SUPPLY AND DEMAND FOR ECOSYSTEM SERVICES FROM CROPLAND
IN MICHIGAN
By
Shan Ma

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Agricultural, Food and Resource Economics
2011

ABSTRACT
SUPPLY AND DEMAND FOR ECOSYSTEM SERVICES FROM CROPLAND
IN MICHIGAN
By
Shan Ma
Payment-for-Environmental-Services (PES) programs that translate external ecosystem
values into direct financial incentives for local providers are gaining appeal globally as flexible
approaches to inducing the voluntary provision of ecosystem services (ES). Working land PES
programs that promote conservation in the agricultural production process have great potential to
address the challenge of feeding growing global population while maintaining environmental
sustainability. The importance of working land PES programs calls for efficient and effective
design of public policies that facilitate the voluntary provision of ES. However, the design of
current PES programs is rarely based upon a comprehensive understanding of the underlying
supply and demand for ecosystem services. This dissertation thus aims to provide empirical
insights for PES design by combining a supply-side cost function of farmers’ willingness to
adopt practices that provide enhanced ES with a demand-side social benefit function of
residents’ willingness to pay (WTP) for these ES.
This dissertation is comprised of three essays. Essay 1 investigates the farmer supply of
ecosystem services via four hypothetical PES programs using a stated preference survey of 3000
Michigan corn and soybean farmers. This essay complements existing literature by dividing the
decision on whether to enroll in PES programs into two stages: whether even to consider
enrolling in the program and, if yes, whether to participate. Analyzed using a double-hurdle
econometric model, results suggest the first-stage willingness to consider decision chiefly

depends on farm and farmer characteristics, while the second-stage decisions on whether and
how much land to enroll in the program depend more on payment offer and benefit-cost criteria.
Essay 2 examines public demand for environmental improvements measured by
willingness to pay (WTP) for reductions in the number of eutrophic lakes and greenhouse gas
(GHG) emissions using a stated preference survey of 6000 Michigan residents. This essay
evaluates alternative methods of modeling WTP that incorporate respondent preference
uncertainty. Using two different functional forms, it tests the sensitivity of WTP estimates to
different functions. Results suggest that the conventional dichotomous choice model without
uncertainty provides a reliable median WTP estimate that reflects the influence of key variables,
although incorporation of self-reported uncertainty may to improve our understanding of the ES
demand and the estimation efficiency of WTP.
Essay 3 combines the farmer cost for providing ecosystem services with the public
benefit from environmental improvements derived in first two essays in simulations to explore
the empirical welfare-maximizing conditions for effective PES design. This essay uses nonparametric aggregation of benefit and cost, as well as biophysical linkages between farming
practices and ES outcomes. Results show that the simplest cropping system with the least ES
improvement is dominated by the other three systems, which offer similar economic welfare
gains with varying trade-offs in cost and environmental performance. The choice of system
largely depends on the goal of the PES program and evolving demand for specific ES by
consumers. Allowing farms to choose different cropping systems that lower their individual costs
or targeting farms that provide additional environmental services beyond their current practices
would improve the cost-effectiveness of PES programs.

ACKNOWLEDGEMENTS

This dissertation witnesses a process of questioning, exploring, learning, and progressing
during my four and half years of graduate study, which is not even possible without the support
from many others.
First, my sincere gratitude is given to my major professor and thesis committee chair, Dr.
Scott Swinton. His insightful thoughts and practical advice clearly directed my path throughout
this study. He also strongly encouraged and supported me to take any potential opportunities to
interact with scholars from different disciplines, present research findings to a variety of
audience, and participant in professional fellowship programs. His patience and friendliness have
made the challenging process more tangible and inspiring as well. I would also like to thank my
committee members, Dr. Frank Lupi, Dr. Soren Anderson, and Dr. G. Phillip Robertson, helped
me to refine the initial ideas, discussed with me about the theory, empirical model and key
results, carefully read through the paper draft, and provided valuable comments. I am grateful for
the career advice and recommendations provided by Dr. Swinton, Dr. Lupi and Dr. Anderson
during my job application. I also highly appreciate the guidance from my visiting mentor Dr.
John Antle from the Department of Agricultural and Resource Economics at Oregon State
University, and the AFRE Glenn and Sandy Johnson Fellowship that made this advising
opportunity possible.
I would also like to thank my former colleagues, Christine Jolejole-Foreman and Huilan
Chen for sharing the farmer and resident survey data and relevant research material with me, and
for being patient with all my inquiries through these years. As a challenging project requiring

iv

aggregation of economic with ecological sciences, my dissertation will not be complete without
valuable assistance and advice by researchers at the MSU Kellogg Biological Station (KBS),
including Dr. Sieglinde Snapp, Dr. Neville Millar, Dr. Stephen Hamilton, and Dr. Dan Brainard.
I would like to acknowledge the financial support for the project from the National Science
Foundation under Human and Social Dynamics Grant No. 0527587, Long-Term Ecological
Research Grant No. 0423627, MSU AgBioResearch, and the MSU Environmental Science and
Policy Program, as well as the MSU Hagen-Bashian scholarship that supported me to complete
this dissertation in Fall 2011.
My gratitude also extends to the my fellow graduate students, faculty, and staff in the
Department of Agricultural, Food and Resource Economics, who made my four and half years
graduate study at MSU beneficial and memorable.
At last, I would like to thank my family and friends, who are always supportive and
willing to share every moment in my life, no matter up and down. Especially, I am deeply
indebted to my parents ZHANG Ping and MA Xingqiao, and my husband XU Yunfei for their
enormous spiritual and physical support during the past years and particularly during the
challenging period of dissertation research/writing.

v

TABLE OF CONTENTS

LIST OF TABLES ......................................................................................................................... ix
LIST OF FIGURES ..................................................................................................................... xiii
LIST OF ABBREVIATIONS ........................................................................................................xv
INTRODUCTION ...........................................................................................................................1
REFERENCES ............................................................................................................................ 5
ESSAY 1: FARMERS’ WILLINGNESS TO PARTICIPATE IN PAYMENT-FORENVIRONMENTAL SERVICES PROGRAMS ............................................................................7
1.1
Introduction ...................................................................................................................... 7
1.2
Conceptual model........................................................................................................... 11
1.2.1
Utility function ........................................................................................................ 11
1.2.2
Willingness to accept .............................................................................................. 12
1.2.3
Decision rule ........................................................................................................... 13
1.3
Data and questionnaire design........................................................................................ 15
1.4
Empirical model and variables ....................................................................................... 18
1.4.1
Choice of models .................................................................................................... 18
1.4.2
Econometric model ................................................................................................. 21
1.4.3
Specification issues ................................................................................................. 23
1.4.4
Variables ................................................................................................................. 24
1.5
Results ............................................................................................................................ 27
1.5.1
Willingness-to-consider decision ............................................................................ 28
1.5.2
Acreage enrollment decision................................................................................... 30
1.5.3
Supply curves .......................................................................................................... 31
1.6
Conclusion ...................................................................................................................... 33
APPENDICES ........................................................................................................................... 44
APPENDIX 1-1: ECONOMETRIC MODELS ........................................................................ 45
APPENDIX 1-2: STATISTICAL TESTS FOR MODEL SELECTION .................................. 49
APPENDIX 1-3: REGRESSION RESULTS (MARGINAL EFFECTS) FOR DIFFERENT
MODELS .................................................................................................................................. 51
APPENDIX 1-4: SUPPLY CURVES FROM DIFFERENT MODELS ................................... 58
APPENDIX 1-5: DATA TREATMENT FOR ORGANIC FARMS ........................................ 61
APPENDIX 1-6: SELF-SELECTION IN RESPONSES TO QUESTIONNAIRES ................ 62
REFERENCES .......................................................................................................................... 65
ESSAY 2: MODELING CERTAINTY-ADJUSTED WILLINGNESS TO PAY FOR
ECOSYSTEM SERVICE IMPROVEMENT FROM AGRICULTURE ......................................73
2.1
Introduction .................................................................................................................... 73
2.2
Theoretical model........................................................................................................... 76
vi

2.3
Data ................................................................................................................................ 79
2.4
Empirical model and variables ....................................................................................... 82
2.4.1
Econometric model of WTP ................................................................................... 82
2.4.2
Methods for incorporating preference uncertainty ................................................. 84
2.4.3
Welfare estimation .................................................................................................. 88
2.4.4
Preference certainty model ..................................................................................... 89
2.4.5
Variables ................................................................................................................. 89
2.5
Results ............................................................................................................................ 90
2.5.1
Preference certainty model ..................................................................................... 90
2.5.2
Conditional willingness to pay................................................................................ 91
2.5.3
Spike model ............................................................................................................ 93
2.5.4
Welfare effect.......................................................................................................... 93
2.6
Conclusion ...................................................................................................................... 96
REFERENCES ........................................................................................................................ 117
ESSAY 3: AGGREGATE SUPPLY AND DEMAND FOR ECOSYSTEM SERVICES FROM
CROPLAND IN MICHIGAN AND POLICY SIMULATION ..................................................121
3.1
Introduction .................................................................................................................. 121
3.2
Conceptual model......................................................................................................... 124
3.2.1
Input-output system for ecosystem services ......................................................... 124
3.2.2
Utility maximization models for ES supply and demand ..................................... 124
3.3
Data and tools ............................................................................................................... 128
3.3.1
Survey data............................................................................................................ 128
3.3.2
Ecosystem services from farming practice ........................................................... 129
3.4
Empirical analysis ........................................................................................................ 132
3.4.1
ES supply and aggregate cost ............................................................................... 133
3.4.2
Measuring additionality of ES supply from changes in farming practices ........... 135
3.4.3
Link additional change in practices to ES improvements ..................................... 136
3.4.4
ES demand and aggregate benefit ......................................................................... 138
3.4.5
Welfare maximization by combining supply and demand ................................... 140
3.5
Results and discussion.................................................................................................. 142
3.5.1
Payment for enrollment scenario .......................................................................... 142
3.5.2
Payment for additionality scenario ....................................................................... 144
3.5.3
Comparison with current commodity subsidies .................................................... 146
3.6
Conclusion ................................................................................................................... 147
APPENDICES ......................................................................................................................... 159
APPENDIX 3-1: CALCULATION OF CROPLAND UNDER CORN-SOYBEAN
ROTATION IN MICHIGAN .................................................................................................. 160
APPENDIX 3-2: MAJOR CROP PRODUCTION COUNTIES AND REPRESENTATIVE
SOIL TYPES IN MICHIGAN ................................................................................................ 162
APPENDIX 3-3: CALCULATION SOIL EROSION REDUCTION USING RUSLE2 ....... 165
APPENDIX 3-4: CALCULATION OF EUTROPHIC LAKE REDUCTION FROM
REDUCED SOIL EROSION .................................................................................................. 168
APPENDIX 3-5: GHG REDUCTION CALCULATION USING US CROPLAND GHG
CALCULATOR ...................................................................................................................... 171
APPENDIX 3-6: OPTIMAL CHOICE BY COMBINING FOUR SYSTEMS ...................... 173
vii

APPENDIX 3-7: DETAILED RESULTS FOR BENEFIT AND COST SIMULATION...... 176
APPENDIX 3-8: DETAILED RESULTS FOR BENEFIT AND COST SIMULATION
(PAYMENT FOR ADDITIONALITY).................................................................................. 191
REFERENCES ........................................................................................................................ 206

viii

LIST OF TABLES

Table 1-1 Four cropping systems offered to farmers .................................................................... 39
Table 1-2 Environmental services and outcomes from proposed farming practices in cropping
systems .......................................................................................................................................... 40
Table 1-3 Summary statistics for dependent variables ................................................................. 40
Table 1-4 Summary statistics of independent variables ............................................................... 41
Table 1-5 Marginal effects from Probit estimation of farmers’ consideration (double hurdle),
weighted by stratum, by Cropping Systems, 1688 Michigan corn or soybean farmers, 2008 ..... 42
Table 1-6 Marginal effects from Tobit estimation of farmers’ acreage enrollment (double
hurdle), weighted by stratum, by Cropping Systems, 1688 Michigan corn or soybean farmers,
2008............................................................................................................................................... 43
Table 1-A1 Correlation between predicted and actual acreage enrollment .................................. 49
Table 1-A2 Vuong test results for model selection ..................................................................... 50
Table 1-A3 Marginal effects from Probit estimation of farmers’ dichotomous enrollment
decision (extended double hurdle model), weighted by stratum, by Cropping Systems, 1688
Michigan corn or soybean farmers, 2008 ..................................................................................... 51
Table 1-A4 Marginal effects from Probit estimation of farmers’ dichotomous participation
decision (single hurdle model), weighted by stratum, by Cropping Systems, 1688 Michigan corn
or soybean farmers, 2008 .............................................................................................................. 53
Table 1-A5 Marginal effects from Probit estimation of farmers’ positive acreage enrollment
decision (single hurdle & extended double hurdle model), weighted by stratum, by Cropping
Systems, 1688 Michigan corn or soybean farmers, 2008 ............................................................. 54
Table 1-A6 Marginal effects from Tobit estimation of farmers’ enrollment decision, weighted by
stratum, by Cropping Systems, 1688 Michigan corn or soybean farmers, 2008 .......................... 56
Table 1-A7 Proportional distribution and acreage enrollment for farms with partial/full organic
production ..................................................................................................................................... 61
Table 1-A8 Probit regression of binary survey response on survey version attributes, 3000
Michigan Corn or Soybean Farms, 2008 ...................................................................................... 63

ix

Table 1-A9 Heckman probit model for binary participation decision, 3000 Michigan Corn or
Soybean Farms, 2008 .................................................................................................................... 63
Table 1-A10 Heckman model for acreage enrollment decision, 3000 Michigan Corn or Soybean
Farms, 2008................................................................................................................................... 64
Table 2-1 Variable description, 2211 Michigan residents, 2009 ................................................ 101
Table 2-2 Descriptive statistics of variables ............................................................................... 103
Table 2-3 Dependent variable for probit model with different cutoff certainty levels ............... 104
Table 2-4 Dependent variables for ordered probit model ........................................................... 104
Table 2-5 Dependent variables for fractional response models .................................................. 104
Table 2-6 Spike probability model, 1429 Michigan residents, 2009 .......................................... 105
Table 2-7 Determinants of preference certainty for yes/no responses, 2211 Michigan residents,
2009 (Dependent variable: certainty scale [1-very uncertain; 10- very certain]) ....................... 106
Table 2-8 Comparison of coefficient estimates on the probability of voting “yes” to proposed tax
payment with and without certainty, 1293 Michigan residents, 2009 [mixed log-log function] 107
Table 2-9 Comparison of coefficient estimates on the probability of voting “yes” to proposed tax
payment with and without certainty, 1293 Michigan residents, 2009 [semi-log function] ........ 109
Table 2-10 Comparison of marginal effects on the probability of voting “yes” to proposed tax
payment with and without certainty, 1237 Michigan residents, 2009 [mixed log-log function] 111
Table 2-11 Comparison of marginal effects on the probability of voting “yes” to proposed tax
payment with and without certainty, 1237 Michigan residents, 2009 [semi-log function] ........ 113
Table 2-12 Comparison of median WTP (in U.S. dollars) and estimation efficiency [mixed loglog function] ................................................................................................................................ 115
Table 2-13 Comparison of median WTP (in U.S. dollars) and estimation efficiency [semi-log
function] ...................................................................................................................................... 116
Table 3-1 Environmental improvements from farming practices in four cropping systems ...... 155
Table 3-2 Calculation of effective acreage for each practice in four cropping systems that results
in eutrophic lakes reduction ........................................................................................................ 156
Table 3-3 Calculation of effective acreage for each practice in the four cropping systems that
results in greenhouse gas reduction ............................................................................................ 156
x

Table 3-4 Average reduction in eutrophic lakes from farming practices. .................................. 157
Table 3-5 Average reduction in GHG emission due to farming practices. ................................. 157
Table 3-6 Economically optimal conditions for the “payment for land enrollment” scenario in
five cropping system alternatives................................................................................................ 158
Table 3-7 Economically optimal conditions for the “additionality targeting” scenario in five
cropping system alternatives ....................................................................................................... 158
Table 3-A1 Rotation rate calculation based on Michigan ARMS data ...................................... 161
Table 3-A2 Corn-soybean rotation area calculation ................................................................... 161
Table 3-A3 Major counties and their representative soil types .................................................. 164
Table 3-A4 Calculation of erosion reduction rate with RUSLE 2 .............................................. 166
Table 3-A5 Operations in each management scenario assumed with RUSLE 2 ........................ 166
Table 3-A6 Calculation of GHG emissions rate with Farming Systems Greenhouse Gas Emission
Calculator .................................................................................................................................... 172
Table 3-A7 Enrollment, environmental and welfare measures for cropping system A.............. 176
Table 3-A8 Enrollment, environmental and welfare measures for cropping system B .............. 179
Table 3-A9 Enrollment, environmental and welfare measures for cropping system C .............. 182
Table 3-A10 Enrollment, environmental and welfare measures for cropping system D............ 183
Table 3-A11 Enrollment, environmental and welfare measures for mixed-choice cropping system
alternative.................................................................................................................................... 188
Table 3-A12 Enrollment, environmental and welfare measures for cropping system A (payment
for additionality) ......................................................................................................................... 191
Table 3-A13 Enrollment, environmental and welfare measures for cropping system B (payment
for additionality) ......................................................................................................................... 194
Table 3-A14 Enrollment, environmental and welfare measures for cropping system C (payment
for additionality) ......................................................................................................................... 197
Table 3-A15 Enrollment, environmental and welfare measures for cropping system D (payment
for additionality) ......................................................................................................................... 200

xi

Table 3-A16 Enrollment, environmental and welfare measures for mixed-choice cropping system
alternative (payment for additionality) ....................................................................................... 215

xii

LIST OF FIGURES

Figure 1-1 Illustration of changes in utility by four hypothetical farmers from adopting specified
production practices as a function of the associated PES payment .............................................. 36
Figure 1-2 Conceptual diagram of farmers' participation decisions in a PES program ................ 37
Figure 1-3 Number of farms that fell into the three participation categories for each of the four
cropping systems (N=1688 Michigan corn and soybean farms, year=2008) ............................... 37
Figure 1-4 Predicted State-level Supply Curves of Enrolled Acres by Cropping System from
Double Hurdle Estimation, 1688 Michigan Corn or Soybean Farms, 2008 ................................. 38
Figure 1-A1 Predicted State-level Supply Curves of Enrolled Acres by Cropping System from
Extended Double Hurdle Estimation, 1688 Michigan Corn or Soybean Farms, 2008 ................. 60
Figure 1-A2 Predicted State-level Supply Curves of Enrolled Acres by Cropping System from
Single Hurdle Estimation, 1688 Michigan Corn or Soybean Farms, 2008 .................................. 61
Figure 1-A3 Predicted State-level Supply Curves of Enrolled Acres by Cropping System from
Tobit Estimation, 1688 Michigan Corn or Soybean Farms, 2008 ................................................ 61
Figure 2-2 Numerical certainty scale used in survey, 2211 Michigan residents, 2009 ................ 98
Figure 2-3 Numerical certainty scale used in Loomis and Ekstrand (1998)................................. 98
Figure 2-5 Probability of voting “yes” as a representation of underlying WTP with preference
uncertainty..................................................................................................................................... 98
Figure 2-4 Binary response percentage in sample, 2211 Michigan residents, 2009.................... 99
Figure 2-5 Certainty-adjusted response percentage under the Symmetric Uncertainty Model
(SUM) in sample, 2211 Michigan residents, 2009 ....................................................................... 99
Figure 2-6 Median WTP in conventional dichotomous choice model with respect to eutrophic
lake and GHG improvements [mixed log-log function] ............................................................. 100
Figure 2-7 Median WTP in conventional dichotomous choice model with respect to eutrophic
lake and GHG improvements [semi-log function]...................................................................... 100
Figure 3-2 State-level benefit (WTP) and cost (WTA) for ES from Michigan cropland ........... 151
Figure 3-1 Input-output system of ecosystem services from croplands ..................................... 151
xiii

Figure 3-3 State-level benefit (WTP) and cost (WTA) for ES from Michigan cropland ........... 152
Figure 3-4 State-level benefit (WTP) and cost (WTA) for ES from Michigan cropland ........... 152
Figure 3-5 State-level benefit (WTP) and cost (WTA) for ES from Michigan cropland ........... 153
Figure 3-6 Number of farms using each cropping system at different price levels for the scenario
with mixed choice of systems but no requirement of additionality. ........................................... 153
Figure 3-7 Number of farms using each cropping system at different payment levels for the
scenario allowing mixed choice of system and paying for farms with additionality in at least one
environmental improvement. ...................................................................................................... 154
Figure 3-A1 Major counties for corn, soybean and wheat production in Michigan ................... 164

xiv

LIST OF ABBREVIATIONS

ARMS

Agricultural Resource Management Survey

ASUM

Asymmetric Uncertainty Model

CDL

Cropland Data Layer

CRP

Conservation Reserve Program

CSP

Conservation Stewardship Program

CV

Contingent Valuation

CWTP

Conditional Willingness to Pay

EQIP

Environmental Quality Incentives Program

ES

Ecosystem Services

FSGGEC

Farming Systems Greenhouse Gas Emissions Calculator

GEE

Generalized Estimating Equations

GHG

Greenhouse Gas

GW

Global Warming

KBS

Kellogg Biological Station

LR

Likelihood ratio

LTER

Long Term Ecological Research

MLE

Maximum Likelihood Estimation

MWTA

Marginal Willingness to Accept

MWTP

Marginal Willingness to Pay

NASS

National Agricultural Statistics Service

NCS

Numerical Certainty Scale
xv

NRCS

Natural Resource Conservation Service

PC

Polychotomous Choice

PES

Payment for Environmental Services

PSNT

Pre-Sidedress Nitrate Test

RUSLE

Revised Universal Soil Loss Equation

SOCRATES Soil Organic Carbon Reserves and Transformations in EcoSystems
SPC

Stochastic Payment Card

STATSGO

United States General Soil Map (original title: State Soil Geographic)

SUM

Symmetric Uncertainty Model

TP

Total Phosphorus

USDA

United States Department of Agriculture

WTA

Willingness to Accept

WTO

World Trade Organization

WTP

Willingness to Pay

xvi

INTRODUCTION

Agriculture is an ecosystem transformed by humans for establishing production of crops
and livestock. In addition to supplying market farm products, such as food, fiber and fuel,
agriculture can also jointly provide nonmarket benefits to people by farmers’ choice of
production inputs and management practices (Wossink and Swinton, 2007). These benefits
people obtained from ecosystems are defined as Ecosystem services (ES) (Millennium
Ecosystem Assessment, 2003). Examples of nonmarket ecosystem services from agriculture
include soil erosion control from conservation tillage, water quality improvement from reduced
fertilizer input, and greenhouse gas (GHG) mitigation from adoption of winter cover crops.
However, farmers typically gain little private reward from those nonmarket services, as many of
them accrue to people beyond the farm gate. In the absence of policy incentives, the supply of
nonmarket ecosystem services is mostly determined by the price incentives to supply market
products (Antle and Valdivia, 2006). Payment-for-Environmental-Services (PES) programs that
translate external ecosystem values into direct financial incentives for local providers are gaining
appeal globally as flexible approaches to inducing the voluntary provision of ES (Engel, et al.,
2008). In the United States and Europe, the PES programs are also viewed as a trade-neutral
alternative to direct commodity subsidies to support farmer income under the World Trade
Organization (WTO) rules (Swinton, et al., 2006).
The worldwide population boost and environmental degradation have posed enormous
challenges to agriculture to support the sustainability for both livelihood and the environment.
Working land PES programs that promote conservation activities during the agricultural
production process have a great potential to address these challenges. The importance of working
1

land PES programs calls for public policies that facilitate the voluntary provision of ecosystem
services in an efficient and effective fashion. The design of PES programs should be based upon
a comprehensive understanding of the underlying supply and demand for ecosystem services,
which is rarely addressed in previous studies. To provide empirical insights for designing
efficient and effective PES program, this dissertation thus combines farmers’ willingness to
adopt improved environmental stewardship in exchange for payments on the supply side, with
the public’s willingness to pay for resulting ecosystem services on the demand side. Specifically,
this study focuses on the ecosystem services from changing cropland management practices in
Michigan.
Essay 1 investigates the farmer supply of ecosystem services via four hypothetical PES
programs using a stated preference survey of 3000 Michigan corn and soybean farmers. This
essay is built on an earlier study by Jolejole (2009), but complements existing literature by
dividing the decision on whether to enroll in PES programs into two stages: whether even to
consider enrolling in the program given incentive payments that presumably are politically
feasible, if yes, whether to participate. The decision process is analyzed using a double hurdle
model. Results suggest the first-stage willingness to consider decision chiefly depends on farm
and farmer characteristics, while the second-stage decisions on whether and how much to enroll
depend more on payment offer and benefit-cost criteria. The results also show that the price
elasticity of enrollment decreases with the number of cropping practices required. These twostage decisions are integrated to predict the state-level ES-providing land enrollment in response
to PES payment.
Essay 2 examines public demand for environmental improvements measured by
willingness to pay (WTP) for reductions in the number of eutrophic lakes and greenhouse gas

2

(GHG) emissions using a stated preference survey of 6000 Michigan residents. This essay is
built on an earlier study by Chen (2010), but particularly evaluates alternative methods of
modeling WTP that incorporate respondent uncertainty. The hypothetical markets for contingent
valuation and respondents’ unfamiliarity with certain ecosystem services may enhance their
preference uncertainty, which may increase variance and even cause bias in WTP estimates. Two
functional forms, semi-log and mixed log-log, are adopted to test the sensitivity of conditional
WTP estimates to different functions. Results suggest that the incorporation of self-reported
uncertainty into binary choice models appears to improve our understanding of the demand for
ecosystem services and provide more efficient estimates of WTP. Both functional forms lead to a
common finding that is consistent with the analytical expectations: the symmetrically calibrated
certainty-adjusted models yield indifferent WTP estimates compared to the conventional model,
whereas the asymmetrically calibrated certainty-adjusted models lead to significantly lower
WTP. The unbiased conventional dichotomous choice model still provides a reliable median
WTP estimate that reflects the influence of key variables.
Essay 3 combines the farmer cost for providing ecosystem services with the public benefit
from environmental improvements derived in first two essays to explore the welfare-maximizing
conditions for PES design. This essay especially contributes to the literature by proposing

agricultural PES policies based on the underlying supply-demand mechanism embedded in
empirical stated preference estimates. Individual values are aggregated for the State of Michigan by
linking ecological processes to benefit and cost functions. Results reveal the economic optimal levels
of PES payment, land enrollment and environmental outcomes for five hypothetical PES programs,
and how these outcome change under different policy scenarios. Comparing across programs,

results suggest that the simplest cropping system with the least ES improvement dominated by
other three systems, which offer similar economic welfare gains with varying trade-offs in cost
3

and environmental performance. The choice of system largely depends on the goal of PES
program and evolving demand for specific ES by consumers. Allowing farms to choose different
cropping systems that lower their individual costs or targeting at farms that provide additional
environmental services beyond their current scenario would improve the cost-effectiveness of
PES programs.

4

REFERENCES

5

REFERENCES

Antle, J., and R. Valdivia. 2006. "Modelling the supply of ecosystem services from agriculture:
A minimum-data approach." Australian Journal of Agricultural and Resource Economics
50(1):1-15.
Chen, H. 2010. "Ecosystem services from low input cropping systems and public's willingness to
pay for them." M.S. Thesis, Michigan State University, Department of Agricultural, Food and
Resource Economics. http://www.aec.msu.edu/theses/fulltext/chen_ms.pdf
Engel, S., S. Pagiola, and S. Wunder. 2008. "Designing payments for environmental services in
theory and practice: An overview of the issues." Ecological Economics 65(4):663-674.
Jolejole, M.C.B. 2009. "Trade-offs, incentives and the supply of ecosystem services from
cropland." M.S. Thesis, Michigan State University, Department of Agricultural, Food and
Resource Economics. http://aec3.aec.msu.edu/theses/fulltext/jolejole1_ms.pdf
Millennium Ecosystem Assessment. 2003. Ecosystems and human well-being: A framework for
assessment. Washington, DC: Island Press.
Swinton, S.M., F. Lupi, G.P. Robertson, and D.A. Landis. 2006. "Ecosystem services from
agriculture: Looking beyond the usual suspects." American Journal of Agricultural Economics
88(5):1160-1166.
Wossink, A., and S. Swinton. 2007. "Jointness in production and farmers' willingness to supply
non-marketed ecosystem services." Ecological Economics 64(2):297-304.

6

ESSAY 1: FARMERS’ WILLINGNESS TO PARTICIPATE IN PAYMENT-FORENVIRONMENTAL SERVICES PROGRAMS

1.1

Introduction

Agriculture is an ecosystem transformed by humans for establishing agricultural
production. It supplies market goods, such as food, fiber and fuel. In addition, agriculture also
provides non-market environmental services (ES) that depend on farmers’ choices of production
inputs and management practices (Wossink and Swinton, 2007). However, because only a small
portion of the benefits from non-market ES accrue to farmers, they have little incentive to
produce these services.
Various agri-environmental policies have been implemented to motivate the supply of
1

environmental services. One prominent example is payment-for-environmental-services (PES) ,
which attracts increasing attention globally as a policy innovation that translates external
ecosystem values into real financial incentives for local providers (Engel, et al., 2008). In the
United States, land retirement programs, such as the Conservation Reserve Program (CRP) have
played an important role in providing environmental services since 1985. Recently, as
exemplified by the Environmental Quality Incentives Program (EQIP) initiated in 1996 and the
2

Conservation Security Program (CSP) initiated in 2002 , the policy focus has shifted to
conservation on working lands—land used primarily for crop production and grazing (Cattaneo,
1

An earlier version of this essay was submitted for publication as S. Ma , S.M. Swinton, F. Lupi,
and M.C. Jolejole-Foreman, "Farmers’ Willingness to Participate in Payment-for-Environmental
Services Programs" (July 2011). PES is formally defined as a voluntary transaction where a welldefined environmental service or a land use likely to secure that service is being ‘bought’ by a
service buyer from a service provider if and only if the service provider secures service provision.
(Wunder, 2005)
2
The EQIP and CSP programs are classified as PES programs by Wunder, et al. (2008).
7

et al., 2005). The 850 million acres of working lands, which is equivalent to 45% of land area of
the 48 contiguous U.S. states, have a great potential to cost-effectively provide environmental
services, such as reduced nutrient runoff, from changes in production practices. Government
spending in the four largest working land programs is projected to grow to $11.7 billion during
3

2008-2012, an 85% increase over the period 2002-2009 . Most of this spending is allocated to
4

the EQIP and CSP . The focus of these programs has evolved from restricting local negative
externalities, such as soil erosion and nitrate run-off, to providing public goods, such as
greenhouse gas mitigation and biodiversity. Similar PES programs that pay land owners for
effective agricultural land management are also launched in other developed countries. Examples
include the Environmental Stewardship Scheme (ESS) for environment and wildlife protection in
the United Kingdom, the user-financed Vittel (Nestlé Waters) watershed protection program in
Eastern France, the Northeim Model Project for agrobiodiversity in Germany, and the Wimmera
Catchment pilot program for salinity control in Australia.
An essential precondition for the success of an agricultural PES program is that farmers
be willing to participate. If they are, then the next question becomes how much they will
participate. Both decisions involve weighing the potential benefits and costs in PES programs.
This study thus aims to investigate the determinants of farmers’ willingness to participate and the
degree of participation in hypothetical PES programs.
Prior to the majority of research on PES programs, many economic studies examined
farmers’ choices about adoption of conservation practices without incentive payments. Some of
3

Source: Briefing Rooms for Conservation Policy, Economic Research Service, United States
Department of Agriculture (USDA).
http://www.ers.usda.gov/Briefing/ConservationPolicy/background.htm
4
The Conservation Security Program was replaced by Conservation Stewardship Program (CSP)
in the 2008 Farm Act.
8

these adoption studies focused on single practices, such as conservation tillage (Davey and
Furtan, 2008, Epplin and Tice, 1986, Rahm and Huffman, 1984, Sheikh, et al., 2003), reduced
fertilizer and pesticide use (Bosch, et al., 1995, Lasley, et al., 1990), and cover crops (Neill and
Lee, 2001). Other studies focused on adoption combinations of multiple practices (Ervin and
Ervin, 1982, Lynne, et al., 1988, Negatu and Parikh, 1999, Nowak, 1992, Roberts, et al., 2006,
Soule, et al., 2000, Wu and Babcock, 1998). Yet other adoption studies examined the number of
farm-level practices adopted (Lynne and Rola, 1988, Wei, et al., 2009), land area allocated for
certain practices (Gould, et al., 1989) and expenditure on permanent conservation structures
(Norris and Batie, 1987). This earlier literature provides a solid empirical foundation for PES
studies by attributing farmers’ adoption decisions to various natural, social and economic factors.
However, apart from partial cost-sharing in several cases, these articles involve no incentive
payment. Hence, decisions were chiefly based on the net benefits from adopting farming
practices.
Farmer participation in early paid conservation programs was studied by Purvis et al.
(1989), who examined farmers’ willingness to accept payment in a hypothetical program to
adopt filter strips. They found that farmer decisions were determined by the size of the payment
offer, perceptions of environmental change, and farmers’ opportunity costs. For observed
enrollment choices, Zbinden and Lee (2005) investigated participation in a PES program in
Costa Rica by farmers and forest owners. They found that farm size, household farm income, and
familiarity with the program significantly influence participation. The 2001 United States
Department of Agriculture (USDA) Agricultural Resource Management Survey reported that the
farms most likely to participate in working land PES programs were larger, operated by younger
farmers, and more reliant on income from farming (Lambert, et al., 2006). Compared with the

9

research on unpaid adoption of farming practices, these PES studies have further investigated the
influence of payment on farmer decisions.
Although the decision on whether to adopt conservation farming practices with or
without incentive payment is well examined, all previous studies overlook an implicit prior
decision on whether seriously to consider participating in the proposed program. This
willingness-to-consider decision addresses whether a proposed program is sufficiently acceptable
to merit closer evaluation of the financial assistance offered. Some farmers are very unlikely to
consider providing ES through payment programs, because those programs do not pass certain
prior screening criteria due to unfavorable physical settings or substantial cost for adoption.
These farmers’ decision is not likely to change with the increased payment levels that are
perceived to be in a politically feasible range. Other farmers may be willing to consider the
program, and would choose to participate given a suitable payment that is high enough to make
the operation rewarding. Only a proportion of farmers who consider participating will elect to
enroll, as the rest are unsatisfied with the program payment offered. Explicitly modeling this
additional consideration decision may improve the understanding of farmers’ participation and
amount of environmental services supplied under payment schemes. Using the same stated
preference survey data as Jolejole (2009), but with additional information permitting separation
of the consideration and participation decisions, this essay analyzes Michigan corn and soybean
farmers’ decisions in four hypothetical PES programs, in order to:
1) Reveal determinants of farmers’ consideration and participation decisions;
2) Derive the supply of land that provides environmental services in response to payment based
on aggregate decisions;

10

1.2

Conceptual model

1.2.1

Utility function

Following Dupraz et al. (2003), farmers are assumed to maximize utility that is based
upon consumption of market goods (Z) and non-market environmental services (E), which are
co-produced by farming activities. They face a budget constraint that the cost of consumption
cannot exceed the sum of profit from farm production and nonfarm income (NFI). Farm profit
(π) is earned from selling agricultural products (Y) at price ry minus variable cost (rxX) and fixed
cost (FC). Output Y is a function of inputs X and FC. The variable cost refers to material and
hired labor associated with the level of production, while fixed cost in this study refers to
predetermined resources, including family labor (L), capital (K), land area (A), biophysical
conditions (B) and information (I) available to farmers. Environmental services (E), which are
produced jointly with market goods (Y) using variable and fixed inputs, may also affect the
magnitude and timing of variable input (X) employment in turn (Zhang, et al., 2007). F
represents farmer traits that condition the production function and hence condition the effects of
PES offers.
max U ( Z , E | F )
Z ,E

s.t.

Z ≤ π + NFI

π = ryY ( X , FC ) − rx X ( E ) − FC ( L, K , A, B, I )
E = f ( X , FC )

(1.1)
(1.2)
(1.3)
(1.4)

The maximized utility given optimal choices of consumption level (Z*) and
environmental services (E*) can be represent by the indirect utility function V.

V (π + NFI | F ) = U ( Z *, E*| F )
11

(1.5)

1.2.2 Willingness to accept
Enrollment in a PES program could change farmers’ maximized utility by requiring a
higher level of environmental services or by receipt of a payment. Farmers’ willingness to
participate in a PES program depends on the magnitudes of the change in utility. This change can
be measured monetarily by willingness to accept (WTA) payment, which is the minimum amount
of payments that the farm household would require to provide specified environmental services
in the program (Jolejole, 2009). The farmer is assumed to increase the environmental service
supply, E, by a fixed quantity such that: ΔE = E1 – E0 > 0. Their total spending on production is
likely to increase with adoption of new practices. The expenditure function e (r, E, U0),
represents the minimum amount of income that is needed to produce a fixed quantity of
environmental services ΔE while maintaining constant utility (Equation 1.6). The input and
output prices are represented by r for simplicity.
e(r , E , U 0 ) = Min[ Z − π (r , E ) | U ( Z , E ) ≥ U 0 ]

(1.6)

WTA can be represented as the change in expenditure levels of the farm household in response to
change in the level of environmental services produced, given that utility is kept the same
(Equation 1.7)
WTA = e(r , E1, U 0 ) − e(r , E0 , U 0 )

(1.7)

Letting Z*(r, E, U0) denote the solution of the cost minimization problem in Equation 1.5, the
expression in Equation 1.8 becomes:
WTA = [π ( r , E0 ) − π ( r , E1 )] − [ Z * ( r , E0 , U 0 ) − Z * ( r , E1, U 0 )]

12

(1.8)

The first term in brackets in Equation 1.6 is the farm’s foregone profit. The second term is the
amount that the household is willing to pay for an increase in environmental service. In other
words, the WTA equals the foregone profit offset by the monetary value of change in the
farmer’s utility from producing more environmental services. Based on Equation 1.8, WTA can
be zero or even negative if the foregone profit from farm production is completely offset or
outweighed by the benefits from higher level of ES.
Combining Equations 1.5 and 1.8, the influence of the PES program payment P on the
change of farmer’s utility can be represented by Equation 1.9. Under common assumptions that
farmers prefer more payment than less but have a decreasing marginal rate of substitution
between payment and other goods, the change of utility is an increasing and concave function of
payment.
ΔU ( P ) = V (π1 + NFI1 + P, E1 | F ) − V (π 0 + NFI 0 , E0 | F )

(1.9)

Farmers’ WTA is a payment level that would make the utility change equal to zero:
ΔU (WTA ) = V (π1 + NFI1 + WTA, E1 | F ) − V (π 0 + NFI 0 , E0 | F ) = 0

1.2.3

(1.10)

Decision rule

The farmer decision on participating in PES programs involves two steps. The first step
for farmers to consider a PES program implies that the program is acceptable and utilityincreasing if a sufficiently high payment is offered. Although in theory the payment offer could
be massive, in practice the “sufficiently high payment” would be filtered by what farmers believe
to be politically feasible. This politically feasible payment level varies across farmers and largely
depends on their previous experience with government programs. Thus, farmers would consider
high

a PES program only if the perceived maximum politically feasible payment P
13

is greater than

high

their WTA (i.e., P

> WTA), which makes the change of utility equals zero (ΔU (WTA) = 0).

The second step, for farmers willing to consider the program, is how much land to enroll.
Farmers are assumed to enroll in a specific program only if the real program payment P* is
*

greater than their WTA (i.e., P > WTA). When the utility gain is increasing and concave,
farmers’ decision rule can be represented as follows.

(

)

( )


 Enroll
ΔU P high > ΔU P* > ΔU (WTA)


high
> ΔU (WTA ) = 0 
Consider ΔU P

 Not enroll ΔU P high > ΔU (WTA ) > ΔU P*
Decision = 


high
 Not consider ΔU P
≤ ΔU (WTA ) = 0



(

)

(

)

(

)

( )

The levels of utility change in response to adoption of paid conservation farming
practices are unique to individual decision makers under specific settings. Figure 1-1 illustrates
four indicative utility gain (ΔU) curves from a given set of production practices in response to
high

PES payment level (P). At the maximum politically feasible payment level P

, representative

farmers 1, 2, 3 would consider enrolling in the PES program as the payment is greater than their
1,2,3

WTA (i.e., ΔU

high

(P

1,2,3

) > ΔU

(WTA) = 0). However, fundamental incompatibility may

deter some others who have unfavorable physical settings, unacceptably high adjustment cost,
negative attitudes toward the proposed practices, or unsuitable management skills. Those farmers
are unlikely to consider the program at any payment that is politically feasible, represented by
4

high

farmer 4 in the figure (ΔU (P

4

) <<ΔU (WTA) =0). The payment level that would motivate

farmer 4 to enroll is far beyond the feasible range, so any variation in the actual payment will not
have a significant effect on his/her decision. Among those who would consider enrolling, farmer
1 and 2 would elect to enroll in a PES program with specific program payment P*, which is
14

1,2

greater than their WTA (i.e., ΔU

1,2

(P*) > ΔU

(WTA) =0). Notably, farmer 1 has positive

utility gain from the proposed production practices and would adopt the practices without any
1

payment (WTA <0; ΔU (0)>0). Farmer 2 is only willing to adopt the practices with incentive
payment P*. In contrast, farmer 3 who face higher costs of adoption is deterred from enrolling in
the program by insufficient payment, but would consider doing so with a higher but feasible
3

3

3

high

payment (ΔU (P*) < ΔU (WTA) < ΔU (P

) ). Each farmer perceives a uniquely different

change in utility for a given combination of changed production practices. Likewise, each
farmer will have a different perception of the maximum feasible payment that determines
whether they believe that conditions exist for a higher payment that they might be willing to
accept. This study aims to expand our understanding of farmers’ participation in PES in a
manner that distinguishes the above four cases.

1.3

Data and questionnaire design

Data for this study come from a 2008 mail survey of Michigan corn and soybean farmers
that yielded 1688 responses (56% response rate) (Jolejole, 2009). The survey used a four contact
version of the tailored design method (Dillman, 2007) consisting of 1) a pre-notice letter, 2) a
questionnaire and one dollar incentive, 3) a postcard reminder, and 4) a replacement
questionnaire. The survey design and questionnaire development were preceded by a series of
farmer focus groups and pre-tests to ensure validity and clarity of the questions as well as an
appropriate range of payment offers for those cropping practices. Six farmer focus groups were
conducted during February and March of 2007, while in-person questionnaire pre-tests were
conducted in January of 2008. A stratified random sample of 3,000 corn and soybean farmers

15

was provided by the National Agricultural Statistics Service (NASS) from the 2007 agricultural
census mailing list. The farms were stratified into four groups by farmland area. Different
sampling percentages of farms were drawn from the four strata with 0 to 100, 101 to 500, 501 to
1000 and 1000 or more acres, respectively. Larger farms were oversampled in order to capture
how most land is managed, and also because of lower expected response rates among operators
of large farms. Sample weights are incorporated in the empirical analysis to appropriately correct
for the stratification.
The survey questionnaire presented each respondent with four hypothetical cropping
systems that provided sequence of cropping practices linked to environmental service levels.
System A, the base system, was a corn-soybean rotation with chisel tillage, pre-sidedress nitrate
test (PSNT) in corn, all agrochemicals broadcast in the field according to Michigan State
University recommendations or pesticide label instructions. System B added a winter cover crop,
System C added wheat to the crop rotation, and System D added a requirement to band fertilizer
and pesticides application over the crop row and therefore reduce rates by one third below
university recommendations or label rates (Table 1-1). Based on agro-ecological research, five
major environmental improvements would be generated from the four hypothetical programs
compared to a conventional corn-soybean system (Table 1-2). Soil erosion would be lessened by
switching to chisel plow tillage from intensive tillage tools like the moldboard plow (Reganold,
et al., 1987), planting cover crops over winter (Delgado, et al., 1999, Joyce, et al., 2002, Oades,
1984), and adding wheat into the corn-soybean rotation (Peel, 1998). Reduced erosion not only
improves soil fertility and crop productivity (Pimentel and Kounang, 1998), but is also likely to
mitigate the eutrophication problem of lakes by carrying less phosphorus-rich topsoil into surface
water (Correll, 1998, Poudel, et al., 2001). Greenhouse gas emission in the form of carbon

16

dioxide (CO2) and nitrous oxide (N2O) can be reduced by adding cover crops (Lal, et al., 2004,
McSwiney, et al., 2010), switching to chisel tillage (Reicosky and Lindstrom, 1993), PSNT
(Musser, et al., 1995), and reduced fertilizer application (Hoben, et al., 2011, McSwiney and
Robertson, 2005). Farming practices related to nitrogen fertilizer application, such as cover
crops, reduced fertilizer rate and PSNT, would also improve the groundwater quality due to less
nitrogen leaching (Borin, et al., 1997, Poudel, et al., 2001). Reduced pesticide rate would also
mitigate on-site and off-site air pollution and possible health risks for human (Glotfelty, et al.,
1987, van den Berg, et al., 1999).
A main effect orthogonal design framework was constructed for the 16 questionnaire
versions. The versions varied by payment levels offered (4), payment provider (federal
government or non-governmental organization) and sequence of cropping practices (increasing
or decreasing in complexity and expected environmental benefits). For each cropping system,
respondents were first offered a specific payment if they would adopt the system for a period of
five years, and they were asked how many acres they would enroll in such a program.
Respondents who chose not to enroll any land were asked whether they would consider enrolling
in that system if the payment were higher. Thus, the “consider” group and “not consider” group
are distinguished based upon this question and assuming that all farmers who chose to enroll
would also consider the program with a higher payment. The “enroll” and “consider but not
enroll” group are further identified by the first acreage enrollment question. Unlike the
conceptual model, the willingness-to-enroll question is presented ahead of the willingness-toconsider question in order to facilitate the flow of thinking for respondents. It is easier for them
to make a decision about a real payment than to think about the system abstractly at first. The
follow-up question on considering enrollment with a higher payment comes out naturally if they
17

decide not to enroll. See Figure 1-2 for conceptual differentiation of those groups, and Figure 1-3
for the number of farms falling into different groups in our data set.
Besides farmer choices associated with each cropping system, other information collected
includes current crop management practice, farmers’ perception of benefits from changed
farming practice, attitudes on the importance of enhanced environmental services, past adoption
of beneficial farming practices, participation in four hypothetical cropping systems containing
those practices, as well as the demographic background. Detailed information about data
collection and questionnaire design can be found in Jolejole (2009).

