 ∈ 𝛿𝑦𝐿𝑜𝑐𝑎𝑙
Compute: 𝑓𝑗,𝑙 = 𝑓(𝛿𝑦,𝑗,𝑙 )
End for
Declare local winner: 𝛿̂𝑦 = arg min{𝑓𝑗,𝑙 }
𝑗,𝑙
Set: 𝑓𝑇 = min{𝑓𝑗,𝑙 }
𝑗,𝑙
If: 𝑓𝑇 ≥ 𝑓𝑇−1
Keep 𝛿𝑦 ; Discard 𝛿̂𝑦
End Until
Else if: 𝑓𝑇 < 𝑓𝑇−1
Discard 𝛿𝑦 ; Set 𝛿𝑦 = 𝛿̅
End if
T=T+1
End Until
Replace: 𝛿𝑦 ∈ 𝛿 with new 𝛿𝑦
End for
DIRECT
The DIRECT algorithm attempts to find a global optimum of a multivariate function using a
systematic adaptive search of the solution space. We use a version coded in Matlab by Kuminoff and
Fackler (Kuminoff 2004). DIRECT was selected because it is well suited for bound constrained problems
with complicated objective functions, and because the derivatives of the objective function do not need to
be provided.
The DIRECT algorithm first evaluates the objective function at the center of the domain (the user
provided bounds of the parameter values) and trisects the longest coordinate direction of the potentially
optimal hyperrectangle. The loss function is then evaluated at the center of each of the newly created
hyperrectangles, and it is determined if these new observations are potentially optimal. The algorithm
then trisects another area of the solution space based on whether the space contains a potentially optimal
solution, and the size of the space (larger spaces are more likely to be trisected than small spaces, as this
signifies that the algorithm has not searched this space frequently). The user is able to specify how the
algorithm weights the importance of these two criteria. Due to the nature of the trisection procedure, as
the algorithm iterates, the hyperrectangles that are potentially optimal (have low function values) are
sampled more frequently.
To determine whether a rectangle is potentially optimal, DIRECT uses the following definition
(D. R. Jones, Perttunen, and Stuckman 1993). For a given interval [𝑙, 𝑢], with subdivided intervals
19
[𝑎𝑖 , 𝑏𝑖 ] and midpoints 𝑐𝑖 , for 𝑖 = 1 … 𝑚. For a given 𝜀 > 0, and 𝑓𝑚𝑖𝑛 the current best loss function value.
̃ > 0 such that:
Interval 𝑗 is potentially optimal if there exists some rate-change-constant 𝐾
̃ [(𝑏𝑗 − 𝑎𝑗 )/2] ≤ 𝑓(𝑐𝑖 ) − 𝐾
̃ [(𝑏𝑖 − 𝑎𝑖 )/2], ∀ 𝑖 = 1, … , 𝑚
𝑓(𝑐𝑗 ) − 𝐾
̃ [(𝑏𝑗 − 𝑎𝑗 )/2] ≤ 𝑓𝑚𝑖𝑛 − 𝜀|𝑓𝑚𝑖𝑛 |.
𝑓(𝑐𝑗 ) − 𝐾
Steps in the DIRECT Algorithm (adapted from Jones, Perttunen and Stuckman (1993))
(1) Evaluate the loss function at the center point of the given bounds
(2) Identify the set (𝑆) of potentially optimal hyperrectangles
(3) Select any potentially optimal hyperrectangle, 𝑠𝑖 , from 𝑆
(5) Subdivide 𝑠𝑖 and evaluate objective function at the center of each of the newly created
hyperrectangles (note it is in this step that the user is able to specify the importance of the
hyperrectangle size versus the function value).
(6) Remove 𝑠𝑖 from 𝑆 and select another hyperrectangle from 𝑆
(7) Identify a new set of potentially optimal hyperrectangles 𝑆 and go back to step 3.
Descent Algorithm
The simple descent algorithm operates by evaluating the loss function for a positive and negative
perturbation of each parameter around a central value. The perturbation that resulted in the lowest loss
function value (relative to the other perturbations) is then taken as the central value, and the process
iterates. The steps in the descent algorithm are given below, where 𝐸 is the value of an evaluation of the
̅ is the parameter vector with
loss function 𝑓, 𝛿̅ is the central parameter vector of length 𝐽, and 𝛿𝑗𝑑
parameter 𝑗 perturbed in direction 𝑑.
Steps in the descent algorithm
(1) The loss function is evaluated at a central (or starting) parameter vector: 𝐸̅ = 𝑓(𝛿̅)
(2) The loss function is then evaluated for each perturbation of the starting parameter vector:
𝐸̃𝑗𝑑 = 𝑓(𝛿̃𝑗𝑑 ) for every 𝑗 ∈ 𝐽 and 𝑑 ∈ 𝐷
(3) The perturbed parameter vector that results in the lowest loss function evaluation is found:
𝛿̂ = 𝛿𝑗𝑑 such that 𝑓(𝛿̂ ) = min (𝑓(𝛿̃𝑗𝑑 )).
(4) The process repeats with the minimum value perturbed parameter vector taken as the new
central parameter vector (𝛿̅ = 𝛿̂ ).
Tillage Elasticities of Substitution
We have been unable to find an estimate of tillage system supply response in the literature. This
response is captured by the elasticity of substitution across tillage systems for each crop, 𝜎𝑘 , in equations
2.2.1-2.2.5. The REAP model (Johansson, Peters, and House 2007) uses values of 10.0 for these
elasticities, and we adopt this practice as well.
3. Ethanol Production
Data
The benchmark quantity of ethanol, 𝐸, is 2.75 billion gallons. This value is the total ethanol used
by passenger vehicles as reported in the Highway Statistics Dataset (FHWA 2003). This value is
estimated from Internal Revenue Service data on gasohol tax collections, refunds and credits.
