FARMERS’ SWITCHGRASS ADOPTION DECISION UNDER DIFFERENT MARKET SCENARIOS -- AN AGENT BASED MODELING APPROACH By Haoyang Li A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Agricultural, Food and Resource Economics—Master of Science 2014 ABSTRACT FARMERS’ SWITCHGRASS ADOPTION DECISION UNDER DIFFERENT MARKET SCENARIOS -- AN AGENT BASED MODELING APPROACH By Haoyang Li The Energy Independence and Security Act of 2007 mandates the production of 36 billion gallons of biofuels per year by the year of 2022, including 21 billion gallons of cellulosic and advanced in addition to 15 billion gallons of conventional (corn) ethanol. It thus becomes important to know the conditions under which farmers are willing to adopt energy crop and which institutional arrangements could facilitate the adoption process. This paper uses agent based simulation to study farmers’ switchgrass adoption decisions under multiple market scenarios using contracts: single-outlet (one biorefinery procures from individual farmers), quasi-multiple outlets (one biorefinery procures from farmers’ cooperative) and multiple outlets (several easily accessible market outlets procure switchgrass from individual farmers). The focus of this paper is to model the contract hold-up problem and its influence on farmers’ switchgrass adoption decisions under the three market scenarios. The use of an agent based model makes it possible to take multi-level heterogeneity into consideration. We found that the appearance of an alternative market outlet lowers farmers’ perceived risk and drives up their expected switchgrass growing gross margin, leading to a higher switchgrass adoption rate. It is also found that procuring from a farmers’ cooperative is an efficient and feasible arrangement. However, commercial operation of a large-scale biorefinery is still not quite feasible in this particular region. Copyright by HAOYANG LI 2014 ACKNOWLEDGMENTS It is a great honor of me to finally finish this thesis and receive my degree in the Department of Agricultural, Food and Resource Economics at Michigan State University. When I look backward at this point of my life journey, I am really filled with gratefulness to those who helped me a lot in achieving this great accomplishment. First I would like to thank my parents for their consistent support of my own choice and their encouragement when I was in depression. Thanks very much for the enormous sacrifice you made to help me pursue advanced degrees. I would like to especially thank my major professor, Dr. Satish Joshi and my research supervisor, Dr. R. Brent Ross for the consistent help in forming the final research topic and the subsequently guidance when I work on the thesis. I’d also like to thank my other thesis committee members, Dr. Scott Loveridge and Dr. Jinhua Zhao for their brilliant ideas on the methodological part and the writting of the thesis. I couldn’t reach this point without your patience in guiding me through the steps of writing a good research paper. I also want to present my gratitude to Dr. Arika Ligmann-Zielinska for your help in handling the softwares and providing me part of the data I use, to all the graduate students in my department for your encouragement along my journey. Finally I would like to thank to U.S. Department of Agriculture’s (USDA) National Institute of Food and Agriculture (NIFA) for the funding support provided to the research project that I am enrolled in. iv TABLE OF CONTENTS LIST OF TABLES ............................................................................................................ vii LIST OF FIGURES ......................................................................................................... viii CHAPTER 1: INTRODUCTION ....................................................................................... 1 1.1 Background ............................................................................................................... 1 1.2 Goal of the Thesis ..................................................................................................... 4 1.3 Thesis Outline ........................................................................................................... 5 CHAPTER 2: LITERATURE REVIEW ............................................................................ 6 2.1 Agricultural Land use decision studies ..................................................................... 6 2.1.1 Optimization-based simulations ......................................................................... 6 2.1.2 Willingness to adopt new crop studies ............................................................... 7 2.1.3 Agent-based land use and land cover change simulations ................................. 8 2.2 How Economic Agents Learn ................................................................................. 12 2.2.1 General Learning Theory in Economics........................................................... 12 2.2.2 Learning in agent based models ....................................................................... 14 2.3 Effect of risk and transaction cost on transaction parties ........................................ 15 2.3.1 Risk and Transaction Cost ................................................................................ 15 2.3.2 Risk & transaction in agricultural market ........................................................ 16 2.4 Literature Gaps and Research Questions ................................................................ 17 CHAPTER 3: THE AGENT BASED MODEL FRAMEWORK..................................... 18 3.1 Basic Farmer Decision Method ............................................................................... 18 3.2 Market Scenarios for Switchgrass ........................................................................... 21 3.2.1 Single-Outlet (Biorefinery) in the Region Procures from Individual Farmers . 21 3.2.2 Quasi-Multiple Outlets – A Biorefinery Procures From a Farmer Cooperative ................................................................................................................................... 23 3.2.3 Multiple Easily Accessible Outlets in the Region for Individual Farmers ....... 25 3.3 Farmer’s Learning on Crop Gross Margin .............................................................. 27 3.3.1 Learning Traditional Crops’ Gross Margin ...................................................... 27 3.3.2 Learning Switchgrass’s Gross Margin ............................................................. 29 3.4 Additional Farmer Decision Constraints ................................................................. 30 3.5 Market Scenarios and Agents’ Learning on Contract Hold-Up .............................. 31 3.5.1 Single-Outlet (Biorefinery) in the Region Procures from Individual Farmers. 32 3.5.1.1 Biorefinery’s Learning and Decision Process............................................ 32 3.5.1.2 Farmers’ Learning on Contract Hold-Up Percent Probability ................... 34 3.5.2 Quasi-Multiple Outlets – A Biorefinery Procures from a Farmer Cooperative 36 3.5.2.1 Biorefinery’s Learning and Decision Process............................................ 37 3.5.2.2 Farmers’ Learning on Contract Hold-Up and Cooperative’s action .......... 38 3.5.3 Multiple Easily Accessible Outlets in the Region for Individual Farmers ....... 40 3.5.3.1 Biorefinery’s Learning and Decision Process............................................ 41 v 3.5.3.2 Farmers’ Learning on Contract Hold-Up Percent Probability ................... 43 3.6 Treat Switchgrass Adoption as Technology Diffusion ........................................... 44 CHAPTER 4: DATA, INITIALIZATION AND BASELINE VALIDATION ............... 46 4.1 Review of the Study Area ....................................................................................... 46 4.2 Farm Endowment Data and Land Ownership Data ................................................ 47 4.3 Projection of Future Traditional Crop Price and Yield ........................................... 48 4.4 Model Initialization ................................................................................................. 50 4.5 Baseline Validation ................................................................................................. 51 CHAPTER 5: AGENT BASED MODEL RESULTS AND DISCUSSION .................... 55 5.1 Single-Outlet (Biorefinery) in the Region Procures from Individual Farmers ....... 55 5.1.1 Key Parameters Used in the Model .................................................................. 55 5.1.2 Simulation Result for the Single-Outlet Scenario ............................................ 56 5.1.2.1 Comparison of Contracts with Different Per-ton Payment ........................ 56 5.1.2.2 Contract with $85/dry ton Contracted Payment......................................... 59 5.1.3 Sensitivity Analysis .......................................................................................... 61 5.2 Quasi-Multiple Outlets – A Biorefinery Procures from a Farmer Cooperative ..... 63 5.2.1 Parameter Used in the Model ........................................................................... 63 5.2.2 Simulation Result for the Quasi-Multiple Outlets Scenario ............................. 63 5.2.2.1 Contract Price Choice under Different Cooperative’s Alternative Market Searching Transaction Cost ................................................................................... 63 5.2.2.2 Comparing Results with First Scenario Best Contract Price Case ............ 66 5.2.3 Sensitivity Analysis .......................................................................................... 68 5.3 Multiple Easily Accessible Outlets in the Region for Individual Farmers ............. 69 5.3.1 Parameter Used in the Model ........................................................................... 69 5.3.2 Simulation Result for the Multiple-Outlets Scenario ....................................... 70 5.3.2.1 Comparison of Contracts with Different Per-ton Payment ........................ 70 5.3.2.2 Comparing Results of Best Contract Prices under the 3 Scenarios ........... 73 5.3.3 Sensitivity Analysis .......................................................................................... 76 5.4 Large Scale-Commercial Biorefinery? .................................................................... 77 CHAPTER 6: CONCLUSIONS, IMPLICATIONS AND LIMITATIONS .................... 79 6.1 Major Findings ........................................................................................................ 79 6.2 Study Limitations .................................................................................................... 81 6.3 Contributions ........................................................................................................... 82 6.4 Directions for Future Research................................................................................ 83 APPENDICES .................................................................................................................. 86 APPENDIX A. Projected Crop Input Cost ................................................................... 87 APPENDIX B. Crop Budgets Used in the Thesis ......................................................... 88 BIBLIOGRAPHY ............................................................................................................. 90 vi LIST OF TABLES Table 1 Biofuel Production Mandated by EISA ................................................................. 3 Table 2 Representative Farm Resource Constraints Included in Existing Literatures ..... 11 Table 3 Crop Upper Limit Used in the Model .................................................................. 31 Table 4 Total Farm Acres and Farm Cropland Acres ....................................................... 51 Table 5 2007 Farm Income Distribution ........................................................................... 51 Table 6 Single-Outlet Scenario (Scenario 1) Model Parameters ...................................... 55 Table 7 Comparison of Different Contract Configuration in Single-Outlet Scenario ...... 57 Table 8 Sensitivity Analysis on Switchgrass Upper Limit for Single-Outlet Scenario .... 62 Table 9 Quasi-Multiple Outlets Scenario (Scenario 2) Model Parameters....................... 63 Table 10 Sensitivity Analysis on Switchgrass Limit for Quasi-Multi-Outlets Scenario .. 69 Table 11 Multiple-Outlets Scenario (Scenario 3) Model Parameters ............................... 69 Table 12 Comparison of Different Contract Configuration for Multi-Outlets Scenario .. 71 Table 13 Sensitivity Analysis on Switchgrass Limit for Multiple-Outlets Scenario ........ 77 Table 14 Comparison of Energy Crop Land Conversion in Different Studies ................. 80 Table 15 Projected Input Cost during Pre-simulation and Simulation Period .................. 87 Table 16 Input needed For Corn, Soybeans and Winter Wheat ....................................... 88 Table 17 Input Amount Needed for Switchgrass .............................................................. 88 Table 18 Input Amount Needed for Alfalfa (From Second Year) .................................... 89 vii LIST OF FIGURES Figure 1 RFS Yearly Biofuel Objective.............................................................................. 2 Figure 2 Decision Tree for the Single-Outlet Scenario (Scenario 1) ................................ 23 Figure 3 Decision Tree for Multiple-Outlet Scenario (Scenario 3) .................................. 26 Figure 4 Alpena County Land Use and Land Cover 2008................................................ 46 Figure 5 Real (2002~2012) and Projected (2013~2022) Crop Yield (in bushels/acre) .... 49 Figure 6 Real (2002~2012) and Projected (2013~2022) Crop Price (in $/bushel) ........... 49 Figure 7 US DOE Predicted Ethanol Price during Simulation Period.............................. 50 Figure 8 Annual Corn Real Data and Simulated Data 2007 to 2012 ................................ 52 Figure 9 Annual Soybeans Real Data and Simulated Data 2007 to 2012 ........................ 52 Figure 10 Annual Corn and Soybeans Real Data and Simulated Data 2007 to 2012 ....... 53 Figure 11 Annual Wheat Real Data and Simulated Data 2007 to 2012 ........................... 53 Figure 12 Switchgrass Areas (in Acres) under Different Contract Price.......................... 57 Figure 13 Switchgrass Procured (in tons) under Different Contract Price ....................... 57 Figure 14 Switchgrass Adopters (in numbers) During Simulation under Different Contract Price.................................................................................................................... 58 Figure 15 Contract Hold-Up Times (in times) under Different Contract Price ................ 58 Figure 16 Traditional Crop Areas (in Acres) under Single-Outlet Scenario .................... 60 Figure 17 Switchgrass Acres (in Acres) under the Single-Outlet Scenario ...................... 60 Figure 18 Payment Percent (in %) under the Single-Outlet Scenario .............................. 60 Figure 19 Adopter Number (in numbers) under the Single-Outlet Scenario .................... 61 Figure 20 End-Simulation Biorefinery NPV (in 1000 $) under Different Cooperative’s Alternative Market Searching Transaction Cost ............................................................... 64 viii Figure 21 End-Simulation Switchgrass Areas (in Acres) under Different Cooperative’s Alternative Market Searching Transaction Cost ............................................................... 64 Figure 22 Switchgrass Areas (in Acres) Comparison between the Single-Outlet and Quasi-Multiple Outlets Scenario....................................................................................... 66 Figure 23 Switchgrass Production (in tons) Comparison between the Single-Outlet and Quasi-Multiple Outlets Scenario....................................................................................... 66 Figure 24 Payment Percent (in %) Comparison between the Single-Outlet and QuasiMultiple Outlets Scenario ................................................................................................. 67 Figure 25 Switchgrass Adopters Comparison between the Single-Outlet and QuasiMultiple Outlets Scenario ................................................................................................. 67 Figure 26 Biorefinery NPV (in 1000$) Comparison between the Single-Outlet and QuasiMultiple Outlets Scenario ................................................................................................. 67 Figure 27 Switchgrass Areas (in Acres) under Different Contract Price in Multiple Outlets Scenario (Main Biorefinery) ................................................................................ 71 Figure 28 Switchgrass Production (in tons) under Different Contract Price in Multiple Outlets Scenario (Main Biorefinery) ................................................................................ 72 Figure 29 Switchgrass Adopters (in numbers) under Different Contract Price in Multiple Outlets Scenario (Main Biorefinery) ................................................................................ 72 Figure 30 Contract Payment Percent (in %) under Different Contract Price in Multiple Outlets Scenario (Main Biorefinery) ................................................................................ 72 Figure 31 Switchgrass Areas (in Acres) Comparison among All Scenarios .................... 74 Figure 32 Switchgrass Production (in tons) Comparison among All Scenarios ............... 74 Figure 33 Number of Adopters (in numbers) Comparison among All Scenarios ............ 75 Figure 34 Payment Percent (in %) Comparison among All Scenarios ............................. 75 Figure 35 End Simulation Biorefinery NPV (in 1000 $) Comparison among All Scenarios ........................................................................................................................................... 