1.4

Empirical model and variables

1.4.1

Choice of models

To model the participation in conservation programs, several functional forms have been
used in the literature. Since the basic participation or adoption decision is a dichotomous choice,
binary response models, such as probit (Bosch, et al., 1995, Davey and Furtan, 2008, Rahm and
Huffman, 1984, Sidibe, 2005) and logit (Lee and Stewart, 1983, Pautsch, et al., 2001, Sheikh, et
al., 2003, Soule, et al., 2000, Upadhyay, et al., 2003) are widely applied. Ordered probit (Negatu
and Parikh, 1999) and multinomial logit (Wu and Babcock, 1998, Zbinden and Lee, 2005) have
sometimes been used to model choices among more than two alternatives.
When the choice concerns the level of participation, commonly the land acreage
promised for certain practices, a continuous variable needs to be selected in addition to the
binary participation choice. In certain circumstances, a corner solution may arise. This occurs
when some acreage enrollment responses pile up at zero while others take strictly positive
values. The simplest way to model a corner solution is the tobit model (Tobin, 1958), which

18

assumes all zeroes are generated due to the same mechanisms underlying the positive values.
The tobit model has been used for adoption of farming practices in the literature (Lynne, et al.,
1988, Mazvimavi and Twomlow, 2009, Norris and Batie, 1987, Wei, et al., 2009).
One extension to the tobit model is a hurdle model (Cragg, 1971), in which different
mechanisms are allowed for the participation and level decisions. A probit model is used for the
binary participation decision and a truncated normal regression or log-normal regression is used
for the positive amount choice. Both regression variables and estimated coefficients can differ in
the two decisions. A likelihood ratio test (Greene, 2000) or Lagrange multiplier test (Lin and
Schmidt, 1984) can be used to choose between the tobit and hurdle alternatives. Studies that
applied both tobit and hurdle models to WTP for natural amenities (del Saz-Salazar and RausellKoster, 2008, Goodwin, et al., 1993) and WTA for wildlife habitat preservation (Shrestha, et al.,
2007) suggested the hurdle model was preferred. A further extension to the tobit model and
hurdle model is a P-tobit model (Deaton and Irish, 1984), which assumes that the proportion of
potential participants is p and the proportion of respondents who would never participate is 1-p.
Both the proportion p for non-participants and the tobit model for the potential participants need
to be estimated. A more flexible form of the p-tobit model that replaces the proportion p by a
probit model was the double hurdle model (Blundell and Meghir, 1987). In this case, two types
of zeros are implied, namely zeros due to non-participation and zeroes chosen by potential
participants conditional on unsatisfied economic circumstances. The double hurdle model has
been adopted in studies of food the consumption, such as meat (Burton, et al., 1996, Su and Yen,
1996), cheese (Yen and Jones, 1997), alcohol (Yen and Jensen, 1996) and prepared meals
(Jensen and Yen, 1996, Newman, et al., 2003).

19

In this study, there are two types of zero responses by farmers that enrolled zero acres to the
program. As mentioned in the conceptual model section, one type of zero response refers to
those who are unwilling to consider the program, while the other refers to potential participants
who are limited by the payment offer, namely those who will consider it but choose not to enroll.
The second type of zero determined by the payment offer is likely to be underlain by the same
choice mechanism as the affirmative enrollment responses. Thus, a standard double hurdle
specification seems to be suitable for our data set. Probit regression is used in the first stage to
distinguish between potential participants and those who would not consider the program. For
the second stage, I test both a tobit specification as in the standard double hurdle model and a
two-part hurdle (Cragg) model as in the extended double hurdle model. Although the extended
double hurdle model is preferred to the double hurdle model based on statistical tests for two of
the four cropping systems (Appendix 1-2), the double hurdle model performs better in terms of
theoretical consistency (Lau, 1986) and ease of interpretation (Fuss and McFadden, 1978). Based
on the conceptual model, once the zero-enrollment responses deterred by fundamental
incompatibilities are picked up by the first-stage probit, the driving forces that distinguish
positive acreage enrollment from zero enrollment in the second stage should only pertain to the
benefit-cost criteria. The second stage tobit model adequately captures those influential factors,
while also providing more easily interpreted results than the extended double hurdle model.
Hence, the standard two-stage double hurdle (probit plus tobit) is adopted for the rest of the
5

essay. The complete econometric derivation of the double hurdle model is shown in the next
section.
5

Fuller discussion of econometric foundations, statistical choice of model test results, and
empirical results from the four models tested--the standard double hurdle model, the one-stage
tobit model, the one-stage hurdle model (probit plus truncated regression), and the extended
20

1.4.2

Econometric model

Participation in agricultural PES program may involve two corner solutions before the
real positive acreage enrollment can be observed. The farmland area that respondents choose to
enroll in the program is represented by y, which is a compound function of the binary
consideration decision c, and the continuous choice of acreage enrollment, a, which can be zero
or positive.
y = c⋅a

(1.11)

Probit estimation is used for the binary choices of consideration is The latent variable indicating
farmers’ utility gain by considering enrolling in the program with a suitable payment is c* , x1
is a vector of attributes determining utility, and the random term e is assumed to follow a normal
distribution with standard deviation σe (Equation 1.12). Farmers would consider the program
(c=1) only if their utility increases (Equation 1.13). The probability of willingness-to consider is
estimated by a cumulative normal density function as in Equation 1.14.
c* = x1γ + e

e ~ N ( 0, σ e )
c* > 0
c* ≤ 0

1
c=
0

P ( c = 1| x1 ) = E ( c | x1 ) = Φ ( x1γ σ e )

(1.12)
(1.13)
(1.14)

The acreage enrollment variable a is indicated by a latent variable a* and cornered at
zero (Equation 1.15). Latent variable a* depends on farm and farmers characteristics x2 that
influence their amount choice for enrollment (equation 1.1.16). The random term u has a zero
double hurdle model (first-stage probit plus second-stage probit and truncated regression)—can
be found in Appendices 1-4.
21

2

mean and variance σ . The positive enrolled acreage can be observed only if farmers consider the
program and choose to participate given a specific payment (Equation 1.16).

a = max [ a*, 0]

(

u ~ N 0, σ u 2

a* = x2 β + u > 0
a *
y=
0

if

(1.15)

)

(1.16)

c = 1, a > 0
otherwise

(1.17)

The conditional expected enrollment acres, conditional on c=1 is:

E ( y | x2 , c = 1) = Φ ( x2 β / σ u ) x2 β + σφ ( x2 β / σ u )

(1.18)

The probability density functions for the consideration and enrollment decisions are shown in
Equations 1.19 and 1.20.
1[ c = 0]

f ( c | x1 ) = 1 − Φ ( x1γ σ e ) 



Φ ( x1γ σ e ) [

1 c =1]

(1.19)

1[ a > 0]

1[ a = 0] 

σ u −1φ ( y − x2 β / σ u ) 

f ( a | x2 , c = 1) = 1 − Φ ( x2 β / σ u ) 





(1.20)



The unconditional density of y is derived by taking into account all decisions:
1[ y = 0]

f ( y | x1, x2 ) = 1 − Φ ( x2 β / σ u ) Φ ( x1γ σ e ) 



{

+ Φ ( x1γ σ e )  φ ( ( yi − xi β ) / σ u )  σ u

 


(1.21)

1[ y > 0]

}

The associated log-likelihood function used for ML estimation is:

li ( γ , β ) = 1[ y = 0] log 1 − Φ ( x2i β σ u ) Φ ( x1iγ σ e ) 



{

{





+ 1[ y > 0] log Φ ( x1iγ σ e )  + log φ ( ( yi − x2i β ) σ u )  σ u

}}

(1.22)

The results from the double hurdle model are important in predicting the supply curve,
i.e., estimating the potential enrollment of land providing enhanced environmental services in
22

response to per-acre payment variation. Intuitively, the predicted acreage is the conditional
predicted enrollment acreage multiplied by the probabilities of consideration. It can be computed
from the unconditional expected value of acres choice y (equation 1.23), which is derived from
two conditional expected value functions (equations 1.19 and 1.20). The predicted supply of land
contributing ES is depicted by systematically increasing the payment variable upward from zero
while holding other variables at their mean values for each farm (equation 1.24).
E ( y | x1, x2 ) = P ( c = 1| x1 ) ⋅ E (a | x2 , c = 1)
= Φ ( x1iγ σ e )  Φ ( x2 β / σ u ) x2 β + σφ ( x2 β / σ u ) 



) ((

(

)

ˆ ˆ
ˆ
ˆ
ˆ
y = Φ xi ( pay )γˆ + γˆ pay x pay σ e Φ xi ( pay ) β + β pay x pay / σ u



(

)

ˆ ˆ
ˆ
⋅ xi ( pay ) β + β pay x pay + σ uφ

((

)

)

)

ˆ ˆ
ˆ
xi ( pay ) β + β pay x pay / σ u 



(1.23)

(1.24)

In estimating the supply curves, only variables that are significant with 90% probability
are included. An F-test is used to ensure the joint significance of remaining variables. The
coefficients are re-estimated with these variables and substituted into the above function.

1.4.3

Specification issues

There are several specification issues associated with the double hurdle model (Smith,
2002). Dependence of errors, non-normality and heterogeneity in error terms have received the
most attention in empirical studies.
The dependence of errors emerges when error terms in the probit regression and
truncated regression are correlated (Smith, 2003). With dependence, multivariate maximum loglikelihood estimation needs to be conducted rather than two or three independent estimations.
Independence of errors is a common assumption adopted by studies using a double hurdle model.
Studies that compare the results with and without independence assumptions found little
23

improvement from assuming dependence (Jones, 1992, Uri, 1997). This assumption is also
maintained in our study, namely e and u in the probit and tobit models are assumed to be
independent.
Normality and homogenous errors are assumptions underlying both two regressions in
our econometric models. Violation of either of these assumptions will lead to inconsistent
estimates. To account for the heteroskedasticity problem, some studies have specified the
standard deviation σ as an exponential function of exogenous variables that varies across
observations (Jensen and Yen, 1996, Newman, et al., 2003). The normality problem can be
remedied by Box-Cox transformation (Burton, et al., 1996, Martínez-Espiñeira, 2006) or Inverse
Hyperbolic Sine transformation (Jensen and Yen, 1996, Newman, et al., 2003, Yen, et al., 1997).
However, as pointed out by Woodridge (2008), the inconsistent coefficient estimates that result
from conventional estimation methods in the absence of normal and homoskedastic distributions
still yield reasonably close partial effects, and the signs of estimates should be consistent. Since
the major focus of this study is to understand the signs and marginal effects of farmers’
participation determinants, no adjustment is made for possible non-normality and
heteroskedasticity problems.

1.4.4 Variables
There is one probit regression for consideration and one tobit regression for acreage
enrollment in the double hurdle model. The dependent variable for the consideration model is
farmers’ dichotomous choice of considering enrollment in the program, which is contingent on
belief that the payment is politically feasible. The dependent variable for the acreage enrollment

24

model is the acres that farmers would enroll in the program, including both zero and positive
acreages. See Table 1-3 for descriptive statistics of dependent variables.
The same set of independent variables is employed in both probit and tobit regressions
for comparison. Six broad categories of explanatory variables linked to the conceptual model are
defined as follows (Table 1-4): First, the design attributes category, corresponding to the
attributes of the programs that were a part of our experimental design. These include the peracre program payment, P*, for each cropping system, the sequence in which the four cropping
systems were presented to respondents, and whether the payment is provided by government.
With the adoption of different cropping practices, farmers are assumed to incur additional direct
costs (e.g., for labor and/or material inputs) and opportunity costs (e.g., for growing a less
6

profitable crop). Following exploratory results from farmer focus group interviews in 2007 , the
payment offer ranges for the four cropping systems were: A: $4 to $17; B: $10 to $36; C: $15 to
$55; and D: $20 to $75. The payment offer is hypothesized to have more effect for acreage
enrollment than for the willing-to-consider decision, for which a larger but politically feasible
payment is assumed to be provided. The descending sequence dummy variable denotes
respondents who received questionnaires with the sequence of cropping systems decreasing in
stringency and associated payment offers.
Second, the perception and attributes category of variables corresponds to environmental
services E. These variables depict farmer perceptions of ES benefits from certain cropping
systems, and their attitudes on whether nature provides services that could benefit their crop

6

See Lupi, et al. (2007) for detailed focus group experiments on the performance of
conservation auctions.
25

production. These variables are measured with 5 point Likert scale questions (1 for strongly
disagree, 2 for disagree, 3 for neutral, 4 for agree and 5 for strongly agree).
The third category describes the biophysical attributes of farms corresponding to
biophysical conditions B, which includes farm size and soil types. Larger farms are expected to
be more likely to enroll in a PES program because they have a higher capacity to invest and to
withstand risks from changed practices (Knowler and Bradshaw, 2007, Prokopy, et al., 2008).
Soil type refers to dummy variables for soil texture. Clay soils may be more fertile but less welldrained than the loam soil baseline, whereas sandy soils are less fertile but better drained due to
looser particles. Soil attributes exhibited mixed effects in different studies depending on the
specific practices. In this study, enrollment in the reduced chemical system is expected to be
positively related to clay soil, which tends to be more fertile than sandy soil and silty soil.
Cropping systems with soil conservation practices, such as cover crops and corn-soybean-wheat
rotation are expected to be positively related to sandy soil, which is more erodible. The fourth
category measures farm management attributes, corresponding to variable inputs X, labor L and
7

capital K. The current practices of tillage, wheat acreage, cover crops, irrigation, organic crops ,
8

fertilizer and pesticides are expected to have positive effects if they are similar to the new
cropping system. The influence of irrigation on the adoption of new practices is ambiguous.
Intensive irrigated agriculture tends to facilitate adoption of nitrate testing, but deters reduced
tillage and crop rotation (Bosch, et al., 1995, Wu and Babcock, 1998). These results depend on
the payoff of irrigation associated with different practices.

7
8

Data treatment for organic farms can be found in Appendix 5.

Reduced fertilizer and pesticides are dummy variables with one indicating currently band apply
fertilizer/pesticide at 2/3 of full field rate.
26

The fifth category of operator attributes includes age, level of formal education of farm
operators, and whether farm income is the major source of household income. This category may
influence farmers’ information I and choice of practice X, L and K. Farmers who are younger and
have higher education are expected to be more likely to participate. . Farms deriving most of
their income from agricultural production are hypothesized to be more likely to work on farming
practices improvement and possible benefits from it.
The last category includes market prices, which are represented by the output price vector
ry in the conceptual model. Prices are represented by ratios of farmers’ expected prices for wheat
compared to corn and soybean. Both price ratio variables are expected to be positively related to
adoption of cropping systems that require wheat, namely systems C and D.

1.5

Results

Although the willingness-to-consider and acreage enrollment decisions are modeled
using the same set of variables, results of the double hurdle model suggest that the first-round
willingness-to-consider decision depends chiefly on non-price farm and farmer characteristics.
By contrast, the second-round enrollment decision depends more on payment-driven benefit-cost
criteria.
Both consideration and enrollment decisions are influenced by two common factors.
First, the perceived environmental performance of each system significantly contributes to both
enrollment and willingness to consider each of the four cropping systems. This finding is
consistent with previous studies (D'Emden, et al., 2008, Gould, et al., 1989, Purvis, et al., 1989,
Sidibe, 2005, Traore, et al., 1998, Wei, et al., 2009), as the perceived ES benefits both individual
farmers and the society. A new finding from this study is that the marginal effects of perceived
27

environmental performance increase from System A to D for the willingness-to-consider
decision, but they decrease for enrollment decision. This suggests that farmers would be more
willing to consider a system with larger environmental benefits, but would be reluctant to enroll
proportionally more land, perhaps due to higher costs associated with realizing these benefits.
The second common factor for two decisions is the sequence of presenting cropping systems to
farmers. Farmers who were presented with the higher-complexity and higher-payment cropping
system first were less likely to consider or enroll in the other three cropping systems.

1.5.1

Willingness-to-consider decision

The double hurdle model complements previous PES studies by revealing several
differences between the attributes that motivate the consideration decision and those that
motivate the subsequent enrollment choice. These differences cannot be detected by a single
hurdle model or a simple tobit model that lacks information on what farmers would respond to a
higher payment offer. Three categories of variables drive the consideration decision (Table 1-5).
First, farmers who believe their production can benefit from nature are 5% more likely to
consider enrolling in the program. Previous studies also found that positive attitudes tended to
promote enrollment in conservation programs (Lynne, et al., 1988, Sheikh, et al., 2003). Their
attitudes further enhance participation when combined with perceived positive environmental
services.
Second, the similarity of current farm management practices to the proposed cropping
system also increases willingness to consider the PES program. This effect is likely motivated by
lower perceived risk and less extra cost. Prior practice of conservation tillage, wheat planting,
and reduced fertilizer input are illustrative examples. Farmers with an additional 10% of land

28

under no-till are 3% more likely to consider adopting the program that requires conservation
tillage. Farmers with an additional 10% more of their land planted to wheat are 4% more likely
to adopt two cropping systems that add wheat into the crop rotation. Those who currently own
equipment to band apply fertilizer at a reduced rate are 10% more likely to consider System D,
which requires this.
Third, information variables such as education and past experience with a governmental
PES program generally promote willingness to consider. One more year of education increases
the probability of considering the PES program by about 3%. Prior research has also shown
positive effects of education on adoption of farming practices as education largely links to
knowledge (Bosch, et al., 1995, Ervin and Ervin, 1982, Rahm and Huffman, 1984, Warriner and
Moul, 1992, Wu and Babcock, 1998). Past program experience with EQIP, which is a
governmental PES-type program, facilitates consideration of systems C and D by an additional
10%. However, experience with the Michigan Agriculture Environmental Assurance Program
(MAEAP) reduces the probability of considering enrollment by 20%. This may due to
differences in program goals between MAEAP and our hypothetical program. TMAEAP does
not involve adoption of changed practices to benefit the environment; instead, it certifies
compliance with “generally accepted agricultural practices”. Previous studies have also found
that farmers currently or previously involved in conservation programs were more likely to
participate in a new program since they had more information and assistance (Bosch, et al., 1995,
Ervin and Ervin, 1982, Wei, et al., 2009, Wu and Babcock, 1998).

29

1.5.2

Acreage enrollment decision

While the consideration decision is driven by feasibility and awareness factors, the
acreage enrollment decision by the tobit regression is driven chiefly by benefit-cost criteria
(Table 1-6). First and foremost, the per-acre payment offer has prominent effects on area
dedicated to all four cropping systems. As expected, the price-elasticity of land supplied is
declining with increasing system complexity. An increase in the annual payment of $1/acre
would raise the land area enrolled in systems A, B, C and D by 18, 10, 7 and 4 acres,
respectively. Compared with the other three systems, System A, which requires the smallest
change from a conventional cropping system, has the greatest potential to be expanded.
Second, larger farms enroll more land in the program. A typical farm with 100 more
acres in total cropland area would enroll 20-30 more acres, presumably because more land is
available for production and any fixed costs of adoption can be spread over more output. This is
a common finding in previous studies on conservation practice adoption (Gould, et al., 1989,
Lambert, et al., 2006, Lee and Stewart, 1983, Norris and Batie, 1987, Rahm and Huffman, 1984,
Wu and Babcock, 1998, Zbinden and Lee, 2005).
Third, the percentage of moldboard-tilled land has a substantial negative effect on
enrollment but no effect on the consideration decision in any system. One more percentage point
of land under moldboard tillage would decrease land enrollment by 8.8 acres for System A and
7.6 acres for System B. This is presumably due to the fixed cost of converting from a moldboard
plow to a chisel plow, which is required by all four proposed cropping systems.
Fourth, farms with a higher proportion of irrigated land, more income from farming or
older decision makers are also likely to enroll more acreage in some of the four systems.
Irrigated land tends to use more fertilizer and would need soil test to reasonably reduce the

30

nitrogen application. Consistent with Bosch (1995), farms with higher irrigation ratio are more
likely to enroll in systems A and B, which include PSNT for reducing fertilizer application
properly but do not strictly cut fertilizer use by one third. Similar to Lambert et al. (2006), this
study suggests farms that rely chiefly on income from agricultural production devote more time
and effort to farming and thus may enroll more land in the proposed programs. Older farmers
tend to enroll more acreage enrollment if they consider enrolling, though the consideration probit
model indicates that they are less likely to consider enrollment in the program. The age variable
has shown both positive (Okoye, 1998, Warriner and Moul, 1992) and negative (Gould, et al.,
1989, Lambert, et al., 2006, Neill and Lee, 2001) effects in previous studies.
In sum, these empirical results suggest different underlying determinants for the two
participation decisions. The first-stage willingness-to-consider decision depends chiefly on farm
and farmer characteristics, such as environmental attitudes, experience in conservation programs,
education, and ownership of large equipment. In contrast, the second-stage enrollment decisions
depend more on payment-driven benefit-cost factors, such as the per-acre payment offer, total
cropland area, irrigated land proportion, moldboard tillage and whether main income is from
farming.

1.5.3

Supply curves

The acreage supply curve predicts farmers’ potential provision of environmental benefits
in response to increasing levels of payment. As shown in Equation 1.20, the predicted supply of
cropland reflects composite effects from the consideration and acreage enrollment decisions. The
farm-level supply curves for double hurdle model are calculated from the predicted probability
of consideration times the acreage enrollment conditional on consideration. State-level supply

31

curves are calculated by proportionally magnifying individual farm-level supply given each
farm’s cropland area and the total number of farms in each sample acreage stratum (Figure 1-4).
The payment range for each system is extrapolated upwards and downwards at the same
proportion to the payment range offered in the survey, namely A: $0 to $21; B: $0 to $46; C: $0
to $65; and D: $0 to $95.
Supply curves aggregating all participation decisions for the state of Michigan suggest
two general effects. First, the price elasticity of land enrollment decreases with cropping system
complexity. The basic cropping system that requires the fewest management practices has the
greatest potential to be expanded. Farmers would voluntarily enroll more land in this system than
any other at any payment level above $35/acre. Second, without payment, more Michigan
farmers prefer an integrated, low-input conservation-till corn-soybean-wheat system (System D)
than a conventional conservation-till corn-soybean rotation (System A). These two systems are
both preferred over intermediate variants that add individual reduced input practices to the
conventional conservation-till system (Systems B and C). The surprising zero-payment
enrollment for System D may be because a proportion of farms are already in a low-input
conservation cropping system that is closer to or even more advanced than System D. The
summary statistics in Table 1-4 suggest that about 20% cropland in the sample is not tilled and
over 30% is using other conservation tillage methods than chisel plow. In addition, over 20%
farms are band applying fertilizer and pesticides at a reduced rate as proposed in cropping system
D.

32

1.6

Conclusion

This study deepens our understanding of farmers’ willingness to participate in paymentfor-environmental-services programs by separating the initial decision on whether even to
consider the program from the final decision on how many acres to enroll at a given payment
level. Comparison of different econometric models for estimating and predicting PES enrollment
leads to selection of a double hurdle model, comprised of a probit for willingness to consider and
a tobit for acreage enrollment.
Empirical results suggest that the first-stage willingness-to-consider decision depends
more on farm and farmer characteristics, while the second-stage enrollment decisions depend
more on payment-driven benefit-cost criteria. According to the first-stage probit for willingness
to consider, farmers who would participate in a PES program at a payment level that they
perceive to be politically feasible are motivated by feasibility variables, such as environmental
attitudes, experience in conservation programs, education, and ownership of large equipment.
The second-stage tobit for land enrollment reveals influential economic factors, such as the peracre payment offer, total cropland area, irrigated land proportion, moldboard tillage and whether
main income is from farming. The two stages are underpinned by two common factors:
perceived environmental performance of the proposed systems and sequence of presenting the
systems to respondents.
The supply curves aggregating all participation decisions for the state of Michigan
illustrate both the price elasticity effect and the start-up effect for enrollment without payment.
As expected, the system with least requirements—a conventional conservation-till corn-soybean
rotation—is most payment responsive. However, the most stringent system— an integrated, lowinput conservation-till corn-soybean-wheat system— surprisingly attracts more participants

33

without any incentive payments, probably due to the number of respondent farms that had
already adopted comparable conservation practices.
Understanding farmers’ decision processes is an essential precondition for designing
effective and efficient agricultural PES programs. As revealed by the consideration model, PES
programs with proposed practices that significantly conflict with farm operations or farmer
characteristics are unlikely to be adopted given any payment that is feasible within the context of
current conservation programs. Thus, PES programs can enhance adoption by targeting more
educated, experienced and properly equipped farmers who are favorably disposed toward
environmental stewardship. Research and outreach that build farmer understanding of
environmental services from agriculture also contribute to the appeal of agricultural PES
programs. For those farmers willing to consider the program, the enrollment model finds that
higher payment rates induce greater area to be enrolled in the PES program. By modeling the
first-stage “consideration” decision, this essay identifies important non-monetary preconditions
for farmer willingness to consider participating in a payment for environmental services
program.
The hypothetical PES programs in this study focus on total environmental services
generated, rather than additional ones. This approach has the advantage of treating equitably
both initial and additional providers of environmental services. However, for the design of costeffective PES policies, it is desirable not to pay for environmental services that would be
provided for free. Future research should measure the cost difference between paying for all
environmental services and paying only for additional environmental services generated by
farms enrolling in new practices. By combining such supply-side information with estimates of

34

demand for environmental service improvements, it should be possible to assess the potential for
a PES market in agriculturally generated environmental services.

35

Figures and Tables
Change in Utility (ΔU)
1

ΔU
Actual Payment

2

ΔU

3

ΔU

4

ΔU
0

*

P

P

high

PES payment (P)

Enroll
Consider but not enroll
Not consider
Politically feasible payment range

Figure 1-1 Illustration of changes in utility by four hypothetical farmers from adopting
specified production practices as a function of the associated PES payment

36

Would you consider enrolling in the conservation
program for a reasonable yearly per-acre payment?
Yes

No
Not Consider (0 acres)

Consider

Would you participate in the conservation
program for a payment of $/acre/year?
Yes

No

Enroll (+ acres)

Not Enroll (0 acres)

Figure 1-2 Conceptual diagram of farmers' participation decisions in a PES program

1400
1200

No. of farms

1000

Not consider

800

Consider but Not
Enroll

600
400

Enroll

200
0

SystemA

SystemB

SystemC

SystemD

Figure 1-3 Number of farms that fell into the three participation categories for each of the four
cropping systems (N=1688 Michigan corn and soybean farms, year=2008)

37

100

Payment Offer (USD)

80
60

System A
System B

40

System C
20

System D

0
0.0

0.5

1.0

1.5

2.0

2.5

Enrolled Acreage(million acres)
Figure 1-4 Predicted State-level Supply Curves of Enrolled Acres by Cropping System from
Double Hurdle Estimation, 1688 Michigan Corn or Soybean Farms, 2008
(For interpretation of the references to color in this and all other figures, the reader is referred to
the electronic version of this dissertation.)

38

Table 1-1 Four cropping systems offered to farmers
Cropping System
A
B
C
D

Practice

Description

Tillage
Soil Test
Cover Crop

Chisel plow with cultivation as needed
Pre-sidedress Nitrate Test (PSNT)
None
Any type present over winter
Corn-Soybean
Corn-Soybean-Wheat
Broadcast fertilizers at full MSU rates and
split Nitrogen based on PSNT
Band apply over row at MSU rates and split
Nitrogen based on PSNT

×
×
×

Broadcast pesticides at a label rate

×

Rotation
Fertilization

Pesticide
Rate

Band apply pesticides over row at a label
amount

39

×

×
×

×
×

×
×

×

×

×

×

×
×

×

×

×
×

×

×
×

Table 1-2 Environmental services and outcomes from proposed farming practices in cropping
systems
Practice

Tillage

Soil Test

Cover
Crops

Rotation

Fertilizer

Pesticide

Change from
Cropping Environmental
conventional system systems
services
Soil erosion ↓
(Phosphorus
Moldboard Plow 
A,B,C,D
Chisel Plow
surface runoff ↓)
CO2 emission ↓
Nitrogen
Adopting Pre-sidedress
A,B,C,D leaching ↓
Nitrate Test (PSNT)
N2O emission ↓
Soil erosion ↓
(Phosphorus
surface runoff ↓)
Adopting Winter
B,C,D Nitrogen
Cover Crops
leaching ↓
CO2 and N2O
emission ↓
Soil erosion ↓
Adding Wheat in
C,D
(Phosphorus
Corn-Soybean Rotation
surface runoff ↓)
Broadcast N&P
Nitrogen
Fertilizer at Full Rate
leaching ↓
D
 Band Application
N2O emission ↓
at 2/3 Rate
Broadcast Pesticides
Pesticide into air
at Full Rate
D
 Band Application
↓
at 2/3 Rate

Environmental
outcomes
Soil fertility ↑
Surface water quality
↑
↑

↑

Global warming ↓
Groundwater quality
Global warming ↓
Soil fertility ↑
Surface water quality
Groundwater quality

↑
Global warming ↓
Soil fertility ↑
Surface water quality
↑
Groundwater quality
↑
Global warming ↓
Health risk ↓
Air pollution↓

Table 1-3 Summary statistics for dependent variables
Dependent Variable
system unit
Obs
Mean Std. Dev. Min Max
Probit model: consideration
Consider VS Not consider
A
dummy 1146
0.57
0.49
0
1
B
dummy 1124
0.59
0.49
0
1
Consider VS Not consider
Consider VS Not consider
C
dummy 1112
0.64
0.48
0
1
D
dummy 1149
0.61
0.49
0
1
Consider VS Not consider
Tobit model: acreage enrollment
Acreage enrollment
Acreage enrollment
Acreage enrollment
Acreage enrollment

A
B
C
D

acres
acres
acres
acres
40

658
666
717
701

331
278
361
416

840
608
608
690

0
0
0
0

15000
10000
7000
7000

Table 1-4 Summary statistics of independent variables
Independent Variables
Units
Obs Mean Std. Dev. Min
Questionnaire Version
Government
dummy
1796 0.497
0.500
0
dummy
1796 0.503
0.500
0
Descending sequence
Payment offer (System A)
dollars
1796
10.2
4.78
4
Payment offer (System B)
dollars
1796
23.2
9.05
10
Payment offer (System C)
dollars
1796
36.7
12.5
15
Payment offer (System D)
dollars
1796
51.0
16.7
20

Max
1
1
17
36
55
75

Perception and attitudes
Perceived env performance (A)
Perceived env performance (B)
Perceived env performance (C)
Perceived env performance (D)
General attitudes of ES

Likert 1-5
Likert 1-5
Likert 1-5
Likert 1-5
Likert 1-5

1245
1189
1200
1245
1475

2.97
3.24
3.37
3.46
3.12

0.808
0.776
0.784
0.794
1.11

1
1
1
1
1

5
5
5
5
5

Farm biophysical attributes
Total land
Sandy soil
Silty soil
Clay soil

acres
dummy
dummy
dummy

1521
1796
1796
1796

1151
0.274
0.028
0.434

1408
0.446
0.165
0.496

2
0
0
0

21500
1
1
1

Farm management attributes
Moldboard tillage land percent ratio
No till tillage land percent
ratio
Conservation land percent
ratio
Wheat land percent
ratio
Cover crops land percent
ratio
PSNT land percent
ratio
Organic land percent
ratio
ratio
Irrigation land percent
Reduced Fertilizer use
dummy
Reduced Pesticide use
dummy
MAEAP
dummy
EQIP
dummy
CRP
dummy
CSP
dummy

1486
1486
1486
1486
1489
1489
1477
1796
1444
1442
1371
1379
1421
1324

0.067
0.185
0.342
0.083
0.047
0.050
0.002
0.048
0.218
0.209
0.142
0.298
0.349
0.120

0.178
0.244
0.286
0.103
0.149
0.170
0.025
0.165
0.413
0.407
0.349
0.458
0.477
0.325

0
0
0
0
0
0
0
0
0
0
0
0
0
0

1
1
1
0.714
1
1
.63
1
1
1
1
1
1
1

Operator attributes
years
Age
Education
years
Main income source from farm dummy

1501
1488
1488

54.8
13.4
0.718

11.6
2.56
0.450

21
6
0

94
20
1

Market prices
Wheat/corn price
Wheat/soybean price

1059
1049

1.682
0.732

0.323
0.358

0.15
0.2

3.33
7

ratio
ratio

41

Table 1-5 Marginal effects from Probit estimation of farmers’ consideration (double hurdle),
weighted by stratum, by Cropping Systems, 1688 Michigan corn or soybean farmers, 2008
System A
Coef.
P>z
Government
0.009
0.886
Descending sequence -0.178 *** 0.003
Payment offer
0.016 ** 0.015
Perceived env perf
0.082 ** 0.039
General ES attitudes 0.069 ** 0.012
Total land
0.000
0.130
Sandy soil
-0.109
0.267
Clay soil
-0.045
0.605
Moldboard tillage
-0.194
0.269
No till tillage
0.366 ** 0.036
Conservation tillage 0.019
0.872
Wheat ratio
0.179
0.492
Cover crops ratio
-0.209
0.146
Organic ratio
-0.023
0.971
Irrigation ratio
0.035
0.829
Reduced fertilizer
0.101
0.151
Reduced pesticide
0.082
0.235
MAEAP
-0.237 *** 0.007
EQIP
0.088
0.172
CRP
0.002
0.971
CSP
-0.117
0.240
Age
-0.004
0.137
Education
0.024 *
0.067
Wheat/corn price
0.155
0.278
Wheat/soybean price 0.059
0.850
farm income
-0.039
0.548
Intercept
-3.034 ** 0.017

System B
System C
System D
Coef.
P>z Coef.
P>z Coef.
P>z
0.017
0.790 0.023
0.698 -0.038
0.489
-0.127 *
0.051 -0.042
0.446 0.072
0.186
-0.002
0.432 0.001
0.758 -0.001
0.467
0.127 *** 0.002 0.181 *** 0.000 0.193 *** 0.000
0.046 *
0.098 0.051 ** 0.041 0.038 *
0.082
0.000
0.427 0.000
0.467 0.000
0.277
-0.084
0.397 0.027
0.739 0.000
0.997
-0.051
0.553 0.064
0.407 0.107
0.258
-0.264
0.122 -0.073
0.621 -0.197
0.134
0.384 ** 0.032 0.411 ** 0.018 0.246
0.108
-0.016
0.905 0.021
0.862 0.118
0.258
0.246
0.308 0.436 *
0.070 0.412 *
0.066
-0.161
0.294 -0.246
0.138 -0.081
0.576
0.592
0.575 0.567
0.595 0.841
0.530
0.029
0.867 0.132
0.401 0.074
0.588
0.145 ** 0.011 0.117 ** 0.026 0.110 ** 0.036
0.134 ** 0.041 0.013
0.842 0.075
0.217
-0.186 ** 0.028 -0.144
0.104 -0.186 ** 0.020
0.066
0.273 0.114 *
0.068 0.137 ** 0.012
0.107
0.154 0.052
0.532 0.153 ** 0.021
-0.175 *
0.066 -0.088
0.382 -0.165 *
0.057
0.000
0.858 -0.001
0.691 -0.004
0.103
0.011
0.445 0.033 *** 0.002 0.027 ** 0.013
0.251 ** 0.037 0.047
0.694 0.115
0.267
-0.280
0.280 -0.121
0.617 -0.196
0.392
-0.046
0.494 -0.013
0.836 0.041
0.528
-2.623 *
0.056 -4.496 *** 0.000 -3.963 *** 0.006

Number of obs
Wald chi2(26)
Prob>chi2
Pseudo R2
Log likelihood

594
66.03
0
0.2192
-319.2

600
77.57
0
0.226
-321.5

604
71
0
0.2404
-306.2

Note: ***significant at 1% level, **significant at 5% level, *significant at 10% level

42

613
92.48
0
0.2713
-303.5

Table 1-6 Marginal effects from Tobit estimation of farmers’ acreage enrollment (double
hurdle), weighted by stratum, by Cropping Systems, 1688 Michigan corn or soybean farmers,
2008
System A
System B
System C
System D
Coef.
P>z Coef.
P>z Coef.
P>z Coef.
P>z
Government
-133
0.115 -2.07
0.975
34.2
0.445 -5.20
0.900
Descending sequence
-363 *** 0.000 -57.5
0.364
-163 *** 0.000 -65.2
0.135
Payment offer
18.9 ** 0.020
11.0 *** 0.009
6.61 *** 0.000
3.64 ** 0.013
Perceived env perf
187 *** 0.004
146 *** 0.005
118 *** 0.001
139 *** 0.000
General ES attitudes
-8.24
0.815 -19.8
0.535 -35.9 ** 0.037 -39.5 ** 0.044
Total land
0.26 *** 0.000
0.28 *** 0.004
0.24 *** 0.000
0.33 *** 0.000
Sandy soil
240 * 0.071
24.5
0.815
17.0
0.797
74.6
0.322
Clay soil
391 *** 0.003
33.7
0.734
22.6
0.708
84.5
0.197
Moldboard tillage
-884 *** 0.004
-761 ** 0.018
-193
0.159
-108
0.425
No till tillage
-121
0.617
238
0.138
88.3
0.448
305 *** 0.007
Conservation tillage
115
0.537
121
0.296
14.2
0.865
153 ** 0.049
Wheat ratio
-457
0.106
315 * 0.098
207
0.191 -4.24
0.975
Cover crops ratio
-495
0.112
-112
0.675 -58.8
0.772
83.4
0.323
Organic ratio
-347
0.657
-437
0.701
324
0.690
-173
0.797
Irrigation ratio
624 ** 0.011
574 ** 0.040 -73.4
0.661
51.5
0.725
-105
0.322 -37.8
0.689
14.3
0.791 -20.3
0.703
Reduced fertilizer
Reduced pesticide
-65.2
0.527
-127
0.190
-117 ** 0.026
-125 ** 0.017
MAEAP
69.8
0.565
-110
0.282
40.5
0.546
14.0
0.825
EQIP
60.4
0.544
44.7
0.577
15.2
0.802
125 ** 0.040
CRP
79.6
0.401 -36.7
0.629
2.47
0.963 -38.6
0.516
CSP
365 *** 0.004
171
0.152
104
0.205 -45.3
0.629
Age
3.64
0.238
4.62
0.218
1.33
0.408
4.51 *** 0.010
Education
19.9
0.233
2.43
0.862 -4.96
0.577 -3.36
0.722
Wheat/corn price
443
0.106 -30.8
0.850
-140
0.176
-360 *** 0.000
Wheat/soybean price
-462
0.424
50.8
0.883
140
0.515
708 *** 0.000
farm income
81.6
0.381 -54.7
0.574
94.6 * 0.058
9.36
0.872
Intercept
-2126 *** 0.000 -1269 ** 0.013
-512 * 0.064
-880 *** 0.002
/sigma
528
448
362
366
Number of obs
364
372
430
406
Wald chi2(26)
2.91
1.56
4.96
5.66
Prob>chi2
0.00
0.04
0.00
0.00
Pseudo R2
0.06
0.05
0.04
0.05
-733
-897
-1302
-1318
Log likelihood
Note: ***significant at 1% level, **significant at 5% level, *significant at 10% level

43

APPENDICES

44

APPENDIX 1-1: ECONOMETRIC MODELS

Tobit model
It is common in conservation program participation surveys that some responses pile up
at zero while some others take strictly positive values. The tobit model is a straightforward
method to deal with those zero responses (Tobin, 1958). It allows for one type of zero
observations based on the implicit assumption that negative values are underpinned by the same
mechanism as positive responses but can only be observed as zero.
The acreage enrollment a is indicated by a latent variable a*, which depends on farm and
farmer characteristics x that influence the amount they choice to enroll. The random term u has a
2

zero mean and variance σ . Zero responses are observed when a* is less than or equal to zero.

a = max [ a*, 0]

a* = x β + u > 0

(

u ~ N 0, σ 2

)

(1. A1)

The probability density function for estimation is:
1[ a = 0]  −1

1[ a > 0]

σ φ ( y − xβ / σ ) 

f ( a | x, c = 1) = 1 − Φ ( xβ / σ ) 







(1. A2)

The unconditional expectation of acreage enrollment for supply curve derivation is:

E ( a | x ) = Φ ( xβ / σ ) xβ + σφ ( xβ / σ )

(1. A3)

Single hurdle model (Cragg model):
The single hurdle model (Cragg, 1971) extends the tobit model by allowing different
mechanisms to drive 1) the dichotomous decision of whether to enroll, and 2) the level decision
on how many acres to enroll. The cropland acres that respondents choose to enroll in the

45

program are represented by y, which is a compound function of binary participation decision p
and choice of positive acreage enrollment a*.
y = p⋅a*

(1. A4)

Probit estimation is used for binary choice of participation. p* is the latent variable indicating
farmers’ utility gain by enrolling in the program given a specific level of payment, where x1 is a
vector of attributes determining this utility. Farmers would consider the program (p=1) only if
their utility increases.
p* = x1α + ε

ε ~ N ( 0, σ ε )

p* > 0
p* ≤ 0

1
p=
0

(1. A5)

P ( p = 1| x1 ) = E ( p | x1 ) = Φ ( x1α σ ε )

(1. A6)

The continuous acreage variable a* depends on farm and farmers characteristics x2 that influence
their amount choice for enrollment. The random term u has a zero mean and variance σu2. Thus,
a truncated normal regression model is adopted based on the fact that all zero enrollment
acreages are truncated at this stage. The enrolled acreage is positive and equal to a* only if the
farmers choose to participate in the program, and is zero otherwise.