Ethanol production is specified with Leontief (fixed proportions) technology. The parameters
used in the production function represent the national average corn, energy, labor and capital
requirements per gallon of ethanol produced. The ethanol production process also produces a number of
20
other saleable outputs, or co-products. The production of these co-products is also specified using fixed
proportions technology, such that for each gallon of ethanol produced, fixed quantities of co-products are
also produced.
Most ethanol plants in the U.S. are grouped according to production technology (wet or dry
milling) and primary fuel source (natural gas or coal). Wet milling and dry milling are inherently
different technologies, produce different co-products and have different corn and energy requirements.
The choice of primary fuel is considered for an accurate assessment of greenhouse gas emissions. To
generate national level parameters for ethanol production, data for the four distinct combinations of
ethanol production technology and primary fuel are aggregated according to the observed share of each
category.
Ethanol Production Technologies
Wet and dry mills are the two main processes for producing ethanol from corn, but there are
significant differences in the input requirements and output between these technologies. Therefore it is
necessary to deal with these processes separately. Dry-milling differs from wet milling in that the wet
milling process separates the corn starch from the other parts of the corn kernel before the fermentation
process. Once the starch has been separated, it is possible to create a number of products, such as ethanol,
corn syrup or corn starch. The dry milling process does not separate the corn starch from the rest of the
kernel and can produce only ethanol and certain co-products. Although the wet milling process can
produce a number of outputs, the plants are larger, more expensive to construct and less efficient (in terms
of energy and conversion of corn to ethanol).
In the dry-milling process, the corn kernel is ground into meal and mixed with water to form a
slurry. To this slurry, enzymes are added that convert the corn starch to dextrose, a simple sugar. Yeast
is added and the slurry is allowed to ferment, converting the sugars into ethanol and CO2. After
fermentation, the ethanol is distilled from the slurry and then dehydrated to pure alcohol. The remaining
slurry is centrifuged and dehydrated to create distillers’ grains with solubles (DGS).
In the wet-milling process, the corn kernels are soaked in water and acid for 1 to 2 days. The
corn is then sent through grinders that separate the corn starch from the germ, fiber, and gluten portions of
the kernel. Since the starch has been isolated, it can be processed into ethanol or corn syrup, or sold as
corn starch. Once the starch has been separated, the ethanol fermentation process is nearly identical to
that of the dry-mill process. Co-products are created from the remaining portions of the corn kernel.
Corn oil is extracted from the germ, the gluten can be dried and sold as corn gluten meal, and the liquid
from the soaking process can be concentrated into corn gluten feed14.
Primary Fuel
We consider only natural gas and coal fueled ethanol plants15. Natural gas is the primary energy
source for the majority of ethanol plants currently in operation. According to the USDA's Shapouri and
Gallagher (2005), none of the dry-mill plants surveyed used coal as an energy input, although the survey
covered only a fraction of total dry mill ethanol plants. It is thought that local air pollution laws have
prevented plants from using coal (Wang, Saricks, and Sanfini 1999). A more recent survey conducted by
the Renewable Fuels Association (RFA) and analyzed by Argonne National Labs, shows that about 13%
of U.S. dry mill ethanol is produced using coal (Wu 2008).
Technology and Primary Fuel Share Assumptions
Our assumptions on the technological make-up of the U.S. ethanol sector follow those in GREET
1.8b (Wang 2008). These assumptions reflect the known make-up of the ethanol sector. In the baseline
we assume that dry mills fired by natural gas and coal account for 57% and 18% of total ethanol
The description of the ethanol production processes are from the Renewable Fuels Association’s website (www.ethanolrfa.org)
Additional fuels are used but uncommon; waste coal and biomass are examples. Combined heat and power technology could
be exploited to reduce electricity costs to ethanol plants.
14
15
21
production respectively. Wet mills fired by natural gas account for 15% of total production and wet mills
fired by coal make up the remaining 10%.
Parameter Assumptions
Dry mills and wet mills convert corn to ethanol at different rates. We assume that to produce a
gallon of ethanol, dry mills require 0.38 bushels of corn and that a wet mill requires 0.39 bushels of corn.
These values are derived from GREET 1.8b and are well within the reported range. For example
Shapouri and Gallagher (2005) find a corn-to-ethanol conversion efficiency of dry mill ethanol plants of
0.375 bushels per gallon. In 2003, 𝜆𝐸,𝑘=1 from equation 3.1.1 is 0.38 bushels per gallon (the average
conversion efficiency for wet and dry mills).
The energy efficiency of dry mill and wet mill ethanol plants are allowed to exogenously improve
over time. We assume that to produce a gallon of ethanol, dry mills require 47,060 BTUs of primary fuel
and wet mills require 52,293 BTUs of primary fuel. These values are reported in EBAMM version 1.1
(Farrell et al. 2006) but attributed to a presentation by Shapouri and McAloon in 2004. It is these values
that are used in the ‘Ethanol Today’ scenario, Farrell’s best estimate of U.S. ethanol production in 2006.
The data comes from a BBI International survey of ethanol plants which is the same survey that provides
the data for Shapouri and Gallagher (2005). After converting from BTUs of primary fuel to equivalent
units of natural gas, 𝜆𝐸,𝑁 from equation 3.1.1 is set 0.042 thousand cubic feet of natural gas per gallon16.
It is also assumed that wet and dry mill ethanol plants have the same capital and labor costs per
gallon of ethanol. Each gallon of ethanol requires an expenditure of $0.064 on labor (Shapouri and
Gallagher 2005). Capital costs of 0.19 $/gallon ethanol are derived from the same report. This value
includes expenditures on all variable factors of production not already accounted for, including: waste
management, water, enzymes, yeast, chemicals, and denaturant. To generate units of labor and capital,
total expenditures are divided by the benchmark prices of labor and capital respectively. In the
benchmark, 𝜆𝐸,𝐾 and 𝜆𝐸,𝐿 , in equation 3.1.1 are set to 0.027 units of capital per gallon and 0.02 hours of
labor per gallon respectively.