75 ix CHAPTER 1: INTRODUCTION 1.1 Background Renewable Fuel Standard (RFS) provisions of The Energy Independence and Security Act of 20071 (EISA) mandates the production of 36 billion gallons of biofuels per year by 2022, including 21 billion gallons of cellulosic and advanced biofuels (increasing from 2 billion gallon per year in 2007), in addition to 15 billion gallons of conventional (corn) ethanol (refer to Figure 1, up). Studies of biomass potential by the USDOE indicated that over a billion tons of biomass feedstocks may be available in the US (Perlack et al. 2005). Furthermore, Epplin.,et al (2007) estimates that a billion tons of cellulosic biomass might be converted to 90 gallons of biofuel under standard conversion technology. This could be used to produce ethanol comprising approximately 26% of the BTUs of the 2005 U.S. net crude oil imports, alleviating the U.S’s dependence on foreign oil (Demirbas, 2009). Table 1 reviews the types of biofuel mandated by EISA and the required environmental performance in terms of reductions in life cycle GHG reductions compared with gasoline. It could be seen that cellulosic biofuel is the most environmentally friendly biofuel type – it has the highest GHG reduction among all the categories. Although corn ethanol production has increased fast enough to keep up with the mandates, the production of cellulosic and advanced biofuels has been well below the targets (the targets for cellulosic and advanced biofuels are shown separately in Figure 1,down) despite significant government support. This has necessitated a downward revision of advanced fuel requirements. The problem seems to be more acute as corn 1 See http://www1.eere.energy.gov/femp/regulations/eisa.html 1 ethanol production competes with food markets for corn and has led to increased corn and food prices (Carter, Rausser & Smith, 2012). Figure 1 RFS Yearly Biofuel Objective2 2 Source: http://libcloud.s3.amazonaws.com/93/72/c/2270/Issue_Brief_RFS_101.pdf 2 Table 1 Biofuel Production Mandated by EISA3 Fuel Conventional Biofuel Advanced biofuel Biomassbased Diesel (subset of advanced) Cellulosic Biofuel (subset of advanced) Example feedstock Reduction in GHG emissions Total gallons mandated by 2022 corn At least 20% reduction 15 billion sugarcane At least 50% reduction 21 billion Diesel produced from plant oil or animal fat soybean, palm, canola At least 50% reduction 1 billion Fuel derived from the structural tissues of crop residues switchgrass, algae, Stover, wood At least 60% reduction 16 billion Short Description Any biofuelprimarily corn ethanol Includes cellulosic, biomass-based diesels, and any other biofuel not made from corn starch Recently, a number of pilot and demonstration scale advanced biofuel facilities like API in Michigan, Genera in Tennessee and Buckeye Technologies in Florida have been established, but commercial scale facilities are yet to become operational. To make informed decisions about this emerging critical industry as well as to ensure a stable feedstock supply, potential biorefinery entrepreneurs and regional policy makers need significant analysis and information on farmers’ willingness to adopt these feedstock and how will they switch land into bio-feedstock use. The commonly cited reasons that impede farmers’ perennial energy crop adoption include (1) price uncertainty due to the lack of mature market; (2) a high conversion cost; (3) a high sunk cost for long-term commitment and (4) low yield level in the establishing years. Researchers have estimated 3 Source: http://libcloud.s3.amazonaws.com/93/72/c/2270/Issue_Brief_RFS_101.pdf 3 that the fraction of farmers willing to adopt switchgrass ranges between 30~70% (Jensen et al., 2007; Wen et al., 2009; Rossi & Hinrichs, 2011), varying substantially by regions. Hipple & Duffy (2002) also observed a significant “test the water” behavior among farmers. Those findings further warrant a detailed scrutiny of farmers’ adaptive behaviors towards perennial energy crops (e.g. switchgrass). However, many of those uncertainties could be alleviated by contracting between farmers and the biorefinery (e.g. a per ton payment scheme transfer the part of price risk farmers undertake to the biorefinery) (Alexander et al., 2012). But farmers also express their worry on being held-up by the biorefinery (Jensen et al., 2007), which means the refinery would have the potential to default or reduce the payment due to the monopsony power it possesses. In reality, contract is most commonly used in incumbent demonstration biorefineries to procure switchgrass from farmers (e.g. Genera and API biorefinery)4. It could also be seen that the strength of the procurer’s monopsony power will also affect farmers’ adoption decision. As a response, market arrangements should be adjusted to alleviate this concern. Two ways are most commonly considered: (1) introducing competition for procurer, and (2) increase farmers’ bargaining power by institutional arrangement. 1.2 Goal of the Thesis As stated above, market condition plays an important role in influencing farmers’ switchgrass adoption decision, so this paper will look into to what extent different market scenarios will impose their influence on farmers based on the data for a North Michigan County. In particular, how different farmers’ switchgrass land use will change over time 4 Genera is a partner of UT Bioenergy Initiative and it currently uses a contract of per acre payment plus per ton payment to procure switchgrass (year1: $450/acre; year2: $250/acre + $40/ton; year3: $150/acre+$50/ton) 4 under multiple switchgrass outlets market and farmer cooperative market compared with when single procurer purchase switchgrass from individual farmers (more detail in Chapter 2 and 3). To achieve this goal, agent based simulation will be carried out using Repast Simphony toolkit. Different from traditional economic models, Agent Based Simulation is a widely used bottom-up approach that allows the researchers to specify different attributes and behavioral decision rules for different agents or actors in the model (i.e. capture agent heterogeneity) and then study the interaction of these agents and the consequences of the interactions (Heckbert, Baynes & Reeson, 2010). Therefore, not only the interaction between farmers that emphasizes the social learning process, but also the interaction between farmers and biorefinery that could represents the influence of contract hold-up5 by biorefinery on farmers, could be modelled. 1.3 Thesis Outline The thesis is organized as follows: Chapter 2 makes a brief review of the existing literatures; chapter 3 introduces different market scenarios in detail, builds the agent based model framework, and describes agents’ decision rules under different market scenarios; chapter 4 introduces the study region, provide detailed reason for choosing this study area and provides a description of data; chapter 5 shows the agent based simulation experiment results; chapter 6 concludes. 5 We define contract hold-up as the fact that the biorefinery will not pay farmers the full contracted price at the end of some transaction years. 5 CHAPTER 2: LITERATURE REVIEW Agricultural Land use decision-making is being analyzed by different disciplines using various methods, either theoretical or empirical. Therefore, this section will summarize some of those studies on modelling farmers’ land use decision (including but not limited to energy crop land use) and different methods they use to provide a general background of the ongoing research. 2.1 Agricultural Land use decision studies In this sub-section, a review on land use decision studies is presented, categorized by the method those studies use with an emphasis on the application of agent based models on land use change. 2.1.1 Optimization-based simulations Consisting with economic theory, simulations based on mathematical optimization or risk/uncertainty decision rules that apply to representative farms or regional planner is widely used as a method to study land use decision, especially for crops without a mature market. For example, Egbendewe-Mondzozo et al. (2011) simulated biomass supply in southwestern Michigan using detailed production data and showed that the minimum biomass to corn price ratio is in the range of 0.15 to 0.18, varying by energy crops. Larson, English & Lamber (2007) simulated over different contract scenarios (spot market contract, acreage contract, revenue-sharing contract, etc.) on bio-crop land use change in Tennessee’s biomass initiative region. Their results showed that spot market price were not high enough to induce biomass production. Khanna et al (2011) also introduced a larger-scale and longer-time math programming model of biomass supply under different yield and price scenarios. They found that 6 besides price, farmers’ biomass land use amount also depends heavily on residue collection technology, cost of producing bioenergy crops and land availability. With regard to risk/uncertainty, Song, Zhao & Swinton (2011) adopted a stochastic process model showing that uncertainty and sunk cost will influence farmers’ option value of converting land to switchgrass use (see Corato & Hess, 2013 for another application). However, though math programming and stochastic programming models are commonly used in land use models, the drawback is the underrepresentation of farmlevel heterogeneity and other farmer-level conceptual perceptions for different crops. The two methods below supplement this optimization based models by looking at different aspects of farmers’ land use decision process 2.1.2 Willingness to adopt new crop studies Willingness to adopt studies are also common in the agricultural land use literature. Among the methods used in this subset of studies are focus group talking, discrete choice analysis (e.g. contingent valuation and choice experiment), or the combination of the two. The latter approach is particularly popular with respect to studying the WTP of energy crops. This method provides a way to identify what factors (e.g. demographic characteristics, perceptual concept) other than optimization would influence farmers’ land use decisions. Literatures in this way show that among various factors that influence farmers’ willingness to adopt switchgrass, the relative newness of switchgrass to farmers are the most frequently mentioned (Jensen et al., 2007; Wen et al., 2009) since it brings farmers a high level of uncertainty. 7 Other factors such as farms’ characteristics (farm head’s age, farm size, initial capita), the lack of mature market (if no contract exists), the trust on biorefineries, and even farmers’ environment concern will also impose some influence on farmers’ adoption decisions (Hipple & Duffy, 2002; Wen et al., 2009; Paulrud & Laitila, 2010; Rossi & Hinrichs, 2011). Researches like Scheffran., et al (2007) and Shastri., et al (2011) show that land opportunity cost and farmers’ social networks are important determinants of farmers’ Miscanthus adoption rate using agent based modeling approach for a case study in Illinois. Besides the contributing factors to land use change, researchers also estimated that for switchgrass, the fraction of farmers willing to adopt switchgrass is between 30~70% (Jensen et al., 2007; Wen et al., 2009; Rossi & Hinrichs, 2011) varying by regions. Hipple & Duffy (2002) also observed a significant “wait-and-see” behavior among farmers. This finding warrants further investigation of the effect of the adaptive behavior has on adopting switchgrass. 2.1.3 Agent-based land use and land cover change simulations Agent-based models give every agent a specific decision rule and then study the interaction of these agents in a bottom-up manner (Ross & Westgren, 2009; Heckbert, Baynes & Reeson, 2010; Anderson, 2012). This approach might generate emergent behavior of the system which is hard to predict otherwise (Shastri et al, 2011) due to a lack of interaction and adaptive learning behavior in pure math programming models. Agricultural land use is greatly discussed using agent based modeling method since highdegree heterogeneity among farmers and the environment, high frequency of interaction among farmers and interaction between farmers and environment exist in the real world (Verburg & Overmars, 2009; Shastri et al, 2011; Kelly & Evans, 2011). Kelly & Evans 8 (2011) successfully modelled and calibrated the impact of farmers’ preference on their land use pattern in Indiana Creek Township. Scheffran et al (2007) modeled the spatial dynamics of biofuel crop growth in Illinois by emphasizing the effect of the introducing biomass on the price evolution for both regular crops and biofeedstocks, which was also emphasized by Lundberg (2012), who, after comparing his agent-based modeling result with a similar conceptual model, found out the equilibriums in the two models were similar though using different price determination mechanisms. However, although agent heterogeneity is fully represented in most agent based land use models, they often ignore various constraints (e.g. capital, labor, etc.) that might greatly influence farmers’ decisions. As a response, to incorporate the benefits of optimization in math programming models and agent based modelling’s flexibility in representing heterogeneity, another method called mathematical programming based multi-agent system (MP-MAS) has emerged (Schreinemachers, Berger & Aune, 2007; Schreinemachers et al, 2010). This method combines math programming with agent based modeling, thus fills an important gap in literature. By incorporating economic constraints into the model, the simulations are able to address the potential socioeconomic feasibilities for different land use patterns (A summary of the mostly often used constraints are listed in Table 2). However, drawbacks also exit: most studies either ignore the learning process (Anderson, 2012) or just incorporate self-learning without learning from others (Schreinemachers, Berger & Aune, 2007). In addition, perceived and real production risk/uncertainty are not adequately modeled in agent’s decision process. The reason might be that most studies deal with existing crop systems, where crops and technologies are already familiar to them. However, for a new energy crop, as 9 noted by Hipple & Duffy (2002), farmers will have to learn the real production potential and risk level by observing others and learning from self-experience together. When detailed existing farmer household data and environmental data are not available, the initialization of land ownership is to random allocates all land parcels (Schreinemachers, Berger & Aune, 2007; Stolniuk, 2008) to different farmers. This willresult in possible rather biased simulated farm land use pattern as the results will be influenced by the random distribution of transportation cost and land quality associated with random farm land location. The generation of farmers conforms to two ways: (1) The first way is to randomly sample farmers and environmental variables, and then populate the rest of farmers in the study area by either replicating the self-conducted survey results to un-surveyed areas and farmers (e.g. Schreinemachers, Berger & Aune, 2007), or populating according to cluster effects among variables in the survey data (Berger & Schreinemachers, 2001). The problems for this method are that without reference like census data (solely relying on survey data), we are not sure if the final result is a representative of the study region; (2) The second way of initializing the model when we do not have detailed farm-level data is to get the farmer household character statistical distributions from census or other related data source and generate synthetic farmers accordingly (Happe, 2004; Stolniuk, 2008; Anderson, 2012). The drawbacks for this method is that completely relying on census data to populate farms might loss specific farm level accuracy though the final farm endowments might conform to the census average. 10 Table 2 Representative Farm Resource Constraints Included in Existing Literatures Study Schrein emache rs et al (2009a) & Schrein emache rs et al (2009b) Resource Constraints Objective function Artificially located based on qualitative information Linear Programming Labor Convert Household members to man-day Liquid Cash (other assets not used) Credit availability (Boolean: 0/1) Water (Irrigation, ground) Crop area for different crops * average cash need for each crop whether the farmer got loan during the year before survey (yes =1, no = 0) Component: 1. Crop profit 2. Off farm profit Green Houses Numbers Assign Survey results Cash Credit (Detail see below) Debt/Asset Ratio (determine the accessibility to access land market) Labor/Machine Package Kelly & Evans (2011) Initial constraints Sources Land Land Anderso n (2012) Initialization Labor hours Assign Survey results to randomly created farmers 1. Divide region into equal size parcels 2. Randomly assign parcel to farmer 3. Land value determined by productivity index $50*(Total land acres + 4*herd size) The ability to borrow is determined by farm debt/asset ratio 1. Debt: assigned randomly, referring to a mean value from census record) 2. Asset: cash, land value, cropping equipment Farm household survey data Replicate surveyed household to the rest of the region Mixed Integer Programing Average data from regional census No individual farmer data Random assignment according to distribution data Fixed number for each household Source: Author self-summarization 11 Note: Off farm incomes comes from other farms who need additional labor Self-assigned Component: 1. Crop profit 2. Net Livestock incomes 3. Off farm income is initially set according to the size of farm and is kept constant during the model run Component: 1. Peculiar utility 2. Farmer Preference Alternatively, if detailed or partially-detailed farmer data and farm land ownership data are available, model validity would be increased (e.g. Kelley & Evans, 2011). For example, if detailed data on a portion of farmers is available, we could populate those real data into the model and then initialize the rest of lands and farmers based on the census data and existing data, which will give a more accurate result. Due to the significant data requirements of the second model initialization method, the first method is more widely used in the existing literatures. Even if we could get the required data from conducting survey or purchasing, there is also tradeoff between accuracy and cost. Among the agent based land use models, only Evans & Kelly (2004) focused on land-level initialization and showed that a 50m * 50m grid resolution of land might balance model precision and run speed. Further research may be appropriate to compare methods of creating farm households and allocating lands to farms. 