THE POTENTIAL AND COST OF CARBON SEQUESTRATION IN
AGRICULTURAL SOIL; EMPIRICAL STUDY OF DYNAMIC MODEL IN THE
MIDWESTERN U.S.
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the
Graduate School of The Ohio State University
By
Suk-Won Choi, M.A.
*****
The Ohio State University
2004
Dissertation Committee:
Associate Professor Brent Sohngen, Adviser
Professor Alan Randall
Professor Lynn Forster
Approved by
__________________________
Adviser
Graduate program in
Agricultural, Environmental,
and Development Economics
ABSTRACT
This study investigates the cost and potential of carbon sequestration in
agricultural soil in the Midwest U.S. Previous economic studies ignored several
important features such as the range of residue management intensity level, dynamic soil
carbon properties, cyclical patterns of crop rotations, alternatives on the baseline
scenarios, and spatial pattern of carbon gains.
Developing the empirical dynamic model that maximizes the net present value of
market welfare on corn and soybean, two different carbon programs are applied: carbon
renting program and fixed payment per hectare with minimum residue management
intensity. Several empirical estimations are employed to obtain parameters for the
dynamic model, in particular, residue management impacts on crop yield and carbon
dynamics are estimated. The crop yield loss by conservation practice is greater in high
quality soil than the low quality class. Sensitivity analysis on different baseline scenario
suggests that carbon sequestration path could be altered by different assumptions. It
suggests that the estimates of the carbon gains from any carbon policy would be
sensitively affected by how baseline scenario is assumed. In general, the adoption rate of
conservation practice is higher in soybean and low quality soil classes than in corn and
high quality soil classes.
ii
Carbon renting analysis shows that corn price could rise and soybean price could
decrease, but the magnitude is not immense. Overall, the average cost of carbon
sequestration is the lowest with carbon renting policy and the highest with fixed payment
per hectare with low minimum residue management requirement. The average cost rages
from $0.06 to $4.50 per ton with carbon renting scenario. With fixed payment scenario,
the average cost rises to $40-$613 per ton with 35 % minimum residue management and
$18-$304 per ton with 75% minimum residue management requirement.
The area with high yield potential does not necessarily provide the carbon gains
because the residue management intensity is minimal at 35 %. The source of carbon gains
in the study region is from the middle quality soil class. However, low quality soil class
does not provide carbon either because conservation practice adoption rate was already
high in the baseline scenario and also the total potential for the carbon gain is small.
iii
To my parents and wife
iv
ACKNOWLEDGMENTS
This work would not have been possible at all without countless helps and
supports from many people. First, I would like to express heartfelt gratitude to my
advisor Dr. Brent Sohngen for his relentless provision of intellectual guidance and
financial support for this study. Along with him, my committee members, Dr. Alan
Randall and Dr. Lynn Forster helped me improve my thesis with economic insights and
inspiration. Second, I would like to thank my parents who make my entire pursuit of
degree possible. They provide everlasting support throughout the long period of graduate
program. Last, and not the least, I would like give my appreciation to my wife Garam
who has been all the time with me and my twin boys for her encouragement and support.
v
VITA
Nov. 13, 1968 ………………………Born - Seoul, Republic of Korea
1991 ………………………………..B.S. Agricultural Economics, Korea University.
1999 ………………………………..M.A. Economics, The Ohio State University.
1999 – present ……………………...Graduate Research Associate,
The Ohio State University
FIELDS OF STUDY
Major Field: Agricultural, Environmental, and development Economics
Minor Fields: Environmental & resource economics, Econometrics
vi
TABLE OF CONTENTS
Page
ABSTRACT........................................................................................................................ ii
DEDICATION................................................................................................................... iv
ACKNOWLEDGMENTS .................................................................................................. v
VITA .................................................................................................................................. vi
TABLE OF CONTENTS.................................................................................................. vii
LIST OF TABLES.............................................................................................................. x
LIST OF FIGURES .......................................................................................................... xii
CHAPTERS:
1.
INTRODUCTION ...................................................................................................... 1
1.1
1.2
1.3
1.4
2.
Background ......................................................................................................... 1
Objectives ........................................................................................................... 6
Literature review................................................................................................. 8
Organization...................................................................................................... 13
DYNAMIC CROP CHOICE MODEL..................................................................... 15
2.1
Baseline............................................................................................................. 15
2.2
Carbon scenario ................................................................................................ 22
2.2.1
Carbon rental payment.............................................................................. 22
2.2.2
Per hectare payment with minimum tillage .............................................. 24
3.
DATA AND PARAMETERS .................................................................................. 27
3.1
Land distribution............................................................................................... 28
3.2
Crop yield and economic data........................................................................... 30
3.2.1
Estimation of yield impacts of residue management ................................. 32
3.2.2
Cost and residue management .................................................................. 36
3.2.3
Yield functions and parameters ................................................................ 37
3.2.4
Crop prices and elasticities ....................................................................... 39
3.3
Soil carbon data................................................................................................. 42
vii
3.3.1
Estimates of initial carbon ........................................................................ 42
3.3.2
Carbon Dynamics...................................................................................... 43
3.3.3
Empirical Carbon Dynamics..................................................................... 49
3.4
Land use projection........................................................................................... 52
3.4.1
Model and data.......................................................................................... 52
3.4.2
Estimation result ....................................................................................... 59
3.4.3
Projection of land use................................................................................ 65
4.
BASELINE AND SENSITIVITY ANALYSIS ....................................................... 68
4.1
4.2
4.3
4.4
4.5
5.
Total crop choices ............................................................................................. 69
Total conservation land use .............................................................................. 73
Crop prices ........................................................................................................ 77
Residue management intensity ......................................................................... 80
Total carbon sequestration ................................................................................ 81
CARBON POLICY RESULTS ................................................................................ 84
5.1
Carbon policies with the baseline ..................................................................... 85
5.1.1
Carbon renting policy ............................................................................... 85
5.1.2
Fixed payment per hectare ........................................................................ 91
5.1.3
Cost of carbon sequestration................................................................... 100
5.2
Carbon policy when total cropland changes ................................................... 108
5.2.1
Land use projection by carbon policy..................................................... 108
5.2.2
Results of model with cropland changes ................................................ 112
6.
CONCLUSIONS..................................................................................................... 118
6.1
6.2
6.3
Summary ......................................................................................................... 119
Implications..................................................................................................... 122
Limitation and future development................................................................. 123
BIBLIOGRAPHY........................................................................................................... 125
viii
LIST OF TABLES
Page
Table
2.1
Definition of model variables and functions.........................................................18
3.1
Land distribution in the study region (000 hectares) ............................................30
3.2
Variables in crop yield estimation ........................................................................33
3.3
Estimation results of crop yield functions ............................................................34
3.4
Marginal impacts of residue management on yield by land quality .....................36
3.5
Parameters for the crop yield functions ................................................................41
3.6
Initial carbon stored in the study region for upper 30cm soil depth .....................44
3.7
Average clay contents in 30cm soil depth ............................................................47
3.8
Definition of variables for area base model..........................................................53
3.9
Estimation results of three models........................................................................60
3.10
Land use projections (000 hectares) .....................................................................67
4.1
Average tillage intensity under different scenarios ..............................................81
5.1
Average tillage intensity with carbon renting policy............................................91
5.2
Cost of carbon (Carbon renting policy) ..............................................................104
5.3
Cost of carbon (Fixed payment with 35 % minimum till)...................................105
x
5.4
Cost of carbon (Fixed payment with 75 % minimum till)...................................105
5.5
Total Cropland changes (000ha)..........................................................................111
5.6
Average tillage intensity of carbon renting policy
when total cropland changes .................................................................................. 115
5.7
Cost of carbon (Carbon renting policy when total cropland changes).................117
xi
LIST OF FIGURES
Figure
Page
3.1
Aggregated soil and yield type .............................................................................29
3.2
Carbon dynamic examples (ton/ha) ......................................................................51
3.3
Density and distance to large cities. Reordering data
from the nearest distance to large city. (1997 data) ..............................................64
3.4
Density and crop to forestland ratio. Reordering data
from the highest density. (1997 data) ...................................................................64
4.1
Total crop choices .................................................................................................71
4.2
Total conservation crop.........................................................................................75
4.3
Crop prices ............................................................................................................78
4.4
Total carbon sequestration (million tons of carbon) .............................................83
5.1
Total crop choice with carbon renting policy .......................................................86
5.2
Total conservation crop with carbon renting policy .............................................88
5.3
Crop prices with carbon renting policy.................................................................89
5.4
Total cumulative carbon gain above the baseline
with carbon renting policy ...................................................................................91
5.5
Total crop choice with per hectare payment .........................................................93
5.6
Total crop choices with
per hectare payment (75% minimum tillage)........................................................94
5.7
Total conservation crop land
with per hectare payment (35% minimum) ..........................................................97
xii
5.8
Total conservation crop land
with per hectare payment (75% minimum tillage) ...............................................98
5.9
Total cumulative carbon gain above the baseline (35% minimum till) ................99
5.10
Total cumulative carbon gain above the baseline (75% minimum till) ................99
5.11
Cumulative carbon gains in 2044 (carbon renting with $40 per ton) .................106
5.12
Cumulative carbon gains in 2044
($20 per hectare with 35 % minimum tillage) ....................................................106
5.13
Cumulative carbon gains in 2044
($20 per hectare with 75 % minimum tillage) ....................................................107
5.14
Cropland changes with $40 per ton of carbon price ...........................................111
5.15
The comparison of total conservation land .........................................................114
5.16
Total carbon gain by carbon renting policy
when total cropland changes..............................................................................117
xiii
CHAPTER 1
INTRODUCTION
1.1
Background
In recent years, there has been growing concern about the potential adverse
impacts of climate change. In response, the global community is considering actions to
mitigate the accumulation of green house gases (GHG) in the atmosphere. After series of
conference among countries, the first agreement (Kyoto Protocol) was made in 1997 as
mandatory sets of rules targeting reduction of GHG emission for participating countries.
The Kyoto Protocol provided the guidance of alternatives for the mitigation commitments
and most countries in the agreement started considering GHG reduction as a major policy
project. Among these GHG, carbon is the major target component for the efforts of
mitigation because of its tractability and major impacts (IPCC, 1996).
To mitigate the accumulation of carbon in the atmosphere, several different
alternatives have been encouraged, such as directly reducing carbon emissions and
storing carbon in "sinks," such as forests and forest and agricultural soil. Among these
alternatives, the potential for carbon to be sequestered in agricultural soils has recently
1
gained considerable attention because carbon in the soil pool could be an attractive
mitigation alternative. For example, estimates by Lal et al. (1995) suggest that the total
soil carbon pool contains 3.5 % of the earth’s carbon stock, compared with 1.7 % in the
atmosphere (Lal et al, 1995). It is also estimated that US cropland could sequester up to
75-208 million tons of carbon per year which is up to 8 % of carbon emission in the U.S.
(Lal et al, 1998).
Carbon in agriculture soil can be restored through alternative management than
currently occurs on large areas of cropland. One of the main potential methods for
increasing the stock of carbon in soils involves encouraging the adoption of conservation
tillage. Conservation tillage system uses crop residue to serve as mulch to protect and
increase soil organic carbon level. Conventional tillage, on the other hand, disturbs the
soil and leads to oxidation and subsequent loss of soil carbon and leaves it to wind and
rainfall, resulting in decrease in soil organic carbon level (Lal et al., 1998).
To date, several studies have examined the potential and the cost of carbon
sequestration in agricultural soils in the United States (McCarl & Schneider, 2001; Antle
et al., 2003; Pautsch et al., 2001;Feng et al., 2002; Lewandrowski et al., 2004). The
studies to date use a wide variety of methods and many of them focus on particular
regions. McCarl and Schneider (2001), for example, use a mathematical programming
model for the entire U.S. agricultural sector. Antle et al (2001) integrate a bio-physical
process model and econometric simulation model for the Northern Plains region. Pautsch
et al (2001) estimates the probability of tillage adoption in Iowa, and links these results to
a physical process model. The estimate of soil carbon sequestration cost from the studies
2
ranges from $2 to $60 per ton of carbon. These studies provide important insights on the
cost of carbon sequestration, but to date, several important intertemporal aspects have
been ignored.
This study addresses several missing components in earlier analysis. First, soils
accumulate carbon slowly, and different levels of residue management could lead to the
different rates of accumulation and different steady-state levels in the future (Lal et al.,
2000). This could have important implications for carbon sequestration because different
types of soils in different regions could lead to a wide range of observed residue levels.
Most studies to date have compared conventional tillage systems to no-till systems, or
they have used fixed rental payments per acre to spur conversion of land to no-till, and
thus have ignored the effects of the intensity of residue management on the costs of
carbon sequestration. In practice, farmers are observed to undertake a wide range of
residue intensity levels, and it is important to account for these differences when
estimating costs. There could be efficiency gains associated with designing policies that
match payments more closely to the intensity of carbon stored on a site, however. This
may be particularly important because landowners are observed to choose a range of
residue levels, depending on their equipment, rotations, and other factors.
Second, there is evidence that even small reductions in residue on a site could
lead to instantaneous emissions of much of the stored carbon into the atmosphere by
plowing the land (Pierce et al, 1994; Reicosky et al, 1995; Reicosky, 1997; Gilley &
Doran, 1997; Hansmeyer et al, 1998; Reicosky et al., 2002; Lal, 2002). Data from the
USDA Natural Resource Inventory (NRI, 2001) suggests that since 1982, farmers have
3
shifted into and out of conservation tillage frequently. Further, evidence from eastern
Corn Belt states, such as Ohio, Indiana, and Illinois, suggests that farmers typically use
conservation tillage with soybeans but not with corn (CTIC, 2002). Thus, many typical
rotations used in eastern Corn Belt states would lead to cycles of carbon accumulation
followed by instantaneous emissions when the land is plowed. When designing policies
for carbon sequestration, it is thus important to account for crop rotations and potential
cycles in sequestered carbon that could occur. Further, given the potentially important
link between carbon payments, conservation tillage, and crop rotations, payments could
alter the proportion of land in different types of crops, and ultimately prices. Several
existing studies ignore these price effects, potentially leading to biased estimates of the
cost of carbon sequestration.
Third, given the unstable property of carbon in soil and the possibility of cyclical
pattern in soil carbon accumulation, it is important to reflect the soil carbon sequestration
pattern likely to occur in the baseline carbon storage path in agriculture soils before
estimating potential gains. The key issue that arises under the Kyoto Protocol is the
baseline-how much carbon are we likely to get from soil management in the absence of
carbon policy. However, none of the studies so far takes account of cyclical soil carbon
sequestration pattern in their baseline. In addition, given the fact that carbon potential
could be affected by baseline scenario, none of the studies examines how the total carbon
sequestration would be sensitive with respect to different assumptions on the baseline
scenario. Several studies account for baseline sequestration, but they do not account for
the dynamics of soil storage. Moreover, as addressed in previous studies (McCarl &
4
Schneider, 2000; Marland et al., 2001; Feng et al., 2002), it is critical to design carbon
policy which could secure the sequestered carbon in the soil. Therefore, proper baseline
estimates could provide more accurate carbon policy evaluation.
Lastly, none of studies so far has investigated soil carbon potential in the eastern
Midwest Corn Belt region which is the highly productive area. Previous studies have
investigated different scales such as regional and U.S. level. Depending on the scope of
study, there could be different achievements from each study. National scale study such
as McCarl & Schneider (2000) could examine the entire agricultural sector and
understand the overall market impacts and feedbacks of prices for the entire U.S.
However, given the highly heterogeneous property in soil, there could be aggregation
bias and incorrect results (Antle & Mooney, 1999; Easterling, 1997; Swallow et al.,
1994). Regional studies (Antle et al., 2003; Pautsch et al., 2001) could utilize more
detailed information and derive more efficient policy implications but these studies have
not provided important price impacts. This study examines the regional scope that could
provide more detailed results such as county level and derive the price impacts. The
regional analysis as in this study is also appropriate to the Climate Change Action Plan
(EPA, 1998) that suggests states identify, develop, and eventually implement mitigation
plan for effective policy.
5
1.2
Objectives
In order to tackle the issues discussed previous section, this study will be broken
into three major objectives. The first objective of this study is to develop an empirical
dynamic simulation model that examines optimal solutions for crop choices and residue
management intensity in row crop agriculture production activities. To accomplish this
objective, I develop a theoretical model of crop choice and residue management intensity
over corn and soybean. The theoretical model is a dynamic optimization problem that
maximizes the net present value of market welfare from these crops. The model
investigates the optimal solution for the rotation between corn and soybean, residue
management intensity. This study focuses on three Midwestern U.S. states, Ohio,
Indiana, and Illinois. These states are located in the Corn Belt. The entire Corn Belt
produces more than 75 % of total corn and soybeans in the U.S., and these three states
product approximately 43% (USDA, 2004). These states have high productive agriculture
land and contribute heavily to the U.S. agriculture. However, some parts in this region,
such as southern Ohio and Indiana, corn and soybean production is limited by a number
of geographical considerations that reduce the value of land for agricultural production.
In order to develop the empirical model, a number of estimations are undertaken
to develop parameters for the model. The functions or parameters estimated include crop
yield functions, soil carbon sequestration functions, residue management impacts on crop
yields, and land use changes. Particular emphasis is placed upon the model that estimates
the influence of residue management on corn and soybean crop yields. While residue
6
management reduces yields for some crops, like corn, and potentially raises yields for
others, like soybeans, it reduces costs for both. The simulation model described above
accounts for the reduction in costs when converting to conservation tillage, so it is
important to have good estimates of the influence of conservation tillage on crop yields.
A regression model is therefore developed to explore how residue management affects
yields for different types of crops, and how these impacts vary across land of different
quality, as suggested by Porter et al. (1997). The results indicate that crop yields are
highly sensitive to residue management, and that this influences the optimal spatial
strategy for sequestering carbon.
The second objective of this study is to apply the theoretical model to simulate the
set of different baseline scenarios and to compare the crop rotations and carbon storage in
the region in the absence of carbon incentives. The model is deterministic, so to account
for potential uncertainty in the evolution of important parameters in the model, such as
demand, technology, etc., I develop a sensitivity analysis that shows how crop choices
and carbon sequestration may be influenced by alternative baseline assumptions. The
model is developed with empirical data for the three state region of interest. The model
is solved for a 40 year time period for 16 sub-regions, and 3 land productivity types in
each subregion using GAMS software and the MINOS solver.
The third objective of this study is to apply carbon policies to the empirical crop
choice model in order to examine the cost and potential for carbon sequestration in the
agriculture soil for the study region. I apply two different carbon policies to the model.
Carbon policy instruments include carbon rental scenario (Sohngen & Mendelsohn,
7
2003) and fixed per hectare payment scenario with different minimum residue
management requirements (35 % minimum residue intensity & 75 % minimum residue
intensity). The carbon policy analysis shows how crop choices, residue management
intensity, crop prices, and total carbon gains may be affected by different carbon policies.