(

)

(1. A7)

p =1
otherwise

(1. A8)

u ~ N 0, σ u 2

a* = x2 β + u > 0
a *
y=
0

if

The probability density function for estimation is:
1[ y = 0]

f ( y | x1, x2 ) = 1 − Φ ( x1α σ ε ) 



{

−1

⋅ Φ ( x1α σ ε ) Φ ( x2 β / σ u )  φ ( y − x2 β / σ u )  σ u





1[ y > 0]

}

The unconditional expectation of acreage enrollment for supply curve derivation is:

46

(1. A6)

E ( y | x1, x2 ) = P ( p = 1| x1 ) ⋅ E ( y | x2 , c = 1, p = 1)
= Φ ( x1α σ ε )  x2 β + σλ ( x2 β / σ u ) 



(1. A7)

Extended double hurdle model:
The extended double hurdle model is built on both single hurdle model and double hurdle
model. It is similar to the double model in the sense that a prior willing-to-consider decision is
explicitly modeled by probit. It is similar to the single hurdle model because the decision on
whether to enroll and the decision on how much to enroll are modeled separately by probit and
truncated regression. Generally, the acreage response y is a compound function of binary
consideration decision c, binary participation decision p, and choice of positive enrollment
acreage, a*.
y = c⋅ p⋅a*

(1. A8)

Probit estimation is used for binary choices of consideration c. c* is the latent variable
indicating farmers’ utility gain by enrolling in the program with the maximum politically feasible
payment, where x1 is a vector of attributes determining utility and the random term e follows a
normal distribution. Farmers would consider the program (c=1) only if their utility increases. The
probability of consideration is estimated by a cumulative normal density function.
c* = x1γ + e

e ~ N ( 0, σ e )

1 c* > 0
c=
0 c* ≤ 0

P ( c = 1| x1 ) = E ( c | x1 ) = Φ ( x1γ σ e )

(1. A9)

(1. A10)

The participation decision p, and choice of positive enrollment acres, a* are defined as in
single hurdle model:
47

p* = x2α + ε

ε ~ N ( 0, σ ε )

1
p=
0

p* > 0
p* ≤ 0

(1. A11)

P ( p = 1| x2 ) = E ( p | x2 ) = Φ ( x2α σ ε )
a* = x3β + u > 0
a *
y=
0

if

(

u ~ N 0, σ u 2

(1. A12)

)

(1. A13)

c = 1, p = 1
otherwise

(1. A14)

The probability density function derived from all three decisions for estimation is:
1[ y = 0]

f ( y | x1, x2 , x3 ) = 1 − Φ ( x1γ σ e ) Φ ( x2α σ ε ) 



{

−1

⋅ Φ ( x1γ σ e ) ⋅ Φ ( x2α σ ε ) Φ ( x3β / σ u )  φ ( y − x3β / σ u )  σ u





1[ y > 0]

}

(1. A15)

The unconditional expectation derived from all three decisions for supply curve derivation is:
E ( y | x1, x2 , x3 ) = P ( c = 1| x1 ) ⋅ P ( p = 1| x2 ) ⋅ E ( y | x3 , c = 1, p = 1)
= Φ ( x1γ σ e ) Φ ( x2α σ ε )  x3β + σ u λ ( x3β / σ u ) 



48

(1. A16)

APPENDIX 1-2: STATISTICAL TESTS FOR MODEL SELECTION

Model selection based on prediction correlation:
Prediction correlation is calculated between predicted acreage enrollment based on
estimation and the actual enrollment for farms that enrolled positive land area in the hypothetical
PES. The following table suggests that the correlation coefficients are close among four models,
though the extended double hurdle model and single hurdle model have relatively higher
correlation.
Table 1-A1 Correlation between predicted and actual acreage enrollment
Model
Regression
Correlation
Extended double hurdle model
probit + probit + truncated normal 0.6172
Single hurdle model
probit + truncated normal
0.6147
Double hurdle model
probit + tobit
0.5696
Tobit model
tobit
0.5499

Model preference based on goodness-of-fit (LR test and Vuong test):
The likelihood ratio (LR) test is commonly used for selection between nested models.
However, the test is not valid after estimating weighted or clustered Maximum Log-likelihood
Estimations (MLE). The “likelihood” for weighted or clustered MLEs is not a true likelihood for
sample distribution because individual observations are no longer independent, and the
9

“likelihood” does not fully account for the “randomness” of the weighted sampling . Thus,
Vuong test that is based on individual likelihood is applied for model selection (Vuong, 1989).
The likelihood is calculated for each observation and each model. The difference is taken

9

http://www.stata.com/support/faqs/stat/lrtest.html
49

between two alternative models and is tested for which model fit better statistically. The test
results suggest that the order of models in terms of likelihood maximization is: extended double
hurdle model, single hurdle model, double hurdle model and tobit model.
Table 1-A2 Vuong test results for model selection
Vuong test
Extended double
hurdle
- Single hurdle
preferred model
Double hurdle
- Extended double
hurdle
preferred model
Double hurdle
- Single hurdle
preferred model
Tobit
- Single hurdle
preferred model
Tobit
-Double hurdle
preferred model

System A
coef
p-value

System B
coef p-value

0.911

0.423

0.000

extended double
hurdle
-0.177

0.041

extended double
hurdle
-0.083

0.102

single hurdle
-0.100

0.045

single hurdle
-0.017

0.333

indifferent

0.000

extended double
hurdle
-0.335

0.207

indifferent
-0.204

0.217

indifferent
-0.222

0.159

indifferent
-0.019

0.466

indifferent

50

System C
coef p-value
-0.070

0.156

indifferent
-0.166

0.108

indifferent
-0.181

0.007

single hurdle
-0.207

0.003

single hurdle
-0.025

0.342

indifferent

System D
coef p-value
0.048

0.358

indifferent
-0.397

0.001

extended double
hurdle
-0.147

0.037

single hurdle
-0.250

0.004

single hurdle
-0.103

0.025

double hurdle

APPENDIX 1-3: REGRESSION RESULTS (MARGINAL EFFECTS) FOR DIFFERENT
MODELS

Table 1-A3 Marginal effects from Probit estimation of farmers’ dichotomous enrollment
decision (extended double hurdle model), weighted by stratum, by Cropping Systems, 1688
Michigan corn or soybean farmers, 2008
System A
Coef.
P>z
Government
-0.090
0.198
Descending sequence -0.224 *** 0.000
Payment offer
0.011 * 0.072
Perceived env perf
0.160 *** 0.000
General ES attitudes
0.005
0.861
Total land
0.000
0.168
Sandy soil
0.153 * 0.097
Clay soil
0.192 ** 0.019
Moldboard tillage
-0.238
0.210
No till tillage
0.093
0.570
Conservation tillage
0.325 ** 0.025
Wheat ratio
-0.257
0.307
Cover crops ratio
-0.334
0.119
Organic ratio
0.097
0.867
Irrigation ratio
0.293
0.117
Reduced fertilizer
-0.116 * 0.096
Reduced pesticide
-0.071
0.336
MAEAP
0.027
0.713
EQIP
0.156 ** 0.021
CRP
0.057
0.418
CSP
0.285 *** 0.001
Age
0.006 ** 0.017
Education
0.017
0.260
Wheat/corn price
0.499 *** 0.005
Wheat/soybean price -0.608
0.111
farm income
0.037
0.624
Intercept
-6.564 *** 0.000
Number of obs
364
Wald chi2(26)
104.71
Prob>chi2
0
Pseudo R2
0.3106
Log likelihood
-169.64

System B
System C
System D
Coef.
P>z Coef.
P>z Coef.
P>z
0.085
0.245 0.084 0.208 0.013
0.813
-0.238 *** 0.001 -0.178 ** 0.013 -0.103 * 0.075
0.005
0.168 0.003 0.328 0.002
0.253
0.196 *** 0.000 0.083 * 0.074 0.176 *** 0.000
-0.043
0.147 -0.027 0.373 -0.001
0.967
0.000
0.773 0.000 0.326 0.000
0.424
0.142
0.170 -0.091 0.354 -0.018
0.844
0.046
0.633 -0.044 0.644 0.106
0.186
-0.128
0.595 -0.596 ** 0.017 -0.061
0.742
0.067
0.651 0.382 ** 0.023 0.386 ** 0.013
-0.120
0.385 0.325 ** 0.023 0.342 ** 0.014
0.028
0.910 0.323 0.324 -0.047
0.839
-0.342
0.118 -0.350 * 0.100 0.377 ** 0.036
0.045
0.939 -1.051 0.490 -0.330
0.585
-0.071
0.729 0.018 0.931 0.238
0.136
0.043
0.525 -0.064 0.542 -0.053
0.482
0.013
0.864 -0.116 0.234 -0.125 * 0.091
0.010
0.913 -0.178 ** 0.028 -0.022
0.781
0.087
0.200 0.142 ** 0.030 0.193 *** 0.000
-0.004
0.960 -0.071 0.398 -0.077
0.295
0.097
0.381 -0.037 0.741 -0.011
0.912
0.007 * 0.063 0.005 0.124 0.005 ** 0.038
-0.007
0.584 0.005 0.750 0.003
0.796
-0.166
0.458 0.166 0.323 -0.270 * 0.052
0.168
0.719 -0.433 0.204 0.588 * 0.079
-0.044
0.587 -0.046 0.569 -0.086
0.210
-2.029
0.191 -2.212 0.120 -3.836 *** 0.005
372
430
406
64.48
52.91
75.08
0
0.0014
0
0.2181
0.2036
0.257
-191.22
-235.01
-179.87
51

Table 1-A3 (cont’d)
Notes: 1. This is the probit regression for the decision on whether to enroll (second hurdle)
in the extended double hurdle model. The first hurdle probit result is shown in Table 1-4.
The second hurdle truncated regression is shown in Table 1-A5
2. The estimated coefficient for intercept is reported.
3. ***significant at 1% level, **significant at 5% level, *significant at 10% level

52

Table 1-A4 Marginal effects from Probit estimation of farmers’ dichotomous participation
decision (single hurdle model), weighted by stratum, by Cropping Systems, 1688 Michigan corn
or soybean farmers, 2008
System A
Coef.
P>z
Government
-0.043
0.341
Descending sequence -0.225 *** 0.000
Payment offer
0.010 ** 0.022
Perceived env perf
0.164 *** 0.000
General ES attitudes
0.018
0.313
Total land
0.000 * 0.061
Sandy soil
0.075
0.268
Clay soil
0.126 ** 0.037
Moldboard tillage
-0.405 *** 0.007
No till tillage
0.138
0.180
Conservation tillage
0.198 ** 0.022
Wheat ratio
-0.147
0.454
Cover crops ratio
-0.328 ** 0.035
Organic ratio
-0.061
0.927
Irrigation ratio
0.279 ** 0.034
Reduced fertilizer
-0.077
0.104
Reduced pesticide
-0.034
0.531
MAEAP
-0.079
0.127
EQIP
0.163 *** 0.003
CRP
0.046
0.328
CSP
0.104
0.156
Age
0.002
0.278
Education
0.017 * 0.074
Wheat/corn price
0.358 *** 0.001
Wheat/soybean price -0.344
0.117
farm income
0.029
0.545
Intercept
-7.053 *** 0.000
Number of obs
Wald chi2(26)
Prob>chi2
Pseudo R2
Log likelihood

600
149.18
0
0.3255
-209.03

System B
System C
System D
Coef.
P>z Coef.
P>z Coef.
P>z
0.015
0.761 0.079
0.156 -0.019
0.715
-0.135 ** 0.011 -0.220 *** 0.000 -0.001
0.977
0.007 *** 0.006 0.007 *** 0.000 0.001
0.433
0.171 *** 0.000 0.216 *** 0.000 0.241 *** 0.000
0.015
0.497 -0.008
0.732 0.030
0.193
0.000
0.134 0.000
0.187 0.000
0.684
-0.059
0.491 0.043
0.614 -0.011
0.892
0.018
0.831 0.052
0.504 0.185 *** 0.008
-0.584 *** 0.004 -0.183
0.239 -0.240 * 0.065
0.411 *** 0.001 0.341 ** 0.019 0.343 *** 0.008
0.169 * 0.100 0.049
0.663 0.196 * 0.084
0.438 * 0.053 0.444 ** 0.044 0.309
0.142
-0.310 * 0.055 -0.399 ** 0.015 0.034
0.819
-0.260
0.738 0.165
0.797 -0.052
0.945
0.231 * 0.084 -0.021
0.898 0.281 ** 0.043
-0.005
0.940 0.087
0.124 0.061
0.331
-0.064
0.379 -0.040
0.530 -0.024
0.706
-0.161 ** 0.027 -0.089
0.253 -0.119 * 0.058
0.196 *** 0.000 0.109 * 0.065 0.226 *** 0.000
-0.011
0.857 0.038
0.499 0.060
0.380
-0.021
0.792 0.024
0.770 -0.104
0.152
0.003
0.213 0.003
0.224 0.000
0.932
0.013
0.251 0.015
0.193 0.020 * 0.059
0.180 * 0.087 0.026
0.823 0.006
0.955
-0.150
0.484 0.007
0.978 0.120
0.600
-0.035
0.551 0.021
0.717 -0.026
0.646
-5.676 *** 0.000 -5.484 *** 0.000 -5.831 *** 0.000
594
119.99
0
0.2817
-251.86

604
133.69
0
0.2884
-291.41

613
128.97
0
0.2753
-301.93

Notes: 1. This is the probit regression for the decision on whether to participate in the single
hurdle model. The truncated regression hurdle is shown in Table 1-A5
2. The estimated coefficient for intercept is reported.
3. ***significant at 1% level, **significant at 5% level, *significant at 10% level
53

Table 1-A5 Marginal effects from Probit estimation of farmers’ positive acreage enrollment decision (single hurdle & extended double
hurdle model), weighted by stratum, by Cropping Systems, 1688 Michigan corn or soybean farmers, 2008
System A
Government
Descending sequence
Payment offer
Perceived env perf
General ES attitudes
Total land
Sandy soil
Clay soil
Moldboard tillage
No till tillage
Conservation tillage
Wheat ratio
Cover crops ratio
Organic ratio
Irrigation ratio
Reduced fertilizer
Reduced pesticide
MAEAP
EQIP
CRP
CSP
Age
Education
Wheat/corn price
Wheat/soybean price

Coef.
-101
-173
16.1
10.1
-98.0
1.53
284
482
-2768
-1649
-1869
-1690
-2663
-2844
677
133
210
51.8
-96.9
-46.0
284
-23.4
28.1
-1063
230

*

**
***
***
***
*
*

**

*

*
**

*

System B
P>z
0.233
0.077
0.428
0.663
0.023
0.000
0.152
0.003
0.003
0.081
0.054
0.853
0.118
0.033
0.153
0.104
0.076
0.629
0.325
0.559
0.068
0.022
0.162
0.247
0.084

Coef.
14.4
17.2
-8.65
-186
-31.8
-14.3
88.1
117
-2783
266
355
316
-338
-5054
2580
83.7
78.5
-50.7
-89.7
75.7
104
-23.4
-9.14
446
-808

**
***
*

**
*
*

*
**
**
**
54

System C
P>z
Coef.
0.252
-48.5
0.76
-28.0
0.814
4.46
0.429
-33.3
0.026
-34.2
0
2.34
0.263
-44.6
0.067
55.1
0.414
-1061
0.698
-244
0.7
-425
0.402
665
0.591
-198
0.015
700
0.052
593
0.067
59.7
0.137
-68.9
0.546
32.5
0.118
-1.28
0.18
17.2
0.1
85.8
0.014
1.94
0.897
-3.10
0.015
-306
0.017
432

***

**

*
**

System D
P>z
Coef.
0.194
-32.6
0.538
5.04
0.284
10.2
0.69
-61.6
0.112
-46.7
0
3.64
0.374
47.3
0.32
9.24
0.014
236
0.679
452
0.622
-538
0.543
3194
0.735
-800
0.441
-454
0.209
414
0.154
40.0
0.252
-23.2
0.343
23.0
0.899
2.20
0.652
28.9
0.076
16.0
0.02
-0.82
0.933
-13.6
0.338
-691
0.612
468

*
**
***

**

**

P>z
0.785
0.645
0.061
0.824
0.019
0
0.362
0.663
0.016
0.661
0.19
0.247
0.201
0.829
0.148
0.221
0.578
0.484
0.926
0.408
0.614
0.934
0.218
0.178
0.012

Table 1-A5 (cont'd)

farm income
Intercept
/sigma
Number of obs
Wald chi2(26)
Prob>chi2
Log likelihood

1402 **
-2983
822
176
81.5
0
-550

0.045
0.443
0.000

575 *
-339
895
211
79.5
0
-688

0.069
0.919
0.000

750 ***
-1074
754
293
63.4
0
-1059

0.008
0.621
0.000

641 **
-2651
679
292
108.8
0
-1063

0.017
0.164
0.000

Notes: 1. This is the truncated normal regression for the level decision on how many acres to enroll that common to both single hurdle
and extended double hurdle model. The other regression for single hurdle model is shown in Table 1-A4. The other
regressions for extended double hurdle model are shown in Table 1-4 and 1-A3.
2. The estimated coefficient for intercept is reported.
3. ***significant at 1% level, **significant at 5% level, *significant at 10% level

55

Table 1-A6 Marginal effects from Tobit estimation of farmers’ enrollment decision, weighted by stratum, by Cropping Systems, 1688
Michigan corn or soybean farmers, 2008
System A
Government
Descending sequence
Payment offer
Perceived env perf
General ES attitudes
Total land
Sandy soil
Clay soil
Moldboard tillage
No till tillage
Conservation tillage
Wheat ratio
Cover crops ratio
Organic ratio
Irrigation ratio
Reduced fertilizer
Reduced pesticide
MAEAP
EQIP
CRP
CSP
Age
Education
Wheat/corn price
Wheat/soybean price

Coef.
-87.9
-492
23.9
308
25.7
0.241
171
352
-1155
90.6
164
-468
-736
-672
662
-143
-30.9
-91.9
207
73.5
217
1.51
29.5
585
-480

***
***
***
***
***
***

**
***

**
*
*
**

System B
P>z
0.278
0.000
0.004
0.000
0.463
0.000
0.174
0.004
0.001
0.665
0.340
0.142
0.019
0.634
0.010
0.189
0.769
0.453
0.033
0.407
0.094
0.639
0.087
0.016
0.353

Coef.
39.2
-147
9.88
256
18.6
0.223
-73.2
32.8
-1044
465
134
449
-284
-422
624
28.4
-113
-254
192
23.5
-35.7
3.46
14.3
126
5.02

**
**
***
***

***
***
*

**

**
**

56

System C
P>z
Coef.
0.559
36.87
0.036
-198
0.018
7.07
0.000
232
0.580
-18.4
0.008
0.188
0.516
3.23
0.763
58.7
0.002
-302
0.007
275
0.290
5.63
0.054
398
0.258
-328
0.744
536
0.018
-26.2
0.772
47.6
0.268
-128
0.045
-39.2
0.019
122
0.761
19.6
0.762
44.2
0.351
1.06
0.324
11.9
0.468
-73.1
0.989
100

***
***
***
***

*
**
**
*

**
*

System D
P>z
Coef.
0.487
-29.4
0.000
-29.9
0.000
2.99
0.000
282
0.421
-11.1
0.000
0.212
0.971
8.98
0.448
185
0.078
-316
0.033
431
0.955
195
0.048
309
0.079
-54.1
0.565
82.3
0.894
175
0.420
36.0
0.033
-76.5
0.635
-84.7
0.060
243
0.742
39.8
0.606
-117
0.638
1.41
0.268
18.7
0.543
-180
0.692
484

*
***
***
**
**
***
**
*

***

*
*
**

P>z
0.554
0.556
0.057
0.000
0.627
0.000
0.915
0.017
0.034
0.001
0.043
0.090
0.668
0.926
0.288
0.549
0.198
0.271
0.000
0.524
0.225
0.496
0.077
0.090
0.031

Table 1-A6 (cont'd)

farm income
Intercept
/sigma
Number of obs
Wald chi2(24)
Prob>chi2
Pseudo R2
Log likelihood

103
-3158 ***
602
600
3.16
0.00
0.08
-772

0.266
0.000

-42.3
-2296 ***
514
594
1.59
0.03
0.06
-946

0.654
0.000

107 *
-1511 ***
424
604
4.34
0.00
0.05
-1379

0.064
0.000

64.6
-2068 ***
458
613
3.9
0.00
0.05
-1411

0.296
0.000

Notes: 1. This is the tobit regression for the level decision on how many acres to enroll, including zero and positive responses in the
whole dataset.
2. The estimated coefficient for intercept is reported.
3. ***significant at 1% level, **significant at 5% level, *significant at 10% level

57

APPENDIX 1-4: SUPPLY CURVES FROM DIFFERENT MODELS

Farmers supply environmental services via the land acreage enrolled in PES programs.
Thus, the acreage supply curve predicts farmers’ potential provision of environmental benefits in
response to payment offer variation. The predicted acreage supply for each farm is calculated
based on the unconditional expectation for the extended double hurdle model, single hurdle
model and tobit model respectively (Appendix 1-1). Each farm’s predicted acreage supply is
limited by its total land area. State-level supply curves are calculated by 1) proportionally
magnifying individual farm-level supply by the ratio of total number of farms in the state to that
in the sample in each of four sample stratum, and 2) summing up total acreage enrollment in four
sample strata. The supply curves are computed using re-estimated regression coefficients with
only variables that are significant at 90% level in the original regression. The p-values of the Ftests for joint variable removal are all greater than 0.1.

58

Payment Offer (USD)

100
80
System A

60

System B
40

System C
System D

20
0
0.0

0.5

1.0

1.5

2.0

2.5

Enrolled Acreage(million acres)

Figure 1-A1 Predicted State-level Supply Curves of Enrolled Acres by Cropping System from
Extended Double Hurdle Estimation, 1688 Michigan Corn or Soybean Farms, 2008 (For
interpretation of the references to color in this and all other figures, the reader is referred to the
electronic version of this dissertation.)

59

Payment Offer (USD)

100
80
60

System A
System B

40

System C
System D

20
0
0.0

0.5

1.0
1.5
2.0
2.5
Enrolled Acreage(million acres)

Figure 1-A2 Predicted State-level Supply Curves of Enrolled Acres by Cropping System from
Single Hurdle Estimation, 1688 Michigan Corn or Soybean Farms, 2008

Payment Offer (USD)

100
80
60

System A
System B

40

System C
System D

20
0
0.0

0.5

1.0

1.5

2.0

2.5

Enrolled Acreage(million acres)
Figure 1-A3 Predicted State-level Supply Curves of Enrolled Acres by Cropping System from
Tobit Estimation, 1688 Michigan Corn or Soybean Farms, 2008

60

APPENDIX 1-5: DATA TREATMENT FOR ORGANIC FARMS

Our hypothetical cropping systems proposed reduced use of fertilizer and pesticides,
which are not compatible with organic production. The inclusion of organic farms may cause
bias in the estimation. Based on our observation, there are 27 farms that have organic production
on all or part of their lands. Among these farms, 15 farms have partial organic land, 9 of which
enrolled positive land acreage in at least one proposed cropping system. This suggests that farms
with partial organic land would still participate in our hypothetical program, and should be
included in the sample. Thus, only farms with 100% organic land were removed from the
regression dataset. Details of those organic farms are shown in the following table.
Table 1-A7 Proportional distribution and acreage enrollment for farms with partial/full
organic production
Organic
land Number Percent
ratio of farms
0.01
0.02
0.04
0.05
0.06
0.07
0.13
0.14
0.22
0.32
0.53
0.63
1
Total

1
2
1
2
1
1
1
2
1
1
1
1
12
27

3.7
7.41
3.7
7.41
3.7
3.7
3.7
7.41
3.7
3.7
3.7
3.7
44.44
100

Cumulative
Percent
3.7
11.11
14.81
22.22
25.93
29.63
33.33
40.74
44.44
48.15
51.85
55.56
100

Average acreage enrolled
System
A
2000
200
0
800
0
200
0
0
0
0
0
0

61

System
B
0
200
777
0

System
C
0
650
0
1550

0
100
0
0
0
370
0
0

600
200
655
0
0
0
0
89

System
D
0
650
0
1550
800
600
100
480
0
300
0
0
94

APPENDIX 1-6: SELF-SELECTION IN RESPONSES TO QUESTIONNAIRES

Mail surveys for contingent valuation studies are often criticized for the self-selection
problem, namely that questionnaire recipients choose to respond to the questionnaire based on
their own characteristics or the survey attributes. Due to the lack of information for nonrespondents in the survey, only the self-selection issue due to different survey versions is
examined. There are 16 versions of the questionnaire based on the main effects orthogonal
design with 6 variables, i.e., sequence of cropping system difficulty (ascending or descending)
which correlated positively with payment level, payment vehicle (Federal government or a nongovernmental organization), and the four varying payment levels for the four cropping systems.
A probit model is used to test whether each cropping system is influenced by selfselection in response. The dependent variable is whether the questionnaire recipients respond to
the questionnaire. The independent variables are the six variables that determine questionnaire
versions. The probit regression is applied for each cropping system separately. Regression results
suggest that only responses to System D are influenced by the payment offer and its square term
(Table 1-A8). Then Heckman selection models are applied to binary participation decision and
positive acreage enrollment decision for cropping system D to test the significance of selfselection problem (Heckman, 1979). Both the Heckman probit regression and the two-step
Heckman regression suggest that self-selection due to survey design is not significant in the
sample.

62

Table 1-A8 Probit regression of binary survey response on survey version attributes, 3000
Michigan Corn or Soybean Farms, 2008
system
response
Coef.
Std. Err.
P>z
price
0.007
0.026
0.786
price square
0.000
0.001
0.817
A
constant
0.208
0.120
0.083
price
0.012
0.016
0.463
price square
0.000
0.000
0.544
B
constant
0.097
0.172
0.573
price
0.012
0.011
0.281
price square
0.000
0.000
0.391
C
constant
0.001
0.191
0.996
price
0.018
**
0.008
0.023
price square
0.000
**
0.000
0.023
D
constant
0.183
0.196
0.349
Table 1-A9 Heckman probit model for binary participation decision, 3000 Michigan Corn or
Soybean Farms, 2008
Participation
Coef.
Std. Err.
z
P>z
[95% Conf. Interval]
acres_d
price
0.009***
0.002 4.250 0.000
0.005
0.014
government 0.038
0.077 0.500 0.618
0.112
0.189
sequence
0.017
0.079 0.210 0.834
0.171
0.138
constant
0.755
0.836 0.900 0.367
2.392
0.883
response
government 0.022
0.051 0.430 0.664
0.078
0.123
sequence
0.027
0.052 0.520 0.601
0.075
0.130
price
0.020**
0.009 2.150 0.032
0.002
0.038
price square 0.000**
0.000 2.190 0.028
0.000
0.000
constant
0.446**
0.216 2.070 0.039
0.869
0.023
/athrho
0.021
1.026 0.020 0.984
2.031
1.989
rho
0.021
1.025 0.966 0.963
LR test of indep. eqns. (rho = 0): chi2(1) =0.00 Prob > chi2 = 0.9837
Number of obs
2481
Wald chi2(3)
19.1
Prob>chi2
0.0003
Log likelihood -2554.75

63

Table 1-A10 Heckman model for acreage enrollment decision, 3000 Michigan Corn or Soybean
Farms, 2008
Coef.
Std. Err.
z
P>z
[95% Conf.
Interval]
Acreage enroll
acres
acres_d
3.17***
1.03
3.08
0.002
1.15
5.18
price
38.7
36.1
1.07
0.284
32.1
109
government
33.1
37.3
0.890 0.375
106
34.0
sequence
269.500
387
0.700 0.487
1029
490
response
government
0.023
0.051
0.450 0.649
0.077
0.124
sequence
0.026
0.052
0.500 0.617
0.076
0.128
price
0.020**
0.009
2.16
0.031
0.002
0.038
price square
0.000**
0.000
2.21
0.027
0.000
0.000
constant
0.448**
0.216
2.08
0.038
0.871
0.026
mills
lambda
431
479
0.9
0.368
508
1370
rho
0.666
sigma
647
Number of obs
2480
Wald chi2(3)
12.4
Prob>chi2
0.0062

64

REFERENCES

65

REFERENCES

Blundell, R., and C. Meghir. 1987. "Bivariate alternatives to the tobit model." Journal of
Econometrics 34(1-2):179-200.
Borin, M., C. Giupponi, and F. Morari. 1997. "Effects of four cultivation systems for maize on
nitrogen leaching 1. Field experiment." European Journal of Agronomy 6(1-2):101-112.
Bosch, D.J., Z.L. Cook, and K.O. Fuglie. 1995. "Voluntary versus mandatory agricultural
policies to protect water quality: Adoption of nitrogen testing in Nebraska." Review of
Agricultural Economics 17(1):13-24.
Burton, M., R. Dorsett, and T. Young. 1996. "Changing preferences for meat: Evidence from UK
household data, 1973-93." European Review of Agricultural Economics 23(3):357-370.
Cattaneo, A., R. Claassen, R. Johansson, and M. Weinberg. 2005. "Flexible conservation
measures on working land: What challenges lie ahead?". United States Department of
Agriculture, Economic Research Service. http://www.ers.usda.gov/publications/err5/err5.pdf
Correll, D. 1998. "Role of phosphorus in the eutrophication of receiving waters: A review."
Journal of Environmental Quality 27(2):261-266.
Cragg, J.G. 1971. "Some statistical models for limited dependent variables with application to
thedemand for durable goods." Econometrica 39(5):829-844.
D'Emden, F.H., R.S. Llewellyn, and M.P. Burton. 2008. "Factors influencing adoption of
conservation tillage in australian cropping regions." Australian Journal of Agricultural and
Resource Economics 52(2):169-182.
Davey, K.A., and W.H. Furtan. 2008. "Factors that affect the adoption decision of conservation
tillage in the prairie region of canada." Canadian Journal of Agricultural Economics 56(3):257275.
Deaton, A., and M. Irish. 1984. "Statistical models for zero expenditures in household budgets."
Journal of Public Economics 23(1-2):59-80.
del Saz-Salazar, S., and P. Rausell-Koster. 2008. "A double-hurdle model of urban green areas
valuation: Dealing with zero responses." Landscape and Urban Planning 84(3-4):241-251.
Delgado, J., R. Sparks, R. Follett, J. Sharkoff, and R. Riggenbach. 1999. "Use of winter cover
crops to conserve soil and water quality in the San Luis Valley of south central Colorado, soil
quality and soil erosion." Soil and Water Conservation Society:125–142.
66

Dillman, D.A. 2007. Mail and Internet Surveys: The Tailored Design Method. 2nd ed. New
York: John Wiley.
Dupraz, P., D. Vermersch, B.H. De Frahan, and L. Delvaux. 2003. "The environmental supply of
farm households: A flexible willingness to accept model." Environmental and Resource
Economics 25(2):171-189.
Engel, S., S. Pagiola, and S. Wunder. 2008. "Designing payments for environmental services in
theory and practice: An overview of the issues." Ecological Economics 65(4):663-674.
Epplin, F.M., and T.F. Tice. 1986. "Influence of crop and farm size on adoption of conservation
tillage." Journal of Soil and Water Conservation 41(6):424-427.
Ervin, C.A., and D.E. Ervin. 1982. "Factors affecting the use of soil conservation practices:
Hypotheses, evidence, and policy implications." Land Economics 58(3):277-292.
Fuss, M.A., and D. McFadden (1978) Production economics: A dual approach to theory and
applications, ed. M.A. Fuss, and D.L. McFadden, vol. 1. Amsterdam, North-Holland, pp. 219268.
Glotfelty, D.E., J.N. Seiber, and A. Liljedahl. 1987. "Pesticides in fog." Nature 325(6105):602605.
Goodwin, B., L. Offenbach, T. Cable, and P. Cook. 1993. "Discrete/continuous contingent
valuation of private hunting access in Kansas." Journal of Environmental Management 39(1):112.
Gould, B.W., W.E. Saupe, and R.M. Klemme. 1989. "Conservation tillage - the role of farm and
operator characteristics and the perception of soil-erosion." Land Economics 65(2):167-182.
Greene, W.H. 2000. Econometric Analysis. Fourth ed. Englewood Cliffs, NJ: Prentice Hall.
Heckman, J.J. 1979. "Sample selection bias as a specification error." Econometrica: Journal of
the Econometric Society:153-161.
Hoben, J.P., R.J. Gehl, N. Millar, P.R. Grace, and G.P. Robertson. 2011. "Nonlinear nitrous
oxide (N2O) response to nitrogen fertilizer in on-farm corn crops of the us midwest." Global
Change Biology 17(2):1140-1152.
Jensen, H.H., and S.T. Yen. 1996. "Food expenditures away from home by type of meal."
Canadian Journal of Agricultural Economics 44(1):67-80.
Jolejole, M.C.B. 2009. "Trade-offs, incentives and the supply of ecosystem services from
cropland." Michigan State University. http://aec3.aec.msu.edu/theses/fulltext/jolejole1_ms.pdf

67

Jolejole, M.C.B. 2009. "Trade-offs, incentives and the supply of ecosystem services from
cropland." M.S. Thesis, Michigan State University, Department of Agricultural, Food and
Resource Economics. http://aec3.aec.msu.edu/theses/fulltext/jolejole1_ms.pdf
Jones, A. 1992. "A note on computation of the double-hurdle model with dependence with an
application to tobacco expenditure." Bulletin of Economic Research 44(1):67-74.
Joyce, B., W. Wallender, J. Mitchell, L. Huyck, S. Temple, P. Brostrom, and T. Hsiao. 2002.
"Infiltration and soil water storage under winter cover cropping in California's Sacramento
Valley." Transactions of the ASAE 45(2):315-326.
Knowler, D., and B. Bradshaw. 2007. "Farmers' adoption of conservation agriculture: A review
and synthesis of recent research." Food Policy 32(1):25-48.
Lal, R., M. Griffin, J. Apt, L. Lave, and M. Morgan. 2004. "Managing soil carbon." Science
304(5669):393.
Lambert, D., P. Sullivan, R. Claassen, and L. Foreman. 2006. Title. Economic Research Report
No. 14. Economic Research Service, U.S. Department of Agriculture.
Lasley, P., M. Duffy, K. Kettner, and C. Chase. 1990. "Factors affecting farmers' use of practices
to reduce commercial fertilizers and pesticides." Journal of Soil and Water Conservation
45(1):132-136.
Lau, L.J. (1986) Functional forms in econometric model building, ed. Z. Griliches, and M.D.
Intriligator, vol. 3. Amsterdam, North-Holland Publishing Co., pp. 1515-1566.
Lee, L.K., and W.H. Stewart. 1983. "Landownership and the adoption of minimum tillage."
American Journal of Agricultural Economics 65(2):256-264.
Lin, T.-F., and P. Schmidt. 1984. "A test of the tobit specification against an alternative
suggested by cragg." The Review of Economics and Statistics 66(1):174-177.
Lynne, G.D., and L.R. Rola. 1988. "Improving attitude-behavior prediction models with
economic variables - farmer actions toward soil conservation." Journal of Social Psychology
128(1):19-28.
Lynne, G.D., J.S. Shonkwiler, and L.R. Rola. 1988. "Attitudes and farmer conservation
behavior." American Journal of Agricultural Economics 70(1):12-19.
Martínez-Espiñeira, R. 2006. "A box-cox double-hurdle model of wildlife valuation: The
citizen's perspective." Ecological Economics 58(1):192-208.
Mazvimavi, K., and S. Twomlow. 2009. "Socioeconomic and institutional factors influencing
adoption of conservation farming by vulnerable households in Zimbabwe." Agricultural Systems
101(1-2):20-29.
68

McSwiney, C.P., and G.P. Robertson. 2005. "Nonlinear response of n2o flux to incremental
fertilizer addition in a continuous maize (zea mays l.) cropping system." Global Change Biology
11(10):1712-1719.
McSwiney, C.P., S.S. Snapp, and L.E. Gentry. 2010. "Use of N immobilization to tighten the N
cycle in conventional agroecosystems." Ecological Applications 20(3):648-662.
Musser, W.N., J.S. Shortle, K. Kreahling, B. Roach, W.-C. Huang, D.B. Beegle, and R.H. Fox.
1995. "An economic analysis of the pre-sidedress nitrogen test for Pennsylvania corn
production." Review of Agricultural Economics 17(1):25-35.
Negatu, W., and A. Parikh. 1999. "The impact of perception and other factors on the adoption of
agricultural technology in the Moret and Jiru Woreda (district) of Ethiopia." Agricultural
Economics 21(2):205-216.
Neill, S.P., and D.R. Lee. 2001. "Explaining the adoption and disadoption of sustainable
agriculture: The case of cover crops in northern honduras." Economic Development and Cultural
Change 49(4):793-820.
Newman, C., M. Henchion, and A. Matthews. 2003. "A double-hurdle model of irish household
expenditure on prepared meals." Applied Economics 35(9):1053 - 1061.
Norris, P., and S. Batie. 1987. "Virginia farmers’ soil conservation decisions: An application of
tobit analysis." Southern Journal of Agricultural Economics 19(1):79-90.
Nowak, P. 1992. "Why farmers adopt production technology." Journal of Soil and Water
Conservation 47(1):14-16.
Oades, J. 1984. "Soil organic matter and structural stability: Mechanisms and implications for
management." Plant and Soil 76(1):319-337.
Okoye, C.U. 1998. "Comparative analysis of factors in the adoption of traditional and
recommended soil erosion control practices in Nigeria." Soil and Tillage Research 45(3-4):251263.
Pautsch, G., L. Kurkalova, B. Babcock, and C. Kling. 2001. "The efficiency of sequestering
carbon in agricultural soils." Contemporary Economic Policy 19(2):123-134.
Peel, M. 1998. "Crop rotations for increased productivity, eb-48. North Dakota State University
extension service." http://www.ag.ndsu.edu/pubs/plantsci/crops/eb48-1.htm
Pimentel, D., and N. Kounang. 1998. "Ecology of soil erosion in ecosystems." Ecosystems
1(5):416-426.
Poudel, D., W. Horwath, J. Mitchell, and S. Temple. 2001. "Impacts of cropping systems on soil
nitrogen storage and loss." Agricultural Systems 68(3):253-268.
69

Prokopy, L.S., K. Floress, D. Klotthor-Weinkauf, and A. Baumgart-Getz. 2008. "Determinants
of agricultural best management practice adoption: Evidence from the literature." Journal of Soil
and Water Conservation 63(5):300-311.
Purvis, A., J. Hoehn, V. Sorenson, and F. Pierce. 1989. "Farmers' response to a filter strip
program: Results from a contingent valuation survey." Journal of Soil and Water Conservation
44(5):501.
Rahm, M.R., and W.E. Huffman. 1984. "The adoption of reduced tillage - the role of humancapital and other variables." American Journal of Agricultural Economics 66(4):405-413.
Reganold, J., L. Elliott, and Y. Unger. 1987. "Long-term effects of organic and conventional
farming on soil erosion."
Reicosky, D., and M. Lindstrom. 1993. "Fall tillage methods: Effect on short-term carbon
dioxide flux from soil." Agronomy Journal 85(6):1237-1243.
Roberts, R.K., B. English, Q. Gao, and J.A. Larson. 2006. "Simultaneous adoption of herbicideresistant and conservation-tillage cotton technologies." Journal of Agricultural and Applied
Economics 38(3):629.
Sheikh, A.D., T. Rehman, and C.M. Yates. 2003. "Logit models for identifying the factors that
influence the uptake of new 'no-tillage' technologies by farmers in the rice-wheat and the cottonwheat farming systems of pakistan's punjab." Agricultural Systems 75(1):79-95.
Shrestha, R.A.M., J. Alavalapati, A. Seidl, K. Weber, and T.R.I. Suselo. 2007. "Estimating the
local cost of protecting koshi tappu wildlife reserve, nepal: A contingent valuation approach."
Environment, Development and Sustainability 9(4):413-426.
Sidibe, A. 2005. "Farm-level adoption of soil and water conservation techniques in northern
Burkina Faso." Agricultural Water Management 71(3):211-224.
Smith, M. 2003. "On dependency in double-hurdle models." Statistical Papers 44(4):581-595.
Smith, M. 2002. "On specifying double-hurdle models." Handbook of Applied Econometrics and
Statistical Inference:535-552.
Soule, M., A. Tegene, and K. Wiebe. 2000. "Land tenure and the adoption of conservation
practices." American Journal of Agricultural Economics:993-1005.
Su, S.-J.B., and S.T. Yen. 1996. "Microeconometric models of infrequently purchased goods: An
application to household pork consumption." Empirical Economics 21(4):513-533.
Tobin, J. 1958. "Estimation of relationships for limited dependent variables." Econometrica
26(1):24-36.

70

Traore, N., R. Landry, and N. Amara. 1998. "On-farm adoption of conservation practices: The
role of farm and farmer characteristics, perceptions, and health hazards." Land Economics
74(1):114-127.
Upadhyay, B.M., D.L. Young, H.H. Wang, and P. Wandschneider. 2003. "How do farmers who
adopt multiple conservation practices differ from their neighbors?" American Journal of
Alternative Agriculture 18(1):27-36.
Uri, N. 1997. "Conservation tillage and input use." Environmental Geology 29(3):188-201.
van den Berg, F., R. Kubiak, W.G. Benjey, M.S. Majewski, S.R. Yates, G.L. Reeves, J.H. Smelt,
and A.M.A. van der Linden. 1999. "Emission of pesticides into the air." Water, Air, & Soil
Pollution 115(1):195-218.
Vuong, Q.H. 1989. "Likelihood ratio tests for model selection and non-nested hypotheses."
Econometrica: Journal of the Econometric Society:307-333.
Warriner, G., and T. Moul. 1992. "Kinship and personal communication network influences on
the adoption of agriculture conservation technology." Journal of Rural Studies 8(3):279-291.
Warriner, G.K., and T.M. Moul. 1992. "Kinship and personal communication network influences
on the adoption of agriculture conservation technology." Journal of Rural Studies 8(3):279-291.
Wei, Y.P., D. Chen, R.E. White, I.R. Willett, R. Edis, and J. Langford. 2009. "Farmers'
perception of environmental degradation and their adoption of improved management practices
in Alxa, China." Land Degradation & Development 20(3):336-346.
Woodridge, J. (2008) Econometric analysis of cross-section and panel data, 2nd Edition.
Cambridge, MA, The MIT Press, pp. 453-481.
Wossink, A., and S. Swinton. 2007. "Jointness in production and farmers' willingness to supply
non-marketed ecosystem services." Ecological Economics 64(2):297-304.
Wu, J., and B. Babcock. 1998. "The choice of tillage, rotation, and soil testing practices:
Economic and environmental implications." American Journal of Agricultural Economics
80(3):494-511.
Yen, S., P. Boxall, and W. Adamowicz. 1997. "An econometric analysis of donations for
environmental conservation in Canada." Journal of Agricultural and Resource Economics
22:246-263.
Yen, S., and H. Jensen. 1996. "Determinants of household expenditures on alcohol." Journal of
Consumer Affairs 30(1).

71

Yen, S.T., and A.M. Jones. 1997. "Household consumption of cheese: An inverse hyperbolic
sine double-hurdle model with dependent errors." American Journal of Agricultural Economics
79(1):246-251.
Zbinden, S., and D.R. Lee. 2005. "Paying for environmental services: An analysis of
participation in Costa Rica's PSA program." World Development 33(2):255-272.
Zhang, W., T.H. Ricketts, C. Kremen, K. Carney, and S.M. Swinton. 2007. "Ecosystem services
and dis-services to agriculture." Ecological Economics 64(2):253-260.

72

ESSAY 2: MODELING CERTAINTY-ADJUSTED WILLINGNESS TO PAY FOR
ECOSYSTEM SERVICE IMPROVEMENT FROM AGRICULTURE

2.1

Introduction
The public demand for nonmarket ecosystem services (ES) stems from people’s desire

for a better environment for living, such as clean air and drinking water for health, abundant
natural resources for recreation, and diverse landscapes for scenic views. A broad variety of
environmental improvements that would affect the welfare of local communities and the general
public can be generated from land management practices in agricultural ecosystems. Examples
include water quality improvement from less fertilizer input, and greenhouse gas (GHG)
mitigation from winter cover crops. Payment-for-Ecosystem-Service (PES) programs have been
increasingly implemented around the world to facilitate the provision of these ecosystem services
(ES). In order to design efficient public policies for enhancing ecosystem services from
agriculture, the demand for ES needs to be addressed in addition to the supply side analysis on
farmers. The public willingness to pay (WTP) from stated preference studies is an important
measure of the demand for non-market ES.
However, the survey-based contingent valuation is likely to suffer from respondents’
preference uncertainty, which may increase the variance and even cause bias in the estimation of
WTP. The valuation of public goods like ecosystem services is likely to be subject to even larger
bias than valuation of private goods (List and Gallet, 2001). Based on review of the literature, the
uncertainty in preference may originate from the three sources.
First, uncertain responses can be caused by incomplete knowledge of the hypothetical
markets (Li and Mattsson, 1995). The good or service to be valued may be unclear to

73

respondents who have never experienced or used it, such as mitigation of greenhouse gas
emissions. For tangible goods or services, the result of changes in quality/quantity may not be
fully understood (Wang and Whittington, 2005). For example, the degree of improvement in
eutrophic lakes may be unclear to some people.
Second, respondents may have different understanding of the proposed policy instrument
for providing the good (Shaikh, et al., 2007), such as how an increased income tax would serve
as a payment vehicle to collect public funding. The implementation of policy can influence their
certainty of payment.
Third, individuals may also have specific uncertainties in their evaluation of trade-off
between amenity and dollar values (Shaikh, et al., 2007), the perception of substitutes for the
hypothetical goods, or their expectation of future income (Wang and Whittington, 2005).
Given the potential for preference uncertainty in willingness to pay estimation, ES
demand estimates should be tested and, if necessary, adjusted accordingly. Taking advantage of a
unique stated preference data set that includes a follow-up question rating the respondent’s
certainty level, this study evaluates alternative methods of modeling certainty-adjusted WTP for
two important ecosystem services from cropland management--improvement in eutrophic lakes
and mitigation of global warming.
Previous studies have used various ways to incorporate preference uncertainty into
contingent valuation. In the case of binary choice format with a follow-up 10-point numerical
certainty scale, “yes” and “no” responses were recoded to a grid of probability ranging from 0 to
1 (Chang, et al., 2007, Li and Mattsson, 1995, Loomis and Ekstrand, 1998, Shaikh, et al., 2007).
Alternatively, “no” responses were recoded as “yes” based on a fixed cutoff level of certainty
(Champ and Bishop, 2001, Champ, et al., 1997, Ethier, et al., 2000, Loomis and Ekstrand, 1998,

74

Samnaliev, et al., 2006). In the case of a polychotomous choice format with uncertain choices
such as “probably yes”, “not sure”, and “probably no”, the responses were analyzed directly
(Lundhede, et al., 2009, Wang and Whittington, 2005), or re-categorized to binary responses
under different assumptions (Chang, et al., 2007, Johannesson, et al., 1998, Samnaliev, et al.,
2006, Vossler, et al., 2003, Whitehead, et al., 1998). There are also other unique attempts to
model preference uncertainty. For example, Li and Mattsson (1995) treated respondent
uncertainty as one source of measurement error and weighted the individual dichotomous-choice
responses directly in the likelihood function by a numerical certainty scale. Van Kooten et al.
(2001) introduced a fuzzy model that assumes two fuzzy sets for willingness to pay and
unwillingness to pay. This model was then extended to a fuzzy random utility maximization
framework by Sun and van Kooten (2009). Wang and Whittington (2005) developed a noneconometric approach relying on the stochastic payment card for modeling preference
uncertainty. Moore et al. (2010) assumed that the certainty scale embodied a flexible mapping
between the probability of payment and the integers 1-10, and applied maximum likelihood
estimation (MLE) to obtain the parameters of a mapping rule for a specific dataset.
Examples of goods and services that have been valued with preference uncertainty
include conservation of a lagoon (Chang, et al., 2007, Whitehead, et al., 1998), private access to
public land (Samnaliev, et al., 2006, Vossler, et al., 2003), green energy (Champ and Bishop,
2001, Ethier, et al., 2000, Poe, et al., 2002), and endangered species (Loomis and Ekstrand,
1998).
Compared to previous studies, this essay complements the literature in three ways. First, I
compare four calibration methods to incorporate numerical certainty using a large dataset with
panel data structure. The number of observations used in previous studies typically range from

75

300 to1600 (Akter, et al., 2008), whereas this study has a sample of about 3000 observations
including multiple choices made by the same respondent. In the process, econometric treatment
for panel data is applied to models that symmetrically or asymmetrically recode binary responses
into a grid of probability based on 10-point certainty scale. Second, two functional forms for
WTP are compared to examine the consistency of the influence from preference uncertainty on
WTP estimation. Third, the regime of preference uncertainty estimation is extended beyond
single tangible goods or services in a local setting (such as green energy, lagoon conservation
and endangered species) to ecosystem services from agriculture, which include both a global
public good, greenhouse gas mitigation, and a regional public good, eutrophic lake abatement.