2.2 How Economic Agents Learn 2.2.1 General Learning Theory in Economics Self-learning (learning from one’s own experience) and social learning (learning from both others’ and the agents’ own experience) are two major types of learning models。 The applications of those models are heavily dependent on both how well they represent the real world and the ease of fitting them to the main research method in a study. While self-learning such as adaptive expectation and adaptive risk learning (Nerlove, 1958; Just, 1974) are widely used in econometric analysis due to statistical tractability, social learning models are plentiful in theoretical applications and empirical simulations (e.g. Feder & Mara, 1982) as they do better represent communication in real world. 12 Brenner (2006) provides a summary of existing learning models and classifies them into different categories from the perspective of who are actually learning and the level to which the learning is rational. Neoclassical economists often assumes that people are fully rational, which leads to the predominance of the Bayesian learning approach (Feder & Mara, 1982; Jordan, 1991; Kalai & Lehrer, 1993). While the strength of Bayesian approach is the mathematical tractability and the ability to incorporate social learning, it is also widely critiqued by its assumption of complete information, fullyrational optimization and ignorance of psychological effects such as the differential effects of recent vs. past experience (Brenner, 2006). Lindner & Gibbs (1990), for example, find that Bayesian learning fails to represent part of the learning phenomena observed in South Australia on farmers’ belief about the yield distribution of a new wheat variety. Besides the Bayesian approach, economists also frequently use two other simple learning models: The first model combines routine-based processes of experimentation, experience collection and communication (Kirchkamp, 2000). In this model, weights are given to different observations in different historical years. The second model is reinforcement learning proposed by searching theory: people make simple adjustments to their previous strategies locally or globally (Ross & Westgren, 2009), depending on the payoff from that strategy. While these two approaches do catch some of observed learning result patterns, they are also criticized by their oversimplification of people’s comprehensive learning abilities such as forming probability distributions of the outcome in Bayesian models (Brenner, 2006). 13 2.2.2 Learning in agent based models Agent based models assume that people are bounded rational, which means although people are trying to optimize, they still have to learn from experience to update their belief (Kirman, 2010). Depending on study goals and the methods adopted, different agent based models use different learning algorithms. In agent based models where farm land allocation is studied, farmers’ learning is primarily concerned on the parameters of the optimization. For example, in farm land use agent based models (ABMs), adaptive self-learning or Bayesian updating are widely used in farmers’ learning on crop gross margin per acre (e.g. Berger & Schreinemachers, 2001) (Exceptions like Freeman, Nolan & Schoney, 2009 doesn’t model learning because crops under consideration are quite familiar to farmers). On the other hand, searching theory (or reinforcement learning) is also used frequently when an explicit searching space (all potential outcomes) is defined (e.g. Kollman, Miller & Page, 2000; Ross & Westgren, 2009). For example, Tesfatsion (2006) proposed a learning algorithm for firms where a finite supply offer options were defined and firms base their choice each year on the success of previous year’s strategy as well as its willingness to experiment with new options. This strategy is consistent with the exploration and exploitation approach taken in Chang & Harrington (2003) to avoid being stuck in a local optimum at the early stage. The main difference in the two learning categories is that the former method is used when the objective people learn is not directly the results of potential strategies – the things they learn are rather something that influences the successfulness of the strategies. 14 2.3 Effect of risk and transaction cost on transaction parties 2.3.1 Risk and Transaction Cost Different institutional arrangements (including market structures) often impose different levels of risk and transaction cost (Coase, 1992; Besley, 1995; Dorward, 1999). Here we define market structures as any real-world settings that impose rules to which market parties should conform, which include but not limited to contract regulations, presence of alternative marketing channels and production organization formations. In economics, risk refers to the variability of outcomes. “Rational people” are always trying to maximize their expected utility taking the risk they are facing into account (Neumann & Morgenstern, 1944). According to expected utility theory, people with high and low level of risk preference will act significantly different when they are facing the same level of risk. With respect to new crop adoption, the more risk averse a farmer is, the more reluctant he will be to adopt a relatively new crop – the unfamiliarity brings a high level of risk. While there might be several drivers of outcome variability, one source is likely related to market arrangement. In order to manage market risk, the common practice is to rearrange risks born by different transaction parties so that entities whose risk tolerance is high could take over some uncertainties facing those who are more risk averse to achieve win-win trade (Kocherlakota, 1996). Another component of a transaction that may affect transacting parties is the cost of the transaction. As Coase (1937) and Williamson (1996) indicate, costs of participating in a market (or using other transactional mechanisms) exist. Such costs include search costs, negotiating or bargaining costs, contract design costs or monitoring costs . Williamson (1996) further claims that risk and transaction costs might interact: one 15 parties’ risk is marked up by the afraid of another parties’ opportunistic behaviors caused by the high transaction costs of preventing those actions. 2.3.2 Risk & transaction in agricultural market Risks farmers face could be categorized into production risk (e.g. yield risk, input price risk), marketing risk (e.g. output price risk) and financial risk (e.g. high leverage). Contracts are commonly used (Key & Runsten, 1999) to alleviate those risks by imposing different compensation mechanisms (Rothschild & Stiglitz, 1976; Alexander et al, 2012) and contracting periods (Jensen et al., 2007; Rossi & Hinrichs, 2011). But farmers might also face the risk of contractual holdup by procurers, in which case their payment might be delayed or be canceled due to various reasons (e.g. quality satisfaction, procurer bankruptcy, procurer market power, high spot market price). The hold-up problem is especially eminent for perennial switchgrass if there is only one buyer in the market. In this case, land devoted to perennial switchgrass may be classified as a relationshipspecific asset and provides an opportunity for a opportunistic procurer to extract further rents from the farmer through the threat of contractual holdup (Hipple & Duffy, 2002). At the same time, the literatures also focus on the difference of market participation among farmers with different size. Janvry, Fafchamps & Sadoulet (1991) and Besley (1994) argue that the high transaction cost brought by high information searching costs, high supervision cost and poor market infrastructure may limit farmers’ market participation. Various organization/institutional arrangements have, therefore, emerged overtime to overcome the high transaction cost facing farmers in both input and output market. Cook (1995) found that farmer cooperative could also reduce transaction 16 cost associated with getting loans, designing contracts or searching markets to some extent and brings economic of scale, if properly organized. 2.4 Literature Gaps and Research Questions By reviewing the above related literatures, this thesis identifies the following literature gaps in modeling farmers’ switchgrass land used decision in agent based models: (1) Optimization based decision rules haven’t been incorporate with more realistic social learning models and haven’t dealt with risk of farming. (2) Nearly all existing agent based energy crop adoption models assume that there is aspot energy crop market where farmers could sell all of their energy crops. The effect of major different market scenarios that impose different risk and transaction cost for farmers when no mature spot market exists have not been studied yet. Therefore, the research question of the thesis examines to what extent farmers’ switchgrass adoption decisions and biorefineries’ contract hold up decisions will be affected by different market scenarios, particularly when social learning occurs over time. The market scenarios we are looking at include: 1. A biorefinery procures switchgrass from individual farmers. 2. A biorefinery procures switchgrass from a farmer cooperative. 3. Multiple easily accessible market outlets channels procure switchgrass from individual farmers. 17 CHAPTER 3: THE AGENT BASED MODEL FRAMEWORK 3.1 Basic Farmer Decision Method Farmers are assumed to be partially-rational individuals who maximize their expected utilities at the beginning of each year based on their current knowledge on crop yield, price and risk. Following the combination of expected utility theory (EU) in Bocqueho & Jacquet (2010) and Larson, English & Lamber (2007), farmer’s problem could be described as a multi-period risk programming: ( ) ( ) Where X is a vector of land devoted to different cropping activities (corn, soybeans, winter wheat, alfalfa and switchgrass); time t; the resource constraints at ( ) the whole farm expected utility at time t. The traditional way of modeling ( ) for a farm risk programming is to use a mean-variance formula: ( Where ) [ ] ( ) represents the coefficient of absolute risk aversion of a farmer; the variance-covariance matrix for different cropping activities; is is the expected transpose vector of gross margin per acre for crop X. However, due to the availability of proper java quadratic risk programming library for the agent based model toolkits 6 , this thesis transformed the quadratic risk 6 Currently only CPLEX solver could handle non-convex quadratic programming in java. However, as the problem under consideration is multi-period and is subjected to a lot of constraints, the solver is quite slow in solving even a single farmer’s optimization problem. 18 programming problem to a linear programming one using MOTAD model proposed by Hazell (1971) as follows7: ( ) ∑∑ {∑ ∑ ( ) ̅ ) ∑ ∑( ( ∑ ( } ( ) ) ( ) ) Here k denotes the number of historical periods we use to calculate historical gross margin deviations from the mean, s denotes the number of different soil types. In this application, the period’s numbers are set to 4 (k = 1, 2, 3 and 4). is the kth historical gross margin for crop i on the most commonly seen soil type in the region (productivity index equal to 10, see section 4 for detail), is the absolute value of negative deviation of the kth historical year’s crop gross margin occurrence from the mean gross margin. The sum of together with the second constraint, approximate the variance part in the utility function described in equation (1). For simplicity and tractability, it is also assumed here that farmer’s subjective deviation of gross margin ( ̅ ) calculated by the historical years doesn’t change overtime for traditional crops (for switchgrass, refer to section 3.2 and section 3.4 for detail). The only thing that changes is the expected gross margin for each crop (Hazell & Norton, 1986). 7 For a detailed description of MOTAD model, please refer to Hazell (1971). 19 Unlike many other literatures that uses math programming to study land conversion (Berger, 2001; Schreinemachers & Berger, 2006; Anderson, 2012) where lands could only be converted out of perennial crop use until the end of their life cycle, the vector of X not only includes planting crops on currently available lands (lands that are not occupied by perennial crops), but also includes cutting perennial crops and convert the land back to other crops when the perennial crops haven’t reached the end of life cycle. This is the first attempt in agent based farm optimization model to allow for converting perennial crop lands back to other uses. It is especially important in analyzing contract hold up issues because farmers are prone to revert to traditional crops when the risk of contract holding up is high. The gross margin and planting cost/conversion cost for perennial grasses are represented by annuity value (Song, Zhao & Swinton, 2011). Finally, the realized gross margin for traditional crop i (that is, excluding switchgrass) in time t could be expressed as: ( ) ( ) is the price of crop i and PI is the soil productivity index. Here we assume out production fixed cost and the variable cost could be decomposed into yield-related variable cost ( ) and acre-related variable cost ( ).We also assume that crop yield changes linearly corresponding to soil productivity index: ( ) For traditional crops, we assume that assume that ( ) are continuous, but for switchgrass, we has only two states: high yield and low yield year (Kells & Swinton, 2014). Notice that 10 is the dominant PI in the region (i.e. the productivity index that is 20 most commonly seen among soils in this region). is a coefficient representing the crop yield’s sensitivity to PI. Therefore, if we know , we could also know: ( )( ) ( ) 3.2 Market Scenarios for Switchgrass Contract is a fairly common procurement practice when no mature markets for a commodity exist (Jensen et al., 2007). This also applies to Michigan as the market for switchgrass is negligible. Therefore, contract pricing exists under all market scenarios in this study. Shown in the literature review section, as contract hold-up (delay or reduce payment by the biorefinery) is an eminent risk in contract relationships especially for perennial energy crop, all the market scenarios analysis below will treat it as an important factor. 3.2.1 Single-Outlet (Biorefinery) in the Region Procures from Individual Farmers As a new energy crop, switchgrass has very few outlets. The most commonly seen outlets are for ethanol production and electricity generation by combustion. However, most of those factories are rather regional and their switchgrass collecting areas do not usually overlap so much. Therefore, if farmers in one region were to sell to an outlet in another region, he had to transport the switchgrass for a long distance. This is difficult as the transportation cost for grass is exhibitive high. In addition, it is also difficult for individual farmers to get enough information for other market outlets far away. All of the above stated facts show that the transaction cost for information searching and trading with those distant outlets is very high. Therefore, for a county under consideration, the usual case is that they are facing a single outlet. As a result, the thesis will study this case first. 