THE POTENTIAL AND COST OF CARBON SEQUESTRATION IN AGRICULTURAL SOIL; EMPIRICAL STUDY OF DYNAMIC MODEL IN THE MIDWESTERN U.S.

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1 THE POTENTIAL AND COST OF CARBON SEQUESTRATION IN AGRICULTURAL SOIL; EMPIRICAL STUDY OF DYNAMIC MODEL IN THE MIDWESTERN U.S. DISSERTATION Preented in Partial Fulfillment of the Requirement for the Degree Doctor of Philoophy in the Graduate School of The Ohio State Univerity By Suk-Won Choi, M.A. ***** The Ohio State Univerity 24 Diertation Committee: Approved by Aociate Profeor Brent Sohngen, Advier Advier Profeor Alan Randall Graduate program in Agricultural, Environmental, Profeor Lynn Forter and Development Economic

2 ABSTRACT Thi tudy invetigate the cot and potential of carbon equetration in agricultural oil in the Midwet U.S. Previou economic tudie ignored everal important feature uch a the range of reidue management intenity level, dynamic oil carbon propertie, cyclical pattern of crop rotation, alternative on the baeline cenario, and patial pattern of carbon gain. Developing the empirical dynamic model that maximize the net preent value of market welfare on corn and oybean, two different carbon program are applied: carbon renting program and fixed payment per hectare with minimum reidue management intenity. Several empirical etimation are employed to obtain parameter for the dynamic model, in particular, reidue management impact on crop yield and carbon dynamic are etimated. The crop yield lo by conervation practice i greater in high quality oil than the low quality cla. Senitivity analyi on different baeline cenario ugget that carbon equetration path could be altered by different aumption. It ugget that the etimate of the carbon gain from any carbon policy would be enitively affected by how baeline cenario i aumed. In general, the adoption rate of conervation practice i higher in oybean and low quality oil clae than in corn and high quality oil clae. ii

3 Carbon renting analyi how that corn price could rie and oybean price could decreae, but the magnitude i not immene. Overall, the average cot of carbon equetration i the lowet with carbon renting policy and the highet with fixed payment per hectare with low minimum reidue management requirement. The average cot rage from $.6 to $4.5 per ton with carbon renting cenario. With fixed payment cenario, the average cot rie to $4-$613 per ton with 35 % minimum reidue management and $18-$34 per ton with 75% minimum reidue management requirement. The area with high yield potential doe not necearily provide the carbon gain becaue the reidue management intenity i minimal at 35 %. The ource of carbon gain in the tudy region i from the middle quality oil cla. However, low quality oil cla doe not provide carbon either becaue conervation practice adoption rate wa already high in the baeline cenario and alo the total potential for the carbon gain i mall. iii

4 To my parent and wife iv

5 ACKNOWLEDGMENTS Thi work would not have been poible at all without countle help and upport from many people. Firt, I would like to expre heartfelt gratitude to my advior Dr. Brent Sohngen for hi relentle proviion of intellectual guidance and financial upport for thi tudy. Along with him, my committee member, Dr. Alan Randall and Dr. Lynn Forter helped me improve my thei with economic inight and inpiration. Second, I would like to thank my parent who make my entire puruit of degree poible. They provide everlating upport throughout the long period of graduate program. Lat, and not the leat, I would like give my appreciation to my wife Garam who ha been all the time with me and my twin boy for her encouragement and upport. v

6 VITA Nov. 13, 1968 Born - Seoul, Republic of Korea B.S. Agricultural Economic, Korea Univerity M.A. Economic, The Ohio State Univerity preent...graduate Reearch Aociate, The Ohio State Univerity FIELDS OF STUDY Major Field: Agricultural, Environmental, and development Economic Minor Field: Environmental & reource economic, Econometric vi

7 TABLE OF CONTENTS Page ABSTRACT... ii DEDICATION... iv ACKNOWLEDGMENTS... v VITA... vi TABLE OF CONTENTS... vii LIST OF TABLES... x LIST OF FIGURES... xii CHAPTERS: 1. INTRODUCTION Background Objective Literature review Organization DYNAMIC CROP CHOICE MODEL Baeline Carbon cenario Carbon rental payment Per hectare payment with minimum tillage DATA AND PARAMETERS Land ditribution Crop yield and economic data Etimation of yield impact of reidue management Cot and reidue management Yield function and parameter Crop price and elaticitie Soil carbon data vii

8 3.3.1 Etimate of initial carbon Carbon Dynamic Empirical Carbon Dynamic Land ue projection Model and data Etimation reult Projection of land ue BASELINE AND SENSITIVITY ANALYSIS Total crop choice Total conervation land ue Crop price Reidue management intenity Total carbon equetration CARBON POLICY RESULTS Carbon policie with the baeline Carbon renting policy Fixed payment per hectare Cot of carbon equetration Carbon policy when total cropland change Land ue projection by carbon policy Reult of model with cropland change CONCLUSIONS Summary Implication Limitation and future development BIBLIOGRAPHY viii

9 LIST OF TABLES Table Page 2.1 Definition of model variable and function Land ditribution in the tudy region ( hectare) Variable in crop yield etimation Etimation reult of crop yield function Marginal impact of reidue management on yield by land quality Parameter for the crop yield function Initial carbon tored in the tudy region for upper 3cm oil depth Average clay content in 3cm oil depth Definition of variable for area bae model Etimation reult of three model Land ue projection ( hectare) Average tillage intenity under different cenario Average tillage intenity with carbon renting policy Cot of carbon (Carbon renting policy) Cot of carbon (Fixed payment with 35 % minimum till)...15 x