Co-products
As mentioned above, the ethanol production process produces a variety of co-products depending
on the production technology used. The quantity of each co-product is modeled in relation to the corn-toethanol conversion efficiency (𝜆𝐸,𝑘=1 ) and the production technology shares.17 In each case, an increase
in conversion efficiency will lead to a decrease in the quantity of co-products produced. This is a
reasonable assumption as improved ethanol conversion efficiency implies that more of the corn kernel is
being converted to ethanol and less is available for co-products. Following GREET 1.8b , we assume that
dry mills produce only distillers’ grains with solubles (DGS), while wet mills produce corn gluten meal
(CGM), corn gluten feed (CGF) and corn oil. We also calculate the CO2 that could be captured in the
fermentation process.
Distillers’ grains with solubles (DGS) are a co-product of dry mill ethanol production. The
remnants of the fermentation and distillation processes, called stillage, are separated into solids and
liquids. The liquids are concentrated and added to the solids. This mixture is dried, and sold as a high
protein animal feed. We model the quantity of DGS produced according to an equation from GREET
1.8b (Wang 2008) which gives pounds of DGS in terms of the conversion efficiency of ethanol.
𝐷𝐺𝑆 = (44.658 – 11.083𝜆𝐸,𝑘=1 )/𝜆𝐸,𝑘=1
16
The 2003 prices of coal (17.85 $/short ton) and natural gas (8.4 $/1000 cubic feet) sold to commercial facilities (EIA 2008a)
are used to calculate total energy expenditures on energy. This value is divided by the price of natural gas to generate the “units”
of energy used in the model.
17 Throughout the co-product section 𝜆
E,k=1 refers to the specific corn to ethanol conversion efficiency of wet milling or dry
milling, not the weighted average parameter.
22
Corn gluten meal (CGM) is a co-product of the wet-milling process, which is often sold as
poultry feed. CGM is the dried gluten component of the corn kernel that remains after the wet milling
process isolates the corn’s starch. The equation for pounds of CGM in terms of the conversion efficiency
of ethanol is:
𝐶𝐺𝑀 = 2.60𝜆𝐸,𝑘=1
Corn gluten feed (CGF) is a co-product of the wet milling process that is sold as a livestock feed.
CGF is the liquid remnants of the corn and water mixture that is generated at first stage of the wet milling
process that is dried with the remaining fiber components of the corn kernel.
𝐶𝐺𝐹 = 11.20𝜆𝐸,𝑘=1
Corn oil is extracted from the corn germ that is separated from the corn kernel in the wet milling
process and can be sold as is, or used as a replacement for soybean oil.
𝐶𝑜𝑟𝑛 𝑜𝑖𝑙 = 2.08𝜆𝐸,𝑘=1
CO2 is released during the fermentation process. It is possible to capture, upgrade and sell this
CO2 to companies that produce carbonated drinks or dry ice. In ideal conditions the saleable CO2
produced in the fermentation process is dependent on chemical properties of ethanol and CO2 (Dale and
Tyner 2006). Under ideal conditions 2 moles of CO2 is produced for every 2 moles ethanol produced.
Using the molecular weight of each chemical, along with the density of ethanol, it is possible to obtain a
value of 6.3 lbs CO2/gallon ethanol. We assume that ethanol plants are not selling this CO2, as Wu (2008)
finds that only 30% of ethanol plants actually capture and sell CO2.
Table 17. 2003 Ethanol Production Data
Dry Mill Ethanol Production
Value
0.75 share of total production
0.76 share natural gas
Units/gallon ethanol
0.3765 bushels corn
47,060 BTU
0.064 $ labor
0.185 $ capital
5.73 lbs DGS
Wet Mill Ethanol Production
Value
0.25 share of total production
0.40 share natural gas
Units/gallon ethanol
0.3912 bushels corn
52,293 BTU
0.064 $ labor
0.185 $ capital
1.02 lbs CGM
4.39 lbs CGF
0.82 lbs Corn oil
Source
GREET 1.8b
GREET 1.8b
GREET 1.8b
Farrell et al. (2006)
Shapouri and Gallagher (2005)
Shapouri and Gallagher (2005)
GREET 1.8b
Source
GREET 1.8b
GREET 1.8b
GREET 1.8b
Farrell et al. (2006)
Shapouri and Gallagher (2005)
Shapouri and Gallagher (2005)
GREET 1.8b
GREET 1.8b
GREET 1.8b
23
Calculation of the Corn Equivalent Value of Co-Products
The co-products of ethanol production are consumed in the food sector. DGS is assumed to
displace a total quantity of corn and soybeans that is roughly equal in weight to the DGS. CGM, CGF
and corn oil are each assumed to displace a fixed quantity of corn.
In the feed ration of livestock, DGS can be used to in place of corn or soybean meal. There have
been a number of attempts to quantify this displacement ratio. Baker and Babcock (2008) calculate the
displacement ratio by solving a linear program for the least cost feed ration with and without DGS
entering as an input. The displacement ratio is the difference between the two optimal rations. An
advantage of this approach is that the displacement ratio depends on the prices of corn, soybeans and
DGS. There analysis is conducted for beef and dairy cattle as well as hogs and poultry. They find that at
2008 prices and livestock makeup (share of DGS consumed by animal), a displacement of 0.79 lbs corn
per pound DGS and 0.47 lbs soybean meal18 per pound DGS.
Arora et al. (2008) updated the displacement ratios for DGS that are used in the GREET lifecycle
emissions model. They reviewed a number of studies that assessed animal performance, in terms of
growth or milk production, with different levels of DGS included. To calculate displacement ratios, the
total lifetime dry matter intake of an on a standard ration was compared to the total lifetime intake of an
animal with the optimal, in terms of performance, level of DGS, assuming that the animals had the same
lifetime performance. They find that, assuming 2008 shares of DGS consumption by animal type, that a
pound of DGS displaces 0.955 lbs of corn and 0.291 lbs of soybean meal. They also find that urea can be
displaced by DGS in the feed ration of beef cattle.