21 Consider a contract with a quantity/yield price ( ) and gross margin ( compensation per acre ( ). The total contracted ) contracted for farmer i could be expressed as: ( ) ( Here ( ) ( ) denotes the percentage payment if contract is held up by the procurer ), which is assumed to be constant during the simulation period. The smaller is, the less payment will be received by farmers. In this scenario, farmers and biorefinery act following the flowchart shown in Figure 2. At the beginning of each year, farmers will get to know the compensation mechanism in the contract and form their expectations on crop gross margins. For traditional crops, the expectations are formed according to Bayesian rule; for switchgrass, farmers observe biorefinery’s past hold-up behavior (illustrated in more detail below) and past switchgrass production real cost as well as past ethanol price. That information will be used to determine farmers’ expectations of the amount of payment biorefinery will hold up for the coming year. Based on the expectations, farmers will carry out a linear programming optimization that incorporates risk and decide the land allocation for each year. Then biorefinery will be informed how many acres have been allocated to switchgrass use. It will utilize this information and the expectation on the ethanol price to decide the profit gain in this period and the future profit loss if hold up contract. Then the biorefinery decide whether and how much payment to hold up farmers based on the calculation above. Finally, based on biorefinery’s hold-up decision, biorefinery’s and 22 farmers’ profits are realized and the available resources are updated for farmers. The model repeats this behavior for the simulation period (1 year = 1 time step). Farmers Biorefinery Get Contract Information Hold-up Amount Form Expectation Gross Margin (Traditional) Percent Payment Gross Margin (Switchgrass) Realization Farm-Level Optimization Land Allocation Gross Margin Ethanol Price Profit Realization Current period hold up gain Switchgrass Acres Future Profit Loss Resource Update Form Expectation Cash Available Land Available (Not Occupied by Perennial Crops) Ethanol Price Figure 2 Decision Tree for the Single-Outlet Scenario (Scenario 1) 3.2.2 Quasi-Multiple Outlets – A Biorefinery Procures From a Farmer Cooperative In the first scenario, we say that for individual farmers, it is usually rather unfeasible to sell their switchgrass to market outlets far away due to the high grass transportation cost and transaction cost of finding another outlet, thus they are in fact facing a single outlet. However, when farmers form a cooperative, several different things might happen to facilitate the cooperative to find out alternative market outlets -- farmers will indeed gain a much higher bargaining power than when they are operating individually: 23 First, the cooperative could own a pelletizer, converting switchgrass from grass to pelletize, which saves the transportation cost to a great extent, thus makes relatively longdistance transportation more feasible and extends the potential of multiple outlets appearance. Second, it is much easier for a cooperative to get necessary information of other market outlets than individual farmers due to more specialized management and more efficient contacting methods, reducing the transaction cost of searching and trading with alternative marketing outlets. As the alternative switchgrass outlet depends on incurring some extent of transaction cost by the cooperative, this scenario could be regarded as a “quasi-multiple outlets” scenario. The next market scenario would be an ideal (or hypothetical) scenario that assumes there are multiple readily available market outlets. On the other hand, if farmers want to sell switchgrass via a farmers’ cooperative, they need to pay salaries to the management team to guarantee the regular functioning of the cooperative. But it is inferred here that the salary paid is much less than the potential profit gain of the appearance of competition between procures that brought by the alternative outlets found by the biorefinery.. It is expected that under this case, the biorefinery will be more unwilling to hold up contract than the first scenario and the amount of switchgrass land will be higher than in the first scenario: if holding up contract, biorefinery will face the risk of losing a great amount of profit even in the current year. At the beginning of each year, farmers will form expectation on switchgrass gross margin for continue working with the cooperative and allocate their land. At the end of 24 each year, cooperative collects its farmers’ harvested switchgrass, and then the biorefinery decides what percent of the payment it is going to offer this year based on its expectation on current and future loss of paying different percent of the full payment. Next, the cooperative will decide whether to sell switchgrass to biorefinery or sell them to the alternative outlet it could find. Finally, farmers got their payment from the biorefinery and step into the next year’s planning. 3.2.3 Multiple Easily Accessible Outlets in the Region for Individual Farmers Ideally, when multiple switchgrass outlets exist for farmers, the risk of being held up by it transaction partner is relatively lower than single outlet case due to the competition between the two outlets. Biorefinery’s capacity will also increase at a faster rate as lower hold-up amount will lead to higher farmers’ switchgrass grows margin expectation, making farmers less frequently to convert current switchgrass lands back to other crops. In addition, farmers do not need to incur high transaction cost to find out another outlet, so their switchgrass gross margin expectation is expected to be higher than under the cooperative’s “quasi-multiple outlet” situation. In this case, we consider two biorefineries 8 procure switchgrass from individual farmers (the difference between the two biorefineries is discussed in section 3.5.3). The flowchart in Figure 3 representing the interaction between farmers and biorefinery is quite similar with the single biorefinery & individual farmer case except that farmers need to consider with which biorefinery they sign the contract based on the 8 This could be easily changed to different sectors procuring switchgrass, such as a biorefinery and a cofiring plant. The only difference is that different sector may have different switchgrass quality standard. Here we consider two biorefineries and we consider it to be a reasonable assumption as it could simplify other factors outside the analysis of hold-up problem. 25 expected gross margin of contracting (which is determined by the expected payment amount percent probability). Farmers Biorefinery Get Contract Information Opponent Hold-up History Hold-up Amount Form Expectation Gross Margin (Traditional) Percent Payment Gross Margin (Switchgrass) Realization Farm-Level Optimization Land Allocation Gross Margin Ethanol Price Opponent Hold-up Amount Profit Realization Current period hold up gain Switchgrass Acres Future Profit Loss Resource Update Form Expectation Cash Available Land Available (Not Occupied by Perennial Crops) Ethanol Price Figure 3 Decision Tree for Multiple-Outlet Scenario (Scenario 3) Note that in the figure above, opponent’s behavior follow the same rule with the biorefinery’s strategy. Biorefineries will also form expectation on each other’s hold-up amount. This is done by forming a best response function based on the expected current and future profit loss (gain) if it holds up (doesn’t hold up) the contract. By solving the best response function, each biorefinery will set its hold up amount at every simulation tick (More details below). 26 We have to acknowledge that this scenario is the most unlikely to happen case as it is quite unfeasible that the switchgrass procure areas for two industries overlap. But it is still interesting to compare this results to the cooperative case as that is more realistic to happen and so we want to see how large the difference between the “easy to realize” case and “quite ideal” case will be. 3.3 Farmer’s Learning on Crop Gross Margin For simplicity of the future market scenario analysis 9, this paper uses different learning algorithms for traditional crops (corn, soybean, wheat and hay) and switchgrass. 3.3.1 Learning Traditional Crops’ Gross Margin As the expected gross margin but not in equation (4) enters into farmers’ linear programming objective function, farmers need to form expectation on the current year’s gross margin for each crop at the beginning of each simulation year based on their prior knowledge and new observations utilizing Bayesian learning. We assume that gross margin for farmer i follows a normal distribution10: ( ( ) ( ) ) ( ) A common practice for Bayesian learning is to assume that farmers, while ( is known to is unknown and conform to a normal prior distribution ) (Feder & O’Mara, 1982). We update belief for the gross margin of 9 For detail, refer to section 3.4 The gross margin here excludes transportation costs from farmers’ fields to storage and/or to the biorefinery. Later when farmers have formed the expected gross margin for different crops, the transportation cost is then deducted from the gross margin. 10 27 traditional crops as a whole, but not form expectation for price and yield separately as we assume that is a constant for farmers in the expectation formation process11. At the end of the year, crops realize their true gross margin. Notice that in equation (5), price is fixed for each crop in a given year, and crop yield response proportionally to soil productivity. Therefore, farmers could merely update their belief on the gross margin for each crop on the soil type with PI equals to 10. In addition, we assume that the realized gross margins for different farmers are the same in the same year if the soils’ PI are the same. Accordingly, if the farmer or his neighbors have grown one crop for a year, the farmer will get the new observation on that crop’s realized gross margin, forming his posterior on the mean: ( | ) ( { ̅ Here m and ) } ( ) are the prior mean and variance of ( ) ( ) and ( ) are the posterior mean and variance of , and ̅ is the average of observed gross margin (including own realized gross margin in the last year, if any).N is the total number of observations of crop gross margin. Equation (9) shows the posterior of the distribution of the mean (Lindner & Gibbs, 1990). More realistically, if we assume that the one farmer’s observed gross margin from other farmers may subject to some error, , which comes from some farm-specific attributes or communication information distortion, we could make 11 However, the realized gross margin is calculated using crop price, yield and input cost. 28 ( ) which is known to all farmers (Ma & Shi, 2011). Then slightly modify what Ma & Shi (2011) proposed the posterior belief on crop gross margin could be formulated as follows ( is the realized own gross margin, while ̅ is the mean of observed others’ gross margin and n is the number of observations from other farmers): ̅ ( ) ( ) Here Me = 1 if the farmer grew the crop in the last year and equals to 0 if not. Notice that we treat the gross margin as a whole here (even though the realizations of gross margins are determined by the realization of price and yield) but not separately update the belief for price and yield. 3.3.2 Learning Switchgrass’s Gross Margin As no official record of historical switchgrass yield and gross margin exists, this paper considers two switchgrass yield scenarios according to Kells & Swinton (2014), one high yield (4.7 tons/acre) and one low yield (4.1 tons/acre) and they are randomly assigned to different simulation years. In addition, farmers’ expected gross margin is also determined by their expectation of whether the biorefinery will hold up the contract. At the beginning of every simulation tick (year), farmers will update the expectation of the perceived contract payment percent for the current year ( ) and expected yield ( ), following the procedure defined in section 3.5. The expected gross margin for switchgrass is thus: ( ) (∑ [( ) ( 29 )] ( )) ( ) At the beginning of each simulation tick (year), biorefinery will choose whether to hold up the contract at the current year according to the updating rule in section 3.5.1. Farmers’ learning on switchgrass yield and contract hold up follows a Bayesian procedure for binomial variables. Let’s denote the probability of the occurrence of high yield (or contract hold up) by . { } Following Bolstad (2007), ( let’s set the prior of Bayesian method as ). The posterior becomes: ( Here denotes the number of observations and ) the number of realizations of the defined occurrence. Then the new mean and variance of are updated as: ( ) ( ) ( ) ( ) ( ) ( ) 3.4 Additional Farmer Decision Constraints In order to prevent the occurrence of unrealistic land allocation results, additional crop rational constraints (maximum proportion of a crop) are imposed on the farm optimization problem following Hazell & Norton (2006) and Anderson (2012). In their model, Kelley & Evans (2011) also impose limitations on farmers’ preference for tree and crop, which plays a similar role in the objective function with crop rational constraints. The rational constraints imposed here include the maximum proportion of perennial grasses/annual crops that could be grown each year on the unused land and the proportion of each annual crop acres (corn, soybean and wheat) to the total annual crop acres. These constraints are chosen based on historical data or calibration process. That is, 30 the set of proportions are chosen so that the simulated crop acre patterns best fit for the observed historical pattern12. Table 3 below shows the calibrated crop rational constraint parameters combination. Table 3 Crop Upper Limit Used in the Model Crop Type Parameters Perennial Alfalfa/TC* Perennal Switchgrass/TC* Annual Corn/Annual Annual Soybean/Annual Annual Wheat/Annual Total Annual Annual/TC* 13 * TC: Total Cropland Value 0.6 0.3 0.5 0.4 0.3 0.5 Value Source Calibration Arbitrarily Choosen Historical Data Historical Data Historical Data Historical Data Limit Max Max Max Max Max Max 3.5 Market Scenarios and Agents’ Learning on Contract Hold-Up As we aresaying that the contract prices during all the simulation years are constant, the learning problem for biorefineries is mainly to determine whether to hold up the contracts. We use different learning algorithms to model biorefineries’ learning problem under different scenarios. We are interested in how the land devoted to switchgrass and the possibility that biorefinery might hold-up the contract will evolve overtime, given specific contract compensation. It is also interesting to see how these two trends affect each other. The model framework for contract hold-up presented here is a first attempt to quantify the qualitative assessment used in many literatures (Klein, 1996; Gow, Streeter & Swinnnen, 2001 etc.). 12 As switchgrass is historically not presented, it is not included in the calibration process. As a result, no switchgrass maximum proportion is included in the first several years. Switchgrass proportion is set manually based on current literatures after the tick when switchgrass is included in the model. 13 The use of total croplands could be: grow annual crops, grow perennial crops and left fallow. When there is not enough working capital or the expected gross margin goes to negative, farmers might be prone to left some of their croplands to fallow 31 3.5.1 Single-Outlet (Biorefinery) in the Region Procures from Individual Farmers 3.5.1.1 Biorefinery’s Learning and Decision Process Biorefinery has Sixteen levels of payment options (hold-up options): Holding up 0%, 5%, 10% ……. 80% of the full payment (paying 100%, 95%, 90% …… 20% of the full payment, respectively). { Denote the percent payment by . }. The reason that we cut the payment percent at 20% is to provide a coarse representation of an amount below which farmers are unwilling to give their switchgrass to the biorefinery (e.g., the payment is lower than their switchgrass transportation cost and some other necessary cost of delivering switchgrass to the biorefinery). Define as the expected utility biorefinery could get by paying full payment at year t. The value of ∑ (( Here paying percent of the is set according to: ) ( ) ) ( ) is the profit that the biorefinery could gain in the current year by percent of the full contract payment in this year, is the price of ethanol at year stage 0, c is the conversion cost per gallon of ethanol, rate is the conversion rate from switchgrass to ethanol, is switchgrass yield for land parcel i in year t, contracted full payment of switchgrass ($/ton). is the is the expected potential future profit loss of the currently contracted land for contract hold up (paying percent of the contract price). The fixed cost of switchgrass to ethanol conversion is converted to the per gallon cost included in c taken from Haque & Epplin (2010). The per gallon cost (c) 32 is assumed to be $1.57/gallon14 according to their study. The conversion rate (rate) of 1 dry ton switchgrass to ethanol is set to 91gallon/dry ton according to Haque & Epplin (2010) and Song, Zhao & Swinton (2011). is determined by the change of the amount of switchgrass land under contract if ) and the expected net present value percent of the full payment is paid ( of current switchgrass land per acre (∑ ): ∑ ) (( ( ( ) ) ( ( ( ) ∑ { ) } ( ) ) ) ( ) ( ) ( ) ( ) ( ) is the expected net present value of one acre switchgrass land, is the discount rate of future value to present value, is defined as the expected portion of future ethanol production profit to revenue, which is the average of historical profit to revenue. Assuming that biorefinery knows how farmers update their beliefs on switchgrass gross margin (details are in the next sub-section), ( ) is the biorefinery’s expected average farmer switchgrass growing gross margin in the next year for lands under its contract if the biorefinery pays percent of the full payment this year, is biorefinery’s expected average farmer “other crops” growing gross 14 Different conversion cost is used in different studies. Dipardon (1999) uses $1.29/gallon in 1998 dollars, McAloon et al., (2000) uses $1.30 in 1999 dollars, Happe & Epplin (2010) uses $1.57/gallon in 2010 dollars, and Tao et al., (2013) uses $1.96/gallon in 2012 dollars. All of these estimates exclude the cost of feedstock. We choose Happe & Epplin (2010)’s estimated cost as the value is neither too high nor too low and year 2010 dollar is also an acceptable measurement. 33 margin for their lands. is biorefinery’s expected loss coefficient that describes what percent of current land will be converted out of switchgrass use in the current year if the biorefinery pays percent in this year 15 . ( ) represents biorefinery’s expected { farmers’ perceived payment percent probability ( beginning of next year if the refinery pays } ) in the percent at the end of this tick. ( ) is switchgrass gross margin if the biorefinery pays percent of the full payment in the next year. The equation for says that under most circumstance, the higher the difference between traditional crop and switchgrass profitability is, the higher amount of switchgrass land you will loss. At each time period, the biorefinery will choose the payment rate that maximizes its utility. That is: (∑ ( ) ( ) ) ( ) Assuming that biorefinery and farmers know how the other party updates his expectation on contract hold-up probability and how he makes his decision, and thus ( ) could be calculated according to the next section. 