Essays on Applied Resource Economics
Using Bioeconomic Optimization Models
by
Ermanno Affuso
A dissertation submitted to the Graduate Faculty of
Auburn University
in partial fulfillment of the
requirements for the Degree of
Doctor of Philosophy
Auburn, Alabama
December 12, 2011
Keywords: Bioenergy, Stochastic Frontier Analysis, Bioeconomics, Stochastic Dynamic
Optimization, Econometric Mathematical Programming
Copyright 2011 by Ermanno Affuso
Approved by
Diane Hite, Chair, Professor of Agricultural Economics and Rural Sociology
Norbert L. W. Wilson, Professor of Agricultural Economics and Rural Sociology
Denis Nadolnyak, Professor of Agricultural Economics and Rural Sociology
Abstract
With rising demographic growth, there is increasing interest in analytical studies that
assess alternative policies to provide an optimal allocation of scarce natural resources while
ensuring environmental sustainability. This dissertation consists of three essays in applied
resource economics that are interconnected methodologically within the agricultural produc-
tion sector of Economics.
The first chapter examines the sustainability of biofuels by simulating and evaluating an
agricultural voluntary program that aims to increase the land use efficiency in the production
of biofuels of first generation in the state of Alabama. The results show that participatory
decisions may increase the net energy value of biofuels by 208% and reduce emissions by
26%; significantly contributing to the state energy goals.
The second chapter tests the hypothesis of overuse of fertilizers and pesticides in U.S.
peanut farming with respect to other inputs and address genetic research to reduce the use
of the most overused chemical input. The findings suggest that peanut producers overuse
fungicide with respect to any other input and that fungi resistant genetically engineered
peanuts may increase the producer welfare up to 36.2%.
The third chapter implements a bioeconomic model, which consists of a biophysical
model and a stochastic dynamic recursive model that is used to measure potential economic
and environmental welfare of cotton farmers derived from a rotation scheme that uses peanut
as a complementary crop. The results show that the rotation scenario would lower farming
costs by 14% due to nitrogen credits from prior peanut land use and reduce non-point source
pollution from nitrogen runoff by 6.13% compared to continuous cotton farming.
ii
Acknowledgments
?Nissuna umana investigazione si p`o dimandare vera scienzia s?essa non passa
per le matematiche dimostrazioni.?
Leonardo Da Vinci, Trattato Della Pittura (1651)
I would like to offer my sincerest gratitude to my advisor and friend Dr. Diane Hite for
being a guide that always gave me great professional and academic advice. I also would like
to thank my committee members Drs. Norbert Wilson and Denis Nadolnyak who afforded
me the opportunity to work on challenging and formative projects and travel across the U.S.
to present our work at academic conferences. I offer many thanks to my external reader,
Prof. David Bransby, for his thoughtful comments/suggestions on my dissertation, as well
as his advice for my future career.
My genuine appreciation also goes to Drs. Robert Taylor, Henry W. Kinnucan and
Henry Thompson, Professors of Economics at Auburn University, who dedicated a significant
amount of their time to engage my inquisitive mind and to facilitate my academic success.
Outside Auburn I would like to thank my former advisor Prof. Dino Borri, Technical
University of Bari, who taught me the importance of integrated and multidisciplinary re-
search; additionally I would like to thank the wonderful scholars who promptly replied to
all of my emails when I was in search of help or clarification on many topics. These schol-
ars include Prof. Thomas Heckelei, University of Bonn (Germany), Prof. Quirino Paris,
University of California at Davis, Prof. James D. Hamilton, University of California at San
Diego, Prof. Steven B. Caudill, Rhodes College, Prof. William H. Greene, New York Univer-
sity, Prof. Bruce McCarl, Texas AM, Prof. Pierre Merel, University of California at Davis,
Prof. Filippo Arfini, University of Parma (Italy), Prof. Stephen Rice, Rhodes College, Prof.
iii
Giuseppe Squadrito, University of Alabama at Birmingham, Prof. Charles Bos, VU Univer-
sity Amsterdam, Miss Georgie Mitchel, Grassland Soil and Water Research Laboratory, Mr.
Johannes Fernandes Huessy, NORC Data Enclave at the University of Chicago and finally
Miss Leah M. Duzy, National Soil Dynamics Laboratory, who has been a great co-worker.
This dissertation is dedicated to my father Pino who introduced me to computer pro-
gramming on a Commodore PET 3032 when I was only 7 years old, to my mother Lell`e
who exposed me to foreign languages since I was a little child and to my wife Olivia who
surrounds me with her love and dedication that simplified my hard work at Auburn.
This research was funded in part by a grant from the National Peanut Research Labora-
tory and the Economic Research Service of USDA.
iv
Table of Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 A model for integrated and participatory decisions of optimal land use in biofuel
production: An application to the State of Alabama . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Review of previous research . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Theoretical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Econometric Calibration of the Model . . . . . . . . . . . . . . . . . . . . . . 14
1.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2 A Stochastic Frontier Analysis to Examine Research Priorities for Genetically
Engineered Peanuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.3 Theoretical Consideration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.1 An Alternative Approach . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 Econometric Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5 Data and Empirical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.6.1 Environmental Implications . . . . . . . . . . . . . . . . . . . . . . . 49
2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
v
3 Rotation of Peanuts and Cotton for Optimal Nitrogen Applications . . . . . . . 53
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2 Review of Previous Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3 Bioeconomic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.1 Net Revenue Function . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.2 Crop yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5 Econometric Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.5.1 Cotton Response and Peanut Yield . . . . . . . . . . . . . . . . . . . 64
3.5.2 Nitrogen Elasticity of Supply . . . . . . . . . . . . . . . . . . . . . . 66
3.5.3 Transitional equations . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.6 Markovian prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
A GME - GCE Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
B Net Energy Value and Carbon Emissions Calculation . . . . . . . . . . . . . . . 92
C Biomass Crop Residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
vi
List of Figures
1.1 Probability Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 NEG and CO2 emissions in the transitional phases . . . . . . . . . . . . . . . . 23
1.3 Land and Agricultural subsidies in the baseline and optimal scenarios . . . . . . 25
2.1 Technical and Allocative Inefficiencies . . . . . . . . . . . . . . . . . . . . . . . 37
3.1 The Study Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.2 Mitscherlich-Baule cotton response to nitrogen . . . . . . . . . . . . . . . . . . . 68
3.3 Markow Switching Autoregressive Model . . . . . . . . . . . . . . . . . . . . . . 72
3.4 Time Path ? Nitrogen Decision Rule . . . . . . . . . . . . . . . . . . . . . . . . 74
3.5 Expected Net Return in 2019 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
vii
List of Tables
1.1 Economic Data and Estimated Fossil Fuel Energy Ratio . . . . . . . . . . . . . 14
1.2 Observed Land Allocation and land opportunity costs (Base Year 2009) . . . . . 19
1.3 Estimated Q and d matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4 Long Run Expected Optimal Land Use and Subsidies . . . . . . . . . . . . . . . 22
2.1 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.2 Estimated Nutrients Expenditures . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3 Stochastic Frontier Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4 Model Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.5 Overuse of Fungicide with respect to other inputs . . . . . . . . . . . . . . . . . 49
3.1 Economic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.2 Management Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.3 Markov Switching Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.4 Time path - optimal decision rule for nitrogen applications . . . . . . . . . . . . 73
A.1 Range of own and cross price elasticities of supply . . . . . . . . . . . . . . . . . 89
B.1 Energy Gains and Energy Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
viii
List of Abbreviations
AAEA Agricultural and Applied Economics Association
ADF Augmented Dickey Fuller
AIC Akaike Information Criteria
ARMS Agricultural Resource Management Survey
BFGS Broyden?Fletcher?Goldfarb?Shanno
BTU British Thermal Units
DCP Direct and Counter-cyclical Payment
DOE Department of Energy
DP Dynamic Programming
DSP Discrete Stochastic Programming
EISA Energy Independence and Security Act
EMP Econometric Mathematical Programming
ENSO El Ni?no Southern Oscillation Phases
ERS Economic Research Service
EVS Expected Value Solution
EWG Environmental Working Group
FDA Food and Drug Administration
ix
GE Genetically Engineered
GHG Green House Gasses
HRU Hydrological Response Unit
ILUC Indirect Land-Use Change
MB Mitscherlich-Baule
NASS National Agricultural Statistics Service
NCI National Cancer Institute
NEG Net Energy Gain
NOAA National Oceanic and Atmospheric Administration
ORNL Oak Ridge National Laboratory
PMP Positive Mathematical Programming
QWML Weighted Quasi-Likelihood Function
RFS Renewable Fuel Standard
RPS Recursive Problem Solution
SDP Stochastic Dynamic Programming
SWAT Soil and Water Assessment Tool
US-EPA United States Environmental Protection Agency
USDA United States Department of Agriculture
VSS Value of Stochastic Solution
WESML Weighted Exogenous Sampling Estimator
x
Chapter 1
A model for integrated and participatory decisions of optimal land use in biofuel
production: An application to the State of Alabama
enc-56enc-56enc-56
?Use of [liquid transportation] fuels has given rise to energy security concerns,
contributions to climate change and other environmental challenges.?
- National Biofuels Action Plan (2008)
1.1 Introduction
In 2008, the total US demand for transportation fuel accounted for 179% of the total
oil produced in the country. The total consumption of fossil fuel was 22,606.7 trillion BTU.
(Davis et al., 2010)[1]. The Renewable Fuel Standard (RFS), a key provision of the Energy
Independence and Security Act of 2007 (EISA), aims to replace imported oil with 36 billion
gallons of biofuels by 2022. According to RFS, these renewable fuels produced by modern
biorefineries, will reduce the emissions of green house gasses (GHG) relative to the life cycle
emissions from gasoline and diesel by at least 20%. As a consequence of the development of
clean energy substitutes for fossil fuels, energy crops are becoming increasingly popular in
the United States accounting for 12 billion gallons of corn ethanol and 0.60 billion gallon of
soybean biodiesel production annually. The United States became the top world producer
of bioethanol followed by Brazil (Renewable Fuel Association, 2011)[2].
As energy crops gain importance, their efficiency and environmental impact are becom-
ing an issue that is hotly debated by the scientific community. The RFS mandate may have
a significant impact on land-use change. Searchinger et al. (2008)[3] estimated that land-use
1
change associated with corn-based ethanol production would double GHG emissions over 30
years rather than reduce it by 20% as suggested by EISA.
Soils and plant biomass are the largest natural sources for carbon sequestration con-
taining almost 2.7 times the carbon content of the atmosphere. Conversion of rainforests,
peat lands, savannas and grasslands would release CO2 as a result of microbiological pro-
cesses resulting in decomposition of organic carbon naturally stored in plant biomass and
soils. Consequently, a phenomenon called carbon emissions from indirect land-use change
(ILUC) will occur. Fargione et al. (2008)[4] defined the carbon debt of land conversion as the
amount of CO2 released during the first 50 years after conversion, from the decay processes
of organic matter. Over time, the biofuel produced from converted land would repay the
carbon debt; however, the authors estimated an increase of 420 times in GHG emissions in
the atmosphere instead of a reduction as found by previous studies.
A GHG federal cap-and-trade program may benefit the US agricultural sector and may
increase social welfare if the improvement in air and water quality and wildlife conservation
derived from agricultural and forestry mitigation activities are considered (Baker et al.,
2010)[5]. However, there may be some issues in the implementation of such a policy if
the ILUC emissions are included in the regulation. Khanna et al. (2011)[6] argue that the
large variability of ILUC estimates within studies and between different studies may produce
subjective policies rather than policies designed according to scientific evidence. Moreover,
if such a policy would promote the production of biofuels with a lower ILUC factor, it will
not guarantee global reductions in GHG emissions. Whether or not biofuels are a possible
solution to climate change mitigation is strongly dependent on the type of biofuel or even
the mix of biofuels considered. The authors conclude that an alternative policy approach
would be
?[...]creating incentives for sustainable land management practices, such as land
zoning regulations and payments to landowners for environmental protection?1
1Khanna, M., C. L. Crago, and M. J. Black. 2011. ?Can Biofuels be a Solution to Climate Change? The
Implications of Land Use Change Related Emissions for Policy?, Interface Focus, 1, p. 245
2
that may produce global reductions of GHG.
Based on their conclusion, an interesting question would be whether participatory deci-
sions on land management, made by landowners and institutions, would lead to sustainable
production of biofuels. The objective of this study is to test this hypothesis in the State of
Alabama where the State Energy Program was awarded with $55.57 million from the Amer-
ican Recovery and Reinvestment Act (2009) by the Department of Energy (DOE) to invest
in public and private sectors aimed at building a sustainable energy economy and reducing
GHG emissions in the state.
To my knowledge, there is no other study that has attempted to examine the above
hypothesis. This study is unique in the literature of biofuels and bioenergy for several
reasons. First, the current research presents the first normative analysis that quantitatively
assesses the potential environmental benefits deriving from a cooperative outcome. Secondly,
in this study the hypothesis is tested simulating a voluntary program that could promote a
sustainable land use to produce biofuels in Alabama. Finally, the simulation of the voluntary
program in this study is performed using an original multidisciplinary integrated model that
differs from any other model used in the bioenergy and applied economics literature.
This article is organized as follows. Section two reviews previous research; section three
presents the theoretical model; section four explains the source of data used in this study;
section five focuses on the econometric calibration of the model; and section six presents and
discusses the results of the empirical analysis. Lastly section seven gives some concluding
remarks.
1.2 Review of previous research
In order to ensure a sustainable economic growth, subject to an improvement in resource
efficiency and pollution reduction, voluntary environmental programs became increasingly
popular in Europe and in the U.S. in the past two decades. These programs are based on vol-
untary agreements among firms that cooperate in reducing pollution associated with their
3
production processes to a level that is regulated by the government. For example, ?EPA
33/50? was a voluntary program that aimed to reduce the toxic release of U.S. chemical
industrial sector. Khanna and Damon (1999)[7] evaluated the impact of this program over
the period 1991-1993 and they found a significant decline of toxic release among the par-
ticipants. In Europe voluntary environmental initiatives are more popular than in the U.S.
Voluntary agreements that aimed to increase energy efficiency while reducing carbon dioxide
have been examined by Krarup and Ramesohl (2002)[8] in five countries of the European
Union during the 1990s. The authors argue that voluntary agreements are more effective
when are integrated in a broader climate policy mix with regular monitoring, support, and
economic incentives. In the forestry sector, Auld et al. (2008)[9] found that voluntary
initiatives in sustainable forest management, that involve the cooperation of government,
non-governmental organizations, and private stakeholders, led to substantial GHG emission
reductions.
Environmental Planners have the unique role to bridge the gap between the technical
knowledge of the environment and the understanding of the sociopolitical context of commu-
nities (Ali, 2002)[10]. Consequently, implementing a program that aims to increase land use
efficiency would require the integration of other technical factors such as the knowledge of
yield growth that is an important determinant of land conversion for production of biofuels.
If forest land conversion has a negative environmental effect, if one considers the un-
certain but non-null ILUC factor, then a research analysis would consist of finding the best
combination of energy crops to grow restrictively in cropland areas that would provide the
largest energy supply. While the demand for ethanol increased by 235% in the past five years,
demand for biodiesel registered the most rapid growth of approximately 1,680% (Davis et
al., 2010)[1] ; therefore, investigations should not be restricted solely to corn-based ethanol.
The impact of energy crops on land-use change plays a significant role in choosing
between different crops in biofuels production. Bioenergy productivity of land should be
the key element of a participatory program that intends to promote sustainable practices
4
of land management. Each energy crop has a unique energy yield that can be expressed in
British thermal units (BTU) per unit of land. The most efficient energy crop is the one that
supplies the largest value of energy per unit of land at the same amount of energy required to
produce the energy supplied. A better way to assess the bioenergy efficiency of energy crops
is by using the net energy value or net energy gain (NEG) of biofuels, which is the difference
between the energy produced and the energy expended in the stages of production. Net
energy gain also has an environmental meaning; it can be considered as the net quantity of
fossil fuel avoided during the production stages of biofuels. Crops that have large NEG also
have a lower carbon footprint2.
There are some studies that have dissenting opinions regarding the efficiency of biofu-
els. While Shapouri et al. (2002)[11] report 34% energy gain for corn ethanol, Pimentel
and Patzek (2005)[12] found 29% energy deficit; however, these studies either used state
aggregated yield data or did not include crop residues. Certainly they ignored phenological
parameters that vary from place to place and in general determine the growth and yield
of crops. Crop yield variation plays a significant role in the assessment of the net energy
balance. An assessment of the variability of climate and soil characteristics in the calculation
of NEG of corn-based ethanol has been made by Persson et al. (2009)[13]. The research
conducted in four regions of Southeast U.S. found that different soils and different climate
conditions impact consistently the net energy values.
However, all the previous studies are conducted in the realm of pure agronomy and
engineering and they all ignore the important economic agents, such as public decision
makers and landowners that make the ultimate decision on land use. Public decision makers
design agricultural policies that may affect land allocation choices made by landowners who
wish to maximize their future returns by choosing among alternative energy crops at their
present value.
2There would be a low positive emission of GHG during the production stage.
5
In the current debate, a continuum between the hard and the social sciences is missing.
Therefore, the literature suffers from the lack of analyses that are focused on policies aimed
at maximizing the efficiency of land use while reducing the environmental impact of the
production of biofuels.
1.3 Theoretical Framework
A simple way to calculate the environmental benefit of a cooperative outcome is to
simulate a voluntary program that aims to maximize the net energy produced from first
generation biofuel in Alabama. Maximizing the net energy from a mix of energy crops
consists essentially in an abatement of GHG associated with the production of biofuels.
A key assumption is that landowners who participate in this hypothetical program will
voluntarily seek an environmental improvement of their region. Farmers are also assumed to
have knowledge of past climatic events as a result of consultation with agricultural extension
personnel who advise them on how to be prepared for possible future weather scenarios.
Furthermore they will share information on soil productivity, management practices and
individual farms? characteristics with the experts. The extension personnel would use this
information and give appropriate technical advice on the most suitable energy crop to grow
under different climatic conditions and landowners? individual farms? characteristics. It is
also assumed that the program will include the adoption of sustainable farming techniques
resulting in the practice of appropriate crop rotations. Finally, participants will receive a
premium from the government if they decide to participate in the program and follow the
prescribed cropping recommended by the extension service specialists.