The EPA discusses the displacement ratios of ethanol co-products in the ‘Draft Regulatory
Impact Analysis: Changes to the Renewable Fuel Standard Program’ (US EPA 2009). They argue that
the Arora et al. (2008) ratios are too high, and follow the results of the Forest and Agricultural Sector
Optimization Model (FASOM) and the FAPRI models.19 The FASOM model assumes that DGS
displaces 0.9 lbs of corn and 0.1 pounds of soybeans. The FAPRI model assumes that DGS displaces
0.95 lbs of corn and 0.05 lbs of soybeans. Note that in each of these models the displacement ratios are
dependent on the share of co-products fed to the specific animal types. We assume that these shares are
constant over time. We use the FAPRI assumptions in our analysis.
The displacement ratios of CGF and CGM are not as well studied as wet mills are not the growth
area in ethanol production and therefore make up a small part of the co-products produced. We use
GREET 1.8c (Wang 2009) assumptions for the displacement ratios of CGF and CGM. It is assumed that
a pound of corn gluten meal displaces 1.53 pounds of corn, and a pound of corn gluten feed displaces a
pound of corn.
The displacement ratio for corn oil represents the price ratio between vegetable oil and feed corn
in 2003 (Shapouri and Gallagher 2005). The justification for this is that corn oil is used for many uses
other than animal feed so an energy based calculation underestimates the price of corn oil relative to the
price of corn. The specific values used to link the quantities of co-products to the quantity of traditional
crops, ΦCO in equation 7.1.1, are given in Table 18.
Table 18. Displacement Ratios (lbs feed per lb co-product)
DDGS
Corn Gluten Feed
Corn Gluten Meal
Veg. (Corn) Oil
Corn
0.95
1.53
1
3.04
Soybeans
0.05
0
0
0
Source
FAPRI
GREET 1.8c
GREET 1.8c
Price ratio
18
We assume that 1 pound of soybean meal is equivalent to 1 pound of soybeans which is an assumption used in GREET 1.8c.
The FAPRI models refer to a set of partial equilibrium econometric models of various US and World agricultural commodities
markets built and maintained by the Food and Agricultural Policy Research Institute at Iowa State University and University of
Missouri.
19
24
Co-Product Prices
The price of each co-product is assumed to be fixed in relationship with the price of corn and
soybeans. To calculate each co-products price, we multiply the displacement ratios by the price of corn
and soybeans. Effectively, we are assuming that ΦCO represents the price relationship between each coproduct and commodities.
4. Regular Gasoline Production
Data
The benchmark price of gasoline is the 2003 retail price of motor gasoline in areas that do not
require the sale of conventional gasoline (EIA 2008a). From the reported price of 1.52 $/gallon, we
subtract the average state and federal fuel taxes to arrive at a pre-tax price of 1.15 $/gallon.
Total gasoline production was 128.14 billion gallons in 2003. This was based on total fuel
consumption by passenger and other two-axle four tire vehicles (PC24) reported in the Highway Statistics
(FHWA 2003). To calculate total gasoline consumption, we subtracted total ethanol consumption (see the
Ethanol Production section) from total fuel consumption for PC24 vehicles.
Calibration
Elasticities of Substitution
A value of 0.061 has been chosen for the elasticity of substitution between crude oil, and the
labor and capital composite, 𝜎𝑃1 , from equation 4.1.2. This value was selected to prevent unrealistic
substitutions away from crude oil. The elasticity of substitution between labor and capital used in regular
gasoline production from equation 4.1.3, 𝜎𝑃2 , is set to 2.0.
Benchmark Shares
The share of labor expenditures to total value of regular gasoline, 0.06225, is derived from Table
3.2 of the BEA’s 1992 Input/Output Tables. The share of expenditures on crude oil to the total value of
gasoline, 0.5162, is calculated using the baseline quantities and price of crude oil. The remaining value of
gasoline production, 0.4126, is classified as the share of capital expenditures to the total value of regular
gasoline.
5. Fuel Blenders
Data
The benchmark quantity of fuel is 130.9 billion gallons. The total is made up of 128.14 billion
gallons of regular gasoline and 2.75 billion gallons of ethanol. This data is discussed in more detail in the
Ethanol Production and Regular Gasoline Production sections.
6. Natural Gas Production
Data
The initial price of natural gas is 8.4 $/1000 cubic feet, which is the average delivered price paid
by commercial customers in 2003 as reported in the Energy Information Administration (EIA) Annual
Energy Review (EIA 2008a). The price of natural gas evolves so that the relationship between the price
of imported crude oil and the commercial price of natural gas matches the projections of the EIA’s
Annual Energy Outlook (AEO) (EIA 2008b). For example, in our central crude oil price case, the
relationship between crude oil and natural gas is fixed following the projections of the AEO 2008
Reference Scenario, while in our low crude oil case the relationship is fixed according to the AEO 2007
Reference Scenario. Fixing the natural gas-crude oil price relationship follows a number of studies that
have shown that the two prices are strongly coupled.
25
Brown and Yucel (2008) argue that, while close substitutability existed between natural gas and
the residual fuel (a crude oil refinery co-product) market prior to 1993, that in the last 15 or so years this
relationship is less consistent. Bachmeier and Griffin (2006), using data from 1994-2004 and error
correction modeling, find that a $1 per million BTU increase in natural gas prices raises crude oil prices
by $3.12 per barrel (or about $0.60 per million BTU). Thus, while BTU parity in crude oil and natural
gas markets does not seem to exist, there is modest evidence of some cointegrated relationship between
crude oil and natural gas prices. Bachmeier and Griffin (2006) find a long-run cointegration parameter of
3.12 as opposed to a value of 5 for full market integration. Brown and Yucel (2008) characterize this
finding as “weak.” Villar and Joutz (2006) find oil and natural gas prices to be cointegrated with a trend.