3.5.1.2 Farmers’ Learning on Contract Hold-Up Percent Probability Define { by farmers expected biorefinery’s } percent this year if it pays probability of paying percent of the full payment last year . It could be expressed as: 15 It has to be admitted that this is only a rough estimation as the expected loss coefficient depends on farmers’ expected profitability of crops in the next period, which depends on quite heterogeneous factors such as soil productivity, farmers’ capital available and crop upper limits. Those factors are difficult to tract mathematically, so a rough estimation is used here in the equation. But we do take biorefinery’s expected farmer profit expectation in the next period into consideration in the equation for . Thus we say that this approach is valid. 34 ( ) ( ) are the weights farmers assign to rational calculated holdup probability ( ) and historical biorefinery hold up probability ( ( ) ). A weighted average is used here. is the expected hold-up possibility in this year calculated by farmers following rational expectations. () could be calculated as: ( ( ( ))) ( )16 ( ) is the list of payment percentages that doesn’t contain . We could calculate each ( ) in the following way: ( (( ) ( ) )̅ (( ( ( ) ) ) Therefore, the probability of choosing each level of payment ( ) 17 ) ̅) ( ) ( ) could be expressed as a segment of the ethanol price axis and the probability could be calculated out assuming the ethanol price conforms to a normal distribution. CA is the current lands under the biorefinery’s contract. Given that the ethanol price follows a normal distribution and farmers will update their beliefs on the mean and variance of ethanol price, could be calculated easily. 16 In the calculation, we could calculate only pairs of ( ) that . The rest combinations could be calculated based on these results. 17 The final sign of the comparator could be either “greater than” or “less than”, depending on the sign of . It is obvious that if , 35 If we apply the same equation of ( history ( ) ( ) , the only difference between (in the equation below) exists in the biorefinery’s hold-up ( )). Thus could be expressed as: ( ( to ) ∑ ( ( ( ( ) ( ) ∑ ( ) )) ( ( ) ) ) and thus ) ( ) ( Therefore, for farmers, ( ) ( ( )) ( ( ) ) ) could be calculated. As biorefinery knows farmers’ decision rule (more specifically, it knows the way farmers calculate , it could estimates farmers’ perceived which means ( ) and consequently and ( ), in the above section’s equations could be estimated. 3.5.2 Quasi-Multiple Outlets – A Biorefinery Procures from a Farmer Cooperative Under this scenario, after biorefinery announces its payment percent of the full payment, the cooperative will sequentially determine whether to sell the switchgrass of its farmers to the biorefinery or to find out an alternative seller based on the comparison of the real price of the two. For simplicity, using the same method used in Song, Zhao & Swinton (2011), we assume that the nominal switchgrass price per ton offered by alternative outlet found by the cooperative is determined by ethanol price ( to ethanol conversion rate (rate): 36 ), conversion cost (c) and switchgrass ( ) ( ) However, the real price of the alternative market scenario facing the cooperative should also take the transaction cost (TC)18 of trading with the outlet into consideration: ( ) ( ) 3.5.2.1 Biorefinery’s Learning and Decision Process As in the first scenario, the biorefinery’s expected utility of paying percent of the full payment at time t to the cooperative is: ( ) is modified to reflect the effect of the potential cooperative’s alternative outlet on the biorefinery’s decision: ) ∑ (( { The equation for Here ( ) ( ) ( ) is quite similar with that used in the first scenario, except a modification of ( ) : ( ) ( ( ) ) ) ( ) includes not only the expectation for traditional crop’s gross margin, but also includes the expectation of farmers’ (cooperative’s) expectation on its alternative outlet’s switchgrass gross margin. ( ) is the expected gross margin of trading solely with the biorefinery. 18 Note that here our definition of transaction cost (TC0 is a little different from the traditional way: The traditional definition of TC only include cost such as information searching cost, bargaining cost, contracting cost, etc. Our definition follows the way suggested by Dorward (1999) such that it also includes other quasi transaction cost (e.g. transportation cost) 37 3.5.2.2 Farmers’ Learning on Contract Hold-Up and Cooperative’s action Farmers first form expectation on biorefinery’s hold-up probability, and then form the expectation on the probability of cooperative choosing to cooperate with the biorefinery or to sell to the alternative outlet it could find. Everything for farmer is the same as in the first scenario except used in the calculation of and the expectation formation formula for switchgrass growing in the linear programming’s objective function: { ) ∑ (( Let’s set { ) ( ) ( ) ( ) as: ( ) The equation for ( ) ( ) ( ) states that if the price the biorefinery pays in the current year is less than that offered by the alternative outlet, the cooperative could sell the switchgrass to the alternative and the biorefinery would get nothing in the current year. However, it will gain a profit of ( ) from each acre of contracted switchgrass in the current year if the price it pays is higher than that the alternative outlet. For any I. , there are three possible combinations of ; II. ; and III. and , namely: . The probabilities for the 3 conditions are: I. { ( ( ( ) ) ( ( ) ) ( 38 ) ) ( ) II. { III. { ( ( ( ( ) ) ( ( ) ) ( ( ) ) ( ( ) ) ( ( The calculation of each ( ) ) ) ) ) ( ) ( ) for the final part under the three combinations becomes: [( ( [( ] ) ( ( ) [( ) ]) ] ) ( ) ) { Consequently, ( ) is calculated as the probability of the intersection of the three conditions. is then calculated following the method used in the first scenario. Farmers’ perceived probability that biorefinery will hold up i percent of the payment this year after they observed percent realized hold up amount in the last year could still be calculated by: ( ) ( ) Also as biorefinery knows farmers’ decision rule (more specifically, it knows the way farmers calculate ( ) , which means , it could estimates farmers’ perceived ( ) and consequently equations could be estimated. 39 and in the above section’s Another difference for this scenario compared with the first one exists in the objective function of the linear programming model: when farmers form their gross margin expectations from growing switchgrass in the linear programming’s objective function, they consider both (1) the expected payment percent by the biorefinery, and (2) the probability that the cooperative will chose the alternative market outlet for their switchgrass. Therefore, the expectation of the gross margin from growing switchgrass becomes: ( (∑ ( )) ( ) ( ) ) means the probability that the cooperative will continue to cooperate with biorefinery this year and the biorefinery will pay i percent of the full payment. ( ) is the probability that the cooperative will sell the switchgrass to alternative market this year. is the expected gross margin if the biorefinery pays i percent of the contracted; is the expected gross margin for the alternative market outlet’s switchgrass; ( ) ( ) ( ) is the probability that the biorefinery will choose to pay percent of the full payment, which is calculated following the method in the beginning of this section. ( ) ( ∑ ) ( ) 3.5.3 Multiple Easily Accessible Outlets in the Region for Individual Farmers In this case, two biorefineries compete for the same farmers’ switchgrass. Additional assumptions used in this scenario are defined as: 40 Assumption 1: The contracts used by the two biorefineries are the same. The only difference regarding the contract between the two refineries is their hold-up amounts in each period. Assumption 2: There is no communication between the two biorefineries. That is, no collusion behavior exists. Assumption 3: If one biorefinery holds up more payment in one period while the other biorefinery holds up less, the one that holds up more will loss all of its biofeedstock in this period (i.e. farmers can sell all switchgrass to the biorefinery with the higher payment in this tick). However, the expected future switchgrass that could be procured for each biorefinery depends upon the biorefinery’s expectation of the farmers’ perceived payment amount for each biorefinery in the future. The assumptions above basically state that there are no differences between the two biorefineries except for the distance to the farmers’ land. Although this is a simplification of the problem and it might not be the case in the real world, the essential strategic components between actors have been captured and thus it is believed to adequately demonstrate the effect of multiple outlets on farmers’ switchgrass adoption. 3.5.3.1 Biorefinery’s Learning and Decision Process When a biorefinery chooses whether to hold up the contract or how much to hold up, it has to consider: (1) how much profit in this year it will loss (gain) due to the lower (higher) level of hold-up percent used by a competing biorefinery (farmers sell switchgrass that is under contract to a competing biorefinery); (2) how much profit it will 41 loss (gain) in the future due to the lower (higher) level of hold-up percent used by a competing biorefinery (farmers might choose to switch land under contract to a competing biorefinery’s contract). Therefore, the formula for in the last section could be modified as below: ( Here ) represents the expected profit change if the biorefinery pays percent of the full payment. If the biorefinery pays less than the competing biorefinery, it will get all the switchgrass from the farmers contracted to the competing biorefinery in the current year (see Assumption 3). Otherwise, it will loss all the switchgrass from contracted farmers in this tick: ( ) ( ) Here and ) ( ( ) denotes the switchgrass profits for farmers contracted to grow switchgrass for a competing biorefinery (superscript B) and for the biorefinery (superscript A). The calculation of uses a weighted average approach: the first term is the weighted current period profit that the biorefinery could get (profit from own contracted lands) if payment is equal to that of the competing biorefinery ( ); the second term shows biorefinery’s profit (profit from own contracted and competing biorefinery’s contracted switchgrass land) if payment is higher ); in fact, there should be a term that than that of the competing biorefinery ( shows the situation when the payment is less than that of my opponent ( However, in this case the profit will be 0 thus it doesn’t shown up in the equation. 42 );. The formula of is adopted from the first scenario case: ∑ However, the formula of ( ) is modified so as to include the effect of the competing biorefinery’s hold-up strategy on the biorefinery’s strategy: ( ( ) ( ( ( ) ) ∑ ( ) ) ) ( ( ) ( ) ) ( ) ( ) ( ) is calculated the same as in the first scenario. At each time period, the biorefinery will choose the payment rate that maximizes its utility: (∑ ( ) ( ) ) ( ) 3.5.3.2 Farmers’ Learning on Contract Hold-Up Percent Probability The same as in the first scenario, the process for farmers to learn both biorefineries’ hold-up probability is formed as the weighted average of a rationally calculated probability and an experience based probability. The probability difference exists in the process of calculating the rational : In this scenario, farmers need to consider not only biorefinery’s future loss from paying a certain amount, but also the current profit loss (gain) from paying the amount, which comes from the probability of the expected hold-up percent of each biorefinery’s opponent. It is straightforward to show the equations used for farmers 43 to calculate one biorefinery’s hold up probability as below using the equation of defined in the last sub-section; those used for the other biorefinery are exactly the same. ( Define ) ( ) ( could be defined as: the calculation of the probability that ( ( [( ) ] ) [( ), then for any [( ] ) ] ) [( ( ( [( ( ( ) ( ) ) ) ( ] ) )( ] ( ) ) ) ( is the biorefinery’s current contracted farmers’ switchgrass land while its opponent. ( ) ) ) is that of ) means the biorefinery’s expected probability that its opponent will pay less than me. It is calculated using the payment history of the biorefinery’s opponent19. The calculation of ( ) in biorefinery’s problem also follows the same procedure. 3.6 Treat Switchgrass Adoption as Technology Diffusion As a relatively new crop to be introduced in the area, switchgrass is analogous to a new technology, whose diffusion always empirically follows an “S” shape path such that the diffusion rate is slow at the beginning as only bold farmers will be willing to adopt, but then accelerates due to social learning and finally becomes stable (Alexander et al, 2013). 19 ( ) should also be calculated based It should be acknowledged that for a fully rational agent, on its opponent’s profit function. However, for a highly heterogeneous environment like this case, that method becomes intractable quickly. Therefore, we consequently loose that requirement and use an algorithm that assembles fictitious play (Berger, 2007) to represent the concept. 44 Therefore, following the method used in Alkemade & Castaldi (2005) and Alexander et al (2013), we first defined each farmers’ “willingness to consider” adoption of switchgrass. Farms who are willing to consider the adoption will include switchgrass in the optimization model and subsequently update their beliefs proposed above. Farmers who are not willing to consider switchgrass at the initialization phase will look at their neighbor’s adoption. If the percentage of neighbors who have already adopted switchgrass exceeds the farmers’ threshold, then the farmer becomes willing to consider planting switchgrass. This approach is also consistent with the use of “social” and “factual” farmers in Shastri et al. (2011). Farmers’ thresholds are assigned randomly following a normal distribution (If a farmer’s assigned threshold is less than or equal to zero, then the farmer is willing to consider switchgrass in the initialization stage). 45 CHAPTER 4: DATA, INITIALIZATION AND BASELINE VALIDATION 4.1 Review of the Study Area Alpena County, located at North Michigan’s Lower Peninsula (also the north tier of Michigan), is chosen as the study area of the thesis. The major crops here are alfalfa, corn, winter wheat and soybeans, while the vast majority of live stocks are cattle. Figure 4 below provides a spatially explicit description of Alpena County agricultural zone land cover situation (green color is soybean, yellow color is corn, brown color is wheat and pink color represents alfalfa). Those green colors represent forest, woody wetland and other non-arable lands. According to NASS Census Statistics 200720, there are 573 farms with an average size of 150 acres/farm, covering 85,947 acres of land in total (with 46,450 acres harvested cropland, an approximate of 59577 acres planted cropland). Figure 4 Alpena County Land Use and Land Cover 2008 The harvested area for hay (alfalfa hay and other hays), corn, winter wheat and soybeans are 25,265 acres (with alfalfa hay for 17,858 acres, taking a share of 71%), 20 See http://www.nass.usda.gov/Data_and_Statistics/ for detailed information and census statistics 46 7810 acres, 3695 acres and 2802 acres, respectively 21 . The major crops mentioned account for up to 85% of the total harvested cropland (it ranges from 87% ~ 92% during 2008~2012). Historically, no energy crop like switchgrass or miscanthus has been adopted across the county. The dominance of alfalfa hay is determined by the weather and soil conditions in this region and it becomes one of the reasons that this county is chosen as the study area (i.e. the competition of energy crops vs. food crops are not as fierce as other counties in central and south Michigan). 4.2 Farm Endowment Data and Land Ownership Data The farm endowment data and land ownership data are required to initialize the model. The data we need comes from three sources: The first data source is USDA NASS agricultural census data 2007, which contains the average farm characteristics across Alpena County (e.g. farm size, crop composition and net farm income). We also utilized NASS survey data for the historical average crop price and yield of the county. The second data source is farm land ownership data recorded in Common Land Unit (CLU) data22 provided by Farm Market Id Company, which is not publicly available. There are totally 4808 CLUs in Alpena County recorded by the company, among which 3481 CLUs have a farmer name (property right) in record, and the percentage of acres covered by CLUs with farmers’ name reaches 62% of all the farmlands. This data source 21 This data only exist for census years, available every fifth year (e.g. 2002, 2007), the CDL data is quite inaccurate in Alfalfa Acres after comparing it with the census data 2007. 22 According to USDA FSA, A Common Land Unit (CLU) is the smallest unit of land that has a permanent, contiguous boundary, a common land cover and land management, a common owner and a common producer in agricultural land associated with USDA farm programs. The CLUs in Alpena County cover almost all the farm lands in the area. 47 also includes 178 farmers’ records (30% of the total farms in the county) on farm stead location, credit availability and gross farm income for the previous year. The third data source is Michigan soil productivity index (PI) data produced jointly from NASS SSURGO soil data and USDA forest service by Schaetzl, Krist & Miller (2012). The index ranges from 0 (quite unproductive) to 14 (very productive). Farmers differ in terms of owning different amount of lands with different soil productivity index, which plays an important role in determining crop yield and consequently the gross margin. The last data source is USDA NASS Cropland Data Layer (CDL), which is a ESRI raster data file that depicts the land cover in the whole Alpena County. The land cover types are further classified into 3 categories in the thesis: croplands, pasture lands and woody wetlands/Forests. Currently in this study, only croplands are available for crop farming. Later researches should include raising livestock on pasture lands. 