2.2

Theoretical model
Public demand for nonmarket ecosystem services is assumed to be rooted in the

individual utility model (Flores, 2003). That model holds that utility depends on a bundle of
market goods, Z, and the level of environmental improvements, ES, conditioned on residentspecific characteristics, R, such as age, education, gender and voter registration. People choose
the level of market goods to maximize utility subject to a budget constraint that the expenditure
cannot exceed income y, given price vector Pz.

(

MaxU R Z R , ES (lake, GHG) | R
Z

)

R
s.t. PZ Z ≤ y

(2.1)

(2.2)

The demand function for market good is

Z R* = Z ( PZ , ES , y | R )
The indirect utility function at the optimal level of the market good bundle is
76

(2.3)

(

)

U R* Z R* , ES | R = V ( PZ , ES , y | R )

(2.4)

At the status quo level of ecosystem services, the indirect utility can be written as

(

V PZ , ES 0 , y | R

)

(2.5)

0

1

If there is an improvement in ecosystem services from ES to ES , such as reduction in eutrophic
lakes and greenhouse gas emissions, then the individual would be willing to give up a certain
amount of income, known as willingness to pay (WTP), such that:

(

) (

V PZ , ES 0 , y | R = V PZ , ES1, y − WTP | R

)

(2.6)

The true WTP can be solved as a function of those characteristics in the indirect utility function

(

)

WTP PZ , ES 0 , ES1, y | R . However, for each individual, the observed WTP in stated preference
surveys is comprised of the true willingness to pay, WTPi*, and an error term εi, which
represents stochastic disturbances that are not captured by the indirect utility function.

(

)

WTPi = WTPi* PZ , ES 0 , ES1, y | R + ε i

(2.7)

In an ordinary contingent valuation study, the error term, which is typically specified as
following a normal distribution with zero mean and constant variance, is assumed to reflect the
observer uncertainty arising from omitted variables. However, the stochastic disturbance may
also be related to the respondent due to their inherent randomness in preferences (Li and
Mattsson, 1995). For the dichotomous choice question, the respondent’s one-shot response is a
realization of the underlying probabilistic mechanism because they may not give the same
response each time when facing the same conditions. Li and Mattsson (1995) showed that the
maximum likelihood estimate of the valuation distribution incorporating both observer
77

uncertainty and respondent uncertainty would be flattened compared with the true distribution.
The associated overestimation of the standard deviation may lead to value inference bias,
although the parameter vector is still consistent. Different approaches to capture and model this
preference uncertainty are discussed in sections 3 and 4.
In dichotomous-choice contingent valuation surveys in a referendum format, respondents
are typically asked to vote “yes” or “no” for a payment level associated with an improvement in
the quality of non-market goods. They would vote “yes” if WTP is greater than the given
program cost C as shown in equation 2.8.

) (
))
((
= Pr (V ( ES , y − C ) > V ( ES , y − WTP ) ) = Pr (WTP > C )

Pr( yesi ) = Pr V ES1, yi − Ci > V ES 0 , yi
1

i

1

i

i

i

i

(2.8)

i

As pointed out by Wang (1997), an individual’s valuation of any good or service is best
characterized as a random variable with an unspecified probability. Such a probability can be
represented by the probability of voting “yes” in equation 2.8. An example probability
distribution is illustrated in Figure 2-1. Normally, if the mean of WTP is greater than proposed
tax payment (C), the respondent would vote “yes”. When considering preference uncertainty, the
decision rule depends on the whole distribution rather than the mean. The variance of
distribution reflects both observer uncertainty and respondent uncertainty. The shaded area that
is below the function and greater than the proposed tax payment represents the probability of
voting “yes” in empirical estimation. Higher certainty for voting “yes” means higher probability,
which is typically associated with higher mean of WTP.
Following Chen (2010), this study adopts a spike probability model to distinguish people
who have zero willingness to pay for the ecosystem services and are not responsive to price

78

change. The unconditional probability of voting “yes” to the program is a product of the
probability of positive WTP and the conditional probability of “yes” vote as in equation 2.9.

Pr( yesi | WTPi ) = Pr (WTPi > 0 ) Pr ( yesi | WTPi > 0 )

(2.9)

The probability of having positive willingness to pay is endogenously modeled with
environmental quality changes and individual characteristics.

2.3

Data
Data for this study come from a 2009 mail survey of Michigan residents that yielded

2211 responses (40% response rate). The contingent valuation (CV) question was posed as a
dichotomous choice referendum with income taxes as the payment vehicle. Each respondent was
asked to vote on three independent land stewardship programs, which provide different
greenhouse gas and eutrophic lake reductions from changes in land management practices
associated with a tax payment. Respondents were informed that if more than 50% of the voters
voted for the program, it would be implemented and they would have to pay the cost.
The reductions in eutrophic lake numbers and greenhouse gas emissions were selected
among a series of environmental improvements from agriculture because of their significant and
measurable impact on the public based on both an ES quantification study and a survey pretest
(Chen, 2010). Five levels of the two environmental improvements offered were: zero change,
10

low change, median change, high change and double of the high change . The high change was
maximum possible reduction calculated by Chen (2010).

10

In pretest interviews for this contingent valuation survey, some respondents reported that the
ecosystem service changes were too small to influence their choices. To reduce the probability of
scope insensitivity problem, the original maximum change is doubled as the new range of the
two attributes (Chen, 2010).
79

The cost for each program was expressed as the respondent’s own share of increased
annual federal income tax, which would only be used in the state of Michigan. The costs for all
three land stewardship programs were the same to each respondent but were varied across
residents. Based on the questionnaire pretest, the program cost levels were set at $10, $30, $50,
$100, and $200 per year. If the respondent voted “no” for the WTP question, a follow-up
question asked whether she would vote for the program if it did not cost her anything. That
response is used to identify respondents who have zero WTP.
To test the effect of provision mechanisms on respondents’ WTP, two alternative
versions of the questionnaire were provided. One specified that the land stewardship program
was to pay farmers to adopt environmental friendly farming practices, while the other was to pay
general land owners.
To capture the individual preference uncertainty, several formats have been used in the
literature. The simplest format is to add a “not sure” or “don’t know” option to the dichotomous
“yes/no” choice to a given price (Balcombe and Fraser, 2009, Fenichel, et al., 2006, Haener and
Adamowicz, 1998, Krosnick, et al., 2002, Wang, 1997). A similar but extended format is the
polychotomous choice (PC) method, in which respondents are provided with a set of uncertainty
options, for example, “definitely yes”, “probably yes”, “not sure”, “probably no”, and
“definitely no” (Alberini, et al., 2003, Chang, et al., 2007, Johannesson, et al., 1998, Samnaliev,
et al., 2006, Vossler, et al., 2003, Whitehead, et al., 1998). The third way is to follow the
standard “yes/no” choice by a numerical certainty scale ranging from 1 to 10, with which the
respondents can indicate the level of certainty about their “yes/no” voting decision (Champ and
Bishop, 2001, Champ, et al., 1997, Chang, et al., 2007, Ethier, et al., 2000, Li and Mattsson,
1995, Loomis and Ekstrand, 1998, Moore, et al., 2010, Poe, et al., 2002, Samnaliev, et al., 2006,

80

Shaikh, et al., 2007). A fourth approach that directly elicits the distribution of preference
uncertainty is the stochastic payment card (SPC) format, which presents each respondent with
numerical likelihood that the she would vote “yes” to a series of payment levels (Ichoku, et al.,
2009, Wang and Whittington, 2005).
Among those formats for eliciting preference uncertainty, this study adopted the 10-point
numerical certainty scale approach in a follow-up question, which asked how certain the
respondents were with their “yes/no” answers to the WTP question. The survey question is
shown in Figure 2-2.
Fourteen questionnaire versions were generated from an experimental design with three
CV questions per respondent. Information was provided about eutrophication of lakes and global
warming (GW), how residents would be affected and how land management practices would
improve environmental qualities. Additional questions covered residents’ responses to the
backgrounds, demographic status and their attitudes on various environmental issues. Variable
descriptions appear in Table 2-1 with descriptive statistics in Table 2-2. Among 2211 responses,
3396 observations from 1293 respondents are used for analyzing the certainty-adjust models with
panel data structure. Detailed information about data collection and questionnaire design can be
found in Chen (2010).

81

2.4
2.4.1

Empirical model and variables
Econometric model of WTP
The model for estimating empirical WTP conforms to the theoretical structure presented

in equation 2.9, which combines a spike for zero WTP with conditional positive WTP. Following
Chen (2010), the spike probability of positive WTP for individual i is a function of the change in
ecosystem services, and individual resident characteristics Ri. Lake and GHG represent the effect
of the hypothetical program in terms of the number of eutrophic lakes cleaned and the percentage
of greenhouse gas emission reduced from the year 2000 level.
Pr (WTPi > 0 ) = Φ ( a + bL Lake + bG GHG + cRi )

(2.10)

As respondents who have a zero WTP have been separated by the spike model, the WTP
from the rest of respondents is strictly positive, which is then ensured by the semi-log functional
form in equation 2.11. In this equation, ESL and ESG represent the abatement in eutrophic lakes
and GHG emissions. A is respondent’s attitude towards global warming. R indicates individualspecific characteristics. An interaction of concern about global warming and greenhouse gas
reduction is generated to test the aggregate effect.

(

WTP |WTPi >0 = exp δ + β L ES L + βG ESG + α Ai + ϕ ESG Ai + γ Ri + ε ij
i

)

(2.11)

Two functional forms different in the expression of lake and GHG variables are
compared to examine the consistency of influence from incorporating preference uncertainty on
the WTP estimation. In the first semi-log function, ESL and ESG represents the number of
cleaned eutrophic lakes and percentage of greenhouse gas emission reduced from the 2000 level
as in the spike model (equation 2.12).

82

(

WTP |WTPi >0 = exp δ + β Llake + βGGHG + α Ai + ϕGHG ⋅ Ai + γ Ri + ε ij
i

)

(2.12)

This assumption of linearity in environmental improvements within the semi-log function is
common in the literature. However, the projected resident’s WTP would be growing at an
increasing rate with respect to the environmental services, while the economic theory of demand
typically assumes an increasing and concave benefit (WTP) function due to diminishing
marginal utility (Marshall, 2009). To maintain the assumptions of both positive conditional
WTP and diminishing marginal utility, the mixed log-log functional form is proposed in equation
2.13, where the number of cleaned eutrophic lakes and percentage of greenhouse gas mitigation
are transformed by taking the natural logarithm in addition to first functional form in equation
11

2.12 .

(

WTPi |WTPi >0 = exp δ + β Llnlake + βG lnGHG + α Ai + ϕ lnGHG ⋅ Ai + γ Ri + ε ij

)

(2.13)

Assuming the error term ε is normally distributed with mean zero and constant variance σ2, the
conditional probability distribution of voting “yes” to the dichotomous-choice valuation question
with cost Ci is

Pr(Yi = 1|WTPi >0 ) = Pr (WTPi > Ci )

( (

)

= Pr exp δ + β L ES L + βG ESG + α Ai + ϕ ESG Ai + γ Ri + ε ij > Ci

(

= Pr δ + β L ES L + βG ESG + α Ai + ϕ ESG Ai + γ Ri + ε ij > ln Ci

)

)
(2.14)

ε ij 
 δ − ln Ci + β L ES L + βG ESG + α Ai + ϕ ESG Ai + γ Ri
= Pr 
>− 
σ
σ 

β
β
α
ϕ
γ 
δ 1
= Φ  − ln Ci + L ES L + G ESG + Ai + ESG Ai + Ri 
σ
σ
σ
σ
σ 
σ σ
11

-12

The Lake variable is adjusted by adding 1*10 to all observation to produce valid estimation
as some observations have zero values for this variable. Likewise, the GHG variable is adjusted
-15
by adding 1*10
as its mean is about 300 times smaller than Lake.
83

The unconditional probability of voting “yes” is:

Pr(Yi = 1) = Pr (WTPi > 0 ) Pr (Y = 1i | WTPi > 0 )
= 1 − Φ ( a + bL ES L + bG ESG + cRi )  ⋅



(2.15)

β
β
α
ϕ
γ 
δ 1
Φ  − ln Ci + L ES L + G ESG + Ai + ESG Ai + Ri 
σ
σ
σ
σ
σ 
σ σ
The first term represents the probability of having positive WTP. The second term
represents the probability of WTP conditional on willingness to pay a positive amount for the
environmental improvements. Since the two decisions are assumed to be independent, the
probability of zero WTP and a positive amount of WTP can be estimated separately. As the
response to the zero WTP question is binary and the probability is assumed to follow a normal
distribution, standard probit regression can be applied to the spike model. Since each respondent
was presented with three independent alternative programs, random effect probit is used to
account for the correlation among the three decisions made by the same respondent.

2.4.2

Methods for incorporating preference uncertainty
For the conditional probability of positive WTP, conventional dichotomous-choice CV

studies employ binary response models, such as probit or logit. In this essay, the dichotomous
responses are calibrated by numerical certainty scale from a follow-up question and adopt the
following econometric models to estimate the adjusted WTP.
•

Probit model with different fixed cutoff certainty levels
With the 10-point numerical certainty scale, the dichotomous choice regarding program

participation at a given price can be recoded based on an arbitrarily chosen cutoff level of
certainty. The binary “yes” response (Yi=1) is recoded as “no” (Yi=0) if the respondent’s

84

certainty is less than a specific cutoff level. Four cutoff levels are considered, at 10, 9, 8 and 7,
as shown in Table 2-3. The adjusted responses are then used in the standard random effect probit
model. In this essay, the cutoff point is set at 7 when comparing results with other methods. This
method translates some “yes” responses into “no”, and is expected to reduce the WTP estimates.

•

Ordered probit model with polychotomous response
The binary responses are recoded as “yes” (Yi=1), “indifferent” (Yi=0.5) and “no” (Yi=0)

depending on a cutoff level of certainty as shown in Table 2-4. The cutoff certainty level is set at
7, so answers of “yes” or “no” with certainty values of 7 or higher are coded as Yi=1 or Yi=0.
Certainty levels of 6 or lower are coded Yi=0.5 for “uncertain.” As the probability is increased
for “no” responses and reduced for “yes” responses, the total effect of adjustment on WTP can
be either positive or negative, depending on the original binary choice and the magnitude of
associated certainty.
The adjusted responses are then estimated by ordered probit with the following loglikelihood function, where δi and ηi are unknown cut points.
log L =



Yi = 2

+

 ln Ci + δ i − β L ES L − βG ESG − α Ai − ϕ ESG Ai − γ Ri  

σ


 log 1 − Φ 



  ln Ci + δ i − β L ES L − βG ESG − α Ai − ϕ ESG Ai − γ Ri 

σ



 log Φ 


Yi =1

 ln Ci − ηi − β L ES L − βG ESG − α Ai − ϕ ESG Ai − γ Ri
−Φ 
σ

+

  ln Ci − ηi − β L ES L − βG ESG − α Ai − ϕ ESG Ai − γ Ri  

σ



 log Φ 


Yi = 0





85

(2.16)

•

Symmetric/ Asymmetric uncertainty model
The original responses are recoded as probability of “yes” by combining the certainty

score with dichotomous choices. Different recoding approaches have been applied in previous
studies (Chang, et al., 2007, Li and Mattsson, 1995, Loomis and Ekstrand, 1998, Shaikh, et al.,
2007). Li and Mattsson (1995) coded a 60% certainty level following “yes” response as 0.6,
while a 60% certainty level following “no” response was coded as 1−0.6=0.4. Loomis and
Ekstrand (1998) criticized this coding scheme as it altered the original “yes” or “no” choice
made by the respondent. Instead, they implemented a slightly different numerical certainty scale
to separate “yes” and “no” response as shown in Figure 2-3, where 0 and 1 indicate the most
certain extremes of the “no” and “yes” responses respectively, and 0.5 indicates uncertainty of
either response. They and others have adopted logit models to estimate the recoded data by
transforming the dependent variable as log [ Pr(Yes ) / (1 − Pr(Yes ))] (Chang, et al., 2007, Loomis
and Ekstrand, 1998, Shaikh, et al., 2007). When both “yes” and “no” responses are recoded, the
method is referred as the Symmetric Uncertainty Model (SUM). The Asymmetric Uncertainty
Model (ASUM) refers to the case when only “yes” responses are recoded.
This essay also applies the SUM and ASUM methods, but with a different coding scheme
and econometric models. For the Symmetric Uncertainty Model, the binary responses are
recoded as continuous responses ranging from 0 to 1 depending on the level of certainty. If a
respondent voted “yes”, the lowest probability for her to pay is 0.5. As shown in Table 2-3, each
one point increase in the certainty level adds 0.05 to 0.5, so a “yes” response with certainty of 1
gives a probability of 0.55 and whereas a “yes” with a certainty of 10 gives a probability of
“1.00”. Similarly, the “no” responses are recoded from a highly certain 0 to a very uncertain 0.45

86

in response to certainty levels 10 to 1. For the Asymmetric Uncertainty Model, only “yes”
responses are recoded while “no” is left as zero probability. The details of calibration are shown
in Table 2-5. Figures 2-4 and 2-5 display the percentage of binary responses and certaintyadjusted responses under SUM method in the survey sample.
The probability of these adjusted responses can be estimated using a fractional binary
response models, such as fractional probit. Since Pr(Yi=1|WTP>0) is normally distributed in [0,1],
nonlinear least squares (NLS) can be used to consistently estimate the model. However, NLS is
unlikely to be efficient because common distributions for a fractional response imply
heteroskedasticity. Thus, a quasi-MLE approach can be a good alternative to consistently
estimate model parameters (Wooldridge, 2010). The log-likelihood function is as follows:
N

{

log L =  1 − Pr(Yi = 1|WTPi > 0 )  ⋅


i


β
β
α
ϕ
γ 
δ 1
log 1 − Φ  − ln Ci + L ES L + G ESG + Ai + ESG Ai + Ri  
σ
σ
σ
σ
σ   (2.17)
σ σ

+ Pr(Yi = 1|WTPi >0 ) ⋅
 δ 1
β
β
α
ϕ
γ  
log Φ  − ln Ci + L ES L + G ESG + Ai + ESG Ai + Ri   
σ
σ
σ
σ
σ  
 σ σ
A panel data structure should be imposed on the model due to correlation among multiple
choices made by each respondent. The common random effects approach, which attempts to
obtain a joint distribution and to integrate out unobserved heterogeneity, is computationally
demanding and would require additional assumptions on distribution. The generalized estimating
equations (GEE) method with a specified correlation matrix provides a tractable solution
(Wooldridge, 2010) that is estimated using STATA 10.1. Similar to the indifference adjustment,
the WTP estimates using SUM can either increase or decrease compared to the conventional

87

model, whereas the WTP will be reduced undoubtedly with ASUM, as only downward
transformation are made to the dependent variables.

2.4.3

Welfare estimation
In order to compare different econometric specifications that incorporate preference

uncertainty, the mean WTP, median WTP and efficiency of WTP estimation are calculated for
these certainty-adjusted models and the conventional dichotomous-choice CV model.
The mean and median willingness to pay conditional on WTP greater than zero are


σ2 
E (WTPi |WTPi >0 ) = exp  δ + β L ES L + βG ESG + α Ai + ϕ ESG Ai + γ Ri +


2 



(2.18)

Median(WTP |WTPi >0 ) = exp (δ + β L ES L + βG ESG +α Ai + ϕ ESG Ai + γ Ri )
i

(2.19)

Since the semi-log function of WTP typically has a fat tail and may lead to extremely large mean
values, the median WTP is computed and compared across different methods.
The unconditional median willingness to pay that combines the prior probability of
having a positive WTP shown in Equation 2.10 and the conditional WTP shown in Equation 2.19
is presented as:

Median(WTP ) = Pr (WTP > 0 ) ⋅ Median(WTP |WTPi >0 )
i
i
= Φ ( a + bL ES L + bG ESG + cRi ) 



(2.20)

⋅ exp (δ + β L ES L + βG ESG + α Ai + ϕ ESG Ai + γ Ri )
The efficiency of WTP estimation is measured by comparing the relative variability
around the median WTP using equation 2.19, where CIU and CIL are upper and lower bounds of
a 95% confidence interval (Loomis and Ekstrand, 1998).

88

EF (WTP) = (CIU–CIL) / Median (WTP)

(2.21)

Based on a review by Akter et al. (2008), empirical evidence indicated that various
certainty measurements and calibration techniques generate inconsistent welfare estimates in
terms of value and efficiency, though it is expected that the certainty-adjusted WTP estimate
should be lower and more efficient than the conventional WTP.
The median spike probability and conditional WTP are calculated for each respondent
using individual-specific values for attributes that are significant at 80% level. The conditional
WTP, unconditional WTP and their confidence intervals in the entire sample are estimated by
bootstrapping the mean from individual median WTPs with 100 replications.

2.4.4

Preference certainty model
To explore the determinants of certainty in respondents’ willingness-to-pay decisions, the

10-point numerical certainty scale is regressed on a set of variables nearly identical to those in
the conditional WTP model. Given the categorical nature of the certainty scale, the ordered
probit model is applied to two subsets of observations with “yes” and “no” responses separately.
Following Loomis and Ekstrand (1998), a variable measuring the square of proposed tax
payment is added to the variable set from the WTP model to capture the nonlinear effect of
certainty on cost.

2.4.5 Variables
The dependent variables have been described with the econometric model in Section 4.2.
There are seven categories of independent variables corresponding to the conceptual model: 1)

89

quantitative environmental improvements in eutrophic lakes and greenhouse gas emission; 2)
cost of hypothetical programs; 3) questionnaire version for type of land management to generate
the ES (farming practice or general land management); 4) resident’s perception of and attitudes
about eutrophic lakes and global warming; 5) resident’s opinion on general environmental issues;
6) demographic characteristics, including age, gender, education, income, household size, length
of residency, whether the respondent is a farmer or forester, whether the respondent is a
registered voter, and whether the respondent considers himself or herself a Michigan resident;
and 7) frequencies of fishing, swimming, boating and hiking in Michigan. The variable
definitions and summary statistics can be found in Tables 2-4 and 2-5.

2.5

Results
With both the semi-log and the mixed log-log functional forms, the certainty-adjusted

models are found to differ slightly from the conventional dichotomous choice model in several
aspects, including the significant variables, the magnitude of marginal effects, as well as the
value and efficiency of welfare estimation. Comparing the two functional forms, the
significance of variables and their marginal effects are similar. Although the two functional
forms lead to different median WTP estimates and variation of WTP in response to
environmental improvements, the differences are generally not statistically significant.

2.5.1

Preference certainty model
The results from two ordered probit models on determinants of certainty following “yes”

and “no” responses are shown in Table 2-7. The two models share a common set of influential
demographic characteristics, such as age, whether the respondent is a Michigan resident, and
90

whether she belongs to environmental organizations. These variables enhance the certainty of
“yes” responses while decreasing the certainty of “no” responses. The certainty of “yes”
responses increases with the proposed reduction in GHG for those who are very concerned about
global warming. The respondents are more certain about “yes” responses if they are registered
voters, or frequently hike near inland lakes. The certainty following “no” responses increases if
the respondents have been living longer in Michigan, work in the forest, frequently swim or fish
in inland lakes more or rarely go boating. Depending on a “yes” versus a “no,” certainty of
response is influence in opposite (but economically logical) ways by the hypothetical tax
payment. For “yes” responses, decision certainty declines with increasing cost, whereas for “no”
responses it rises with cost. The quadratic forms of cost are not significant in either “yes” or “no”
response models, suggesting a linear relationship between cost and certainty. These results are
similar to previous studies that found influential variables to include the bid level, prior
knowledge (Loomis and Ekstrand, 1998), and respondents' attitudes towards the hypothetical
market (Champ and Bishop, 2001, Samnaliev, et al., 2006).

2.5.2

Conditional willingness to pay
Incorporating decision certainty results in more significant variables in both the semi-log

and mixed log-log versions of the random effect probit models (Tables 2-8 and 2-9). The
conventional random effect probit model suggests that the probability of voting “yes” to the
proposed tax program significantly increases with higher reduction in eutrophic lakes, more
concern about global warming, higher income, age and education levels, and if the respondent is
a registered voter. The probability is negatively associated with the proposed tax payment, as
expected. The certainty-adjusted voting probabilities depends on these same factors, but is also
91

positively influenced if the respondent goes boating and hiking more often, is involved in
environmental organizations, and consider himself/herself a Michigan resident. The constant
term also becomes significant in all certainty-adjusted models.
The major difference between the two functional forms in coefficient estimates is
represented by the interaction between GHG reduction and whether the respondent is concerned
about global warming. With the semi-log function, this interaction variable is only significant at
54-82% probability levels in certainty-adjusted models, while it is significant at the 90% level in
the conventional model. In contrast, with the mixed log-log function, this variable is significant
in the conventional model and three out of four certainty-adjusted models with at least 95%
probability and is significant in the remaining model at the 80% level. In terms of overall
statistical significance and goodness-of-fit, the two functional forms perform similarly. Based on
chi-square test of differences between the log-log and semi-log Wald statistics, the mixed loglog functional form leads to higher statistical significance measure by Wald test in the
conventional model (p-value=0.0006), whereas the semi-log function performs better in the
SUM (p-value=0.0000), ASUM (p-value=0.002) and fixed-cutoff model (p-value=0.05) with
higher Wald test statistics. The two statistics are not statistically different in the certainty model
with an “indifference” option (p-value=0.13). The goodness of fit measured by likelihood can
only be calculated in three models. The two functional forms have similar degree of fit in the
conventional model and Indifference model, while the semi-log model has better fit in the fixedcutoff model (p-value=0.0001).
The marginal effects of significant variables are generally smaller in certainty-adjusted
models than in the conventional model. This is true of both the semi-log and mixed log-log
functions (Tables 2-10 and 2-11). The variations of dependent variables are smaller in the

92

Symmetric Uncertainty Model, the Asymmetric Uncertainty Model and the Indifferent ordered
probit model due to the finer recoding of the binary responses, hence it is not surprising that the
probabilities of voting “yes” are less sensitive to those significant variables. As an exception, the
model with fixed cutoff point shows either larger or smaller marginal effects on different
variables compared with the conventional model, because transforming a portion of “yes”
responses to “no” would not change the nature of the dependent variable.

2.5.3

Spike model
The spike model that estimates the influence of various attributes on the probability of

having a positive WTP is a prior estimation to the conditional willingness to pay. With all the
methods for adjusting preference certainty in WTP, the spike model is used to calculate the
unconditional WTP. Results from the spike probability model (Table 2-6) suggest that the
probability that a respondent had a positive WTP depends endogenously on the level of
environmental improvement in eutrophic lakes and greenhouse gas, as well as the resident’s
concern about global warming, and demographic traits such as income, whether respondents are
Michigan residents and how long they have been living in Michigan.

2.5.4 Welfare effect
Both the conditional and unconditional median WTP for 140 fewer eutrophic lakes and a
GHG emission reduction of 0.4% from the Year 2000 level were calculated for each respondent
following the conventional CV model and the four certainty-adjusted models. The semi-log and
mixed log-log functional forms are used for estimating the conditional WTP to test the
consistency of preference certainty on WTP estimation. The average median WTP across
93

residents and a bootstrapped 95% confidence interval following the two functional forms are
shown in Tables 2-12 and 2-13.
With the mixed log-log function, the median WTP from the symmetric uncertainty model
(SUM) is the highest among all methods--$164 tax payment per year conditional on having a
positive WTP and a $144 unconditional WTP. The conventional random effects model and
polychotomous response (Indifferent) model have the same WTP estimates, which reduce the
conditional and unconditional WTP to $142 and $124 respectively. The two asymmetric models
yield the lowest estimates, i.e., the conditional and unconditional WTP are $73 and $64 in the
asymmetric uncertainty model (ASUM), and are $48 and $42 in the dichotomous response
(Fixed Cutoff) model. The relative changes of WTP with respect to the conventional
dichotomous choice model are consistent with several prior studies (Chang, et al., 2007, Loomis
and Ekstrand, 1998, Shaikh, et al., 2007).
By contrast, the semi-log function generates a median WTP from the conventional
method that is the highest among all methods--$134 per year conditional WTP and $118
unconditional WTP. The SUM reduces the conditional and unconditional WTP to $76 and $67
respectively, while the ASUM method further lowers them to $34 and $30. The polychotomous
response (Indifferent) model and dichotomous response (Fixed Cutoff) model with cutoff point
both generate slightly higher WTP than the SUM and ASUM methods.
Based on the 95% confident intervals for WTP estimates with both functional forms, the
median WTP estimates from the two symmetrically calibrated models are no different from the
conventional model. Due to the symmetric calibration, the probability of voting “yes” is
increased for “no” responses and reduced for “yes” responses. Thus, the total effect of
adjustment on WTP can be positive or negative depending on the magnitude of associated

94

certainty and the original binary choice. It seems the preference certainties associated with “yes”
responses are similar to those associated with “no” responses in this sample, and hence do not
lead to major influence on the median WTP estimates. In addition, the two asymmetrically
calibrated models give median WTP estimates that are lower than those from symmetrically
calibrated models. Given the asymmetric calibration, only the probability of voting associated
with “yes” responses is adjusted downwards, which leads to an under-estimated median WTP.
Thus, the results of bias conform to the analytical expectation. The inconsistency of the influence
from preference uncertainty on WTP estimates between the two functional forms echoes results
from previous of certainty-adjusted WTP estimates, especially in symmetrically calibrated
models (Akter, et al., 2008).
The variations of estimation efficiency among five models are consistent between two
functional forms. The conventional model, which does not incorporate the preference
uncertainty, is clearly the least efficient with a high variability measure. The indifference ordered
probit model and the fixed cutoff model, which reduce variability by 60%-80%, are more
efficient than the conventional model. The SUM and ASUM certainty-adjusted models result in
the highest efficiency levels, which reduce the variability by about 90%. These findings reinforce
the body of literature showing that certainty-adjusted models increase the efficiency (Champ, et
al., 1997, Shaikh, et al., 2007), although other researchers have observed the opposite effect
(Chang, et al., 2007, Loomis and Ekstrand, 1998, Samnaliev, et al., 2006).
Comparing the predicted WTP curve based on the semi-log and mixed log-log functional
forms for conventional dichotomous choice models (Figures 2-6 and 2-7), the WTP shows a
different pattern of responses to environmental improvements. As constrained by the functions,
the WTP estimated with the semi-log function follows a steady, exponentially increasing rate,

95

while the WTP estimated with the mixed log-log function rises sharply at low values of
environmental improvements and then grows slowly at a diminishing rate with little sensitivity to
environmental improvement. However, the predicted WTPs based on both functional forms
share a common range of values from $15 to $45 per person, and the goodness of fit of the two
models does not diff, as shown by the likelihood statistics. As the predicted values and goodness
of fit offer no obvious choice between two functions, the mix log-log function that is
12

theoretically consistent and statistically significant

2.6

would be a better choice.

Conclusion
Over half of the respondents to this stated-preference survey displayed uncertainty about

their willingness to pay for a public program to reduce numbers of eutrophic lakes and to
mitigate greenhouse gas emissions (Figure 2-5). To examine the influence of preference
uncertainty on their stated willingness to pay, this essay compares four calibration methods to
incorporate numerical certainty with the conventional dichotomous-choice model for estimating
WTP. Two functional forms, semi-log and mixed log-log, are evaluated to test the sensitivity of
conditional WTP estimates to different functions. Compared to the conventional probit, the
certainty-adjusted models are more sensitive to underlying determinants of WTP related to the
demographics and recreational experience of respondents. Moreover, these models largely
improve the efficiency of estimation. Comparing the welfare estimates with 95% confident
interval based on two functional forms, both reveal that the median WTP estimated from the
conventional model is not significantly different from the two symmetrically calibrated certaintyadjusted models, although the mixed log-log functional form leads to higher WTP estimates in
12

Wald statistic in the mixed log-log model is significantly higher than the semi-log model with
p-value equal to 0.0006.
96

those models than the semi-log does. The two asymmetrically calibrated certainty-adjusted
models generally have lower WTP than the conventional models. The biased WTP estimates are
expected analytically because the probability of voting “yes” is calibrated downwards. Thus,
there is no concrete evidence that one specific certainty-adjusted model should replace the
conventional model for estimating WTP. The WTP responses predicted from the conventional
dichotomous choice model using two functional forms show a similar range of WTP values and
goodness of fit, although the shapes of the WTP curves differ due to their functional forms. The
mixed log-log function, which embodies the diminishing marginal utility theory, has higher
statistical significance.
In sum, incorporating self-reported certainty in the willingness to pay estimation appears to
improve our understanding of the demand for ecosystem services by revealing more variables
that are influential and providing a range of possible estimates. However, the unbiased
conventional dichotomous choice model still provides a reliable median WTP estimate that
reflects the influence of key variables. For further analysis that combines demand for ecosystem
services with their supply, the mixed log-log function for conditional WTP seems to be a better
choice than the traditional semi-log function due to its theoretical consistency and statistical
significance.

97

Figures and Tables
Probability
Prob (Yes)

C

E (WTP)

Payment ($)

Figure 2-5 Probability of voting “yes” as a representation of underlying WTP
with preference uncertainty

Figure 2-2 Numerical certainty scale used in survey, 2211 Michigan residents, 2009

Figure 2-3 Numerical certainty scale used in Loomis and Ekstrand (1998)

98

Figure 2-4 Binary response percentage in sample, 2211 Michigan residents, 2009

Figure 2-5 Certainty-adjusted response percentage under the Symmetric Uncertainty Model (SUM)
in sample, 2211 Michigan residents, 2009

99

WTP $/person

50
40
30
20
10
0

20

40

60

80

100

Environmental improvements (1 unit=2 cleaned eutrphic lakes
& 0.01% GHG mitigation compared to 2000 level)
Figure 2-6 Median WTP in conventional dichotomous choice model with respect to eutrophic
lake and GHG improvements [mixed log-log function]

WTP $/person

50

40

30

20

10
0

20

40

60

80

100

Environmental improvements (1 unit=2 cleaned eutrphic
lakes & 0.01% GHG mitigation compared to 2000 level)
Figure 2-7 Median WTP in conventional dichotomous choice model with respect to eutrophic
lake and GHG improvements [semi-log function]

100

Table 2-1 Variable description, 2211 Michigan residents, 2009
Variable name

Unit of
Ranges and levels
measure

Definition

Contingent
voting
Vote yes

Vote on program A/B/C with
proposed tax payment
Certainty
How certain with vote on program
A/B/C
No-cost vote
Vote on program if it did not cost
anything
Ecosystem service change
Lake
Eutrophic lakes that would be
reduced if the program were to be
implemented
GHG
Greenhouse gas reduction of the
2000 emission level that would be
achieved if the program were to be
implemented
Cost
Cost
The amount of annual tax increase
that would be used to fund the
program
Version
Farm version
Whether the questionnaire version
is the agricultural-farmer version or
the general land management
version
Perception and attitudes
GW concern
Whether the respondent is
concerned about global warming
(GW)
Demographics
MI years
MI resident
Male
Household num
Age
Farmer
Forester
Env org

Length of continuing to live in MI
Michigan resident
Male respondent
Number of people in the household
Age
Whether work on a farm
Whether work in forests
Belong to environmental
organizations
101

binary

1-yes, 0-no

category

1-very uncertain, …,
10-very certain

binary

1-yes, 0-no

number

0, 70, 140, 200, 400

%

0, 0.2, 0.4, 0.6, 1.2

USD/year 10, 30, 50, 100, 200

NA

0-Land management version,
1-Agricultural-farmer
version

0-Not concerned or
somewhat concerned, 1-Very
category
concerned

category
binary
binary
number
year
binary
binary
binary

1-less than 1 year, 2- 1-5
years, 3- 5-10 years
1-yes, 0-no
1-yes, 0-no

1-yes, 0-no
1-yes, 0-no
1-yes, 0-no

Table 2-1 (cont’d)
Income
Household annual pretax income
Education
Education level

Voter
Registered voter
Recreational experiences
Fishing freq
How often go fishing

1-Never, 2-In some years, 3In most years, 4-Every year
1-Never, 2-In some years, 3category
In most years, 4-Every year
1-Never, 2-In some years, 3category
In most years, 4-Every year
1-Never, 2-In some years, 3category
In most years, 4-Every year

How often go boating

Hiking freq

1-Some high school or less,
2-High school diploma, 3Technical training beyond
category high school, 4-Some college,
5-College degree, 6-Some
graduate work, 7-Graduate
degree
binary
1-yes, 0-no
category

Swimming freq How often go swimming
Boating freq

1000 USD

How often hike

102

Table 2-2 Descriptive statistics of variables
Variable
Definition
Contingent voting
Vote yes
Vote on program A/B/C
How certain with vote on program
Certainty
Vote on program if it did not cost
No-cost vote
anything
The amount of annual tax increase that
Cost
would be used to fund the program
Ecosystem service change
Eutrophic lakes that would be reduced
Lake
if the program were to be implemented
Greenhouse gas reduction of the 2000
GHG
emission level that would be achieved
if the program were to be implemented
Version
Whether the questionnaire version is
Farm version the agricultural-farmer version or the
general land management version
Perception and attitudes
Whether the respondent is very
GW concern
concerned about global warming
The interaction of GW concern and
GW*GHG
GHG reduction level
Demographics
MI years
Length of continuing to live in MI
MI resident
Michigan resident
Male
Gender: male
Household
Number of people in the household
Age
Age of respondent
Farmer
Whether work on a farm
Forester
Whether work in forests
Env org
Belong to environmental organizations
Household annual pretax income
Income
Education
Education level
Voter
Registered voter
Recreational experiences
Fishing freq
How often go fishing
Swimming freq How often go swimming
Boating freq How often go boating
Hiking freq
How often hike

103

Obs Mean Std. Min Max
3396 0.631 0.482
3396 7.889 2.25

0
1

1
10

4125 0.832 0.374

0

1

4125 64.5 62.78

10

200

4125

111.3

0

400

4125 0.527 0.319

0

1.20

1429 0.482 0.500

0

1

1429 0.394 0.489

0

1

4125 0.208 0.326

0

1.20

1429
1429
1429
1429
1429
1429
1429
1429
1429
1429
1429

1
4
0
1
0
1
0
9
13 96.5
0
1
0
1
0
1
5 250
1
7
0
1

1429
1429
1429
1429

169

3.66 0.688
0.990 0.0985
0.659 0.474
2.54 1.37
54.9 15.3
0.0399 0.196
0.0168 0.129
0.0777 0.268
68.3 50.5
4.25 1.74
0.947 0.224
2.20
2.37
2.43
2.24

1.17
1.14
1.11
1.15

1
1
1
1

4
4
4
4

Table 2-3 Dependent variable for probit model with different cutoff certainty levels
Cutoff level
Certainty scale
Yi if answer Yes
Yi if answer No

10
1--9
0

9
10
1

1--8
0

8
9--10
1

0

7

1--7
0

0

8--10
1

1--6
0

7--10
1

0

0

Table 2-4 Dependent variables for ordered probit model
Certainty scale
Yi if answer Yes
Yi if answer No

1

2

3

4

5

6

7

8

9

10

1
0

0.5

Table 2-5 Dependent variables for fractional response models
Symmetric Uncertainty Model
Certainty scale

1

2

3

4

5

6

7

8

9

10

Pr(Yi=1|WTP>0) if answer Yes

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1

Pr(Yi=1|WTP>0) if answer No

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0

Certainty scale

1

2

3

4

5

6

7

8

9

10

Pr(Yi=1|WTP>0) if answer Yes

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1

Asymmetric Uncertainty Model

0

Pr(Yi=1|WTP>0) if answer No

104

Table 2-6 Spike probability model, 1429 Michigan residents, 2009
Regression
coefficient
Coef.
P>z

Variable
Version
Farm version
-0.051
ES change and concern
Lake
0.004 ***
GHG
0.383 **
GW concern
1.271 ***
Demographics
MI years
-0.204
MI resident
0.907
Male
-0.085
Household num -0.014
Age
0.003
Farmer
-0.563
Forester
-0.041
Env org
-0.146
Income
0.004 **
Education
0.005
Voter
0.339
Recreational experiences
Fishing freq
-0.100
Swimming freq -0.003
Boating freq
-0.022
Hiking freq
-0.100
Constant
1.030
/lnsig2u
1.77
sigma_u
2.43
rho
0.85
Number of obs 4125
Number of group 1429
Wald chi2(22) 104.58
Prob > chi2
0
Log likelihood -1350

Marginal Effect
Coef.