Hartley, Medlock and Rosthal (2008) find that substitution between residual fuel oil and natural gas is
particularly strong in the U.S. North American Electric Reliability Council (NERC) regions where there is
sufficient fuel-switching capability.
Brown and Yucel (2008) expand on previous efforts by being the first to integrate other factors
other than the price of crude oil such as: weather, inventories, and shut in production. Once these other
factors are controlled for, they find that movements (especially long-run) in natural gas prices are well
explained by crude oil prices. Brown and Yucel outline two ‘rules-of-thumb’ that are used to explain the
relationship between crude oil and natural gas prices. The first, the ten-to-one rule, performs better for
the pre-2000 period and states simply that the price of natural gas per million BTU is one tenth the price
of a barrel of crude oil. The second rule, the six-to one rule, performs better in the post-2000 period.
Calibration
Elasticities of Substitution
We choose a value of 2.0, for the elasticity of substitution between labor and capital used in
natural gas production, 𝜎𝑁 from equation 6.1.1.
Benchmark Shares
The BEA’s 1992 Input/Output Tables (BEA 2008a) suggests that the size of the natural gas sector
relative to total GPD is 0.0055. The share of labor expenditures to the total value of natural gas
production is 0.066. This value is also derived from the BEA’s 1992 Input/Output Tables (BEA 2008a).
The share of capital expenditures to the total value of natural gas production is then 0.93.
7. Food Producers
Data
Price indices are used to calibrate the different levels of the food sector. These price indices are
from the Bureau of Labor Statistics Consumer and Producer Price Index online databases (Bureau of
Labor Statistics 2009). The benchmark price of the corn soybean (CS) index 𝑤𝑉 , from equation 7.1.8 is
202.7, the 2003 CPI for Cereal and Bakery Products. The benchmark price for the food crop (CSHW)
index 𝑤𝑍 , from equation 7.1.7 is 94.1, the June 2004 Crude Foodstuffs and Feedstuffs Producer Price
Index. The benchmark price of food 𝑤𝑋 , from equation 7.1.6 is set to 180, the 2003 Consumer Food
Price Index.
Calibration
Elasticities of Substitution
We choose a value for the elasticity of substitution between the composite feedstuffs index
(consisting of all four food crops and all four co-products), labor and energy from equation 7.1.2, 𝜎𝑋1 , of
0.08. We choose this small value, effectively imposing perfect complements across the three inputs in
this nest, in order to restrict unlikely substitution from feedstuffs towards labor or energy.
The elasticity of substitution between hay, wheat and the composite index of corn and soybean
equivalents, 𝜎𝑋2 from equation 7.1.3, is set to 0.3. We choose a value for the elasticity of substitution
between the corn equivalents and soybean equivalents, 𝜎𝑋3 from equation 7.1.4, of 0.25.
26
Benchmark Shares
We treat all crops that are produced in the base year, but which are not exported or used in
ethanol production as the total quantity of crops used in food production. We assume that the total
quantity of co-products generated by ethanol production is consumed by the food sector in the base year.
The natural gas used in food production is assumed to be all natural gas produced in the base year which
is not used in crop or ethanol production. Finally, the quantity of labor used in food production is chosen
such that the overall size of the food sector reflects its share of total GDP.
8. Other Intermediate Sectors
8.1. Numeraire Good
Data
The price of the numeraire good 𝑤𝑐 , from equation 8.1.1 used for calibration is 193.2, the 2003
Consumer Price Index excluding food and energy (Bureau of Labor Statistics 2009).
Calibration
We choose a value for the elasticity of substitution between labor and capital used in numeraire
production from equation 8.1.1, 𝜎𝐶 , of -2.0.
8.2. Fertilizer
Data
We assume that the baseline price of fertilizer is the 2003 price of anhydrous ammonia (NH3)
reported by the USDA (NASS 2006). This value is 373 $/ton.
9. Rest-of-World Import and Export Markets
9.1. Agricultural Products
Calibration
Crop Export Shares
The shares of US crop production exported were calculated using the USDA’s Foreign
Agricultural Service Production, Supply, and Distribution Online dataset (FAS 2009). The benchmark
export shares are reported in Table 19 and represent 2003 data. To follow the structure of our economic
model, in which cotton is not demanded within the US, we assume that all cotton produced in the US is
exported (export share set to 1). This assumption is reasonable as in 2003, 75% of total cotton produced
in the US was exported. Likewise, in each year between 2004 and 2008 more than 60% of US cotton
production was exported (FAS 2009).
Crop Export Elasticities
We use for 𝜂𝑅𝑂𝑊,𝑘 , in equations 9.1.1 to 9.1.5, the crop export elasticities for corn, soybeans,
wheat and cotton reported by Gardiner and Dixit (1987). These values are reported in Table 19. Gardiner
and Dixit (1987) report estimates for corn export demand elasticities between –0.47 and –0.16, with a
mean value of –0.27. Haniotis et al. (1988), report a value of –1.73. DeGorter and Just (2009) use a
value of –0.10. For soybeans, Gardiner and Dixit (1987) report estimates between –2.00 and –0.14, with
a mean value of –0.96, while Haniotis et al. (1988) report a value of –0.60. Gardiner and Dixit (1987)
report estimates for wheat demand elasticities between –3.13 and –0.15, with a mean value of –0.60.
Haniotis et al (1988) report a value of 0.74 (positive). We have chosen the Gardiner and Dixit values
because they are consistent across crops, unlike those reported by Haniotis et al (1988).
27
Table 19. Crop Export Shares and Elasticities
Crop
Corn
Soybeans
Hay
Wheat
Cotton
Export Share
0.19
0.36
0.00
0.49
1.00
Elasticity
-0.65
-0.6
n/a
-0.55
-0.75
9.2. Crude Oil
Data
We have estimated that total crude oil available for gasoline production in 2003 was 2.6 billion
barrels. This value is calculated, given that the average refinery yield for finished motor gasoline was
47% in 2003 (EIA 2009), and that refineries and blenders used 5.59 billion barrels of crude in 2003 (EIA
2008a). The benchmark price of crude oil is 28.85 $/barrel, which is the average 2003 price of Brent
Blend 38º (EIA 2008a).