4.3 Projection of Future Traditional Crop Price and Yield Crop price is adopted from the USDA prediction for the next decade. The method to project future crop yield is adopted from Richardson, Klose & Gray (2000), simulating a multivariate Empirical (MVE) probability distribution. The multivariate empirical probability distribution is drawn from historical years (1998~2012) for the four traditional crops: alfalfa, corn, soybeans and winter wheat. During the simulation, the inter-temporal and intra-temporal relationships among the four crop yields are captured by an inter- and intra-temporal matrix derived from historical data. Figure 5, and Figure 6 48 show the final real and projected yields and prices for corn, soybeans, and winter wheat23. Figure 7 illustrates the projected ethanol prices from the U.S. Department of Energy for the simulation period (2011-22). Also see Appendix A for projected input cost during the pre-simulation and simulation period. See Appendix B for Crop Budget that adopted from MSU Extension and Kells & Swinton (2014). 160 140 120 100 80 60 40 20 0 Corn Yield Soy Yield Wheat Yield Figure 5 Real (2002~2012) and Projected (2013~2022) Crop Yield (in bushels/acre) 16 14 12 10 8 6 4 2 0 Corn Price Soy Price Wheat Price Figure 6 Real (2002~2012) and Projected (2013~2022) Crop Price (in $/bushel) 23 The projection methods for alfalfa price and yield are the same as for traditional crops. However, as the unit of alfalfa price and yield ($/ton and tons) are different from those of annual crops ($/Bushel and Bushel), the projected alfalfa price and yield are not shown here 49 Ethanol Price ($/gallon) 3.4 3.2 3 2.8 2.6 2.4 2.2 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Figure 7 US DOE Predicted Ethanol Price during Simulation Period 4.4 Model Initialization The model initialization proceeds as follows: First, we initialize the recorded 178 farmers’ farm location, farm acres, cropland acres, and net cash income of the last year according to CLU data. Then the rest 395 farmers are initialized according to the census distribution. In addition, to take the possible clustering relationship between these variables into account (Berger & Schreinemachers, 2006), total farm acres is chosen as the clustering reference for farm cropland acres, consistent with NASS census convention (i.e. all other farm resource variables are set referring to farm size if detailed data are not available). According to the census data, the total farm size in the region is 59577 acres. As we only have harvested acres but not total cropland size in each farm acre level, we make a simple assumption here that the cropland size increases proportionally with harvested acres for farms in each farm size level. Table 4 summarizes some of the census and generated total farm characters. Farm size is also chosen as the reference for farm income under the assumption that the larger the farm is, the higher income it has (Generated net income distribution for 2007 is shown in Table 5). 50 Table 4 Total Farm Acres and Farm Cropland Acres Farm Category by Size Farm Size (Acres) 1~9 10 ~ 49 50 ~ 69 70 ~ 99 100 ~ 139 140 ~ 179 180 ~ 219 220 ~ 259 260 ~ 499 500 ~ 999 1,000 ~ 1,999 Sum Farm Number 16 195 43 96 63 44 28 10 41 29 8 573 Total Farm Acres Census (Acres) 82 5,593 2,515 7,663 7,418 6,946 5,454 2,339 14,314 20,982 12,641 85,947 Generated (Acres) 86 5,648 2,511 7,667 7,415 6,931 5,453 2,328 14,301 20,968 12,639 85,947 Farm Cropland Acres Census Generated (Acres) (Acres) 21 21 2,044 2,041 1,240 1,244 3,132 3,130 3,739 3,736 2,977 2,980 2,951 2,952 1,933 1,935 10,628 10,629 18,870 18,870 12,042 12,039 59,577 59,577 Table 5 2007 Farm Income Distribution Farm Size (Acres) 1~9 10 ~ 49 50 ~ 69 70 ~ 99 100 ~ 139 140 ~ 179 180 ~ 219 220 ~ 259 260 ~ 499 500 ~ 999 1,000 ~ 1,999 NASS census (No stratification) Generated Data Distribution Min ($) 3,549 7,611 12,390 16,711 21,522 25,807 30,692 35,142 39,480 44,346 44,092 3,020 Mean ($) 5,532 9,803 14,593 19,066 23,399 28,158 32,797 37,387 41,580 46,239 45,776 Max ($) 7,266 12,109 16,615 21,221 25,658 30,279 34,769 38,936 43,954 48,142 47,835 48,550 4.5 Baseline Validation As historical Data from 2007 to 2012 regarding the total corn, soybeans and wheat planted acres 24 is available, the simulation is set to start from 2007 using the 24 Alfalfa acres are not reported in the yearly statistic book, and CDL data that comes from satellite map has a low reliability of distinguishing between grass crops and non-crop pasture. Therefore, historical alfalfa acre is not included in the validation process, but the simulated amount will be included in the later 51 calibrated parameters in Table 3 and the simulation results are compared to the real data to see whether the simulation produces a similar crop acres pattern with the real world empirical data. Note that during this period, switchgrass is not included in the model as there is historically no switchgrass grown in this region. The figures below show the comparison of the simulated (the value of each year is the average value of 10 simulation runs with different random seed) versus real crop acres in each simulation years. 10000 9000 8000 7000 6000 5000 4000 2007 2008 2009 2010 Corn Real (Acres) 2011 2012 Corn Simulated (Acres) Figure 8 Annual Corn Real Data and Simulated Data 2007 to 2012 9000 8000 7000 6000 5000 4000 3000 2000 2007 2008 2009 2010 Soybeans Real (Acres) 2011 2012 Soybeans Simulated (Acres) Figure 9 Annual Soybeans Real Data and Simulated Data 2007 to 2012 ABM simulation experiment. Another reason for not including alfalfa acres into the validation is that alfalfa is a perennial grass thus we do not know how many acres have been already allocated to alfalfa and how many acres is about to turn out of alfalfa use in one year. 52 16000 15000 14000 13000 12000 11000 10000 9000 2007 2008 2009 2010 Corn and Soybeans Real (Acres) 2011 2012 Corn and Soybeans Simulated (Acres) Figure 10 Annual Corn and Soybeans Real Data and Simulated Data 2007 to 2012 6500 6000 5500 5000 4500 4000 3500 3000 2007 2008 2009 2010 Wheat Real (Acres) 2011 2012 Wheat Simulated (Acres) Figure 11 Annual Wheat Real Data and Simulated Data 2007 to 2012 From Figure 8 to Figure 11, we could see that the acres change trends of the simulated results are quite similar with that shown by the real empirical data -- the simulated and real crop acres gradually converge to each other during the last few years. It is reasonable because at the beginning of the simulation, the crop acres for each crop are 0. But as we have perennial alfalfa in this region, the starting point is actually not 0 for alfalfa. As some farmers might be in corn and soybean rotation, the good matching between real and simulated total corn and soybean acres shows that the simulation result 53 is quite satisfactory. After several years’ of learning and farming in the simulation, each simulated crop converges to the real data. Therefore, as the overall trend changes and the last few years’ simulated acres are quite similar with the real world data, we could say that the calibrated model is validated. 54 CHAPTER 5: AGENT BASED MODEL RESULTS AND DISCUSSION In this section, the ABM experiment results are shown and discussed: subsection 5.1 for the first scenario, 5.2 for the second scenario and 5.3 for the third. 5.1 Single-Outlet (Biorefinery) in the Region Procures from Individual Farmers The results for the scenario where one biorefinery procures from individual farmers (or single outlet scenario) are shown below. The logic of this section could be found at section 3.2.1 and 3.5.1. 5.1.1 Key Parameters Used in the Model Before running the simulation, the parameters shown in the above sections are parameterized. Table 6 below shows the initialized parameter used in the major runs in this scenario. Table 6 Single-Outlet Scenario (Scenario 1) Model Parameters Whose Parameter sw ( ) Farmer ( ) Meaning Switchgrass upper limit Initial perceived payment (hold up) { }) percent probability ( Initial perceived probability of high yield High yield of switchgrass Low yield of switchgrass Weight on historical hold-up probability Payment per ton Refinery Payment percent under consideration Value 0.3 0.0625…..0.625 U(0.3, 0.5) 4.7 4.1 0.5 75, 85, 95, 105, 115, 125 0.2, 0.25, ….., 1 Farmers’ expected probability of different payment percent levels are set to be equal. That is, ∑ ( ) ( ) ( ) s a new crop, the perceived yield by farmers at first is usually low. Therefore, a low range (0.3 to 0.5) is randomly assigned to each farmer on the possibility of high switchgrass yield in a particular year (except the first year in switchgrass’s life cycle. In addition, as the 55 switchgrass upper limit is set arbitrarily, a sensitivity analysis regarding this parameter will be conducted at the end of this section. Shown by Zhou (2013), the contract price for switchgrass in Tennessee needs to go up to $475/acre under acreage contract or $77/ dry ton under tonnage contract. In order to compare with existing contract prices in other researches, we take the payment suggested by Zhou (2013) into consideration when choosing the value for per ton payment. By choosing different values for the per ton payment, it is possible to get a feasible estimation of the payment schedule under which both biorefinery and farmers would be profitable from an ex-post perspective. 5.1.2 Simulation Result for the Single-Outlet Scenario 5.1.2.1 Comparison of Contracts with Different Per-ton Payment Biorefineries want more land dedicated into switchgrass such that they could procure more switchgrass every year. One way to doing so is to contract for a high price. However, unprofitable results will come if that price level is high, leading to an incentive to hold up contract when its expected ethanol price is low in the future. Consequently, farmers’ expectation on contract hold up amount will go higher and devote less land to switchgrass. Therefore, the biorefinery should balance this two factors when determine the price level. Thus different payment schedules are tested to compare potential different contract configuration results. When comparing the payments, the two criteria used are: (1) biorefinery’s net present value (NPV) for the 10 simulation years (from 2013 to 2022); (2) the ability to keep a stable feedstock supply (capacity increases or stabilizes at a certain level after several years). 56 Table 7 Comparison of Different Contract Configuration in Single-Outlet Scenario Mid End of Simulation Crop Acres Contract End (T=2017) price Simulation Corn ($/dry Bio-NPV Switchgrass Switchgrass Wheat Alfalfa Soybeans ton) (1000 $) (Acres) (Acres) (Acres) (Acres) (Acres) 0 15,634 5,447 32,099 (T=2012) (T=2012) (T=2012) (T=2012) 75 23.846 69 241 20,038 6,674 27,742 85 108.927 232 1,582 20,267 6,868 26,691 95 92.125 772 2,274 9,971 20,287 6,821 105 74.679 105 3,314 20,571 6,761 25,167 115 73.333 60 2,012 20,063 6,670 27,706 125 7.292 165 2,526 20,288 6,814 25,953 3500 Total Cropland: 59,577 Acres 3000 2500 2000 1500 1000 500 0 2013 2014 $75/ton 2015 $85/ton 2016 2017 2018 $95/ton 2019 $105/ton 2020 2021 $115/ton 2022 $125/ton Figure 12 Switchgrass Areas (in Acres) under Different Contract Price 2500 2000 Capacity: 730,000 tons/year 1500 1000 500 0 2013 $75/ton 2014 2015 $85/ton 2016 2017 $95/ton 2018 $105/ton 2019 2020 $115/ton 2021 2022 $125/ton Figure 13 Switchgrass Procured (in tons) under Different Contract Price 57 200 180 160 140 120 100 80 60 40 20 0 Total Farmers: 573 2013 2014 $75/ton 2015 $85/ton 2016 2017 $95/ton 2018 $105/ton 2019 2020 2021 $115/ton 2022 $125/ton Figure 14 Switchgrass Adopters (in numbers) During Simulation under Different Contract Price 5 4 3 2 1 0 75 85 95 105 115 125 $/ton Figure 15 Contract Hold-Up Times (in times) under Different Contract Price According to Table 7 and Figure 12~15 above, the biorefinery’s net present value (NPV) increases when per-ton payment increases before the payment reaches $85/ton. But after the price becomes higher than $85/ton, the biorefinery’s NPV decreases. Ideally, the difference of switchgrass area and biorefinery’s net present value under different contract price should be quite similar when the refinery could choose the amount to hold 58 up freely (that is, ideally, the real price they pay should be quite similar when using different nominal contract price and thus farmers’ expected payment percent should be similar). However, several factors generates the differences among the results: (1) farmers are risk averse: even when the expected payment for farmers in each tick under different contract price might be similar, difference exists in the variance of income; (2) we are saying that at the beginning of the simulation, farmers’ perceived possibilities of being held up of different amounts are equally divided. It will take the farmers some time to adjust this perceived probability to the real value. Therefore, under the interaction of farmers and biorefinery, a contracted price of $85/dry ton will be considered the best in the case for the biorefinery. Compared the results to the $77/ton calculated by Zhou (2013) and $250 + $50/ton that is currently used in the University of Tennessee Biofuel Initiative, the satisfactory price I get is a slightly higher at $85/ton. This is because we take biorefinery’s hold up decision into consideration and thus the final price incorporates farmers’ risk premium. 5.1.2.2 Contract with $85/dry ton Contracted Payment In this section, the detailed simulation results for the contract with $85/dry ton contracted price (the most satisfactory contract price we got) is shown and discussed. Figure 16 to Figure 19 show the traditional crops and switchgrass grown and biorefinery’s hold-up probability at each year for the contract with $85/ton payment (the value at each tick is the average value of 10 simulation runs25). 25 Sensitivity analysis is done for the simulation run times and it is found that the difference between 10 runs, 20 runs, 30 runs and 100 runs are quite small. Therefore, to save computational time, 10 runs are used in all analysis. 59 35000 30000 25000 20000 15000 10000 5000 0 2013 2014 2015 Corn Acres 2016 2017 Soybeans Acres 2018 2019 2020 Wheat Acres 2021 2022 Alfalfa Acres Figure 16 Traditional Crop Areas (in Acres) under Single-Outlet Scenario 2000 Total Cropland: 59,577 Acres 1500 1000 500 0 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Figure 17 Switchgrass Acres (in Acres) under the Single-Outlet Scenario 120 100 80 60 40 20 0 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Figure 18 Payment Percent (in %) under the Single-Outlet Scenario26 26 A deviate from 100% payment reflects that the contract is held up 60 120 100 Total Farmers: 573 80 60 40 20 0 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 Figure 19 Adopter Number (in numbers) under the Single-Outlet Scenario The introduction of switchgrass under the single outlet case doesn’t significantly alter the agricultural structure in this region. One of the reasons that not so many farmers want to consider switchgrass (and those who consider it won’t turn a great amount of land into switchgrass use) is that farmers believe that biorefinery will hold-up the contract. Farmers form their perceived contract payment percent possibility using their rational calculation and the biorefinery’s hold-up history (shown in figures above). This argument is supported by many researches on farmers’ attitude of biorefinery and switchgrass adoption (e.g. Hipple & Duffy, 2002; Jensen et al., 2007). 5.1.3 Sensitivity Analysis The sensitivity analysis is conducted for switchgrass upper limit (the max percent that switchgrass could occupy the unused land) as it is imposed arbitrarily in this study and are not subject to any calibration process as no switchgrass is grown in the county historically. The contract price is held constant at $85/ton, while varying the value of the switchgrass limit from 10%, 30% to 100% of the total cropland per year. 61 Table 8 Sensitivity Analysis on Switchgrass Upper Limit for Single-Outlet Scenario Mid End of Simulation Crop Acres End Simulation Switchgrass Simulation Limit Corn Bio-NPV Switchgrass Switchgrass Wheat Alfalfa (Percent) Soybeans (1000 $) (Acres) (Acres) (Acres) (Acres) (Acres) 0.1 48.442 116 834 20,191 6,687 27,401 0.3 108.927 232 1,582 20,267 6,868 26,691 1 106.413 131 1,218 20,193 6,769 26,896 The sensitivity analysis results show that the simulation results are quite insensitive to the switchgrass upper limit we impose, especially when the limit is greater than or equal to 0.3. This result is supported by the fact that farmers are really cautious on perennial energy crops to “test the water”, even if they are profitable from farmers’ prospective (Hipple & Duffy, 2002). The fact that energy and agriculture are characterized by lock in and resistant to change (Unruh, 2000) could also empirically support this argument. Generally, this is because farmers are uncertain about the new crop’s profitability. More specifically, in our study, this uncertainty on profitability is primarily driven by farmers’ fear of being held up – the number of years that the biorefinery holds up farmers reaches up to 4 (40% of the total simulation years). Therefore, this study takes an upper limit of 0.3 and believes that it is reasonable. To test whether the use of different switchgrass upper limit will influence the choice of contract price, an additional sensitivity analysis is also conducted (results not reported here) by testing the 6 price schemes used before under different switchgrass upper limit (0.3 and 0.1). It is found that the choice of switchgrass upper limit doesn’t influence the relative merits of different contract price configurations – the price of $85/ton has a higher NPV for the 10 simulation years. 