The government is represented by a Social Planner who seeks to maximize the social
welfare SWF = B(n ? a) + n?(x,a) ? TS(n ? a)3 that, in case of one pollutant (GHG), is
the environmental benefit plus net returns for farmers less total social costs of the policy.
3B is the environmental benefit deriving from the GHG abatement (a) of n farms. ?(x,a) is the net
return of an individual farmer that depends on production level (x) and abatement (a). TS is the total
social cost of the agricultural/environmental policy.
6
Baumol and Oates (1989)[14] suggest that when a tax mechanism cannot be used as a policy
instrument, as in the current and similar studies where the GHG emissions derived from
ILUC are difficult to measure, then a subsidy can produce the same first-best outcome.
The premium received by the farmer is twofold: it provides an incentive to maximize
the net energy produced in the area and also creates an abatement of GHG emissions that
will result in an environmental benefit shared by the entire community.
Because the objective of the social planner is to find the best crop pattern that would
maximize net bioenergy produced in the state as a whole, considering different weather
conditions, a classical general equilibrium framework4 based on supply and demand for crops
and biofuels, would not be the best tool for this purpose. Besides, the complexity of the
vertical structure of the market for biofuels that includes an intermediate market between
processors and fuel blenders would deserve a separate study specifically for the calibration
of the model if the ultimate goal of the research is an accurate analysis as in the current case
in Alabama.
Therefore, if the farmer has the ultimate decision on land use, even when this is affected
by other exogenous factors such as crop market prices, agricultural policies, or weather
conditions, it is plausible to study the problem using a partial equilibrium model, assuming
that the crop price taken by the farmers, under the hypothesis of perfect competition, clears
the market and that the price is the same as that paid by the biofuel processors.
In order to quantify the environmental value of the program it is convenient to compare
its impact (social optimization problem) to a real baseline scenario (self-optimization)5. To
isolate the value of the cooperative outcome, we assume that the social cost of the programs
4GTAP-BIO and MIRAGE are computable general equilibrium models and FASOM (Beach and McCarl,
2010)[15], a dynamic partial equilibrium model, are being currently used for land-use change analyses in
biofuel production. Besides the different resolution of these models that lie on large agro-ecological zones,
as far as I know, they do not explicitly maximize the net energy gain of biofuels simulating a cooperative
outcome of the economic agents.
5In the real scenario it is assumed that farmers made rational choices and they maximized their net return
excluding external environmental costs.
7
incentives (TS) is equal to the total agricultural subsidies provided by Direct and Counter-
cyclical Payment (DCP) program of the USDA for the state of Alabama in 2009. The
DCP program, a provision of the 2008 Farm Bill, provides payments from 2009 through the
2012 crop year (USDA, 2008)[16]. Consequently, we also assume that the voluntary program
simulated in the current study has the same time horizon of three years as the DCP program.
A more sustainable land use can be achieved optimizing the land productivity of biofuel.
Therefore, the social planner problem is that of choosing the optimal amount of agricultural
subsidies (to be given to the energy crop farmers) in order to maximize the Net Energy Gain
(NEG) of biofuel produced from energy crops. Under these circumstances, if ? is the amount
of land to be allocated to energy crop (i), and j represents the counties, then the objective
function to be maximized will be similar to a linear profit function summationtextij(EGi?ij ? ELi?ij).
EGi. EGi6 is revenue per unit of land expressed in terms of energy while ELi7 is energy
expended to produce biofuels expressed in BTU per unit of land. The optimum-optimorum
is reached when the objective function is maximized. In fact the optimal amount of land
that maximizes the production of green energy, by symmetry, minimizes fossil fuel (EL) used
to produce biofuels and the GHG emissions associated with the whole process.
A simple way to simulate this decision-making process that includes climate information
is to use a recursive discrete stochastic programming (DSP) algorithm as formulated by
Rae (1971a; 1971b)[17][18]. The advantages of using this technique are several. A general
algorithm in a simple algebraic framework converges to the same solution obtainable as do
more complex algorithms of dynamic programming. Moreover, using the DSP approach
simplifies the econometric calibration of the mathematical model. Consequently, a holistic
analysis (from a single county to the whole state) would produce results that are more
6Ebiofuel
i +E
coproduct
i is the energy content of the biofuel produced from crop i and from the crop residue
(biomass) expressed in MMBtu/acre
7Efarm
i +E
trip
ij +E
process
i is the total energy consumed during the different stages of production such as
energy used for farming operations, energy used to transport the crop from the farm to the biofuel processor
plant and the energy spent to convert the crop in ethanol or oil. All these energy expenditures are fossil fuel
based and expressed in MMBtu/acre.
8
realistic and robust with respect to the outliers8. Furthermore, the multistage characteristic
of models of the type proposed provides the analyst with knowledge of the transitional phases
of the system in the sequential states of nature.
Formally, if we assume the existence of a probability space (?,?,?) and a random
state variable (?t ? ?) that defines a climatic state of nature at time t, ? is a ?-algebra9
collection of all weather events and ? is a likelihood function that measures the probability
?(S) ? [0,1] of the occurrence of an element s ? ?, the Social Planner?s multistage stochastic
problem for optimal land productivity can be formulated as
max
?ijt?0;sijt?0
nsummationdisplay
i=1
Jsummationdisplay
j=1
NEGi?ij0 +E?t
nsummationdisplay
i=1
Jsummationdisplay
j=1
3summationdisplay
t=1
NEGit(?t)?ijt(?t) (1.1)
subject to
nsummationdisplay
i=1
?ij0 ? bj (1.2)
?ijt ??ijt?1 ? 0 (1.3)
di?ij0 ? 12
nsummationdisplay
i?=1
?ij0qii??i?j0 ?sij0 ? piyij0?ij0 (1.4)
di(??ijt ??ijt?1)? 12
nsummationdisplay
i?=1
(??ijtqii??i?jt ??ijt?1qii??i?jt?1)??sijt ?
pi(yijt??ijt ?yijt?1?ijt?1)?sijt?1
(1.5)
nsummationdisplay
i=1
Jsummationdisplay
j=1
sijt ? TS (1.6)
with reference to the i major crops (biofuels), corn (ethanol), cotton (cottonseed oil),
peanuts (peanut oil) and soybeans (soybean oil) grown in county j, NEGi is the net energy
gain of the biofuel produced from energy crop i, estimated as difference between the energy
content of the biofuel (EGi) and the energy loss (ELi) during the stages of production (see
8Optimal land solutions will be produced for each county in the sample.
9Given a set A = {0,1,2}, a possible ?-algebra collection of A will be a set B =
{{0},{1},{2},{0,1},{0,2},{1,2},{1,0},{2,0},{2,1},{0,1,2},{0,2,1},{1,0,2},{1,2,0}} or any other sim-
ilar combination of elements of A.
9
Appendix B for technical details). The state variable ?t refers to the weather, ?ijt10 is the
amount of land devoted to growing energy crop i in the state of nature ?t expressed in acres,
sijt is a policy variable, optimal subsidy (US$) given for energy crop i in the weather state ?t
for county j; yijt is the stochastic yield (lbs./acre) of crop i in county j in the weather state
?t; bj is a vector of cropland available in the county to be allocated to energy crops (acres);
and di and qii?11 are linear and quadratic calibration parameters, respectively, correspondent
to the linear and the quadratic coefficient of a quadratic cost function that will be discussed
in Section 1.5. The vector pi consists of cash price for each crop i (US$/lbs.), ? is a discount
rate, TS is the total cost of the program and E?t is the mathematical expectation operator.
Constraints (2) and (3) are first period and intermediate constraints related to the land
fixed resource. This inequality guarantees that the land used for biofuel production will not
exceed the total cropland existing in each county, avoiding undesired ILUC emissions from
conversion of forests and pastures to crop land. Constraint (4) is a behavioral constraint that
implicitly assumes perfect competition and rational choices made by farmers who maximize
their profit. In fact, if the total cost (di?ij0 ? 12summationtextni?=1 ?ij0qii??i?j0 in US$)12 is less than the
revenue (piyij0?ij0 in US$) then the farmer is making a profit. The contrary is true if the
total cost exceeds the revenue so that a compensation sij0 in US$ would be given to the
farmer for his or her loss. Constraint (5) replicates constraint (4) in the transitional phases.
It should be noticed that the compensation is a specific subsidy for crop i for the particular
county j that maximizes the NEGit in the state of nature (?t) resulting in a first-best
agricultural policy. Because subsidy and land are endogenous variables, their simultaneous
solution serves to quantify the cooperative outcome that is the purpose of this study.
10The land choice variableis function of the weather state, therefore, correctly should be written as ?ijt(?t),
however the functionality relationship (?t) has been omitted for convenience. The same convention is made
for the other endogenous variable sijt and for the stochastic yield yijt.
11qii? is a (4 x 4) positive semidefinite matrix where i? is the index i transposed. This matrix will have the
crops as rows and columns.
12This is a cost function that is quadratic in ?. In a scalar notation with respect to only one crop it
would have been written as d?? 12q?2 where d and q are linear and quadratic coefficient of the cost function,
respectively.
10
The objective function (1) is a sequential probability model that can be represented as
the tree diagram in Figure 1, where the expected value of the net energy gain after 3 years,
assuming, for example, the sequence of states of nature 1?2?1,13 would be ?1NEG1 +
?1?2NEG2+?1?2?114NEG1. The ? parameters are the probabilities of the occurrence of each
single state of nature. Halter and Dean (1971)[19] specify six different weather conditions
and index them from ?poor? to ?very good?. The probability of occurrence of each of these
conditions may be subjectively assessed by the decision maker (Rae, 1971b)[18].
A scientific approach for computation of probabilities based on history, that would avoid
ad-hoc assessments, can be done under the assumption that climatic states of nature occur
as a sequence of martingales and that the weather can be separated into categories that
comprise a finite Markov chain. Under this assumption, the climatic state variable is a
member of a discrete set K(1,2,...,kt) and the stationary probabilities are determined by
?ij = Pr(?t+1 = j|?t = i).
NEG0
NEG1
?1
NEG1,1
?1?1
NEG1,1,1?1?1?1
NEG1,1,2?1?1?2
NEG1,1,3?1?1?3
NEG1,2
?1?2
NEG1,2,1 ? ?1NEG1 +?1?2NEG1,2 +?1?2?1NEG1,2,1?1?2?1
NEG1,2,2?1?2?2
NEG1,2,3?1?2?3
NEG1,3
?1?3 NEG1,3,1?1?3?1
NEG1,3,2?1?3?2
NEG1,3,3?1?3?3
NEG2...?2
NEG3...
?3
Figure 1.1: Probability Model
13This sequence would be an element of the ?-algebra set ?.
14?1?2 and ?1?2?1 are joint probailities.
11
Alabama?sweather patterns areaffectedby ElNi?noSouthernOscillation Phases (ENSO),
and thus are very suitable for a scientific assessment of the probabilities. In fact, the Na-
tional Oceanic and Atmospheric Administration (NOAA) labels a particular year ?El Ni?no?
or ?La Ni?na? if the Oceanic Ni?no Index 3.4 hits or exceeds the bounds of +0.5 C or -0.5
C, respectively, for five consecutive overlapping seasons, and ?Neutral? otherwise. In this
study, there is no distinction between weak and strong ENSO events.
Under this assumption ENSO events from 1950 to 2009 represent an observed first
order Markov chain that is also the simplest case for the estimation of the transitional
probabilities. Prof. James D. Hamilton (2010)[20], in a personal communication, suggested
that if the weather state vector ?t can take values ?El Ni?no?, ?La Ni?na?, or ?Neutral?,
respectively, in a given year t, then when the transitional probabilities are stationary15 the
likelihood function of the transition matrix is given by
L(?ij) =
50productdisplay
t=1
3productdisplay
i,j=1
?nij(t)ij =
3productdisplay
i,j=1
?nijij (1.7)
where nij is the number of times that an ENSO event in state i was followed by an
ENSO event in state j. Taking the log of function (1.7) and maximizing the log-likelihood
function with respect to the probabilities under the adding-up restrictionsummationtext3j=1 ?ij = 1, leads
to the maximum likelihood estimates of the matrix ??ij = nijsummationtext3
j=1 nij
.
Anderson and Goodman (1957)[22] show the consistency of this result in addition to
providing a log-likelihood ratio test for homogeneity. In fact, since a second order Markov
chain is always reducible to a first order chain, the authors suggest testing the null hypothesis
that the chain is first order against the alternative that it is second order by calculating the
log-likelihood ratio as LL =summationtextmj=1 ?2?j = 2summationtext3i=1summationtext3j,k=1 nijk(log??ijk ?log??jk).16
15For an introduction to finite Markov Chains and their properties see H?aggstr?om (2002)[21].
16See Anderson and Goodman (1957)[22], p. 101. The asymptotic distribution of ?2?j is ?2 with (m?1)2
degrees of freedom where m is the number of states. Consequently, summationtextmj=1 ?2?j ? ?2[m(m? 1)2] where in
the current study m = 3 states and the degrees of freedom become 12.
12
In the current study, the test provided the result of LL = 0.663 < 21.026?2(12) at 5%
level of significance failing to reject the null that the ENSO phases are a first order Markov
chain. The chain converges to the steady state after the fourth year and the stationary
transition probabilities of having El Ni?no, La Ni?na, or a Neutral event are 0.33, 0.30 and 0.37,
respectively. According to these figures, the deterministic equivalent of the probability model
(1) becomes: maxsummationtext4i=1summationtextJj=1(NEGi?ij0 +0.33NEGi?ij1 + 0.30NEGi?ij1 + 0.37NEGi?ij1 +
0.09NEGi?ij2 + 0.099NEGi?ij2 + 0.111NEGi?ij2 +...+ 0.050653NEGi?ij3).
1.4 Data Sources
Economic data used in this study for the year 2009 are available at the Economic
Research Service of the United States Department of Agriculture (ERS-USDA). The total
agricultural subsidies are based on a projection for the year 2009 made by the Environmental
Working Group (EWG, 2011)[23] and the USDA Census of Agriculture for the state of
Alabama in 2007 (United States Department of Agriculture). A discount rate of 3.29% is
the average return on assets from US agricultural income as suggested by the Agricultural
and Applied Economics Association (AAEA, 2000)[24]. The observed land allocations in the
base year are part of the National Agricultural Statistics Service (NASS) database of the
USDA 2009 as well as the historical yields of the four major crops modeled. To capture the
yield response to the ENSO phases, the crop yields time series, from 1950 to 2009, have been
detrended using autoregressive linear techniques and brought to the 2009 level for all the 38
counties considered in this study. This is a common procedure that was implemented in a
previous study that analyzed the irrigation profitability of corn in Northern Alabama under
different ENSO scenarios (Novak et al., 2008)[25] . Detrending the yields serves essentially
as a mitigation of market and agricultural policies effects (as, for instance, the peanut quota
system) that would confound the estimation of crop supply responses to climate and soil
variability. Therefore, the average yields used under the three different states of nature can
be plausibly considered as historical yields that were achieved as a response to pedological
13
characteristics of each county. Because data on biomass crop residue are not available,
simulated data obtained by the Soil and Water Assessment Tool (SWAT) supported by the
Agricultural Research Service of the USDA have been employed. Details on the simulation
are available in Appendix C.
Table 1.1 reports the economic data andthe estimated Fossil FuelEnergy Ratio(FER)17,
that is the net return in terms of bioenergy of one unit of fossil fuel energy spent.
Table 1.1: Economic Data and Estimated Fossil Fuel Energy Ratio
cash pricea accounting costsb Total Subsidiesc FERd
corn 4.15 294.43 10,418,808 1.18?0.03
cotton 0.538 521.14 91,407,357 1.36?0.03
peanuts 0.222 513.67 12,471,234 1.78?0.05
soybeans 10.4 155.38 8,873,174 2.76?0.06
aCorn and soybeansare expressed in US$/bu. bAccounting costs are expressed in US$/acres.
c Projection in 2009 of the total subsidies are in US$ and refers to the all state of Alabama.
Source: Environmental Working Group. dFER has been estimated by the author according
to the guidelines reported in Appendix C and refers to average values ? the standard
deviation of the ENSO response.
1.5 Econometric Calibration of the Model
The reason for using a discrete mathematical program to solve for optimal land alloca-
tion lies in the normative nature of this study. However, a normative linear mathematical
programming procedure can produce solutions that would be far from reality if it does not
allow for spatial variation18 of crop yields. Such solutions may show some counties to be
overspecialized19 in energy crops that would easily maximize the objective function and sat-
isfy the constraints imposed to the model. A possible solution from linear models, produced
by design, is to have the whole cropland of the state of Alabama allocated to soybeans. This
17FERi = EGi
ELi18
Spatial variation would be a consequence of soil heterogeneity that is unobserved. This would produce
different yields for the same crops across the counties.
19Overspecialization is a term used by agricultural economists to refer to an economic solution commonly
called the corner solution.
14
will be the result of soybeans being the energy crop with the best fossil fuel energy ratio
among the first generation biofuel produced in Alabama.
To overcome the problem of overspecialization, Howitt (1995)[26] and Paris and Howitt
(1998)[27] introduced positive econometric modeling characteristics into the mathematical
programming framework. The positive mathematical programming approach is a procedure
that consists of three steps. First, the dual variable ?, marginal profit of land, is calculated
from a linear program of profit maximization where the production level of the farm is
forced to favor the observed production level in the base year. Next, the variable ? that
is, by symmetry, the opportunity cost of land, is then added to the total observed costs of
the firm to estimate the linear and non-linear parameters of a cost or supply function20 that
serves to capture unobserved farm characteristics; these characteristics can be heterogeneous
land quality or the adoption of non-linear technologies that are unknown to the analyst and
determine the observed land allocation in the base year (Howitt, 1995)[26]. The final step
of PMP is to write a calibrated model for agricultural policy analyses that includes the
recovered cost or supply function and would reproduce the base year land allocation as its
baseline.
Heckelei and Wolff (2003)[28] extend positive mathematical programming to the case of
a cross sectional study and examine the methodology from the point of view of an econo-
metrician proposing a calibration procedure that avoids the first step of PMP. I refer now
to this procedure as Econometric Mathematical Programming (EMP); that is the procedure
that has been used to calibrate the decision model of this study.
Let us consider the following profit maximization problem for farmers in matrix notation
max
x?0
p??x?c??x+s??x?d??x? 12?x?Q?x
subject to ?A?x ? b
(1.8)
20Generally a quadratic cost function.