P>z

0.760

-0.002

0.713

0.000
0.032
0.000

0.000
0.015
0.019

0.107
0.267
0.648
0.835
0.677
0.195
0.951
0.648
0.032
0.933
0.351

-0.008 *
0.018 ***
-0.004
-0.001
0.000
-0.036
-0.002
-0.007
0.000 **
0.000
0.010

0.067
0.002
0.595
0.793
0.602
0.263
0.940
0.609
0.017
0.915
0.124

0.305
0.976
0.853
0.277
0.338

-0.004
0.000
-0.001
-0.004

0.217
0.970
0.815
0.191

105

*** 0.000
** 0.021
*** 0.000

Table 2-7 Determinants of preference certainty for yes/no responses, 2211 Michigan residents,
2009 (Dependent variable: certainty scale [1-very uncertain; 10- very certain])

Certainty

Ordered probit
for Yes responses
Coef.
P>t

Ordered probit
for No responses
Coef.
P>t

Cost
Cost
Cost square
Ecosystem service change
Lake
GHG
Version
Farm version
Perception and attitudes
GW concern
GW*GHG
Demographics
MI years
MI resident
Male
Household num
Age
Farmer
Forester
Env org
Income
Education
Voter
Recreational experiences
Fishing freq
Swimming freq
Boating freq
Hiking freq
Number of obs
Wald chi2(48)
Prob > chi2
Pseudo R2
Log pseudo likelihood

-0.004
9.03E-06

0.030
0.230

0.003
-1.36E-05

0.114
0.158

0.000
-0.029

0.162
0.759

0.000
-0.065

0.245
0.565

-0.061

0.198

0.030

0.623

0.166
0.364

0.252
0.000

-0.068
-0.037

0.722
0.760

0.097
-0.967
0.006
-0.012
-0.004
0.004
0.625
-0.217
0.000
-0.005
-0.094

**
***

*

0.471
0.050
0.124
0.503
0.005
0.306
0.145
0.000
0.257
0.175
0.081

0.071
0.082
-0.126
0.006
1253
52.1
0.0003
0.0091
-2389.4

**
**
***

***

0.334
0.724
0.769
0.004

-0.024
0.817
0.086
0.013
0.005
-0.122
0.320
0.351
0.001
-0.022
0.194
0.028
0.012
-0.010
0.077
2143
173.07
0
0.0237
-3719.1

106

**

***

**

***

***

*
**
**

0.021
0.001
0.931
0.595
0.072
0.985
0.020
0.039
0.969
0.807
0.401
0.050
0.030
0.001
0.846

Table 2-8 Comparison of coefficient estimates on the probability of voting “yes” to proposed tax payment with and without certainty,
1293 Michigan residents, 2009 [mixed log-log function]
Basic model
SUM
ASUM
Indifferent
Cutoff=7
Ordered probit robust
Model
RE probit
GEE fractional probit GEE fractional probit
RE probit
error
variable
Coef.
P>z
Coef.
P>z
Coef.
P>z
Coef.
P>z
Coef.
P>z
Version
Farm version
-0.0564
0.813
-0.0176
0.741
-0.0157
0.793
-0.0499
0.227
-0.246
0.304
Cost
Ln(cost)
-1.35 *** 0.000
-0.274 *** 0.000
-0.307 *** 0.000
-0.292 *** 0.000
-1.09 *** 0.000
ES change and concern
Ln(Lake)
0.0303 *** 0.000
0.00714 *** 0.000
0.00801 *** 0.000
0.0105 *** 0.000
0.0260 *** 0.000
Ln(GHG)
-0.00706
0.444 -0.0000870
0.962 -0.000879
0.680 0.000123
0.973
0.00604
0.499
GW* Ln(GHG)
0.0436 *** 0.001
0.00838 ** 0.011
0.0101 *** 0.006
0.0124 ** 0.030
0.0179
0.163
GW
1.89 *** 0.000
0.447 *** 0.000
0.496 *** 0.000
0.490 *** 0.000
2.09 *** 0.000
Demographics
MI years
-0.0813
0.649
-0.0311
0.438
-0.0181
0.692
-0.0401
0.186
-0.0695
0.695
MI resident
1.62
0.199
0.591 ** 0.015
0.529 ** 0.043
0.649 *** 0.000
3.10 *** 0.007
Male
-0.194
0.476
-0.0360
0.550
-0.0365
0.590 -0.00392
0.932
0.273
0.305
Household num
-0.0254
0.803
-0.00215
0.927
-0.00247
0.925
0.0137
0.446
0.0780
0.446
Age
0.0301 *** 0.001
0.00683 *** 0.001
0.00714 *** 0.002
0.00906 *** 0.000
0.0328 *** 0.000
Farmer
-0.579
0.374
-0.122
0.368
-0.144
0.350
-0.105
0.348
-0.537
0.399
Forester
0.692
0.473
0.134
0.613
0.200
0.488
-0.098
0.603
0.439
0.619
Env org
0.512
0.252
0.184 * 0.083
0.182
0.118
0.262 *** 0.004
1.076 ** 0.015
Income
0.0146 *** 0.000
0.00296 *** 0.000
0.00337 *** 0.000
0.00276 *** 0.000
0.0102 *** 0.000
Education
0.182 ** 0.023
0.0305 * 0.095
0.0377 * 0.068
0.0449 *** 0.001
0.190 ** 0.018
Voter
1.71 *** 0.002
0.372 *** 0.005
0.416 *** 0.007
0.386 *** 0.000
1.49 *** 0.005

107

Table 2-8 (cont’d)
Recreational experiences
Fishing freq
0.211
Swimming freq
0.102
Boating freq
0.121
Hiking freq
0.152
Constant (cut 1)
-1.84
Cut point 2
/lnsig2u
2.54
sigma_u
3.57
Rho
0.927
3396
No. of obs
1293
No. of group
242
Wald chi2(22)
0.00
Prob > chi2
-1367
Log-likelihood

0.132
0.520
0.470
0.262
0.255

0.028
0.015
0.048
0.042
-0.67 *

0.379
0.674
0.206
0.155
0.052

0.041
0.028
0.036
0.050
-0.85 **

3396
1293
285
0

3396
1293
268
0

108

0.245
0.482
0.400
0.128
0.026

0.029
0.006
0.055 **
0.048 **
0.46
1.20

3396
533
0
-3238

0.232
0.820
0.048
0.036

0.133
0.178
0.124
0.247 *
-6.23 ***
2.51
3.52
0.925
3396
1293
270
0
-1471

0.337
0.251
0.453
0.063
0.000

Table 2-9 Comparison of coefficient estimates on the probability of voting “yes” to proposed tax payment with and without certainty,
1293 Michigan residents, 2009 [semi-log function]
Basic model
SUM
ASUM
Indifferent
Cutoff=7
Ordered probit robust
Model
RE probit
GEE fractional probit GEE fractional probit
RE probit
error
variable
Coef.
P>z
Coef.
P>z
Coef.
P>z
Coef.
P>z
Coef.
P>z
Version
Farm version
-0.0643
0.790
-0.0240
0.654
-0.0233
0.698
-0.0481
0.241
-0.263
0.291
Cost
Ln(cost)
-1.45 *** 0.000
-0.289 *** 0.000
-0.321 *** 0.000
-0.311 *** 0.000
-1.20 *** 0.000
ES change and concern
Lake
0.00375 *** 0.000
0.00088 *** 0.000
0.00093 *** 0.000 0.000959 *** 0.000
0.00412 *** 0.000
GHG
-0.220
0.403
-0.0154
0.778
-0.0429
0.495
0.0294
0.723
-0.0129
0.961
GW*GHG
0.628 * 0.078
0.111
0.180
0.135
0.139
0.118
0.385
0.246
0.466
GW
1.50 *** 0.000
0.369 *** 0.000
0.401 *** 0.000
0.397 *** 0.000
2.02 *** 0.000
Demographics
MI years
-0.0893
0.623
-0.0317
0.434
-0.0190
0.679
-0.0418
0.169
-0.0856
0.643
MI resident
1.67
0.193
0.591 ** 0.016
0.531 ** 0.044
0.651 *** 0.001
3.23 *** 0.007
Male
-0.190
0.494
-0.0344
0.569
-0.0330
0.628 -0.00209
0.964
0.291
0.295
Household num
-0.0239
0.817
-0.00323
0.891
-0.00335
0.899
0.0131
0.468
0.0774
0.472
Age
0.0302 *** 0.002
0.00664 *** 0.001
0.00696 *** 0.003
0.00892 *** 0.000
0.0336 *** 0.000
Farmer
-0.657
0.317
-0.135
0.315
-0.162
0.294
-0.122
0.279
-0.614
0.346
Forester
0.788
0.403
0.167
0.523
0.233
0.410
-0.069
0.712
0.529
0.550
Env org
0.529
0.243
0.184 * 0.081
0.181
0.117
0.255 *** 0.004
1.12 ** 0.014
Income
0.0148 *** 0.000
0.00297 *** 0.000
0.00336 *** 0.000
0.00272 *** 0.000
0.0107 *** 0.000
Education
0.185 ** 0.023
0.0299
0.103
0.0373 * 0.073
0.0445 *** 0.001
0.192 ** 0.023
Voter
1.77 *** 0.002
0.372 *** 0.005
0.414 *** 0.007
0.391 *** 0.000
1.57 *** 0.005

109

Table 2-9 (cont’d)
Recreational experiences
Fishing freq
0.207
Swimming freq
0.0891
Boating freq
0.141
Hiking freq
0.150
Constant (cut 1)
-2.05
Cut point 2
/lnsig2u
2.60
sigma_u
3.66
Rho
0.93
No. of obs
3396
No. of group
1293
Wald chi2(22)
234
Prob > chi2
0
Log-likelihood
-1367

0.143
0.581
0.405
0.274
0.218

0.0245
0.0132
0.0509
0.0417
-0.717 **

0.442
0.712
0.178
0.161
0.040

0.0372
0.0262
0.0389
0.0502
-0.885 **

3396
1293
299
0

3396
1293
274
0

110

0.295
0.515
0.365
0.130
0.022

0.0257
0.00234
0.0580 **
0.0506 **
0.538
1.27

3396
530
0
-3239

0.294
0.930
0.036
0.027

0.125
0.170
0.147
0.259 *
-6.80 ***
2.61
3.68
0.93
3396
1293
273
0
-1461

0.387
0.295
0.395
0.062
0.000

Table 2-10 Comparison of marginal effects on the probability of voting “yes” to proposed tax payment with and without certainty,
1237 Michigan residents, 2009 [mixed log-log function]
Basic model
SUM
ASUM
Indifference
Cutoff7
Ordered probit robust
Model
RE probit
GEE fractional probit GEE fractional probit
RE probit
error
variable
Coef.
P>z
Coef.
P>z
Coef.
P>z
Coef.
P>z
Coef.
P>z
Version
Farm version
-0.00859
0.767 -0.00623
0.677
-0.00557
0.741
0.0146
0.133
-0.0440
0.190
Cost
Ln(cost)
-0.206 *** 0.000
-0.097 *** 0.000
-0.109 *** 0.000
0.0856 *** 0.000
-0.193 *** 0.000
ES change and concern
Ln(Lake)
0.00461 *** 0.000
0.00252 *** 0.000
0.00284 *** 0.000
-0.00309 *** 0.000
0.00462 *** 0.000
Ln(GHG)
0.000
1.000
0.000
1.000
0.000
1.000
0.000
1.000
0.000
1.000
GW* Ln(GHG)
0.000
1.000
0.000
1.000
0.000
1.000
0.000
1.000
0.000
1.000
GW
0.211 *** 0.000
0.146 *** 0.000
0.165 *** 0.000
-0.122 *** 0.000
0.342 *** 0.000
Demographics
MI years
-0.0124
0.566
-0.0110
0.328
-0.00640
0.617
0.0118 *
0.096
-0.0123
0.622
MI resident
0.191 ** 0.017
0.186 *** 0.000
0.175 *** 0.004
-0.151 *** 0.000
0.446 *** 0.000
Male
-0.0301
0.378
-0.0128
0.453
-0.0130
0.498
0.00115
0.915
0.0488
0.198
Household num -0.00388
0.753 -0.000758
0.908 -0.000874
0.906
-0.00402
0.337
0.0138
0.338
Age
0.00458 *** 0.000
0.00241 *** 0.000
0.00253 *** 0.000
-0.00266 *** 0.000
0.00583 *** 0.000
Farmer
-0.0926
0.277
-0.0435
0.261
-0.0515
0.239
0.0318
0.249
-0.0931
0.272
Forester
0.0965
0.311
0.0466
0.515
0.0696
0.371
0.0295
0.523
0.0784
0.531
Env org
0.0734
0.122
0.0634 ** 0.024
0.0635 ** 0.044
-0.0707 *** 0.000
0.190 *** 0.001
Income
0.00223
0.000
0.00104
0.000
0.00119
0.000 -0.000810
0.000
0.00181
0.000
Education
0.0276 *** 0.004
0.0107 ** 0.035
0.0133 ** 0.021
-0.0132 *** 0.000
0.0338 *** 0.003
Voter
0.198 *** 0.000
0.123 *** 0.000
0.140 *** 0.000
-0.100 *** 0.000
0.257 *** 0.000

111

Table 2-10 (cont’d)
Recreational experiences
Fishing freq
0.0322 *
Swimming freq 0.0155
Boating freq
0.0184
Hiking freq
0.0231

0.056
0.417
0.360
0.156

0.00989
0.00529
0.0168
0.0149 *

0.267
0.596
0.110
0.073

0.0146
0.0100
0.0127
0.0178 *

112

0.142
0.375
0.288
0.055

-0.00860
-0.00178
-0.0160 **
-0.0141 ***

0.131
0.774
0.013
0.008

0.0237
0.0316
0.0220
0.0438 **

0.225
0.147
0.344
0.018

Table 2-11 Comparison of marginal effects on the probability of voting “yes” to proposed tax payment with and without certainty,
1237 Michigan residents, 2009 [semi-log function]
Basic model
SUM
ASUM
Indifference
Cutoff7
Ordered probit robust
Model
RE probit
GEE fractional probit GEE fractional probit
RE probit
error
variable
Coef.
P>z
Coef.
P>z
Coef.
P>z
Coef.
P>z
Coef.
P>z
Version
Farm version
-0.00939
0.740 -0.00844
0.573
-0.00823
0.626
-0.0172
0.139
-0.0449
0.180
Cost
Ln(cost)
-0.211 *** 0.000
-0.102 *** 0.000
-0.114 *** 0.000
-0.1113 *** 0.000
-0.204 *** 0.000
ES change and concern
Lake
0.000549 *** 0.000 0.000311 *** 0.000
0.000327 *** 0.000
0.000344 *** 0.000
0.000700 *** 0.000
GHG
-0.0322
0.291 -0.00542
0.722
-0.0152
0.390
0.0105
0.655
-0.00219
0.951
GW*GHG
0.0918 ** 0.025
0.0391 * 0.091
0.0476 * 0.062
0.0424
0.274
0.0418
0.359
GW
0.175 *** 0.000
0.122 *** 0.000
0.135 *** 0.000
0.140 *** 0.000
0.319 *** 0.000
Demographics
MI years
-0.0131
0.535
-0.0111
0.323
-0.00672
0.602
-0.0150 *
0.082
-0.0145
0.559
MI resident
0.188 ** 0.016
0.185 *** 0.000
0.175 *** 0.005
0.223 *** 0.000
0.441 *** 0.000
Male
-0.0283
0.398
-0.0122
0.474
-0.0117
0.542 -0.000748
0.954
0.0496
0.188
Household num -0.00350
0.771 -0.00114
0.862
-0.00118
0.873
0.00471
0.360
0.0131
0.364
Age
0.00442 *** 0.000
0.00234 *** 0.000
0.00246 *** 0.000
0.00320 *** 0.000
0.00571 *** 0.000
Farmer
-0.102
0.224
-0.0483
0.210
-0.0576
0.187
-0.0436
0.169
-0.102
0.220
Forester
0.104
0.229
0.0573
0.408
0.0805
0.284
-0.0247
0.641
0.0901
0.449
Env org
0.0724
0.114
0.0631 ** 0.023
0.0630 ** 0.044
0.0910 *** 0.000
0.189 *** 0.001
Income
0.00216
0.000
0.00104
0.000
0.00119
0.000
0.000974
0.000
0.00181
0.000
Education
0.0270 *** 0.004
0.0105 ** 0.040
0.0132 ** 0.024
0.0160 *** 0.000
0.0326 *** 0.004
Voter
0.196 *** 0.000
0.123 *** 0.000
0.140 *** 0.000
0.138 *** 0.000
0.257 *** 0.000

113

Table 2-11 (cont’d)
Recreational experiences
Fishing freq
0.0303 *
Swimming freq 0.0130
Boating freq
0.0206
Hiking freq
0.0219

0.064
0.487
0.291
0.167

0.00863
0.00463
0.0179 *
0.0147 *

0.332
0.642
0.089
0.077

0.0131
0.0092
0.0137
0.0177 *

114

0.186
0.412
0.253
0.056

0.00921
0.000839
0.0208 ***
0.0181 ***

0.185
0.912
0.008
0.005

0.0212
0.0289
0.0249
0.0440 **

0.275
0.186
0.284
0.017

Table 2-12 Comparison of median WTP (in U.S. dollars) and estimation efficiency [mixed
log-log function]
Method
Basic model
SUM
ASUM
Not sure Cutoff7
GEE
GEE
Ordered
Econometric Model RE probit fractional fractional
RE probit
probit
probit
probit
Conditional WTP
Median WTP
142
164
73
142
48
95% lower CI
-365
55.1
27.8
-91
2
95% upper CI
648
273
119
375
94
efficiency
7.15
1.33
1.24
3.29
1.93
Mean spike Prob
0.876
0.876
0.876
0.876
0.876
Unconditional WTP
Median WTP
124
144
64
124
42
95% lower CI
-320
48
24.4
-80
1
95% upper CI
568
239
104
329
83
efficiency
7.15
1.33
1.24
3.29
1.93
*Notes:
• Median WTP is calculated instead of mean due to the fat tail in the mixed log-log
functional form of WTP.
• Only variables that are significant at 90% level are included in the WTP calculation.
• 95% confidence interval is obtained by bootstrapping with 200 replications.
• Efficiency is calculated as (CIupper–CIlower) / Median (WTP). A lower value indicates
higher efficiency.
• The 18.6% protest rate of nonresponse is not factored into the results

115

Table 2-13 Comparison of median WTP (in U.S. dollars) and estimation efficiency [semi-log
function]
Method
Basic model
SUM
ASUM
Not sure Cutoff7
GEE
GEE
Ordered
Econometric Model RE probit fractional fractional
RE probit
probit
probit
probit
Conditional WTP
134
76
34
98
40
Median WTP
-867
16
16
-29
1
95% lower CI
1135
136
52
225
79
95% upper CI
14.9
1.57
1.04
2.59
1.96
efficiency
Mean spike Prob
0.876
0.876
0.876
0.876
0.876
Unconditional WTP
Median WTP
118
67
30.1
86
35
95% lower CI
-760
14
14
-25
1
95% upper CI
995
119
46
197
70
efficiency
14.9
1.57
1.04
2.59
1.96
*Notes:
• Median WTP is calculated instead of mean due to the fat tail in the semi-log functional
form of WTP .
• Only variables that are significant at 90% level are included in the WTP calculation.
• 95% confidence interval is obtained by bootstrapping with 200 replications.
• Efficiency is calculated as (CIupper–CIlower) / Median (WTP). A lower value indicates
higher efficiency.
• The 18.6% protest rate of nonresponse is not factored into the results

116

REFERENCES

117

REFERENCES

Akter, S., J. Bennett, and S. Akhter. 2008. "Preference uncertainty in contingent valuation."
Ecological Economics 67(3):345-351.
Alberini, A., K. Boyle, and M. Welsh. 2003. "Analysis of contingent valuation data with
multiple bids and response options allowing respondents to express uncertainty." Journal
of Environmental Economics and Management 45(1):40-62.
Balcombe, K., and I. Fraser. 2009. "Dichotomous-choice contingent valuation with "don’t know"
responses and misreporting." Journal of Applied Econometrics 24(7):1137-1152.
Champ, P.A., and R.C. Bishop. 2001. "Donation payment mechanisms and contingent valuation:
An empirical study of hypothetical bias." Environmental and Resource Economics
19(4):383-402.
Champ, P.A., R.C. Bishop, T.C. Brown, and D.W. McCollum. 1997. "Using donation
mechanisms to value nonuse benefits from public goods." Journal of Environmental
Economics and Management 33(2):151-162.
Chang, J.I., S.H. Yoo, and S.J. Kwak. 2007. "An investigation of preference uncertainty in the
contingent valuation study." Applied Economics Letters 14(9):691 - 695.
Chen, H. 2010. "Ecosystem services from low input cropping systems and public's willingness to
pay for them." M.S. Thesis, Michigan State University, Department of Agricultural, Food
and Resource Economics. http://www.aec.msu.edu/theses/fulltext/chen_ms.pdf
Ethier, R.G., G.L. Poe, W.D. Schulze, and J. Clark. 2000. "A comparison of hypothetical phone
and mail contingent valuation responses for green-pricing electricity programs." Land
Economics 76(1):54-67.
Fenichel, E., F. Lupi, J. Hoehn, and M. Kaplowitz (2006) Split-sample tests of" don't know" and"
indifferent" responses in an attribute based choice model, American Agricultural
Economics Association (New Name 2008: Agricultural and Applied Economics
Association).
Flores, N.E. (2003) Conceptual framework for nonmarket valuation, ed. P. Champ,K. Boyle,
and T. Brown, A primer on nonmarket valuation. Boston, MA, Kluwer Academic
Publishers.
Haener, M., and W. Adamowicz. 1998. "Analysis of "don't know" response to referendum
contingent valuation questions." Agricultural and Resource Economics Review 27(2).
118

Ichoku, H., W. Fonta, and A. Kedir. 2009. "Measuring individuals’ valuation distributions using
a stochastic payment card approach: Application to solid waste management in nigeria."
Environment, Development and Sustainability 11(3):509-521.
Johannesson, M., B. Liljas, and P. Johansson. 1998. "An experimental comparison of
dichotomous choice contingent valuation questions and real purchase decisions." Applied
Economics 30(5):643-647.
Krosnick, J.A., A.L. Holbrook, M.K. Berent, R.T. Carson, W. Michael Hanemann, R.J. Kopp, R.
Cameron Mitchell, S. Presser, P.A. Ruud, V. Kerry Smith, W.R. Moody, M.C. Green,
and M. Conaway. 2002. "The impact of "no opinion" response options on data quality:
Non-attitude reduction or an invitation to satisfice?" Public Opinion Quarterly 66(3):371403.
Li, C.-Z., and L. Mattsson. 1995. "Discrete choice under preference uncertainty: An improved
structural model for contingent valuation." Journal of Environmental Economics and
Management 28(2):256-269.
List, J., and C. Gallet. 2001. "What experimental protocol influence disparities between actual
and hypothetical stated values?" Environmental and Resource Economics 20(3):241-254.
Loomis, J., and E. Ekstrand. 1998. "Alternative approaches for incorporating respondent
uncertainty when estimating willingness to pay: The case of the mexican spotted owl."
Ecological Economics 27(1):29-41.
Lundhede, T., S. Olsen, J. Jacobsen, and B. Thorsen. 2009. "Handling respondent uncertainty in
choice experiments: Evaluating recoding approaches against explicit modelling of
uncertainty." Journal of Choice Modelling 2(2):118.
Marshall, A. (2009) Graduations of consumers' demands, Principles of economics, 8th Edition.
New York, NY, Cosimo Classics, pp. 78-85.
Moore, R., R.C. Bishop, B. Provencher, and P.A. Champ. 2010. "Accounting for respondent
uncertainty to improve willingness-to-pay estimates." Canadian Journal of Agricultural
Economics 58(3):381-401.
Poe, G.L., J.E. Clark, D. Rondeau, and W.D. Schulze. 2002. "Provision point mechanisms and
field validity tests of contingent valuation." Environmental and Resource Economics
23(1):105-131.
Samnaliev, M., T.H. Stevens, and T. More. 2006. "A comparison of alternative certainty
calibration techniques in contingent valuation." Ecological Economics 57(3):507-519.
Shaikh, S.L., L. Sun, and G. Cornelis van Kooten. 2007. "Treating respondent uncertainty in
contingent valuation: A comparison of empirical treatments." Ecological Economics
62(1):115-125.
119

Sun, L., and G. van Kooten. 2009. "Comparing fuzzy and probabilistic approaches to preference
uncertainty in non-market valuation." Environmental and Resource Economics
42(4):471-489.
van Kooten, G., E. Krcmar, and E. Bulte. 2001. "Preference uncertainty in non-market valuation:
A fuzzy approach." American Journal of Agricultural Economics 83(3):487-500.
Vossler, C.A., J. Kerkvliet, S. Polasky, and O. Gainutdinova. 2003. "Externally validating
contingent valuation: An open-space survey and referendum in Corvallis, Oregon."
Journal of Economic Behavior & Organization 51(2):261-277.
Wang, H. 1997. "Treatment of "don't-know" responses in contingent valuation surveys: A
random valuation model." Journal of Environmental Economics and Management
32(2):219-232.
Wang, H., and D. Whittington. 2005. "Measuring individuals' valuation distributions using a
stochastic payment card approach." Ecological Economics 55(2):143-154.
Whitehead, J.C., J.-C. Huang, G.C. Blomquist, and R.C. Ready. 1998. "Construct validity of
dichotomous and polychotomous choice contingent valuation questions." Environmental
and Resource Economics 11(1):107-116.
Wooldridge, J. 2010. Econometric Analysis of Cross Section and Panel Data. 2nd ed.
Cambridge, MA: The MIT Press.

120

ESSAY 3: AGGREGATE SUPPLY AND DEMAND FOR ECOSYSTEM SERVICES
FROM CROPLAND IN MICHIGAN AND POLICY SIMULATION

3.1

Introduction
The two previous essays have estimated supply and demand for ecosystem services (ES)

from croplands. On one hand, farmers showed interest in providing ecosystem services if paid.
On the other hand, Michigan residents cared about the environmental improvements from land
management practices and were willing to pay for them. The stated-preference estimates of ES
demand and supply from the previous essays can potentially be integrated to inform the design of
economically efficient Payment-for-Environmental-Services (PES) programs. This essay
explores two key policy questions: First, does public willingness to pay for ecosystem services
exceed the required payment by service providers? Second, could one design an efficient
payment system for ecosystem services from agriculture?
The market equilibrium for different commodities has been investigated in a large
number of studies of marketed ecosystem services from agriculture, such as grain and livestock
(Balagtas and Kim, 2007, Jayne, et al., 2008, Willett and French, 1991). These studies assumed
that market prices are determined by a clearing process that equilibrates supply and demand,
sometimes with quantity rationing on one or both sides due to trade and storage. A few previous
studies have combined the benefit and cost estimates from contingent valuation to examine the
potential demand and supply of natural habitat preservation (Amigues, et al., 2002, Thomas and
Blakemore, 2007) and farmland preservation programs (Welsch, et al., 2005). However, to my
knowledge, the aggregate supply and demand of nonmarket ecosystem services from working-

121

land farming practices has not been studied. Three potential challenges might have prevented
progress in this area.
First, the way that ES are supplied by producers is not equivalent to the way that they are
experienced by consumers. In this case, the residents pay for the final environmental
improvements in lake water quality and global warming. Although farmers produce these two
ecosystem services jointly with marketed products, what they are really paid for is the land
enrolled in PES programs that guarantees a set of conservation practices. Moreover, even if the
quantitative relationship between a set of land management practices and subsequent
environmental improvements can be established, a farmer’s land enrollment in PES programs
does not necessarily lead to real change in the environment, as they may have already adopted
the required practices on lands enrolled. The extra environmental services that would have not
been produced without the PES are commonly referred to as “additional”. The establishment of
a baseline and the verification of additionality is a crucial issue in PES programs and ecosystem
markets for land conservation, water quality, wetland mitigation banking, and carbon credits
(Wunder, 2005). Under the hypothetical PES programs analyzed in Essay 1, the proposed
practices and farmers’ previously adopted practices need to be compared to identify those
practices that offer additional ES.
The second challenge to combining supply and demand estimates of ES from working
land is the jointness of production. On the supply side, one practice may produce multiple ES
while one environmental improvement may be triggered by multiple practices. For example,
adding cover crops to a corn-soybean rotation leads to less soil erosion and N2O volatilization,
which then reduce eutrophic lakes and greenhouse gas (GHG) emission respectively. GHG
emissions may also be mitigated by planting cover crops, adopting the Pre-Sidedress Nitrate Test

122

(PSNT) and applying reduced fertilizer. The weighted aggregation of multiple ecosystem
services is being addressed in the U.S. Department of Agriculture’s Conservation Reserve
Program (CRP) using an “environmental benefits index,” which is based on weights given to
different environmental service components and regional population density (Antle, 2007).
However, further linkage between joint production and consumption is rare.
The third potential challenge is that even if functions for the supply and demand for ES
could be developed, the measurement of actual ES outcomes is prohibitively costly due to the
non-point source nature of most ES. Yet measured ES outcomes are needed to derive a truly
optimal payment for ES. The optimal payment levels can be derived so that they maximize
economic welfare, where economic welfare is defined narrowly as the difference between
resident WTP for environmental improvements due to working land conservation programs and
farmer WTA to enroll in these programs. As payment is associated with farming practices
instead of ecosystem service outcomes, and because PES programs typically have uncertainty
and incomplete information, the payment can be characterized as second-best socially optimal
condition (Lipsey and Lancaster, 1956).
Given these challenges, this essay aims to analyze the socially optimal conditions for the
provision of two major ecosystem services from a set of cropland management practices by
matching the (marginal) benefit from consumption and cost of production. Taking advantage of
unique, coupled datasets of stated preferences, this essay combines a supply-side cost function of
farmers’ willingness to adopt practices that provide increased ecosystem services with a demandside social benefit function of residents’ willingness to pay (WTP) for these ES. The
additionality from enrollment in PES programs and the linkage from joint farming practices to

123

joint environmental outcomes are also examined to achieve the aggregation. Variations of the
second-best optimal conditions under different policy scenarios are discussed as well.

3.2
3.2.1

Conceptual model
Input-output system for ecosystem services
In general, the hypothetical PES programs presented to farmers in the 2008 survey of

Michigan corn and soybean farmers are multi-input, multi-output systems. The inputs related to
ES production include seed for wheat and cover crops, mineral fertilizer, pesticides, banded
spray application, pre-sidedress nitrate soil test (PSNT), labor, and chisel plowing. The outputs
are the market goods corn, soybean and wheat, and non-market ecosystem services, e.g.,
enhancing soil fertility by adopting cover crops, improving lake water quality by reducing soil
erosion and phosphorus runoff, and mitigating global warming by reducing nitrogen leaching
and carbon dioxide emission. Among these, the final ES outputs consumed by residents and
evaluated in this paper are lake quality reduction and GHG mitigation. The relationships between
outputs and inputs are also shown in Figure 3-1.

3.2.2

Utility maximization models for ES supply and demand
Both consumers and producers are assumed to maximize their utility. Farmers as

producers not only benefit from income generation but also from ecosystem services provided
from their own land. Thus, the expected level of ES, which influences their production decisions,
needs to be incorporated in their utility. The conceptual model of farmer behavior is a
constrained utility maximization model. Farmers are assumed to maximize utility by choosing
the level of market goods (Z) and non-market environmental services (ES), which are co-

124

produced by farming activities. The budget constraint limits the cost of consumption to the sum
of profit from farm production (π) and nonfarm income (NFI). Farm profit is earned from selling
agricultural products (Y) at price ry minus variable cost (rxX) and fixed cost (FC). Output Y is a
function of inputs X and FC. Variable cost refers to material and hired labor associated with the
level of production, while fixed cost in this study refers to predetermined resources, including
family labor (L), capital (K), land area (A), biophysical conditions (B) and information (I)
available to farmers. Environmental services (ES), which are produced jointly with market goods
(Y) using variable and fixed inputs, may also affect the magnitude and timing of variable input
(X) employment in turn (Zhang, et al., 2007). F represents farmer traits that condition the
production function and hence condition the effects of PES offers.

(

Max U F Z F , ES | F
Z , ES

s.t.

)

PZ Z F ≤ π + NFI

π = ryY ( X , FC ) − rx X ( ES ) − FC ( L, K , A, B, I )
ES = f ( X , FC )

(3.3)

(3.4)
(3.5)
(3.6)

Enrollment in a PES program could change a farmer’s maximized utility by requiring changed
land management practice accompanied by receipt of a payment. Farmer participation decision
in a PES program depends on the change in utility. This change can be measured monetarily by
willingness to accept (WTA) payment, which is the minimum payment that the farm household
would require to adopt or maintain specified farming practices. WTA is represented as the change
in expenditure levels e of the farm household in response to change in the level of environmental
0

1

services produced from ES to ES at the maximized utility level (Equation 3.7).

125

WTA = e( r , ES1, U 0 | F ) − e(r , ES 0 , U 0 | F )

(3.7)

In this equation, the expenditure function e (r, ES, U0), represents the minimum amount of
1

0

income that is needed to produce a fixed change in environmental services ΔES= ES -ES , while
maintaining utility at its maximized level U0 (Equation 3.8). The input and output prices are
represented by r for simplicity. Farmer total spending on production is likely to increase with
adoption of new practices that increases output.
e(r , ES , U 0 ) = Min[ PZ Z − π (r , ES ) | U ( Z , ES ) ≥ U 0 ]

(3.8)

The WTA can be measured as a function of those characteristics in the expenditure function
(Equation 3.9). WTA represents farmer’s cost associated with land enrollment in a PES
program, which requires a bundle of farming practices and leads to improvements in ecosystem
services.

(

WTA = f F PZ , r , ES 1 ( AE ) , ES 0 ( AE ) ,U 0 | F

)

(3.9)

The supply function of land in PES program can be written as the marginal WTA, i.e. the
additional PES payment required per acre enrolled (PA), in response to land enrollment AE, which
is a specified set of inputs and farming practices with an associated bundle of expected outputs.
PA =

(

ΔWTA
= g F PZ , r , ES1, ES 0 , U 0 | F
ΔAE

)

(3.10)

Residents are also assumed to maximize utility, which depends on a bundle of market
R

goods Z , the level of environmental improvements, ΔES, and is conditioned on resident-specific
characteristics, R, such as age, education, gender and voter registration. Residents choose the
level of market goods to maximize utility subject to a budget constraint that the expenditure
cannot exceed income y, given price vector Pz.
126

(

MaxU R Z R , ES (lake, GHG) | R
Z

)

(3.11)

R
s.t. PZ Z ≤ y and ES ≤ ES 0

(3.12)

The indirect utility function V measures the maximized utility at the optimal level of the market
good bundle.

(

V ( PZ , ES , y | R ) = U R* Z R* , ES | R

)

(3.13)

Residents’ WTP for nonmarket ES is derived as the monetary equivalent change in maximized
utility associated with an increase in non-marketed ES consumption as shown in Equation 3.14.
0

1

With a change in ecosystem services from ES to ES , such as higher level of lake water
pollution or greenhouse gas emission, the individual would be willing to give up a certain
1

amount of income, namely their WTP, to maintain their optimized utility V to the status quo
0

level V .

(

)

(

V 0 PZ , ES 0 , y | R = V 1 PZ , ES1, y − WTP | R

)

(3.14)

The WTP can be solved as a function of those characteristics in the indirect utility function
(Equation 3.15). WTP represents the benefit or utility that residents obtain from improvements in
ecosystem services, and thus is a measure of resident welfare.

(

WTP = f R PZ , ΔES ( ES 0 , ES1 ), y | R

)

(3.15)

For the demand curve, the payment for ES can be written as a function of price for normal good,
ecosystem services and household income conditioned on resident-specific characteristics.

PES =

ΔWTP
= g R ( PZ , ES , y | R)
ΔES
127

(3.16)

A critical challenge in the current instance is that ES are experienced very differently by
consumers than they are by producers. Making the linkage is discussed in section 3.3.2 below.
In principle, the first-best optimal condition is achieved when the economic surplus from
the supply and demand of final ecosystem services is maximized with certainty and complete
information. However, the economic surplus in this study is defined as the difference between
the sum of individual residents’ WTP for environmental improvement and farmers’ total WTA
for adopting practices that lead to enhanced ES. Because this involves payment prior to
realization of ES outcomes, only the second-best optimal condition (referred as “economic
optimum” hereafter) can be reached. Since the goods to be valued are different on the supply and
demand sides, i.e., land enrollment AE for farmers and environmental improvement ES for
residents, a critical step is to link farming practices to predicted ES outcomes. In the following
sections, the WTP and WTA are estimated empirically based on the supply function for land
managed with more sustainable cropping systems and the WTP function derived in two previous
essays using coupled stated preference datasets from Michigan. The biophysical linkage between
farming practices and predicted environmental outcomes are also derived.

3.3

Data and tools

3.3.1

Survey data
The data for supply side analysis of farmer’s willingness to enroll land in PES program

was collected from a mail survey of 3000 Michigan corn and soybean farmers (56% response
rate) in 2008. Each respondent was presented with four hypothetical cropping systems that
provide sequentially increased levels of ecosystem services with increasing management
requirements. For each cropping system, respondents were offered a specific payment if they
128

would adopt the system for a period of five years, and they were asked how many acres they
would enroll in such a program. Information related to farmers’ previous farming practices,
attitudes on ecosystem services, and demographics were also collected from the survey (Jolejole,
2009).
The data for demand side analysis of resident willingness to pay for two types of
environmental improvements was collected from a mail survey of 6000 Michigan residents (40%
response rate) in year 2009. The survey provided information about eutrophication of lakes and
global warming, how residents would be affected and how land management practices would
improve these two ES. The survey elicited resident attitudes on various environmental issues and
details about demographic status (Chen, 2010). Then each respondent was asked to vote on
different tax payments for three independent land stewardship programs, which provide different
GHG and eutrophic lake reductions from changes in land management practices.

3.3.2

Ecosystem services from farming practice
Four hypothetical cropping systems in the farmer survey provided sequence of cropping

practices linked to environmental service levels. Requirements on cover crop, corn-soybeanwheat rotation, and band fertilizer application were sequentially added to the conventional cornsoybean rotation system in Systems A-D (Table 1-1). Based on agro-ecological research, five
major environmental improvements are generated from the four hypothetical cropping systems
as compared to a conventional corn-soybean system. The improvements include soil fertility
(Reganold, et al., 1987), surface and ground water quality improvement (Correll, 1998, Poudel,
et al., 2001), global warming mitigation (Lal, et al., 2004, McSwiney, et al., 2010), reductions in
air pollution and health risk (Glotfelty, et al., 1987, van den Berg, et al., 1999) (Table 1-2).
129

Among these outcomes, the benefit from lake water quality improvement and global warming
mitigation are evaluated by the residents on the demand side, because the physical levels of these
two environmental outcomes are significantly influenced by improvement in farming practices
but the monetary values of the influence are absent in the literature (Chen, 2010). The farming
practices required by each of the four cropping systems and their relations to the two major
environmental improvements can be seen in Table 3-1.

•

Lake eutrophication
Eutrophic lakes with excessive plant growth and algae bloom have a great impact on

water-related recreational activities and on possible health risk. Excessive concentration of
phosphorus is the most common cause of eutrophication in freshwater lakes, and phosphorus
from fertilizer runoff has a major influence (Carpenter, et al., 1998). Since the fertilizer runoff is
carried by phosphorus-rich topsoil in most cases (Carpenter, et al., 1998, Correll, 1998, Poudel,
et al., 2001), farming practices that mitigate soil erosion would contribute to improving lake
water quality.
Soil erosion can be lessened by switching to chisel plow tillage from intensive tillage
tools such as the moldboard plow, because more crop residue kept on the soil surface slows soil
detachment and transport (Ghidey and Alberts, 1998, Reganold, et al., 1987). Winter cover crops
also reduce soil erosion by dissipating the energy of raindrop impact and by renewing the residue
cover to hold soil (Delgado, et al., 1999, Joyce, et al., 2002, Langdale, et al., 1991). Adding
wheat into corn-soybean rotation also plays a positive role since solid seeded crops like wheat
provide more protection against water erosion than row crops (Peel, 1998), while crops are in the
field.

130

The potential to reduce soil erosion with different farming practices in the hypothetical
cropping system is calculated in this study using the Revised Universal Soil Loss Equation,
Version 2. RUSLE2 is “a computer model containing both empirical and process-based science
in a Windows environment that predicts rill and interrill erosion by rainfall and runoff” (Soil and
Water Conservation Society, 1993). As the degree of erosion largely varies with the erosivity of
rainfall, the erodibility of soil, the slope of the land, the nature of the plant cover and the land
management (Morgan, 2005), a large scale estimate needs to capture the spatial variation of soil
erosion. RUSLE2 is able to perform this task by simulating soil erosion under the prevailing
climate conditions and soil textures in different counties. See Appendix 3-3 for more information
about RUSLE2 and how it was used to scale up soil erosion effects to the state of Michigan. See
Appendix 3-4 for the linkage between soil erosion and lake eutrophication.

•

Greenhouse gas mitigation
Cropland management mainly contributes to the global greenhouse gases fluxes in the

form of carbon dioxide (CO2) and nitrous oxide (N2O) (Robertson and Grace, 2004). Nitrous
oxide is a major greenhouse gas that has 298 times more impact per unit weight than carbon
dioxide over a 100 year period (Forster, et al., 2007). In cropping systems, its emission is closely
tied to the rate of nitrogen fertilizer use in a positive but nonlinear relationship (Hoben, et al.,
2011, McSwiney and Robertson, 2005). The pre-sidedress nitrate soil test (PSNT), required in all
four cropping systems offered to farmers in the 2008 survey, aims to provide an accurate
nitrogen fertilizer recommendation based on plant-available nitrate in soil. It may either increase
or decrease fertilizer use according to different weather, soil and crop conditions, but empirical
evidence suggests a general reduction in fertilizer use after PSNT in research trials in

131

13

Michigan

and other regions (Musser, et al., 1995). Adding wheat into a corn-soybean rotation

may have either positive or negative impact on the total annual fertilizer use in the system. As
wheat requires more fertilizer than soybeans but less than corn, the net effect largely depends on
the pre-wheat level of fertilizer application. Winter cover crops also decrease nutrient losses and
N2O emission during periods when the primary crop is not growing (Lal, et al., 2004, McSwiney,
et al., 2010). Although it is widely believed that reduced tillage favors carbon sequestration, the
difference between moldboard tillage and chisel tillage in CO2 emission is fairly small
(Reicosky, et al., 1995, Reicosky and Lindstrom, 1993).
This analysis obtains rates of nitrogen fertilizer use under different management practices
from the literature or personal communications with experts. Like soil erosion, GHG emissions
also vary spatially by local climate, soil properties and crop yield (McSwiney, et al., 2010).
Thus, in order to calculate the state-level estimates of GHG emissions in different regions with
different fertilizer use levels, I used the web-based U.S. Cropland Greenhouse Gas Calculator,
which aims to calculate the GHG impact of different field crop management practices
(McSwiney, et al., 2010). See Appendix 3-5 for more information about the tool and its usage in
the study.

3.4

Empirical analysis
There are five steps to combine the supply and demand estimates to derive the socially

optimal payment for ES from changed cropping systems. These are described below.

13

Based on personal communication with Prof. Sieglinde Snapp from the Department of Crop
and Soil Science at Michigan State University during March and April 2011, and Michigan State
University extension initial report by George Silva, Jon Dahl, and Natalie Rector on June 15,
2001
132

3.4.1

ES supply and aggregate cost
In the supply side analysis, the farmers predicted utility-maximizing enrollment of land

(A) from Essay 1 is shown in Equation 3.18:

E ( A ) = Φ ( xγ σ e ) ⋅
 Φ ( ( ap * + x β ) / σ u ) ( ap * + x β ) + σφ ( ( ap * + x β ) / σ u ) 



(3.18)

In the function, p* indicates the payment offer for each hypothetical cropping system,
while x represents other variables significant at 90% level, which may include perception and
attitudes of ecosystem services, total land area managed, current practices, biophysical variables,
future expectations variables, experiential variables, and demographics. Equation 3.18 was
estimated empirically in Essay 1 using data from the farmer survey and the double hurdle
econometric results reported in Tables 1-5 and 1-6. The first term in the equation represents the
probability that a farmer is willing to consider the PES program if offered a suitable payment.
The willingness to consider is a prior examination of the compatibility of the proposed cropping
system with farm’s biophysical setting, existing farming practices and other relevant factors. The
actual program payment offer was found to play a minor important role at this stage. The
empirical analysis from essay 1 suggests this probability generally does not depend on the level
of payment, except for System A. The second term represents the land acreage enrollment
conditional on willingness to consider the program. Acreage enrollment can be either zero or
positive values. The case of zero enrollment indicates that the specific payment for this PES
program is not attractive to the farmer even though they are open to the idea of enrolling.
By varying the payment offer p* from 0 to 120 dollars, land acreage enrolled in each
cropping system for each responding farm from the 2008 survey can be simulated using Equation
133

3.18. Each farm’s predicted enrollment Ai is bounded between zero and its total cropland
acreage. Depending on their total cropland area, the farms surveyed were divided into four strata
with different probability of being sampled. The state-level enrollment is derived by
proportionally magnifying individual farm-level supply in each sample acreage stratum given the
number of farms in the sample (N) and the total number in the state (TN). The procedure is
shown in Equation 3.19, where k indicates the price, i indicates the individual farm, and the
subscripts 1 - 4 indicate four sample strata. The per-acre payment is the marginal WTA or
marginal cost to farmers to enroll in one of the four cropping systems. A supply curve can be
derived from Equation 3.18 as the marginal WTA (MWTA) in response to land enrollment
measured in acreage.