The spatial patterns of carbon gains along these carbon programs will be examined as
well. With the presence of different yield potential over the study region, it could provide
useful insights where the carbon gains could occur.
Note that there could be several additional benefits from enhancing soil carbon
sequestration with conservation tillage, such as reducing soil erosion, improving water
quality by reducing run off from fields, improving soil fertility, minimizing nutrient
losses, improving nutrient cycling (Lal et al., 1998), and increasing wildlife by providing
shelter and food (CTIC, 2004). While these benefits are certainly important, they are
beyond the focus of this research, and therefore not considered in this study.
1.3
Literature review
Long before the issue of the carbon sequestration in soil emerged, soil
conservation issue traces back to the era of European colonization, and initial field
experiments on soil erosion started during 1920’s (Moldenhauer et al., 1994). Organized
comprehensive assessment of soil conservation began when Soil Conservation Service,
currently Natural Resources Conservation Service (NRCS), was established in 1935.
8
Since the Food Security Act of 1985, there has been substantial progress on the
improving conservation process (Weber & Margheim, 2000).
As the soil conservation issue drew public attentions, there have been numerous
studies examine soil conservation problem (for examples, McConnell, 1983; Clarke,
1992; LaFrance, 1992; Goetz, 1997; Hopkins et al, 2001). For a brief and non-exhaustive
review, early study by McConnell (1983) investigates optimal private path of soil erosion
with maintaining soil depth in agricultural production. The author suggests that social and
private erosion rate would be the same.
Clarke (1992) and LaFrance (1992) examine the impacts of input and output price
on the soil erosion problem. Clarke (1992) argues that crop price or input price changes
could provide incentives to reduce the soil degradation with increasing soil saving inputs.
LaFrance(1992) shows that subsidy on the output price could degrade the soil quality.
Also subsidy on the conservation activities and taxes on cultivation intensity may reduce
the soil stock.
Unlike the above studies with single crop analysis, Goetz (1997) explores the
optimal soil erosion with multiple crop case. The author argues that diversification and
rotation crops are the steady state results when soil loss affects the productivity. Myopic
farmers have monoculture and it is not steady state equilibrium.
Recent empirical study by Hopkins et al (2001) investigates farmers’ optimal
decision practices with two different soil degradation characteristics, soil depth profile
and soil nutrient. The authors suggest that optimal residue management vary with respect
9
to soil types and nutrient depletion is more important factor for the optimal decision than
the soil depth depletion.
Factors that affect the conservation adoption behavior have been analyzed by
many studies (Griliches, 1957: Antle & McGuckin, 1993: Wu & Babcock, 1998; Uri,
1999; Fuglie & Kascak, 2001). The implementation of conservation tillage depends on
site-specific factors such as soil type, topsoil depth, and local climatic conditions and also
geographic and demographic factors are important for adoption (Uri, 1999). These
studies have investigated many factors such as relative profits from practice alternatives,
risk, financial constraints, size of farm, education of farmers, and site-specific soil
characteristics. Among others, most these studies confirmed that soil characteristics and
profits significantly affect the conservation tillage adoption behavior.
In economics within recent years, several studies investigate cost of carbon
sequestration and policy implications in agricultural soil management (Antle et al., 2003;
Pautsch et al., 2001; McCarl & Schneider, 2001; Feng et al, 2002). Pautsch et al. (2001)
investigate the expected cost of carbon sequestration in Iowa. The authors first estimate
the probability of adopting conservation tillage practices using large sample points from
NRI data with logit estimation. From the probability of adoption of conservation tillage,
it is integrated with other simulation approach such as EPIC. The authors compared two
different carbon policy scenarios, single fixed payment per acre vs. discriminative
payment per acre scheme, and with two different types of farmers, newly adopting
farmers vs. all adopting farmers. From their empirical estimates of average cost of carbon
sequestration in Iowa, the scenario of discriminative payment to newly adopting farmers
10
results in less cost than the fixed subsidy scheme. Although carbon payment per ton gives
the most efficient policy outcome, there is technical difficulty in measuring carbon in soil
or the cost of measuring carbon is extremely high. However, the better understanding
carbon potential would enable to design more efficient policy from lower bound
estimates from per ton payment analysis.
For a different regional study in the North Plains U.S. (Antle et al., 2003), the
authors compare the cost of carbon sequestration for different contract methods, per
hectare payment and per ton of carbon payment. They also examine the measurement
costs to implement the per ton payment contract. Econometric estimation was applied to
obtain the production and profit and it is applied to get the discrete land use choice by
simulation model. The authors suggest that contract based on per hectare payment is five
times more costly than the contracts based on per ton of carbon payment. The
measurement cost of per ton carbon payment is estimated to be at least smaller than the
efficiency losses of per hectare payment contract.
In general, these studies compare two different types of carbon incentive
programs such as fixed payment scheme (per hectare) and flexible payment scheme (per
ton of carbon). The authors argued that previous environmental policy such as
Conservation Reserve Program (CRP) is believed to be inefficient for the carbon policy
because it does not consider heterogeneous soil characteristics and cost under the fixed
per acre payment system. Both studies utilize detailed samples from the study regions and
they provide statistically representative results. However, the carbon policy simulations
11
are based on the static analysis and it is not clear how the carbon policy would change the
production and price of crops.
Combining two carbon strategies for carbon program was considered in the study
by McCarl and Schneider (2001). In their sectoral analysis for the U.S., several
mitigation strategies such as afforestation, soil sequestration, bio-fuel offsets, and
livestock management were investigated at the same time. The authors considered
emission taxes and sequestration subsidies for policy instruments. Although detailed
description of the model is not available from their study, they argued that total
mitigation potential is sensitive to the carbon price and adopting mitigation strategies
decreases the total agricultural output and increases the price. It is important to
investigate the potential and cost of carbon sequestration when both alternatives are
included in the carbon program.
A theoretical study by Feng et al (2002) develops a dynamic optimization model
to investigate optimal paths of carbon emission, carbon sequestration, and carbon stock.
In their study, the authors suggest that carbon sequestration in sinks should be
implemented as early as possible to reduce the pressure on the emission abatement. They
also argue that any cyclical pattern of carbon sequestration and carbon release is not
optimal. In their study, there are three different carbon policy systems are introduced and
derived efficient conditions theoretically but the authors argue that actual implementation
depends on the cost of implementation and other political feasibility.
In the field of physical science, enormous amount of studies have investigated soil
carbon response to changes in tillage and crop rotations. The study by West and Post
12
(2002) provides the lengthy summary and tabulation of 67 long term agricultural
experimental studies, consisting 276 paired treatments from the global database and
synthesizes those previous estimates of carbon sequestration rate. The authors suggest, on
average, that converting conventional tillage to no till could sequester 57 ± 14 g Cm-2 yr-1.
Also, enhancing rotation complexity could sequester about 20±12g Cm-2 yr-1, excluding
continuous corn to corn-soybean rotation. Carbon sequestration rates reach to peak in 5 to
10 years after converting to no-till.
1.4
Organization
The organization of this study is as following. In the next chapter, the theoretical
dynamic optimization model is introduced. The baseline model analysis is first developed
and two different carbon policy scenarios, carbon rental and fixed payment per hectare,
follow.
In chapter 3, data and parameters for the dynamic model are provided. It begins
with the description of the study region. In the second section, the estimation of residue
management impacts on yield and its results are introduced. In the third section, carbon
information in agriculture soil is presented. In the fourth section, area base model is
introduced and its estimation results are provided. From the estimation results, land use
projection is presented.
In chapter 4, the empirical dynamic model result for the baseline is presented. It
includes the optimal path of crop prices, crop choice, tillage intensity, and crop yield
13
level over time. After adopting different assumptions on the crop demand, input price,
and crop yield growth, the optimal solution for sensitivity analysis are provided.
In chapter 5, model simulation results are provided for the two different carbon
scenarios, carbon rental payments and fixed hectare payment with two different minimum
residue management intensity. The result of carbon rental policy applied to the land use
change assumption is provided.
The last chapter is the conclusion of this study. It summarizes the findings from
this study and provides the implications. The limits and future development from this
study are discussed.
14
CHAPTER 2
DYNAMIC CROP CHOICE MODEL
The purpose of this chapter is to present a theoretic dynamic crop choice model.
First, I develop the model to obtain optimal rules for the crop choice between corn and
soybean, residue intensity under the baseline scenario. Then I expand the model with
carbon policy scenarios and examine how the optimal solution would be affected by the
carbon policy implementation.
2.1
Baseline
The dynamic model in this study is similar to the previous studies in the economic
literature (for examples, Goetz, 1997; Alig et al., 1997; Parks, 1995; Sohngen et al.,
1999). The dynamic simulation model in this study maximizes the sum of consumer and
producers’ surplus, which is the area difference between demand curve and total cost for
the production (Alig et al., 1997). The choice variables for the problem are the land
allocation of row crops in corn versus soybean, land allocation between conservation and
conventional tillage, fertilizer inputs, and residue management intensity for each crop.
15
The model accounts for land transfer between the two crops and conservation
choice. The baseline model investigates the landowner'
s problem when there is no carbon
policy involved. The cost function involves fertilizer inputs, residue management
intensity, and cost for the conservation versus conventional land choice for each crop.
The objective function and constraints for the baseline are shown in equations (2-1) to (22).
t
Max
fc , fs , Rc , Rs
ST ,CT , SV ,CV ,
CH ,CB , SH , SB
ρ {
C
T Q
1
0
c
c
c
c
D (Q ( Rc , Y (a, f c ), X )) +
s.t.
S
T Q
1
0
D s (Q s ( R s , Y s (a, f s ), X s ))
− C ( Rc , R s , f c , f s , X c , X s )}
(2-1)
X ctc ,i, j ,t = X ctc ,i , j ,t −1 − STi , j ,t −1 + CTi , j ,t −1 − CH i , j ,t −1 + CBi, j ,t −1
c
c
X cv
,i , j ,t = X cv ,i , j ,t −1 − SVi , j ,t −1 + CVi , j ,t −1 + CH i , j ,t −1 − CBi , j ,t −1
X cts ,i, j ,t = X cts ,i , j ,t −1 + STi, j ,t −1 − CTi , j ,t −1 − SH i , j ,t −1 + SBi , j ,t −1
s
s
X cv
,i , j ,t = X cv,i , j ,t −1 + SVi , j ,t −1 − CVi , j ,t −1 + SH i , j ,t −1 − SBi , j ,t −1
c
c
s
ST + CH ≤ X ct
, SV + CB ≤ X cv
, CT + SH ≤ X cts , CV + SB ≤ X cv
f c , f s , Rc , R s , ST , CH , SV , CB, CT , SH , CV , SB ≥ 0
(2-2)
0.35 ≤ Rc & R s ≤ 1
The notations t, i, and j denote time, regions, and land class respectively. For the
empirical estimates in this study, there are 40 years (t), 30 different regions (i), and 3 land
classes (j). The equations of motions in the equations (2-2) are for the stock of
16
conservation corn land (Xcct), conventional corn land (Xccv), conservation soybean land
(Xsct), and conventional soybean land (Xscv). Each land stock changes as shifts occur
among land usages. The land use shifts involve the conversion between corn and soybean
on the conservation use (ST & CT), between conventional corn and soybean (SV & CV),
between conservation and conventional corn (CH & CB), and between soybean
conservation and conventional (SH & SB). The description of the functions and variables
for in model is listed in table 2.1. The first two terms in the objective function (2.1) are
the sums of area under the demand curve for corn and soybean. The function QC(.) and
QS(.) is the total quantity production of the corn and soybean that depends on the yield
function (Yc & Ys), fertilizer input (fC & fs), total years continuously in corn and soybean
(a), total land of corn (XC) and soybean (XS), and the residue management intensity (RC
&RS). The last term C(.) is the cost function for corn and soybean which is the function
of fertilizer inputs, residue management intensity, and fixed cost for the land in each
crop.
Let the notation i and j be suppressed and the equation (2.1) and (2-2) could be
expressed as current value Hamiltonian,
H = V − C + λ1 (− ST + CT − CH + CB ) + λ2 (− SV + CV + CH − CB )
+ λ3 ( ST − CT − SH + SB) + λ4 ( SV − CV + SH − SB)
V=
C
T Q
1
0
c
c
c
c
D (Q ( Rc , Y (a, f c ), X )) +
17
S
T Q
1
0
D s (Q s ( R s , Y s ( a, f s ), X s ))
(2-4)
Notation
Definition
QC(.),QS(.)
YC(.),YS(.)
DC(.),DS(.)
XCct ,XSct
XCcv ,XScv
fc*,fs*
RC*, RS*
ST*
CT*
SV*
CV*
CH*
CB*
SH*
SB*
C
t
i
j
a
Discount factor
Total quantity of corn and soybean
Yield function of corn and soybean
Demand function of corn and soybean
Total conservation land area of corn and soybean (000 ha)
Total conventional land area of corn and soybean (000 ha)
Fertilizer input for corn and soybean
Residue management intensity for corn & soybean
Conversion from conservation corn to conservation soybean
Conversion from conservation soybean to conservation corn
Conversion from conventional corn to conventional soybean
Conversion from conventional soybean to conventional corn
Conversion from conservation corn to conventional corn
Conversion from conventional corn to conservation corn
Conversion from conservation soybean to conventional soybean
Conversion from conventional soybean to conservation soybean
Cost function
Time (total 40)
Study regions (total 30)
Land class (total 3)
Years counting in continuous corn and soybean
Table 2.1 Definition of model variables and functions
*; Control variables in the model
18
V is the value function of the first two brackets in equation (2-1), which is the
sum of integrals of demand function for corn and soybean. C is the cost function consists
of input costs such as fertilizer, fixed costs for corn and soybean, and residue
management. The variable
1
through
4
are costate variables. To maximize the problem,
following conditions should be satisfied. Equations in 2-5 indicate the first order
conditions for the fertilizer inputs and residue management intensity. They are just the
simple marginal rules for the inputs.
∂V ∂C ∂V ∂C
=
,
=
∂f c ∂f c ∂f s ∂f s
∂V
∂C ∂V
∂C
=
,
=
∂Rc ∂Rc ∂Rs ∂Rs
(2-5)
Let the demand and total quantity of each crops as following,
1
1
D c = P c = a − bQ c ; D s = P s = c − dQ s
2
2
c
s
Q c = Yctc X ctc + Ycvc X cv
; Q s = Yctc X cts + Ycvs X cv
Combining crop demand and yield functions with the optimal rules in (2-5), the optimal
fertilizer and residue management are:
Pc
P
∂Yctc ∂C s ∂Ycts ∂C
=
,P
=
∂fc ∂fc
∂fs ∂fs
c
c ∂Yct
∂Rc
=
(2-6)
s
s ∂Yct
∂C
∂C
,P
=
∂Rc
∂Rs ∂Rs
19
The first two equations indicate the first order condition for the fertilizer inputs for crops.
Marginal value of additional fertilizer input should be equated to the marginal cost of
fertilizer inputs. The next two conditions show the marginal rules for the residue
intensity. Marginal changes of value with respect to residue inputs should be equated to
the marginal cost of residue managements.
The control variables for land shifts are all linear in the equation (2-4), so it will
lead to the boundary solutions for these variables. The conditions are listed in the
equation (2-7) below.
Max
i ) ST = 0 < ST < Max
0
0
& CT = 0 < CT < Max
Max
λ1 > λ3
if λ1 = λ3
λ1 < λ3
Max
ii ) CH = 0 < CH < Max
0
0
& CB = 0 < CB < Max
Max
λ1 > λ 2
if λ1 = λ 2
λ1 < λ 2
Max
iii ) SV = 0 < SV < Max
0
0
& CV = 0 < CV < Max
Max
λ2 > λ4
if λ 2 = λ 4
λ 2 < λ4
Max
iv ) SH = 0 < SH < Max
0
0
& SB = 0 < SB < Max
Max
(2-7)
λ3 > λ 4
if λ3 = λ 4
λ3 < λ 4
Each control variables for the land use shift are dependent on the combination of costate
variables. The conditions in equations (2-7) indicate that there are pair wise patterns
which cause land shifts. For an example, the decision on shifting land between
20
conservation corn and conservation soybean (ST vs. CT in 2-7 i) takes place with
opposite pattern as the relative value between
1
and
3 changes.
The crop yield function (described in chapter 3) indicates that crop yields
decrease the longer land remains in a given crop, i.e. Y/ a < 0, where a is the year that
land parcels stay in the same crop. Thus, the co-state variables are decreasing over time
as the land parcel stays in the same crop over time. Combining with demand and yield
functions above, the equations of motion for each costate variables are expressed as:
i )λ1 − rλ1 = −
∂V
∂X ctc
ii )λ 2 − rλ 2 = −
iii )λ3 − rλ3 = −
iv )λ 4 − rλ 4 = −
+
∂V
c
∂X cv
∂V
∂X cts
∂V
s
∂X cv
∂C
∂X ctc
+
+
+
= C1 − P c ⋅ Yctc e ( −αt )
∂C
c
∂X cv
∂C
∂X cts
∂C
s
∂X cv
= C 2 − P c ⋅ Ycvc e ( −αt )
(2-8)
= C 3 − P s ⋅ Ycts e ( − βt )
= C 4 − P s ⋅ Ycts e ( − βt )
From the equations (2-8), the path of costate variables over time decrease as time
changes. The equations in (2-8) show the costate variable for the conservation land in
corn (i), conventional land in corn (ii), conservation in soybean (iii), and conventional
soybean (iv). In conjunction with the relation in equation (2-7), the land shifts among
crops and conservation practice occur as the costate variables change, in turn, yield level
changes. For example, from the equation (2-7, i), the choices on the conversion from
conservation corn to conservation soybean (ST) and conversion from conservation
soybean to conservation corn (CT) could be affected by the relation between the costate
21
variable
1
and
3.
As can be seen from the equation (2-8), the costate variables for each
cropland change by yield impacts on the continuous crop year for corn ( ) and soybean
( ). Depending on the different continuous crop year for each crop and conservation use,
the land use shifts would occur in different manner. The value of costate variable for the
conservation corn ( 1) is also related with the conventional corn ( 2) (2-7, ii). It would
affect the decision on the conversion from conservation corn to conventional corn (CH)
and conversion from conventional corn to conservation corn (CB). Other relations for
soybean land for both conservation and conventional use could be compared as the same
manner.
2.2
Carbon scenario
2.2.1
Carbon rental payment
This section presents a dynamic model that includes a carbon policy that pays
carbon rental on each ton sequestered each year, following Sohngen and Mendelsohn
(2003),. The objective function when augmented with carbon rental payment is shown in
equation (2-9):
Max
t
fc , fs , Rc , Rs
ST ,CT , SV ,CV ,
CH ,CB , SH , SB
ρ {
C
T Q
1
0
c
c
c
c
D (Q ( Rc , Y (a, f c ), X )) +
S
T Q
1
0
D s (Q s ( R s , Y s (a, f s ), X s ))
+ R ⋅ K ( Rc , Rs , X ctc , X cts ) − C ( f c , f s , X c , X s , Rc , Rs )}
K t = K t −1 + g ( Rc , Rs )
22
(2-9)
R in the objective function is the carbon rental rate and K is the total carbon stock stored
in agriculture soil. There is an additional equation of motion for the total carbon stock
which is the function of residue management intensity and conservation land area in corn
and soybean.