15
Considering only the land as the sole limiting resource, the expected level of energy crop
production is ?x = ?y??21 where p is the cash price of the energy crop, c is a vector of variable
accounting cost that excludes the rent of land, s represents direct payments received by the
government, d and Q are the linear and non-linear coefficient of a quadratic cost function22,
and ?A is the expected matrix of technical coefficients, which in this case would be equal
to tildewidesty?1 and have the dimension of acres/lb23. Q is a (n x n) positive-semidefinite matrix
given the quadratic functional form and its symmetry can be imposed through a Cholesky
factorization in order to ensure the right curvature of the cost function; as a consequence,
the number of parameters in the matrix to be estimated is n(n+1)/2.
From (1.8), the Lagrangean function, will be
L(?x,??) = p??x?c??x+s??x?d??x? 12?x?Q?x+??[b? ?A?x] (1.9)
ignoring slackness conditions for simplicity. From the first order conditions it follows
that
?L(?x,??)
??x = p?c+s?d?Q?x?
?A??? = 0
? ?x = Q?1(p?c+s?d? ?A???)
(1.10)
?L(?x,??)
??? = b?
?A?x = 0 (1.11)
Substituting the right-hand side of (1.10) into (1.11) and solving for ?? yields
?? = (?AQ?1?A?)?1[?AQ?1(p?c+s?d)?b] (1.12)
21?y is the yield expressed in lb/acres and ?? is the land expressed in acres. The tilde sign indicates the
expected value. As always the deterministic equivalent of ?y = 0.33yElNi?no + 0.30yLaNi?na + 0.37yNeutral.
The same convention is valid for the expected values of ?x, ?? and ?A.
22Heckelei and Wolff (2003, p. 32)[28] replace p ? c with a vector of gross margin gm, in this case because
I want to include also subsidies s in the calibration procedure I did not use the gross margin specification
leaving the model transparent for the sake of clarity.
23This simplification is a consequence of having only the land as a limiting factor, see also Paris (2011)[30]
p. 401
16
Plugging (1.12) into (1.10) will lead to the expected optimal value of energy crop activity
level ?x as a function of the exogenous parameters of the model
?x = Q?1(p?c+s?d)?Q?1?A?(?AQ?1?A?)?1[?AQ?1(p?c+s?d)?b] (1.13)
In case of a change in crop price, the response of the expected optimal supply level will
depend on the full information of the Q matrix that encompasses the full set of crops.
??x
?p = Q
?1 ?Q?1?A?(?AQ?1?A?)?1?AQ?1 (1.14)
For ill?posed24 problems, the entropy econometrics criterion (Golan et al., 1996)[31] can
result in a solution for estimating the unknown parameters that calibrate the decision model.
Maximum entropy estimation is a statistical inference that allows to derive probability dis-
tributions on the basis of partial information. This technique provides the best unbiased
estimator possible on available information (Jaynes, 1957)[32].
Another factor that would favor the entropy criterion over other estimation techniques is
the stochastic nature of the model andprior informationof the ENSO transition probabilities,
which is the ideal case for the implementation of the generalized maximum entropy ? cross
entropy econometric formulation (GME?GCE).
The idea behind the entropy estimation is to find a set of posterior distributions of
support points of the topological space of parameters25 that satisfies the sample observations
and have the least distance to a prior distribution of the supports. Such support points can
be identified with the moments of the population of parameters. Although there is no limit
on the number of supports that can be employed, choosing two support points is equivalent
24A problem is ill-posed if it has negative degrees of freedom, that is when the number of parameters to
be estimated exceeds the number of observations available.
25In case of well?posed problems support points can be defined also for the unknown disturbances. For
further details see Golan et al. (1996)[31] chap. 6, and for an application to well?posed problems in
Mathematical Programming see Paris (2001)[33] p. 1052 and Heckelei and Wolff (2003)[28] p. 33.
17
to specify the mean and variance of the sample of parameters that are going to be estimated
and the results can be quite satisfactory26.
To avoid subjective specifications of the support points, Heckelei and Wolff (2003)[28]
suggest using out of sample land elasticities of the gross margin. However, such prior infor-
mation is not always available. Therefore, in this case an alternative method would be to
use the prior price elasticities of supply. In fact, multiplying both sides of (1.14) by the ratio
of the average crop price to the average state production will yield
??x
?p ?
bracketleftbigg ?p
??xo
bracketrightbigg?
=
bracketleftBig
Q?1 ?Q?1?A?(?AQ?1?A?)?1?AQ?1
bracketrightBig
?
bracketleftbigg ?p
??xo
bracketrightbigg?
27 (1.15)
Expression (1.15) is the matrix of own and cross price elasticities of supply. The range
of these elasticities, previously estimated by Shumway (1986; see Appendix A)[29], can
replace uninformative priors of the support points. The simultaneous estimation of (1.15)
and (1.10) allows recovery of missing information of the parameters of the quadratic cost
function and the dual variable ?. The recovered vectors ??, d and Q, that calibrate the social
planner model, capture individual farm characteristics and the opportunity cost of land
that the program?s participants share with the extension specialists during the program?s
participatory activities to obtain the advice on best farming practices28. Details on the
entropy formulation are available in Appendix A.
The base year land allocations and the estimated expected opportunity costs of land for
each county are reported in Table 1.2, while the parameters of the cost function estimated
with the entropy criterion are reported in Table 1.3.
26See Golan et al. (1996)[31] p. 139 for an extensive explanation on the number of supports.
27??? is the Hadamard entrywise product: given two matrices A,B ? R(m?n) then A?B = Aij ?Bij.
28d, Q and the expected opportunity cost of land that is affected by the climate (ENSO) capture infor-
mation such as farmers risk aversion, machinery failure, plant disease and non linear technologies that are
unknown to the analysts (see Howitt, 2005)[26].
18
Table 1.2: Observed Land Allocation and land opportunity costs (Base Year 2009)
County Crop Area (acres) Land Opp. Cost
corn cotton peanuts soybeans ??a (US$/acre)
Autauga 5,100 1,900 5,000.17
Baldwin 4,600 8,350 16,200 23,600 618.81
Barbour 2,800 3,280 3,797.00
Blount 800 12,917.13
Calhoun 1,100 1,700 4,200 2,484.80
Cherokee 2,200 5,910 23,700 617.84
Coffee 5,600 12,700 7,800 6,800 1,477.99
Colbert 16,400 2,700 22,900 448.75
Conecuh 900 3,300 2,700 3,711.08
Covington 2,500 12,600 6,400 2,200 2,563.82
Cullman 2,400 5,300 2,136.71
Dale 2,800 9,400 9,300 1,835.92
Dallas 4,050 4,450 3,800 9,100 1,308.92
DeKalb 10,900 10,800 878.40
Elmore 9,110 2,200 4,273.24
Escambia 4,700 12,100 9,600 11,900 1,018.05
Etowah 1,800 5,500 2,058.72
Fayette 1,600 6,371.88
Geneva 6,200 22,600 16,300 6,600 1,063.94
Henry 6,000 14,200 18,700 1,175.21
Houston 2,600 19,400 33,500 7,600 945.54
Jackson 18,600 31,800 289.58
Lamar 1,200 8,528.53
Lauderdale 20,200 10,800 21,900 266.23
Lawrence 34,700 4,300 23,900 77.39
Limestone 23,100 11,000 63,900 0.00
Macon 2,300 2,300 4,240.89
Madison 18,500 18,800 45,800 41.83
Marshall 3,000 6,000 1,886.71
Mobile 6,900 2,300 4,191.83
Monroe 1,800 16,000 5,780 4,200 2,326.27
Morgan 3,700 6,900 1,669.59
Pike 4,900 4,100 3,200 1,500 2,048.03
Shelby 700 2,500 14,854.04
Sumter 800 11,328.46
Talladega 7,250 2,810 10,000 1,205.51
Tuscaloosa 2,650 5,000 2,210.37
Washington 600 2,250 5,527.41
The opportunity cost of land is solution of the entropy econometric model and the value
reported refers to the expected value and is calculated as ??.
19
Table 1.3: Estimated Q and d matrices
Q corn cotton peanuts soybeans
corn 0.0034 0.0137 -0.0018 0.0041
cotton 0.0137 0.0549 -0.0074 0.0166
peanuts -0.0018 -0.0074 0.0010 -0.0022
soybeans 0.0041 0.0166 -0.0022 0.0050
d 48.80 1,562.87 -184.36 -181.03
Notes: Quadratic and linear coefficients of the cost function esti-
mated with the entropy criterion.
1.6 Results and Discussion
Before revealing the results, it would be convenient to summarize the sequential steps
that were followed to conduct hypothesis tests. First, calibration of the social planner
model was conducted using the econometric entropy criterion with respect to the observed
land allocation of the 4 major crops grown in 38 Alabama counties in 2009. Secondly, the
calibration allows recovery of the expected opportunity cost of land and provides a quadratic
cost function that captures unobservable farm information that explain the land allocation
chosen by the landowners in the base year. Lastly, the recovered function is used with a
linear revenue function as a constraint in the stochastic model that maximizes the net energy
produced in the state. The reason for the behavioral constraint was to include the program?s
incentives and impose the assumption of a perfectly competitive market.
The central hypothesis is that the voluntary program would indeed increase the pro-
duction efficiency of biofuels while reducing carbon emissions. The impact evaluation of the
program can be performed by calculating the Value of Stochastic Solution (VSS).
Birge (1982)[34] defines VSS as the benefit of considering uncertainty during the decision
process. This value can be calculated as the difference between the long run solution of the
stochastic recursive problem (1.1) and the expected value solution (EVS) of a deterministic
problem. In the latter case, the optimal decision on land allocation is made individually and
20
it is based on average value of yields ignoring advice provided by the climate experts of the
Extension Service. In mathematical notation
VSS = max
x,s
{Ey(?)[NEG(?(y(?)),y(?)}?Ey [NEG(?o(?y),y)] (1.16)
Let us make this point clear and demonstrate how this concept can be exploited to
support the central hypothesis test of this study. The first term of (1.16) is the long run
solution29 of (1.1) and represents the impact of the program. This is calculated as the sum
over the all modeled counties of the product of the net energy value of each single energy
crop (NEGi) by the optimal land allocations as reported in Table 1.4. The second term in
(1.16) can be calculated as the sum of the product of NEGi by the observed land allocations
in 2009 as reported in Table 2 that assumes farmers do not participate in the program and
make individual decisions on land use. As a result, if all farmers were to participate in the
program, a total net energy gain of 7.05 Trillion BTU obtained from the optimal mix of
biofuels produced in Alabama would occur. This value in percentage terms corresponds to
an increase of 208% in net energy compared to the baseline. This result is not surprising
considering that soybeans biodiesel has a net energy value of almost 300%. Figure 1.2
provides a graphical illustration of the response of (1.16) to climate phases in terms of net
energy and carbon emissions.
For example, Figure 1 illustrates 2730 possible ENSO sequences in 3 years. If we assume
the possible sequence El Ni?no - La Ni?na - Neutral, then the Blue curve in figure 1.2 is
the recursive problem solution (RPS) of (1.1). The solution depicts the net energy gain
(carbon emissions) from the biofuel produced in the entire state if farmers participated in
the voluntary program. The red curve by contrast, represents the net energy produced
(carbon emissions released) in the baseline. The green curve is the difference between the
previous curves and represents the impact of the program expressed in terms of net energy
29The long run solution is calculated as the sum of the expected land allocation over the time horizon
modeled divided by the number of years, see Birge and Louveaux (1997)[35], p. 9 and pp. 137-152.
3027 possible sequences are determined as 3 states of nature raised to 3 years.
21
Table 1.4: Long Run Expected Optimal Land Use and Subsidies
County Crop Area (acres) Direct Paymenta
corn cotton peanuts soybeans ?s (US$/acre)
Autauga 7,000 626,118.71
Baldwin 38,508 14,242 12,330,250.00
Barbour 6,080 455,189.28
Blount 17 6 777 34,181.71
Calhoun 7,000 2,014,072.00
Cherokee 22,267 8,875 668 13,775,560.00
Coffee 402 495 32,003 7,986,210.00
Colbert 1,760 6,087 33,802 3,850,806.00
Conecuh 6,900 40,153.62
Covington 4,601 15,607 3,492 1,422,224.00
Cullman 5,390 2,234 76 5,290,972.00
Dale 8,907 1,209 11,399 5,080,161.00
Dallas 14,719 1,229 5,453 7,894,680.00
DeKalb 735 1,470 19,495 1,663,674.00
Elmore 693 1,111 9,506 1,301,411.00
Escambia 24,512 13,788 9,051,999.00
Etowah 5,110 2,118 72 4,885,541.00
Fayette 133 41 1,426 270,041.54
Geneva 12,208 39,492 3,792,075.00
Henry 10,160 1,866 26,247 6,635,935.00
Houston 28,561 30,387 4,230 6,059,995.00
Jackson 686 490 49,224 1,098,576.00
Lamar 1,200 0.00
Lauderdale 1,216 1,918 49,213 2,342,874.00
Lawrence 822 159 61,919 1,280,461.00
Limestone 11,490 1,914 83,914 637,598.30
Macon 3,031 791 778 2,545,430.00
Madison 2,355 3,935 76,811 1,383,760.00
Marshall 4,525 4,475 1,664,700.00
Mobile 9,200 63,161.29
Monroe 10,279 17,501 4,141,769.00
Morgan 7,420 223 2,957 3,327,253.00
Pike 13,700 3,254,491.00
Shelby 194 3,006 361,894.47
Sumter 11 788 4,442.25
Talladega 20,060 7,044.39
Tuscaloosa 5,583 1,991 76 4,927,116.00
Washington 482 2,368 106,948.61
a ?s is the expected value of the optimal direct payment in each ENSO scenario and is
calculated as summationtexti si?, where s is the (4 ? 38 ? 3) vector of optimal subsidies and ? is the
(3?1) vector of Markovian ENSO probabilities.
22
Total Energy Gain
El Ni?no La Ni?na Neutral
Tr
illio
nB
TU
2
4
6
8
10
12
Total Carbon Emissions
El Ni?no La Ni?na Neutral
Millio
nM
etr
ic
To
ns
?50
0
50
100
150
200
ENSO Sequence
? Solution of the voluntary program (RPS)
? Baseline Solution (EVS)
? Impact of the program (VSS)
Figure 1.2: NEG and CO2 emissions in the transitional phases
and green house gas emissions. The chart on the right presents negative values of the VSS
related to total carbon emissions. This result indicates that such a program would reduce
emissions in each ENSO scenario.
The model, however, does not consider the complete life cycle of biofuels because further
reductions that occur when biofuel is substituted for fossil-fuel in the transportation sector
depend strongly on the degree of blending. The optimal degree of blending of alternative
fuels is beyond the scope of this research. However, Sheehan et al. (1998)[36] argue that if
the Chicago metropolitan area school transportation system were to use biodiesel B2031 to
fuel bus engines, then a further 15.66% emissions reduction would be achievable.
The program, in terms of reduction of GHG emissions, could result in 51.84 million
metric tons of CO2 in the long run. This figure in percentage terms would consist of a 26%
GHG reduction compared to the baseline scenario. As illustrated in Figure 1.3, the majority
of energy gains can be attributed to a hypothetical increase in acreage of soybeans and
31B20 is a mixture of 20% seeds crop oil and 80% petrol-diesel that is commonly used in the U.S.
23
peanuts, which are crops with a high percentage of oil content assuming that the average
value of peanut yields achievable in Alabama produce an oil yield that is more than twice
the oil yield from soybeans. However, the use of large quantities of pesticides in production
stages lowers the fossil-fuel energy ratio of this crop, in this case making peanuts the second
best choice after soybeans. Because peanuts could be the crop with the strongest response to
the program (the total acreage in the state could almost double) future research in genetics
can aim to design an engineered crop that needs less chemical inputs, increasing the FER.
In this case, peanuts may become the best choice, and further reduction in carbon emissions
may be achievable.
Cellulosic ethanol would be certainly the optimal solution in terms of FER, but given
the economic limitations of production of second generation biofuels (Khanna, 2008)[37],
at the moment biodiesel seems to be the best alternative option in Alabama. This option
should not be discarded if we take into account the fact that in 2008, total consumption
of petrol-diesel in the state was 26.8 million barrels, making diesel the second most used
commercial fuel. Considering that diesel is also the first fuel used for farming activities,
production expansion of biodiesel can be viewed as an opportunity for development of the
rural areas of the state. Positive macroeconomics effects of the expansion of biodiesel have
been examined by Van Dyne et al. (1996)[38] in agricultural areas of Missouri that are
similar to the areas studied in this research.
To capture the effect of the technical support provided by extension personnel to farmers,
the analysis is conducted considering only the effect of climate and soil, ceteris paribus.
Because crop price and average farming costs are held constant for the three years? time
horizon, and the policy variable is tied to the estimated federal direct payments received by
farmers in 2009, there is no change in welfare for landowners. In other words, the social
planner makes a redistribution of the 2009 total level of subsidies towards the most efficient
energy crops, reducing the opportunity cost of land that is borne by the participants. In this
setting the incentives given to the farmers would represent a first-best agricultural policy.
24
Corn
223150
Cotton
220830
Peanuts
136110
Soybeans
373300
Observed Acreage ? Baseline 2009
Corn
213665
Cotton
43251
Peanuts
270768
Soybeans
425706
Long?Run Optimal Acreage
Corn
10418808
Cotton
91407357
Peanuts
12471234
Soybeans
8873174
Agricultural Subsidies ? Baseline 2009 US$
Corn
53864450
Cotton
38425870 Peanuts
26766350
Soybeans
4113903
Estimated Direct Payments US$
Figure 1.3: Land and Agricultural subsidies in the baseline and optimal scenarios
25
A natural question would be to ask how a new policy that incentivizes the farmers towards
more sustainable land use affects the crop price in the next period? To answer this question,
further assumptions that would increase the complexity of the model should be considered.
For example, if one assumes that crop prices are not Markovian32 then direct payments
can create pecuniary externalities, resulting in an increase in food prices that will impact
economic welfare. However, questioning the ethics of producing biofuels in place of foodcrops
as well as the actual federal system of the agricultural subsidies is not the main objective of
this research. The economic welfare implications of participatory programs of optimal land
management may be the objective of future studies.
On the other hand, results achieved through this research seem clear. Integrated and
participatory decisions made by landowners and the government that create incentives to-
wards more efficient use of land can potentially create an environmental benefit, resulting in
a consistent reduction of carbon emissions. Carbon reductions, besides contributing to the
goal of the current state energy program and the RFS, would increase social welfare by im-
proving environmental quality. In addition, expansion of the biodiesel industry in Alabama
may have macroeconomic implications not accounted for the current paper and needs to be
explored in future research.