62 5.2 Quasi-Multiple Outlets – A Biorefinery Procures from a Farmer Cooperative 5.2.1 Parameter Used in the Model The parameters used in this scenario are listed below in Table 9: Table 9 Quasi-Multiple Outlets Scenario (Scenario 2) Model Parameters Whose Parameter sw ( ) Farmer ( ) Meaning Switchgrass upper limit Initial perceived payment (hold up) { }) percent probability ( Initial perceived probability of high yield High yield of switchgrass Low yield of switchgrass Payment per ton Refinery Cooperative TC Payment percent under consideration Transaction Cost of Alternative Outlet Value 0.3 0.0625…..0.0625 U(0.3, 0.5) 4.7 4.1 75, 85, 95, 105, 115, 125 0.2, 0.25, ….., 1 $10/ton~$45/ton 5.2.2 Simulation Result for the Quasi-Multiple Outlets Scenario 5.2.2.1 Contract Price Choice under Different Cooperative’s Alternative Market Searching Transaction Cost Through the analysis in section 3, it is straightforward to say that the profitability of the biorefinery depends not only on its own action, but also on how attractive the price of cooperative’s alternative outlet is, which relies heavily on the transaction costs of the cooperative to trade with that outlet. Therefore, this study will analysis biorefinery’s satisfactory contract price choice among the given 6 contract prices when the cooperative is facing different transaction cost of searching for alternative outlets. After the simulation, we found that the contract prices that guarantee the highest biorefinery’s NPV vary with transaction cost: For transaction cost from $10/ton to $35/ton, the chosen contract price is $125/ton. However, when transaction cost is higher than $35/ton, the chosen contract price becomes $105/ton or $85/ton. Figure 20 and 63 Figure 21 below shows the biorefinery’s net present value and switchgrass acres under contract as a function of the total transaction cost: 700 600 500 400 300 200 100 0 $125/ton $125/ton $125/ton $125/ton $105/ton 10 $85/ton $105/ton $125/ton 15 20 25 30 35 40 TC($/ton) 45 Figure 20 End-Simulation Biorefinery NPV (in 1000 $) under Different Cooperative’s Alternative Market Searching Transaction Cost 18000 16000 14000 12000 10000 8000 6000 4000 2000 0 Total Cropland: 59,577 Acres 10 15 20 25 30 35 40 TC($/ton) 45 Figure 21 End-Simulation27 Switchgrass Areas (in Acres) under Different Cooperative’s Alternative Market Searching Transaction Cost From the figures above, some general results could be presented: First, the general trend for switchgrass acres is to decrease as cooperative’s transaction cost with alternative outlet increases. The reason is that the higher the transaction cost is, the more difficult the cooperative could find out an economically feasible alternative market outlet 27 The end of simulation switchgrass acres is used here is because we want the farmers to adjust their expectation on contract hold up for a while. 64 and thus the biorefinery will possess higher market power, which will drive up farmers’ expectation that the biorefinery is prone to hold up a relatively high amount of payment. In fact, the higher the transaction cost is, the situation is more similar with the first scenario where one market outlet (biorefinery) procures switchgrass from individual farmers; Second, as the cooperative’s transaction cost of trading with the alternative outlet increases, the net present value of the biorefinery will first increase and then decrease, reaching the highest point at a transaction cost of ($25/ton) For the biorefinery, the effect of increasing transaction cost could be decomposed into two parts: (1) The marginal side effect of increasing transaction cost is the decreasing switchgrass lands as its market power goes up. (2) The marginal benefit of market power is that as the “real switchgrass price” of alternative outlet decrease with higher transaction cost, the amount of payment it could hold up increases. At first, the marginal side effect of increasing transaction cost does not outweigh the marginal benefit. However, after the transaction cost is higher than $30/ton, the marginal benefit goes below the marginal side effect. An important implication of Figure 20 and Figure 21 above is that the biorefinery might be willing to encourage other market outlets in some other regions to increase its own profitability, as long as the transaction cost for the cooperative to deal with that market outlet keeps in a reasonable range. By doing so, the refinery could decrease farmers’ perceived risk of trading with itself and gain profit by increasing the amount of switchgrass lands contracted. 65 In the next sub-section, more detailed analysis over the full simulation period will be conducted. To save space and be more specific, it is decided to choose only one transaction cost scenario to conduct the analysis. As the scenario with a transaction cost equals to $25/ton while the chosen contract price equals to $125/ton as it guarantees the highest NPV level for the biorefinery, it is chosen for the detailed analysis. 5.2.2.2 Comparing Results with First Scenario Best Contract Price Case The results of the best contract price schedule under the two scenarios – (1) $85/ton for the case that one biorefinery procures from individual farmers, and (2) $125/ton with $25/ton transaction cost for the cooperative are compared: 15000 10000 Total CropLand: 59,577 Acres 5000 0 2013 2014 2015 2016 2017 scenario1 2018 2019 2020 2021 2022 scenario2 Figure 22 Switchgrass Areas (in Acres) Comparison between the Single-Outlet and Quasi-Multiple Outlets Scenario 20000 15000 10000 Capacity: 730,000 tons/year 5000 0 2013 2014 2015 2016 2017 scenario1 2018 2019 2020 2021 2022 scenario2 Figure 23 Switchgrass Production (in tons) Comparison between the Single-Outlet and Quasi-Multiple Outlets Scenario 66 120 100 80 60 40 20 0 2013 2014 2015 2016 2017 scenario1 2018 2019 2020 2021 2022 scenario2 Figure 24 Payment Percent (in %) Comparison between the Single-Outlet and Quasi-Multiple Outlets Scenario 400 300 200 Total Farmers: 573 100 0 2013 2014 2015 2016 2017 scenario1 2018 2019 2020 2021 2022 scenario2 Figure 25 Switchgrass Adopters Comparison between the Single-Outlet and QuasiMultiple Outlets Scenario 700 600 500 400 300 200 100 0 scenario 1 scenario 2 Figure 26 Biorefinery NPV (in 1000$) Comparison between the Single-Outlet and Quasi-Multiple Outlets Scenario 67 It could be seen that when a farmers’ cooperative is introduced, there is a substantial increase in lands that are turned into switchgrass use. The incomplete competition brought by the cooperative’s ability to adopt more efficient transportation method (via pelletizing switchgrass) and more efficient information searching of alternative outlets contributes to biorefinery’s less contract hold up amount – If the price paid by the biorefinery is lower than the real price of the alternative outlet, the cooperative will sell switchgrass to that alternative outlet, thus farmers would form a higher switchgrass growing gross margin expectation as well as a lower risk level compared with that in the single-outlet scenario as their perceived contract hold-up amount by the biorefinery is low. We could say that the introduction of farmers’ cooperative is a Pareto Improvement -- This arrangement will not only increase farmers’ profitability and increases the land areas devoted to switchgrass use (thus moves closer to US DOE’s objective), but also increase the long-run profitability of the biorefinery (shown in Figure 26 on biorefinery’s end of simulation NPV) . 5.2.3 Sensitivity Analysis The Sensitivity Analysis for the most artificial parameter – farmers’ switchgrass conversion percent per year, sw (sw=0.1, 0.3 and 1), is tested here. As a number of simulation experiments have been conducted with different transaction cost, only the case with $125/ton contract price and $25/ton transaction cost dealing with alternative market outlet is chosen to do the sensitivity analysis for simplicity. The results of the sensitivity analysis are reported in Table 10 below: 68 Table 10 Sensitivity Analysis on Switchgrass Limit for Quasi-Multi-Outlets Scenario Mid End of Simulation Crop Acres End Simulation Switchgrass Simulation Limit Corn Bio-NPV Switchgrass Switchgrass Wheat Alfalfa (Percent) Soybeans (1000 $) (Acres) (Acres) (Acres) (Acres) (Acres) 0.1 117.479 897 4,103 20,431 6,733 25,050 619.14 3,148 10,372 20,251 6,718 20,115 0.3 1 1536.7 5,918 15,794 19,082 6,294 16,673 The sensitivity analysis result shows that the results for this scenario are quite sensitive to the parameters we choose. However, the upper limit that 100% of croplands could be converted to switchgrass is too high and is unlikely to be the true value for a new energy crop (Hipple & Duffy, 2002). Therefore, choosing a number (0.3) between a quite low value 0.1 and a quite high value 1 is still reasonable. To see whether the chosen values for the switchgrass upper limit parameter will affect the contract choice under different transaction cost, an additional sensitivity analysis is conducted -- the results are all the same under different parameter values, which says that the choice of contract price is not sensitive to that parameter (detailed results not shown as the resulting contract price choices are exactly the same). 5.3 Multiple Easily Accessible Outlets in the Region for Individual Farmers 5.3.1 Parameter Used in the Model The parameters used in this scenario are listed below in Table 11: Table 11 Multiple-Outlets Scenario (Scenario 3) Model Parameters Whose Parameter sw Farmer ( ) ( ) Meaning Switchgrass upper limit Initial perceived payment (hold up) { }) percent probability ( Initial perceived probability of high yield 69 Value 0.3 0.0625,…,0.0625 U(0.3, 0.5) Table 11 (cont’d) High yield of switchgrass Low yield of switchgrass Farmer Payment per ton Refinery ( ) Payment percent under consideration Initial perceived payment (hold up) { }) percent probability ( of its opponent refinery 4.7 4.1 75, 85, 95, 105, 115, 125 0.2,0.25,…,1 0.0625,…, 0.0625 5.3.2 Simulation Result for the Multiple-Outlets Scenario 5.3.2.1 Comparison of Contracts with Different Per-ton Payment In this scenario, we consider two biorefineries procure switchgrass from individual farmers using the same switchgrass procure contract price 28 , guaranteeing multiple (two) relatively easily available switchgrass outlets for individual farmers. One biorefinery is set to be close to most farmers while the other one is set to be relative distant – that is, the difference between the two biorefinery exists in the distance to farmers. Therefore, it could be expected that the closer biorefinery has a much higher procurement amount than the further biorefinery. This difference is made here due to: (1) the two easily available switchgrass outlets needn’t to be all the same in every aspect. The difference between them could make some farmers prefer one while others prefer another; (2) It is relatively easy to report results and choose a satisfactory contract if we set one outlet more preferred than the other; (3) Even though one refinery is farther to farmers than the other, the distance difference is not high, thus still guaranteeing easy access for farmers to both outlets, retaining the competition between two easily accessible market outlets. 28 We consider this assumption to be feasible as when there is direct competition between biorefineries when we assume that no difference exists among farmers’ switchgrass, the final contract price should tend to be the same. 70 Therefore, only the closer biorefinery’s simulation results will be reported in this section. As a first step, different payment schedules are tested to compare potential different contract configuration results using the initial parameters shown above, as what has been done for the first two scenarios. Table 12 Comparison of Different Contract Configuration for Multi-Outlets Scenario Contrac ted Price ($/dry ton) 75 85 95 105 115 125 Mid End of Simulation Crop Acres End Simulation Simulation Corn Bio-NPV Switchgrass Switchgrass Wheat Alfalfa Soybeans (1000 $) (Acres) (Acres) (Acres) (Acres) (Acres) 0 15,634 5,447 32,099 (T=2012) (T=2012) (T=2012) (T=2012) 89.43 4,140 10,591 20,462 6,830 19,259 345.21 10,436 12,849 20,558 6,740 19,018 438.4 10,556 12,379 20,437 6,700 18,712 639.57 12,213 14,892 20,591 6,833 18,944 235.45 10,069 7,766 20,473 6,875 22,070 65.43 10,499 9,688 20,353 6,758 20,442 16000 14000 12000 Total Cropland: 59,577 Acres 10000 8000 6000 4000 2000 0 2013 $75/ton 2014 2015 $85/ton 2016 2017 $95/ton 2018 $105/ton 2019 2020 $115/ton 2021 2022 $125/ton Figure 27 Switchgrass Areas (in Acres) under Different Contract Price in Multiple Outlets Scenario (Main Biorefinery) 71 40000 30000 Capacity: 730,000 tons/year 20000 10000 0 2013 2014 $75/ton 2015 $85/ton 2016 2017 $95/ton 2018 2019 $105/ton 2020 2021 $115/ton 2022 $125/ton Figure 28 Switchgrass Production (in tons) under Different Contract Price in Multiple Outlets Scenario (Main Biorefinery) 500 Total Adopters: 400 300 200 100 0 2013 2014 2015 $75/ton $85/ton 2016 2017 $95/ton 2018 2019 $105/ton 2020 $115/ton 2021 2022 $125/ton Figure 29 Switchgrass Adopters (in numbers) under Different Contract Price in Multiple Outlets Scenario (Main Biorefinery) 120 100 80 60 40 20 0 2013 2014 $75/ton 2015 $85/ton 2016 2017 $95/ton 2018 $105/ton 2019 2020 $115/ton 2021 2022 $125/ton Figure 30 Contract Payment Percent (in %) under Different Contract Price in Multiple Outlets Scenario (Main Biorefinery) 72 The NPV of the main biorefinery increases at first and then decreases after the contracted payment are higher than $105/ton. Several points need to be noticed: First, under the competition of another easily accessible switchgrass outlet for farmers, the biorefinery is less willing to hold up a relatively large amount when the ethanol price is in a reasonable range as it will experience not only future loss, but also current loss of switchgrass land. Second, under almost all feasible and reasonable payment schedule, the switchgrass land devoted to the biorefinery and the refinery’s realized capacity (switchgrass tons procured) are higher when there is competition than when only single outlet exists. This is because farmers’ expected biorefinery payment percent and thus the expected switchgrass growing gross margin is higher when competition exists. This result is consistent with many others’ conclusion that one of the most serious problems for switchgrass adoption is the lack of alternative market for the crop (Hipple & Duffy, 2002; Jensen et al., 2007). 5.3.2.2 Comparing Results of Best Contract Prices under the 3 Scenarios In this section, the results of the three scenarios are going to be compared simultaneously – (1) single outlet: one biorefinery procures from individual farmers; (2) quasi-multiple outlets: biorefinery procures from farmers’ cooperative and (3) multiple outlets: two easily accessible market outlets (biorefineries) procures from individual farmers. In the quasi-multiple scenario, we say that the appearance of a farmers’ cooperative will introduce incomplete competition to the biorefinery as the cooperative has a much higher possibility to find an alternative market outlet as long as it incurs some 73 form of transaction cost. Under this scenario, there are multiple relatively easily available outlet for individual farmers, thus we could provide a brief discussion of how an ideal multiple outlets market could stimulate farmers’ switchgrass adoption and compare how large the gap between this case and the “quasi multiple outlets” cooperative case is. The comparisons are shown in Figure 31 to Figure 35: 16000 14000 12000 Total Cropland: 59,577 tons/year 10000 8000 6000 4000 2000 0 2013 2014 2015 2016 scenario1 2017 2018 scenario2 2019 2020 2021 2022 scenario3 Figure 31 Switchgrass Areas (in Acres) Comparison among All Scenarios 30000 25000 Capacity: 730,000 tons/year 20000 15000 10000 5000 0 2013 2014 2015 2016 scenario1 2017 2018 scenario2 2019 2020 2021 2022 scenario3 Figure 32 Switchgrass Production (in tons) Comparison among All Scenarios 74 500 400 300 Total Farmers: 573 200 100 0 2013 2014 2015 2016 scenario1 2017 2018 scenario2 2019 2020 2021 2022 scenario3 Figure 33 Number of Adopters (in numbers) Comparison among All Scenarios 120 100 80 60 40 20 0 2013 2014 2015 2016 scenario1 2017 2018 scenario2 2019 2020 2021 2022 scenario3 Figure 34 Payment Percent (in %) Comparison among All Scenarios 800 600 400 200 0 scenario 1 scenario 2 scenario 3 Figure 35 End Simulation Biorefinery NPV (in 1000 $) Comparison among All Scenarios It is easy to see that when competition between two easily accessible market outlets exists, switchgrass contracted, adopter number and switchgrass production 75 (biorefinery’s realized production capacity) will be higher than those of the quasimultiple outlet case. The payment percent will be also be higher on average. However, as discussed above, although we make one biorefinery superior than the other in terms of transportation distance, the switchgrass acres, switchgrass production and biorefinery NPV values are in fact for two biorefineries in the multiple outlets scenario 29 . It could be seen that during early years, both switchgrass acres and switchgrass production (tons) in the third scenario (two easily accessible biorefineries) are more than twice of that in the second scenario (cooperative quasi-multiple outlets scenario). However, as time proceeds, the amount of switchgrass produced under the cooperative scenario goes up gradually and the difference between this amount and the third scenario’s amount goes down. As in the cooperative scenario, all realized switchgrass production and biorefinery profit goes to one biorefinery, it becomes more and more efficient overtime than the two biorefinery case from the perspective of switchgrass procurers. However, the fact that switchgrass acre reaches the highest amount in the multiple easily accessible market scenario case shows implicitly that it is still the ideal market condition from the perspective of farmers. 