Applying the demand and yield functions from the last section to this problem, the
optimal residue management could be found as following rules,
∂Yctc ∂C
∂K
∂K
P
−
+R
+ λ5
=0
∂Rc ∂Rc
∂Rc
∂Rc
c
s
∂K
∂K
∂C
s ∂Yct
P
−
+R
+ λ5
=0
∂Rs ∂Rs
∂Rs
∂Rs
(2-10)
Compare (2-10) with the baseline case in (2-6), there are two additional terms for the
carbon rental payment. Invoking the negative impacts of the residue intensity on the crop
yield level and the variable cost, the optimal residue input in (2-10) would be greater than
the residue level in (2-6) if other things are all equal. Moreover, it indicates that as the
carbon rental payment R increases, to make the equality in (2-10), residue management
increases.
The optimal rules for the land use shifts as in (2-7) are identical in this problem.
However, the costate variables with carbon policy would be altered.
23
i )λ1 − rλ1 = −
∂V
∂X ctc
ii )λ 2 − rλ 2 = −
iii )λ3 − rλ3 = −
iv )λ 4 − rλ 4 = −
v )λ5 − rλ5 =
+
∂V
c
∂X cv
∂V
∂X cts
∂V
s
∂X cv
∂C
∂X ctc
+
= C1 − P c ⋅ Yctc e ( −αt ) − R
∂C
c
∂X cv
+
+
∂C
∂X cts
∂C
s
∂X cv
∂K
∂X ctc
= C 2 − P c ⋅ Ycvc e ( −αt )
= C 3 − P s ⋅ Ycts e ( − βt ) − R
∂K
(2-11)
∂X cts
= C 4 − P s ⋅ Ycts e ( − βt )
∂RK
= −R
∂K
Now the costate variables for the conservation land use in corn and soybean are different
from (2-8) so the relative values between these variables would occur differently and
therefore the rules in (2-7) are affected.
2.2.2
Per hectare payment with minimum tillage
In this section, the model includes a carbon policy that pays fixed payment per
hectare basis if any parcel of land is entered into the conservation usage. The model
assumes that once the land parcel is enrolled, the enrolled land parcels cannot be reversed
back to the conventional usage. For the conservation land, there is minimum required
residue intensity level. The model is shown in equations (2-12) below;
24
t
Max
fc , fs , Rc , Rs
ST ,CT , SV ,CV ,
CH ,CB , SH , SB
ρ {
C
T Q
1
0
c
c
c
c
D (Q ( Rc , Y (a, f c ), X )) +
S
T Q
1
0
D s (Q s ( R s , Y s (a, f s ), X s ))
+ CP ( X ctc + X cts ) − C ( f c , f s , X c , X s , Rc , Rs )}
s.t.
X ctc ,i, j ,t = X ctc ,i , j ,t −1 − STi , j ,t −1 + CTi , j ,t −1 + CBi , j ,t −1
c
c
X cv
,i , j ,t = X cv,i , j ,t −1 − SVi , j ,t −1 + CVi , j ,t −1 − CBi , j ,t −1
X cts ,i , j ,t = X cts ,i , j ,t −1 + STi , j ,t −1 − CTi , j ,t −1 + SBi , j ,t −1
s
s
X cv
,i , j ,t = X cv,i , j ,t −1 + SVi , j ,t −1 − CVi , j ,t −1 − SBi , j ,t −1
K t = K t −1 + g ( Rc , Rs )
c
s
ST ≤ X ctc , SV + CB ≤ X cv
, CT ≤ X cts , CV + SB ≤ X cv
f c , f s , Rc , R s , ST , SV , CB, CT , CV , SB ≥ 0
(2-12)
R ≤ Rc , R s ≤ 1
Now the model has the term for the fixed payment (CP) on the conservation corn
and soybean land parcels (Xcct & Xccv). Note that the equations of motion for the
conservation corn and soybean are different from previous models. There are not land
shifts from conservation to conventional land for both crops. However, the other land use
shifts such as transfers between corn and soybean are identical as before.
Using the same demand and yield functions from (2-5), the optimal rules for the
residue management intensity could be obtained as following.
25
∂Yctc ∂C
∂K
P
−
+ λ5
=0
∂Rc ∂Rc
∂Rc
c
(2-13)
∂Y s ∂C
∂K
P s ct −
+ λ5
=0
∂Rs ∂Rs
∂Rs
Note that the carbon policy pays for the conservation land hectares. Compare the
equations in (2-13) with the baseline results (2-6) and the carbon rental scenario (2-10),
the optimal rules for the residue management intensity with per hectare payment policy
give the level between the baseline and carbon rental scenario.
i )λ1 − rλ1 = −
∂V
∂X ctc
ii )λ 2 − rλ 2 = −
iii )λ3 − rλ3 = −
iv )λ 4 − rλ 4 = −
+
∂V
c
∂X cv
∂V
∂X cts
∂V
s
∂X cv
∂C
∂X ctc
+
+
+
= C1 − P c ⋅ Yctc e ( −αt ) − CP
∂C
c
∂X cv
∂C
∂X cts
∂C
s
∂X cv
= C 2 − P c ⋅ Ycvc e ( −αt )
= C 3 − P s ⋅ Ycts e ( − βt ) − CP
= C 4 − P s ⋅ Ycts e ( − βt )
v )λ5 − rλ5 = 0
To apply the model for the empirical study, various parameters and data are
required. In the next chapter, data for the crop yield, residue management impacts on the
yield, and carbon information are presented. Based on the model in this section, the
empirical dynamic model will be solved in chapter 4. Carbon policy will be analyzed in
chapter 5.
26
CHAPTER 3
DATA AND PARAMETERS
Before developing the numerical simulation model, it is useful to describe the
data necessary to carry out the simulations. This chapter begins by describing the study
region using NRI data. Second, an empirical estimation is conducted to estimate the
effect of residue management on crop yields in the study region.. Third, functional forms
for crop yields that incorporate these results are described, and additional parameters
influencing crop yields are provided. Fourth, carbon dynamics with respect to the residue
management are described, and an empirical equation built upon several studies in the
literature are provided. In addition to various studies from agronomy, crop science, and
soil science that are used to estimate initial carbon levels, carbon dynamics, and “steady
state” of carbon, I develop empirical estimates of the effects of residue management and
soil quality on corn and soybean yields. Lastly, an area base model is estimated to project
the future land use changes, in particular, the urbanization and change of cropland. The
projection results will be incorporated into the empirical dynamic model. It is expected
that the total available cropland in the future would be different from now and the pattern
of urbanization would affect the carbon sequestration potential in the study region.
27
3.1
Land distribution
There are total 282 counties and over 19.5 million hectares of cropland in Ohio, Indiana,
and Illinois. In order to make the model tractable, regions with similar soil types have
been accumulated into 16 geographically distinct regions: 5 in Ohio, 5 in Indiana, and 6
in Illinois (Figure 3.1). The aggregation of counties in the study region is based upon the
distribution of major soil types using detailed soil information in SOILS5 data that is
provided with NRI. In addition to grouping soil types, NRI dataset is used to further
classify soil quality within geographical regions. Thus, within each region, cropland is
divided into three land classes that have the different potential for crop productivity and
carbon sequestration. Within the NRI dataset, there are eight (VIII) different land
classes. The first two highest land quality class (I & II) are assigned to land class 1 in this
study, the next three land classes (III, IV, V) are allocated to the land class 2, and the
remaining land is allocated land class 3. The land distributions in each region and soil
quality class are listed in the table 3.1.
This study focuses on corn and soybean alone because they are the major land use
in the Eastern Corn Belt study region in general. Between 2000 and 2002, the average
proportion of total corn and soybean planted land among total planted crop land is 76 %
in Ohio, 91 % in Indiana, and 92 % in Illinois (USDA, 2003).
28
29
Figure 3.1 Aggregated soil and yield type in the study region
Ohio
1
2
3
4
5
Indiana
1
2
3
4
5
Illinois
1
2
3
4
5
6
(000 Hectares)
Class 1 Class 2 Class 3
430
368
86
998
314
28
1210
178
42
114
68
84
626
126
32
Class 1 Class 2 Class 3
852
198
110
1368
92
46
678
166
128
670
136
74
626
180
102
Class 1 Class 2 Class 3
710
524
196
1684
468
44
1382
208
64
852
276
130
910
374
134
1514
200
48
Table 3.1 Land distribution in the study region (000 hectares)
Class1; High land quality class
Class2; Medium land quality class
Class3; Low land quality class
3.2
Crop yield and economic data
30
The effects of residue management on crop yields have been investigated in
numerous studies (for examples, Uri, 2000; Dick et al., 1997; Stecker et al, 1995; Dick &
Van Doren, Jr., 1985; Bone et al, 1977). These authors suggest a wide range of impacts
of residue management on crop yields, depending on crop, location, soil type, and
experimental design. Despite the numerous studies, the effect of residue management on
the crop yield level differs among the studies. There are many potential reasons for the
wide differences. First, many of these studies are based on specific sites with specific
types of soils. Across the landscape, however, there are numerous different types of
soils, and likely numerous different impacts of adoption of conservation tillage. Further,
site specific studies often assume specific types of management, whereas in reality
farmers have adopted a wide range of crop management regimes. Thus, the findings in
many site specific studies usually do not capture the relation between yield and actual
land owners’ behaviors, and they are not statistically representative (Antle et al, 2001;
Segerson & Dixon, 1999). In order to develop statistically reliable estimates of the effect
of conservation tillage on crop yields for the entire region under study, I instead develop
crop yield estimates based on several different data sources, as noted in the next section.
31
3.2.1
Estimation of yield impacts of residue management
Following Segerson and Dixon (1999), yield impacts of residue management for
corn and soybean are estimated using annual county level data for the study region from
1988 to 1998. The estimations in this section specifically explore the impact of residue
management on corn and soybean yield by regressing bushel per acre on the independent
variables such as precipitation, soil physical characteristics, and tillage adoption rates
(See table 3.2 for variables). Lagged dependent variables for corn and soybean yields are
also included (CLAG for corn and SLAG for soybean) to capture possible
autocorrelation. Yield data for each crop were obtained from USDA National
Agricultural Statistic Service (NASS, 2004) data base for each year.
Total precipitation for January, April, July, and October in each year are used to
capture climatic impacts on yield. Climatic data is obtained from 10 different climatic
divisions in Ohio and it is estimated for each county (MRCC, 2002). The K-factor
measures how erodible the soil is. The higher the number for the k-factor, the less
productive the land. For the analysis, the average k-factor for each county is used (NRI,
2001). Residue management is captured by the variables CTIX, STIX, INTC, and INTS
variables. Extensive information on residue management and crop types for each county
were available from CTIC (2002). The data contains different tillage adoption acres such
as no-till, ridge- till, mulch-till, reduced-till, and conventional till for corn and soybean
since 1988 to 1998. The level of residue that remains on the fields varies by tillage
practice. Conventional tillage is the practice that leaves less than 15 % of residue,
32
reduced tillage is the type that leaves between 15-35 % of residue, mulch till and ridge till
leaves between 35 % to 70 % residue, and no-till is the type that residue level is more
than 70 %. CTIX and STIX variables are calculated as the proportion of weighted
average of residue remains to total harvested land for corn and soybean respectively. The
next variable INTC and INTS are interaction variables between k-factor and tillage
intensity index which is multiplication of two variables. I further test out hypothesis of
residue manage impacts on yield level using these interaction variables. It is assumed that
residue management intensity could affect differently on different quality land. This
interaction variable could provide additional relation of residue management on yield
through different land quality classes. So the coefficient of interaction variables could
capture the effects of residue management under given quality of land, k-factor. The last
variable T is a time trend variable starting from 1 in 1998 that could capture technical
progress and any fundamental changes within 10 years.
Dependent variable: Corn(Bu/ac)
Dependent variable: Soybean(Bu/ac)
Variables definition
Variables Definition
Const
constant
Const
Constant
CLAG
lag of corn yield
SLAG
lag of soybean yield
JANP
precipitation in January
JANP
precipitation in January
APRP
precipitation in April
APRP
precipitation in April
JULP
precipitation in July
JULP
precipitation in July
OCTP
precipitation in October
OCTP
precipitation in October
KFACT
k-factor
KFACT
k-factor
CTIX
Index of residue
STIX
index of residue management
management intensity
intensity
INTC
Interaction variable of
INTC
Interaction variable of
k-factor and conservation
K-factor and conservation
T
T
time trend
time trend
Table 3.2 Variables in crop yield estimation
33
The estimation results in Table 3.3 show expected results overall. Lagged
dependent variables on both equations have positive relation but insignificant result for
soybean equation. Weather variables show reasonable results that precipitation on
growing season such as July has positive impact on yield but precipitation on harvest
season in October has negative impacts. January precipitation in corn equation shows
significant negative impacts on yield level that could possibly capture the effects of
moisture on seeding season in spring. Soil quality variable k-factor shows expected
relation on both crop yields because higher number of k-factor is less productive land.
Corn equation(Bu/ac)
Variable
Coefficient
Const
132.91
CLAG
0.04
JANP
-4.01
APRP
0.62
JULP
4.25
OCTP
-1.81
KFACT
-111.23
CTIX
-65.26
INTC
173.18
T
3.01
t
11.11
3.35
-4.69
1.33
14.15
-3.97
-3.23
-2.14
1.9
12.53
Soybean equation
Variable
Coefficient
Const
42.56
SLAG
0.01
JANP
-0.54
APRP
-0.57
JULP
0.5
OCTP
-0.32
KFACT
-23.92
STIX
-11.11
INTS
40.98
T
0.88
Table 3.3 Estimation results of crop yield function
34
t
12.09
1.33
-2.1
-4.04
5.63
-2.33
-2.33
-1.45
1.79
10.81
Residue management variable CTIX and STIX show negative impacts on yield
level which has been suggested by several studies (for examples, Bone et al, 1977; Dick
& Doren, 1985;Stecker et al, 1995). Although these variables show negative impacts of
residue management on yield level, note that the conservation tillage intensity variables
are interacted with the soil quality variable KFACT. The marginal effect of a 1 % change
in residue management is therefore estimated as: is expressed as follows
dYield
= β + γKFACT
dCTIX
where
(3-1)
is the coefficient of CTIX and is the coefficient of INTC. To show how crop
yield is affected in regions with different soil types, the data is ordered from lowest to
highest k-factor, and the marginal effects calculated for each observation using equation
(3-1). Table 3.4 shows four different land qualities by k-factor percentiles packets, and
the numbers are average of marginal yield change on both crops. The results suggest that
with different land qualities residue management has different effects on yield. Corn
yield is more heavily influenced by additional residue management in higher land quality.
Residue management does not heavily affect corn yield on lower quality land. Soybean
yield, however, is not affected by residue management overall. These findings are used in
the dynamic model.
35
k-factors
Upper 25% percentile(Highest quality)
Between 50% and upper 25%
Between 50% and lower 25%
Lower 25% percentile (Lowest quality)
Corn(Bu/ac)
Soybean(Bu/ac)
-17.4
0.0
-7.5
1.4
-4.4
1.9
-0.9
2.3
Table 3.4 Marginal impacts of residue management on yield by land quality
3.2.2
Cost and residue management
Although higher residue management inputs reduce crop yields, farm profitability
may still rise because no-till management is observed to reduce input costs for fertilizers,
fuel for machines, machinery repair cost, and labor costs. Numerous studies investigate
how these input costs change with tillage choice (for example, Lines et al., 1990;
Clements et al., 1995; Sijtsma et al., 1998;Yiridoe et al., 2000; Katsvairo & Cox, 2000;
Uri, 2000). The estimates of input costs with respect to tillage intensity vary depending
on the study region and crop types.
Experimental study in Canada (Sijtsma et al., 1998) proposes that there are 44-60
% of annual cost savings with minimum tillage in potato-barley-forage rotation and 10-40
% cost savings in barley-soybean rotation compare to conventional tillage. However,
another Canadian experimental study (Yiridoe et al., 2000) of farm level profitability
analysis in Ontario region suggests that the average annual variable machinery cost with
no-till practice is the highest.
36
For the study in the Midwest U.S., Lines et al (1990) provides the budget analysis
on the representative farm of 1500 acres with corn, soybean, and wheat rotation in Ohio.
It suggests that the total annual machinery, labor, and herbicide cost on the conventional
tillage is about $47 per acre and $33 per acre with no-till practice. For this study, the cost
information on corn and soybean is adopted from the recent enterprise budgets analysis
(Moore, 2003). Total variable cost for conventional corn is about $168 per acre and $173
per acre for no-till corn. Based on these results, for this study I assume that total fixed
cost for conventional corn is about $177 and $115 per acre for no-till corn. For soybean,
however, total variable cost for both conventional and no-till are about $104 per acre.
Total fixed cost for conventional soybean is about $160 and $103 for no-till practice.
3.2.3
Yield functions and parameters
For the carbon study, it is important to examine crop rotation as well as tillage
intensity because carbon dynamics for different rotations are different along tillage
choices (Lal et al, 1998). Crop rotations are recommended for numerous reasons such as
higher yield, preventing pathogen build up, weed and insect controls, and for overall
lower costs (Beuerlein, 2001). Apparently, farmers also believe in crop rotations, as NRI
data suggests that farmers frequently shift their land usage between corn and soybean in
this region.
Experimental studies show that continuous corn yield levels are lower than corn
yield levels when corn is rotated with and soybean (Porter et al., 1997; Stecker et al.,
37
1995). In Ohio, for example, corn yields are generally higher by 5 - 15 % when corn is
rotated with soybean, rather than planted continuously (Beuerlein, 2001). For the
dynamic crop choice model, it is assumed that yield level declines the longer an
individual maintains land in a single crop type, and that the magnitude of this reduction in
yield depends on the land quality. This assumption follows Porter et al (1997), who
showed that corn and soybean rotation yields are up to 25 % higher than continuous corn
in poor production region and up to 15 % higher in high production regions.
Incorporating the above assumptions, quadratic functions of yield response by
fertilizer for corn and soybean were estimated from agronomy and crop science studies
(Vitosh et al., 2002; Munn et al., 1998). The functional forms are in equations (3-2).