1.7 Conclusions
The Renewable Fuel Standard, a key provision of the Energy and Independent Security
Act (2007), aims to expand the production of biofuels to improve energy efficiency and
decrease the greenhouse gas emissions in the US. The effectiveness of this regulation is being
hotly debated by the scientific community, which has some concerns about carbon emissions
from direct and indirect land-use change (ILUC). Given the uncertainty associated with
32Under the non-Markovian assumption, direct payments do have an impact on crop prices in the next
period. In contrast, under the Markovian assumption of two price regimes (low and high) the cause of
switching between the two regimes is unknown. In this case, the state variables of the model respond to 24
states of nature (4 crops ? 2 price regimes ? 3 weather states). The probability model (1.1) would consist
of 324 possible states at the end of the modeling period.
26
estimation of ILUC factors, some authors are also skeptical about the effectiveness of carbon
tax and cap-and-trade policies when these factors are considered in designing regulations.
A valid alternative may be to design policies that can create incentives for sustainable land
use in biofuel production.
In this article a mathematical model was developed that simulates a voluntary agricul-
tural program to increase land use efficiency in the production of first generation biofuels in
Alabama. Under the common goal to reduce the carbon emissions in the state, landowners
who participate in this hypothetical program can follow advice given by extension specialists
on land use best practices under climate uncertainty. Participants would receive a direct
payment from the government if they agree to follow the recommendations and plant the
energy crop that provides the best energy gain given the soil and climate conditions of the
farm. Participatory decisions were simulated through an original dynamic partial equilib-
rium model based on a discrete stochastic programming algorithm where land allocations and
agricultural policy variables are endogenized to maximize net energy returns from biofuels
that can be produced in Alabama. The model was calibrated using econometric mathe-
matical programming techniques that involve the entropy criterion in order to recover the
behavior of the farmers in Alabama.
Although the analysis is based on first generation biofuels and is restricted to the agri-
cultural crop land area, given the current economic limitations of production of second
generation biofuels, simulation results show an increase of 208% in the net energy gain from
a mix of biofuels produced in the state that correspond to a carbon emission abatement of
26% if all farmers were to participate in the program. Environmental quality improvements
derived from the implementation of this program may provide external benefits that further
increase the social welfare, and produce a contribution to meet the goal of the current state
energy programs. Specifically, at the current level of agricultural subsidies ($123.2 M) in the
form of incentives to farmers to participate in the hypothetical voluntary program, it can
27
be concluded that a more efficient use of crop land use would result in a more cost-effective
subsidy program.
Given the flexibility of the model, future high resolution studies can extend the analysis
to all the counties in the United States to simulate the economic welfare implications of
participatory decisions that induce a more sustainable use of land in biofuel production.
28
Chapter 2
A Stochastic Frontier Analysis
to Examine Research Priorities for Genetically Engineered Peanuts
enc-56enc-56enc-56
2.1 Introduction
Peanuts (Arachis Hypogaea L) are the seeds of a legume that has high nutritional ener-
getic values and represents one of the major commodities produced worldwide. In 2009 the
United States, with a production of 1.67 million metric tons, was the fourth largest world
producer after China, India and Nigeria (FAO, 2011)[46].
The highest acreage of peanut planting in US was reached in 1943 with 3.5 million acres.
From the end of World War II until 1981, the land devoted to peanut production had been
restricted by acreage allotments to a limit of 1.5 million acres annually. After that period,
poundage quotas replaced the acreage allotments reaching a new peak of 2.04 million acres
in 1991, and subsequently, peanut acreage steadily declined to an average of 1.49 million
acres (Dohlman et al., 2004)[47]. Despite the decline in production in several southeastern
counties of the United States, peanuts, for several of these counties, still represent from 50%
to 70% of the total agricultural income (Fletcher, 2002)[48].
Given the high oil content of peanuts (Duke, 1983)[43], this crop may be an attractive
choice for alternative fuels in a bio-based economy. Therefore, the recent decline in domestic
peanut production may be offset if the demand for peanut oil increases to meet the rapid
growth of biodiesel consumption (Davis, 2010)[1]. Therefore, peanuts are a commodity crop
that deserves particular attention.
29
An important issue that threatens the productivity of peanuts is the susceptibility of
this cultivar to several types of fungal pathogens. In particular, Aspergillus (flavus, fumiga-
tus, parasiticus), a group of fungi responsible for producing mycotoxins and aflatoxins which
have serious consequences in food safety. Specifically, A. flavus, the most dangerous hepa-
tocarcinogen known to man, has been associated with an increased risk of liver cancer and
is commonly found in peanuts (Hedayati, et al., 2007)[49]. Although the rates of primary
liver cancer are highest in places where peanuts are a mainstay in the diet (e.g. Asia and
Africa), each year more than 15,000 men and 6,000 women are found to have primary liver
cancer in the US (Wu and Khlangwiset, 2010; NCI, 2011)[50][51]. In 2011, the number of
new cases of liver cancer is projected to reach over 26,000 persons along with approximately
20,000 deaths (NCI, 2011)[51]. To reduce the level of aflatoxin exposure and the risk of
liver cancer, the FDA maintains a tightly controlled screening program of the food supply
including peanut products (FDA, 2011)[52]. To mitigate the presence of the A.flavus mold,
peanut producers use large amounts of chemicals to prevent fungal growth.
Therefore, the use of chemical factors has a positive effect on social welfare by reducing
the risk exposure to human carcinogenic that may be present in edible peanuts; on the
other hand, the excessive use of pesticides may also have a negative effect on the social
welfare by degrading the quality of the ecosystems surrounding the peanuts farms. For
example Carsel et al. (1987)[53] simulate the level of mass fluxes of aldicarb, an insecticide
commonly used by peanut growers in North Carolina, to the groundwater, and they assessed
a concentration level between 0.01 and 0.1 Kg ha?1 within a radius of 120 m downgradient1
from the application point. Pesticides residual can be transported and be a serious threat
for public health when they reach water bodies that are source of drinkable water.
In the past decade, genetic engineering has offered a potential remedy to help peanut
producers successfully defeat the problem of fungal pathogens. For example Jonnala et al.
(2005)[54] analyze the differences between three transgenic peanut lines (resistant to fungal
1Downgradient is a term used in water sciences that indicates the direction of groundwater flows.
30
pathogens) in the southwestern United States. From the comparison with the parent line,
they found that genetic modification did not cause substantial unintentional changes in the
nutritional value of peanuts.
Price et al. (2003)[55] argue that, the adoption of agricultural biotechnologies for cotton,
soybean and corn, has increased the US total welfare by US$ 750 million. The world benefit,
from adopting herbicide tolerant cotton, is shared by the consumers (57%), US farmers
(4.1%), biotech firms (4.6%), seed firms (1.6%) and other producers from the rest of the world
(32.6%). The use of genetically engineered (GE) crops in agriculture may have environmental
benefits such as improved water use efficiency, for crops that are modified to be adapted to
arid climates, or abatement of non-source point pollutants. This is the case with GE crops
that have a high resistance to pests and reduce the need of pesticides. GE peanuts, still in
the developing stage, may represent a promising alternative that may reduce the costs of
inputs and increase crop yield and productivity (Fernandez-Cornejo and Caswell, 2006)[56].
In the current study, microdata of U.S. peanut production are used to make an economic
analysis on technical and allocative inefficiency of chemical factors related to the stochastic
production of the peanuts sector. From the analysis we intend to capture the needs of
peanut producers, related to the use of inorganic inputs, and address research priorities
in agricultural biotechnology. To my knowledge this is the first study that addresses this
question in the peanuts sector.
The essay is organized as follows: section two reviews previous research, section three
offers theoretical considerations, section four presents the econometric model, section five
describes the data used in this research and further details on the applied econometric
model; section six discusses the results. Section seven concludes.
2.2 Literature Review
Holbrook and Stalker (2010)[57] provide a review of the hybridization efforts that the
agronomic science has done with the Arachis Hypogaea. The authors cite several studies
31
that addressed the issue of breeding peanuts with resistance to root-knot nematode, fungal
pathogens and drought. Although there is a large qualitative and quantitative variation2 of
the U.S. domesticated peanut, the genetic traits has been studied only for few traits (Wynne
and Coffelt, 1982; Murthy and Reddy, 1993; Knauft and Wynne 1995)[58][59][60].
Few studies reported the economic losses of peanut producers due to fungal pathogens
or soil born diseases that could be mitigated if a GE cultivar was available to the farmers.
For example, Lamb and Sternitzke (2001)[61] argue that the average annual cost of aflatoxin
borne by all segments of the southeast peanut industry is approximately US$ 25.8 million.
Isleib et al. (2001)[62] report that the breeding program, which improved the resistance of
domesticated peanuts to Sclerotinia blight, root-knot nematodes, and tomato spotted, had
increased producer welfare by more than $200 million over a twenty year period.
While the first study is an accounting estimation of the costs of plant disease based
on four years period (1993-1996) only in one region, the second study calculates the farmer
benefits by comparing the advantage of the increased yield obtained from the resistant cul-
tivar to the old yield. The authors also accounted for the reduction costs of pesticides. Both
studies do not use a neo-classical economic framework for estimating the potential benefit
deriving from the improved genetic traits, and they both ignore climatic variable that may
also affect the crop yield of both traditional and new cultivars. The current literature is
missing a large-scale positive economic analysis of the potential benefits deriving from the
use of GE peanuts.
A positive economic study that examined the potential benefit of biotechnology has
been done by Hanson, Hite and Bosworth (2001)[63] in the fishery sector. The authors
conducted an economic analysis of the value of various forms of farm-raised catfish in the
attempt to help geneticists determine on which inherited traits breeders should focus their
research. The methodology used is based on an economic framework consisting of a complete
demand system derived from an indirect translog utility function. The estimation of these
2The authors refer to discontinuous and continuous genotypic variations of the cultivar.
32
simultaneous equations allows calculating a substitution matrix of different product forms
while the change in welfare is measured by the change in compensation variation. This highly
flexible model is used to simulate different welfare scenarios deriving from the potential
genetic manipulations which may increase the quantity and cut of catfish available in the
market.
Replicating this methodology to estimate a complete demand system of inorganic factors
used by peanut farmers may be economically sound but it would not be supported by a
scientific rationale in this study. For example, one would expect no substitution between
nitrogen and fungicide because these two factors serve two different tasks. To mirror the
example in multi-budget consumer theory, this would consist of assuming that economic
agents would not substitute house appliances with clothing because those commodities would
belong to different branches of the purchasing decision tree.
The hypothesis of no substitution among chemical factors in agricultural economics is
supported by several authors (Paris and Knapp, 1989; Frank et al. 1990; Ackello-Ogutu, et
al., 1985; Grimm et al., 1987)[64][65][66][67]. Those authors propose crop response functions
to chemical factors that exhibit a plateau effect.
2.3 Theoretical Consideration
Paris (1992)[68] tested the von Liebig hypothesis which consists of a linear response
model with plateau. The author argues that such a functional form is superior to any other
response function that exhibits a plateau. This formulation is based on the von Liebig?s law
of the minimum that can be expressed as
y = min{f(xj)(xj,u(xj))} (2.1)
where xj is the jth chemical input and uxj is an experimental error associated with that
input. Although f in (2.1) can be a linear function of inputs xj, such a functional form
33
presents few shortcomings: Mitscherlich switching-regimes should be included to make this
function differentiable. In general, the function does not allow substitution between factors;
?[...]it is not possible to separate issues of plateau growth and factor substitution?
as pointed out by Frank et al. (1990, p. 597)[65]. A plausible alternative may be the
Mitscherlich-Baule (MB) response function, which can be expressed by
y = ?0
Jproductdisplay
j=1
{1?exp[??2j?1(?2j +xj)]} (2.2)
where ?0 is the yield plateau and ?2j?1 and ?2j are nonlinear coefficients of the MB
response function. An indirect profit function based on (2.2) can be obtained by substitut-
ing the peanut yield ? right-hand side of (2.2) ? in a profit function and solve a simple
optimization problem. From the first order necessary condition and the implicit function
theorem, the profit maximizing value of the endogenous variable x?j, as function of input
and output prices can be substituted into the profit function to derive an indirect profit
function. The indirect specification may be used to derive the elasticities of substitution
that are expected to be of small magnitude.
This exercise in mathematical economics was performed for this study but the result
was inconclusive because the indirect profit function does not have a closed form. Although,
a second-order Taylor approximation reduces the production function to a quadratic form,
the approximation consistently misspecifies the original MB form. The approximation error
is relevant considering that, in economics, we stop the approximation at the second order as
we are often interested in finding elasticities ? in the current problem the elasticities of sub-
stitution. Therefore, estimating the inorganic factor demand system, based on misspecified
functional forms, would not be the appropriate strategy to make policy recommendations.
34
2.3.1 An Alternative Approach
Since directly estimating the substitution elasticities of inputs (nutrients and pesticides)
used in peanut production is flawed, an alternative approach to study the input use of peanut
farmers is to assess inefficient use of these inputs. For example, producers may overuse an
herbicide with respect to labor.3 In other words, peanut farmers may systematically overuse
a particular chemical input, say herbicide, because they believe that using large quantities
of this factor can help them to defeat unwanted weeds.
The overuse of an input is an example of allocative inefficiency. Schmidt and Lovell
(1979)[71] define allocative inefficiency as a failure to allocate inputs in the right proportions
given the input prices. In a production process that has an allocative inefficiency, the product
of the marginal revenue of an input is not be equal to its marginal cost. Technically inefficient
producers fail to maximize the output given a bundle of inputs. In reference to allocative
efficiency, Kumbhakar and Lovell (2000, p. 152)[69] state that
?Another example is provided by agriculture, in which evidence suggests that in
a wide variety of environments farmers use excessive amounts of fertilizers and
pesticides relative to other inputs.?
Kumbhakar and Wang (2006)[72] extend the primal system approach of Schmidt and
Lovell (1979)[71] by using the more flexible transcendental logarithmic functional form of
the stochastic frontier. The authors argue that if the input endogeneity is considered during
the implementation of the econometric problem, then the output-oriented or input-oriented
technical inefficiencies are the same.
The primal system technique consists of estimating simultaneously a parametric self-
dual production function
3Labor and nutrients, in general, are complementary factors. However, different nutrients? application
techniques may have different labor costs associated. For example, it is logical that there is no substitution
betweenwater andlabor; farmerscanselectan irrigationtechnique whichrequireslesslabor (seeNeswiadomy,
1988)[70].
35
lny = lnf(x) +v ?u (2.3)
and the first-order conditions of a cost minimization problem that can be implicitly
formulated as
fj
f1 =
wj
w1e
?j ?j = 2,...,J (2.4)
where y is the level of production; x is a vector of inputs; v is a vector of unobserved
farmers? heterogeneities; u is the vector of technical inefficiencies; fj and f1 are the marginal
products of input j and input 1, respectively; wj and w1 are prices of input j and input 1,
respectively and ?j is a vector of allocative inefficiencies.
The cost minimizing condition for a profitable producer is that the marginal rate of
technical substitution of input j with respect to input 1 should equal the price ratio wj and
w1. This condition occurs if the allocative inefficiency term equals zero ?j = 0. However,
this condition is violated if ?j negationslash= 0. Assuming a small substitution between chemical factors,
if the allocative inefficiency for the input pair (j, 1) is ?j < 0 then wje?j < wj that consists
of an overuse of input j with respect to input 1. In other words, the farmer will reduce
the use of input 1 in favor of input j. This problem can be graphically illustrated by figure
2.1a. Point B is the observed combination of input 1 and input j that produces the peanut
quantity y. However if the farmer optimally allocates a bundle of input 1 and input j to
produce y then the expected allocative inefficiency of input j would be ?j = 0, i.e. the
optimal bundle of input 1 and input j would lie on the tangency point A. Point B violates
the optimal condition given the input price ratio. The difference in slopes between the dotted
and continuous isocost is the measure of the allocative inefficiency of input j with respect to
input 1.
If the peanut producer is also technically inefficient then the isoquant would shift from
y to y ?eu further increasing the costs of producing peanuts (fig 2.1b). A cost analysis in a
36
B, fjf1 = wjw1e?j
wj
w1e
?j
A, fjf1 = wjw1
wj
w1 y
x1
xj
y
x1
xj
y ?eu
(a) Allocative Inefficiency (b) Technical Inefficiency
Figure 2.1: Technical and Allocative Inefficiencies
stochastic frontier framework would provide results which are less biased by including the
inefficiency terms that raise the costs of production. Furthermore, the knowledge of the
overuse of a particular chemical input should be exploited as precious information to address
research priority in genetic manipulations of inherited traits. For example, if farmers overuse
herbicides then the adoption of a new cultivar with enhanced traits that are more resistant
to weeds, thus reducing the need of the herbicide, will increase the welfare of the farmers by
lowering the cost of this chemical factor in addition to reducing the induced cost increase
due to the allocative inefficient use of herbicides
2.4 Econometric Model
The analytical expression that allows the econometric estimation of technical and alloca-
tive inefficiency using the primal approach is formulated assuming a cost functionc(w,y) and
using Shephard?s lemma to derive the conditional demand of factor xj(wj,y). In logarithmic
form it follows that
?lnc(wj,y)
?lnwj =
?c(wj,y)
?wj
wj
c(wj,y) =
wjxj
c(wj,y) = sj ? wj =
sjc(wj,y)
xj (2.5)
37
This result is used to substitute the new expression of wj in (2.4) to obtain
fj
f1 =
wj
w1e
?j = sjc(wj,y)
xj
x1
s1c(wj,y)e
?j ? sjx1
s1xj =
wj
w1e
?j
? sjs
1
= wjxjw
1x1
e?j ?j = 2,...,J
(2.6)
Taking the logarithm of (2.6) we get
?j = lnsj ?lns1 ?ln(wjxj) + ln(w1x1) ?j = 2,...,J (2.7)
Where sj are cost shares of the input xj given the input price wj.
The econometric estimation of the primal system described by (2.3) and (2.7) can be
performed under the assumption that the error components have the following distributions
as suggested by Kumbhakar and Lovell (2000)[69]
v ? N(0,?2v), is a vector of normally distributed random noises that capture specific
heterogeneities of peanut farmers;
u ? N+(0,?2u), is the vector of technical inefficiencies half-normally distributed;
? = (?2i,?3i,...,?Ji)? ? N(0,?) is the vector of allocative inefficiencies for the ith peanut
farmer; ?j are assumed to be independent of v and u for simplicity.