Calibration
Crude Oil Supply Elasticity
As our baseline value for the crude oil supply elasticity, 𝜂𝑂𝐼𝐿 in equation 9.2.1, we use a central value
from reviewed literature of 0.5. In addition, we conduct sensitivity analysis on this parameter using
values of 1.0 and 0.2.
Krichene (2002) reports a mean long-run ROW supply elasticity of 0.044 and short-run estimates
of 0.25, 1.10, and 0.10 for the periods 1918-1999, 1918-1973, and 1973-1999 using an error correction
model with co-integration. He also reports short-run estimates using 2 stage least squares for these
periods of -0.08, -0.08, and -0.07, respectively. Krichene (2006) reports estimates of long-run supply for
the period 1970-2005 of 0.007 to 0.08, again using an error correction model with co-integration. She
also provides short-run estimates over this period between 0.005 and -0.03 using 2 staged least squares.
The OECD Economic Outlook uses a supply elasticity of 0.04 (the short-term elasticity applied in
Brook et al., (2004)). Huntington (1991) found a range of short-run elasticity estimates from 0.0 to 0.137,
with an average or 0.052. They also found long-run elasticities of oil supply ranged from 0.162 to 0.662,
with an average of 0.39. Porter (1992) calculates an implied long-run supply elasticity of 0.29. Greene
and Tishchishyna (2002) use short-run estimates between 0.028 and 0.049. Bohringer and Rutherford
(2002) use values of 0.5 to 2.0. Alhajji and Huettner (2000) have computed a ROW supply elasticity of
0.21.
10. Government
Data
Our estimate of total government expenditures in 2003 of $2,828.90 billion includes the sum of
current tax receipts plus contributions for government social insurance from the BEA’s NIPA dataset
(BEA 2009). Using data on total fuel usage and average fuel taxes per gallon of fuel, we are able to
calculate the amount of government revenue generated by fuel taxes. In 2003, the average per-gallon
combined federal and average state fuel tax was 0.375 $/gallon (FHWA 2003), resulting in fuel tax
revenue of $49.08 billion.
Using data on ethanol usage in 2003, we are able to compute the total amount dispersed by the
government for the Volumetric Ethanol Excise Tax Credit (VEETC). In 2003, the VEETC was 0.52
$/gallon ethanol (Wright et al. 2006) , implying that $1.43 billion was dispersed to ethanol producers.
Given an average CRP rental rate of $46.35 per acre (see CRP Rental Rate section), in 2003 we compute
total government payments to CRP land of $1.55 billion.
28
Subtracting these transfers from total government expenditures provides an estimate for the total
government revenue generated by taxes on capital and labor. We assume that labor and capital are taxed
at a single rate and calculate this rate to be 0.37.
11. Baseline Prices
The prices listed in Table 20 are discussed in more detail throughout the text. This table only
serves to consolidate the most important prices.
Price
Unit
Labor
9.05 $/hour
Capital
1.025 $/unit capital
Energy (Natural Gas)
8.4 $/1000 ft^3 NG
Crude Oil
28.85 $/barrel
Gasoline
1.145 $/gallon
Fertilizer
373 $/ton NH3
Corn
2.42 $/bushel
Soybeans
7.34 $/bushel
Hay
85.5 $/ton
Wheat
3.23 $/bushel
Cotton
0.47 $/pound
CRP Rental Rate
46.35 $/acre
Food
180 CPI
Feed grains
202.7 CPI
Numeraire Good
193.2 CPI
All values are for 2003 unless noted.
Table 20. Baseline Prices
Description
Wage rate of hired farm labor
1+real interest rate on long run T-bills
U.S. average price for commercial consumers
Average price of Brent Blend 38º
Average retail price of gasoline less taxes
U.S. average price paid, anhydrous ammonia
Average U.S. price of corn
Average U.S. price of soybeans
Average U.S. price for all hay
Average U.S. price for all wheat
Average U.S. price for cotton (2001-05 average)
see 'CRP Rental Rate' section
CPI for food
CPI for cereal and bakery products
CPI excluding food and energy
Source
NASS (2003)
U.S. Treasury (2009)
EIA (2008)
EIA (2008)
EIA (2008)
NASS (2005)
NASS (2005)
NASS (2005)
NASS (2005)
NASS (2005)
NASS (2005)
FSA (2006)
BLS (2009)
BLS (2009)
BLS (2009)
12. Description of Data Sources
USDA FAS Production, Supply and Distribution Online
The USDA Foreign Agricultural Service Production, Supply and Distribution Online database
(FAS 2009) is an online tool that provides access to USDA data on the production, distribution and
supply of agricultural commodities. Data is available for the U.S. and other major producing and
consuming countries. The statistics are updated monthly by a number of USDA agencies including: the
Foreign Agricultural Service, the Economic Research Service, the Farm Agency Service and the
Agricultural Marketing Service.
Bureau of Economic Analysis Benchmark Input-Output
The Bureau of Economic Analysis’s Benchmark Input-Output tables (BEA 2008a) are prepared
by the Industry Benchmark division every five years (years ending in 2 and 7). These tables are based on
economic censuses conducted every 5 years by the Bureau of the Census. The goal of these tables is to
quantify how industries interact and to provide information on how goods and services flow between
different industries.
Bureau of Economic Analysis’ National Income and Product Accounts
The U.S. National Income and Product Accounts (NIPA) are one of three main parts of the U.S.
economic Accounts (the BEA I/O tables are another). The goal of the NIPAs is to quantify and report the
value and composition of national output along with the distribution of incomes generated in production.