Y C = [(α1 + α 2 f C − α 3 f C2 ) ⋅ e (α 5 a ) ]
Y S = [( β1 + β 2 f S − β 3 f S2 ) ⋅ e( β 5 a ) ]
Q C = Y C ⋅ e(α 4 Rc ) X ctc + Y C X cvc
Q S = Y S ⋅ e( β 4 Rs ) X cts + Y S X cvs
The parameters
(3-2)
and were estimated using the 10 year average crop yield
(USDA data base, 2002). The constant term
1
and
1 were
estimated to reflect different
yield potential in different region and land class. The estimates of parameters
1
and
1
are shown in table 3.5. The yield function curvature is assumed to be the same for the
entire region so the parameter
2,
2,
3,
and
38
3
are the same. The last two terms capture
yield effects by residue management and continuous corn and soybean effect. The
magnitude of each effect is different with land class (table 3.5). The negative signs in
4,
5,
and
5
4,
indicate that yield level declines as residue management (RC & RS) increases
and as a parcel of land continues in corn or soybean production without conversion to the
other crop type (a). The impacts of yield loss by residue management (
4,
4)
are obtained
from the estimation results from the previous section in 3.2.1. Note that the magnitude of
yield loss by residue management for corn is greater than soybean. Moreover, for the
middle soil class (class 2) is not affected by residue management and there is positive
impacts on the yield in the low soil class (class 3). The yield impact by continuous
cropping is negative for both crops (
5
&
5).
The magnitude is greater in corn than
soybean.
3.2.4
Crop prices and elasticities
As introduced in the previous chapter, the model in this study incorporates crop
demand so that the prices of corn and soybean vary over time as the total output of each
crop changes. The estimates of own-price elasticity of corn and soybean (Lin et al, 2000;
Huang & Lin, 2000) are applied to treat the demand curve as the total output changes.
The authors provide many useful estimates of elasticities such as own price and cross
price elasticities, but to make the study straightforward, the average estimates of own
39
price elasticities are applied. On average, the own price elasticity for corn is about 0.35
and 0.43 for soybean in the U.S.
These price elasticities are used to derive demand curve to set up the initial price
of corn and soybean, adjusted with total amount of crop production in the year 2003. The
regional average corn price was 2.48 dollars per bushel and soybean price was 7.25
dollars per bushel in 2003. The total quantity produced in the study region was about 3
billion bushels of corn and 740 million bushels of soybean in 2003. The empirical
derived crop demand functions are following.
D c = P c = 14 − 0.003 * Q C ,
D s = P s = 7 − 0.00094 * Q S
This study examines the regional scope in the Midwestern U.S. and the price
elasticity estimates above are from the U.S. national level estimates. To apply the U.S.
national elasticity estimates to the study region, I assume that the price adjustment by
quantity changes in the study region would occur exactly same manner in other regions as
the national estimates. So if there is 1 % corn production reduction in the study region by
carbon policy, there would be the same policy impacts on the corn production (1 %
reduction) elsewhere in the U.S. and the price impact would be the same in other regions
as well.
The regional model with in this study could omit certain important features. There
would be different policy impacts on the regional production level so the price impacts
would be different even with the same price elasticity assumptions. Price elasticities
40
would be different region to region and price impacts involve more complexity such as
import and export demand. Although regional model overlooks some important features,
this study focuses on the elements that cannot be investigated by full-scale models. This
study could examine more detailed information such as soil properties, production
potentials, and carbon dynamics.
Region
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
All
All
All
All
Parameter
Class2
148
199
203
140
164
213
199
173
189
218
202
153
195
188
170
195
Parameter
0.7167
0.7167
Parameter
0.004
0.004
Parameter
-0.17
-0.13
Parameter
-0.2
-0.15
Class1
159
212
217
151
176
227
212
185
202
232
215
165
209
201
182
208
1
2
3
4
5
Class3
134
182
186
126
149
196
183
158
166
194
178
133
173
166
149
172
0.7167
0.004
-0.1
-0.13
Table 3.5 Parameters for the crop yield functions
41
Parameter
Class2
29
34
35
32
31
41
33
36
40
52
41
36
41
37
37
40
Parameter
2.1575
2.1575
Parameter
0.0173
0.0173
Parameter
-0.07
0.001
Parameter
-0.12
-0.11
Class1
33
37
39
36
35
44
43
40
44
56
45
40
46
41
41
44
1
2
3
4
5
Class3
25
29
30
27
26
36
34
31
35
46
36
31
36
32
32
35
2.1575
0.0173
0.05
-0.1
3.3
Soil carbon data
3.3.1
Estimates of initial carbon
To investigate the carbon sequestration potential for the study region, initial
carbon levels in agricultural soil is required. The initial carbon in the study region is
estimated using soil information from NRI (USDA, 2001). Following the estimation
method by Mitchell et al (1998) and Lal (2000), the initial carbon in the top 30cm soil
depth was estimated. The equations (3-3) through (3-5) were applied to get the initial
estimates of carbon using NRI soil information.
AOM n =
0.5747
(OMLn + OMH n )
2
BM n = [0.5( BDLn + BDH n ) − 0.06]
IC =
W
30
n
( AOM × BM × [ DU n − DLn ])
(3-3)
(3-4)
(3-5)
The equation (3-3) estimates the average of organic matter percent (AOM) and
conversion factor 57.47 % for the percent of organic carbon for each layer. OML and
OMH are the low and high percent of organic matter for each soil column. Bulk density
average (BM) is estimated as in the equation (3-4) with dry bulk density conversion factor
0.06 for each layer. BDL and BDH are the low and high range of bulk density in each soil
column. Initial carbon IC (kg m-2) is estimated by using the equation (3-5). The depth of
upper and lower column is DU and DL respectively. It is the sum of each soil column up
42
to 30cm depth from the soil surface. After estimating the initial carbon for each point in
NRI sample point, it is estimated for the whole region using the weight W which is the
expansion factor in the NRI data for each sample point. The estimates of initial carbon in
each region are shown in table 3.6.
3.3.2
Carbon Dynamics
Carbon dynamics in the agricultural soil is affected by many physical, biological
and chemical processes (Lal, 2002). This study focuses on the impact of residue
management on organic carbon in the first 30cm of the soil column. The dynamics of soil
organic carbon with respect to residue management are obtained from various studies
(Lal et al., 2002 & personal communication, 2003; West & Post, 2002; West & Marland,
2002b; Paustian et al., 1997). Among others, Lal (1998) suggests that the gross rate of
soil organic carbon sequestration is about 400 to 800 kg per hectare per year in cold and
humid regions. In addition to the rate of soil carbon sequestration, there is a linear
relationship between residue management and carbon sequestration (Duiker & Lal, 1999;
Paustian et al., 1997).
Although enhanced residue management accumulates organic carbon in soil, the
accumulation slows as carbon reaches a steady state level. In general, soil scientists
suggest that for intensive residue management practices, such as no-till (where >90 %
residue remains on the site) steady state carbon levels are attained in 12 – 20 years (Dick
et al., 1997; Pierce & Fortin, 1997;Vitosh et al, 1997; West & Post, 2002).
43
Ohio
1
2
3
4
5
Indiana
1
2
3
4
5
Illinois
1
2
3
4
5
6
(Ton of C / Ha)
Class 1 Class 2 Class 3
43
41
30
36
31
29
54
53
31
50
53
17
34
33
25
Class 1 Class 2 Class 3
46
34
15
53
29
8
24
33
23
26
29
23
39
34
20
Class 1 Class 2 Class 3
38
29
25
35
30
15
30
20
17
29
22
14
61
43
25
50
30
13
Table 3.6 Initial Carbon stored in the study region for upper 30cm soil depth.
44
The potential carbon sequestration through changing residue management practice
ranges from 5-10 % (Houghton et al., 1997) to 30-50 % (Donigian et al., 1994; Bowman
et al., 1999) from the original carbon level. Acknowledging that there are differences in
these estimates, for this study, it is assumed that the maximum attainable carbon is about
30 % above the initial carbon level. Therefore, once there is 30 % gain above the initial
level of carbon, there is not additional carbon gain regardless of enhanced residue
management such as no till.
For the purpose of numerical simulation model, I adopt the assumption that
carbon accumulation is linear to residue management. Different rate of carbon
accumulation, however, are applied to the different regions and land qualities explored in
this study. Previous studies suggest that there are positive relations between carbon
accumulation rate and also soil clay content (Campbell et al, 1996; Bruce & Langdale,
1997). It is suggested that finer textured soil types can store carbon faster than coarse
textured soil types. This relation is also assumed in the CENTURY C model (Parton et al,
1987). According to Campbell et al (1996), there is 0, 1.6, and 3.9 ton of carbon per
hectare gain in the coarse-textured, medium-textured, and fine-textured soils respectively
after an 11 year period of continuous no till. The positive relation between the clay
content and soil organic matter, which is in turn the relation between clay content and soil
organic carbon, is also supported by Bruce & Langdale (1997). However, Campbell et al
(1996) also find out that carbon gain was not significant in the low productive region
regardless of clay content level across the soil in the low productive area. So it is
45
assumed in this study that low productive soils contain less initial carbon and carbon gain
compare to high productive soils but there is not variation in carbon gains across the
different region.
To reflect the difference in carbon accumulation rate for the different regions and
land quality, I adopt the estimate result of Campbell et al (1996). According to the
authors, there is a linear relationship between clay contents and carbon gain. The carbon
gain difference is about 0.01 ton per 100g/kg clay contents. The average clay contents in
each region and soil quality class is estimated from NRI soil information SOILS5 (Table
3.7). Calibrating the average clay contents, the carbon accumulation rate was obtained by
following rule.
C = C 0 + ( R × 12 × Clay × α ) / B
(3-6)
The equation (3-6) searches for the appropriate parameters to reflect the carbon
accumulation assumption in this study. The left hand side is the maximum carbon level
which is assumed 30 % above the initial carbon level. The first term on the right hand
side C0 is the initial carbon level. Then apply the clay contents to obtain the parameter
and B. The residue level R was applied 1 indicating 100 % residue intensity and 12 is the
year that is assumed for the consecutive years when the maximum carbon level obtained.
46
Average clay (10g/kg)
Ohio Class 1 Class 2 Class 3
1
18.6
15.2
20.6
2
16.3
16.6
15.0
3
20.8
17.4
20.5
4
22.9
16.0
40.5
5
21.5
16.6
20.3
Indiana Class 1 Class 2 Class 3
1
16.7
19.5
26.8
2
21.6
18.8
18.4
3
28.6
23.2
20.8
4
20.2
17.6
26.7
5
24.4
16.8
10.0
Illinois Class 1 Class 2 Class 3
1
26.3
20.6
24.0
2
23.7
18.8
29.9
3
24.4
18.1
25.0
4
26.3
21.7
26.6
5
24.3
20.9
24.1
6
20.7
22.0
23.0
Table 3.7 Average clay contents in 30cm top depth
47
Several authors suggest that most carbon in agricultural soil with enhanced
residue management would be lost into the atmosphere immediately when the soil is
disturbed by plowing (for examples, Reicosky et al, 1995; Reicosky, 1997; Lal, 2002).
However, there are several different estimates on the amount of carbon lost by plowing
after some period of carbon storage (Pierce et al, 1994; Gilley & Doran, 1997; Reicosky
et al., 1995; West & Post, 2002; Smith, 2004). Although the study by West and Post
(2002) concentrated on the effect of the conversion from conventional tillage to no-till,
the extensive summary in their paper suggests that there are various estimates of carbon
loss after plowing. The amount of carbon loss by intensive tillage such as moldboard
plowing is the most extensive, at more than 4 tons per hectare after 19 days once plowing
applied (Reicosky et al, 1995). It is about 134 percent of the carbon in that years crop
residue. From the study of the tillage effects on the Conservation Reserve Program (CRP)
site (Gilley & Doran, 1997), there was more than 8 tons of carbon loss per hectare after
nine month of winter fallow condition following tillage on the CRP site. In this study, it
is assumed that the most of carbon stored by enhanced residue management would be lost
if there is plowing, so the carbon level is assumed to be the initial carbon level. That is to
say, all the carbon stored by residue management is lost when the parcels of land
converted to back to conventional practice.
48
3.3.3
Empirical Carbon Dynamics
This section describes how I have taken the empirical results in the literature and
used them to develop a dynamic model of carbon sequestration in agricultural soils. This
model is used in the economic model described in chapter X of this thesis. Equation 3-7
shows the hypothesized carbon accumulation process.
Ct = Ct −1 + βRt −1 ⋅ X tcs−1 + γ X tcv−1
(3-7)
The carbon level at time t depends on the residue management level Rt-1 and the total
hectare on the conservation land Xcs. The parameter
is different by region and land
class. The relation between the residue management and carbon accumulation is linear.
The conventional land Xcv has the initial carbon level γ . Figure 3.2 represents examples
of carbon accumulation dynamics. There are three different carbon paths in the figure.
Vertical axis is carbon per hectare with 35 tons per hectare initial level. Horizontal axis is
year up to 30 years. The solid line (Case 1) represents the case when there is continuous
not-till for 30 years. Carbon level is increasing from the initial carbon level at 35 tons per
hectare until around the year 12 and stays at the constant level 45 tons per hectare, which
is about 30 % above the initial carbon level. The flat line with circle marker (Case 2)
shows the path when there is continuous conventional till, which is less than 35 % of
residue management. The dotted line (Case 3) shows the path of carbon when the residue
management intensity is same as the Case 1 except there is plowing at year 8. The carbon
49
increases until year 8 but decreases to the initial carbon level after plowing and increases
at the same rate as previous years and reach to the maximum level at year 22.
For carbon accounting, there could be additional carbon gains from conservation
tillage because there would be less fuel uses for machinery so there could be less carbon
emission into the atmosphere. However, there could be more emission of GHG from
conservation tillage compare to conventional way because conservation practice involves
more herbicide and pesticide inputs (West & Marland, 2002a). According to the authors,
the major portion of carbon accounting is in agricultural soil and regardless of carbon
effects by reduced fuel usage and more herbicide uses, these factors are not considered in
this study.
50
Carbon dynamic examples
C(tons/ha)
50
45
40
35
30
Case 1
Case 2
25
Case3
Year
20
1
3
5
7
9
11
13
15
17
19
21
23
25
27
Case 1: Continuous no-till (over 95% residue management)
Case 2: Continuous convention till (less than 35% residue management)
Case 3: Continuous no-till, plowing at year 9, and continuous no-till
Figure 3.2 Carbon dynamic examples (tons/ha)
51
29
31
3.4
Land use projection
Land use change in the study region is estimated following Hardie and Parks
(1997) and Plantinga et al. (1999). Given the emergence of the literature on spatial
econometrics (see Anselin, 1988), I test for the presence of spatial autocorrelation in the
estimated models. Spatial autocorrelation could be important if, for instance, there is
some unobserved relationship between the policies in two nearby counties. If these
unobserved factors are related to the errors (i.e. they are correlated), then the standard
errors for the parameter estimates could be biased. I thus develop three alternative
specifications for the area-base model of the Midwest, given different assumptions about
the form of the spatial relationships between county level observations. Estimates of
future land use areas are then developed and compared across the alternative models.
3.4.1
Model and data
The models estimate the share of land usage in forest, agriculture, and urban uses
in the study region. Each share of land usage is expressed as multinomial logistic
function with explanatory variables such as forest rent, crop rent, urban rent, distance to
the nearest city, population density, land quality indices, and dummy variables for
specific years (See Table 3.8).
52
Variables
CONST
FORENT
DISTANCE
DENS
LCC
AVLCC
D82
D87
D97
Crent
D1
D2
D3
D4
Rho
Definition
Constant term
Forest rent
Minimum Distance from major cities to the center of each county
Total population divided by total area in each county
The ratio of the first two highest land class
Average land class in each county
Dummy variable for 1982 data
Dummy variable for 1987 data
Dummy variable for 1997 data
Crop rent obtained by budget information
Dummy for the counties that population density is upper 20%
Dummy for the counties that population density is between 40%~ 21%
Dummy for the counties that population density is between 60%~41%
Dummy for the counties that population density is between 61%~80%
Coefficients for the weight matrix in Spatial model.
Table 3.8 Definition of variables
53
The functional form of a multinomial logistic function is following
βjX
e
Pj =
m −1 β X
1+ e j
j =1
, j = 1, , , m − 1
(3-8)
The left hand side is the proportion of land allocated to j usage and X is the vector of
independent variables and β is the vector of coefficients to be estimated. To have an
estimable functional form, this model can be expressed by log of proportions in different
land uses such as
ln
pj
pm
= βX + u i ,
(3-9)
where ui is assumed to be an independently and identically distributed, normal error term.
Because the errors could display heteroskedasticity, I adopt White’s suggestion to correct
the covariance matrix (White, 1980).
In addition to the heteroskedasticity that may occur as a result of the log
transformation in (3-9) or as a result of the underlying data, one must carefully consider
other problems that could arise with the errors in equation (3-9). One problem may be
the presence of spatial autocorrelation or omitted variable bias. For instance, the errors of
54
two counties next to each other may be more closely related than the errors of two
counties that are further apart. Alternatively, some unobserved factors that affect the
proportion of land uses in different counties could be omitted, but correlated with error ui.
The correlation with the error term can bias estimates of the standard errors. With county
level data, such unobserved factors could relate to policy variables that are similar across
counties, or it could be related to economic growth. For instance, economic growth in
one county could raise prices in that county, causing potential new migrants to move to
nearby counties where land prices are lower (Hsieh, 2000).
Despite the growth of the literature on spatial econometrics, relatively few studies
have attempted to apply the techniques to land-use change models. For policy purposes,
it would be useful to know if the techniques can help make better predictions of future
land use change. Literatures on spatial econometrics suggest that there could be different
specifications for capturing spatial process (Anselin, 1988). The spatial correlation could
occur on the error term, dependent variable, independent variables, or on both sides. The
choice of spatial process in the model relies on the empirical process and theoretical
background (Anselin, 2003). The most commonly used spatial model is autoregressive
model that spatial correlation occurs in the error term. The model in this study in equation
(3-8) and (3-9), spatial process could only be tractable in the error as in the equation (310) and (3-11). I thus test spatial dependency using following functional forms,
Y = Xβ + u
(3-10)
u = ρWu + e
(3-11)
55
The left hand side Y in equation (3-10) is the dependent variable as before, X is the set of
independent variables, and u is the error term which is spatially correlated. In equation
(3-11), W is an n-by-n weight matrix (where n is the number of observations) that defines
spatial dependency among observations, and e is i.i.d. error term. The coefficients to be
estimated are β and ρ. The weight matrix is chosen arbitrarily, although there have been
many studies investigating the optimal choice of weight matrices (Cliff & Ord, 1982;
Upton and Fingleton, 1985; Anselin, 1988). After testing a range of alternatives, I use a
distance criteria that allows 8 counties as neighbors. The weight matrix is rowstandardized so that the sums of each row in the weight matrix sum to 1.
An alternative method for capturing spatial effects is to utilize a fixed effects
estimator, which recognizes that certain observations behave similarly (Case, 1992). For
example, one might expect that land at the urban rural fringe in the sample would have
higher levels of opportunity costs than land further from cities. One would then want to
treat these counties differently from rural counties, by using a fixed effects estimator.
With a fixed effects estimator, the error terms are specifically assumed to be correlated
with the terms in X. I explored a number of alternative fixed effects, but settled on
population density for this study. This makes some sense if counties closer to cities
behave differently from rural counties. I rank each county in the dataset by population
density and then use dummy variables to represent the quintiles (Table 3.8).