The joint density function of the three error components can be simply calculated by
multiplying their probability density functions. Consequently, the log-likelihood function for
the ith peanut farmer will be
lnLi = ln2? ? 12 ln?2 + ln?(?i?) + ln?(??i?? )? 12 ln|?|? 12??i??1?i + ln|Ji| (2.8)
where the error components u and v and the related standard deviations are reparame-
terized as ? = v?u, ? = ?2u+?2v ? = ?u?v, ?(?) and ?(?) are probability density and cumulative
38
density functions of a standard normal variable, respectively. Note that the |J| is the de-
terminant of the Jacobian matrix of the transformation from (?,?) to (lnx1,lnx2,...,lnxj)
that serves to capture endogeneity of input x under the cost minimizing assumption (farm-
ers choose the inputs x?s). In other words, the determinant of the Jacobian is the degree
of homogeneity or the return to scale that may lower the production costs if the producers
adopt economies of scale.
The number of parameters to be estimated can be reduced if (2.8) is concentrated with
respect to ?. Schimdt and Lovell (1979)[71] show that the element ?jk of ?, when (2.8)
reaches its maximum, can be expressed as
?jk = 1N
Nsummationdisplay
i=1
?ji?ki ?j,k = 2,...,J;viz, (2.9)
? = 1N
Nsummationdisplay
i=1
?i??i (2.10)
Substituting (2.10) into (2.8) leads to the concentrated log-likelihood function
LLi(yi|xji,?j,?,?) as a function of the technical parameters ?j and the parameters ? and ?
that allow the recovery of the vector of inefficiencies. In particular, the technical efficiency
can be calculated using the formula suggested by Jondrow et al. (1982)[73] that is
E{u(v ?u)} = ?? +?? ?(
??
??)
?(????) (2.11)
Where ?? = (?v ? u)?2u?2 and ?? = ?u?v? , while the allocative inefficiencies ?j for the
input bundle (j,1) can be calculated from the residuals of the FOC in (2.7).
Knowing the allocative inefficiency would be enough to address research priority in
biotechnology to produce a crop that has resistant traits that would reduce the (over)use
of the chemical input that is applied inefficiently. However, to quantify the economic and
environmental impact of the allocative inefficiency Kumbhakar and Wang (2006)[72] suggest
39
placing the estimated ? into the input demand equation. The authors derive the demand
equation that for the Cobb-Douglas case will be
lnxj = bj + 1r
Jsummationdisplay
k=1
?k lnwk ?lnwj + 1r lny + 1r
Jsummationdisplay
k=2
?k?k ??j ? 1r(v ?u) (2.12)
lnx1 = b1 + 1r
Jsummationdisplay
k=1
?k lnwk ?lnw1 + 1r lny + 1r
Jsummationdisplay
k=2
?k?k ? 1r(v ?u) (2.13)
where r =summationtextJk=1 ?k (return to scale) and ?j = ln?j ? 1r[?0summationtextJk=1 ?k ln?k]; j=1,2,...,J.
Notethat intheabove demand equations, components due toallocative (?)andtechnical
inefficiency (v) are added to the neoclassical demand for input (first part of 2.12 and 2.13
that does not include ?, v and u). Furthermore, a higher r (return to scale) would imply
lower values of all the other components, ceteris paribus. Those equations can be used
to make a simulation to capture the actual input demand increase due to the allocative
inefficiencies that would be: [lnxj|? = ??]?[lnxj|? = 0] = 1r summationtextJk=2 ?k?k ? ??j percent increase
for input xj and 1r summationtextJk=2 ?k?k percent for input x1. That information can be used to calculate
the potential welfare change for the farmers who adopt genetically modified peanuts. The
welfare change is the result of the abolishment of the use of the inefficiently used chemical
factor. Additional welfare change derives from a re-adjustment in the use of the other inputs
once the inefficient input is not used (as shown in equation 2.12 and 2.13).
Overuse of chemical factors can occur systematically and such systematic inefficient
farming behavior can be modeled by assuming the following multivariate normal distri-
bution of the allocative inefficiencies: ? ? N(?,?) where ?j = ??j = 1N summationtextNi=1 ?ji ?j =
2,...,J and i = 1,...,n.
40
2.5 Data and Empirical Model
Peanut production data are part of the USDA Agricultural Resource Management Sur-
vey (ARMS) on cost and returns sponsored by the Economic Research Service (ERS) and the
National Agricultural Statistical Service (NASS). In 2004 ARMS collected data regarding
peanut farming operations in three phases. A screening phase (Phase I) conducted in the
summer of 2004 served to identify peanut farmers who were operative. In Phase II (fall 2004
and winter 2004-2005), NASS randomly selected a sample of peanut farmers from Phase I
and interviewed them concerning their production practices and chemical use. Finally, in
Phase III (spring 2005) a national representative sample of peanut farmers provided infor-
mation on costs and returns during the crop year 2004. Components of Phase II and Phase
III surveys are related.
Additional climatic data such as average temperature, average precipitation and average
dew point temperature (air moisture - humidity) of each farm in the 2004 growing period
were calculated through a geospatial analysis conducted on gridded data from the National
Oceanic and Atmospheric Administration (NOAA), USDA and PRISM Oregon State Uni-
versity. Such variables were merged with the ARMS dataset and used as exogenous frontier
shifters in the following model
lnyi = ?0 +?1 lnx1i +?2 lnx2i +?3 lnx3i +?4 lnx4i
+?5 lnx5i +?6 lnx6i +?7 lnx7i +?1 lnz1i +?2 lnz2i +?3 lnz3i +vi ?ui
(2.14)
Where y is the total physical production of peanuts expressed in pounds, x1 is hired
labor expressed in hours, x2, x3, x4, x5, x6, x7 are Nitrogen, Phosphate, Potash, Insecticide,
Herbicide, Fungicide expressed in pounds, respectively; z1, z2, z3 are rainfall, temperature
and relative humidity (dew point) expressed in millimeters and Celsius degrees, respectively.
41
The most parsimonious first order approximation (Cobb-Douglas) is used for conve-
nience. Although the quadratic translog specification would be more economically appealing,
in this case it would imply the estimation of 68 parameters4 considering all the interaction
terms. These parameters would be part of the entries of the Jacobian matrix in (2.8) and
such elements would also be non-linear. In the attempt to calculate the symbolic determi-
nant of such a matrix on a new generation UNIX5 workstation, the computer system was
not able to allocate all its resources to accomplish the task.
Using Labor (x1) as the numeraire, the first order condition of cost minimization would
produce the column vector of allocative inefficiencies with wj (j = 1,2,...,7) as prices of
production factors expressed in US$/lbs.
? =
?
??
??
??
??
??
??
??
?
?2
?3
?4
?5
?6
?7
?
??
??
??
??
??
??
??
?
=
?
??
??
??
??
??
??
??
?
ln?2 ?ln?1 ?ln(w2x2) + ln(w1x1)
ln?3 ?ln?1 ?ln(w3x3) + ln(w1x1)
ln?4 ?ln?1 ?ln(w4x4) + ln(w1x1)
ln?5 ?ln?1 ?ln(w5x5) + ln(w1x1)
ln?6 ?ln?1 ?ln(w6x6) + ln(w1x1)
ln?7 ?ln?1 ?ln(w7x7) + ln(w1x1)
?
??
??
??
??
??
??
??
?
(2.15)
while the determinant of the Jacobian matrix of the transformation from (v ?u, ?) to
(lnx1,lnx2,...,lnx7) will be
4The number of parameters including intercept, ? and ? is 2 + (n2 + 3n+ 2)/2
5Unix/Debian 6.0 Dual Core workstation with 2.8Ghz CPU and 4Gb RAM software: Maxima Computer
Algebra System
42
|J| =
?
??
??
??
??
??
??
??
??
??
??1 ??2 ??3 ??4 ??5 ??6 ??7
1 ?1 0 0 0 0 0
1 0 ?1 0 0 0 0
1 0 0 ?1 0 0 0
1 0 0 0 ?1 0 0
1 0 0 0 0 ?1 0
1 0 0 0 0 0 ?1
?
??
??
??
??
??
??
??
??
??
= ?1 +?2 +?3 +?4 +?5 +?6 +?7
(2.16)
The NASS survey design is a stratified sample frame according to farms? characteristics
(ERS, 2011)[74]. For each observation, the dataset includes sampling weights or expansion
factors (Qi = 1/?i) that are based on the probability of the farmers being selected within a
stratum. Therefore, in order to provide unbiased estimators, (2.8) must be weighted using
the weighted exogenous sampling estimator (WESML) suggested by Manski and Lerman
(1977)[75]. According to the authors, with reference to this study, the quasi-loglikelihood
function will be
QWML(?,?,?,?) =Qi{lnLi = ln2? ? 12 ln?2 + ln?(?i?) + ln?(??i?? )? 12 ln|?|
? 12??i??1?i + ln|Ji|}
(2.17)
Cameron and Trivedi (2005)[76] show that even if the sampling process is affected by
endogeneities, WESML6 estimator is still consistent. Since the information matrix does
not hold for the quasi-maximum likelihood estimator (QWML), the asymptotic variance-
covariance matrix can be calculated using the sandwich estimator n?1summationtextni=1(Qi?Hi)?1(Q2i ?
GiG?i)(Qi ?Hi)?1 where n is the sample size, G and H are the gradient and the Hessian of
6WESML is also called sometimes Weighted Endogenous Sampling Estimator
43
(2.17), respectively, Qi is the sampling weight associated with each observation and ? is the
element by element Hadamard product (Cameron and Trivedi, 2005, p. 828)[76].
Table 2.1: Descriptive Statistics
Variable Unit Mean Std Dev
Production Lbs. 839,158.580 1,180,553.940
Hired Labor Hr 32.460 86.149
Nitrogen Lbs. 2,447.960 5,382.990
Phosphate Lbs. 2,164.480 3,012.960
Potash Lbs. 2,471.720 3,149.980
Insecticide Lbs. 138.460 297.241
Herbicide Lbs. 175.458 257.082
Fungicide Lbs. 195.972 304.414
Price Labor US$/Hr 7.708 1.517
Price Nitrogen US$/Lbs. 2.779 1.959
Price Phosphate US$/Lbs. 1.274 1.991
Price Potash US$/Lbs. 1.299 2.120
Price Insecticide US$/Lbs. 10.208 3.373
Price Herbicide US$/Lbs. 38.150 17.502
Price Fungicide US$/Lbs. 60.396 27.727
Precipitation mm 120.985 24.124
Dew Point ?C 16.148 2.735
Temperature ?C 22.126 1.310
Sample Size 389
Notes: Nutrients and pesticides refer to the actual weight of the active
chemical component. The actual active component of the commercial pes-
ticides has been calculated using the specific gravity of each chemical com-
ponent as reported by the ?EPA Pesticides Standard Reference Guide?.
Prices of Nitrogen, Phosphate and Potash have been simulated through an
OLS model.
The ARMS survey does not report the price of single nutrients applied by the respon-
dents; therefore, it was necessary to derive these data on the basis of available information
provided by the survey. The sample of peanut farmers was asked to report: (i) total cost of
all commercial fertilizer products applied in their field7, (ii) total acres treated with these
products, (iii) quantity applied per acre, (iv) percentage analysis of plant nutrients applied
7This cost refers only to the cost of materials (N-P-K nitrogen-phosphorus-potash) and it excludes lime,
gypsum, manure and application costs.
44
per acre. Consequently, the prices of nutrients have been calculated using an ordinary least
square model where the fertilizer expenditure (E)8 per unit of land (US$/acre) was regressed
on the actual acreage treated 9 with the chemical components producing the estimates as
reported in table 2.210.
Table 2.2: Estimated Nutrients Expenditures
Dependent Variable: Expenditure per unit of land (E)
Intercept 41.014???
(2.092)
Acres treated with Nitrogen (AN) 0.045??
(0.017)
Acres treated with Phosporus (AP) -0.085??
(0.042)
Acres treated with Potash (AK) 0.077??
(0.038)
F-statistics 6.22???
Observations 389
Notes: ???99%, ??95%, ?90% Confidence Interval. Standard Errors in
parentheses.
The single nutrient?s expenditure per acre (US$/acre) has been calculated by simulation
setting equal to zero the mutually exclusive components? acreages (AN, AP or AK). For
example, the phosphorus? expenditure per unit of land is EP = 41.014? 0.085AP. Finally
the nutrients? price for each farmer is calculated by the ratio of the total nutrient expenditure
(US$) to thetotalpoundsof nutrient applied; for example the price ofphosphorus (US$/Lbs.)
for each farmer is calculated as PP = (E ?AP)/P where P are total Lbs. of phosphorus.
8is calculated as the ratio of the total expenditure on fertilizer to the total acres treated.
9The actual acreage treated with a specific nutrient is calculated by the product of the total acres treated
and the percentage of plant nutrient applied per acre.
10Ei = ?0 +?1ANi +?2APi +?3AKi +?i i = 1,...,n where where AN, AP and AK are acreages treated
with nitrogen, phosphorus and potash, respectively.
45
2.6 Results
The quasi-loglikelihood function (2.17) is optimized using the Broyden?Fletcher?Gold-
farb?Shanno (BFGS)method fornon-linear optimization availablein theoptimizationlibrary
of the Ox Matrix language (Doornik, 2006)[77]. The BFGS algorithm is widely used to
numerically solve very complex unconstrained problems such as the optimization of equation
(2.17) using a limited amount of computer memory. Furthermore, this algorithm numerically
approximates theHessian matrixof(2.17)with apositive?semidefinite matrix thatisupdated
at each step by an iterative procedure based on gradients evaluation. As a consequence, it
could be avoided to provide the analytical Hessian of (2.17) that can be cumbersome while
ensuring a convergent solution of the numerical optimization problem.
Table 2.3 presents the parameter estimates of the production function with and without
systematic errors in allocation. The parameter ? is statistically different from zero at the 10%
confidence level; therefore, the peanuts production frontier is stochastic as also previously
found by Nadolnyak et al. (2006)11[78].
In terms of the magnitude of the parameters, no substantial differences exist between
the model that includes systematic error in allocation and the model that disregards them.
However, given the lower Akaike Information Criteria (AIC), the model representing the
production function that accounts for systematic errors better fits the data. Additionally,
given the hypothesis that agricultural producers systematically overuse chemical inputs, the
model with systematic errors is a better choice.
Table 2.4 reports the model statistics also in case of systematic error in allocation. On
average peanut farmers have a technical efficiency that is 65.3%. The hypothesis of overuse of
chemical production factors is confirmed by the negative sign of all the allocative inefficiency
terms ??s. In particular fungicides, by the magnitude of their mean allocative inefficiency,
appear to be the chemical factor that is used in the least efficient way. In fact, with reference
11The authors conducted a stochastic cost frontier analysis in the peanut sector.
46
Table 2.3: Stochastic Frontier Analysis
Parameter Estimates Estimates with systematic
error in allocation
Constant 8.134??? 8.134???
(0.022) (0.022)
Hired Labor 0.455??? 0.453???
(0.003) (0.003)
Nitrogen 0.243??? 0.242???
(0.115) (0.114)
Phosphate 0.284?? 0.284??
(0.134) (0.133)
Potash 0.260? 0.259?
(0.136) (0.135)
Insecticides 0.275??? 0.274???
(0.043) (0.042)
Herbicides 0.268??? 0.267???
(0.077) (0.077)
Fungicides 0.234??? 0.234???
(0.077) (0.077)
Precipitation -0.241?? -0.240??
(0.105) (0.104)
Temperature 3.832??? 3.833???
(0.068) (0.068)
Dew Point -1.666??? -1.666???
(0.061) (0.061)
? 1.242??? 1.237???
(0.178) (0.177)
? 0.208? 0.205?
(0.087) (0.087)
Log-Likelihood -206,763 -191,445
AIC 413,529 382,893
Observations 389 389
Notes: ???99%, ??95%, ?90% Confidence Interval. Standard Errors
in parentheses. AIC = Akaike Information Criteria.
47
to figure 2.1a at the mean value it results in wF ? exp(?F) = 0.38 < wF = 60.39, and the
labor/fungicide ratio is lower than the cost minimizing condition.
Table 2.4: Model Statistics
Model Model with systematic
error in allocation
mean St. Dev. mean St. Dev.
Technical Efficiency 0.645 0.056 0.653 0.055
?N -3.764 1.052 -3.763 1.052
?P -3.602 0.754 -3.600 0.753
?K -3.624 0.915 -3.623 0.915
?I -1.910 0.929 -1.911 0.929
?H -4.790 1.918 -4.790 1.918
?F -5.058 1.012 -5.056 1.011
Cost increase Cost increase with
systematic error in allocation
Technical Allocative Technical Allocative
Inefficiency Inefficiency Inefficiency Inefficiency
Mean 0.219 0.847 0.214 0.849
1st Quartile 0.186 0.612 0.182 0.614
2nd Quartile 0.218 0.701 0.213 0.703
3rd Quartile 0.249 1.101 0.243 1.103
Notes: 389 observations. Technical Efficiency and Cost increases are expressed in percentage.
The over-use of fungicide with respect to all the other inputs is also confirmed by the
fact that (wF/wi)?exp(?F/?i) < wF/wi (i = N,P,K,I,H) and (wF/wL)?exp(?F) < wF/wL.
Table 2.5 reports these inequalities evaluated at mean values.
A comparison of the results in table 2.5 indicates that the price ratio of fungicide to
other inputs price is on average always lower than the cost minimizing ratios. The derivation
of the cost increase due to both technical and allocative inefficiency is the percentage cost
increase of allocative inefficiency
1
r
7summationdisplay
j=2
?j?j + ln[?1 +
7summationdisplay
j=2
?je??j]?2lnr (2.18)
48
Table 2.5: Overuse of Fungicide with respect to other inputs
(wF/wi)?exp(?F/?i) wF/wi
Nitrogen 0.274 21.737
Phosphorus 0.233 47.406
Potash 0.239 46.508
Insecticides 0.043 5.917
Herbicides 0.766 1.583
(wF/wL)?exp(?F) wF/wL
Labor 0.001 7.836
Notes: Input price ratios are evaluated at the mean value of the variables.
while the percentage cost increase of technical inefficiency is 100?(u/r)% (Kumbhakar
and Wang 2006, pp. 435-436)[72].