The NIPAs have been designed to answer three questions: What is the output of the U.S.? What are the
sources of sources of income in the U.S.? What sectors are the savings (investment for future production)
from? The data used to compile these tables comes from a variety of public and private sources.
Government sources include the Bureau of the Census, the Bureau of Labor Statistics, the Treasury
Department and the Department of Agriculture (BEA 2008b).
29
Federal Highway Administration’s Highway Statistics
The Federal Highway Administration’s Highway Statistics reports (FHWA 2003) are an annual
series that contain data on motor fuel, motor vehicles, driver licensing, highway mileage, and highway
taxation. The data is collected from state agencies, and is checked against other state and federal data.
Commodity Costs and Returns (CCR)
Commodity Costs and Returns data (sometimes referred to as Phase III of the ARMS) provides
cost estimates by crop type for several input categories (ERS 2008a). Some of these categories are
collapsed to generate the labor and capital input requirements for each cropping practice, while others are
used in combination with the ARMS data to generate an estimate of fertilizer expenditure (Table 21). The
CCR does not breakdown the data by tillage so other sources are used to impose variation on the crop
level data. The Commodity Costs and Returns data covers corn, soybeans, wheat and cotton.
The USDA has four methods for assembling the cost of production estimates20. ‘Direct costing’
aggregates the survey responses to questions that ask explicitly for the amount spent on a certain input.
‘Valuing input quantities’ uses survey data for the quantities of inputs used, and assumed prices
(secondary data) for these inputs to calculate expenditures. ‘Indirect costing’ uses survey data for
production practices, in combination with technical assumptions and secondary price data. An example
of the technical assumptions would be the efficiency, repair rates and expected lifetime of a machine.
‘Allocating whole-farm expenses’ allocates expenses on the farm level to specific commodities using an
allocation method based on a commodity’s percent share of the farm’s operating margin.
Agricultural Statistical Database (ASD)
The National Agricultural Statistical Services publishes U.S., state, and county level agricultural
statistics for many commodities and data series. Much of this is available on-line in the ASD. From their
on-line query screen one can extract data from numerous datasets up to the county level for several years
for numerous agricultural commodities (1909-2008). This data is also available in annual NASS reports
such as the Crop Production Historical Track Records (NASS 2003) and Agricultural Prices Summaries
(NASS 2006).
Regional Environment and Agricultural Programming Model (REAP)
The Regional Environment and Agricultural Programming Model (REAP) is a commonly cited
model of U.S. agriculture that is based on data from the ARMS. REAP’s data is structured so that
different agricultural production practices (crop/rotation/tillage choice) have different input requirements.
While REAP is disaggregated to a sub-regional level, the crop production expenditure data is generated at
the regional level. Therefore, it was possible to collect expenditure estimates for cropping and tillage
practices at the regional level. Each region does not have data for each rotation-tillage combination, and
many regions have no data for certain rotations. Despite this, it was possible to collect multiple regional
estimates for each crop-tillage combinations relevant for our purposes.
The data used in REAP reflects production practices as of the early 1990’s. While a newer
dataset would be ideal, the age of the data is not likely to be an issue as only the relationships are utilized.
Unless it is believed that the production practices for a certain crop or tillage system changed relative to
other systems since the early 1990’s then using an older dataset should not pose a significant problem.
Agricultural Resource Management Survey (ARMS)
The ARMS is a wide-ranging annual survey of farm and ranch operators administered by USDA's
National Agricultural Statistics Service (NASS). The survey collects data on field-level production
practices, farm business accounts, and farm households. Prior to 2000, the major crops were surveyed
annually. Since 2000, the ARMS dataset is collected by crop on a rotating schedule with the major crops
generally surveyed every 4-5 years.
20
http://www.ers.usda.gov/Data/CostsAndReturns/methods.htm
30
The ARMS is conducted in three phases over the course of the survey year, which runs from June
through April. The first phase (Phase I) is conducted during the summer of the reference year and screens
farmers to determine whether they are producing commodities targeted for data collection. The second
phase (Phase II) is conducted in the fall and winter of the reference year; in this phase farms from Phase I
are randomly selected and interviewed to collect information on their production practices and chemical
use. Phase II data is collected at the individual field or production unit level; it replaces the former Crop
Production Practices Survey. Phase III is conducted in the spring of the year following the reference year;
in this phase a nationally representative sample of farmers are interviewed to obtain information on their
costs and returns during the reference year. In addition, the farmers contacted during Phase II are reinterviewed to obtain information on their costs and returns, including data needed to estimate the costs of
production associated with their production practices. This phase of the survey is conducted at the farm
level21.
Phase II of the ARMS contains information on crop production practices for several primary field
crops (such as corn, soybeans, wheat, and cotton) as well as data on U.S. farmers' agricultural resource
usage. Specifically Phase II includes information on the field itself (such as previous crops planted and
erodibility designation), the size of the field, and the operator's tenure, including rental arrangements.
Seed type, sowing rate, and cost are collected, as well as information on the tillage equipment used on the
field. Nutrient application rates and methods of application for the crop are recorded, including
information on how the nutrient management decisions are made. Pesticide-management variables
include the amount and number of applications of each pesticide ingredient, and the management
information used to make that determination. Additional information includes irrigation water
applications and timing and manure use and management.
Controlling for Temporal Variation
There are many factors that would change input usage for a given year, most notably weather
patterns. Taking a single year of survey data may be problematic because factors not associated with
cropping practices could alter the input usage. Analyzing the time series of a various cropping practice
shows that input usage has remained relatively stable since 1996, with variations that appear to move
around the mean. In other words, the input usage goes both up and down over this time. To handle this
variation, the input usage data is an average of multiple survey years. Specifically, an average is taken
across all available data points (by crop, rotation and tillage) for the years 1996 to 2005.