 TN N1
TN 2
MWTA | p*= k , k ∈[0,120] = f  1 ⋅  Ai1 | p*= k +
N2
 N1 i =1
1


⋅

N2



i2 =1

Ai2 | p*= k

N
N4

TN 3 3
TN 4
+
⋅  Ai | p*= k +
⋅  Ai | p*= k 

N 3 i =1 3
N4 i =4 4
3
1


(3.19)

This state-level empirical marginal WTA is derived directly from respondent farms using
the supply response function in Equation 3.18. The state-level function that measures the total
WTA for each level of payment (P*) is derived by numerically integrating the empirical
marginal WTA.
k

WTA |P*= k =



j =0

MWTA |P*= j dj

134

(3.20)

3.4.2 Measuring additionality of ES supply from changes in farming practices
The WTP from residents on the demand side is based on improvement in lake water
quality and reduction in GHG emissions, while the WTA on the supply side did not require
changes in farm management. To insure the additionality of ES supply for comparison to WTP
for additional ES on the demand side, WTA for effective acreage that entails real change in each
practice is calculated as the difference between the land acreage enrolled and acreage where it
was previously adopted for each respondent farm from the 2008 survey. The additional effective
acreage is calculated conservatively to avoid exaggerating likely environmental outcomes. The
additional land that switches to chisel from moldboard plow tillage is calculated as the enrolled
land acreage minus land using all other types of tillage previously. This only applies to farms
that indicated the use of moldboard plow tillage previously. All other farms are assumed to have
zero additionality in reduced tillage, no matter how many acres they enroll. The additional land
adopting winter cover crops is simply the difference between land area enrolled and previous
cover crop acreage. As PSNT only applies to corn production, the additional PSNT acreage is the
difference between enrolled corn acreage (1/2 of area for systems A and B with corn-soybean
rotation; 1/3 of area for systems C and D with corn-soybean-wheat rotation) and corn land
previously using PSNT. The additional land switching from corn-soybean rotation to cornsoybean-wheat rotation is 1/3 of the enrolled land area minus the previous wheat acreage. The
additional land with band application of fertilizer is the total enrolled acreage if the farm
previously broadcasted fertilizer at the full rate, and is zero otherwise. Tables 3-2 and 3-3
summarize the formulas used to calculate additional acreage for each practice in each cropping
system for eutrophic lakes and GHG reduction, respectively.

135

3.4.3

Link additional change in practices to ES improvements
As identified in the conceptual model, a key step to match supply and demand is to link

change in farming practices to the environmental improvements perceived by residents. In
particular, given the additional effective land acreage calculated in the previous step, the task is
to derive the effect on the number of eutrophic lakes and the amount of GHG emissions of one
additional acre enrolled in each practice. The percentage change of soil erosion between
cropping systems with and without a certain practice is calculated using RUSLE 2 (see Appendix
3-3 for details). Since the erosion rate highly depends on weather conditions and soil type, the
final estimate is an area-weighted average of the dominant soil type in each of Michigan’s 34
major counties for corn, soybean and wheat production. The major counties are selected based on
the total planted area of these crops. A representative soil type in each county is selected for
erosion estimates (see Appendix 3-2 for details). The effect of cropping practice adoption on the
number of eutrophic lakes is described in Appendix 3-4, based on phosphorus leaching reduction
rate, percentage of C-S rotation to cropland erosion, total cropland area under corn-soybean
rotation, fertilizer phosphorus contribution to lakes, and the current number of lakes falling into
different trophic status levels using the method developed by Chen (2010). The synergy among
practices is considered by conditioning marginal change in each practice on other required
practices in the cropping system. For example, the erosion effect from adding wheat into rotation
14

is conditioned on adopting chisel plow and cover crops .
As explained in section 3.3.2, the reduction in GHG emissions is only calculated for N2O
reduction given the ambiguous results of CO2 emission from reduced tillage in the literature. The
14

In some cases, the exact practice combination is not available in RUSLE 2, a close alternative
is chosen for comparison. The “with” and “without” scenario to examine one practice is only
different in the practice itself.
136

differences among practices are due to differences in the rates of fertilizer use. The state average
rate of nitrogen fertilizer using the US Cropland Greenhouse Gas Calculator (see Appendix 3-5)
is 142 lb/acre for corn, zero for soybean and 66.1 lb/acre for wheat. According to a long-term N
credit experiment with different crop management practices conducted by Gentry et al (2011) in
Kalamazoo Michigan, use of the PSNT combined with 2 Mg/ha of red clover biomass provided a
N credit of 35.7 lb/acre to corn. Silva et al. (2011) verified possible N fertilizer reduction ranging
from 30 to 90 lb/ acre from three corn fields in Michigan despite unfavorable weather conditions
due to PSNT. A three-year PSNT experiment in Pennsylvania corn production found the average
reduction of N fertilizer from over 100 observations to range from 15 to 60 lb/ acre each year
(Musser, et al., 1995). Based on these studies, we assume the N fertilizer rate reduction due to
PSNT is 30 lb/ acre for adopting PSNT, 5.7 lb/acre for adopting winter cover crops, 30 lb/acre
further less for incorporating wheat, and a 1/3 reduction of the remaining fertilizer use (142-305.7-30 lb/acre) for adopting band fertilization. Like the erosion estimates, the 34-county areaweighted average of GHG emissions is used to estimate the mitigation of GHG due to different
farming practices. The synergy among practices is calculated by summing up the marginal
changes from each practice in the cropping system. For example, the GHG effect from adopting
a band application is based on prior adoption of PSNT, cover crops and adding wheat to the
corn-soybean rotation. The estimates of these per-acre reductions in eutrophic lakes and GHG
are shown in Tables 3-4 and 3-5.
The estimates of reductions in eutrophic lakes and GHG from land enrollment for each
farm are obtained by multiplying the state-level additional acreages calculated in Tables 3-2 and
3-3 under each practice by the average per-acre reductions in Tables 3-4 and 3-5. The estimates

137

for environmental improvements for each farm are calculated at each price level ranging from 0
to $120.

3.4.4

ES demand and aggregate benefit
The benefit (WTP) function for residents is derived and estimated in Essay 2. For

matching demand with supply at the level of the State of Michigan, the conditional WTP
function is estimated to ensure three properties. First, it is increasing and concave with respect to
reductions in eutrophic lakes and GHG emissions, due to the assumption of diminishing marginal
utility. Second, the conditional WTP should be greater than zero since only respondents
indicating a positive WTP are included in the regression. Respondents that have either zero or
positive WTP are analyzed in the prior spike model to estimate an average participation rate.
Third, the WTP should approach zero with no environmental improvements. Both semi-log
function and mixed log-log function are adopted and compared in Essay 2 (Equations 2.12 and
2.13). Although the shape of WTP curves are different due to the inherent functional form
assumptions (Figures 2-6 and 2-7), the predicted WTP in response to environmental
improvements using two functional forms lies in a common range, and the goodness of fit of the
two functions is not statistically different. The mixed log-log function (Equation 2.13), which
displays diminishing marginal utility starting near the origin, and has higher statistical
significance based on the Wald test, was chosen for estimating resident conditional WTP
(CWTP):

(

CWTP = exp δ + α ln( Lake) + β ln(GHG) + ϕ ln(GHG)* Concern + γ Ri + ε ij

)

(3.20)

In this function, lake and GHG measure the number of eutrophic lakes reduced and tons of GHG
emissions abated. The natural logarithm of CWTP is a function of natural logarithms of lake and
138

GHG. Since CWTP for GHG abatement is closely related to respondents’ concern about global
warming, an interaction of the two variables is included in the function. R indicates residentspecific characteristics. Preference certainty is not included in the estimation because the
unbiased WTP estimates from certainty-adjusted models are not statistically different from the
conventional model, and there is still no consensus regarding the theoretical foundation and the
methodology in the literature (Table 2-12). The average probability of having positive
willingness to pay, η=0.876, which is estimated from the spike model (Essay 2 in Ma, 2011), is
multiplied by the conditional WTP to derive the unconditional state-level WTP.

WTP = η ⋅ CWTP

(3.21)

In the previous step, I have calculated the predicted reductions in lake eutrophication and
GHG emissions from additional effective acres enrolled. , However, the empirical results that
extrapolate down to zero payment from the payment range offered in the survey suggest that
some farmers are willing to enroll land in the PES program with no payment. Some of this land
would even provide additional environmental improvement. Such voluntary enrollment and
environmental stewardship is possible if technical assistance is available and information on the
private and public benefits from conservation practices is clearly conveyed15. Although it is
theoretically possible that farmers may adopt environmental stewardship practices without
15

Some of the acreage enrollment is due to zero additionality, namely farmers who have already
adopted certain practices and are willing to enroll with even zero payment. The 2008 focus group
study associated with the Michigan farmer survey found that farmers revealed zero WTA.
Referring to his bid in an experimental auction, one participant said, “I’m already doing some of
it, A and B, so, I could have bid 0 on those I guess.” However, the significant positive abatement
in eutrophic lakes and GHG in hypothetical systems indicate willingness to make real changes in
farming practices for zero payment. These voluntary changes in practice may be influenced by
implicit factors associated with the proposed PES setting such as information, technology
support, and positive utility from ecosystem services. The positive enrollment and environmental
improvement for zero payment may also be partly attributed to the extrapolation of results
beyond the lower bound of payments offered in the survey (System A: $4, System B:$10,
System C:$15 and System D: $20).
139

compensation and the predicted WTA function suggests such behavior, this analysis builds on
the more conservative assumption that adoption of changed cropping systems requires a non-zero
positive payment for ES. To derive the economic optimal conditions for facilitating ES supply, I
assume that resident WTP corresponds only to additional environmental improvements that are
not likely to occur without incentive payment. Thus, the levels of reductions in eutrophic lakes
and GHG emissions used to predict the state-level WTP is calculated as the difference between
state-level environmental improvements derived in section 3.4.3 and those achieved with zero
payment in each cropping system. . The resident survey was targeted to adults, and the adult
16

population of Michigan residents was 7,539,572 in 2010 . Of that population, 81.4% is used for
state-level estimates because the survey registered an 18.6% protest rate of residents who
disliked the survey provision mechanisms (e.g., taxes and agricultural subsidies).

3.4.5

Welfare maximization by combining supply and demand
The optimal condition for aggregate supply of and demand for ecosystem services from

cropland is achieved by maximizing the economic surplus, which is the difference between
resident WTP and farmer WTA at the state level. The optimal condition in each of the four
cropping systems is identified, as is a mixed choice option designed to offer a low-cost choice
among the four systems. In the mixed-choice alternative, each farm is assumed to choose from
the four systems offered at each payment level the one that minimizes the average farm-level
cost of generating additional ecosystem services. The farm-level average cost per acre is
calculated based on the per-acre payment offer and the corresponding acreage enrollment chosen

16

US Census Bureau, 2010. Demographic Profile Data: Profile of General Population and
Housing Characteristics. http://2010.census.gov/2010census/popmap/ipmtext.php?fl=26
140

by each respondent farmer. Since the option of zero payment for adopting the specified cropping
systems was not offered to farmers in the survey, voluntary enrollment for no payment is not
included in calculating the average cost. Consequently, on farms where a cropping system
offering greater ES was already practiced (e.g., systems C or D), it is possible for the mixed
choice system choice algorithm not to recognize an existing system (available at zero added cost)
as being the least costly at delivering ES.
The state-level enrollment for each system at each payment level is derived by
proportionally scaling up the individual farm-level enrollments of those who choose the system
in each sample acreage stratum, given the number of farms in the sample and the total number of
farms in the state. The total state-level acreage enrollment is the sum of the enrollments in the
four cropping systems. The state-level environmental improvements in lakes and GHG levels are
calculated as the sum of the products of the state-level acreage enrollments and the per-acre
improvements from the four systems. See Appendix 3-6 for details.
Two variants of the economic optimal condition are examined here. The first variant is to
pay farms based on the land acres enrolled in the hypothetical cropping system, which is the
actual setting in the survey. In this case, farmers are still get paid even if no new practice is
adopted with land enrollment. The second variant is to target only farms that offer additionality
in environmental improvement from land enrollment. As some farmers have already adopted
certain practices on some of their land enrolled in the PES program, payments to these farms do
not necessarily pay for additional environmental improvement. To examine a more cost-effective
case, this policy scenario only pays farms that adopt new practices contributing to at least one of
the two environmental improvements, i.e., eutrophic lake abatement and GHG mitigation.
Finally, in order to examine the possibility of expanding PES payments within the budget of the

141

current government subsidy system, the cost of the previous scenarios is compared to the value
of USDA subsidy direct payments to Michigan growers of corn, soybean and wheat.

3.5

Results and discussion
The results below report predicted economically optimal conditions for these PES

programs. Summarizing the procedures described in the previous section, farmer WTA and
resident WTP are derived and combined as follows: Farmer land enrollment in different cropping
systems is predicted using the supply function estimated from the double hurdle model reported
in Tables 1-5 and 1-6. The total WTA in response to land enrollment is empirically aggregated
from the supply response illustrated in Figure 1-4. The enrolled cropland acreage that provides
additional ecosystem services by newly adopting required farming practices is identified from
total enrollment following Tables 3-2 and 3-3. The environmental improvements, measured by
the reductions in the number of eutrophic lakes and GHG mitigation percentage from year 2000
level, are derived following Tables 3-4 and 3-5. The resident WTP is estimated based on the
conditional WTP regression results from Table 2-8 using the mixed log-log function and the
conventional dichotomous random-effect model, along with the average spike probability
calculated as predicted values based on the econometric results in Table 2-6.

3.5.1

Payment for enrollment scenario
The State of Michigan aggregate benefit (WTA) and cost (WTP) simulated for the four

individual hypothetical PES programs are shown in Figures 3-2 to 3-5. The detailed calculations
of welfare measures and environmental improvements at each payment level are shown in
Appendix 3-7. The results reveal that the public benefits from these cropland PES programs are
142

greater than the costs to farmers over the payment range from $0 to $120 per acre.
Economic welfare is maximized where the deviation is largest between aggregate benefit
(WTP) and aggregate cost (WTA). Measures of per-acre payment, land enrollment, welfare and
environmental improvements at the economic optimum are shown in Table 3-6. As shown in
these tables and graphs, the maximized economic welfare is achieved with a set of optimal
conditions in all five system alternatives, among which four alternatives other than System A
exhibit small variation across systems.
At the economic optimum, the marginal per-acre PES payment is highest for System D at
$21/acre, which has the most stringent requirements. It is lowest in the most basic alternative,
System A at $14/acre. These per-acre payments are all within the range of current conservation
program payments. Welfare-maximizing land enrollment levels are similar in the five programs,
ranging from 0.91 to 1.2 million acres. These predictions suggest that about half of Michigan’s
approximately 2.3 million acres under corn-soybean rotation (Appendix 3-1) would be enrolled
in these PES programs under economic welfare-maximizing conditions. When comparing
economic welfare across the five programs, System A apparently generates the lowest economic
surplus, $120 million, and lowest benefit-cost ratio 0.4, due to its low environmental
performance. All remaining systems result in similar economic surplus, ranging between $140
and $142 million. The mixed-choice alternative, which intends to minimize the average payment
per unit of environmental improvement, gives the largest improvement in both lake quality and
GHG mitigation, equally high economic surplus with System C, and the second largest benefitcost ratio, next to System B. The mixed-choice alternative seems to be the most cost-effective
alternative among the five. The component cropping systems enrolled in the mixed-choice
alternative among farms at different payment levels are shown in Figure 3-7. The percentages of

143

farms that enroll in systems A-D are 10%, 13%, 57%, and 20% respectively. The pervasiveness
of System C, which requires corn-soybean-wheat rotation, cover crop, PSNT and chisel tillage, is
presumably due to its high economic surplus and large contribution to eutrophic lake
17

mitigation . If the focus of public demand for ES is on improvement in eutrophic lakes, as
revealed in the 2008 resident survey, System C would be a good choice if a single system
scheme were implemented.

3.5.2

Payment for additionality scenario
In the farm sample, very few farmers agreed to adopt the proposed practices on

completely new land, but likewise very few accepted payment while making no change in at all
in their previous practices. Most farms provide partial additionality from enrollment in PES.
Given the design of the survey, it is impossible to distinguish between the payments for land
enrollment with and without additional ecosystem services. To examine the program design that
promotes cost effectiveness based on additionality, a scenario targeting farms that provide
additionality in at least one ecosystem service is analyzed and compared to the scenario above
that pays for enrollment. The results for the “payment for enrollment” scenario and the “payment
for additionality” scenario are shown in Table 3-7. The economic surplus sequentially increases
from System A at $131 million to the mixed-choice alternative at $143 million, although the
differences among the five cropping system alternatives remain relatively small. The targeting
scheme has the largest impact on System A, the one with least requirements in farming practices
and lowest environmental performance. Compared the “payment for enrollment” scenario, with
17

The average cost of abating eutrophication was given lexicographic priority in the system
selection process over the average cost of GHG mitigation, since residents showed higher
willingness to pay for water quality improvement.
144

only 1/5 of the previous enrolled lands being targeted, System A yields 6 times more
improvement in lakes but 2/3 less GHG mitigation using half of the previous total government
spending. System D, the most stringent one, also benefit from a targeting scheme. With higher
per-acre payment and larger enrollment in System D, the benefit-cost ratio increases from 25.5 to
31.9, ranking first among the five alternatives. System D also has the largest GHG mitigation
potential due to its restriction on fertilizer use. Based on these observations, the targeting strategy
would enhance the cost-effectiveness of PES programs by eliminating land enrollment with little
additionality, such as System A, or by facilitating enrollment in high-cost stringent program with
higher payment, such as System D.
Despite the potential cost-effectiveness of the “payment for additionality” scenarios,
there are still problems associated with this seemingly efficient program. First, as the policy
targets changes in practices, it is essential to verify the baseline practices of each participating
farm, which would require extra administrative cost. Second, this policy may also be criticized
for its inequity, because it would disqualify prior adopters of conservation practices for PES
payment. In the extreme, good environmental stewards may even opt temporarily to switch back
to conventional farming practices in order to qualify to be paid through the PES program. It
seems that one practical strategy is to differentiate payment for land enrollment providing
additionality with new practices and to maintain environmental benefits from existing practices.
This type of payment scheme has been proposed by the USDA Natural Resource Conservation
Service (NRCS). In the recently released final rule for the Conservation Stewardship Program,
the NRCS is implementing a split payment structure with one payment rate for new practices and
a lower rate for existing practices to encourage producers to apply more new activities and

145

generate greater environmental benefits (USDA-NRCS, 2010). The issue of inequity is still a
major concern, even for this payment scheme.

3.5.3

Comparison with current commodity subsidies
To examine the role that PES programs could play in government subsidies, the costs of

the hypothetical PES program described above are compared with current USDA direct
payments to Michigan growers of corn, soybean and wheat. The commodity subsidies in various
forms still account for the largest proportion of farm subsidies in Michigan. Based on data from
1995 to 2010, the average annual subsidy for corn, soybean and wheat was about $190 million
(Environmental Working Group, 2011). Among major types of commodity subsidies (i.e., direct
payments, counter-cyclical payments, and marketing loans), direct payments to corn, soybean
and wheat farmers cost the federal government $78.6 million annually over 1995-2010. The
direct payments were established in 1996 to wean farmers off traditional subsidies that had been
triggered during periods of low prices for corn, wheat, soybeans, cotton, rice, and other crops
(Environmental Working Group, 2011). However, the direct payment program is difficult to
justify, especially in the face of rapidly expanding federal debt, because it has been maintained
beyond its intended transition period and is provided to recipients without economic need.
Further, with the pressure to comply with WTO provisions, the reform of converting direct
commodity payments to conservation payments is taking place in Europe and the U.S. (Swinton,
et al., 2006). The size and scope of U.S. conservation programs have substantially increased
since the 2002 farm bill to partly replace the trade-distorting commodity subsidies (Baylis, et al.,
2004).

146

To examine the possibility to transition commodity subsidies and especially the direct
payment to conservation payment, government spending at the economic optimum for our
hypothetical PES programs is compared with the actual commodity subsidies in Michigan. The
government spending needed at for different cropping systems ranges from $15 to $24 million if
farmers are paid based on land enrollment. The spending is estimated between $6.5 and $27
million if the PES program targets farms with additionality in abating eutrophic lakes and GHG.
Thus, even only replacing the direct commodity payment in corn, soybean and wheat subsidies
would be amply sufficient to achieve the economic optimal conditions for any of these systems.
Recent average expenditures for direct payments to these farmers are more than three times the
PES spending needed to induce adoption of 1.2 million acres in the mixed system, the most costeffective choice among the five alternatives. Since our PES programs would target the same
farmers as the commodity subsidies, predictions from this study highlight the opportunity to
transfer income to the intended recipients of commodity subsidies trade-neutrally via
conservation payments. This transition would also improve the economic efficiency of
government subsidy programs.

3.6

Conclusion
This essay combines a supply-side cost function of farmers’ willingness to adopt ES-

providing practices with a demand-side benefit function of residents’ willingness to pay (WTP)
for resulting ES to derive the welfare-maximizing conditions for efficient design of cropland
PES programs. This study contributes to the literature by proposing agricultural PES policies
based on the underlying supply-demand mechanism embedded in empirical stated preference
estimates. Land enrollment in PES programs is viewed as a bundle for five potential
147

conservation farming programs and two types of resulting environmental improvements. The
payment and quantity of enrollment, as well as derived environmental and welfare measures are
calculated under different policy variants. These include a welfare-maximizing scenario that
pays farmers for land enrollment, a scenario that targets farms with additionality in abating
eutrophic lakes and GHG emissions, and a simple comparison with current commodity subsidies.
In each scenario, five PES programs are examined--four single cropping system programs that
provide sequentially increased levels of lake eutrophication reduction and greenhouse gas
mitigation with increasing management requirements and payments to farmers plus one mixedchoice program that requires farmers to enroll in the cropping system alternative with the lowest
average unit cost for environmental improvements. Farmer costs (and hence PES program costs)
are well covered by resident benefits in all five hypothetical programs under all policy scenarios.
In the welfare-maximizing “payment for land enrollment” scenario, the economically optimal
conditions are achieved in a reasonable payment range of $14 to $21 dollar/acre, for all five
programs. Comparing across programs, the mixed-choice alternative, which allows each farmer
to choose the one of the four cropping systems that minimizes average farm-level cost, is
relatively more cost-effective than the others. However, the mixed-choice alternative would
require great flexibility in program design to allow farmers to identify the most cost-effective
changes on each individual farm, and it would pose major monitoring challenges for PES
program administrators. It is clear that System A, the one with fewest required farming practices
and lowest environmental improvement is dominated by the other four system alternatives.
Given the trivial difference in economic welfare among those four, however, and given the tradeoffs in cost and levels of different ES benefits that each offers, it is difficult to identify any one

148

best system. With particular goals in different PES programs and the evolution of demand for
ES, any of the four systems could be desired.
When the PES program targets farms with additionality, cost-effectiveness is generally
improved in all of the five system alternatives. Targeting would especially improve performance
in the low-cost, low benefit cropping system (System A) by eliminating land enrollment with
little additionality. It would also help the high-cost, high benefit cropping system (System D) by
facilitating enrollment with higher payment. Although targeting payments only to additional
effective acres appears to reduce the cost and improve the efficiency of PES programs, it may
increase administrative costs. It may also cause perceptions of unfairness if pre-PES adopters of
conservation practices are excluded from incentive payments. Therefore, a split-payment scheme
that offers a higher rate for improved stewardship practice and a lower (but positive) rate for
existing practices may be a reasonable solution.
Finally, I compare government spending at the economic optimum in different programs
with current direct payment of commodity subsidy for corn, soybean and wheat in Michigan. The
results confirm the opportunity to replace the direct payment with a PES conservation payment
to the same recipients with less total spending, which would potentially improve the economic
welfare of subsidy policies.
Under the current global trend of rapid-growing population accompanied by degradation
in environmental quality and natural resources, agriculture faces a critical challenge of securing
the global food supply while maintaining a good environmental stewardship. The working land
PES program provides a unique opportunity for conserving the environment without sacrificing
land under production. Improving the efficiency of working land PES programs has long been a
target of PES design, and it becomes especially urgent during this financially difficult period. By

149

combining the supply and demand estimates from stated preference surveys in Michigan, this
study highlights the possibility of designing an efficient program and outlines the features of
such a program. A detailed examination of strategies for targeting farms and differentiating
payments for different degrees of practice adoption is needed in future studies to further improve
the efficiency of agricultural PES programs.

150

Figures and Tables

Practices (inputs)

Ecological process

Wheat planting

Soil erosion

Cover crop

Environmental and
Market Outputs

Chisel plow tillage

Phosphorus
runoff

Lake Eutrophication
Reduction

Band reduced
N&P fertilizer

N 2O
volatilization

GHG Mitigation

Pre-Sidedress
Nitrate Test

CO2
reduction

Corn Soybean Wheat

Payment (million dollars)

Figure 3-1 Input-output system of ecosystem services from croplands

Maximized Welfare:
$128 million

180
150

Farmer WTA
(Cost)

120
90
60

Resident WTP
(Benefit)

30
0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

Cropland acreage enrollment (million acres)

Figure 3-2 State-level benefit (WTP) and cost (WTA) for ES from Michigan cropland
(System A)

151

Payment (million dollars)

Maximized Welfare:
$140 million

180
150
120

Farmer WTA
(Cost)

90
60
30

Resident WTP
(Benefit)

0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

Cropland acreage enrollment (million acres)

Payment (million dollars)

Figure 3-3 State-level benefit (WTP) and cost (WTA) for ES from Michigan cropland
(System B)

Maximized Welfare:
$142 million

180
150

Farmer WTA
(Cost)

120
90
60

Resident WTP
(Benefit)

30
0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

Cropland acreage enrollment (million acres)

Figure 3-4 State-level benefit (WTP) and cost (WTA) for ES from Michigan cropland
(System C)

152

Payment (million dollars)

Maximized Welfare:
$140 million

180
150

Farmer WTA
(Cost)

120
90
60

Resident WTP
(Benefit)

30
0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

Cropland acreage enrollment (million acres)

Figure 3-5 State-level benefit (WTP) and cost (WTA) for ES from Michigan cropland
(System D)

Number of farms

1200
1000
800

System A

600

System B

400

System C
System D

200
0
0

10

20

30

40 50 60 70 80 90 100 110 120
Payment in dollars/acre

Figure 3-6 Number of farms using each cropping system at different price levels for the scenario
with mixed choice of systems but no requirement of additionality.

153

Number of farms

1200
1000
System A

800
600

System B

400

System C

200

System D

0
0

10

20

30

40

50

60

70

80

90 100 110 120

Payment in dollars/acre
Figure 3-7 Number of farms using each cropping system at different payment levels for the
scenario allowing mixed choice of system and paying for farms with additionality in at least one
environmental improvement.

154

Table 3-1 Environmental improvements from farming practices in four cropping systems
Final ES
Intermediate
ES
Practice
System A
System B
System C
System D
Final ES
Intermediate
ES

Eutrophic Lakes Reduction
Soil Erosion Reduction
Moldboard tillage 
No cover crop
Corn-soybean 
Chisel plow
cover crop
corn-soybean-wheat
√
√
√
√
√
√
√
√
√
Greenhouse Gas Emission Reduction
N2O Reduction

Practice

No PSNT
 PSNT

No cover crop
 cover crop

System A
System B
System C
System D

√
√
√
√

√
√
√

CO2 Reduction

Corn-soybean Broadcast fertilizer
Moldboard tillage
 cornat full rate
 Chisel plow?
soybean-wheat Band at 2/3 rate
√
√
√
√
√
√
√

155

Table 3-2 Calculation of effective acreage for each practice in four cropping systems that results
in eutrophic lakes reduction
Final ES

Eutrophic Lakes Reduction

Intermediate ES

Soil Erosion Reduction
Moldboard tillage Chisel No cover crop Corn-soybean  cornplow as principal tillage
cover crop
soybean-wheat

Practice
System A
System B
System C
System D

Max (Acres - Chisel acres
- Other tillage acres, 0)

Acres -previous
cover crop acres

(1/3)* Acres -previous
wheat acres

Table 3-3 Calculation of effective acreage for each practice in the four cropping systems that
results in greenhouse gas reduction
Greenhouse Gas Emission Reduction

Final ES
Intermediate
ES

Practice
System A
System B

N2O Reduction
No PSNT
PSNT

Corn-soybean  Broadcast fertilizer No cover crop
Moldboard 

corn-soybeanat full rate
Chisel plow?
cover crop
wheat
Band at 2/3 rate

(1/2)* Acres previous PSNT
acres

System C
System D

(1/3)* Acres previous PSNT
acres

CO2 Reduction

(1/3)* Acres previous wheat
acres

= Acres if do not
currently band;
=0 if currently
band

Note: See Appendices 3-3 and 3-4 for calculations and references.

156

Max (Acres Chisel acres
Acres - Other tillage
previous cover
acres, 0)
crop acres

Table 3-4 Average reduction in eutrophic lakes from farming practices.
Eutrophic
Erosion
lake
Standard
Practices reductdeviation reduction/
ion rate
acre
Moldboard
chisel
30%
1.4% 0.0000197
plow
Add cover
37%
1.2% 0.0000251
crop
Add wheat
in C-S

9%

1.9%

Ref.

Crops

Location

34 major
field crop
cornproduction
soybean
counties
(total C-SRUSLE2
W harvest
area
corngreater
0.0000059
soybean
than
-wheat
40,000
acres)

Soil

Time

One major
representative
soil type for
Average year
C-S-W
cropland in in a multi-year
each county
rotation
(matching
CDL with
STATSGO2)

Table 3-5 Average reduction in GHG emission due to farming practices.
GWPStandard
Practices CO2
Ref.
deviation
lb/acre/
year
Use
Snapp et
72
10.0
PSNT
al., 2010+
MSU
Add
extension
cover
16
10.0
+GHG
crop
calculator
Reduce
GHG
92
8.8
1/3 N
calculator
fertilizer
Add
GHG
wheat in -21
10.2
calculator
C-S

Crops

Location

Soil

Time

One major
34 major field
cornrepresentative soil
crop production
Average year
soybean
type for C-S-W
counties (total Ccropland in each
in a multiS-W harvest area
county
year rotation
greater than
(matching CDL with
40,000 acres)
STATSGO2)
cornsoybean
-wheat

Note: See Appendix 3-5 for calculations and references. GWP-CO2=global warming potential in
carbon dioxide equivalent units.

157

Table 3-6 Economically optimal conditions for the “payment for land enrollment” scenario in five cropping system alternatives.
GHG
EconoEutroPayTotal
AbateFarmer
Resident
Farmer Resident
Benefit/
Spending
mic
phic
ment/
acres
WTA
ment (%
WTP
Welfare Welfare
Cost
(million
surplus
Lakes
Acre
(million (million (million
of 2000
(million (million
$)
ratio
(million Reduced
($)
$)
$)
emission
$)
$)
$)
(number)
$)
level )
14
1.04
6.10
134
14.6
8.47
120
128
0.38
0.0066
0.4
System A
19
1.14
4.10
144
21.7
17.6
123
140
8.5
0.0074
27.6
System B
18
0.91
3.79
146
16.4
12.7
129
142
9.7
0.0090
22.7
System C
21
1.16
3.56
144
24.4
20.8
119
140
7.5
0.0070
25.5
System D
Mixed
18
1.23
4.47
146
22.1
17.6
124
142
11
0.0093
26.4
choice
Table 3-7 Economically optimal conditions for the “additionality targeting” scenario in five cropping system alternatives
GHG
EconoEutroPayTotal
Farmer Resident
AbateSpenFarmer Resident
mic
phic
ment/
acres
WTA
ment (%
WTP
ding
Welfare Welfare
surplus
Lakes
Acre
(million (million (million (million (million (million
of 2000
(million Reduced
($)
$)
$)
$)
emission
$)
$)
$)
(number)
$)
level )
27
0.22
4.66
136
6.05
1.4
130
131
2.5
0.0019
System A
19
1.10
3.98
142
20.9
17.0
121
138
8.5
0.0041
System B
18
0.89
3.84
142
16.0
12.2
125
138
9.7
0.0029
System C
22
1.25
3.54
144
27.6
24.1
117
141
7.8
0.0077
System D
Mixed
12
0.918
1.25
144
11.0
9.8
133
143
8.4
0.0073
choice

158

Benefit/
Cost
ratio
2.5
27.6
22.7
31.9
23.5

APPENDICES

159

APPENDIX 3-1: CALCULATION OF CROPLAND UNDER CORN-SOYBEAN
ROTATION IN MICHIGAN

The farmer survey used for the aggregate supply and demand analysis primarily focused
on cropland under corn-soybean rotation. The total corn-soybean rotation area in Michigan is
used in this essay to calculate the impact of farming practices on eutrophic lake reduction.
However, this information is not available in current agricultural statistics, so an approximation
is obtained using data from the USDA Agricultural Resource Management Survey (ARMS,
2000-2006). The ARMS is a national survey that provides field-level information about crop
production, farm production, business, and households based on representative sample.
From the online ARMS database, we can obtain the information on “planted area of
previous crop harvested” for corn or soybean in selected survey years under the “Crop
Production Practices Tailored Reports”. The percentage of soybean land previously planted in
corn and the percentage of corn planted in the previous year of soybean are calculated in Table
3-A1. The two land percentages can be taken as the rotation rate approximately. The only caveat
is that the data is only for the most recent crop year before the surveyed crop year, rather than for
multiple years of rotations. Combine the rotation rate for corn and soybean with their planted
area data from year 2008 to 2010 from Michigan Agricultural Statistics, we can deduce the
cropland area under corn-soybean rotation in Michigan in Table 3-A2.

160

Table 3-A1 Rotation rate calculation based on Michigan ARMS data
total corn planted area previous soybean area
year
soybean/corn %
(acres)
(acres)
2005
2250.00
950.49
42.2%
2001
2201.21
936.06
42.5%
2000
2200.73
1047.31
47.6%
Average
44.1%
total soybean planted area previous corn area
year
corn/soybean %
(acres)
(acres)
2006
2000.01
1415.33
70.8%
2002
2049.89
1137.90
55.5%
2000
2099.50
1314.58
62.6%
Average
63.0%
Data Source: USDA ARMS Farm Financial and Crop Production Practices: Tailored Reports,
Michigan, 2000-2006.
Table 3-A2 Corn-soybean rotation area calculation
year

crop

total planted area
(acres)

rotation %

planted area
(acres)

2010

corn

2,400,000

44.1%

1,058,860

soybean

2,050,000

63.0%

1,290,748

corn

2,350,000

44.1%

1,036,800

soybean

2,000,000

63.0%

1,259,267

corn

2,400,000

44.1%

1,058,860

2009
2008

corn-soybean
planted area
(acres)
2,349,608
2,296,067

2,255,163
soybean
1,900,000
63.0%
1,196,303
Average corn-soybean rotation area
2,300,279
Data Source: 1) USDA ARMS Farm Financial and Crop Production Practices: Tailored Reports,
Michigan, 2000-2006; 2) Planted area for major crops, Michigan Agricultural Statistics, 20082010.

161

APPENDIX 3-2: MAJOR CROP PRODUCTION COUNTIES AND REPRESENTATIVE
SOIL TYPES IN MICHIGAN

The estimated soil erosion and GHG emissions depend on not only crop and farm
management practices, but also on soil textures that vary across the state. To capture the
variation of estimates due to soil properties, a subset of Michigan counties that play a major role
in corn, soybean and wheat production was selected. The subset contains 34 counties with total
corn, soybean and wheat harvest area greater than 40,000 acres each, all of which cluster in the
South Lower Peninsula of Michigan (Figure 3-A1). The representative soil types for cropland
area in each county were selected as the largest area of soil for corn, soybean and wheat
production by overlaying the Cropland Data Layer (CDL) database with the U.S. General Soil
Map (STATSGO). A list of major counties and their representative soil types is shown in Table
3-A3.
The soil type information is used as a key input in RUSEL2 to calculate the soil erosion
associated with different cropping systems in 34 counties. The GHG calculator automatically
retrieves the average soil and climate information once a specific county is identified. The statelevel approximation of percentage reductions in soil erosion and GHG emissions due to adoption
of conservation practices are calculated as the average of 34 county-level estimates weighted by
the total planted area of corn, soybean and wheat in each county.

162

Figure 3-A1 Major counties for corn, soybean and wheat production in Michigan

163

County
Allegan
Barry
Bay
Berrien
Branch
Calhoun
Cass
Clinton
Eaton
Genesee
Gratiot
Hillsdale
Huron
Ingham
Ionia
Isabella
Jackson
Kalamazoo
Kent
Lapeer
Lenawee
Livingston
Midland
Monroe
Montcalm
Ottawa
Saginaw
Sanilac
Shiawassee
St Clair
St Joseph
Tuscola
Van Buren
Washtenaw

Table 3-A3 Major counties and their representative soil types
CSW Harvested
Primary
STATSGO Soil type
Area (acres)
texture
143,230
CAPAC-RIDDLES-SELFRIDGE
loam
66,267
MARLETTE-CAPAC-PARKHILL
loam
105,489
LONDO-TAPPAN-WIXOM
loam
89,282
RIDDLES-CROSIER-OSHTEMO
loam
161,328
BARRY-LOCKE-HATMAKER
loam
OSHTEMO-KALAMAZOO136,873
sandy loam
HOUGHTON
OSHTEMO-KALAMAZOO119,624
sandy loam
HOUGHTON
166,768
PARKHILL-CAPAC-LONDO
loam
141,541
MARLETTE-CAPAC-PARKHILL
loam
78,182
CONOVER-BROOKSTON-PARKHILL
loam
186,227
PARKHILL-CAPAC-LONDO
loam
147,048
BARRY-LOCKE-HATMAKER
loam
KILMANAGH-SHEBEON190,493
loam
GRINDSTONE
122,676
PARKHILL-CAPAC-LONDO
loam
133,362
MARLETTE-CAPAC-PARKHILL
loam
95,753
PARKHILL-CAPAC-LONDO
loam
93,304
RIDDLES-HILLSDALE-GILFORD
sandy loam
SCHOOLCRAFT-KALAMAZOO89,310
loam
ELSTON
70,540
MARLETTE-CAPAC-SPINKS
loam
77,443
PARKHILL-CAPAC-LONDO
loam
234,413
HOYTVILLE-NAPPANEE-BLOUNT
clay
41,872
MIAMI-CONOVER-BROOKSTON
loam
42,856
PARKHILL-CAPAC-LONDO
loam
169,264
PEWAMO-SELFRIDGE-TEDROW
loam
91,212
REMUS-SPINKS-COLOMA
sandy loam
57,903
PERRINTON-ITHACA-COLOMA
loam
223,686
PARKHILL-CAPAC-LONDO
loam
247,322
PARKHILL-CAPAC-LONDO
loam
154,580
CONOVER-BROOKSTON-PARKHILL
loam
97,819
BLOUNT-PEWAMO-GLYNWOOD
silty loam
139,210
COLOMA-SPINKS-OSHTEMO
loamy sand
188,072
LONDO-TAPPAN-WIXOM
loam
72,037
COLOMA-SPINKS-OSHTEMO
loamy sand
97,059
MIAMI-CONOVER-BROOKSTON
loam

164

APPENDIX 3-3: CALCULATION SOIL EROSION REDUCTION USING RUSLE2

The Revised Universal Soil Loss Equation (RUSLE) is “a set of mathematical equations
that estimate average annual soil loss and sediment yield resulting from interrill and rill erosion”
(Soil and Water Conservation Society, 1993). It is a well-validated and documented equation
derived from the theory of erosion processes, more than 10,000 plot-years of data from natural
rainfall plots, and numerous rainfall-simulation plots (Soil and Water Conservation Society,
1993). The RUSLE2 program is an upgraded computer model containing both “empirical and
process-based science in a Windows environment”, as well as official NRCS databases for
climate, soil and crop management.
RUSLE retains the structure of its predecessor, the Universal Soil Loss Equation, namely,
A = R K LS C P (Soil and Water Conservation Society, 1993). A refers to average annual soil
loss in tons per acre per year. R represents the erosivity of rainfall and runoff. K is the inherent
erodibility of the soil or surface material under standard experimental conditions. LS represent
the effect of topography, specifically hillslope length and steepness, on rates of soil loss. C
represents the effects of surface vegetative cover and roughness, soil biomass, and soil-disturbing
activities on rates of soil loss. P embodies the effects of conservation practices. The values of
these factors all apply to specific locations. For every county identified in Appendix 3-2, the
changes in erosion rate due to tillage, cover crop and crop rotation in the PES program were
calculated by comparing specific scenarios that have different composition of farming practices
with values in C and P, coupled with local weather, soil and management conditions. Details of

165

the scenarios and the calculated erosion reduction rate for each practice are shown in Table 3-A4,
and detailed operations in each scenario are shown in Table 3-A5.

Table 3-A4 Calculation of erosion reduction rate with RUSLE 2
change in
cover soil loss
erosion
scenario
rotation
tillage
practice
crop
(t/ac/yr)
reduction
spring moldboard
1
corn-soybean
4.9
plow
moldboard
30%
to chisel
spring straight
2
corn-soybean
3.5
point chisel
18
3
3.6
winter corn-soybean
spring disk
37%
cover crop corn-soybean
4
spring disk
rye
2.3
19
corn-soybean
spring disk
rye
2.3
5
wheat in
9%
rotation corn-soybean6
spring disk
rye
2.1
wheat
Table 3-A5 Operations in each management scenario assumed with RUSLE 2
Scenario Date Operation
Crops
1
4/20/1 Plow, moldboard
4/24/1 Disk, tandem secondary operation
4/28/1 Cultivator, field 6-12 in sweeps
5/1/1 Planter, double disk opener
Corn, grain
10/20/1 Harvest, killing crop 50pct standing stubble
5/5/2 Plow, moldboard
5/10/2 Disk, tandem secondary operation
5/15/2 Cultivator, field 6-12 in sweeps
Soybean, Midwest, 7in rows
5/15/2 Drill or airseeder, double disk
10/10/2 Harvest, killing crop 20pct standing stubble
2

4/24/1 Chisel, straight point
4/28/1 Cultivator, field 6-12 in sweeps
5/1/1 Planter, double disk opener
10/20/1 Harvest, killing crop 50pct standing stubble
5/5/2 Chisel, straight point
5/15/2 Cultivator, field 6-12 in sweeps
5/15/2 Drill or airseeder, double disk
10/10/2 Harvest, killing crop 20pct standing stubble

18

Corn, grain

Soybean, Midwest, 7in rows

Spring chisel is not available with cover crop management in the default management
database, another type of reduced tillage, disk till, is selected instead.
19
Same scenario as 4.
166

Table 3-A5 (cont’d)
3
4/23/1 Disk, tandem secondary op.
4/27/1 Cultivator, field 6-12 in sweeps
4/30/1 Planter, double disk opener
10/19/1 Harvest, killing crop 50pct standing stubble
10/20/2 Disk, tandem secondary operation
10/30/2 Cultivator, field 6-12 in sweeps
10/30/2 Drill or airseeder, double disk
3/27/3 Harvest, killing crop 20pct standing stubble

Corn, grain

Soybean, Midwest, 7in rows

4&5

10/21/1 Drill or airseeder, double disk
Rye, winter cover
4/20/2 Disk, tandem secondary operation
4/25/2 Cultivator, field 6-12 in sweeps
Corn, grain
5/1/2 Planter, double disk opener
10/10/2 Harvest, killing crop 50pct standing stubble
10/11/2 Drill or airseeder, double disk
Rye, winter cover
4/27/3 Disk, tandem secondary operation
5/1/3 Cultivator, field 6-12 in sweeps
5/15/3 Drill or air seeder single disk openers 7-10 in space Soybean, Midwest, 7in rows
10/10/3 Harvest, killing crop 20pct standing stubble

6

10/11/1 Drill or airseeder, double disk
Rye, winter cover
4/10/2 Disk, tandem secondary operation
4/15/2 Cultivator, field 6-12 in sweeps
4/21/2 Planter, double disk opener
Corn, grain
10/10/2 Harvest, killing crop 50pct standing stubble
10/11/2 Drill or airseeder, double disk
Rye, winter cover
4/27/3 Disk, tandem secondary operation
5/1/3 Cultivator, field 6-12 in sweeps
5/15/3 Drill or air seeder single disk openers 7-10 in space Soybean, Midwest, 7in rows
10/10/3 Harvest, killing crop 20pct standing stubble
10/11/3 Drill or airseeder, double disk
Rye, winter cover
3/22/4 Disk, tandem secondary operation
3/22/4 Cultivator, field 6-12 in sweeps
3/31/4 Drill or air seeder single disk openers 7-10 in space Wheat, spring 7in rows
7/14/4 Harvest, killing crop 50pct standing stubble

167

APPENDIX 3-4: CALCULATION OF EUTROPHIC LAKE REDUCTION FROM
REDUCED SOIL EROSION

The number of eutrophic lakes reduced from soil erosion abatement is derived using the
method developed by Chen (2010). The total phosphorus leaching reduction rate, percentage of
C-S rotation to cropland erosion, total cropland area under corn-soybean rotation (see appendix
3-1), fertilizer contribution to phosphorus input to lakes, and the current number of lakes falling
into different trophic categories are necessary to calculate lake improvement.
The recreational quality of lakes is classified based on their primary biological
productivity, which can be measured by the total phosphorus (TP) level (Fuller, 2008). A
eutrophic lake has high primary productivity due to excessive nutrients and commonly exhibits
poor water quality with algal blooms. Based on the regional characteristics of Michigan, a lake is
classified as eutrophic if the TP level is in the range of 20-50μg/L. The hypereutrophic lake,
which features severe nuisance algal blooms and low transparency, has a greater TP level than
50μg/L. A lake is classified as mesotrophic if TP is less than 20μg/L and as oligotrophic if TP is
less than 10μg/L. These two categories indicate low primary productivity and clear water bodies.
The reduction in the number of eutrophic lakes is measured by those lakes that transition from
the eutrophic class to the mesotrophic and oligotrophic classes, namely the level of TP drops
below 20 μg/L. Assume r is the change in phosphorus runoff from phosphorus fertilizer
application, and NEutrophic is the original number of eutrophic lakes. The following four
assumptions are used to calculate the reduction in the number of eutrophic lakes.
1. Phosphorus runoff from Phosphorus fertilizer application is proportional to the soil erosion
rate.