In the current study, peanut farmers face a cost increase of 21.4% due to technical ineffi-
ciency on average, while 50% of farmers see their costs augmented by 70.3% due to allocative
inefficiency. Those cost increases could be reduced if peanut farmers appropriately reduced
chemical input use. For example, Nadolnyak et al. (2006)[78] found that the experience and
managerial skill (proxied by education) of the peanut farmer increase technical efficiency and
reduce the associated costs.
Isolating the effect of fungicides, if peanut farmers could cultivate an engineered crop
that would avoid the use of this factor then they would have potentially reduced the total
cost of chemical inputs up to 36.2%.
2.6.1 Environmental Implications
Climate variables have a significant impact on the productivity of peanuts. In partic-
ular the temperature appears to be an important growth factor as also confirmed by field
experiments conducted by Cox (1979)[79]. Farmers who have their farm located in areas
which had on average a temperature of 2? Celsius higher could expand their production by
250,000 lbs. in the 2004 growing period, ceteris paribus. Farms located in wet areas appear
to be less productive. A 10% increase in rainfall would decrease the production of peanuts
49
by 2.4%. A similar negative impact of water was found by Wright and Ross (1986)[80] in
Virginia. These authors attributed the decrease in peanut?s yield to the excess of water that
may increase the proliferation of soil borne disease. In line with the previous result, but to
different extent, this research also finds a negative impact of an increase in relative humidity
(Dew Point). Cotty and Jaime Garcia (2007)[81] found evidence that warm and humid cli-
mates are particularly favorable for Aspergillus? infections and aflatoxin contamination that
may explain the decline in productivity of those areas.
The results of this research are clear: peanut farmers in the United States overuse
fungicides. The impact of allocative inefficiency of fungicide on the demand for other inputs
can be derived easily from equations (2.12) and (2.13)12. This analysis shows that the
inefficient use of fungicides would also increase the demand for other chemical factors in
the extent of 2.43% per farmer. The overuse of all chemical factors can be seen as an
environmental externality connected to the inefficient use of fungicides. The magnitude of
this finding is not extremely severe for the case of non-point source pollution deriving by the
induced over-use of fertilizer; however, considering the cumulative effect of some pesticides
released in the environment over time and the aggregate contribution of all peanut farmers
in the U.S., the inefficient use of fungicides can have a significant negative impact on the
quality of the ecosystems. Between 1992 and 2001 pesticides and their degradates were found
in 4,380 water samples derived from agricultural, urban and mixed-use land streams across
the nation (Gilliom et al., 2007)[82].
Agricultural biotechnological research should pay attention to genetic traits of peanuts
to make this cultivar resistant to fungal pathogens. However, the current study considers the
entire aggregated class of fungicides. Peanuts are known to be affected by more than forty
fungal diseases (Gnanamanickam, 2002)[83]; therefore, a future analysis should be even more
disaggregated and restricted only to the chemical class of fungicides to study the over use of
a particular fungicide with respect to the others. Such an analysis will allow understanding
12Demand increase for input xj due to allocative inefficiency of fungicide is 1
r
summationtextJ
k=2 ?k?k ? ??F.
50
of precisely the particular class of fungal pathogen that should be the research focus of
geneticists.
In addition to the farmers? welfare improving by cutting the cost of fungicide, an increase
in social welfare would be derived by reducing the usage of other chemicals that may affect
soil and water quality of those areas in proximity of peanuts farms. A cultivar that is
genetically manipulated to be resistant to fungal pathogens would also induce the farmers
to reduce the usage of other chemicals decreasing the environmental contamination. The
ecotoxicological impact deriving from the overuse of pesticides in the peanut sector can be
a future research avenue that can be explored in an interdisciplinary effort.
2.7 Conclusions
A consistent amount of agricultural output is known to be lost every year to insects,
weeds and other plant pathogens. The use of pesticides is a common agricultural practice
that, combined with other inorganic factors such as nutrients, produce environmental exter-
nalities. Genetic engineering may mitigate these problems. Additionally, it may also increase
the agricultural productivity and reduce the associated costs of production. While there is
evidence in agricultural sectors such as cotton, corn and soybean, that biotechnology in-
deed increased the economic welfare of producers and consumers (Falk-Zepeda, Traxler and
Nelson, 2000)[84], in the peanut sector biotechnological research is still at the developing
stage.
This study addressed the issue of the economic and environmental benefits that may
potentially derive from using genetically manipulated peanuts. In particular this research
used a cross-sectional sample of U.S. peanut farmers to test the hypothesis of overuse of
chemical factors with respect to labor and to address research priorities in biotechnology
towards the chemical input that has been mostly misused. A primal system approach of a
stochastic frontier analysis, consisting of a self-dual production function and the first order
condition of cost minimization, revealed that U.S. peanut farmers overused fungicides more
51
than any other input. The overuse of fungicide could be a particular need of peanut farmers
to defeat crop infections from fungi that produces mycotoxins. Although this research does
not explain the overuse of this particular factor, that can be a future research direction to
be investigated, the positive analysis shows that misusing fungicide induced also an increase
in demand for other chemical factors.
If peanut farmers could adopt an engineered cultivar that could be resistant to fungal
pathogens, they could potentially reduce on average the total cost of chemicals up to 36.2%
and the demand for all other factors by 2.43%. Considering the cumulative effect of pesticides
in the environment, reducing the use of these factors can be a further contribution towards
the increase in social welfare by improving the quality of the ecosystems in proximity of the
farming areas.
52
Chapter 3
Rotation of Peanuts and Cotton for Optimal Nitrogen Applications
enc-56enc-56enc-56
3.1 Introduction
Webster et al. (2000)[85] argues that diminishing carrying capacity of the land was one
of the reasons for the demise of the Mayan civilization. This society was mainly depen-
dent on maize, the single crop locally grown. Monocultural practices adopted by the Mayan
population diminished and eventually destroyed the productivity of land. If there is environ-
mental historical evidence supporting the thesis that monoculture leads to an unsustainable
land use, the agronomic science provides a systematic proof of this thesis. Spatiotemporal
continuous crop systems may become susceptible to pests and plant disease because of a lack
of crop diversification.
Tilman et al. (2002)[86] provide an exhaustive review of the benefits derived from mul-
tiple cropping systems and the practice of crop rotation. Such practices induce an increase
in economic and social welfare derived from a natural increase in soil fertility. Consequently,
farming activities would benefit from increased agricultural yields and reduce the need for
chemical inputs. For example, the authors cite a study of Zhu et al. (2000)[87] where the
adoption of multiple cropping systems consisting of two different rice varieties increased the
profitability of Chinese farmers partly through reduction of use of powerful pesticides. Rota-
tion practices can complement breeding and genetic programs to meet the future demand for
food of the growing world population. While these practices can promote the sustainability
of agroecological systems, they can also increase the welfare of those who live in agricultural
areas.
53
There is also evidence that including legume species into crop rotation schemes can
reduce the need for nitrogen fertilizers with a consistent positive impact on the cost reduc-
tion of agricultural productions (Yusuf et al., 2009; Umrit, et al., 2009; Farthofer et al.,
2004; Balkcom and Reeves, 2005; Becker and Johnson, 1999)[85][86][87][88][89][90][91][92].
Legumes can fix a considerable amount of atmospheric nitrogen and they can be cultivated
without the need of supplemental fertilization (Giller, 2001)[93].
A rotation practice that is common worldwide is that of cotton (Gossypum hirsitum
L.) and legumes. Kumbhar et al. (2008)[95] conducted a series of experiments in Pakistan
and found a substantial improvement in yield and nitrogen uptake of cotton subsequent to
legumes. This practice is also common among Australian cotton farmers. Rochester et al.
(2001)[94] observed a nitrogen rate reduction up to 52 Kg/Ha in cotton systems following
green-manured legumes versus 179 Kg/Ha in continuous cotton.
In the Southeastern United States, a cotton and peanuts (Arachis hypogea L.) rotation is
common (Johnson, 2001)[96]. Scientific evidence support the complementary role of peanuts
and cotton in multiple cropping systems. For example, Rodriguez-Kabana and Backman
(1987)[97] suggested that the rotation of these two crops would be the optimal choice to
manage the pathogenic nematode Meloidogyne arenaria. From a 2 years field study in
southeast Alabama, the authors found that the occurrence for juvenile M. arenaria was 98%
lower in the peanut plots where the previous year cotton was planted. They concluded that
such a practice would increase peanut yield without using nematicides.
On the other hand, the peanut is a legume that has N2-fixation properties and can
transfer the nitrogen to the next cultivar in intercropping systems (Chu, et al. 2004)[98].
The nitrogen transfer from peanut to cotton can reduce the application of nitrogen fertilizer
the year that cotton is cultivated, thus lowering the costs of producing cotton.
The purpose of the current research is to develop a bioeconomic model that can be
used to design an optimal decision rule for the application of nitrogen that maximizes the
net return of farmers who practice a two-crop agricultural system. Such a decision will be
54
used to compare the economic and environmental implications of a scenario where (a) cotton
(Gossypum hirsitum L.) farmers practice crop rotation using the peanut (Arachis hypogea
L.) as a complementary crop versus (b) a scenario of cotton monoculture in an agricultural
area of Alabama.
Previous studies on the nitrogen contribution of peanuts to cotton are mainly agronomic
in nature. These studies do not use economic data neglecting potential long run environ-
mental and economic benefits derived from this cropping system. To my knowledge only
two studies exist that examine the economic implications of a cotton?peanut rotation to
manage soil-borne diseases from the perspective of peanut farmers. A welfare analysis of
cotton farmers adopting peanuts as a complementary crop needs to be addressed.
This article unfolds as follows: section two reviews previous research, section three
presents the bioeconomic model, section four is dedicated to the data used in this study,
section five presents the econometric part of the bioeconomic model, section six discusses
the results and finally section seven offers some concluding remarks.
3.2 Review of Previous Research
Taylor and Rodriguez-Kabana (1999a)[99] quantified the positive impact of microbivore
nematodes on peanuts and cotton production as being approximately US$ 0.11 and US$
0.13 per 100 cm3 of soil. Subsequently Taylor and Rodriguez-Kabana (1999b)[100] designed
a bioeconomic model to study the optimal decision rule for peanut?cotton crop rotation to
manage soil?borne organisms. They found that the expected return per acre for peanuts
and cotton monocultures would be potentially $133.95 and $10.14 less than what could
be achieved using an optimal rotation scheme. Therefore, these economic studies provide
evidenced that peanut farmers attain higher yields and lowers the pesticide costs if they use
cotton as a complementary crop.
Adams et al. (1998)[101] points out that continuous monocultural production have
been very popular in Alabama for 150 years. For example over the years continuous cotton
55
production induced over?fertilization of soil that may not need more supplemental nutrients.
After a series of chemical tests conducted on the soil of the state of Alabama, the authors
recommend nitrogen applications of approximately 90 Kg/Ha for cotton and no fertilization
for peanuts. These recommendations should be followed especially in those areas where the
nitrogen supplying capacity of soil is low. When cotton is produced subsequent to peanuts,
Adams et al. (1998)[101] recommended nitrogen rate up to 56 Kg/Ha. The reason of the
reduced nitrogen application rateis consistent with nitrogencredits derived from theprevious
land use.
Smith and Sharpley (1990)[102] found evidence of nitrogen mineralization of indigenous
and fertilized soils when peanut residues are retained in the soil. In contrast, Meso et al.
(2007)[103] conducted field experiments at Headland, Alabama during the growing seasons
2003 and 2005 testing the nitrogen contribution of peanut residues to cotton. These experi-
ments occurred in several subplots within Dothan sandy loam soil with and without peanuts
residues. In the experiment, the researchers applied nitrogen to subplots at the rate of 0,
34, 67 and 101 Kg/Ha. Although peanuts residues had total soil nitrogen accumulation
of 46 Kg/Ha (for the entire time of the experiment, i.e. 15.3 Kg/Ha?year), these authors
argue that nitrogen transfers from peanut to cotton do not have a significant contribution
and therefore peanuts should not be promoted as a nitrogen supplier to following crops in
rotation schemes. However, the authors found evidence of an improvement in the physical
and chemical properties of the soil when the crop residues were not removed.
Previous research has not attempted to examine whether previous peanut land use has a
potential economic impact (positive or negative) on cotton farming activities and, moreover,
ignored the potential environmental effects in terms of non-point source nitrogen pollution
that may be reduced in the peanut-cotton rotation system.
56
3.3 Bioeconomic Model
Bioeconomic models have become a common tool to design optimal policies that simul-
taneously maximize human welfare and environmental quality of agro?ecological areas. An
advantage of these models consists of having a more comprehensive view of the interactions
between human activities and natural resources (Holden, 2005).[104].
Stochastic Dynamic Programming (SDP) is the dominant strategy for the bioeconomic
modeling of the current research. This is a necessary choice if the scope of the research is to
design an optimal decision rule for nitrogen applications in a rotation system over a long time
horizon. There are two approaches to solve SDP problems. The first is a recursive model
based on a Lagrangean framework such as the one used in Chapter 1. A second method,
which is more suitable for long time horizons, is a recursive model with Bellman?s Equation.
In both cases an objective function, state, and decision variables need to be specified. In
the current study it would be more suitable to use the second approach based on Bellman?s
Principle of Optimality. Bellman (1957, p. 83)[105] postulated:
?An optimal policy has the property that whatever the initial state and initial
decision are, the remaining decisions must constitute an optimal policy with
regard to the state resulting from the first decision.?
The Bellman?s DP approach is a computer based numerical optimization technique to
solve dynamic models. Before proceeding to the introduction of the formal bioeconomic
model used in this research a simple deterministic numerical example is provided to see
the economic structure behind the Bellman recursive solution. The example is based on a
introductory problem available in Zietz (2007)[106].
For simplicity let us consider a simple linear production function where a generic crop
yield (y) is equal to the amount of nitrogen applied (N) with a quadratic cost function of
0.4N2. Over a two year time horizon, the is to maximize the net returnsummationtext2t=0 ?t(pNt?0.4N2t
subject to the linear transition equation x(t+1) = xt?Nt where Nt is the nitrogen application
57
at time t and xt is the nitrogen present in the soil that describes the state of the system at
period t. Let us also assume that the nitrogen available in the soil is depleted completely
at period 2; therefore, the terminal condition is x2 = 0 and the price of the farmed crop is
p. The problem is to find the optimal application rule that maximizes the net return of the
farmer over the time horizon.
The problem can be rewritten using the Bellman equation introducing the value function
Vt assuming a discount factor ? = 0.9.
Vt = max
Nt
(pNt ?0.4N2t ) + 0.9Vt+1, t = 0,1.
The solution starts recursively backward from the boundary condition x2 = 0 = x1?N1.
Therefore the transition equation at period 1 is x1 = N1 and the value function for this period
is V1 = px1 ?0.4x21 that can be plugged back into the Bellman equation for period 0.
V0 = max
N0
[(pN0 ?0.4N20) + 0.9V1] = max
N0
[(pN0 ?0.4N20) + 0.9(px1 ?0.4x21)].
At period 0 the transitional equation will be x1 = x0N0 that can be substituted back in
the above equation to obtain V0 = maxN0[(pN0 ?0.4N20) + 0.9[p(x0 ?N0)?0.4(x0 ?N0)2]
that can be maximized with respect to N0 to find the optimal nitrogen application rule
N0 = 0.4p?0.32x0. This policy rule maximizes the net return of the farmer over two years.
This procedure is particularly convenient for solving problems over a long time horizon by
simply repeating these recursive steps n times.
However, the degree of complexity of the modeling design increases with the number
of state and decision variables, functional forms of the production and cost functions, and
whether stochastic processes affect the states of the system. Therefore, to find the best deci-
sion rule for optimal nitrogen application in a peanut-cotton rotation system, the recursive
Bellman equation can be formulated as
58
Vt = max
LUt,Nt
{E[Rt(Nt,NPt,PCOTt,PPNTt,LUt?1,LUt?2)]+?Vt+1} (3.1)
where the net return Rt at time t is a function of decision and state variables of the
model. In particular, Nt is a decision variable that is the nitrogen application expressed in
Kg/Ha; NPt is a deterministic state variable related to the nitrogen contribution at time t
deriving from previous peanuts land use; PCOTt and PPNTt are stochastic state variables of
cotton and peanut prices at time t expressed in US$/lbs.; LUt is a binary choice variable that
refers to the land use at stage t and takes value one if cotton is planted and zero otherwise;
E is the mathematical expectation; and ? is a discount factor.
Equation (3.1) is maximized subject to the following transition equations
Nt+1 = Nt +f(NPt) (3.2)
PCOTt+1 = ?COT0 PCOTte?COTt+1 (3.3)
PPNTt+1 = ?PNT0 PPNTte?PNTt+1 (3.4)
Equation (3.2) describes the nitrogen rate that depends on the previous rate plus the
peanut contribution, derived from the previous period, which can be absorbed by the cotton
root system according to a biophysical functional form. Equations (3.3) and (3.4) describe
the price movements of cotton and peanuts disturbed by white noise ?COTt+1 and ?PNTt+1 . The
stochastic prices serve essentially to simulate the uncertainty that is common in agricultural
decision problems (Novak et al., 1994; Danielson, 1993; Duffy, 1993)[107][108][109].
The next two subsections present in some details the net revenue function and the
crop response functions to nitrogen and previous land-use. The reason to specify these
biophysical response functions is strictly connected to the nature of the bioeconomic model.
59
Consequently, the objective value function (1) will be expressed in terms of choice (Nt, LUt)
and state variables (NPt, PCOTt, PPNTt, LUt?1).
3.3.1 Net Revenue Function
The net revenue function that appears in (3.1) has the following structure
Rt = [(PCOTt ?Y COTt)?VCCOTt ?FCCOTt ?PNNt]LUt
+ [(PPNTt ?YPNTt)?VCPNTt ?FCPNTt](1?LUt)
(3.5)
where Y COTt and YPNTt are crop yields in lbs./acres of cotton and peanut at time t,
respectively; VCCOTt and VCPNTt are variable costs in US$/acres that exclude the cost of
nitrogen and the opportunity cost of land for cotton and peanut, respectively; FCCOTt and
FCPNTt are fixed costs in US$/acre for cotton and peanuts; PN is the price of nitrogen
expressed in US$/Kg; the other variable have been defined in the previous section 3.3.