The number of observations for each cropping practice varies. For each crop, the number of
surveys conducted over this timeframe is different. In addition, newer or less prominent cropping
practices may have no data reported, or data that is not reported for a few years. If the remaining data
corresponds to anomalous years, then the averages could be skewed in either direction. More prominent
crops do not face this same problem as these crops have far fewer missing values.
21
The survey data used in estimates for years prior to the Phase III ARMS were collected as part of the annual Farm Costs and
Returns Survey (FCRS) from 1984 to 1995 and the Costs of Production Survey (COPS) prior to 1984.
31
13. Additional Data Tables
Table 21. Commodity Cost and Returns Data
Corn
Labor
Hired labor
Opportunity cost of unpaid labor
Capital
Interest on operating capital
Capital recovery of machinery
Other
Soil Conditioners
Manure
Chemicals
Custom Operations
Repairs
Purchase irrigation water
Taxes and insurance
General farm overhead
Ginning
$/Planted Acre
Soybeans
Wheat
Cotton
Method
3.14
26.53
1.90
16.11
2.66
17.20
16.48
33.86
Direct
Valuing Inputs
0.82
56.67
0.41
43.43
0.36
52.30
1.14
62.45
Valuing Inputs
Indirect
0.00
0.00
26.20
11.17
14.22
0.22
5.54
12.17
-
0.12
0.46
16.92
6.32
9.77
0.12
5.80
11.66
-
0.00
0.00
6.94
7.19
10.85
0.68
3.95
7.40
-
0.00
0.00
65.81
28.38
20.95
3.66
8.81
18.15
88.33
Direct
Direct
Direct
Direct
Indirect
Direct
Allocation
Allocation
Direct
All values for 2003
The ‘Other’ category is included in the Fertilizer variable.
Table 22. Baseline Agricultural Prices
Corn Seed
Soybean Seed
Diesel
LPG
Electricity
Price
102
24.2
1.50
1.10
0.08
Unit
$/80,000 kernels
$/bushel
$/gal
$/gal
$/kwh
Description
US average price paid, all corn hybrids
US average price paid, all soybeans
Retail price diesel
Retail price to commercial costumers
Retail price to commercial customers
Source
NASS (2006)
NASS (2006)
EIA (2008)
EIA (2008)
EIA (2008)
32
Table 23. 2003 Baseline Agricultural Data
Corn
Conventional
Reduced
Mulch
No-Till
Soybeans
Conventional
Reduced
Mulch
No-Till
Hay
Conventional
Reduced
Mulch
No-Till
Wheat
Conventional
Reduced
Mulch
No-Till
Cotton
Conventional
Reduced
Mulch
No-Till
Million
Acres
77.53
24.41
21.29
16.77
15.05
72.48
11.13
13.18
24.92
23.25
63.38
25.00
16.62
12.77
8.99
53.06
19.37
13.11
9.34
11.25
12.00
10.54
0.22
0.55
0.68
Labor
29.67
34.31
28.73
28.75
24.49
18.01
26.31
18.36
18.32
13.51
19.86
25.25
17.45
17.49
12.70
19.86
26.05
17.94
17.89
13.10
50.34
50.34
50.34
50.34
50.34
Input Expenditures ($/acre)
Capital
Energy Fertilizer
57.49
23.09
156.60
62.64
26.25
155.04
57.42
22.45
158.28
54.81
22.46
156.29
52.20
19.55
156.17
43.84
8.77
84.95
49.35
12.42
82.75
45.23
8.92
83.57
43.18
8.91
84.62
41.12
6.79
86.92
52.66
10.95
62.02
56.67
13.75
62.25
51.94
9.70
61.20
49.58
9.72
61.36
47.22
7.23
63.81
52.66
10.95
67.97
57.11
14.16
68.53
52.35
9.95
67.01
49.97
9.93
67.83
47.59
7.44
68.36
63.59
24.39
303.34
63.59
24.39
303.34
63.59
24.39
303.34
63.59
24.39
303.34
63.59
24.39
303.34
Total
266.85
278.25
266.88
262.31
252.42
155.57
170.82
156.09
155.03
148.34
145.49
157.91
140.30
138.14
130.96
151.44
165.84
147.25
145.61
136.49
442.06
442.06
442.06
442.06
442.06
N
36.41
35.96
37.42
36.48
35.38
1.02
1.08
1.26
1.05
0.83
8.14
8.52
7.91
8.22
7.41
17.76
18.31
17.39
18.00
16.51
21.12
21.12
21.12
21.12
21.12
Fertilizer Components ($/acre)
P
K
Seed Chemicals
8.66
7.71 34.30
26.20
8.60
7.63 34.05
25.47
9.26
7.78 34.41
26.09
8.50
8.02 34.74
25.24
8.01
7.40 33.95
28.12
2.19
3.15 27.42
16.92
2.18
3.02 26.79
15.42
2.27
3.06 27.04
15.70
2.19
3.16 27.47
16.51
2.18
3.25 27.78
18.63
6.15
3.11
7.60
6.94
6.36
2.81
7.60
6.90
5.68
3.50
7.60
6.44
5.97
2.83
7.60
6.66
6.70
3.65
7.60
8.37
4.56
1.05
7.60
6.94
4.72
0.94
7.60
6.89
4.23
1.18
7.60
6.53
4.46
0.97
7.60
6.72
4.86
1.18
7.60
8.13
5.49
5.46 37.19
65.81
5.49
5.46 37.19
65.81
5.49
5.46 37.19
65.81
5.49
5.46 37.19
65.81
5.49
5.46 37.19
65.81
Other
43.32
43.32
43.32
43.32
43.32
34.25
34.25
34.25
34.25
34.25
30.07
30.07
30.07
30.07
30.07
30.07
30.07
30.07
30.07
30.07
168.28
168.28
168.28
168.28
168.28
33
14. References
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Cartel, Oligopoly or Competitive? Energy Journal 21, no. 3: 31-60.
Arora, S., M. Wu, and M. Wang. 2008. Update of Distillers Grains Displacement Ratios for Corn
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