168

2. Reduction of phosphorus to lakes leads to proportional decrease in TP concentration.
3. Reduced phosphorus input to the waters by different cropping systems leads to uniform
decrease in total phosphorus in inland lakes all over the state.
4. The TP concentration in eutrophic inland lakes is uniformly distributed in the range of 2050μg/L.
Equation A4.1 shows the derivation of change in phosphorus runoff (r). It is the product
of change in soil erosion (Δerosion%), the percentage contribution of corn-soybean cropland
phosphorus runoff to total cropland phosphorus runoff (PC-S/ Pcropland), the percentage
contribution of cropland phosphorus runoff to annual total phosphorus runoff from all sources
(Pcropland/ TP), and flow-to-stock ratio of phosphorus in lakes (TP/ TP0), where TP0 is the existing
level of phosphorus stock in the lake at status quo. Δerosion% is derived from the RUSLE2
model in Appendix 3-3. PC-S/ Pcropland is calculated approximately by Chen (2006) as 28%.
Pfertilizer/ TP is assumed to be 54.8% following Robertson (1996), where he calculated the
percentage of Phosphorus fertilizer input contribution to total Phosphorus input into Western
Lake Michigan from Wisconsin and Michigan drainages. The flow-to-stock ratio ranges from
0% to 100% depending on specific lake depth, volume, discharge of the outlet and time (Ahlgren,
et al., 1988). As this ratio negatively correlates with total phosphorus concentrations (Janus and
Vollenweider, 1984), the flow-to-stock ratio for lakes for the study area can be derived as
approximately 50% -75%, given the median total phosphorus concentration for southern
Michigan lakes is 0.014 mg/L (Fuller, 2008). The lower bound of 50% is chosen as a
20

conservative estimate .

20

A major barrier in restoration of eutrophic lakes by mitigating P input is the phenomenon of
“internal loading”. Bottom sediments in eutrophic lakes often act as a sink for absorbing excess P.
Once P inputs are reduced by conservation practice, the equilibrium between sediment-sorbed P
169

r = Δerosion% *

PC − S

Pcropland

*

Pcropland
TP

*

TP
TP 0

(3.A1)

Equation A4.2 characterizes the number of lakes transitioning from eutrophic to
mesotrophic or oligotrophic classes (ΔLake).
ΔLake =

r * 20
* N eutrophic
(50 − 20) *(1 − r )

(3.A2 )

The parameter r can be calculated from Equation A4.1 and Neutrophic represents the
number of eutrophic lakes in Michigan. According to a USGS Survey of inland lake quality in
2004, 27% of the 11000 inland lakes in Michigan are eutrophic (Minnerick, 2005). Thus,
Neutrophic is calculated as 2970. The reduction of eutrophic lakes due to each farming practice is
shown in Table 3-4.

and dissolved P can be altered and as a result, the sediments can become a source of P, which is
known as “internal loading”. Thus, the benefits of P mitigation efforts may be delayed for 15-50
years (Hamilton, 2011). This effect is not considered in the paper as the primary focus is the
long-term equilibrium condition.
170

APPENDIX 3-5: GHG REDUCTION CALCULATION USING US CROPLAND GHG
CALCULATOR

The Farming Systems Greenhouse Gas Emissions Calculator (FSGGEC)

21

is a web-

based tool developed by researchers at the W.K. Kellogg Biological Station for calculating the
GHG impact of different crop management practices. It is linked to the Soil Organic Carbon
Reserves and Transformations in EcoSystems (SOCRATES) soil carbon process model
(McSwiney, et al., 2010). To obtain the GHG estimates of a cropping system, we need to specify
the county of interest, crops, yields, tillage practices, or nitrogen fertilizer rates with the tool.
Default values are provided based on conventional systems and county averages. Outputs are the
GHG emissions measured in CO2 equivalents (Mt/ac/year ) from soil carbon change, nitrous
oxide (N2O) emission, fuel use, and fertilizer (McSwiney, et al., 2010).
To calculate the GHG emissions effects due to change of different farming practices, five
scenarios are estimated by the GHG calculator. The baseline scenario is a corn-soybean rotation
system with average nitrogen fertilizer use of 142 lb/acre for the corn crop only. The second
scenario with PSNT has 30 lb/ac less fertilizer rate. The third scenario with both PSNT and cover
crops has 35.7 lb/acre less fertilizer use compared with the baseline. The fourth scenario with
wheat in the rotation has the same fertilizer rate for corn as the previous system and 30 lb/acre
less fertilizer use for wheat compared to its default value 66.1 lb/acre. The last scenario with
band fertilizer application further reduces the N fertilizer rate by 1/3. The marginal reduction of
GHG emissions due to each practice is the difference between each successive pair of systems as
shown in Table 3-A6.
21

http://surf.kbs.msu.edu/ghgcalculator/
171

Table 3-A6 Calculation of GHG emissions rate with Farming Systems Greenhouse Gas Emission
Calculator
N Fertilizer
Marginal
GHG
Cover Band
Rate
Change in
Marginal
Scenario Rotation PSNT
emissions
Crop Fertilizer (lb/acre/
GHG
Practice
(lb/acre)
year)
(lb/acre)
corn1
No
No
No
71
1044
--soybean
corn2
Yes No
No
56
972
72
PSNT
soybean
corn3
Yes Yes
No
53.2
956
16
Cover crop
soybean
corn4
soybean- Yes Yes
No
47.5
977
-21
Wheat
wheat
cornBand
5
soybean- Yes Yes
Yes
31.6
885
92
fertilizer
wheat

172

APPENDIX 3-6: OPTIMAL CHOICE BY COMBINING FOUR SYSTEMS

The economic theory of pollution control suggests the cost effective level of control of
multiple technologies is achieved when their marginal costs are equal (Tietenberg and Lewis,
2000). In this study, the four cropping systems can be viewed as four technologies to mitigate
negative environmental impact from crop production. However, the optimal condition cannot be
reached in the hypothetical PES program because the marginal costs of environmental
improvements vary among farms due to their different levels of additionality. Thus, to explore
the cost-minimizing conditions by combining the multiple cropping systems, the marginal cost of
acreage enrollment at each payment is defined as the sum of the average costs for individual
farms to adopt the cropping systems. Each farm is assumed to choose a system among the four at
each payment level to minimize the average cost of additional ecosystem services. This condition
is calculated following steps:
1. At each payment level from 0 to 120 dollars per acre, farm i’s land acreage enrolled at
i,k

payment k, A

, in each cropping system can be simulated following Section 3.4.1 and

Equation 3.18.
2. At each price level, calculate each farmer’s additional effective acreage for each practice,
defined as the enrolled land acreages that newly adopt the specified practice in each
cropping system. See section 3.4.2 and Tables 3-2 and 3-3 for details.
3. Following section 3.4.3, translate each farm’s additional effective acres into abatement in
eutrophic lakes Lake

i,k

i,k

and GHG emissions GHG .

173

4. Calculate each farmer’s average cost for improving eutrophic lakes and mitigating GHG
emissions in each of the four cropping system using the following equation. Since zero
payment is not offered in the survey, the voluntary enrollment with no incentive payment
by farmers is not included in the average cost.
i, k
ACLake =

i,k
ACGHG =

Payment j ⋅ Ai, k
Lake

(3.A3)

i, k

Payment j ⋅ Ai, k

(3.A4)

GHG i, k

5. At each payment level, select the system with the lowest cost for environmental
i,k

22

improvement for each farm, and summarize farms’ land enrollment A
environmental improvement Lake

i,k

and GHG

i,k

and

by stratum to extrapolate state-level
k

estimates. The state-level enrollment for system t at payment k, At is derived by
proportionally scaling up individual farms that choose system t in each acreage stratum
given the number of farms in the sample (N’), the total number in the state (TN) in
Equation A6.3. The total state-level enrollment is the sum of the enrollment in the four
cropping systems as shown in Equation A6.4. The state-level environmental
improvement in lake and GHG are calculated as the sum of products between the state22

The system with lowest average cost of eutrophic lake improvement is selected first. The
reductions in the number of eutrophic lakes and GHG emissions are highly correlated
(coefficients ranging from 0.7 to 0.99), so the systems with lowest cost for lake quality
improvement and GHG mitigation are likely to be the same. If the lowest cost systems are
different for a farm, the system with the lowest cost for lake quality improvement is still chosen,
because the residents generally showed significant WTP for lake improvement while only those
who are very concerned about global warming were willing to pay for GHG mitigation. If there
are no improvement in lake quality for certain farms, the system with the lowest average cost in
GHG mitigation will be chosen.
174

k

level acreage enrollment, At , and the per-acre improvement Laket or GHGt in the four
systems as shown in Equations 3.A7 and 3.A8.

Atk =

N'
1

N'
3

'
N2

N'
4

TN 3
TN 2
TN 4
⋅  Ai , k +
⋅  Ai , k +
⋅  Ai , k +
⋅  Ai , k (3.A5)
'
'
'
'
N 1 i1 =1 1,t
N 2 i2 =1 2,t
N 3 i3 =1 3,t N 4 i1 = 4 4,t

TN1

4

A =  Atk
k

(3.A6)

t =1

4

Lake =  Ak ⋅ Lake _ acret
k

t =1

t

4

GHG =  Ak ⋅ GHG _ acret
k

(3.A7)

t =1

t

175

(3.A8)

APPENDIX 3-7: DETAILED RESULTS FOR BENEFIT AND COST SIMULATION

Table 3-A7 Enrollment, environmental and welfare measures for cropping system A
Price/acre

Farmer
WTA
(million $)

Resident
WTP
(million $)

Economic
surplus
(million $)

Farmer
Welfare
(million $)

Resident
Welfare
(million $)

Spending
(million $)

Enrollment
(million acre)

Lake
(number)

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

0.00
0.03
0.09
0.19
0.35
0.57
0.84
1.18
1.62
2.15
2.75
3.43
4.23
5.10
6.10
7.24
8.47
9.82
11.3
12.9

39
108
112
114
116
119
121
124
125
127
128
130
132
133
134
135
136
137
138
139

39
108
112
114
116
118
120
122
124
124
126
127
128
128
128
128
128
127
127
126

0.00
0.33
0.69
1.08
1.50
1.96
2.47
3.02
3.62
4.27
4.99
5.76
6.60
7.50
8.47
9.51
10.6
11.8
13.1
14.4

39
108
111
113
114
116
118
119
120
120
121
121
121
121
120
119
117
115
114
111

0.00
0.358
0.777
1.27
1.85
2.53
3.30
4.20
5.24
6.42
7.74
9.20
10.8
12.6
14.6
16.8
19.1
21.6
24.4
27.3

0.33
0.36
0.39
0.42
0.46
0.51
0.55
0.60
0.66
0.71
0.77
0.84
0.90
0.97
1.04
1.12
1.19
1.27
1.35
1.44

0
0.000881
0.00179
0.00271
0.00366
0.00793
0.0144
0.0264
0.0396
0.0543
0.0887
0.148
0.212
0.287
0.377
0.487
0.590
0.694
0.835
1.02

176

GHG (%
of 2000
emission
level )
0
0.000245
0.00053
0.00084
0.00121
0.00161
0.00203
0.00250
0.00301
0.00356
0.00412
0.00470
0.00531
0.00592
0.00659
0.0073
0.0080
0.0087
0.0095
0.0102

Table 3-A7 (cont’d)
20
14.6
21
16.6
22
18.6
23
20.9
24
23.1
25
25.5
26
27.9
27
30.4
28
33.1
29
35.8
30
38.5
31
41.3
32
44.1
33
47.0
34
50.0
35
53.0
36
56.1
37
59.1
38
62.1
39
65.1
40
68.0
41
70.9
42
73.8
43
76.7
44
79.5
45
82.2
46
84.9
47
87.7
90.4
48
49
93.1
50
95.7

140
141
141
142
143
143
144
144
145
145
145
146
146
146
147
147
147
147
148
148
148
148
149
149
149
149
149
149
150
150
150

125
124
123
121
119
118
116
114
111
109
107
104
102
99.3
96.6
93.9
91.1
88.4
85.6
82.9
80.2
77.5
74.8
72.1
69.4
66.8
64.3
61.7
59.1
56.6
54.1

15.9
17.4
19.0
20.7
22.5
24.4
26.4
28.5
30.7
33.0
35.4
37.8
40.4
43.0
45.7
48.6
51.5
54.5
57.5
60.7
63.9
67.2
70.6
74.0
77.5
81.1
84.7
88.4
92.1
95.9
99.8

109
107
104
100
96.9
93.2
89.3
85.2
80.8
76.2
71.4
66.5
61.5
56.3
50.9
45.3
39.7
33.9
28.1
22.2
16.3
10.3
4.2
-1.9
-8.1
-14.2
-20.4
-26.7
-33.0
-39.4
-45.7

177

30.5
34.0
37.7
41.6
45.7
49.9
54.3
58.9
63.8
68.8
73.9
79.1
84.5
90.0
95.7
102
108
114
120
126
132
138
144
151
157
163
170
176
183
189
196

1.53
1.62
1.71
1.81
1.90
2.00
2.09
2.18
2.28
2.37
2.46
2.55
2.64
2.73
2.82
2.90
2.99
3.07
3.15
3.22
3.30
3.37
3.44
3.50
3.57
3.63
3.69
3.75
3.80
3.86
3.91

1.24
1.48
1.73
1.97
2.26
2.54
2.80
3.05
3.32
3.55
3.76
4.00
4.24
4.50
4.75
5.00
5.27
5.48
5.75
6.01
6.25
6.46
6.68
6.91
7.11
7.29
7.45
7.62
7.82
8.02
8.21

0.0111
0.0119
0.0128
0.0137
0.0146
0.0154
0.0163
0.0171
0.0180
0.0189
0.0197
0.0206
0.0214
0.0222
0.0230
0.0238
0.0246
0.0253
0.0260
0.0267
0.0274
0.0280
0.0287
0.0293
0.0299
0.0304
0.0310
0.0315
0.0320
0.0325
0.0330

Table 3-A7 (cont’d)
51
98.3
52
101
53
103
106
54
55
108
56
110
113
57
58
115
59
117
119
60
61
121
62
123
125
63
64
126
65
128
130
66
67
132
68
134
135
69
70
137
71
138
140
72
73
141
74
143
144
75
76
145
77
146
147
78
149
79
80
150

150
150
150
150
150
150
151
151
151
151
151
151
151
151
151
151
151
151
151
151
152
152
152
152
152
152
152
152
152
152

51.6
49.2
46.9
44.6
42.4
40.2
38.0
35.9
33.9
32.0
30.1
28.2
26.4
24.6
22.8
21.1
19.4
17.7
16.0
14.5
13.1
11.7
10.4
9.0
7.8
6.6
5.5
4.4
3.3
2.3

104
108
112
116
120
124
128
132
137
141
145
150
154
158
163
167
172
176
181
186
190
195
199
204
209
213
218
223
228
232

-52
-58
-65
-71
-77
-84
-90
-96
-103
-109
-115
-121
-128
-134
-140
-146
-153
-159
-165
-171
-177
-183
-189
-195
-201
-207
-213
-219
-224
-230

178

202
208
215
221
228
234
241
247
253
260
266
272
279
285
291
297
304
310
316
323
329
335
341
347
353
359
365
370
376
382

3.96
4.01
4.06
4.10
4.14
4.18
4.22
4.26
4.30
4.33
4.36
4.39
4.42
4.45
4.48
4.51
4.53
4.56
4.58
4.61
4.63
4.65
4.67
4.69
4.70
4.72
4.73
4.75
4.76
4.77

8.41
8.58
8.76
8.94
9.11
9.26
9.42
9.57
9.69
9.81
9.94
10.1
10.2
10.4
10.5
10.6
10.8
10.9
11.0
11.1
11.3
11.4
11.5
11.6
11.7
11.8
11.8
11.9
12.0
12.0

0.0335
0.0339
0.0343
0.0347
0.0351
0.0355
0.0358
0.0362
0.0365
0.0368
0.0371
0.0374
0.0377
0.0379
0.0382
0.0384
0.0387
0.0389
0.0392
0.0394
0.0396
0.0397
0.0399
0.0401
0.0403
0.0404
0.0406
0.0407
0.0408
0.0409

Table 3-A8 Enrollment, environmental and welfare measures for cropping system B
Price/acre

Farmer
WTA
(million $)

Resident
WTP
(million $)

Economic
surplus
(million $)

Farmer
Welfare
(million $)

Resident
Welfare
(million $)

Spending
(million $)

Enrollment
(million acre)

Lake
(number)

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

0.000
0.0127
0.0393
0.0815
0.141
0.220
0.319
0.440
0.585
0.757
0.951
1.17
1.43
1.71
2.02
2.35
2.71
3.13
3.59
4.10
4.65
5.26
5.92
6.65
7.44
8.29
9.21

39
123
127
130
132
133
135
136
137
138
139
140
140
141
142
142
143
143
144
144
145
145
146
146
147
147
148

38.9
123
127
130
132
133
134
136
136
137
138
138
139
139
140
140
140
140
140
140
140
140
140
140
139
139
138

0.0
0.8
1.6
2.4
3.2
4.0
4.9
5.7
6.6
7.5
8.4
9.3
10.3
11.3
12.3
13.3
14.3
15.4
16.5
17.6
18.8
19.9
21.1
22.4
23.6
24.9
26.2

39
122
126
127
129
129
130
130
130
130
129
129
129
128
127
127
126
125
124
123
121
120
119
117
116
114
112

0.00
0.788
1.60
2.44
3.32
4.23
5.17
6.16
7.18
8.25
9.36
10.5
11.7
13.0
14.3
15.6
17.1
18.5
20.1
21.7
23.4
25.2
27.0
29.0
31.1
33.2
35.4

0.77
0.79
0.80
0.81
0.83
0.85
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.07
1.09
1.12
1.14
1.17
1.20
1.23
1.26
1.29
1.33
1.36

0
0.3
0.579
0.894
1.23
1.59
1.96
2.36
2.78
3.21
3.66
4.13
4.62
5.13
5.65
6.15
6.68
7.25
7.85
8.47
9.11
9.79
10.5
11.2
12.0
12.8
13.7

179

GHG (%
of 2000
emission
level )
0
0.0002
0.0005
0.0008
0.0011
0.0014
0.0017
0.0021
0.0024
0.0028
0.0032
0.0036
0.0040
0.0045
0.0049
0.0054
0.0058
0.0063
0.0069
0.0074
0.0080
0.0086
0.0092
0.0098
0.0105
0.0112
0.0119

Table 3-A8 (cont’d)
27
10.2
28
11.2
29
12.4
30
13.6
31
14.8
32
16.1
33
17.5
34
18.9
35
20.4
36
21.9
37
23.5
38
25.2
39
27.0
40
28.9
41
30.8
42
32.8
43
34.8
44
36.9
45
39.0
46
41.2
47
43.5
48
45.9
49
48.4
50
50.9
51
53.5
52
56.1
53
58.7
54
61.4
64.2
55
56
67.0
57
69.9

148
149
149
149
150
150
151
151
151
152
152
152
152
153
153
153
154
154
154
154
155
155
155
155
156
156
156
156
157
157
157

138
137
137
136
135
134
133
132
131
130
128
127
125
124
122
121
119
117
115
113
111
109
107
105
102
99.8
97.4
95.0
92.4
89.8
87.1

27.6
29.0
30.4
31.9
33.4
35.0
36.6
38.2
39.9
41.6
43.4
45.2
47.1
49.0
50.9
52.9
54.9
57.0
59.2
61.3
63.6
65.8
68.2
70.6
73.0
75.5
78.0
80.6
83.2
85.9
88.6

110
108
106
104
102
99.0
96.4
93.7
90.9
88.0
84.9
81.7
78.4
75.0
71.4
67.7
63.9
60.0
56.0
51.9
47.6
43.2
38.7
34.0
29.2
24.4
19.4
14.4
9.2
3.9
-1.5

180

37.8
40.3
42.8
45.5
48.2
51.1
54.1
57.1
60.3
63.6
66.9
70.4
74.1
77.8
81.7
85.7
89.7
93.9
98.2
103
107
112
117
121
127
132
137
142
147
153
158

1.40
1.44
1.48
1.52
1.56
1.60
1.64
1.68
1.72
1.77
1.81
1.85
1.90
1.95
1.99
2.04
2.09
2.13
2.18
2.23
2.28
2.33
2.38
2.43
2.48
2.53
2.58
2.63
2.68
2.73
2.78

14.6
15.5
16.4
17.4
18.4
19.4
20.5
21.5
22.6
23.6
24.7
25.9
27.1
28.3
29.5
30.7
31.9
33.2
34.4
35.7
36.9
38.2
39.5
40.9
42.2
43.5
44.8
46.2
47.5
48.9
50.3

0.0127
0.0135
0.0143
0.0151
0.0160
0.0169
0.0178
0.0186
0.0195
0.0205
0.0214
0.0224
0.0234
0.0244
0.0254
0.0264
0.0275
0.0285
0.0295
0.0306
0.0317
0.0327
0.0339
0.0350
0.0361
0.0372
0.0383
0.0394
0.0405
0.0417
0.0428

Table 3-A8 (cont’d)
58
72.8
59
75.7
60
78.6
61
81.4
62
84.4
63
87.3
64
90.1
65
93.1
66
95.9
67
98.7
68
101
69
104
70
107
71
109
72
112
73
115
74
117
75
120
76
123
77
125
78
128
79
131
80
133

157
157
158
158
158
158
158
158
159
159
159
159
159
159
159
159
159
160
160
160
160
160
160

84.4
81.7
79.0
76.3
73.5
70.8
68.1
65.3
62.6
59.9
57.4
54.8
52.2
49.6
47.1
44.6
42.0
39.39
36.80
34.28
31.79
29.37
26.93

91.4
94.2
97.1
100
103
106
109
112
115
119
122
125
128
132
135
139
142
146
149
153
156
160
164

-7.0
-12.5
-18.1
-23.7
-29.5
-35.2
-41.0
-46.9
-52.8
-58.6
-64.5
-70
-76
-82
-88
-94
-100
-106
-112
-118
-125
-131
-137

181

164
170
176
181
187
193
199
205
211
217
223
229
235
241
247
253
260
266
272
278
284
291
297

2.83
2.88
2.93
2.98
3.02
3.07
3.11
3.16
3.20
3.24
3.28
3.32
3.36
3.40
3.44
3.47
3.51
3.54
3.58
3.61
3.65
3.68
3.71

51.7
53.0
54.3
55.5
56.8
58.0
59.3
60.5
61.6
62.8
63.9
64.9
65.9
66.9
67.9
68.8
69.8
70.8
71.7
72.6
73.5
74.4
75.3

0.0439
0.0450
0.0461
0.0471
0.0482
0.0492
0.0502
0.0512
0.0521
0.0530
0.0539
0.0548
0.0556
0.0565
0.0573
0.0581
0.0589
0.0597
0.0605
0.0613
0.0620
0.0627
0.0634

Table 3-A9 Enrollment, environmental and welfare measures for cropping system C
Price/acre

Farmer
WTA
(million $)

Resident
WTP
(million $)

Economic
surplus
(million $)

Farmer
Welfare
(million $)

Resident
Welfare
(million $)

Spending
(million $)

Enrollment
(million acre)

Lake
(number)

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

0.00
0.02
0.05
0.10
0.17
0.26
0.37
0.51
0.66
0.84
1.05
1.29
1.55
1.85
2.17
2.53
2.91
3.34
3.79
4.28
4.80
5.36
5.96
6.60
7.29
8.02

39
125
130
132
134
136
137
138
139
140
141
141
142
143
143
144
145
145
146
146
146
147
147
148
148
149

38.9
125
130
132
134
135
137
138
138
139
140
140
141
141
141
141
142
142
142
142
142
142
141
141
141
141

0.00
0.54
1.10
1.68
2.27
2.88
3.51
4.15
4.82
5.50
6.21
6.94
7.68
8.45
9.25
10.1
10.9
11.8
12.7
13.6
14.5
15.5
16.5
17.5
18.5
19.6

38.9
125
128
130
132
133
133
133
134
134
133
133
133
132
132
131
131
130
129
128
127
126
125
124
122
121

0.00
0.56
1.15
1.78
2.44
3.14
3.88
4.66
5.48
6.35
7.26
8.22
9.24
10.3
11.4
12.6
13.8
15.1
16.4
17.8
19.3
20.8
22.4
24.1
25.8
27.6

0.543
0.559
0.575
0.592
0.610
0.628
0.647
0.666
0.685
0.705
0.726
0.748
0.770
0.792
0.816
0.839
0.863
0.888
0.913
0.939
0.965
0.992
1.02
1.05
1.08
1.10

0
0.410
0.832
1.27
1.72
2.19
2.67
3.16
3.67
4.19
4.73
5.29
5.87
6.47
7.09
7.73
8.38
9.05
9.74
10.4
11.2
11.9
12.6
13.4
14.2
15.0

182

GHG (%
of 2000
emission
level )
0
0.0004
0.0008
0.0012
0.0016
0.0020
0.0025
0.0029
0.0034
0.0039
0.0044
0.0049
0.0054
0.0060
0.0066
0.0072
0.0078
0.0084
0.0090
0.0096
0.0103
0.0110
0.0116
0.0123
0.0131
0.0138

Table 3-A9 (cont’d)
26
8.80
27
9.62
28
10.5
29
11.3
30
12.3
31
13.2
32
14.2
33
15.3
34
16.4
35
17.5
36
18.7
37
19.9
38
21.1
39
22.4
40
23.8
41
25.2
42
26.6
43
28.1
44
29.6
45
31.1
46
32.6
47
34.2
48
35.8
49
37.5
50
39.3
51
41.1
52
43.0
53
44.9
54
46.9
55
49.0
56
51.1

149
149
150
150
150
151
151
151
151
152
152
152
153
153
153
153
154
154
154
154
154
155
155
155
155
155
156
156
156
156
156

140
140
139
139
138
137
137
136
135
134
133
132
131
130
129
128
127
126
124
123
122
120
119
117
116
114
113
111
109
107
105

20.7
21.8
23.0
24.2
25.4
26.7
28.0
29.3
30.6
32.0
33.4
34.9
36.4
37.9
39.4
41.0
42.6
44.3
46.0
47.7
49.4
51.2
53.0
54.9
56.8
58.7
60.6
62.6
64.7
66.7
68.8

119
118
116
114
113
111
109
107
104
102
99.9
97.5
95.0
92.5
89.8
87.1
84.3
81.4
78.4
75.4
72.3
69.2
65.9
62.6
59.2
55.6
52.0
48.2
44.4
40.4
36.4

183

29.5
31.5
33.5
35.5
37.7
39.9
42.2
44.6
47.0
49.5
52.1
54.8
57.5
60.3
63.2
66.2
69.2
72.4
75.5
78.8
82.1
85.4
88.9
92.4
96.0
99.8
104
108
112
116
120

1.13
1.17
1.20
1.23
1.26
1.29
1.32
1.35
1.38
1.42
1.45
1.48
1.51
1.55
1.58
1.61
1.65
1.68
1.72
1.75
1.78
1.82
1.85
1.89
1.92
1.96
1.99
2.03
2.07
2.10
2.14

15.8
16.7
17.5
18.3
19.2
20.0
20.9
21.8
22.6
23.5
24.4
25.3
26.2
27.1
28.1
29.0
30.0
30.9
31.9
32.8
33.8
34.8
35.7
36.7
37.7
38.7
39.7
40.8
41.8
42.9
43.9

0.0146
0.0154
0.0161
0.0169
0.0177
0.0185
0.0193
0.0201
0.0209
0.0217
0.0226
0.0234
0.0243
0.0251
0.0260
0.0269
0.0278
0.0287
0.0296
0.0305
0.0313
0.0322
0.0331
0.0340
0.0349
0.0359
0.0368
0.0378
0.0388
0.0398
0.0408

Table 3-A9 (cont’d)
57
53.2
58
55.3
59
57.5
60
59.8
61
62.1
62
64.4
63
66.7
64
69.1
65
71.5
66
73.9
67
76.3
68
78.8
69
81.3
70
83.8
71
86.3
72
88.8
73
91.3
74
93.8
75
96.4
76
98.9
77
101
78
104
79
106
80
109

157
157
157
157
157
157
158
158
158
158
158
158
158
159
159
159
159
159
159
159
159
159
160
160

103
101
99.3
97.2
95.1
93.0
90.8
88.6
86.4
84.1
81.8
79.4
77.1
74.7
72.4
70.0
67.6
65.2
62.8
60.3
57.9
55.5
53.2
50.8

71.0
73.1
75.4
77.6
79.9
82.2
84.6
87.0
89.4
91.9
94.4
97.0
99.6
102
105
108
110
113
116
119
122
124
127
130

32.4
28.2
24.0
19.6
15.2
10.8
6.2
1.6
-3.1
-7.8
-12.6
-17.5
-22.5
-27.4
-32.5
-37.5
-42.6
-47.8
-53.0
-58.3
-64
-69
-74
-79

184

124
128
133
137
142
147
151
156
161
166
171
176
181
186
191
196
202
207
212
218
223
228
234
239

2.18
2.22
2.25
2.29
2.33
2.36
2.40
2.44
2.48
2.51
2.55
2.59
2.62
2.66
2.69
2.73
2.76
2.80
2.83
2.86
2.90
2.93
2.96
2.99

45.0
46.1
47.1
48.2
49.3
50.4
51.5
52.6
53.6
54.7
55.8
56.9
57.9
59.0
60.0
61.0
62.0
63.0
64.1
65.0
66.0
66.9
67.8
68.7

0.0418
0.0428
0.0438
0.0448
0.0458
0.0468
0.0478
0.0488
0.0498
0.0508
0.0517
0.0527
0.0537
0.0547
0.0556
0.0566
0.0575
0.0584
0.0594
0.0603
0.0612
0.0621
0.0629
0.0638

Table 3-A10 Enrollment, environmental and welfare measures for cropping system D
Price/acre

Farmer
WTA
(million $)

Resident
WTP
(million $)

Economic
surplus
(million $)

Farmer
Welfare
(million $)

Resident
Welfare
(million $)

Spending
(million $)

Enrollment
(million acre)

Lake
(number)

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

0.000
0.0136
0.0411
0.0831
0.140
0.212
0.300
0.403
0.521
0.655
0.804
0.970
1.15
1.35
1.56
1.79
2.04
2.31
2.59
2.90
3.22
3.56
3.92
4.29
4.69
5.10

38.9
124
128
131
132
134
135
136
137
138
139
139
140
140
141
141
142
142
143
143
143
144
144
144
145
145

38.9
124
128
130
132
134
135
136
137
137
138
138
139
139
139
140
140
140
140
140
140
140
140
140
140
140

0.0
0.846
1.71
2.58
3.47
4.37
5.28
6.21
7.16
8.12
9.09
10.1
11.1
12.1
13.1
14.2
15.3
16.3
17.4
18.5
19.7
20.8
22.0
23.2
24.4
25.6

38.9
123
126
128
129
129
130
130
129
129
129
128
128
127
126
125
124
124
123
122
121
119
118
117
116
114

0.00
0.86
1.75
2.66
3.61
4.58
5.58
6.62
7.68
8.77
9.90
11.1
12.2
13.5
14.7
16.0
17.3
18.6
20.0
21.4
22.9
24.4
25.9
27.5
29.0
30.7

0.846
0.859
0.873
0.887
0.901
0.916
0.930
0.945
0.960
0.975
0.990
1.00
1.02
1.04
1.05
1.07
1.08
1.10
1.11
1.13
1.15
1.16
1.18
1.19
1.21
1.23

0
0.321
0.646
0.98
1.32
1.66
2.02
2.36
2.71
3.06
3.41
3.77
4.13
4.48
4.83
5.19
5.55
5.93
6.31
6.69
7.08
7.47
7.85
8.24
8.63
9.03

185

GHG (%
of 2000
emission
level )
0
0.000
0.001
0.001
0.001
0.002
0.002
0.002
0.003
0.003
0.003
0.004
0.004
0.004
0.005
0.005
0.005
0.006
0.006
0.006
0.007
0.007
0.007
0.008
0.008
0.009

Table 3-A10 (cont’d)
26
5.55
27
6.01
28
6.50
29
7.01
30
7.54
31
8.10
32
8.68
33
9.29
34
9.93
35
10.6
36
11.3
37
12.0
38
12.7
39
13.4
40
14.2
41
15.0
42
15.8
43
16.6
44
17.5
45
18.3
46
19.2
47
20.1
48
21.1
49
22.0
50
23.0
51
24.0
52
25.0
53
26.1
54
27.2
55
28.2
56
29.3

145
146
146
146
147
147
147
147
148
148
148
148
148
149
149
149
149
150
150
150
150
150
150
151
151
151
151
151
151
152
152

140
140
139
139
139
139
138
138
138
137
137
136
136
135
135
134
134
133
132
132
131
130
129
129
128
127
126
125
124
123
122

26.8
28.0
29.3
30.6
31.9
33.2
34.5
35.9
37.2
38.6
40.0
41.5
42.9
44.4
45.8
47.3
48.9
50.4
52.0
53.5
55.1
56.7
58.4
60.0
61.7
63.4
65.1
66.9
68.6
70.4
72.2

113
112
110
109
107
106
104
102
100
98.6
96.7
94.9
92.9
90.9
88.9
86.8
84.7
82.5
80.3
78.1
75.8
73.4
71.0
68.6
66.1
63.6
60.99
58.37
55.71
53.01
50.26

186

32.3
34.0
35.8
37.6
39.4
41.3
43.2
45.2
47.2
49.2
51.3
53.4
55.6
57.8
60.0
62.3
64.6
67.0
69.4
71.9
74.4
76.9
79.5
82.1
84.7
87.4
90.2
92.9
95.8
98.6
102

1.24
1.26
1.28
1.30
1.31
1.33
1.35
1.37
1.39
1.41
1.42
1.44
1.46
1.48
1.50
1.52
1.54
1.56
1.58
1.60
1.62
1.64
1.66
1.67
1.69
1.71
1.73
1.75
1.77
1.79
1.81

9.43
9.84
10.3
10.7
11.1
11.5
12.0
12.4
12.9
13.4
13.8
14.3
14.7
15.2
15.7
16.1
16.6
17.1
17.6
18.1
18.5
19.0
19.5
20.0
20.5
21.0
21.5
22.0
22.5
22.9
23.4

0.009
0.009
0.010
0.010
0.010
0.011
0.011
0.012
0.012
0.013
0.013
0.013
0.014
0.014
0.015
0.015
0.016
0.016
0.017
0.017
0.017
0.018
0.018
0.019
0.019
0.020
0.020
0.021
0.021
0.022
0.022

Table 3-A10 (cont’d)
57
30.5
58
31.6
59
32.8
60
34.0
61
35.2
62
36.5
63
37.8
64
39.1
65
40.4
66
41.8
67
43.2
68
44.6
69
46.0
70
47.5
71
49.0
72
50.5
73
52.0
74
53.5
75
55.1
76
56.6
77
58.2
78
59.9
79
61.5
80
63.2

152
152
152
152
153
153
153
153
153
153
153
153
154
154
154
154
154
154
154
154
155
155
155
155

121
120
119
118
117
116
115
114
113
111
110
109
108
106
105
104
102
101
99.3
97.8
96.3
94.8
93.3
91.7

74.0
75.8
77.7
79.5
81.4
83.4
85.3
87.2
89.2
91.2
93.2
95.3
97.3
99.4
101
104
106
108
110
112
115
117
119
121

47.46
44.62
41.73
38.8
35.8
32.8
29.7
26.6
23.4
20.2
16.9
13.6
10.2
6.8
3.4
-0.1
-3.6
-7.2
-10.8
-14.5
-18.2
-22.0
-25.8
-29.6

187

104
107
110
114
117
120
123
126
130
133
136
140
143
147
150
154
158
161
165
169
173
177
181
185

1.83
1.85
1.87
1.89
1.91
1.93
1.95
1.97
1.99
2.02
2.04
2.06
2.08
2.10
2.12
2.14
2.16
2.18
2.20
2.22
2.24
2.26
2.29
2.31

23.9
24.4
24.9
25.4
25.9
26.4
26.9
27.4
27.9
28.5
29.0
29.5
30.1
30.6
31.1
31.6
32.2
32.7
33.3
33.8
34.4
34.9
35.4
36.0

0.022
0.023
0.023
0.024
0.024
0.025
0.025
0.026
0.026
0.027
0.027
0.028
0.028
0.029
0.029
0.030
0.030
0.031
0.031
0.032
0.032
0.033
0.033
0.034

Table 3-A11 Enrollment, environmental and welfare measures for mixed-choice cropping system alternative
Price/acre

Farmer
WTA
(million $)

Resident
WTP
(million $)

Economic
surplus
(million $)

Farmer
Welfare
(million $)

Resident
Welfare
(million $)

Spending
(million $)

Enrollment
(million acre)

Lake
(number)

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

0.000
0.133
0.175
0.240
0.295
0.451
0.467
0.769
0.820
0.928
1.242
1.611
1.81
2.07
2.87
3.29
3.27
4.93
4.47
5.47
5.62
6.76
6.74
8.01
7.92
9.35
9.54

39
140
141
142
142
143
142
143
143
143
144
144
145
144
145
145
145
146
146
147
147
147
147
148
147
148
148

38.9
140
141
141
141
142
142
142
142
142
142
142
143
142
142
142
142
141
142
141
141
140
140
140
140
139
138

0.0
0.7
1.5
2.3
3.2
4.1
5.0
5.9
6.8
7.8
8.8
9.8
10.8
11.8
12.9
14.0
15.2
16.3
17.6
18.8
20.1
21.4
22.7
24.1
25.5
26.8
28.3

38.9
139
139
139
138
138
137
136
136
134
134
133
132
131
129
128
127
125
124
122
121
119
118
116
114
112
110

0.00
0.82
1.67
2.58
3.49
4.52
5.44
6.65
7.65
8.71
9.99
11.4
12.6
13.9
15.8
17.3
18.5
21.3
22.1
24.3
25.7
28.1
29.5
32.1
33.4
36.2
37.8

0.68
0.82
0.84
0.86
0.87
0.90
0.91
0.95
0.96
0.97
1.00
1.03
1.05
1.07
1.13
1.15
1.15
1.25
1.23
1.28
1.29
1.34
1.34
1.39
1.39
1.45
1.46

0
4.17
4.62
5.07
5.22
6.01
5.73
6.56
6.81
6.52
7.45
7.81
8.43
8.35
9.90
9.80
10.0
11.5
11.3
12.2
12.8
13.3
13.7
14.8
14.7
15.8
16.1

188

GHG (%
of 2000
emission
level )
0
0.0043
0.0048
0.0054
0.0054
0.0063
0.0055
0.0064
0.0064
0.0062
0.0065
0.0070
0.0077
0.0076
0.0082
0.0082
0.0082
0.0092
0.0093
0.0098
0.0098
0.0100
0.0102
0.0109
0.0105
0.0111
0.0110

Table 3-A11 (cont’d)
27
12.7
28
12.5
29
13.4
30
16.3
31
17.2
32
16.6
33
17.6
34
21.4
35
21.5
36
21.7
37
24.4
38
25.8
39
26.7
40
27.2
41
29.4
42
31.9
43
32.3
44
33.8
45
35.9
46
36.5
47
37.6
48
38.5
49
39.3
50
41.7
51
42.5
52
45.1
53
47.1
54
51.7
55
51.6
56
54.2
57
60.0

149
149
149
150
150
150
150
150
150
151
151
151
151
152
152
152
152
152
152
152
153
153
153
153
153
153
153
153
153
154
154

136
137
136
133
133
133
132
129
129
129
127
125
125
124
122
120
120
118
116
116
115
114
113
111
110
108
106
102
102
99.5
94.0

29.7
31.3
32.9
34.5
36.2
37.9
39.6
41.3
43.2
45.0
46.9
48.8
50.8
52.7
54.7
56.8
58.9
61.0
63.2
65.4
67.6
69.8
72.1
74.4
76.7
79.0
81.4
83.8
86.3
88.9
91.4

106
105
103
98.9
96.6
95.5
92.7
87.7
85.7
83.8
79.7
76.6
73.9
71.6
67.6
63.2
60.9
57.3
53.2
50.4
47.4
44.4
41.2
36.8
33.7
29.0
24.9
17.9
15.6
10.6
2.58

189

42.4
43.8
46.3
50.8
53.4
54.5
57.2
62.7
64.7
66.7
71.3
74.6
77.5
79.9
84.1
88.7
91.2
94.8
99.1
102
105
108
111
116
119
124
128
136
138
143
151

1.57
1.56
1.60
1.69
1.72
1.70
1.73
1.84
1.85
1.85
1.93
1.96
1.99
2.00
2.05
2.11
2.12
2.15
2.20
2.21
2.24
2.26
2.27
2.32
2.34
2.39
2.42
2.51
2.51
2.55
2.66

18.1
18.8
19.2
21.2
22.0
22.2
22.7
24.3
24.6
25.3
26.8
27.6
28.7
29.4
30.4
31.5
32.3
33.0
34.0
34.4
35.4
36.0
36.4
37.5
38.5
39.8
40.9
42.4
42.8
44.4
46.3

0.0126
0.0128
0.0127
0.0138
0.0143
0.0141
0.0140
0.0146
0.0147
0.0148
0.0157
0.0160
0.0163
0.0168
0.0171
0.0172
0.0176
0.0176
0.0181
0.0179
0.0187
0.0193
0.0183
0.0192
0.0191
0.0197
0.0200
0.0203
0.0200
0.0205
0.0211

Table 3-A11 (cont’d)
58
59.8
59
63.5
60
64.8
61
66.8
62
69.0
63
74.0
64
70.5
65
76.6
66
76.7
67
77.9
68
84.9
69
83.2
70
88.6
71
87.5
72
90.4
73
94.4
74
94.0
75
95.4
76
100.8
77
101.2
78
101.8
79
108.1
80
105.8

154
154
154
154
155
155
155
155
155
155
155
155
155
155
155
156
155
156
156
156
156
156
156

94.3
90.6
89.6
87.6
85.5
80.7
84.2
78.1
78.2
77.1
70.2
72.0
66.7
67.8
65.1
61.1
61.4
60.2
54.9
54.6
54.0
47.8
50.3

94.1
96.7
99.4
102
105
108
111
113
116
119
122
125
128
131
135
138
141
144
147
150
154
157
160

0.26
-6.14
-9.9
-14.6
-19.4
-27.1
-26.5
-35.3
-38.2
-42.2
-52.0
-53.3
-61.6
-63.7
-69.4
-76.5
-79.4
-83.8
-92.2
-95.9
-99.7
-109.2
-110.1

190

154
160
164
169
174
182
181
190
193
197
207
209
217
219
225
232
235
239
248
252
255
265
266

2.65
2.72
2.74
2.77
2.81
2.89
2.83
2.92
2.92
2.94
3.05
3.02
3.10
3.08
3.12
3.18
3.17
3.19
3.26
3.27
3.28
3.36
3.33

47.0
48.2
49.2
50.1
51.2
52.7
52.4
53.9
54.8
55.3
57.4
57.7
59.1
58.9
60.6
61.9
61.9
62.6
64.1
64.5
65.1
66.7
66.8

0.0219
0.0211
0.0223
0.0217
0.0224
0.0228
0.0229
0.0228
0.0230
0.0235
0.0234
0.0240
0.0243
0.0241
0.0246
0.0243
0.0239
0.0247
0.0254
0.0252
0.0249
0.0251
0.0259

APPENDIX 3-8: DETAILED RESULTS FOR BENEFIT AND COST SIMULATION (PAYMENT FOR ADDITIONALITY)

Table 3-A12 Enrollment, environmental and welfare measures for cropping system A (payment for additionality)
Price/acre
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21

Farmer
WTA
(million $)

Resident
WTP
(million $)

Economic
surplus
(million $)

Farmer
Welfare
(million $)

Resident
Welfare
(million $)

Spending
(million $)

Enrollment
(million acre)

Lake
(number)

GHG (% of
2000
emission
level )