3.3.2 Crop yields
In order to determine the optimal nitrogen applications, cotton yield is expressed as a
function of nitrogen. For this purpose it is assumed that the cotton response to nitrogen
is determined by the Mitscerlich-Baule (MB) functional form which exhibits a plateau at
the maximum of the function as in Frank et al. (1990)[65]. In the current study the cotton
response to nitrogen is conditional on previous land use. This condition is necessary to
account for the nitrogen carryover derived from previous crop.
YCOTt = ?0{1?exp[??1t(?2t +Nt)]} (3.6)
Because peanuts do not require supplemental nitrogen, the yield will be the only function
of the previous land use LUt?1 as follows
60
YPNTt = ?4 +?5LUt?1 (3.7)
3.4 Data
The model is parameterized to forecast 25 years of agricultural activities among the
growers of peanuts and cotton in Monroe County in southwest Alabama. This county is a
natural case study candidate because the soil characteristics favor the cultivation of both
peanuts and cotton; however, cotton seems to be the first choice made by the farmers from
this area. In fact, in 2010 the total acres devoted to cotton production were 17,500 versus
8,900 of peanuts (NASS, 2011). These crops represent the main agricultural activities of the
county.
Economic data used in this study for the year 2010 are available at the Economic
Research Service (ERS) of the United States Department of Agriculture (USDA) and are
reported in Table 3.1. Time series data of peanut and cotton prices from 1913 to 2010
have been used to calibrate the price transition equations and are available at the National
Agricultural Statistical Service (NASS) of the USDA. A discount rate of 3.29% is the average
return on assets from US agricultural income as suggested by the Agricultural and Applied
Economics Association (AAEA, 2000)[24].
Table 3.1: Economic Data
cash pricea variable costsb fixed costsb Nitrogen pricec
cotton 0.711 371.90 134.78 0.51
peanuts 0.215 541.25 181.63 ?
aCotton and peanuts are expressed in US$/lbs. bvariable and fixed costs are expressed in
US$/acre and they exclude the cost of nitrogen and the opportunity cost of land. cprice of
nitrogen is expressed in US$/lb.
Agronomic and environmental data were obtained from a biophysical simulation per-
formed at the watershed level using the Soil and Water Assessment Tool (SWAT) supported
61
by the Agricultural Research Service (ARS) at the Grassland Laboratory to estimate the po-
tential nitrogen savings for a peanut-cotton rotation. The analysis has been conducted using
53 sub?basins in Monroe County which are subdivided into 199 independent hydrological
response units (HRUs) as illustrated in Fig. 3.1. Each HRU is unique for geomorphol-
ogy, pedological and phonological characteristics. Data on soil came from the Soil Survey
Geographic (SSURGO2.2) Database for Monroe County from the Natural Resource Con-
servation Service (NRCS) of the USDA while land use has been modeled using the 2010
Cropland Data Layer from NASS (2011). Climate has been modeled using data on pre-
cipitation and minimum and maximum temperatures. Collected at a daily frequency from
01/01/1950 to 10/30/2009, these data, come from rain gauge-climatic stations located at
(LAT 31.71667, LON -87.21666) , (LAT 31.71667, LON -87.26666), (LAT 31.61667, LON
-87.55), (LAT 31.58333, LON -87.26666), and (LAT 31.38333, LON -87.41666) and available
at ARS[110].
The nitrogen applications in each HRU have been simulated by selecting the auto-
fertilization option of SWAT. The advantage of using this option consists of applying an
optimal rate of nitrogen that is a function of the phonological characteristics of the HRU
and the nitrogen stress threshold. This threshold is a function of the potential plant growth.
If the plant goes intonitrogen stress then the SWAT model will apply an optimal amount of
nitrogen in the HRU in order to ensure functional plant growth (Neitsch et al., 2010)[111].
Table 3.2 shows the scheduled annual operations of management.
Table 3.2: Management Operations
Date Operation Cotton Peanuts
1 May Plant ? ?
10 May Plant ? ?
10 June N2 Fertilization ? ?
10 October Harvest ? ?
? indicates the event?s occurrence; ? is the non-occurrence of the event.
62
Figure 3.1: The Study Area
63
3.5 Econometric Calibration
Parameters of the bioeconomic model are econometrically estimated using data for Mon-
roe County as described in the previous section. The econometric estimation of the parame-
ters allows us to calibrate the model to perform simulations that provide realistic scenarios.
The econometric procedure used for the calibration varies according to the mathematical re-
lationship used in the SDP model and the data availability. The next subsections present in
detail those econometric techniques used to estimate the equations that have been defined in
the previous sections. In particular it will be shown the estimation of: (i) cotton and peanut
response function to nitrogen and previous land?use, (ii) nitrogen elasticity of cotton supply
that is used as prior data to calibrate the cotton response function, (iii) the deterministic
transitional equation of nitrogen carryover, and (iv) the Markov switching models used to
predict the transitional equations of cotton and peanut prices.
3.5.1 Cotton Response and Peanut Yield
Equation (3.6) can be estimated following the same econometric procedure proposed
by Heckelei and Wolff (2003)[28] that has been used in Chapter 1, with the difference in
this case that the limiting resource is nitrogen. The problem is to estimate the non-linear
parameters of the MB response function ?0t, ?1t and ?2t. Therefore, the solution of the
econometric problem starts with the profit maximization problem of the cotton grower that
can be written in Lagrangean form as follows
Lt = {PCOT ?YCOTt(Nt)?OCCOT ?PNNt + ?t[bt ?Nt]}|LUt?1 (3.8)
where bt1 is the nitrogen application at time t; ?t is the opportunity cost of nitrogen;
OCCOT are operative costs in US$/acre for the year 2010, which is the sum of variable and
fixed costs as reported in table 3.1; the remaining variables have been previously defined.
1The nitrogen rate is the optimal amount of nitrogen applied by the biophysical simulator. The average
values are between 71.83 Kg/Ha and 135.18 Kg/Ha depending on the previous land use.
64
From (3.8) the first order necessary condition can be written, ?t|LUt?1, as
?Lt
?Nt = PCOT ?
?Y COTt(Nt)
?Nt ?PN ??t = 0
? ?t = PCOT ??0t{?1texp[??1t(?2t +Nt)]}?PN
(3.9)
?Lt
??t = bt ?Nt = 0 (trivial) (3.10)
It can be observed from (3.9) that the crop response to a change of nitrogen application
is
?Y COTt(Nt)
?Nt = ?0t{?1texp[??1t(?2t +Nt)]} (3.11)
By multiplying both sides of (11) by the ratio of the nitrogen to the crop supply observed
in a base year, it follows that
?Y COTt(Nt)
?Nt
No
YCOTo = ?0t{?1texp[??1t(?2t +Nt)]}
No
YCOTo (3.12)
where the superscript ?o? refers to observed quantities. Equation (3.12) represents the
nitrogen elasticity of supply that can be used as prior information to estimate the unknown
parameters of (3.10). The problem is ill?posed because the number of observations (=1
nitrogen applications) is less than the number of parameters that need to be estimated (=3
??s). Therefore the only econometric technique that allows the estimation of ill?posed prob-
lems is the entropy criterion as suggested by Golan, et al. (1996)[31]. The problem consists
of estimating simultaneously the equations (3.9), (3.10) and (3.12). The extreme points of
the interval (variance) of the U.S. nitrogen elasticity of supply can be used as supports to
recover the missing parameters. Therefore the estimated cotton response to nitrogen, al-
though based on simulated nitrogen applications, carries real economic information derived
from prior data.
65
The Generalized Maximum Entropy problem is formulated as
max
wmt,?0t,?1t,?2t,?t
H(wm) = ?
2summationdisplay
m=1
wmt lnwmt (3.13)
Subject to
?t = PCOT ??0t{?1texp[??1t(?2t +Nt)]}?PN (3.14)
Nt = bt (3.15)
2summationdisplay
m=1
vmwmt = ?0t{?1texp[??1t(?2t +Nt)]} N
o
YCOTo (3.16)
2summationdisplay
m=1
wmt = 1 (3.17)
where vm are the support points centered in the midpoint of the elasticities? interval and
wmt is the posterior probabilities of the support points that maximize the entropy (3.13).
Constraint (3.17) is the adding-up condition from the posterior supports? probabilities.
3.5.2 Nitrogen Elasticity of Supply
The prior information on elasticity of supply have been estimated using time series
data from 1964 to 2009 of production and nitrogen use among the cotton farmers in the
United States. These data are available at NASS and ERS. The ADF test (Dickey and
Fuller, 1981)[112] detected a unit root in the log?linear stochastic processes2. However, the
logarithmic form of total cotton production and nitrogen use are I(1) processes as confirmed
by the ADF test3. The Box-Ljung test detected serial autocorrelation on the first lag of
2ln(Cotton): ? = |? 3.10| < ?? = |? 4.15| and ? = |4.94| < ?? = |9.31|; ln(Nitrogen): ? = |? 1.85| <
?? = |?4.15| and ? = |1.82| < ?? = |9.31|. The test failed to reject the null hypothesis of non-stationarity.
3ln(Cotton): ? = |?5.03| > ?? = |?4.15| and ? = |13.73| > ?? = |9.31|; ln(Nitrogen): ? = |?5.28| >
?? = |?4.15| and ? = |14.63| > ?? = |9.31|. The test rejected the null hypothesis of non-stationarity.
66
the residuals obtained from the regression ?ln(Cotton)t = ?0.002+0.798?ln(Nitrogen)t4.
Therefore, the Cochrane-Orcutt (1949)[113] procedure can be implemented to correct this
issue and provide a robust estimator of the elasticity that will be
?ln(Cotton)t = 0.001 +0.988????ln(Nitrogen)t
(0.015) (0.019)
? = 0.15 Adj. R2=0.417
45 observations
(3.18)
with standard errors in parentheses. Consequently, the two support points used in the
entropy model to recover the missing parameters of the MB function are 0.869 and 1.107.
These data5 are used to numerically optimize the entropy problem to provide the estimated
cotton response to nitrogen conditional on the previous land use (3.19; 3.20), while figure
3.2 illustrates the response curves conditional on previous land uses.
1276.001?exp[?0.091(12.29 +Nt)]|LUt?1 = cotton (3.19)
1320.541?exp[?0.056(18.89 +Nt)]|LUt?1 = peanut (3.20)
The estimated peanut yield based on the simulated data of the biophysical model con-
ditioned on previous land use has a linear functional form given by
Y PNTt = 2558.6+ 796.5LUt?1 (3.21)
3.5.3 Transitional equations
The carryover function f(NPt) in equation 3.2, that relates the nitrogen contribu-
tion of peanuts, can be replaced by the nitrogen uptake function estimated by Meso et
4Although the parameters are still unbiased in presence of autocorrelation, the estimated variance of the
parameters is downward biased; consequently, the standard errors are not reported.
5The support points [0.869; 1.107] which are the range of the nitrogen elasticity of cotton supply are
obtained in the following way 0.988-0.119 = 0.869 and 0.988+0.119=1.107.
67
0 50 100 150 200
800
1000
1200
1400
1600
Mitscherlich?Baule Response Curves
Nitrogen (Kg/Ha)
Cotton Y
ield (lbs./acre)
COT
COT?COT
COT?COT?COT
PNT?COT
PNT?COT?COT
Figure 3.2: Mitscherlich-Baule cotton response to nitrogen
al. (2007)[103]. Using this biophysical relationship consists of the assumption that only a
fraction of the nitrogen transferred from peanuts is absorbed by cotton in the soil root zone.
Therefore, equation (3.2) can be rewritten as
Nt+1 = Nt + 17+ 0.27(NPt) (3.22)
3.6 Markovian prices
A common assumption made in stochastic dynamic programming applied to agricultural
economic problems is to consider the price as a result of a hidden Markov chain. Thus,
equations (3.3) and (3.4) can be rewritten in log-linear form as
ln(PCOT)t+1 = ?COT0 +?COT1 ln(PCOT)t +?COTt+1 (3.23)
ln(PPNT)t+1 = ?PNT0 +?PNT1 ln(PPNT)t +?PNTt+1 (3.24)
68
Such log?linear Markovian processes may be subject to structural breaks that may
determine different price regimes. Consequently, Markov switching regime models would be
appropriate to assess the transitional probabilities between two different price regimes. For
example, with reference to cotton (the same applies to peanuts) high and low price regimes
labeled H and L can be assumed. Therefore the following process can be posited
ln(PCOT)t+1 = ?COTH +?COT1 ln(PCOT)t +?COTt+1 where ?COTt+1 ? N(0,?2H)
ln(PCOT)t+1 = ?COTL +?COT1 ln(PCOT)t +?COTt+1 where ?COTt+1 ? N(0,?2L)
(3.25)
where the interecepts ?H and ?L represent the expectations of the cotton price in both
regimes and ?2H and ?2L are price volatilities for the two regimes. Because the Markov chain
is not visible, the transition from a high to a low price state is stochastic; therefore, equation
(3.25) can be rewritten as
ln(PCOT)t+1 = ?COTst +?COT1 ln(PCOT)t +?COTt+1 where ?COTt+1 ? N(0,?2) (3.26)
where the intercept ?COTst is a function of a latent random variable st that would assume
value one if the price of cotton is high (?H) and zero otherwise (?L). In this case st is a
two?state Markov chain where Pr(st = j|st?1 = i) = ?ij (Hamilton, 1994)[114]. The value of
st can be assessed by observing the behavior of the price ln(PCOT)t, ?COT1 , ?2, ?H, ?L and
the probabilities ?HH and ?LL of the price when those are on the same regime. To infer the
value of st, Hamilton (1989)[115] implemented an iterative maximum likelihood algorithm
where at each iteration the inferred probability of being in a regime (say j) will be ?jt =
Pr[st = j|?t;(?,?COT1 ,?H,?L,?HH,?LL)?] with ?t?1 = {PCOTt?1,PCOTt?2,...,PCOT0}
and j = H,L.
If the probability density function for the two regimes is
69
?jt = f[ln(PCOT)t|st = j,?t?1;(?,?COT1 ,?H,?L,?HH,?LL)?]
= 1?2??exp[?(ln(PCOT)t ??j ??
COT
1 ln(PCOT)t?1)
2
2?2 ] with j = H,L
(3.27)
then the transitional probabilities will be filtered in the following step by the Hamilton
filter that is
?jt =
summationtext
i=H,L ?ij?j,t?1?jtsummationtext
i=H,L
summationtext
j=H,L?ij?j,t?1?jt
(3.28)
Results of the numerical analysis used to estimate the Markov switching autoregressive
processes are reported in Table 3.3 while Figure 3.2 offers a graphical illustration of the
stochastic processes, the smoothed6, and the filtered switching regime probabilities.
For simplicity?s sake, it has been assumed that cotton and peanut prices are not corre-
lated and the price volatility does not switch. There is evidence from the analysis that the
second order lagged dependent variable is statistically equal to zero; as a consequence, both
cotton and peanut price are first order Markov chains.
3.7 Results
All the variables of the model have been discretized to simplify the numerical solution.
The model consists of two states for each price variable and two and 250 levels for land use
and nitrogen variables, respectively. There are a total of 2,000 states for the model and
the dynamic program has been written and compiled using the computer language ANSI C
(Kernighan and Ritchie, 1988)[116] to produce the optimal decision rule reported in table
3.4.
6The smooth probability refers to the regime probability based on the available information (up to time
t)
70
Table 3.3: Markov Switching Model
Cotton Peanut
Low Regime High Regime Low Regime High Regime
Intercept -0.481*** 0.481*** -0.532*** 0.532***
(0.041) (0.057) (0.041) (0.049)
ln(Price)t?1 0.799*** 0.799*** 0.782*** 0.782***
(0.195) (0.195) (0.202) (0.202)
ln(Price)t?2 0.074 0.074 0.172 0.172
(0.191) (0.191) (0.209) (0.209)
?2 0.240*** 0.240*** 0.158*** 0.158***
(0.060) (0.060) (0.018) (0.018)
?HH 0.9 0.9
?HL 0.1 0.1
?LH 0.1 0.1
?LL 0.9 0.9
Ergodic Prob-
ability ?H 0.5 0.5
Ergodic Prob-
ability ?L 0.5 0.5
Log-
Likelihood -64.57 -73.29
AIC 146.152 160.58
Observations 97 97
Notes: Standard error in parentheses, ???99%. ??95%,?90% confidence
interval. AIC=Akaike Information Criteria.
71
Cotton
Years
log(Price)
1920 1940 1960 1980 2000
?0.5
0.0
0.5
1.0
1.5
Peanuts
Years
log(Price)
1920 1940 1960 1980 2000
?1.5
?1.0
?0.5
0.0
1920 1940 1960 1980 2000
0.0
0.2
0.4
0.6
0.8
1.0
Switching Price Regimes
Years
Probability
Smooth (high regime)
Smooth (low regime)
Filtered (high regime)
Filtered (low regime)
1920 1940 1960 1980 2000
0.0
0.2
0.4
0.6
0.8
1.0
Switching Price Regimes
Years
Probability
Smooth (high regime)
Smooth (low regime)
Filtered (high regime)
Filtered (low regime)
?1.0 ?0.5 0.0 0.5
0.0
0.5
1.0
1.5
2.0
2.5
Residuals
N = 96   Bandwidth = 0.05941
Density
?1.0 ?0.5 0.0 0.5
0
1
2
3
Residuals
N = 96   Bandwidth = 0.03876
Density
Figure 3.3: Markow Switching Autoregressive Model
72
Table 3.4: Time path - optimal decision rule for nitrogen applications
Scenario (a) Scenario (b)
Year Land Use N2 Rate (Kg/Ha) Land Use N2 Rate (Kg/Ha)
2011 Cotton 123.460 Cotton 204.750
2012 Peanut 0.000 Cotton 95.000
2013 Cotton 79.826 Cotton 71.750
2014 Peanut 0.000 Cotton 71.750
2015 Cotton 80.151 Cotton 100.860
2016 Peanut 0.000 Cotton 100.860
2017 Cotton 80.482 Cotton 101.514
2018 Peanut 0.000 Cotton 101.514
2019 Cotton 80.820 Cotton 102.173
2020 Peanut 0.000 Cotton 102.173
2021 Cotton 81.163 Cotton 102.838
2022 Peanut 0.000 Cotton 102.838
2023 Cotton 81.513 Cotton 103.509
2024 Peanut 0.000 Cotton 103.509
2025 Cotton 81.868 Cotton 104.187
2026 Peanut 0.000 Cotton 104.187
2027 Cotton 82.229 Cotton 104.870
2028 Peanut 0.000 Cotton 104.870
2029 Cotton 82.596 Cotton 105.559
2030 Peanut 0.000 Cotton 105.559
2031 Cotton 82.970 Cotton 106.254
2032 Peanut 0.000 Cotton 106.254
2033 Cotton 83.349 Cotton 106.956
2034 Peanut 0.000 Cotton 106.956
2035 Cotton 51.234 Cotton 107.663
Expected Net
Return $4,128,160.93 $3,540,777.71
Nitrogen
in Runoff
(Kg/acres)
2.450 2.610
Scenario (a) is the peanut cotton agricultural system. Scenario (b) is continuous cotton.