Data used in this study was obtained from various sources. County level land-use
share data is from the NRI database for 1982, 1987, 1992, and 1997 (total 283 counties).
The NRI samples fixed plots on the landscape at five-year intervals. Estimates from these
56
sample plots are aggregated to the county level for the model. Land rental values are
estimated from other data sources for forest, crop, and urban. Following Plantinga et al.
(1999), population density (DENS) is used as a proxy for urban land values. It is assumed
that higher density increases development forces so in turn increase the opportunity cost
of maintaining other land uses. The total area of each county is from NRI data and total
population is from the Bureau of Census data for the same period of time (1982, 1987,
1992, and 1997).
Forest rent (FORENT) is estimated as the discounted net present value of timber
revenue per acre. Yield functions for each of the major species in each county are
weighted by the proportion of the species in each county, using USDA Forest Service
Forest Inventory and Analysis data. Regional timber price are used in Ohio and Illinois
(OASS, 1999 and IASS, 1999) although only state level data is available in Indiana
(Hoover, 2000). Land rents for forestry are obtained with the Faustmann formula
(Johansson and Logfren, 1985), assuming interest rates are 5 %. Land is assumed to be
naturally regenerated, an assumption I suspect is true for most land that converted from
agriculture to forestry in this region over the time period investigated.
In previous research, agricultural rents (CRENT) have been estimated with a
number of different approaches, such as farm revenues and costs (Stavins and Jaffe 1990,
Parks and Murray 1994, Hardie and Parks 1997), ratio of income from competing land
use (Alig 1986, Alig et al. 1988), prices of commodities from agriculture (Lichtenberg
1989, Wu and Brorsen 1995), and revenues less costs as calculated from farm budgets
(Plantinga et al. 1999). In this study, annual revenue above variable cost is used as the
57
estimate of the value of cropland. Crop budgets obtained from the Cooperative Extension
Services of the three states are used to estimate these values for four major crops
produced in the region: corn, wheat, soybean, and oats. Crop yield for each county is
estimated from USDA Agricultural Census (USDA 1999). Price information is obtained
from USDA data base system (USDA 2000). County level estimates of crop rents are
then determined by weighting the returns for each crop in a county by the number of
acres in the crop in the county for each period.
I control for land quality with two additional variables LCC and AVLCC. There
are eight land capability classes in the NRI data that is assessed by slope, soil texture, soil
depth, effects of past erosion, permeability, water holding capacity, and type of clay
minerals. Land in the first four classes is most suitable for common field crops, forest
trees, and range plants (USDA, 1961). Consequently, LCC is the proportion of land in
each county in the first four classes. AVLCC is average class (weighted by area) in each
county. Note that higher AVLCC implies lower quality land.
Distance form the nearest city (DISTANCE) is also used in the models. Similar to
the population density variable, this variable is expected to capture a component of urban
land use demand, although it is likely to play a different role than population density.
Large cities for Ohio are Columbus, Cleveland, Cincinnati, Dayton, Akron, Toledo, and
Pittsburgh (some eastern counties in Ohio are suburbs of Pittsburgh). For Indiana, cities
are Indianapolis, Evansville, Fort Wayne, South Bend, Gary, Chicago, Cincinnati, and
Louisville. For Illinois, cities are Chicago, Springfield, Peoria, Rockford, and St. Louis. I
also include dummy variables for years in most models estimated below. This amounts
58
to estimating a fixed effects model in the panel of data over 4 periods. The fixed effect
model accounts for a number of factors that are unobserved in each county, but which are
expected to remain the same over the time period. Examples of these types of variables
might be lakes and streams, or large capital investments like timber mills. A dummy
variable is also used for the first, second and last years in the analysis (1982 = D82,
1987=D87, and 1997 = D97).
3.4.2
Estimation result
The observations for the four time periods are pooled and fixed effects are used
for three of the years. The results for three alternative models are presented in Table 3.9.
The Base Model does not correct for spatial effects, but it does correct for the presence of
heteroskedasticity with White’s consistent estimator of the variance-covariance matrix
(White, 1980). The remaining heteroskedasticity does not bias the estimates, but it could
underestimate the variance in the model, potentially biasing tests of significance (Greene,
1997). The Fixed Effects Model (FE Model) incorporates the fixed effects based on
population density in each county, and the spatial model accounts for a specific form of
heteroskedasticity, namely spatial autocorrelation.
The estimated coefficients in each of the models generally show expected signs and are
significant. Higher forest rent reduces the proportion of agricultural land to forestland
(A/F equation) and urban land to forestland (U/F equation). Higher crop rent increases
the proportion of agriculture to forestland (A/F) and urban to forestland (U/F). A higher
59
value for the land quality classification (AVLCC) reduces the proportion of land in
agriculture suggesting that lower land quality reduces the proportion of agriculture. This
follows general expectations. Alternatively, a higher proportion of high quality
agricultural land increases the proportion of agricultural to forestry land, and it reduces
the proportion of urban to forest land (although it is insignificant in all three models).
Distance to the nearest city reduces the proportion of agricultural and urban land to
forestland. The result for urban land probably reflects the fact that most population
centers in this region are located in agricultural regions rather than forested regions.
Base Model
A/F
U/F
**
4.803
0.956
**
-0.047
-0.006
**
-0.003
-0.008**
-0.003** 0.015**
0.918** 0.001
-1.094** -0.758**
-0.057
-0.027
-0.012
0.133
0.201** 0.174*
0.005** 0.003*
Regression
CONST
FORENT
DISTANCE
DENS
LCC
AVLCC
D82
D87
D97
CRENT
D1
D2
D3
D4
Rho
**: 95% Confidence interval
Fixed Effect Model
A/F
U/F
**
4.953
-0.035
**
-0.047
-0.009
**
-0.003
-0.006**
-0.002*
0.008**
0.855
0.080
-1.115** -0.666**
-0.075
0.073
-0.041
0.399**
0.173*
0.352**
**
0.005
0.004*
**
-0.249
1.370**
-0.098
0.859**
0.032
0.588**
-0.006
0.050
-
-
*: 90% Confidence interval
Table 3.9 Estimation result of three models
60
Spatial Model
A/F
U/F
4.676** 1.052*
-0.043** -0.009
-0.003*
-0.008**
-0.003** 0.015**
0.870** -0.010
-1.077** -0.771**
-0.009
-0.044
0.007
0.143
0.166*
0.201*
0.005** 0.003*
-
-
-
-
-
-
-
-
0.344
0.176*
Population density (DENS) shows expected sign in the U/F equation, but in the
A/F equation, higher population density reduces the ratio of agricultural land to
forestland. This suggests that population seems to prefer agricultural land for
development purposes. Similar results are found in previous studies (Parks & Murray,
1994; Hardie & Parks, 1997; Ahn et al., 2000). Although these studies did not investigate
the issue further in detail, Parks and Murray (1994) suggest that the relationship could be
coincidental. One explanation for this is that forestland is more expensive to develop, so
that most development occurs on agricultural land rather than forestland. Another
explanation is that most development in this region is occurring around cities, which
happen to be located in agricultural regions. I test this hypothesis more specifically
below.
The dummy variables for population density in the fixed effects model are
significant only for the most populated counties in the A/F equation. These results
suggest that the relationship between agricultural land and forestland is non linear for
different levels of population density. Counties with the highest population density have
a significantly lower ratio of agricultural to forestland. One explanation is that most
development occurs on agricultural land rather than on forestland, perhaps due to costs.
Alternatively, when population density grows around cities, it may induce a shift of
agricultural land to forestland as farmers move away from the region. Similar explanation
was suggested by Hardie and Parks (1997), but they related the issue with farming life
cycle and farmers’ age. Most of the dummy variables are significant in the U/F equation,
61
and they decline towards 0 for lower population densities. As expected, the ratio of
urban to forestland is generally higher for more populated counties.
The spatial model and the base model display different significance levels for a
number of variables. This could reflect correlation between the error term and
unobserved or omitted variables in the base model, or it could just reflect a nuisance
(spatial autocorrelation). However, significance levels change mainly for the two
variables reflecting suburbanization. For example, DISTANCE and DENS become
insignificant in the A/F equation, suggesting that the results above showing that
population prefers agriculture land relative to forest-land could be over-stated. The
remaining results are remarkably consistent with both the base model and the fixed
effects model. These results provide some measure of confidence for hypothesis tests
about the effects of forest and crop rents on the decision to hold land in agriculture and
forestry. The results of the spatial model support Parks and Murray (1994) who suggest
that the relationship of forestland to suburbanization is coincidental. Suburbanizing
trends affect mainly the level of urban to forest and agricultural land, however, the
decision to maintain land to agriculture or forestry depends mainly on land rents (and
consequently land quality).
To investigate the urbanization pattern in this region further, I first examine the
land use pattern in the study area. Figure 3.3 shows the relation of density and distance to
large cities. The data for 1997 is reordered from the nearest counties to the large cities in
the origin of x axis to further away counties as move out from the origin. In general,
density decreases as move away from the large cities. However, there are several peaks of
62
density in further away counties. Obviously, the reason is that I only consider 14 large
cities in this region and there could be other smaller but high density local cities in this
region. Moreover, this could be capturing the recent suburbanization pattern. Figure 3.4
shows the relation of density and crop and forestland ratio (A/F). It is reordered by
density so the origin of x axis has the highest density. It shows that A/F ratio is higher in
lower density counties (as move out from the origin). These two relations support the
regression results in this study and previous findings in other regions that urban area
coexists more with forest land than with agricultural land.
There could be different assumptions for having less agricultural land in high
density area. From the developers’ point of view, it could be less expensive to build up
urban facility on agricultural land because of accessibility to build up infrastructures or
less clean up cost. Rental value of housing after built up also could affect developers.
Where housing would be located could affect the housing value i.e. open space versus
forest area. For the cropland owners, as population increases or urban facility approaches
to their farmland, it could make harder for their activities such as complaints from nearby
housing neighbors, urban road, or isolation from other farmland so they tend to decrease
or stop investment in their farming process that could be hypothesized as impermanence
syndrome (Berry, 1978). It is also argued that there tends to be overvaluation of urban
usage and undervaluation of farm use near urban-rural fringe so farmers tend to behave as
speculators (Nelson et al, 1995).
63
400
350
300
distance
density
250
200
150
100
Counties
50
0
1
51
101
151
201
251
Figure 3.3 Density and distance to large cities. Reordering data from the nearest distance
to large city. (1997 data)
350
300
250
200
150
density
A/F ratio
100
Counties
50
0
1
51
101
151
201
251
Figure 3.4 Density and crop to forestland ratio. Reordering data from the highest
density. (1997 data)
64
3.4.3
Projection of land use
The land use projection for 40 years from now is simulated using the estimates of
area base model with spatial model (equations 3-10 & 3-11). The projection begins with
the year 2004 and makes 10 year predictions to 2044. Although the regressions only
cover the period 1982 to 1997, I obtain an expected value for the year 2004 using actual
price data from that year, and use that year as the base.
Two scenarios are developed to capture a range of potential future changes. Both
scenarios predict the same total population growth for the three-state region; however, the
scenarios disperse the population differently across the landscape. State level population
growth from 2000 to 2040 is projected to be 26% in Ohio, 31% in Indiana, and 22% in
Illinois (Department of Commerce, 1995). The first scenario, uniform population
growth, assumes that population growth occurs uniformly across the counties in each
state. That is, each county experiences the same percentage growth as predicted for the
region as a whole.
The second scenario, suburban population growth, places all the population
growth in suburban counties around metropolitan areas, while allowing population to
decline in rural areas. Thus, in addition to net migration into the region as a whole,
residents are assumed to migrate from rural areas to suburban areas. For the suburban
population growth assumption, we define suburban areas as counties surrounding
metropolitan areas. Both scenarios assume the same total level of population growth in
the entire region, but they allocate the growth differently across counties.
65
In both scenarios, each counties in this region is assumed to be a price taker on
international markets for agricultural and forestry products. Thus, the same changes in
forest and agricultural prices and rents are assumed for each county. Both scenarios
assume that forestland rental rates rise at 0.6% per year, while cropland rental rates are
assumed to rise at 2% per year. Two sources of information were used to develop the
crop rent predictions for major crops in this region, FAPRI (2000) and USDA (2000).
These studies predict increases in crop rents of 2% to 4% per year. I use this lower value
as the baseline assumption for crop rents. Other variables such as distance and soil
quality are expected to be same over the years.
The resulting land use projections are shown in Table 3.10. Both forest and
agricultural land are projected to decrease over this time period while urban area is
expected to increase. The suburban population growth scenario predicts generally larger
shifts towards urban uses than the uniform population growth scenario. Recall that total
population growth in the region is the same for both scenarios, and the only difference is
in where the population growth is predicted to occur. Following the empirical estimates
above, new residents in suburban areas are predicted to use more land per person than
new residents in rural areas.
Although there are differences in projections between the different assumptions
for where population growth occurs, projections of total urbanization are similar across
the three sets of empirical estimates. The main difference among the empirical models
appears to be in how much land is derived from agricultural land versus forest land. All
66
three models suggest more loss of forestland and Suburban population growth scenario
gives more loss of both cropland and forestry and more urbanization rate than Uniform
population growth scenario.
2004
Base model
Uniform
Forest
5857
Crop
19960
Urban
3026
Suburban
Forest
5857
Crop
19960
Urban
3026
FE model
Uniform
Forest
5887
Crop
20434
Urban
2523
Suburban
Forest
5888
Crop
20438
Urban
2519
Spatial model
Uniform
Forest
5565
Crop
20289
Urban
2990
Suburban
Forest
5565
Crop
20289
Urban
2990
2014
2024
2034
5791
19906
3147
5704
19866
3274
5595
19842
3407
5461
19838
3545
-396
-122
518
5773
19833
3238
5661
19707
3476
5520
19595
3729
5352
19510
3983
-506
-450
956
5850
20394
2600
5799
20366
2680
5732
20351
2761
5647
20355
2843
-241
-79
320
5853
20374
2617
5801
20320
2723
5730
20272
2841
5645
20299
2900
-243
-138
381
5510
20213
3121
5438
20146
3260
5296
20154
3394
5083
20240
3520
-481
-49
530
5494
20140
3210
5397
19987
3460
5225
19908
3711
4980
19915
3949
-585
-374
959
Table 3.10 Land use projections (000 ha)
67
2044 Change
CHAPTER 4
BASELINE AND SENSITIVITY ANALYSIS
In this chapter, I present the results of the numerical simulation model for a
baseline scenario, and for a set of different assumptions on important economic
parameters, such as crop demands, input costs, crop yield level, and interest rates. The
different assumptions are used to examine how sensitive the model is to alternative
assumptions, and how the optimal choices are affected by different assumptions. In
particular, the focus is on total land choice for each crop, crop prices, tillage intensity,
total conservation land for each crop, and total carbon sequestration path.
For the baseline, it is assumed that demand for each crops rises at 2 % per year,
input costs rise at 3 % per year, and discount rate is 3 % per year. The crop yield could
rise over time, for example, by technology progress and it is assumed that it rise 2 % per
year. For each assumption, there are two alternatives, high and low. The alternatives are 0
% and 5 % annual growth of demand, 0 % and 4 % of crop yield growth, 0 % and 5 % of
input costs changes, and 5 % interest rate.
The empirical model in this study examines the 40 year simulation. As common
problem for the dynamic study, the terminal condition should be provided so as to
68
prevent the model just shifts all the land into corn or soybean and also conservation or
conventional use. Similar as other previous studies (Sohngen & Mendelssohn. 2003;
Adams et al, 1996), assume that demand and land use shifts do not occur after the final
period and stays for infinite time.
4.1
Total crop choices
Combining all the empirical estimates from the chapter 2 and the different
assumptions, the resulting crop choices under different assumptions are displayed in the
figures 4-1 (A-H). Figure 4.1(A) shows the results of baseline for the total land choices
between corn and soybean over time. The total crop choice shifts between corn and
soybean. One of major forces for making shifts between the two crops is that continuous
land usage in one crop reduces the yield level. In general, the total land in corn is slightly
greater than the total soybean land. This makes sense because the returns to a hectare of
corn are typically higher than the returns to a hectare of soybeans.
In figure 4.1(B), the result of total crop choice under 0 % yield growth
assumption is represented. Crop choice is gradually moving to soybean and all the land
shifts to soybean after 25 years. This occurs because input costs continue to rise, and
without gains in corn yield in particular, soybeans are cheaper to produce and therefore
are more heavily adopted. These results can be contrasted with the higher yield growth
assumption, where more land is used in corn (Figure 4.1, C). With higher yield growth,
69
the returns to corn outpace the returns to soybeans and landowners convert to corn. Few
acres, however, shift into continuous corn, but landowners do more rotations of corn per
soybean rotation to increase returns.
For the demand growth assumption, the lower demand growth assumption (0%)
gives results in a larger proportion of soybeans (Figure 4.1, D), whereas higher demand
growth (5 %) suggests more corn (Figure 4.1,E). With higher prices, landowners can
increase overall returns by planting corn more widely, and vice-versa for lower prices.
The lower input cost (0 %) assumption allocates more land on corn (Figure 4.1, F)
and the higher cost (5 %) scenario gives increasing land use trend on corn (Figure 4.1,
G). One of possible explanation for this is that corn production involves more input costs
than soybean so corn production is more sensitive to the input costs. By imposing high
input costs, it shifts more land to soybean than the baseline scenario. High discount rate
scenario gives similar crop choice trend over time but the magnitude between the crops is
slightly smaller than the baseline.
There are some unrealistic results such as all of the cropland shifts into soybean
(Figure 4.1 B & G). Although it would not likely happen in the real world under such
assumptions, it represents the model boundary for the assumptions and sensitivity of the
model.
70
Total Crop
(000)ha
14000
Total Crop
(000)ha
25000
12000
20000
10000
15000
8000
Corn
Soybean
6000
4000
Corn
Soybean
10000
5000
2000
Year
0
1
5
9
13
17
21
25
29
33
37
1
A) Total crop choice (Baseline)
(000)ha
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
1
Year
0
5
9
13
17
21
25
29
33
37
B) Total crop choice (0% yield)
Total Crop
Total Crop
(000)ha
14000
12000
10000
8000
Corn
Soybean
Year
5
9
13
17
21
25
29
33
6000
2000
Year
0
1
37
C) Total crop choice (4% yield)
Corn
Soybean
4000
5
9
13
17
21
25
29
33
37
D) Total crop choice (0% demand)
Figure 4.1 Total crop choices (continued)
71
Figure 4.1 Continued
(000)ha
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
1
Total Crop
Total Crop
(000)ha
16000
14000
12000
10000
8000
Corn
Soybean
Year
5
9
13
17
21
25
29
33
Corn
Soybean
4000
2000
Year
0
37
1
E) Total crop choice (5% demand)
5
9
13
17
21
25
29
33
37
F) Total crop choice (0% input cost)
Total Crop
(000)ha
25000
6000
Total Crop
(000)ha
14000
12000
20000
10000
15000
8000
10000
Corn
Soybean
5000
Year
0
1
5
9
13
17
21
25
29
33
6000
2000
Year
0
37
G) Total crop choice (5% input cost)
Corn
Soybean
4000
1
5
9
13
17
21
25
29
33
37
H) Total crop choice (5% discount rate)
Figure 4.1 Total crop choices
72
4.2
Total conservation land use
The choices on the conservation land use across corn and soybean under different
assumptions are now examined. For the baseline scenario (Figure 4.2, A), conservation
land usage in soybean is greater than corn. It represents the patterns in the study region
that the adoption rate of conservation tillage in soybean is bigger than corn. The total land
in conservation shifts between corn and soybean as the total crop land. Compare to the
total land use in the figure 4.1(A), in general, the total soybean hectares on conservation
practice moves around at 3 million hectares, which is about a third of total soybean and 2
million hectares for conservation corn, which is about 11 % out of total corn.