0.525
0.718
0.980
1.18
1.46
1.73
2.13

125
126
127
128
130
131
132

14.4
15.4
16.3
17.5
18.7
20.1
21.3

0.00
0.0350
0.0821
0.145
0.218
0.307
0.408

124
125
126
127
128
129
129

0.525
0.753
1.06
1.33
1.68
2.03
2.54

0.0350
0.0471
0.0625
0.0738
0.0883
0.102
0.121

0.382
0.467
0.556
0.674
0.823
1.01
1.20

0.000304
0.000408
0.000542
0.000641
0.000766
0.000883
0.00105

191

Table 3-A12 (cont’d)
22
2.53
23
2.88
24
3.31
25
3.60
26
4.25
27
4.66
28
5.20
29
5.47
30
6.03
31
6.87
32
7.37
33
7.94
34
8.44
35
9.00
36
10.3
37
11.1
38
11.7
39
12.1
40
12.6
41
13.6
42
14.2
43
14.9
44
15.8
45
16.7
46
17.0
47
17.9
48
18.4
49
20.0
50
20.6
51
21.8
52
22.4

133
133
134
135
135
136
136
137
137
138
138
138
139
139
140
140
140
140
141
141
141
141
141
142
142
142
142
142
143
143
143

22.4
23.4
24.4
25.4
25.9
26.6
27.1
27.7
27.9
28.0
28.3
28.6
28.9
29.1
28.6
28.4
28.5
28.8
28.9
28.4
28.4
28.3
27.9
27.5
27.5
27.0
26.9
25.8
25.6
24.9
24.8

0.529
0.668
0.823
0.995
1.18
1.39
1.61
1.85
2.11
2.38
2.68
2.99
3.32
3.67
4.03
4.43
4.85
5.28
5.73
6.19
6.67
7.17
7.68
8.22
8.77
9.33
9.91
10.5
11.1
11.8
12.4

130
130
130
130
130
130
130
129
129
128
128
127
127
126
125
124
124
123
122
121
120
119
118
117
116
115
114
112
111
109
108

192

3.05
3.55
4.13
4.59
5.42
6.05
6.81
7.32
8.13
9.25
10.0
10.9
11.8
12.7
14.4
15.6
16.6
17.4
18.4
19.8
20.9
22.0
23.5
24.9
25.8
27.2
28.3
30.5
31.7
33.6
34.8

0.139
0.154
0.172
0.184
0.209
0.224
0.243
0.253
0.271
0.298
0.314
0.331
0.346
0.362
0.399
0.420
0.436
0.447
0.459
0.483
0.497
0.513
0.534
0.553
0.561
0.579
0.590
0.622
0.635
0.659
0.669

1.41
1.61
1.84
2.07
2.28
2.49
2.71
2.90
3.07
3.30
3.49
3.71
3.92
4.13
4.35
4.52
4.74
4.94
5.13
5.29
5.48
5.66
5.83
5.98
6.10
6.25
6.40
6.56
6.72
6.90
7.06

0.00120
0.00134
0.00149
0.00159
0.00181
0.00194
0.00211
0.00219
0.00235
0.00257
0.00270
0.00286
0.00298
0.00312
0.00345
0.00363
0.00377
0.00386
0.00396
0.00417
0.00428
0.00441
0.00460
0.00476
0.00483
0.00498
0.00508
0.00536
0.00547
0.00563
0.00570

Table 3-A12 (cont’d)
53
23.3
54
23.8
55
24.4
56
25.7
57
26.5
58
26.8
59
27.9
60
28.4
61
29.3
62
30.1
63
31.0
64
32.0
65
32.7
66
33.1
67
33.4
68
33.8
69
34.9
70
35.8
71
36.9
72
37.3
73
37.7
74
38.0
75
38.3
76
38.9
77
39.1
78
39.4
79
39.6
80
39.7

143
143
143
143
144
144
144
144
144
144
144
144
144
144
144
145
145
145
145
145
145
145
145
145
145
145
145
145

24.2
24.2
23.9
23.0
22.6
22.5
21.7
21.5
20.8
20.2
19.6
18.9
18.6
18.4
18.3
18.2
17.3
16.6
15.7
15.5
15.4
15.2
15.1
14.7
14.5
14.4
14.3
14.3

13.1
13.8
14.5
15.2
15.9
16.6
17.4
18.2
18.9
19.7
20.5
21.4
22.2
23.0
23.9
24.7
25.6
26.5
27.4
28.3
29.2
30.1
31.0
31.9
32.9
33.8
34.7
35.7

107
106
104
103
101
100
98.45
97.26
95.73
94.17
92.58
90.92
89.51
88.34
87.18
86.03
84.19
82.4
80.5
79.3
78.1
76.9
75.7
74.2
73.1
71.9
70.8
69.7

193

36.4
37.5
38.8
40.9
42.4
43.5
45.3
46.6
48.2
49.9
51.6
53.3
54.8
56.1
57.3
58.5
60.5
62.3
64.3
65.6
66.8
68.1
69.3
70.9
72.0
73.2
74.3
75.4

0.687
0.695
0.706
0.730
0.743
0.749
0.768
0.776
0.790
0.804
0.819
0.833
0.844
0.850
0.855
0.861
0.876
0.890
0.905
0.911
0.916
0.921
0.924
0.932
0.935
0.938
0.941
0.943

7.22
7.37
7.51
7.69
7.82
7.94
8.04
8.15
8.25
8.36
8.48
8.59
8.71
8.83
8.94
9.04
9.15
9.24
9.33
9.43
9.53
9.63
9.70
9.77
9.83
9.88
9.94
10.0

0.00586
0.00593
0.00602
0.00619
0.00630
0.00636
0.00652
0.00659
0.00671
0.00683
0.00696
0.00708
0.00717
0.00723
0.00727
0.00732
0.00746
0.00758
0.00765
0.00770
0.00774
0.00778
0.00782
0.00789
0.00791
0.00794
0.00796
0.00798

Table 3-A13 Enrollment, environmental and welfare measures for cropping system B (payment for additionality)
price/acre

Farmer
WTA
(million $)

Resident
WTP
(million $)

Economic
surplus
(million $)

Farmer
Welfare
(million $)

Resident
Welfare
(million $)

Spending
(million $)

Enrollment
(million acre)

Lake
(number)

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

0.000
0.0119
0.0386
0.0834
0.137
0.211
0.305
0.415
0.554
0.717
0.896
1.10
1.41
1.68
1.98
2.28
2.63
3.02
3.50
3.98
4.49
5.14
5.77
6.48
7.33
8.14
9.04

39
121
125
128
130
131
133
134
135
136
137
137
138
139
140
140
141
141
142
142
143
143
144
144
145
145
145

69.8
70.2
70.6
71.0
71.4
71.8
72.3
72.7
73.1
73.5
73.9
74.3
74.6
75.0
75.4
75.7
76.0
76.3
76.5
76.7
77.0
77.1
77.2
77.4
77.3
77.4
77.4

0.00
0.746
1.50
2.28
3.06
3.86
4.68
5.51
6.35
7.21
8.10
9.00
9.91
10.9
11.8
12.8
13.8
14.8
15.9
17.0
18.1
19.2
20.4
21.5
22.8
24.0
25.3

38.9
120
124
126
127
127
128
128
128
128
128
127
127
126
126
125
124
123
122
121
120
119
118
116
115
113
111

0.00
0.758
1.54
2.36
3.20
4.07
4.98
5.92
6.91
7.93
8.99
10.1
11.3
12.5
13.8
15.1
16.4
17.9
19.4
20.9
22.6
24.3
26.1
28.0
30.1
32.2
34.3

0.746
0.758
0.771
0.786
0.800
0.814
0.830
0.846
0.863
0.881
0.899
0.918
0.944
0.965
0.986
1.01
1.03
1.05
1.08
1.10
1.13
1.16
1.19
1.22
1.25
1.29
1.32

0
0.28
0.58
0.89
1.23
1.59
1.96
2.36
2.78
3.21
3.66
4.13
4.62
5.13
5.65
6.15
6.68
7.25
7.85
8.47
9.11
9.79
10.5
11.2
12.0
12.8
13.7

194

GHG (%
of 2000
emission
level )
0
0.00013
0.00028
0.00044
0.00060
0.00077
0.00095
0.00113
0.00133
0.00153
0.0017
0.0020
0.0022
0.0025
0.0027
0.0030
0.0032
0.0035
0.0038
0.0041
0.0044
0.0047
0.0050
0.0054
0.0058
0.0062
0.0066

Table 3-A13 (cont’d)
27
10.1
28
11.1
29
12.2
30
13.6
31
14.8
32
16.1
33
17.5
34
19.0
35
20.4
36
21.9
37
23.5
38
25.5
39
27.3
40
29.1
41
31.0
42
33.0
43
35.0
44
37.1
45
39.3
46
41.4
47
43.8
48
46.2
49
48.6
50
51.2
51
54.3
52
56.9
53
59.5
54
62.2
55
64.9
56
67.7
57
70.6

146
146
147
147
148
148
148
149
149
149
150
150
150
151
151
151
151
152
152
152
152
153
153
153
153
154
154
154
154
154
155

77.3
77.2
77.0
76.6
76.4
76.0
75.6
75.1
74.6
74.1
73.5
72.5
71.7
70.9
70.0
69.0
68.0
67.0
65.7
64.5
63.1
61.7
60.2
58.7
56.5
54.9
53.2
51.5
49.7
47.8
45.8

26.6
28.0
29.4
30.8
32.3
33.8
35.4
37.0
38.6
40.3
42.0
43.8
45.6
47.5
49.4
51.4
53.4
55.4
57.5
59.7
61.9
64.1
66.4
68.8
71.2
73.7
76.2
78.7
81.3
84.0
86.7

109
107
105
103
100
98.0
95.4
92.7
89.9
87.1
84.1
80.6
77.3
73.9
70.4
66.7
63.0
59.2
55.09
51.03
46.68
42.35
37.82
33.2
27.9
23.1
18.1
13.1
8.0
2.8
-2.7

195

36.7
39.1
41.6
44.4
47.1
49.9
52.9
56.0
59.0
62.2
65.5
69.3
72.9
76.6
80.4
84.4
88.4
92.5
96.8
101
106
110
115
120
126
131
136
141
146
152
157

1.36
1.40
1.43
1.48
1.52
1.56
1.60
1.65
1.69
1.73
1.77
1.82
1.87
1.92
1.96
2.01
2.06
2.10
2.15
2.20
2.25
2.30
2.35
2.40
2.46
2.51
2.56
2.61
2.66
2.71
2.76

14.6
15.5
16.4
17.4
18.4
19.4
20.5
21.5
22.6
23.6
24.7
25.9
27.1
28.3
29.5
30.7
31.9
33.2
34.4
35.7
36.9
38.2
39.5
40.9
42.2
43.5
44.8
46.2
47.5
48.9
50.3

0.0070
0.0074
0.0079
0.0084
0.0088
0.0093
0.0098
0.0103
0.0108
0.0113
0.0118
0.0124
0.0129
0.0134
0.0140
0.0146
0.0151
0.0156
0.0162
0.0168
0.0174
0.0179
0.0185
0.0191
0.0198
0.0204
0.0210
0.0216
0.0222
0.0228
0.0234

Table 3-A13 (cont’d)
58
73.5
59
76.4
60
79.2
61
82.1
62
85.0
63
87.8
64
90.7
65
93.5
66
96.5
67
99.2
68
102
69
105
70
107
71
110
72
113
73
115
74
118
75
121
76
123
77
126
78
128
79
131
80
133

155
155
155
155
156
156
156
156
156
156
156
156
157
157
157
157
157
157
157
157
157
157
158

43.8
41.8
39.8
37.8
35.7
33.6
31.5
29.4
27.2
25.1
23.0
21.0
19.0
16.8
14.7
12.7
10.6
8.46
6.26
4.19
2.14
0.14
-1.88

89.5
92.3
95.1
98.0
101
104
107
110
113
116
120
123
126
130
133
136
140
143
147
150
154
158
161

-8.2
-13.6
-19.2
-24.8
-30.5
-36.2
-41.9
-47.7
-53.7
-59.4
-65.3
-71
-77
-83
-89
-95
-101
-107
-113
-119
-125
-131
-137

196

163
169
174
180
186
192
198
204
210
216
222
228
233
240
246
252
258
264
270
276
282
289
295

2.81
2.86
2.91
2.95
3.00
3.04
3.09
3.13
3.18
3.22
3.26
3.30
3.34
3.37
3.41
3.45
3.48
3.52
3.55
3.59
3.62
3.65
3.68

51.7
53.0
54.3
55.5
56.8
58.0
59.3
60.5
61.6
62.8
63.8
64.9
65.9
66.9
67.9
68.8
69.8
70.8
71.7
72.6
73.5
74.4
75.3

0.0240
0.0245
0.0251
0.0257
0.0262
0.0268
0.0273
0.0278
0.0284
0.0288
0.0293
0.0298
0.0302
0.0307
0.0311
0.0315
0.0320
0.0324
0.0328
0.0332
0.0336
0.0340
0.0344

Table 3-A14 Enrollment, environmental and welfare measures for cropping system C (payment for additionality)
price/acre

Farmer
WTA
(million $)

Resident
WTP
(million $)

Economic
surplus
(million $)

Farmer
Welfare
(million $)

Resident
Welfare
(million $)

Spending
(million $)

Enrollment
(million acre)

Lake
(number)

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

0.00
0.02
0.05
0.10
0.16
0.25
0.36
0.50
0.65
0.83
1.03
1.26
1.53
1.83
2.17
2.57
2.97
3.39
3.84
4.32
4.82
5.39
6.05
6.68
7.35
8.06
8.85

39
122
126
129
130
132
133
134
135
136
137
138
138
139
139
140
141
141
142
142
142
143
143
144
144
144
145

59.8
60.5
61.2
61.9
62.6
63.3
64.0
64.7
65.3
66.0
66.6
67.2
67.8
68.3
68.9
69.4
69.8
70.3
70.8
71.2
71.6
71.9
72.2
72.5
72.7
72.9
73.1

0.00
0.52
1.06
1.61
2.17
2.76
3.36
3.98
4.62
5.28
5.96
6.66
7.38
8.12
8.89
9.7
10.5
11.3
12.2
13.1
14.0
15.0
15.9
16.9
17.9
19.0
20.1

38.9
122
125
127
128
129
129
130
130
130
130
130
129
129
128
128
127
126
125
125
124
122
121
120
119
117
116

0.00
0.54
1.10
1.70
2.34
3.01
3.72
4.49
5.28
6.11
6.99
7.93
8.91
10.0
11.1
12.3
13.5
14.7
16.0
17.4
18.8
20.3
22.0
23.6
25.3
27.1
28.9

0.519
0.536
0.551
0.568
0.585
0.602
0.620
0.641
0.660
0.679
0.699
0.720
0.743
0.765
0.790
0.817
0.842
0.867
0.891
0.916
0.942
0.969
1.00
1.03
1.05
1.08
1.11

0
0.410
0.831
1.27
1.72
2.19
2.67
3.16
3.66
4.18
4.72
5.29
5.87
6.47
7.08
7.72
8.37
9.04
9.73
10.4
11.1
11.9
12.6
13.4
14.1
15.0
15.8

197

GHG (%
of 2000
emission
level )
0
0.0001
0.0003
0.0004
0.0005
0.0007
0.0008
0.0010
0.0011
0.0013
0.0014
0.0016
0.0018
0.0019
0.0021
0.0023
0.0025
0.0027
0.0029
0.0031
0.0033
0.0035
0.0038
0.0040
0.0042
0.0044
0.0047

Table 3-A14 (cont’d)
27
9.65
28
10.5
29
11.4
30
12.3
31
13.2
32
14.2
33
15.3
34
16.5
35
17.6
36
18.8
37
20.0
38
21.3
39
22.6
40
24.0
41
25.4
42
26.8
43
28.2
44
29.9
45
31.4
46
32.9
47
34.5
48
36.1
49
37.9
50
39.6
51
41.4
52
43.3
53
45.2
54
47.2
55
49.3
56
51.4
57
53.8

145
145
146
146
146
147
147
147
147
148
148
148
148
149
149
149
149
150
150
150
150
150
151
151
151
151
151
151
152
152
152

73.2
73.3
73.4
73.3
73.3
73.2
72.9
72.7
72.4
72.1
71.7
71.3
70.8
70.3
69.8
69.3
68.7
67.8
67.2
66.4
65.7
64.8
63.9
62.9
61.9
60.9
59.7
58.6
57.3
55.9
54.4

21.2
22.3
23.5
24.7
25.9
27.2
28.5
29.8
31.2
32.6
34.0
35.5
37.0
38.5
40.1
41.7
43.3
45.0
46.7
48.4
50.2
52.0
53.8
55.7
57.6
59.5
61.5
63.5
65.5
67.6
69.8

114
113
111
109
107
105
103
101
98.7
96.4
93.9
91.4
88.8
86.2
83.5
80.7
77.8
74.7
71.7
68.7
65.5
62.2
58.9
55.5
51.9
48.3
44.6
40.7
36.8
32.7
28.5

198

30.8
32.8
34.9
37.0
39.2
41.4
43.8
46.3
48.8
51.3
54.0
56.8
59.6
62.5
65.4
68.4
71.5
74.8
78.0
81.3
84.6
88.1
91.7
95.3
99.0
103
107
111
115
119
124

1.14
1.17
1.20
1.23
1.26
1.29
1.33
1.36
1.39
1.43
1.46
1.49
1.53
1.56
1.60
1.63
1.66
1.70
1.73
1.77
1.80
1.84
1.87
1.91
1.94
1.98
2.01
2.05
2.09
2.13
2.17

16.6
17.5
18.3
19.2
20.0
20.9
21.7
22.6
23.5
24.4
25.3
26.2
27.1
28.1
29.0
30.0
30.9
31.9
32.8
33.8
34.8
35.7
36.7
37.7
38.7
39.7
40.8
41.8
42.9
43.9
45.0

0.0049
0.0052
0.0054
0.0057
0.0059
0.0061
0.0064
0.0067
0.0069
0.0072
0.0074
0.0077
0.0080
0.0082
0.0085
0.0088
0.0090
0.0093
0.0096
0.0098
0.0101
0.0104
0.0106
0.0109
0.0112
0.0115
0.0118
0.0120
0.0123
0.0126
0.0129

Table 3-A14 (cont’d)
58
55.9
59
58.1
60
60.3
61
62.6
62
64.9
63
67.4
64
69.8
65
72.2
66
74.6
67
77.1
68
79.5
69
82.2
70
84.7
71
87.2
72
89.8
73
92.3
74
94.8
75
97.4
76
100.0
77
102
78
105
79
107
80
110

152
152
152
153
153
153
153
153
153
153
154
154
154
154
154
154
154
154
155
155
155
155
155

53.1
51.7
50.2
48.7
47.2
45.4
43.8
42.1
40.4
38.7
36.9
35.0
33.1
31.3
29.3
27.5
25.6
23.7
21.7
19.8
17.9
16.0
14.1

71.9
74.1
76.4
78.7
81.0
83.3
85.7
88.1
90.6
93.1
95.7
98.2
101
103
106
109
112
114
117
120
123
126
129

24.3
20.1
15.8
11.4
6.9
2.2
-2.5
-7.2
-11.9
-16.7
-21.6
-26.7
-31.7
-36.7
-41.9
-47.0
-52.2
-57.4
-62.7
-68
-73
-78
-84

199

128
132
137
141
146
151
156
160
165
170
175
180
186
191
196
201
207
212
217
223
228
233
239

2.20
2.24
2.28
2.32
2.35
2.39
2.43
2.47
2.50
2.54
2.58
2.61
2.65
2.69
2.72
2.76
2.79
2.82
2.86
2.89
2.92
2.95
2.98

46.1
47.1
48.2
49.3
50.4
51.5
52.6
53.6
54.7
55.8
56.9
57.9
59.0
60.0
61.0
62.0
63.0
64.0
65.0
66.0
66.9
67.8
68.7

0.0132
0.0135
0.0138
0.0141
0.0144
0.0147
0.0150
0.0153
0.0156
0.0159
0.0161
0.0164
0.0167
0.0170
0.0173
0.0175
0.0178
0.0181
0.0183
0.0186
0.0188
0.0191
0.0193

Table 3-A15 Enrollment, environmental and welfare measures for cropping system D (payment for additionality)
Price/acre

Farmer
WTA
(million $)

Resident
WTP
(million $)

Economic
surplus
(million $)

Farmer
Welfare
(million $)

Resident
Welfare
(million $)

Spending
(million $)

Enrollment
(million acre)

Lake
(number)

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

0.000
0.0150
0.0386
0.0745
0.124
0.186
0.264
0.351
0.455
0.571
0.700
0.844
1.00
1.17
1.36
1.56
1.78
2.10
2.35
2.62
2.92
3.22
3.54
3.89
4.24
4.61
5.13

39
125
129
131
133
134
135
136
137
138
139
139
140
140
141
141
142
142
143
143
144
144
144
145
145
145
146

76.6
77.0
77.4
77.8
78.1
78.5
78.8
79.2
79.5
79.8
80.1
80.3
80.6
80.8
81.0
81.2
81.4
81.5
81.7
81.8
82.0
82.1
82.2
82.2
82.3
82.3
82.2

0.0
0.957
1.93
2.91
3.91
4.92
5.94
6.97
8.02
9.07
10.1
11.2
12.3
13.4
14.6
15.7
16.9
18.0
19.2
20.4
21.6
22.8
24.1
25.3
26.6
27.9
29.2

38.9
124
127
128
129
129
129
129
129
128
128
127
127
126
125
124
123
122
121
120
119
118
117
115
114
113
111

0.00
0.972
1.97
2.99
4.03
5.10
6.20
7.32
8.47
9.65
10.85
12.1
13.3
14.6
15.9
17.3
18.6
20.1
21.6
23.0
24.5
26.1
27.6
29.2
30.8
32.5
34.3

0.957
0.972
0.984
1.00
1.01
1.02
1.03
1.05
1.06
1.07
1.08
1.10
1.11
1.12
1.14
1.15
1.16
1.18
1.20
1.21
1.23
1.24
1.26
1.27
1.29
1.30
1.32

0
0.3
0.6
1.0
1.3
1.7
2.0
2.4
2.7
3.1
3.4
3.8
4.1
4.5
4.8
5.2
5.6
5.9
6.3
6.7
7.1
7.5
7.8
8.2
8.6
9.0
9.4

200

GHG (%
of 2000
emission
level )
0
0.0004
0.0007
0.0010
0.0013
0.0016
0.0020
0.0023
0.0026
0.0030
0.0033
0.0036
0.0040
0.0043
0.0047
0.0050
0.0054
0.0059
0.0062
0.0066
0.0070
0.0074
0.0077
0.0082
0.0085
0.0089
0.0094

Table 3-A15 (cont’d)
27
5.54
28
6.09
29
6.55
30
7.02
31
7.52
32
8.11
33
8.66
34
9.24
35
9.8
36
10.4
37
11.1
38
11.8
39
12.6
40
13.3
41
14.2
42
15.0
43
15.8
44
16.5
45
17.3
46
18.2
47
19.0
48
19.9
49
20.8
50
21.8
51
22.7
52
23.7
53
24.7
54
25.6
55
26.6
56
27.6
57
28.6

146
146
146
147
147
147
148
148
148
148
148
149
149
149
149
150
150
150
150
150
151
151
151
151
151
151
152
152
152
152
152

82.3
82.1
82.1
82.1
82.0
81.9
81.8
81.6
81.5
81.3
81.1
80.9
80.5
80.2
79.8
79.4
79.1
78.8
78.4
78.0
77.6
77.2
76.8
76.2
75.7
75.1
74.6
74.0
73.5
72.8
72.2

30.5
31.8
33.2
34.6
36.0
37.4
38.8
40.2
41.7
43.1
44.6
46.1
47.7
49.2
50.8
52.4
54.0
55.6
57.2
58.9
60.5
62.2
63.9
65.7
67.4
69.2
71.0
72.8
74.6
76.4
78.3

110
108
107
105
104
102
100
98.3
96.5
94.7
92.8
90.8
88.6
86.6
84.4
82.2
80.0
77.8
75.6
73.3
71.0
68.6
66.2
63.6
61.1
58.49
55.92
53.30
50.66
47.94
45.21

201

36.0
37.9
39.7
41.6
43.5
45.5
47.4
49.4
51.5
53.6
55.7
57.9
60.3
62.5
65.0
67.4
69.7
72.1
74.6
77.0
79.6
82.1
84.7
87.4
90.1
92.9
95.6
98.4
101.2
104
107

1.34
1.35
1.37
1.39
1.40
1.42
1.44
1.45
1.47
1.49
1.51
1.52
1.55
1.56
1.58
1.60
1.62
1.64
1.66
1.67
1.69
1.71
1.73
1.75
1.77
1.79
1.80
1.82
1.84
1.86
1.88

9.8
10.3
10.7
11.1
11.5
12.0
12.4
12.9
13.4
13.8
14.3
14.7
15.2
15.7
16.1
16.6
17.1
17.6
18.1
18.5
19.0
19.5
20.0
20.5
21.0
21.5
22.0
22.5
22.9
23.4
23.9

0.0098
0.0103
0.0107
0.0111
0.0115
0.0120
0.0125
0.0129
0.0134
0.0138
0.0143
0.0147
0.0152
0.0157
0.0162
0.0167
0.0172
0.0176
0.0181
0.0186
0.0190
0.0195
0.0200
0.0205
0.0210
0.0215
0.0220
0.0224
0.0229
0.0234
0.0239

Table 3-A15 (cont’d)
58
29.9
59
31.1
60
32.2
61
33.3
62
34.5
63
35.7
64
36.9
65
38.2
66
39.4
67
40.8
68
42.1
69
43.4
70
44.8
71
46.1
72
47.5
73
48.9
74
50.4
75
51.9
76
53.4
77
55.0
78
57.0
79
58.5
80
60.1

152
152
153
153
153
153
153
153
153
154
154
154
154
154
154
154
154
155
155
155
155
155
155

71.3
70.6
69.9
69.2
68.4
67.6
66.8
66.0
65.2
64.2
63.3
62.4
61.5
60.6
59.6
58.6
57.5
56.5
55.3
54.2
52.6
51.5
50.3

80.2
82.1
84.0
85.9
87.9
89.9
91.9
93.9
95.9
98.0
100.0
102.1
104.2
106
109
111
113
115
117
120
122
124
126

42.20
39.29
36.4
33.5
30.5
27.4
24.4
21.3
18.1
14.8
11.6
8.3
4.9
1.6
-1.8
-5.3
-8.8
-12.4
-16.0
-19.8
-23.9
-27.6
-31.4

202

110
113
116
119
122
126
129
132
135
139
142
146
149
152
156
160
163
167
171
175
179
183
187

1.90
1.92
1.94
1.96
1.97
1.99
2.01
2.03
2.05
2.07
2.09
2.11
2.13
2.15
2.17
2.19
2.21
2.23
2.25
2.27
2.29
2.31
2.33

24.4
24.9
25.4
25.9
26.4
26.9
27.4
27.9
28.5
29.0
29.5
30.1
30.6
31.1
31.6
32.2
32.7
33.3
33.8
34.4
34.9
35.4
36.0

0.0245
0.0250
0.0255
0.0259
0.0264
0.0269
0.0274
0.0279
0.0285
0.0290
0.0295
0.0300
0.0305
0.0310
0.0315
0.0320
0.0325
0.0330
0.0336
0.0341
0.0348
0.0353
0.0358

Table 3-A16 Enrollment, environmental and welfare measures for mixed-choice cropping system alternative (payment for
additionality)
Price/acre

Farmer
WTA
(million $)

Resident
WTP
(million $)

Economic
surplus
(million $)

Farmer
Welfare
(million $)

Resident
Welfare
(million $)

Spending
(million $)

Enrollment
(million acre)

Lake
(number)

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24

0.000
0.159
0.193
0.249
0.271
0.394
0.373
0.618
0.619
0.612
0.868
1.13
1.25
1.33
2.07
2.15
2.25
3.44
3.13
3.85
4.12
4.76
5.07
5.92
5.86

39
140
141
142
142
143
142
143
143
143
143
144
144
144
145
145
145
146
146
146
146
146
147
147
147

38.9
140
141
141
141
142
142
142
142
142
142
143
143
143
143
143
143
142
143
142
142
142
142
141
141

0.00
0.60
1.36
2.14
2.94
3.74
4.57
5.39
6.25
7.11
7.97
8.85
9.76
10.7
11.6
12.6
13.6
14.5
15.6
16.6
17.7
18.8
19.9
21.1
22.3

38.9
139.6
139.5
139.3
138.5
138.5
137.1
137.0
136.2
135.0
134.5
133.7
133.3
132.1
131.3
130.1
129.1
127.8
127.0
125.7
124.5
122.9
121.7
120.2
118.9

0.00
0.76
1.56
2.39
3.21
4.14
4.94
6.01
6.87
7.72
8.84
10.0
11.0
12.0
13.7
14.7
15.8
18.0
18.7
20.5
21.8
23.6
25.0
27.0
28.1

0.602
0.762
0.778
0.797
0.803
0.827
0.824
0.859
0.859
0.858
0.884
0.907
0.918
0.924
0.976
0.982
0.988
1.06
1.04
1.08
1.09
1.12
1.14
1.17
1.17

0
4.17
4.62
5.07
5.22
6.01
5.73
6.56
6.81
6.51
7.45
7.81
8.42
8.35
9.89
9.79
10.0
11.5
11.3
12.2
12.8
13.2
13.7
14.8
14.7

203

GHG (%
of 2000
emission
level )
0
0.0045
0.0050
0.0055
0.0055
0.0063
0.0054
0.0063
0.0063
0.0059
0.0062
0.0066
0.0073
0.0070
0.0076
0.0074
0.0075
0.0083
0.0084
0.0088
0.0089
0.0088
0.0092
0.0097
0.0093

Table 3-A16 (cont’d)
25
6.92
26
7.32
27
9.43
28
10.07
29
10.47
30
13.08
31
13.96
32
13.97
33
14.62
34
16.98
35
17.1
36
17.7
37
19.9
38
21.6
39
23.2
40
24.2
41
25.6
42
27.4
43
28.6
44
29.8
45
31.2
46
31.5
47
33.3
48
34.2
49
34.7
50
36.9
51
38.7
52
41.3
53
43.2
54
46.4
55
46.7

147
147
148
149
149
149
150
150
150
150
150
150
150
151
151
151
151
151
152
152
152
152
152
152
152
152
153
153
153
153
153

141
140
139
139
138
136
136
136
135
133
133
132
131
129
128
127
126
124
123
122
121
120
119
118
117
116
114
112
110
107
106

23.4
24.6
25.9
27.2
28.5
29.8
31.3
32.7
34.2
35.7
37.2
38.8
40.3
42.0
43.6
45.4
47.1
48.9
50.7
52.5
54.4
56.3
58.2
60.2
62.1
64.1
66.1
68.2
70.3
72.4
74.6

117.1
115.5
113.0
111.4
109.6
106.3
104.3
102.8
100.7
97.2
95.6
93.6
90.3
87.1
84.1
81.6
78.6
75.2
72.4
69.4
66.3
64.0
60.7
58.0
55.3
51.5
47.7
43.4
39.5
34.3
31.8

204

30.3
32.0
35.3
37.2
39.0
42.9
45.2
46.7
48.8
52.7
54.3
56.5
60.2
63.6
66.8
69.5
72.7
76.3
79.3
82.3
85.6
87.8
91.5
94.4
96.9
101
105
109
113
119
121

1.21
1.23
1.31
1.33
1.34
1.43
1.46
1.46
1.48
1.55
1.55
1.57
1.63
1.67
1.71
1.74
1.77
1.82
1.84
1.87
1.90
1.91
1.95
1.97
1.98
2.02
2.06
2.11
2.14
2.20
2.21

15.8
16.1
18.1
18.7
19.2
21.2
22.0
22.1
22.6
24.3
24.6
25.2
26.7
27.5
28.7
29.4
30.4
31.5
32.3
33.0
34.0
34.4
35.4
35.9
36.4
37.5
38.5
39.8
40.9
42.4
42.8

0.0098
0.0098
0.0111
0.0116
0.0113
0.0124
0.0129
0.0129
0.0126
0.0129
0.0130
0.0132
0.0139
0.0144
0.0148
0.0153
0.0156
0.0156
0.0161
0.0160
0.0164
0.0161
0.0170
0.0175
0.0166
0.0174
0.0175
0.0181
0.0184
0.0185
0.0182

Table 3-A16 (cont’d)
56
49.9
57
54.3
58
55.6
59
57.9
60
59.7
61
61.8
62
64.0
63
67.8
64
66.3
65
70.3
66
71.8
67
72.8
68
77.9
69
78.4
70
82.0
71
81.3
72
85.2
73
88.6
74
88.4
75
90.3
76
94.5
77
95.5
78
96.5
79
101
80
101

153
154
154
154
154
154
154
154
154
154
155
155
155
155
155
155
155
155
155
155
155
155
155
156
156

103
99.3
98.2
95.9
94.4
92.2
90.2
86.6
88.1
84.2
82.8
81.9
76.8
76.5
73.0
73.7
70.0
66.6
66.7
65.0
61.0
60.0
59.0
54.4
54.6

76.8
79.1
81.4
83.8
86.2
88.6
91.1
93.6
96.2
98.7
101
104
107
109
112
115
118
120
123
126
129
132
135
138
141

26.6
20.2
16.8
12.1
8.2
3.6
-0.9
-7.0
-8.1
-14.5
-18.5
-22.0
-29.7
-32.7
-39.0
-41.1
-47.5
-53.8
-56.5
-61.0
-67.9
-71.9
-75.8
-83.4
-86.2

205

127
133
137
142
146
150
155
161
162
169
173
177
184
188
194
196
203
209
212
216
223
227
231
239
242

2.26
2.34
2.36
2.40
2.43
2.47
2.50
2.56
2.54
2.60
2.62
2.64
2.71
2.72
2.77
2.76
2.82
2.86
2.86
2.88
2.94
2.95
2.97
3.03
3.02

44.4
46.3
47.0
48.2
49.2
50.0
51.2
52.6
52.4
53.9
54.8
55.2
57.3
57.6
59.1
58.9
60.5
61.8
61.8
62.6
64.0
64.5
65.0
66.6
66.7

0.0188
0.0193
0.0203
0.0193
0.0205
0.0200
0.0206
0.0210
0.0213
0.0209
0.0213
0.0217
0.0214
0.0223
0.0224
0.0223
0.0229
0.0225
0.0221
0.0230
0.0235
0.0234
0.0231
0.0232
0.0242

REFERENCES

206

REFERENCES

Ahlgren, I., T. Frisk, and L. Kamp-Nielsen. 1988. "Empirical and theoretical models of
phosphorus loading, retention and concentration vs. lake trophic state." Hydrobiologia
170(1):285-303.
Amigues, J.P., C. Boulatoff, B. Desaigues, C. Gauthier, and J.E. Keith. 2002. "The benefits and
costs of riparian analysis habitat preservation: A willingness to accept/willingness to pay
contingent valuation approach." Ecological Economics 43(1):17-31.
Antle, J.M. 2007. "Payments for ecosystem services and US farm policy." The 2007 Farm Bill
and Beyond: Summary for Policymakers:111–113.
ARMS (2000-2006) Usda agricultural resource management survey: Farm financial and crop
production practices. Washington, DC. http://www.ers.usda.gov/Data/ARMS/
Balagtas, J., and S. Kim. 2007. "Measuring the effects of generic dairy advertising in a multimarket equilibrium." American Journal of Agricultural Economics 89(4):932-946.
Baylis, K., G. Rausser, and L. Simon. 2004. "Agri-environmental programs in the United States
and european union." Agricultural policy reform and WTO: where are we heading:210233.
Carpenter, S., N. Caraco, D. Correll, R. Howarth, A. Sharpley, and V. Smith. 1998. "Nonpoint
pollution of surface waters with phosphorus and nitrogen." Ecological Applications
8(3):559-568.
Chen, H. 2010. "Ecosystem services from low input cropping systems and public's willingness to
pay for them." M.S. Thesis, Michigan State University, Department of Agricultural, Food
and Resource Economics. http://www.aec.msu.edu/theses/fulltext/chen_ms.pdf
Correll, D. 1998. "Role of phosphorus in the eutrophication of receiving waters: A review."
Journal of Environmental Quality 27(2):261-266.
Delgado, J., R. Sparks, R. Follett, J. Sharkoff, and R. Riggenbach. 1999. "Conserve soil and
water quality in the San Luis valley of south central Colorado, soil quality and soil
erosion." Soil quality and soil erosion:125-142.
Environmental Working Group. 2011. Farm subsidy database. Retrieved Aug 9, 2011, from
http://farm.ewg.org/region.php?fips=26000

207

Environmental Working Group. 2011. "Farm subsidy primer ". Environmental Working Group,
Washington, DC. http://farm.ewg.org/subsidyprimer.php
Forster, P., V. Ramaswamy, T.B. P. Artaxo, D.W.F. R. Betts, J. Haywood, J. Lean, D.C. Lowe,
G. Myhre, J. Nganga, R. Prinn, G. Raga, M. Schulz, and R.V. Dorland (2007) Changes in
atmospheric constituents and in radiative forcing, ed. S. Solomon, D. Qin, M. Manning, Z.
Chen, M. Marquis, K.B. Averyt, M.Tignor, H.L. Miller, Climate change 2007: The
physical science basis. Contribution of working group i to the fourth assessment report of
the intergovernmental panel on climate change. Cambridge, United Kingdom and New
York, NY, USA, Cambridge University Press.
Fuller, L.M., and Minnerick, R.J. 2008. "State and regional water-quality characteristics and
trophic conditions of michigan's inland lakes 2001-2005." Report U.S. Geological Survey,
Reston, Virginia.
Gentry, L.E., S.S. Snapp, C.P. McSwiney, G.A. Parker, and R.R. Harwood. 2011. Mineralization
and plant available n in rotated and continuous corn systems in a long-term
study:Nitrogen credits for crop rotation, cover crops, and composted dairy manure.
Working paper. Michigan State University. East Lansing, MI.
Ghidey, F., and E. Alberts. 1998. "Runoff and soil losses as affected by corn and soybean tillage
systems." Journal of Soil and Water Conservation 53(1):64.
Glotfelty, D.E., J.N. Seiber, and A. Liljedahl. 1987. "Pesticides in fog." Nature 325(6105):602605.
Hoben, J.P., R.J. Gehl, N. Millar, P.R. Grace, and G.P. Robertson. 2011. "Nonlinear nitrous
oxide (N2O) response to nitrogen fertilizer in on-farm corn crops of the US midwest."
Global Change Biology 17(2):1140-1152.
Janus, L.L., and R. Vollenweider. 1984. "Phosphorus residence time in relation to trophic
conditions in lakes." Verhandlung Internationale Vereinigung Limnologie 22(1).
Jayne, T., R. Myers, and J. Nyoro. 2008. "The effects of NCPB marketing policies on maize
market prices in kenya." Agricultural Economics 38(3):313-325.
Jolejole, M.C.B. 2009. "Trade-offs, incentives and the supply of ecosystem services from
cropland." M.S. Thesis, Michigan State University, Department of Agricultural, Food and
Resource Economics. http://aec3.aec.msu.edu/theses/fulltext/jolejole1_ms.pdf
Joyce, B., W. Wallender, J. Mitchell, L. Huyck, S. Temple, P. Brostrom, and T. Hsiao. 2002.
"Infiltration and soil water storage under winter cover cropping in California's
Sacramento Valley." Transactions of the ASAE 45(2):315-326.
Lal, R., M. Griffin, J. Apt, L. Lave, and M. Morgan. 2004. "Managing soil carbon." Science
304(5669):393.
208

Langdale, G., R. Blevins, D. Karlen, D. McCool, M. Nearing, E. Skidmore, A. Thomas, D. Tyler,
and J. Williams (1991) Cover crop effects on soil erosion by wind and water, Cover
Crops for Clean Water. Ankeny, IA, Soil and Water Conservation Society, pp. 15–22.
Lipsey, R.G., and K. Lancaster. 1956. "The general theory of second best." The Review of
Economic Studies 24(1):11-32.
McSwiney, C., S. Bohn, P. Grace, and G. Robertson. 2010. "Greenhouse gas emissions
calculator for grain and biofuel farming systems." Journal of Natural Resources and Life
Sciences Education 39:125-131.
McSwiney, C.P., and G.P. Robertson. 2005. "Nonlinear response of N2O flux to incremental
fertilizer addition in a continuous maize (Zea mays l.) cropping system." Global Change
Biology 11(10):1712-1719.
McSwiney, C.P., S.S. Snapp, and L.E. Gentry. 2010. "Use of N immobilization to tighten the N
cycle in conventional agroecosystems." Ecological Applications 20(3):648-662.
Minnerick, R. 2005. "Michigan lakes: An assessment of water quality: U.S. Geological survey
fact sheet 2004-3048." USGS Michigan Water Science Center, July 7, 2005.
http://pubs.water.usgs.gov/fs2004-3048/
Morgan, R.P.C. 2005. Soil Erosion and Conservation: Wiley-Blackwell.
Musser, W.N., J.S. Shortle, K. Kreahling, B. Roach, W.-C. Huang, D.B. Beegle, and R.H. Fox.
1995. "An economic analysis of the pre-sidedress nitrogen test for Pennsylvania corn
production." Review of Agricultural Economics 17(1):25-35.
Peel, M. 1998. "Crop rotations for increased productivity " Bulletin. North Dakota State
University Extension Service, Fargo, ND.
http://www.ag.ndsu.edu/pubs/plantsci/crops/eb48-1.htm
Poudel, D., W. Horwath, J. Mitchell, and S. Temple. 2001. "Impacts of cropping systems on soil
nitrogen storage and loss." Agricultural Systems 68(3):253-268.
Reganold, J.P., L.F. Elliott, and Y.L. Unger. 1987. "Long-term effects of organic and
conventional farming on soil-erosion." Nature 330(6146):370-372.
Reicosky, D., W. Kemper, G. Langdale, C. Douglas, and P. Rasmussen. 1995. "Soil organic
matter changes resulting from tillage and biomass production." Journal of Soil and Water
Conservation 50(3):253.
Reicosky, D., and M. Lindstrom. 1993. "Fall tillage methods: Effect on short-term carbon
dioxide flux from soil." Agronomy Journal 85(6):1237-1243.

209

Robertson, D. 1996. "Sources and transport of phosphorus in the Western Lake Michigan
drainages." US Dept. of the Interior, US Geological Survey, Madison, WI.
http://wi.water.usgs.gov/pubs/FS-208-96/FS_208-96.pdf
Robertson, G.P., and P.R. Grace. 2004. "Greenhouse gas fluxes in tropical and temperate
agriculture: The need for a full-cost accounting of global warming potentials."
Environment, Development and Sustainability 6(1):51-63.
Silva, G., J. Dahl, and N. Rector. "Initial PSNT results demonstrate nitrogen credit for corn."
Michigan State University Extension, June 15. 2011.
http://news.msue.msu.edu/news/article/soil_nitrate_n_variability_on_corn_fields_with_hi
gh_mineralization_potentia
Soil and Water Conservation Society. 1993. "RUSLE user's guide." Soil and Water Conservation
Society, Ankeny, IA. .
Swinton, S.M., F. Lupi, G.P. Robertson, and D.A. Landis. 2006. "Ecosystem services from
agriculture: Looking beyond the usual suspects." American Journal of Agricultural
Economics 88(5):1160-1166.
Thomas, R.H., and F.B. Blakemore. 2007. "Elements of a cost–benefit analysis for improving
salmonid spawning habitat in the River Wye." Journal of Environmental Management
82(4):471-480.
Tietenberg, T.H., and L. Lewis (2000) Economics of pollution control: An overview,
Environmental and natural resource economics. Boston, MA, Addison-Wesley Reading.
USDA-NRCS. 2010. "Conservation stewardship program, final rule." Federal Register Vol. 75,
No. 106. June 3, 2010
van den Berg, F., R. Kubiak, W.G. Benjey, M.S. Majewski, S.R. Yates, G.L. Reeves, J.H. Smelt,
and A.M.A. van der Linden. 1999. "Emission of pesticides into the air." Water, Air, &
Soil Pollution 115(1):195-218.
Welsch, B.L., J.H. Dorfman, B. Barnett, and J.C. Bergstrom. 2005. Supply and demand in three
proposed farmland preservation markets. Working Paper. Department of Agricultural &
Applied Economics, University of Georgia. Athens, GA.
http://jdorfman.myweb.uga.edu/farmprsv.pdf
Willett, L., and B. French. 1991. "An econometric model of the US beekeeping industry."
American Journal of Agricultural Economics:40-54.
Wunder, S. 2005. "Payments for environmental services: Some nuts and bolts." Occasional Paper
No. 42. Center for International Forestry Research, Bogor, Indonesia.

210

Zhang, W., T.H. Ricketts, C. Kremen, K. Carney, and S.M. Swinton. 2007. "Ecosystem services
and dis-services to agriculture." Ecological Economics 64(2):253-260.

211