5.3.3 Sensitivity Analysis Sensitivity analysis for farmers’ switchgrass limit is conducted as usual to test whether the parameter value is set to a reasonable level -- the contract price is held constant at $105/ton, while using the value of switchgrass limit by 0.1, 0.3 and 1. The results are shown in Table 13: 29 The condition is that there exists other difference between the two refineries that make both of them preferred by a portion of farmers 76 Table 13 Sensitivity Analysis on Switchgrass Limit for Multiple-Outlets Scenario Mid End of Simulation Crop Acres End Simulation Switchgrass Simulation Limit Corn Bio-NPV Switchgrass Switchgrass Wheat Alfalfa (Percent) Soybeans (million $) (Acres) (Acres) (Acres) (Acres) (Acres) 0.1 78.215 2,529 3,789 20,520 6,729 25,084 639.57 12,213 14,892 20,591 6,833 18,944 0.3 1 986.43 15,037 17,549 19,287 6,242 14,390 The result is a little sensitive to the switchgrass upper limit parameter that we impose. But the difference is not that high (the results are not that sensitive). Following the same logic of the quasi-multiple outlets scenario’s sensitivity analysis, a value of 0.3 for farmers’ switchgrass limit is reasonable. 5.4 Large Scale-Commercial Biorefinery? In the U.S, some small regional trial biorefineries have been set up using government support (e.g. Alpena Biorefinery, UT Biofuel Initiative together with Genera). However, the feasibility of a large scale biorefinery has yet to be scrutinized. For a commercial biorefinery with a capacity of 2,000 tons of switchgrass per day, the per-year capacity is equivalent to 730,000 tons/year. However, if we use a farmer cooperative procurement method (i.e. the most realistic and efficient procurement method shown by the simulation results), the realized capacity is only about 20,000 tons per year at the 10th year. This finding does not indicate that a large-scale biorefinery is not feasible for several reasons. First, we could not expect that switchgrass procured from one single county could satisfy the capacity of one commercial biorefinery. Thus for a large-cale bio refinery, we would expect it to procure from multiple counties. According to our results, if there is one switchgrass cooperative in each county, the biorefinery could contract with 77 36 counties to secure its biomass supply. Second, the county we are studying is in a northern U.S. state where the yield of switchgrass is lower than the in southern U.S. states. If the refinery is set up in a southern U.S. state, a larger portion of the full capacity might be realized. On the other hand, a biorefinery’s contracted switchgrass price might be higher in the South as the opportunity cost of land in those regions are higher due to the high gross margin of traditional crops. Furthermore, in our study area, the most affected crop is alfalfa. In southern states, the crops that are most affected would be food related crops such as corn, soybean and wheat (Larson, English & Lamber, 2007) and decision makers would be faced with the food vs. fuel problem. Third, advanced pelletizing techniques could save significant transportation costs and therefore the extent the collecting area for biorefineries. Thus one collecting depot could collect switchgrass from multiple counties. This is consistent with the regional bio-feedstock processing center concept proposed by Carolan, Joshi & Dale (2007). Another way to save transportation costs is to use water transportation. Since Michigan is surrounded by a number of Great Lakes, future studies should examine the feasibility of this transportation method. 78 CHAPTER 6: CONCLUSIONS, IMPLICATIONS AND LIMITATIONS 6.1 Major Findings In this thesis, I study farmers’ adoption of energy crop production by examining the extent to which farmers will convert land to switchgrass production under different market scenarios. Specifically, three market scenarios are considered: 1) the single outlet case, 2) the “quasi-multiple outlet” case via the introduction of a farmer cooperative, and 3) the multiple outlet case. There are several major findings from this study. First, compared to studies that consider switchgrass uncertainty that comes mainly from yield uncertainty (Zhou, 2013), or from both yield uncertainty and price uncertainty from ethanol markets (Song, Zhao & Swinton, 2011), we also take into consideration uncertainty related to the contract holdup problem. This problem exists due to the fact that a mature market for switchgrass does not exist and thus there is an ex ante probability that the biorefinery will attempt to extract quasi rents for farmers once a production contract is signed and investments are made into relationship specific assets. We found that accepted switchgrass contract prices range from $85/ton to $125/ton under the three scenarios. These prices are higher than the $77/ton optimal switchgrass price calculated by Zhou, (2013). The difference in prices is primarily due to the farmers’ perceived uncertainty related to the potential for contractual hold-up. The second major finding is that, holding other factors constant, the cooperative procurement method (scenario 2) is the most efficient method to procure switchgrass. After several simulated years, the amount of switchgrass procured under this method approached that of the multiple market outlets scenario (scenario 3, which is a nearly 79 ideal case). In the scenario where one biorefinery procures from a farmers’ cooperative, the profitability of the biorefinery depends heavily on the transaction costs related to discovering alternative market outlets. At a transaction cost of around $25/ton, the biorefinery’s profit peaks. Therefore, the biorefinery might want to cooperate with other industries to foster an alternative market outlet for farmers. However, the industries the biorefinery is going to coordinate with should be located somewhere far away from the procurement region. This will keep the transaction cost for farmers’ cooperative to find out the alternative market outlets in a reasonable range to guarantee the biorefinery itself a high profit. Third, under all three scenarios, the amount of switchgrass available might not be enough to satisfy the biorefinery’s capacity even when efficient procurement organization is used. A maximum of 5%, 16.8% and 25% of total cropland is converted into switchgrass under scenarios 1, 2 and 3, respectively. This land conversion rate is consistent with many other studies of land use change to energy crops (See Table 14). Table 14 Comparison of Energy Crop Land Conversion in Different Studies Study Energy Crop Focusing Point This Study Switchgrass Contract Hold Up Switchgrass Farmer Interview Switchgrass Dynamic Optimization of Payoff Uncertainty 30% Bocqueho & Jacquet (2010) Switchgrass Miscanthus Risk Preference and Liquidity Constraint 20% to 40% under most price volatility and loan scenario Shastri et al., (2011) Miscanthus Bidding 60% in the end Hipple & Duffy (2002) Song, Zhao & Swinton (2011) Land Conversion Rate 5%, 17% and 25% under different market scenarios 10% at first and increase slowly overtime Although existing studies use different methodologies, most of these studies come to a conclusion that the conversion rate from traditional cropland to energy crop use will 80 be around 10% to 30%. This study examines the conversion of land to energy crop production from a perspective that focuses primarily on potential contract hold up problem and its effect on the perceived risk face with respect to the adoption of switchgrass. The results of this study are consistent with previous studies. 6.2 Study Limitations This study represents an initial attempt to model the contract hold-up problem using an agent-based approach. While the results are encouraging, future work is needed to address the following study limitations: 1. The crop yield data used in this study is not precise. This study uses a relatively crude method to assign crop yields using only crop type and soil productivity index. Though the method is warranted in this case as the major focus point is modeling hold-up problem, results could be more convincing if more realistic crop yield simulation techniques are used. 2. Although switchgrass adoption is a long-term investment decision, this study is limited to short-term decisions. Due to the computational difficulty of dynamic game modeling under highly heterogeneous environments, long-term decision making techniques are not adopted. Instead, each agent is only allowed to look forward for one period on the other player’s potential strategy. Future research should think about how to extend the planning periods of both farmers and biorefineries. 3. The levels of heterogeneity included in this model needs to be added. For example, the model assumes that all farms 1) enter the same contracts, 2) have the same hold-up rates, 3) learning using the same methods, 4) are located the 81 same distance from the biorefinery, and 5) have the same objective functions (i.e. profit maximizing). Future studies should relax these assumptions and this will be discussed in more detail in section 6.4. 6.3 Contributions This thesis makes several significant conceptual and methodological contributions to the agricultural land use and bioeconomy literature and offers important insights for bioeconomy decision makers. With regards to the conceptual framework adopted and the findings presented, this study offers the following contributions and implications: 1) To the researcher’s knowledge, this is the first attempt to emphasize the contract hold-up problem in an agent-based land use model. The results of the study show that farmers’ perceived contract hold-up risk should not be ignored when considering contract farming. However, it is a particularly important issue when considering the use contracts to coordinate nascent industries where there may be few alternative markets for production or uses for invested capital (e.g. specific equipment); 2) The form of institutional arrangements greatly influence farmers’ perceived risk level and thus influence their willingness to convert land into new energy crops and consequently affect biorefinery’s profitability; 3) In some cases, it is mutually beneficial for transacting parties if the party with less bargaining power gains some bargaining power (e.g. the cooperative could find out another outlet with transaction cost, exhibiting higher bargaining power than individual farmers) as it could decrease the perceived risk of trading with its partner; 82 4) As most pilot biorefineries in the U.S. are now using the most inefficient method (i.e. one biorefinery signs contracts with individual farmers) to procure energy crops, new procurement methods should be initiated (e.g. helping farmers form a cooperative) to meet the renewable fuel standard. Methodologically, the main contributions of this thesis are twofold: 1) While most literature on agent based agricultural land use models omit the risk level of farming, this study embeds a MOTAD (Minimization of Total Absolute Deviation) risk programming method that includes the farmers’ perceived risk level in their farm planning optimization model in the agent based model. This method could be easily generalized into other agent based models as the linearization of a quadratic programming method is easy to implement and makes the model run much faster than a quadratic optimization problem; and 2) This study also provides the first quantitative realization of the contract holdup framework proposed by the seminal work of Klein (1996) in a simulation model and shows that this framework could be applied to certain empirical applications. 6.4 Directions for Future Research Using the framework presented in the thesis, there are several future research directions that could be conducted to extend this study. As shown in the empirical literature (Fewell, 2012; Bergtold et al., 2014), heterogeneity among farmers contributes to farmers’ having different attitudes towards energy crops. Future research may want to examine how this heterogeneity influences farmer decision making. Furthermore, future 83 research may not only look at aggregate land use patterns, but also study emergent patterns at a disaggregated level. For example, future studies may address the following questions: 1. Is there a difference between the switchgrass adoption rates of large farms and small farms? In particular, future models could capture important heterogeneity at the farm level, including differences in: contract selection, contract hold-up rates, learning methods (i.e. social learning vs. learning from experience), and objective functions (e.g. profit-maximizing vs. satisficing behavior) 2. Is there a difference in adoption rates between farmers located close to the biorefinery and those who are far away from the refinery? 3. If we set a absolute lower limit which requires that if the farm size is less than a certain acres 30 , farms will not consider switchgrass, how the land use patterns change? These questions address the distinctive feature of agent based modeling compared with other modeling frameworks, namely heterogeneity and the high degree of interaction among agents. Future research may also include additional procurement scenarios. For example, future research may model the farmers’ switchgrass adoption decision where there is no risk of contractual hold-up. This scenario is similar to that of the production of corn ethanol where there is a mature spot market (i.e. alternative market) for corn. By comparing the results of that scenario with the current scenarios, we could get an 30 This is possible because farmers as well as biorefinery will have to consider the economics of scale according to Hayden (2014). 84 estimation of the amount of social welfare change due to the lack of a mature switchgrass spot market. 85 APPENDICES 86 APPENDIX A. Projected Crop Input Cost Table 15 Projected Input Cost during Pre-simulation and Simulation Period Corn Soybeans Fuel seed seed $/acre $/acre $/acre 1998 1.87797 41.4435 20.91185 1999 1.83191 37.6409 18.99317 2000 2.14484 48.5526 24.49904 2001 2.04578 47.1255 23.77893 2002 1.91771 45.6984 23.05882 2003 2.09465 46.2712 23.34789 2004 2.13458 42.8441 21.6186 2005 2.73552 51.4170 25.94437 2006 2.99545 54.9898 27.74719 2007 3.16439 72.5627 36.61424 2008 4.22532 81.1356 40.94 2009 2.44426 115.708 58.38503 2010 3.17719 105.281 53.12363 2011 4.08413 100.854 50.88977 2012 4.20206 103.427 52.188 2013 2.92116 84.5012 42.63908 2014 4.75532 81.6408 41.19567 2015 5.23753 85.5206 43.15334 2016 5.95860 119.066 60.08033 2017 4.21154 93.2801 47.06872 2018 6.39189 97.1599 49.02637 2019 4.50704 119.987 60.545 2020 6.82519 151.16 76.27448 2021 5.38770 152.307 76.85326 2022 5.72974 179.408 90.52858 Source: Data from 1998 to 2012 comes projected by the author. Years Input Price Wheat seed N P K $/acre $/lb $/lb $/lb 9.125164 0.149609 0.192546 0.143196 8.287925 0.136635 0.189143 0.141583 10.69049 0.145161 0.17374 0.13597 10.37626 0.181687 0.170837 0.134357 10.06203 0.133713 0.158933 0.127243 10.18817 0.165239 0.16553 0.12363 9.43357 0.169265 0.172627 0.127517 11.32118 0.193791 0.184724 0.155404 12.10786 0.205318 0.192821 0.165291 15.97712 0.247344 0.235418 0.164678 17.86472 0.29337 0.422015 0.301065 25.4771 0.256896 0.337112 0.442952 23.18122 0.234422 0.266709 0.267839 22.20644 0.269948 0.325306 0.308726 22.77294 0.280474 0.336903 0.327613 18.60508 0.230505 0.268459 0.233251 17.97531 0.299172 0.288207 0.244997 18.82957 0.326334 0.294397 0.256743 26.21557 0.390152 0.485734 0.390914 20.5381 0.308076 0.383691 0.379093 21.39235 0.38206 0.424979 0.291981 26.41848 0.354178 0.435799 0.33893 33.28199 0.443609 0.622995 0.466636 33.5346 0.348889 0.401017 0.442652 39.50183 0.392669 0.450216 0.458541 from USDA ERS, while data after 2013 are 87 APPENDIX B. Crop Budgets Used in the Thesis Table 16 Input needed For Corn, Soybeans and Winter Wheat Input Corn Wheat Soybeans Variables whose price changes during simulation Nitrogen (lbs) 100 90 0 Phos (lbs) 50 50 60 Potash (lbs) 65 30 90 Fuel & Lube 6 4 5 Drying (tons) 23 20 23 Marketing (tons) 4.5 3 2.63 Trucking 1 1 1 Variables whose price are constant during simulation Herbicide ($) 34 5 21 Insects($) 0 20 20 Crop Insurance ($) 0 15 17 Repair($) 29 20.3 20.3 Supplies($) 7.71 7.71 7.71 Utilities($) 27 4.5 4.5 Labor($) 37.8 29.4 26.6 Note: For variables whose price are assumed to be changing during simulation, as the price changes, we list the input amount needed for one acre of the crop; However, for variables whose price are assumed to be constant during simulation, we just list the input cost needed for one acre of crop. Source: MSU Extension. Table 17 Input Amount Needed for Switchgrass Input Year1 Variables whose price changes during simulation Nitrogen (lbs) 0 Phos (lbs) 3.15 Potash (lbs) 13.25 Fuel & Lube Trucking 0 Variables whose price are constant during simulation Insects($) 27.48 Machine($) 118 Source: Kells & Swinton (2014) 88 Year2 Year3 and after 60 3.15 13.25 60 3.15 13.25 4 4 13.74 111 0 111 Table 18 Input Amount Needed for Alfalfa (From Second Year) Input Alfalfa Variables whose price changes during simulation Nitrogen (lbs) 0 Phos (lbs) 60 Potash (lbs) 235 Fuel & Lube 7 Trucking 4 Variables whose price are constant during simulation Herbicide ($) 0 Insects($) 6 Repair($) 21.25 Supplies($) 5.1 Utilities($) 7 Labor($) 5.5 Note: The difference between first year and the subsequent years only exists in seeding activity. Source: MSU Extension. 89 BIBLIOGRAPHY 90 BIBLIOGRAPHY Alexander, C., Ivanic, R., Rosch, S., Tyner, W., Wu, S. Y., & Yoder, J. R. (2012). 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