In figure 4.2 (A & B), conservation land use with different yield assumptions are
presented. With low yield growth (0 %), the conservation soybean dominates the other
land use choices over time. Compare to the total crop choice with low demand (Figure
4.1, B), all of the land is devoted to soybean with conservation practice. High yield
growth assumption (5 %) gives decreasing trend of conservation land use for both corn
and soybean and it reaches to zero after 21 years. It is assumed in the model that
conservation practice reduces input costs and negative yield impact on soybean is the
least. With rising input costs assumption, low yield growth assumption makes
conservation practice more profitable. Higher yield makes input cost negligible and
conventional practice more profitable and more choice on corn.
For the demand assumptions, low demand gives more land use in conservation
practice for both corn and soybean than the baseline and the magnitude is bigger in
73
soybean (Figure 4.2, D). High demand assumption makes conservation practice for both
corn and soybean reduce rapidly and reach to zero after 10-11 years (Figure 4.2, E). The
explanation for this is similar as the assumptions with yield growth. Low demand makes
conservation soybean more favorable because it could save input costs under increasing
input costs and stagnated demand level. For the high demand scenario, conventional
practice is more favorable because of the high rising demand, i.e. crop price so the input
costs are getting less important. However, the scale of changes is smaller under the
demand assumptions than the yield growth assumptions.
The results with different input costs assumptions are shown in figure 4.2 (F &
G). Low input costs transfers all the land use into the conventional use for both corn and
soybean. However, high input costs assumption gradually moves land into the
conservation practice for soybean over time.
The pattern of conservation practice is similar across assumptions. The
assumptions on high yield, high demand, and low input costs make less land use on the
conservation practice for both crops. The opposite scenarios allocate more land on
soybean with conservation practice with different scales.
For the high discount rate (Figure 4.2, H), the pattern of conservation land use for
both corn and soybean is similar as the baseline scenario over time but as it approaches to
later years the land on conservation practice slightly decreases for both crops. It could be
explained that the higher discount rates at the later period would affect much less present
time compare to the baseline scenario, in particular, input cost savings by conservation
practice. Therefore, total hectares in conservation practice could be decreased.
74
Total conservation crop
(000)ha
7000
Corn
Soybean
6000
5000
Total conservation crop
(000)ha
25000
20000
4000
15000
3000
10000
2000
Corn
Soybean
5000
1000
Year
0
1
5
9
13
17
21
25
29
33
37
1
A) Total conservation crop (Baseline)
5
9
13
17
21
25
29
33
37
B) Total conservation crop (0% yield)
Total conservation crop
(000)ha
8000
Year
0
Total conservation crop
(000)ha
12000
7000
Corn
Soybean
10000
6000
8000
5000
Corn
Soybean
4000
3000
2000
6000
4000
2000
1000
Year
0
1
5
9
13
17
21
25
29
33
1
37
C) Total conservation crop (4% yield)
Year
0
5
9
13
17
21
25
29
33
37
D) Total conservation crop (0% demand)
Figure 4.2 Total conservation crop (continued)
75
Figure 4.2 Continued
(000)ha
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
1
5
Total conservation crop
Corn
Soybean
7000
6000
5000
Corn
Soybean
4000
3000
2000
Year
9
13
17
21
25
29
33
1000
Year
0
37
1
E) Total conservation crop (5% demand)
Total conservation crop
(000)ha
25000
Total conservation crop
(000)ha
8000
5
9
13
17
21
25
29
33
F) Total conservation crop (0% input cost)
Total conservation crop
(000)ha
7000
Corn
Soybean
6000
20000
37
5000
15000
Corn
Soybean
10000
4000
3000
2000
5000
Year
0
1
5
9
13
17
21
25
29
33
1000
Year
0
37
1
5
9
13
17
21
25
29
33
37
G) Total conservation crop (5% input cost) H) Total conservation crop(5% discount rate)
Figure 4.2 Total conservation crop
76
4.3
Crop prices
In this section, the crop prices under different assumptions are displayed in Figure
4.3 (A through H). For the baseline, the prices are stable over time. Soybean price moves
around at $6 per bushel and corn price settles around at $3.5 per bushel. The slight
movement of crop prices is mainly for the reason that the total land use, in turn, the total
output of each crops rises and falls over time.
When the yield growth is assumed at 0 % per year, the price of corn and soybean
rises over time (Figure 4.3, B). It reflects rising demand of each crop while the constant
yield growth of crops by the assumption. Likewise, when the yield level is assumed at 4
% per year (Figure 4.3, C) the overall price of both crops steadily go down over time.
For the 0 % demand assumption, crop prices are steadily going down over time
(Figure 4.3, D) It makes sense because it reflects that the crop yield rises over time while
crop demand is constant over time. For the high demand assumption (5 %), both price of
corn and soybean rise rapidly over time (Figure 4.3, E).
Figure 4.3 (F & G) show the price path with different input costs assumption, For
the low input costs case, the price path for both corn and soybean is stable and similar as
in the baseline scenario. However, with the high input costs assumption, soybean price
gradually reduces but corn price rises over time. From the total crop land in figure 4.1
(G), the total crop choice for soybean steadily rises and opposite for corn make such price
patterns. High discount rate assumption results in little effect on crop prices over time as
the total crop choices.
77
Crop price
Corn
Soybean
($/bu)
8
Crop price
($/bu)
7
7
6
6
5
5
4
4
Corn
Soybean
3
3
2
2
1
Year
0
1
6
11
16
21
26
31
1
Year
0
36
1
A) Crop prices (Baseline)
6
11
16
21
26
31
36
B) Crop prices (0% yield)
Crop price
Crop price
($/bu)
8
($/bu)
7
Corn
Soybean
7
Corn
Soybean
6
6
5
5
4
4
3
3
2
2
1
1
Year
0
1
6
11
16
21
26
31
36
B) Crop prices (4% yield)
Year
0
1
6
11
16
21
26
D) Crop prices (0% demand)
Figure 4.3 Crop prices (continued)
78
31
36
Figure 4.3 Continued
Crop price
Crop price
Corn
Soybean
($/bu)
50
45
40
35
30
25
20
15
10
5
0
Corn
Soybean
($/bu)
8
7
6
5
4
3
2
1
Year
1
6
11
16
21
26
31
Year
0
36
1
E) Crop prices (5% demand)
6
11
16
21
26
31
36
F) Crop prices (0% input costs)
Crop price
Crop price
Corn
Soybean
($/bu)
7
Corn
Soybean
($/bu)
8
6
7
5
6
5
4
4
3
3
2
2
1
1
Year
0
1
6
11
16
21
26
31
G) Crop prices (5% input costs)
Year
0
36
1
6
11
16
21
26
31
36
H) Crop prices (5% discount rate)
Figure 4.3 Crop prices
79
4.4
Residue management intensity
To grasp overall patterns of residue management intensity across scenarios, it is
worthwhile to examine average intensity over time. In table 4.1, the 40 year average
residue management intensity is summarized across the different assumptions. Note that
there are three different land classes in each crop. Class 1 is the best quality soil that has
the greatest yield potential and the Class 3 is the worst quality soil with the least yield
potential.
In general, average residue management intensity is higher in the worst quality
soil class (Class 3) than in the middle and best soil classes for both soybean and corn. For
both crops, the best soil quality class (Class 1) has the minimum residue level which is
about 35 % across the scenarios, except 0 % yield and 5 % input costs cases for soybean.
The results reflect the assumption about the yield impacts by residue intensity that the
high quality soil class losses more yield by residue intensity.
Comparing the average residue intensity across the scenarios, 5 % input costs
assumption results in the highest average residue management intensity in both crops
across overall soil classes. For the best quality soil in soybean, average residue intensity
is about 52 %, middle quality soil is about 84 %, and the worst quality soil class is about
97 %. The major reason for this is that the higher input costs make the more choice on
cost saving activity such as increasing residue input intensity. By the same token, average
residue management intensity is higher than the baseline when crop yield is assumed low
(0 %), demand on crop is low (0 % demand), and higher discount rate (5 %).
80
On the other hand, when there is high crop yield (4 %), high crop demand (5 %),
and low input costs (0 %) scenario, the average residue management intensity for both
crops is lower than the baseline scenario. These assumptions make opposite force that
input costs are getting insignificant compare to these changing forces.
Corn
Scenario
class1 class2
Baseline
35%
35%
0% yield
35%
35%
4% yield
35%
35%
0% demand
35%
35%
5% demand
35%
35%
0% cost
35%
35%
5% cost
35%
36%
5% discount
35%
35%
Class 1: The best quality soil
Class 2: The middle quality soil
Class 3: The worst quality soil
class3
82%
85%
35%
79%
35%
35%
87%
83%
class1
35%
47%
35%
36%
35%
35%
52%
35%
Soybean
class2
58%
81%
37%
70%
36%
36%
84%
59%
class3
96%
97%
78%
97%
68%
71%
97%
96%
Table 0.1Table 4.1 Average residue management intensity under different scenarios
4.5
Total carbon sequestration
The total carbon sequestration pattern over time is shown in Figure 4.4. It shows
that it rises slightly over time. The reason for the increasing trend of total carbon
sequestration is that there is conservation practices involved even without any carbon
81
policies. Mostly it comes from the worst soil class because it has the highest tillage
intensity. It makes sense because there would not be much of loss in yield with
conservation practice on low quality of land while there could be cost savings by high
residue management.
In the figure 4.4, the patterns of total carbon sequestration across the assumptions
are demonstrated. The broad line without a marker is the total carbon path under the
baseline scenario. The three dotted carbon paths below the baseline are the total carbon
with the assumptions of 4 % yield, 5 % demand, and 0 % input costs. It is because total
conservation land usage for both crops with these assumptions approach zero (Figure 4.2
C, E, & G), so the carbon level stays at the initial carbon level.
The total carbon is higher than the baseline with the other assumptions. Under the
low yield assumption (0 %), the total carbon sequestration level is the highest. This is
because the land in conservation practice with this assumption is the highest (Figure 4.2,
B) and the average tillage intensity is higher than the baseline. The high input costs (5 %)
assumption results in the next highest total carbon sequestration pattern. It also propels
the land use shifts to conservation practice in soybean and the highest average tillage
intensity. The low demand assumption (0 %) also results in higher total carbon path and
identical reason could be applied. It has the higher total conservation land in soybean and
corn and higher average tillage intensity. For the higher discount rate assumption also
expects slight higher total carbon than the baseline.
82
MMTC
980
960
940
920
900
Baseline
0% yield
4% yield
0%demand
5% demand
0% input cost
5% input cost
5% discount rate
Total carbon
880
860
Year
840
1
6
11
16
21
26
31
Figure 4.4 Total carbon sequestration (million tons of carbon)
83
36
CHAPTER 5
CARBON POLICY RESULTS
In this chapter, I provide the results of carbon policy scenarios on sets of different
assumptions. The carbon policies considered in this study are carbon renting and fixed
per hectare payments with two different minimum required tillage intensity levels, 35 %
and 75 %. Carbon renting policy pays rental based on the tons of carbon sequestered
(Sohngen & Mendelssohn, 2003). The policy of per hectare payment requires that once
land parcel is involved in the conservation practice, then it is not permitted to transfer
back to conventional tillage. In the first section, these two carbon policies are applied to
the baseline scenario in chapter 4. Total crop choices, conservation cropland, average
tillage intensity, crop prices, amount of carbon gains, and cost of carbon sequestration are
compared along the different carbon policies. So far, the total available cropland is fixed
over time. In the second section, carbon renting policy is applied to the baseline scenario
while the total available cropland changes. The projection of total cropland is utilized by
the area base model estimates in chapter 3.
84
5.1
Carbon policies with the baseline
5.1.1
Carbon renting policy
Carbon renting policy is applied to the empirical dynamic model following
(Sohngen & Mendelssohn, 2003). Several carbon prices are applied in this study, $2, $10,
$40, $100, and $150 per ton of carbon. Assuming the discount rate 3 % per year, the
annual carbon rental is being paid to the landowners are $0.06, $0.3, $1.2, $3, and $4.5
per ton of carbon as long as the stored carbon is residing in the soil. Once the carbon is
emitted into the atmosphere by plowing, these rental payments are not paid any more.
Note that the total crop land is constant over time. The total model runs are applied to 45
years and results are shown only up to 40th year period to reduce impacts by terminal
condition
In the Figure 5.1 (A through E), the crop choice results of carbon renting policy
are listed. In general, the patterns of crop choices are similar as the crop choices under the
baseline. Total crop choice shifts between corn and soybean over time. The rotation
between the two crops still exists under the carbon policy, which is caused by the yield
loss impact of the continuous crop. Same as the baseline results, the total hectares in corn
are greater than the total soybean hectares. As the carbon price rises (move from figure A
to E), the gap between the two crops slightly decreases. In particular, the total soybean
hectares with $150 per ton of carbon price are the highest compare to any other scenarios.
So it indicates that soybean is relatively getting more attractive than corn as the carbon
rental increases but the magnitude is small.
85
Total Crop choice
($2/ton)
(000ha)
14000
Total Crop choice
($10/ton)
(000ha)
14000
12000
12000
10000
10000
8000
8000
6000
Corn
Soybean
4000
2000
Year
6000
Corn
Soybean
4000
2000
0
Year
0
1
6
11
16
21
26
31
36
1
A) Total crop choice ($2/ton)
11
16
21
26
31
36
B) Total crop choice ($10/ton)
Total Crop choice
($40/ton)
(000ha)
14000
6
Total Crop choice
($100/ton)
(000ha)
14000
12000
12000
10000
10000
8000
8000
6000
Corn
Soybean
4000
2000
Year
6000
Corn
Soybean
4000
2000
0
Year
0
1
6
11
16
21
26
31
36
1
C) Total crop choice ($40/ton)
6
14000
12000
10000
8000
6000
Corn
Soybean
4000
2000
Year
0
1
6
11
16
21
26
31
16
21
26
31
D) Total crop choice ($100/ton)
Total Crop choice
($150/ton)
(000ha)
16000
11
36
E) Total crop choice ($150/ton)
Figure 5.1 Total crop choice with carbon renting policy
86
36
The results of conservation practice for each crop under carbon renting policy are
shown in figure 5.2 (A to E). The overall model outcomes show expected results. As
carbon price goes up (move from figure A to E), total conservation practice hectares for
both crops increase. With low carbon price ($2 per ton), average soybean conservation
practice shifts around at 2.5 million hectares and corn stays around at 1.5 million
hectares. It increases to 2.9 million hectares in soybean and 2.2 million hectares in corn
with $40 per ton of carbon price. The highest carbon price ($150 per ton) gives about 8
million hectares in soybean and corn for the conservation practice. As in the baseline in
chapter 4, total hectares on the conservation practice shifts between the two crops. The
total hectares for the conservation practice in soybean are greater than corn. Across the
different carbon price, there is not significant differences in the crop choice pattern
except that the gap between the two crops are slightly reduced (5-2, A vs. 5-2, E).
Results of crop prices with carbon renting policy are provided in figure 5.3 (A &
B). The overall paths of crop prices are stable with small fluctuations over time as in the
baseline scenario. As the carbon price increases, the corn price slightly shifts up (figure
5.3, A). The price path with $150 per ton of carbon price is the highest over time. That is
because the total corn choice is the least with $150 per ton. For the soybean price paths,
however, the highest carbon price ($150 per ton) gives the lowest price path. As shown in
figure 5.1, the total crop choice is the highest with this carbon price. As carbon price rises,
soybean attracts more land and it shifts up the corn price and down the soybean price to
some extent. In general, the impact on price is bigger on soybean and there is not
dramatic change on the crop price by the carbon policy.
87
Total conservation crop
($2/ton)
(000 ha)
8000
7000
Corn
Soybean
6000
7000
5000
5000
4000
3000
3000
2000
2000
1000
Year
0
6
11
16
21
26
31
1000
Year
0
36
1
A) Total conservation crop ($2/ton)
6
11
16
21
26
31
36
B) Total conservation crop ($10/ton)
Total conservation crop
($40/ton)
(000 ha)
9000
Corn
Soybean
6000
4000
1
Total conservation crop
($10/ton)
(000 ha)
8000
Total conservation crop
($100/ton)
(000 ha)
10000
8000
7000
8000
6000
5000
6000
4000
Corn
Soybean
3000
2000
Corn
Soybean
4000
2000
1000
Year
0
1
6
11
16
21
26
31
Year
0
36
1
C) Total conservation crop ($40/ton)
6
11
10000
8000
6000
Corn
Soybean
4000
2000
Year
0
1
6
11
16
21
26
31
21
26
31
36
D) Total conservation crop ($100/ton)
Total conservation crop
($150/ton)
(000 ha)
16
36
E) Total conservation crop ($150/ton)
Figure 5.2 Total conservation crop with carbon renting policy
88
$2/ton
$40/ton
$150/ton
Corn price
$/bu
3.8
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3
2.9
Year
2.8
1
6
11
16
21
26
31
36
A) Corn price with carbon renting policy
Soybean price
$/bu
7.5
7
6.5
6
5.5
$2/ton
$40/ton
$150/ton
5
4.5
4
3.5
Year
3
1
6
11
16
21
26
B) Soybean price
Figure 5.3 Crop prices with carbon renting policy
89
31
36
The average residue management intensity for each crop over different carbon
prices are presented in table 5.1. As in the baseline scenario, residue management
intensity is higher in the low quality soil class for both crops. Also it is higher in soybean
than the corn for the middle and low quality soil classes over the carbon price ranges. As
expected, the average residue intensity is increasing as the carbon price increases except
the best soil class for corn. For the best soil quality class, regardless of carbon price,
residue intensity is at the minimum level (35%) for corn. For soybean, it is required at
least $100 per ton of carbon price to spur more residue intensity than the baseline in the
best quality soil. For the middle quality soil classes, there is slight increase of residue
intensity for corn with $100 per ton of carbon price. There is steady increment of residue
intensity along the carbon price for soybean middle quality soil class. For the low quality
soil class, there is additional residue intensity in corn as the carbon price goes up but
there is not much of gain in soybean because there is high residue intensity in the baseline
for soybean.