The expected net return is the expected return in the long of the cotton farmers in Monroe
county for the two different scenarios.
73
2015 2020 2025 2030 2035
0
50
100
150
200
Optimal Path Decision Rule
Years
Nitrogen Rate (Kg/Ha)
Scenario (a)
Scenario (b)
Figure 3.4: Time Path ? Nitrogen Decision Rule
According to the model, cotton farmers should apply less nitrogen the year that cotton
follows peanuts (scenario a) compared to cotton monocolture (scenario b). Figure 3.4 shows
the dynamic rule of nitrogen applications for both scenarios.
The average nitrogen contribution of peanut is estimated at an average of 23 Kg/Ha per
year. This figure is 33% smaller than the 34 Kg/Ha that are recommended by Adams et al.
(1994)[101]. However, the model estimated nitrogen transfers from peanut to cotton that are
not equal to zero and this result contrasts with the finding of Meso et al. (2007)[103] who
estimated 46 Kg/Ha in 3 year period. The reason for the differences may be attributable
to the different climatic and geographic location and the different source of data used. We
should remember that the authors used experimental data while the model of the current
research adopts data derived from a biophysical simulation.
We should also remember that the objective of this analysis is an economic assessment
of potential benefits resulting from the inclusion of peanuts in a continuous cotton system.
Because the objective function of the model is of an economic nature the output and input
prices play a crucial role on the amount of nitrogen that is applied. While previous studies
74
0 50 100 150 200
0
50
100
150
200
Expected Net Return
Nitrogen (Kg/Ha)
US$/acres
Cotton
Peanuts
Figure 3.5: Expected Net Return in 2019
attempted to measure with a short period of time the optimal amount of nitrogen that
maximizes the cotton yield in both scenarios, the current study is more concerned with
a nitrogen decision rule that maximizes the net return of farmers to reach an economic
optimum. For example Figure 5 is a graphical illustration of the objective function of the
model in the year 2019. The expected net return is a function of nitrogen application and
the maximum return would occur at a lower application rate (80.82 Kg/Ha) compared to
scenario (b). This condition happens to be a consequence of having nitrogen credits from
the previous land use that would lower the nitrogen costs in the cotton year.
If all cotton farmers from Monroe County would adopt peanuts in a rotation scheme and
if they followed the strategy depicted in scenario (a) then their net return would potentially
increase by approximately 14% which aggregates up to a US$ 587,383.21 increase in economic
welfare for the entire area.
A secondary research question was to investigate whether the crop rotation scenario
would also lead to an improvement in the water quality of the watershed by reducing the
non-source nitrogen pollution. Because the nitrogen runoff does not directly affect the choice
75
variables of the model (N2 rate and land use), this state variable was calculated after the
model was solved (post DP). With this state variable, analysis of the environmental conse-
quences of the rational economic behavior of farmers in both scenarios is possible.
The analysis shows that rotation scenario (a) would reduce the long run nitrogen in
runoff by 160 grams/acres corresponding to a reduction of approximately 6.13%. This figure
may seem negligible; however, if the amount of nitrogen reduction is aggregated over the
entire group of farmers (17,500 acres) then the total nitrogen released in the watershed
as non?point source pollution would decrease by 2.8 metric tons per year. Considering a
potential cumulative effect over the years, this result demonstrates a contribution in reducing
the phenomenon of eutrophication of water bodies.
The environmental and agronomic data used in this research are simulated, and the
biophysical model was not calibrated against experimental data from the case study area.
If these data become available in the future, then an extension of this work may consists
of a biophysical calibration and validation of the bioeconomic model to produce results
that are more accurate in agronomic terms. However, despite these agronomical numerical
improvements, results suggest that if cotton farmers adopt peanuts as a complementary crop
in a two crop rotation system they would increase their economic benefit and improve the
sustainability of their agroecological area.
3.8 Concluding Remarks
Rotation of cotton and legumes is an agricultural practice that is common in many rural
areas of the world. Legumes have the property to fix atmospheric nitrogen and grow in soil
with extremely low nitrogen content. In the Southeast of the United States, cotton?peanut
rotation is quite popular. In particular, peanut growers alternate this crop with cotton to
manage nematode and soil-borne diseases. Evidence in the literature suggests that cotton-
peanut rotation can increase the economic returns of peanut farmers by increasing peanut
76
yields and reducing the use of pesticides (Sholar et al., 1995; Taylor and Rodriguez-Kabana,
1999)[117][100].
The peanut as a legume also has a potential benefit for cotton farmers. Peanuts can
provide a nitrogen contribution to the soil in the year subsequent to when the cotton is
planted. As a result, cotton growers may reduce the use of nitrogen fertilizer and benefit
from higher returns the year that cotton is planted. This research tested this hypothesis and
developed a bioeconomic model that compared economic returns in a peanut-cotton rotation
scenario and a cotton monoculture one. As a byproduct of the research, environmental
implications consisting of nitrogen levels in runoff were also estimated for both scenarios as
an indicator of non-point source pollution.
The bioeconomic model consists of a couplage of two models: a biophysical model that
simulates cotton and peanut cultivation at the watershed level and a stochastic dynamic
model that simulates economic decisions made by the farmers at the farm level such that
the comprehensive model can provide important information on the interaction between
farmers, natural resources, and the environmental quality of the watershed. The model was
parameterized to test the hypothesis of the study and forecast the optimal nitrogen rates that
maximize the net returns of cotton farmers in both scenarios for 25 years in an agroecological
area in Monroe County in Alabama.
There is evidence from the analysis that if cotton growers alternate cotton with peanuts
then their net return would increase approximately by 14% in the long run in addition to a
reduction of 6% of nitrogen released into the watershed, thereby improving the social welfare
of the entire area. Future studies may estimate the long run social welfare improvement as a
result of the synergic joint action of this rotation system. Such gains may consist of nitrogen
and pesticides savings in the cotton and peanut year, respectively.
77
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Appendices
87
Appendix A
GME - GCE Formulation
Heckelei and Wolff (2003)[28] assume disturbances in the data generation process of the
model?s variables1. These errors can be thought of as measurement errors or inefficiencies in
productivity or in this case forecast errors made by the climatologists of the extension service.
Therefore, after accounting for the errors, if the crop yield in the k(= 3) states of nature is
yijk ?eyijk and the observed land allocation is ?oij ?summationtext3k=1 ?ke?ijk2, where ? = [0.33,0.30,0.37]?
is the vector of Markovian ENSO probabilities, the reparameterization of the disturbances
and the own and cross price elasticities of supply ?ii? will be,
eyijk = vyijkwyijk, e?ijk = v?ijkw?ijk and ?ii? = v?ii?w?ii? (A.1)
where ws are the posterior probabilities of the vs supports. In particular the support
of the error of the crop yield vyijk was centered around zero and the upper and lower bounds
(variance) have been calculated as plus or minus the difference between the average yield
in the ENSO state of nature and the most recent observed crop yield when the respective
ENSO event occurred yijk ? yoijk. For the land allocation normally distributed errors have
been added with support point centered at zero and standard deviations equal to 10% of
the average land allocation. As supports for the own and cross price elasticities of supply, a
range of elasticities from a previous study by Shumway (1986)[29] in the South U.S. has been
employed. The support points have been centered on the midpoint of the intervals reported
in table A.1.
1The authors assume random errors around land allocations, input allocations and supply quantities. See
Heckelei and Wolff (2003)[28] p. 39.
2The expected value of the disturbances is taken because the observed land allocation is one of the possible
allocations from the discrete probability distribution set.
88
Table A.1: Range of own and cross price elasticities of supply
Quantity Price
corn cotton peanuts soybeans
corn [0.340 ; 1.590] [-0.810 ; 0.092] [-0.230 ; -0.060] [-1 ; +0.91]
cotton [-0.090 ; 0.120] [0.150 ; 0.360] [-0.110 ; -0.061] [-0.01 ; +0.02]
peanuts [-0.230 ; -0.050] [-0.300 ; 0.020] [0.340 ; 0.150] [-0.02 ; 0.06]
soybeans [-0.030 ; 0.030] [-0.300 ; 0.030] [-0.490 ; 0.270] [0.940 ; 3.300]
Source: Shumway (1986). Notes: Because the elasticities for peanuts were not available, elas-
ticities range of oil crops has been used as substitute.
Golan et al. (1996)[31] suggest that relaxing the bounds of the support will give more
power to the data reducing the power of the prior information. According to this suggestion
the 3?3 rule has been used to set the upper and lower bounds of the elasticities support.
Because the problem is well?posed and the number of observation is larger than the num-
ber of parameters to be estimated, including the errors is a straight econometric consequence
that alleviates the computational burden of estimating 38?34 non-linear cost functions.
After the reparameterization, the GME - GCE formulation of the problem is
max
w?ijkm,wyijkm,w?im,d,q,h,?jk
I(w?ijkm,wyijkm,w?im)
= ?
4summationdisplay
i=1
bracketleftBigg 38summationdisplay
j=1
3summationdisplay
k=1
2summationdisplay
m=1
w?ijkmlog
parenleftBigg
w?ijkm
?k
parenrightBigg
+
38summationdisplay
j=1
3summationdisplay
k=1
2summationdisplay
m=1
wyijkmlog
parenleftbiggwy
ijkm
?k
parenrightbigg
+
2summationdisplay
m=1
w?imlog(w?im)
bracketrightBigg
(A.2)
Subject to
3The rule is a direct application of the Chebychev inequality, see Golan et al. (1996)[31] p. 88. Heckelei
and Wolff (2003)[28] use even a wider interval equal to 5?.
4Because the goal is to estimate the quadratic cost function that calibrates model (1.1), an alternative
way could be estimating a cost function for each county for each ENSO scenario.
89
3summationdisplay
k=1
2summationdisplay
m=1
?k pi(yijk ?vyijkwyijkm)?ci +soij ??jk ?di
?
4summationdisplay
i?=1
bracketleftbigq
ii?(?oi?j ?v?ijkw?ijkm
bracketrightbig= 0 (A.3)
4summationdisplay
i=1
3summationdisplay
k=1
2summationdisplay
m=1
parenleftbig?o
ij ?v
?
ijkw
?
ijkm
parenrightbig? bo
j (A.4)
qii? =
4summationdisplay
i?=1
hii?hi?i with hii? = 0 ?i? > i (A.5)
2summationdisplay
m=1
v?iw?im
=
38summationdisplay
j=1
3summationdisplay
k=1
2summationdisplay
m=1
?k
braceleftBiggbracketleftBigg
q?1ii? ?
parenleftBigg 4summationdisplay
i?=1
aijk
qii?
parenrightBigg
qii?
bracketrightBigg?1
pi
(yijk ?vyijkwyijkm) ??oij
bracerightBigg
?i,i?withi negationslash= i?
(A.6)
3summationdisplay
k=1
2summationdisplay
m=1
?kw?ijkm = 1,
3summationdisplay
k=1
2summationdisplay
m=1
?kwyijkm = 1 and
2summationdisplay
m=1
w?im = 1 (A.7)
where the superscript ?o? refers to observed variables, subscript i refers to the crop while
i? is the crop subscript transposed, j are the counties, k the ENSO states of nature and
m is the number of supports. The objective function (A.2) is cross?entropy that needs to
be minimized to reduce the distance between the posterior probabilities of the errors and
the prior information of the Markovian probabilities ?k. Because the cross?entropy is taken
with the negative sign, the problem now is to find the maximum value of the negative cross-
entropy. Equation (A.3) is the reparameterized first order condition (1.10), (A.4) is the
land constraint with the error, (A.5) is the Cholesky factorization that ensures the proper
curvature of the quadratic cost function5, (A.6) is the reparameterized relationship (1.15)
where aijk are the elements of the matrix of technical coefficients calculated as the inverse of
5See Lau (1978)[39], Appendix A.4 p. 422.
90
the crop yield and expressed in acres/lb. As mentioned in the chapter, such a relationship
holds because land is the only limiting factor considered in the analysis. Constraints (A.7)
are the adding up conditions imposed to the supports? probabilities.
91
Appendix B
Net Energy Value and Carbon Emissions Calculation
The total net energy of biofuels produced in the state can be calculated as
NEG =
4summationdisplay
i=1
38summationdisplay
j=1
parenleftBig
Ebiofueli +Ecoproductsi ?Efarmi ?Etripi ?Eprocessi
parenrightBig
?ij (B.1)
where the first two addends under the summation indicate respectively the energy con-
tent of bioethanol or biodiesel and the stochastic biomass of the energy crop i expressed in
MMbtu/acre. The subtrahends are the energy expenditures, also expressed in MMbtu/acre,
respectively for farm practices such as energy content of nitrogen, phosphate, potash, pesti-
cides and fossil fuels used for farming activities in addition to energy used to transport the
crop i from the farm to the processing plant and the energy expended during the industrial
process of biofuel production.
CO2 =
4summationdisplay
i=1
38summationdisplay
j=1
parenleftBig
COdiesel2i +COgasoline2i +COLPG2i +COfarm2i
+COelectricity2i +COtrip2i )?ij
(B.2)
Equation (B.2) is the total emission of carbon dioxide derived from the entire process
of biofuel production and takes into account the emission from diesel, gasoline, LPG used
by the farmers in Alabama during the farming activities in addition to the emission due to
the electricity used during the industrial process and the transportation of the energy crops
from the farm to the conversion plant. The addends of the summation can be expressed in
metric ton of CO2eq/acre.
Net Energy values are calculated, in general, using the methodology of Pimentel and
Patzek (2005) and Persson et al. (2009) with data from the sources reported in table B.1.
92
With reference to equation (B.1), table B.1 shows the values of the energy costs of the
agricultural inputs and the energy gains of the outputs of four different types of biofuels
considered in this study. The energy embodied in the cement, stainless steel and steel of the
conversion plant has been omitted. This amount of energy can be thought of as a fixed cost
in energy terms and its value will vanish in the long run.
The crop residues include 50% moisture. Assuming a natural drying process, the crop
residues are able to support self-combustion (Jenkins et al., 1998)[40]. This calculation
assumes that the conversion of oil seed crops to biodiesel would occur at the processor of
Decatur, Alabama (LAT 34.58, LON -86.98) while the ethanol conversion would be processed
by the plant located at Olbion, Tennessee (LAT 36.26, LON -89.19).
Direct carbon emissions have been calculated using data and guidelines from the 2010
U.S. Greenhouse Gas Inventory Report of US-EPA[41] assuming 99% as an oxidation factor
to carbon dioxide, while the emissions due to the electricity required by the conversion are
available for the states of Tennessee and Alabama at the US Energy Information Adminis-
tration.
93
Table B.1: Energy Gains and Energy Costs
Energy
Content Units Corn Cotton Peanuts Soybeans Source
Outputs
biofuel MMBtu/lb seeds 0.0040 0.0003 0.0004 0.0002 C, ORNL
Crop
residues
MMBtu/
lb 0.0073 0.0073 0.0073 0.0073 J, ORNL
Inputs
Seeds MMBtu/acre 0.8360 0.0840 1.0900 0.1850 PP, D
Nitrogen MMBtu/Kg 0.0633 0.0633 0.0633 0.0633 S
Phosphate MMBtu/Kg 0.0121 0.0121 0.0121 0.0121 S
Potash MMBtu/Kg 0.0044 0.0044 0.0044 0.0044 S
Herbicides MMBtu/Kg 0.2049 0.2049 0.2049 0.2049 Sh
Pesticides MMBtu/Kg 0.2109 0.2109 0.2109 0.2109 Sh
Fuel for
farming
MMBtu/
acre 2.0043 2.0043 2.0043 2.0043
USDA,
ORNL
Conversion
process
MMBtu/
ton 20.7800 55.9100 148.3900 40.4300 PP, B
Electricity
during the
conversion
MMBtu/
ton 392.0000 270.0000 270.0000 270.0000 PP
trip MMbtu/(Km lb) 1.50?10?6 1.50?10?6 1.50?10?6 1.50?10?6 PP
C: Collins et al. (2005)[42], D:Duke (1983)[43], J:Jenkins et al. (1998)[40], ORNL:Oak Ridge
National Laboratory[44], PP:Pimentel and Patzek (2005)[12], S:Sheehan et al. (1998)[36],
Sh:Shapouri et al. (2002)[11], USDA: Census (2007)[45].
94
Appendix C
Biomass Crop Residue
A biophysical analysis has been performed at the watershed level using the Soil and
Water Assessment Tool (SWAT) supported by the United States Department of Agricul-
ture ? Agricultural Research Service (USDA-ARS) at the Grassland Laboratory to estimate
the potential biomass residue for the 4 major crops modeled. Given the substantial soil
heterogeneity (US class B, C and D), the analysis has been conducted on 84 sub-basins in
Lawrence county which have been further divided into 303 pedologically and phenologically
independent hydrological response units (HRUs) with a territory that has three different
geomorphological classes. The total cropland modeled lies on 44 HRUs. Data on soil came
from the detailed Soil Survey Geographic (SSURGO2.2) Database for Lawrence County from
the Natural Resource Conservation Service of USDA while the land use has been modeled
using the National Land Cover Data of United States Environmental Protection Agency
(US-EPA, 2001). The climate has been modeled using data on precipitation, minimum and
maximum temperatures. These data, at daily frequency from 01/01/1950 to 10/30/2009, for
the rain gauge-climatic stations located at (LAT 34.71, LON -86.58) and (LAT 34.75, LON
-87.65) are available at USDA-ARS.
The SWAT model has been calibrated to replicate the farming management practices
in the use of agricultural chemical inputs (fertilizers and pesticides) that are common in
non-irrigated agriculture in Alabama. Parameters of the runoff curve, soil evaporation and
plant uptake compensation factors have been adjusted in the attempt to match the annual
yields of corn, cotton, soybeans for Lawrence County as reported in 2009 by the National
Agricultural Statistical Service (NASS) while peanuts has been modeled using data from
Dale County.
95