The total carbon sequestration over different carbon prices are shown in figure
5.4. The graph shows the total cumulative carbon gains over the baseline for 40 years. It
is expected that the higher carbon price could stimulate more carbon and the figure shows
the results as expected. There is not much of gain with lower carbon price at $2 and $10
per ton of carbon price. The substantial total carbon gain could be found from $40 per ton
of carbon price. With $150 per ton of carbon price, the total carbon gain is the greatest
but the increments of carbon gains above the baseline decreases, which reflects the
maximum attainable carbon limits as introduced in Figure 3.2. The carbon gain comes
90
not only from the higher tillage intensity (Table 5.1) but also form the additional
conservation practice hectares (Figure 5.2).
Corn
Scenario Class1 Class2
Baseline
35%
35%
$2/ton
35%
35%
$10/ton
35%
35%
$40/ton
35%
35%
$100/ton
35%
36%
$150/ton
35%
56%
Class1: The best quality soil
Class2: The middle quality soil
Class3: The worst quality soil
Class3
82%
83%
89%
93%
97%
98%
Class1
35%
35%
35%
35%
39%
51%
Soybean
Class2
58%
59%
60%
68%
82%
89%
Class3
96%
96%
97%
98%
98%
98%
Table 0.1Table 5.1 Average residue management intensity with carbon renting policy
$2/ton
$10/ton
$40/ton
$100/ton
$150/ton
Cumulative carbon gains
(carbon renting scenario)
MMTC
80
70
60
50
40
30
20
10
0
1
6
11
16
21
26
31
36
Year
Figure 5.4 Total cumulative carbon gain above the baseline with carbon renting policy
5.1.2
Fixed payment per hectare
91
For the carbon policy in this section, the payments to land owners are based on
the hectares on which the conservation tillage is practiced. There are two scenarios with
different minimum requirements for the residue intensity, 35% and 75%. It is assumed
that once the land is used on the conservation practice, it is not permitted to move back to
the conventional usage. The prices for this section are $2, $10, $20, and $50 per hectare.
The results of per hectare payments are shown in Figure 5.5 (A to D) for 35%
minimum residue management requirement and in Figure 5.6 (A to D) for 75% minimum
residue management requirement. The patterns of crop choices are similar as before in
the baseline and carbon renting scenario. The total crop choices are shifting between the
two crops and it stays stable across the different payments. The patterns stay similar until
$20 per hectare for both minimum requirements. However, when the payment is the
highest with $50 per hectare, total choice for soybean in the first 10-12 years is the
greatest and corn is the smallest for both requirement scenarios. The magnitude is greater
in 75 % scenario.
92
Total crop choices
($2/ha)
(000ha)
14000
Total crop choices
($10/ha)
(000ha)
14000
12000
12000
10000
10000
8000
8000
6000
Corn
Soybean
4000
2000
Year
6000
Corn
Soybean
4000
2000
Year
0
0
1
6
11
16
21
26
31
1
36
A) Total crop choice ($2/ha, ≥ 35%)
11
Corn
Soybean
14000
21
26
31
36
Total crop choices
($50/ha)
(000ha)
18000
16000
16
B) Total crop choice ($10/ha, ≥ 35%)
Total crop choices
($20/ha)
(000ha)
18000
6
14000
12000
12000
10000
10000
8000
8000
6000
6000
4000
Corn
Soybean
16000
4000
2000
Year
2000
0
Year
0
1
6
11
16
21
26
31
36
C) Total crop choice ($20/ha, ≥ 35%)
1
6
11
16
21
26
31
36
D) Total crop choice ($150/ha ≥ 35%)
Figure 5.5 Total crop choice with per hectare payment (35% minimum residue intensity)
93
Total crop choices
($2/ha)
(000ha)
14000
Total crop choices
($10/ha)
(000ha)
14000
12000
12000
10000
10000
8000
8000
6000
Corn
Soybean
4000
2000
Year
6000
Corn
Soybean
4000
2000
0
Year
0
1
6
11
16
21
26
31
36
1
A) Total crop choice ($2/ha, ≥ 75%)
12000
11
16
21
26
31
36
B) Total crop choice ($10/ha, ≥ 75%)
Total crop choices
($20/ha)
(000ha)
6
Total crop choices
($50/ha)
(000ha)
18000
16000
10000
14000
8000
12000
10000
6000
Corn
Soybean
4000
2000
Year
8000
Corn
Soybean
6000
4000
2000
0
Year
0
1
6
11
16
21
26
31
36
C) Total crop choice ($20/ha, ≥ 75%)
1
6
11
16
21
26
31
36
D) Total crop choice ($150/ha ≥ 75%)
Figure 5.6 Total crop choices with per hectare payment (75% minimum residue intensity)
94
It is of interest how much of hectares would be involved in the conservation
practice with different minimum residue management requirements when the
conservation land parcels are being paid. The results show the expected outcomes in
which the conservation land increases as the price goes up (Figure 5.7 & 5-8). On
average, there are 1.9 million hectares in conservation corn and 2.9 million hectares in
conservation soybean with $2 per hectare payment under 35% minimum residue
management requirements (Figure 5.7, A). For the high residue intensity requirement
(75%), there are 1.8 million hectares in conservation corn and 2.1 million hectares in
conservation soybean with $2 per hectare price. Compare to the total cropland (Figure
5.5), the portion of conservation land is about 18% of total corn and 30% soybean with
35% minimum requirements and 17% of total corn and 23% of total soybean is
transferred into the conservation practice with high residue management requirement
(75%) scenario.
There is rapid transition into the conservation practice when conservation land is
paid at $10 per hectare with 35 % minimum residue input requirement (Figure 5.7, B).
On average, 81 % of total corn and 85% of total soybean is under the conservation
practice with 35 % residue intensity. For the high residue management requirement
(Figure 5.8, B), there is not many transfers into conservation tillage compare to $2 per
hectare payments. It is about 22% and 24% of total corn and soybean is shifted to the
conservation practice.
As the price goes up to $20 per hectare on the conservation usage, after 15 years,
all of the land is under the conservation practice when 35 % residue management
95
intensity is minimally required (Figure 5.7, C). However, with the high residue input
requirement (75 %), 25 % of corn and 28 % of soybean are shifted to the conservation
land.
For the $50 per hectare scenario, all of the cropland is under the conservation
practice with 35 % residue management requirement after 5 years. However, with the
high residue input requirement, 10 % of cropland still remains in the conservation tillage,
which is the highest productive region.
The total cumulative carbon gain above the baseline for 35 % minimum residue
management requirement scenario is displayed in Figure 5.9. As expected, the total
carbon gains increase as the payment price grows. The carbon gain path with $2 per
hectare payment gradually increases in the first 10 years and stays at 6.5 million tons over
time. There is jump on the carbon gain path with $10 per hectare payment in the first 10
years and shifts around at 37 million tons over time. However, there is not substantial
carbon gain with the higher payment such as $20 or $50 per hectare payment scenarios.
For 75 % minimum residue requirement scenario (Figure 5.10), as in the 35 %
minimum residue case, there is slow carbon gain in first 12 years and stays at about 10
million tons. Unlike the low residue requirement, there is not substantial carbon gain up
to $20 per hectare payment. Carbon gain stays at about 15-20 million tons per year over
time for both $10 and $20 per hectare scenario. However, with $50 per hectare payment,
there is a rapid gain in the first 12 years and annual gain is about 80 million tons of
carbon.
96
Total conservation crop
($2/ha)
(000ha)
Total conservation crop
($10/ha)
(000ha)
14000
Corn
Soybean
12000
14000
10000
10000
8000
8000
6000
6000
4000
Corn
Soybean
12000
4000
2000
Year
2000
0
Year
0
1
6
11
16
21
26
31
36
1
6
11
16
21
26
31
36
A) Total conservation crop ($2/ha, ≥ 35%) B) Total conservation crop ($10/ha, ≥ 35%)
Total conservation crop
($20/ha)
(000ha)
Total conservation crop
($50/ha)
(000ha)
14000
14000
12000
12000
10000
10000
8000
8000
6000
4000
Corn
Soybean
6000
Year
2000
2000
Corn
Soybean
4000
0
Year
0
1
6
11
16
21
26
31
36
1
6
11
16
21
26
31
36
C) Total conservation crop ($20/ha, ≥ 35%) D) Total conservation crop (50/ha, ≥ 35%)
Figure 5.7 Total conservation crop land with per hectare payment (35% minimum residue
intensity)
97
Total conservation crop
($2/ha)
(000ha)
Total conservation crop
($10/ha)
(000ha)
14000
14000
12000
Corn
Soybean
10000
12000
8000
8000
6000
6000
4000
4000
2000
Corn
Soybean
10000
2000
Year
0
1
6
11
16
21
26
31
Year
0
36
1
6
11
16
21
26
31
36
A) Total conservation crop ($2/ha, ≥ 75%) B) Total conservation crop ($10/ha, ≥ 75%)
Total conservation crop
($20/ha)
(000ha)
Total conservation crop
($50/ha)
(000ha)
14000
14000
12000
Corn
Soybean
10000
12000
10000
8000
8000
6000
6000
4000
4000
2000
Corn
Soybean
2000
Year
0
1
6
11
16
21
26
31
Year
0
36
1
6
11
16
21
26
31
36
C) Total conservation crop ($20/ha, ≥ 75%) D) Total conservation crop ($50/ha, ≥ 75%)
Figure 5.8 Total conservation crop land with per hectare payment (75% minimum residue
intensity)
98
MMTC
55
Total cumulative carbon gain
(35% minimum till)
45
35
$2/ha
$10/ha
$20/ha
$50/ha
25
15
5
Year
-5 1
6
11
16
21
26
31
36
Figure 5.9 Total cumulative carbon gain above the baseline (35% minimum residue
intensity)
Total cumulative carbon gain
(75 % minimum till)
MMTC
95
85
75
$2/ha
$10/ha
$20/ha
$50/ha
65
55
45
35
25
15
Year
5
-5
1
6
11
16
21
26
31
36
Figure 5.10 Total cumulative carbon gain above the baseline (75% minimum residue
intensity)
99
5.1.3
Cost of carbon sequestration
Once the carbon potential is obtained through the different carbon policies and
prices, it is worthwhile to examine the cost and potential of carbon sequestration across
the carbon scenarios. Several estimates on the cost and carbon sequestration potentials
are summarized in table 5.2 through 5-4. In each table, the first two rows show the total
carbon stock (tons of carbon) per hectare in the beginning (year 2004) and the last period
(year 2044) for different carbon payments. Annual carbon gain is the average value of the
annual gain by the carbon scenario. Present value of the carbon gains (million tons of
carbon) are the sums of all the discounted carbon gains over the period. Annual
equivalent carbon gain is the just the annual number of the present value of carbon gain.
Total cost (million dollars) is the sums of discounted annual rental payments over the
period. Average cost is obtained by dividing the total cost by present value of carbon gain.
For the carbon renting program (table 5.2), there is about 43.4 tons of carbon per
hectare in the beginning year and it ends up with 44.1 tons of carbon per hectare to 46.2
tons of carbon per hectare depending on the carbon price. Although there are not much of
carbon changes between the two time periods, there is more carbon dynamics as shown in
figure 5.4. To analyze the total carbon changes more closely, it is worthwhile to examine
annual carbon gain. On average, the carbon renting policy could gain additional annual
carbon about 149 thousand tons with $2 per ton of carbon price and 1.2 million tons of
average annual carbon gains with $150 per ton of carbon price. Total sums of discounted
carbon gains for 40 years would be 2.8 million tons of carbon with $2 per ton of carbon
100
price and over 42.8 million tons of carbon with $150 per ton of carbon price. With the
discounted carbon term, the annual equivalent carbon gains would be 121 thousand tons
of carbon with $2 per ton of carbon price and 1.8 million tons of carbon gains with $150
per ton of carbon price. The total cost of carbon sequestration in present value term
would range from 170,000 dollars with $2 per ton of carbon price to 193 million dollars
with $150 per ton of carbon price. The average cost with $2 carbon price is $0.06 per ton.
With the highest carbon price at $150 per ton, the average cost of carbon is about $4.5
per ton. In general, the carbon cost estimates is within the ranges of previous carbon
studies.
For the carbon policy with fixed payment per hectare scheme, in general, the
program with 75 % minimum residue management requirement provides more carbon
gains than 35 % minimum residue program across the payment prices (Table 5.3 & 5.4).
There is the same amount of carbon in the initial period, 43.3 tons of carbon per hectare.
In 2044, there would be 44 tons to 45.8 tons of carbon with 35% minimum residue
program, whereas 44.3 to 47.8 tons of carbon per hectare with 75% minimum residue
scenario. For the annual carbon gain, there is about 264 thousand (413 thousand) carbon
gain with $2 per hectare and 1.16 million tons (2.16 million tons) of annual carbon gain
with $50 per hectare program when the 35 % minimum residue (75 % minimum residue)
is required. When the conservation land is paid at $2 per hectare, there could be 5 million
tons (10 million tons) of present value of carbon gains by 35 % minimum (75 %
minimum) residue management requirement. It rises to 36 million tons (71 million tons)
with 35 % minimum (75 % minimum) residue input requirements when $50 per hectare
101
is paid. The present value of total carbon cost climbs from 217 million dollars (183
million dollars) up to 22 billion (21 billion) dollars as the payment per hectare rises when
35 % minimum (75 % minimum) residue is required. With the $2 per hectare payment,
the average cost of carbon is $40 per ton of carbon and $18 per ton of carbon when 35 %
and 75 % minimum residue management program. With the highest payment at $50 per
hectare scenario, the average cost rises dramatically up to $613 per ton with 35 %
minimum residue and $314 per ton with 75 % minimum residue requirement.
The scenario with fixed payment per hectare with 35 % minimum residue
management results in the highest total carbon cost and the carbon renting policy costs in
the least manner. The result confirms the theory and previous studies that there is
efficiency gains in per ton payment than the per hectare payment (Pautsch et al., 2001 &
Antle et al., 2003).
The spatial distribution of cumulative carbon gains in year 2044 are displayed
from figure 5.11 to 5-13. The total cumulative carbon gains by carbon renting policy with
$40 per ton of carbon price in figure 5.11 shows that most of carbons are obtained from
overall area in Ohio, except northwestern and southeastern region, and western region of
Illinois. Interestingly, regions with high quality soils, such as northwestern Ohio,
northern Indiana and northern Illinois do not provide substantial carbon. Within these
regions, it is not advantageous for farmers to intensively adopt conservation tillage and
maintain their land with that technology permanently. At the other end of the land
quality spectrum, such as southeastern Ohio and south region of Indiana, carbon gains are
102
also small because conservation tillage has already been widely adopted and the potential
for carbon sequestration is low.
The two different minimum residue requirements in the fixed payment program
provide interesting spatial patterns of carbon gain. Figure 5.12 and 5-13 show the carbon
gains when $20 per hectare is paid when the minimum residue input requirements for the
program is 35 % (figure 5.12) and 75 % (figure 5.13). In general, there is opposite carbon
gain pattern between the two requirements. Under the 35 % minimum requirement,
northern region in Ohio, Indiana, and Illinois provide most of the carbon gains. However,
the other regions provide more carbon with higher minimum residue (75 %) requirement
case. For the high quality soil, the yield loss by residue inputs is greater than the low
quality soil class and the program requires the conservation land be trapped in
conservation practice over the 40 years. The higher requirements of residue intensity
makes the greater opportunity cost for the high soil quality soils.
However, the lower requirement for the program makes the less yield loss and the
potential of carbon sequestration in high quality soil classes is bigger than the low quality
soil classes. That could be the reason for the more carbon gains in the high productive
regions with 35 % minimum residue requirements program.
103
• Total Carbon stored in soils at year t:
Baseline = X tB
Scenario = X tS
• Annual carbon flux at year t:
Baseline = Ft B = X tB+1 − X tB
Scenario = Ft S = X tS+1 − X tS
• Cumulative carbon gain for scenario by the year t:
CGtS = X tS − X tB
• Annual carbon gain:
Average of ( CGtS+1 − CGtS )
• Present value of carbon gains:
T
1
ρ t (CGtS+1 − CGtS ) , where ρ is the discount factor
Carbon Price ($/ton)
Annual carbon rental ($/ton)
Carbon per ha in 2004
Carbon per ha in 2044
Annual carbon gain
Present value of carbon gain§
Annual equivalent carbon gain
Total cost (Present value)
Average cost($/ton)
†:000 tons
ψ: Million dollars
§: Million tons
$2
$0.1
43.4
44.1
149
2.8
121
0.17
0.06
$10
$0.3
43.4
44.4
318
5.9
254
2
0.30
Table 5.2 Cost of carbon (Carbon renting policy)
104
Carbon Price
$40
$100
$1.2
$3
43.4
43.4
45.4
46.0
809
1077
21.2
35.2
917
1521
25
106
1.20
3.00
$150
$4.5
43.4
46.2
1210
42.8
1853
193
4.50
Carbon per ha in 2004
Carbon per ha in 2044
Annual carbon gain†
Present value of carbon gain§
Annual equivalent carbon gain†
Total cost (Present value) ψ
Average cost($/ton)
†:000 tons
ψ: Million dollars
§: Million tons
Payment per hectare
$2
$10
$20
43.3
43.3
43.3
44.0
45.6
45.8
264
1060
1176
5
31
36
1349
1555
233
217
3750
8726
40
120
243
$50
43.3
45.8
1162
36
1563
22133
613
Table 5.3 Cost of carbon (Fixed payment with 35 % minimum residue intensity)
Carbon per ha in 2004
Carbon per ha in 2044
Annual carbon gain†
Present value of carbon gain§
Annual equivalent carbon gain†
Total cost (Present value) ψ
Average cost($/ton)
†:000 tons
ψ: Million dollars
§: Million tons
Payment per hectare
$2
$10
$20
43.3
43.3
43.3
44.3
44.6
44.7
413
532
599
10
14
16
431
603
697
183
1136
2532
18
81
157
$50
43.3
47.8
2165
71
3056
21500
304
Table 5.4 Cost of carbon (Fixed payment with 75 % minimum residue intensity)
105
* All the numbers are thousand tons
Figure 5.11 Cumulative carbon gains in 2044 (carbon renting with $40 per ton)
* All the numbers are thousand tons
Figure 5.12 Cumulative carbon gains in 2044 ($20 per hectare with 35 % minimum
residue intensity)
106
* All the numbers are thousand tons
Figure 5.13 Cumulative carbon gains in 2044 ($20 per hectare with 75 % minimum
residue intensity)
107
5.2
Carbon policy when total cropland changes
5.2.1
Land use projection by carbon policy
This section explores how potential future land use change influences the carbon
gains suggested above. In particular, the carbon rental policy is re-examined under
alternative scenarios that allow total available cropland to change over time. It is obvious
that the landscape for next 40 years will be different from now. However, what is not
obvious is that how the carbon policy would affect the land use choice in the future. One
of major concerns of land use change is the urbanization pattern that would be influenced
strongly by population growth and location factors and it is not clear how it would affect
the carbon sequestration potential. The future cropland projection is obtained by adopting
the estimate results of area base model, in particular, the base model (equation 3-9)
results with suburban growth scenario in chapter 3.
To have the proper baseline with land use changes in the future, following steps
are applied. First, from the dynamic carbon scenario results in the previous section,
obtain the rental value changes for agricultural land. Apply the new agricultural rental
values to the area base model to project land use change. Second, apply new land use
change to the dynamic model and obtain the second results of dynamic model results and
obtain rental value changes. Apply again this rental value to the area base model and
iterate until the land use change predictions until converge in the agricultural rental
values.
108
While population and agricultural rents rise at the same rate as the projection
simulation, additional carbon rental values are added to forest and agricultural rent
growths and it is re-estimated the land use. Carbon in trees is calculated using the
estimates of Smith et al. (2003) for the above ground carbon only. The data for
distribution and volume of each species were obtained from the USDA Forest Service
FIA data. Forest group types are Conifers, lowland hardwoods (Oak-Gum-Cypress group,
Elm-Ash-Cottonwood, and Aspen-Birch group), Maple-Beech-Birch group, OakHickory, and Oak-Pine group. The relation between timber volume and age class for each
forest groups are estimated using FIA data. The yield functions for these species are
adopted from the ATLAS timber model (Mills and Kincaid, 1992). From the FIA data,
there are different site classes depending on the land quality and yield functions for this
study are estimated using only medium site class that could produce about 85-164 cubic
feet per acre and per year. Yield function captures the growth of each timber over time
but it is limited by maximum yield value by the estimated yield function. As carbon
rental is added to forest rents in the simulation, forestland increases over time so yield
function for each species takes account timber growth on newly established forestland.
Agricultural rental changes for the projections are adopted from the results of the
carbon renting policy with baseline scenario in the first section of this chapter. First,
examine the revenue changes in each region for each carbon prices. Then estimate the
change rates above the baseline for each carbon prices. Second, apply these change rates
of agricultural rental to the area base model to get the new land projection. The results of
land use projection of cropland are listed in table 5.5.
109
After applying carbon policy simulation to the area base model, cropland changes
along the carbon price scenarios are shown in table 5.5. The baseline scenario projects
that cropland declines 450 thousand hectares within next 40 years. With carbon renting
policy, cropland decreases from 446 thousand hectares with $2 per ton of carbon price to
237 thousand hectares with $150 per ton of carbon price scenario. As the carbon price
increases, the loss of cropland decreases. These estimates are incorporated into the
empirical dynamic model for each carbon prices and rerun the model. Total cropland
changes are divided into the annual change rates for each carbon price scenario and total
land constraints are added.
Although the total cropland of the entire study region is projected to lose hectares
over time, the total cropland could increase for some regions by such as deforestation.
One of example of the cropland changes is shown in figure 5.14. The map shows the
projection of cropland with $40 per ton of carbon price scenario. As can be seen, there
are cropland loss around metropolitan area but also there are regions with increasing
cropland. In each region in the dynamic model, there are three different soil classes. To
deal with the land use change, it is assumed that the change occurs equally over the soil
classes.
110
2004
2014
2024
2034
2044
Total changes
Baseline $2/ton
$10/ton $40/ton $100/ton $150/ton
19952
19952
19952
19952
19952
19952
19839
19840
19842
19853
19869
19893
19727
19729
19732
19755
19787
19833
19614
19617
19623
19657
19705
19774
19502
19506
19513
19559
19622
19715
-450
-446
-439
-393
-329
-237
Table 5.5 Total Cropland changes (000ha)
* All numbers are 000 ha
Figure 5.14 Cropland changes with $40 per ton of carbon price
111
5.2.2
Results of model with cropland changes
The comparison of total conservation land between Baseline A and Baseline B is
presented in figure 5.15. It shows the total sums of conservation cropland for corn and
soybean for both scenarios along the baselines and carbon prices. Without any carbon
renting program (figure 5.15, A), overall conservation hectares with Baseline B is bigger
than Baseline A. Over the time, the total conservation land shifts in and out form the
conservation usage. As the carbon price increases (5-15, B through F), both scenarios
give the higher hectares of conservation land use than each baseline. The rate of
conservation tillage adoption is more responsive in the variable total cropland assumption
(Baseline B) than the constant total cropland case (Baseline A). The gap between the two
baseline assumptions is getting bigger as the price of carbon increases until $100 per ton
of carbon price. The gap decreases at $150 per ton of carbon price.
The average residue management intensity results are displayed in table 5.6. For
the comparison, it also shows the previous baseline scenario when the total cropland is
constant (Baseline A). Compare to the baseline in the first section (Baseline A), overall
residue management intensity patterns are similar as before. For both crops, the lower
soil quality adopts the higher average residue input intensity. It also shows that
conservation practice is more intensively adopted in soybean. The best soil quality class
in corn has the minimum residue inputs for any carbon prices.
Although there are several similarities in the patterns of tillage adoption between
this scenario (Baseline B) and the previous baseline (A), for the middle and low quality
112
soil classes, Baseline B results in less intensive residue inputs than the Baseline A. With
the changing total cropland assumption, the increment of residue management intensity
above the baseline is stronger than the previous results along the carbon price increment.
For the worst soil class (Class 3) in both crops, the average residue management intensity
in the baseline line is about 75 % for corn and 91 % for soybean while 82 % for corn and
96 % for soybean in Baseline A. With $150 per ton of carbon price, it rises up to 98 % in
both corn and soybean for both baseline results (Table 5.1 & 5.6). It is important to have
proper baseline because it could affect the estimates of total carbon gains by how the
baseline is assumed.
113
Total conservation land
(Baselines)
(000ha)
Baseline A
Baseline B
8000
7000
6000
6000
5000
5000
4000
4000
3000
3000
2000
2000
Year
0
1
6
11
16
21
26
31
Baseline A
Baseline B
8000
Year
0
1
Total conservation land
($10/ton)
(000ha)
1000
36
A) Total conservation land (Baselines)
7000
Baseline A
Baseline B
8000
7000
1000
Total conservation land
($2/ton)
(000ha)
6
11
16
21
26
31
36
B) Total conservation land ($2/ton)
Total conservation land
($40/ton)
(000ha)
Baseline A
Baseline B
12000
10000
6000
8000
5000
4000
6000
3000
4000
2000
2000
1000
Year
0
1
6
11
16
21
26
31
36
1
C) Total conservation land ($10/ton)
Baseline A
Baseline B
16000
6
11
16
21
26
31
36
D) Total conservation land ($40/ton)
Total conservation land
($100/ton)
(000ha)
Year
0
Total conservation land
($150/ton)
(000ha)
Baseline A
Baseline B
18000
14000
16000
12000
14000
12000
10000
10000
8000
8000
6000
6000
4000
4000
2000
Year
0
1
6
11
16
21
26
31
2000
36
E) Total conservation land ($100/ton)
Year
0
1
6
11
16
21
26
31
36
F) Total conservation land ($150)
Figure 5.15 The comparison of total conservation land
114
Corn
Soybean
Scenario
Class1 Class2 Class3 Class1 Class2
Class3
Baseline A
35%
35%
82%
35%
58%
96%
Baseline B
35%
35%
75%
35%
57%
91%
$2/ton
35%
35%
76%
35%
58%
92%
$10/ton
35%
35%
78%
35%
63%
94%
$40/ton
35%
35%
89%
35%
75%
97%
$100/ton
35%
38%
97%
38%
92%
98%
$150/ton
35%
61%
98%
51%
95%
98%
Class1: The best quality soil
Class2: The middle quality soil
Class3: The worst quality soil
Baseline A: Baseline without cropland changes as in the previous section
Baseline B: Baseline with total cropland changes from table 5.5
Table 5.6 Average residue intensity of carbon renting policy when total cropland changes
The total carbon gain along the carbon prices with Baseline B is presented in
Figure 5.16. The overall outcomes show expected results. As the carbon price rises, the
total carbon gain rises. However, the pattern of carbon gain across the carbon prices
slightly differs from previous results. With the low level of carbon price such as $2 and
$10 per ton of carbon, there are substantial carbon gains with these low prices while there
is not, compared to the carbon gains above Baseline A in figure 5.4. There are two
possible points of explanation for this. First, the Baseline B projects the biggest loss of
available cropland over time so the total carbon in Baseline decreases. From the table 5.5,
the loss of total cropland for the Baseline B is about 450 thousand hectares and it
decreases to 446 thousand hectares and 439 thousand hectares for $2 per ton and $10 per
ton of carbon prices. The total carbon also includes the carbon in conventional cropland,
which is the initial carbon level. Second, as can be seen from the figure 5.15, the growth
115
of conservation total hectares is bigger than the previous results with Baseline A. In
addition, the average tillage intensity enhances more when the total cropland changes.
The carbon gains and cost of carbon sequestration with land use change
assumptions are shown in table 5.7. The average carbon stock in the beginning year is
same as before, 43.3 tons per hectare and it rises up to 44.3 tons per hectare with $2 per
ton of carbon price to 47.8 ton per hectare with $150 per ton of carbon price. The annual
carbon gain ranges from 329 thousand tons of carbon to 143 thousand tons of carbon.
Present value of carbon gains is between 8 million tons 21 million tons. The pattern of
carbon gains show different from the previous constant total cropland assumption (table
5.2). In particular, with the low carbon prices such as $2 and $10 per ton of carbon price,
the annual carbon gain is much bigger than the constant total land assumption.
Explanation for this is similar as for the total cumulative carbon gain (figure 5.16).
Compare to the baseline scenario, the total cropland loss is quite smaller with carbon
payments than the baseline. The total cost ranges from 8 million dollars to 2.96 billion
dollars. The average cost ranges from $1 per ton of carbon to $142 per ton of carbon
depending on the carbon price. With low carbon prices such as $2 and $10 per ton, the
total cost of carbon with reflecting total cropland changes is slightly higher than the fixed
total cropland assumptions but the average cost of carbon is quite similar each other.
However, the high carbon price above $40 per ton, the total and average costs with land
use change assumptions is much higher and the difference is bigger as the carbon price
increases. Without reflecting land use changes in the future, it could underestimate the
cost of carbon sequestration.
116
Total cumulative carbon gain
(carbon renting:cropland changes)
MMTC
60
$2/ton
$10/ton
$40/ton
$100/ton
$150/ton
50
40
30
20
10
0
1
6
11
16
21
26
31
36
Year
Figure 5.16 Total carbon gain by carbon renting policy when total cropland changes
Carbon per ha in 2004
Carbon per ha in 2044
Annual carbon gain†
Present value of carbon gain§
Annual equivalent carbon gain†
Total cost (Present value) ψ
Average cost($/ton)
†:000 tons
ψ: Million dollars
§: Million tons
$2
43.4
43.6
329
8
201
8
1.5
$10
43.4
43.7
323
10
257
65
6.5
Carbon Price
$40
$100
43.4
43.4
44.0
44.4
283
102
14
16
341
408
420
1553
31
95
$150
43.4
45.1
143
21
523
2962
142
Table 5.7 Cost of carbon (Carbon renting policy when total cropland changes)
117
CHAPTER 6
CONCLUSIONS
The objective of this study was to develop the empirical dynamic model, to
compare the carbon storage along different baseline scenarios, and to investigate the
potential and cost of carbon sequestration in the 3 states of Midwestern U.S., Ohio,
Indiana, and Illinois. Several empirical estimations were applied to obtain parameters for
the dynamic model such as crop yield, the impact of residue management on crop yield,
carbon dynamics, input cost, and land use changes. Using GAMS program with MINOS
solver, the empirical dynamic simulation model was solved for different carbon policy
scenarios and assumptions.
In this section, first, I summarize the findings from this study. Second, the
implications of the results are provided. Lastly, the discussion on the limitation and future
development from this study are presented.
118
6.1
Summary
First, given the several different findings on the yield impact by conservation
practice from many field studies, the corn and soybean yield impacts by residue
management is estimated. In general, the yield loss is greater in higher quality soil. For
corn in the Midwest U.S., it is estimated that marginal impacts of residue management on
corn yield loss ranges from 17.4 bushels per acres in the best 25 percentile of high quality
soil to 0.9 bushels per acre in the lower 25 percentile. For soybean, there is not significant
loss of yield but there is slight increase in the yield impact by residue management. There
is about 2 bushels per acre in the lowest 25 % percentile.
Second, factors affecting the land use choices for forestry, cropland, and urban
use in the study region are estimated. After testing three different area base models,
overall, it shows that rental values for forestry and agriculture are significant for each
land use. For the urban use, population density which is the proxy for the urban rental
value shows the significant result. Depending on the models and population growth
assumptions, the land use projection results show that forestland is projected to decrease
about 241 thousand to585 thousand hectares in next 40 years. It is also projected that
there would be loss of 49 thousand to 450 thousand hectares of cropland. Urban area is
expected to increase about 320 thousand to 959 thousand of hectares in the study region
for next 40 years.
Third, the empirical dynamic model is applied to several different baseline
scenarios. The results of the model on the baseline assumption show that the total crop
119
choice shifts between corn and soybean over time and the total land in corn is greater
than the total soybean land. The sensitivity analysis shows that the total crop choice
seems to be mostly sensitive when the crop yields level is constant (0%) and high input
costs (5%). The total crop choice for soybean dominates under these two assumptions.
Conservation practice is more adopted in soybean than corn. As crop yield is low (0%)
and input cost is high (5%), the higher conservation practice adoption rate is in soybean.
Across the different soil quality, the residue management is more adopted in the worst
quality soil class than the best soil class for corn and soybean. Also, the residue intensity
and total carbon sequestration is high when crop yield growth stays at 0 % and input cost
rises high at 5 % per year. All of these results have the similar explanation. Landowners
adopt more soybean and more intensive conservation practice to reduce the input costs
under the low yield and high input costs assumptions because conservation practice could
save input costs and soybean is cheaper.
Fourth, the potential and cost of carbon sequestration is analyzed with three
different carbon policy instruments, carbon renting, fixed payment per hectare with 35 %
minimum residue management intensity, and fixed payment with 75 % minimum residue
management intensity. As expected, in general, higher carbon price and payment per
hectare provide more conservation practice, higher residue management intensity, and
more carbon sequestration. Carbon renting policy tends to shifts the corn price up and
moves down the soybean price to some extent as the carbon price increases but the
magnitude is small. Most of carbon gains by the carbon renting policy come from the
middle quality soil classes. With $20 per hectare payment, most of the cropland is shifted
120
to the conservation practice when the residue intensity requirement is low at 35 % but
there still exists conventional practice croplands even with $50 per hectare payment by
75 % minimum residue requirement. The total carbon gain is the most with 75 %
minimum residue intensity and the least with the carbon rental policy. The total present
value of carbon gain ranges from 10 million tons to 71 million tons with 75 % minimum
residue management and 30,000 tons to 23 million tons with carbon renting policy.
However, carbon renting policy is the most inexpensive way to sequester carbon and
fixed payment with 35 % minimum residue intensity costs the highest. Average cost of
carbon renting policy ranges from $2 per ton to $117 per ton and fixed payment with
75 % minimum residue management gives $18 to $304 per ton of carbon.
Fifth, land use changes are considered in the dynamic model. For the middle
quality soil class, average residue management is less intensive when total land changes.
Reflecting future land use changes, in particular, available cropland provides the higher
cost carbon sequestration cost than the results with constant total cropland assumptions.
The total cost ranges from 183 million dollars to 29.6 billion dollars, whereas constant
total cropland assumptions provides 50.000 dollars to 27.6 billion dollars.
Sixth, spatial patterns of carbon sequestration potential show that regions with
high quality soils do not provide substantial carbon gain under the carbon renting policy.
The foregone profit from the intensive residue management dominates the carbon
payment in this region. However, low quality soil region also do not provide carbon gains
because conservation practice has already widely adopted and potential for carbon is low.
The fixed payment carbon policy provides opposite carbon gain patterns according to the
121
minimum residue requirement. With the low residue requirement (35 %), regions with
high soil quality provide carbon gains but the pattern is opposite when the minimum
residue management requirement is high at 75 %. The yield loss by residue management
is more intense in high quality region. As the program prohibits transfers back to
conventional practice, there would not be many hectares involved in the conservation
program when the tillage requirement is high as 75 %.
6.2
Implications
This study provides several implications regarding carbon sequestration policy
analysis. First, the sensitivity analysis suggests that there could be bias results on the
estimates of carbon sequestration potential unless baseline assumption carefully is
designed. Previous studies in economic literature have not account the possibility of
different assumptions on the baseline scenario. This study shows that there could be
different estimates on the carbon sequestration path over time. Higher input costs and low
yield growth assumptions project the highest baseline carbon sequestration paths.
Moreover, with incorporating future urbanization pattern, the estimates on the carbon
sequestration potential and cost would be altered.
Second, ignoring unstable property of carbon in soil could lead to the
overestimate of the carbon sequestration potential and under estimate the carbon cost.
This study considers unstable carbon dynamic property and cyclical patterns of crop
rotation between corn and soybean. The results indicate that carbon storage over time
122
fluctuates because there are shifts into and out of conservation practice and between two
different crops as well. The total carbon storage gain is smaller than the previous studies.
Compare to the cost estimates from the previous studies, the carbon sequestration cost in
the study region is generally higher than previous results.
Third, this study could identify the regional hot spots of the carbon sequestration
potential and it could provide the useful insights to the landowners and policy makers to
designed more efficient carbon programs. From the results of this study, carbon gains are
mostly from the middle quality soil regions.
6.3
Limitation and future development
There could be several limitations and further developments from this study. First,
several assumptions are imposed on the soil carbon dynamics and soil information in this
study. The linear relation between carbon accumulation and residue management could
be dependent on the soil types. Moreover, it is assumed that soil carbon loss by tillage is
instantaneous for newly stored carbon. This study could be improved with more detailed
soil carbon information from soil science studies. Second, the yield impact by residue
management is same across the region but only differs in soil quality class. Further study
on the yield impacts by residue management could provide more interesting results. Third,
many studies in the field of crop and soil science suggest that long term conservation
practice could enhance the yield level by restoring the soil quality but it is ignored in this
123
study. Fourth, the land use change is obtained in conjunction with area base model. For
better understating with land use choice, the urbanization factor could be engaged in the
dynamic model. Fifth, carbon scenario of fixed payment per hectare with minimum
residue management is assumed that the conversion back to conventional practice is not
allowed for the entire simulation period. However, in reality, the contracts would require
much shorter period of time such as 5-15 years. This study could be extended to consider
different period of contracts. Sixth, if carbon policy is established, it could involve not
only agricultural soil, but also would include forestry and pastureland which can be the
valuable sources for carbon sinks. It could provide full spectrum of carbon sequestration
source if these alternatives included.
124
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