10 5.4 Cot of carbon (Fixed payment with 75 % minimum till) Total Cropland change (ha) Average tillage intenity of carbon renting policy when total cropland change Cot of carbon (Carbon renting policy when total cropland change) xi

11 LIST OF FIGURES Figure Page 3.1 Aggregated oil and yield type Carbon dynamic example (ton/ha) Denity and ditance to large citie. Reordering data from the nearet ditance to large city. (1997 data) Denity and crop to foretland ratio. Reordering data from the highet denity. (1997 data) Total crop choice Total conervation crop Crop price Total carbon equetration (million ton of carbon) Total crop choice with carbon renting policy Total conervation crop with carbon renting policy Crop price with carbon renting policy Total cumulative carbon gain above the baeline with carbon renting policy Total crop choice with per hectare payment Total crop choice with per hectare payment (75% minimum tillage) Total conervation crop land with per hectare payment (35% minimum)...97 xii

12 5.8 Total conervation crop land with per hectare payment (75% minimum tillage) Total cumulative carbon gain above the baeline (35% minimum till) Total cumulative carbon gain above the baeline (75% minimum till) Cumulative carbon gain in 244 (carbon renting with $4 per ton) Cumulative carbon gain in 244 ($2 per hectare with 35 % minimum tillage) Cumulative carbon gain in 244 ($2 per hectare with 75 % minimum tillage) Cropland change with $4 per ton of carbon price The comparion of total conervation land Total carbon gain by carbon renting policy when total cropland change xiii

13 CHAPTER 1 INTRODUCTION 1.1 Background In recent year, there ha been growing concern about the potential advere impact of climate change. In repone, the global community i conidering action to mitigate the accumulation of green houe gae (GHG) in the atmophere. After erie of conference among countrie, the firt agreement (Kyoto Protocol) wa made in 1997 a mandatory et of rule targeting reduction of GHG emiion for participating countrie. The Kyoto Protocol provided the guidance of alternative for the mitigation commitment and mot countrie in the agreement tarted conidering GHG reduction a a major policy project. Among thee GHG, carbon i the major target component for the effort of mitigation becaue of it tractability and major impact (IPCC, 1996). To mitigate the accumulation of carbon in the atmophere, everal different alternative have been encouraged, uch a directly reducing carbon emiion and toring carbon in "ink," uch a foret and foret and agricultural oil. Among thee alternative, the potential for carbon to be equetered in agricultural oil ha recently 1

14 gained coniderable attention becaue carbon in the oil pool could be an attractive mitigation alternative. For example, etimate by Lal et al. (1995) ugget that the total oil carbon pool contain 3.5 % of the earth carbon tock, compared with 1.7 % in the atmophere (Lal et al, 1995). It i alo etimated that US cropland could equeter up to million ton of carbon per year which i up to 8 % of carbon emiion in the U.S. (Lal et al, 1998). Carbon in agriculture oil can be retored through alternative management than currently occur on large area of cropland. One of the main potential method for increaing the tock of carbon in oil involve encouraging the adoption of conervation tillage. Conervation tillage ytem ue crop reidue to erve a mulch to protect and increae oil organic carbon level. Conventional tillage, on the other hand, diturb the oil and lead to oxidation and ubequent lo of oil carbon and leave it to wind and rainfall, reulting in decreae in oil organic carbon level (Lal et al., 1998). To date, everal tudie have examined the potential and the cot of carbon equetration in agricultural oil in the United State (McCarl & Schneider, 21; Antle et al., 23; Pautch et al., 21;Feng et al., 22; Lewandrowki et al., 24). The tudie to date ue a wide variety of method and many of them focu on particular region. McCarl and Schneider (21), for example, ue a mathematical programming model for the entire U.S. agricultural ector. Antle et al (21) integrate a bio-phyical proce model and econometric imulation model for the Northern Plain region. Pautch et al (21) etimate the probability of tillage adoption in Iowa, and link thee reult to a phyical proce model. The etimate of oil carbon equetration cot from the tudie 2

15 range from $2 to $6 per ton of carbon. Thee tudie provide important inight on the cot of carbon equetration, but to date, everal important intertemporal apect have been ignored. Thi tudy addree everal miing component in earlier analyi. Firt, oil accumulate carbon lowly, and different level of reidue management could lead to the different rate of accumulation and different teady-tate level in the future (Lal et al., 2). Thi could have important implication for carbon equetration becaue different type of oil in different region could lead to a wide range of oberved reidue level. Mot tudie to date have compared conventional tillage ytem to no-till ytem, or they have ued fixed rental payment per acre to pur converion of land to no-till, and thu have ignored the effect of the intenity of reidue management on the cot of carbon equetration. In practice, farmer are oberved to undertake a wide range of reidue intenity level, and it i important to account for thee difference when etimating cot. There could be efficiency gain aociated with deigning policie that match payment more cloely to the intenity of carbon tored on a ite, however. Thi may be particularly important becaue landowner are oberved to chooe a range of reidue level, depending on their equipment, rotation, and other factor. Second, there i evidence that even mall reduction in reidue on a ite could lead to intantaneou emiion of much of the tored carbon into the atmophere by plowing the land (Pierce et al, 1994; Reicoky et al, 1995; Reicoky, 1997; Gilley & Doran, 1997; Hanmeyer et al, 1998; Reicoky et al., 22; Lal, 22). Data from the USDA Natural Reource Inventory (NRI, 21) ugget that ince 1982, farmer have 3

16 hifted into and out of conervation tillage frequently. Further, evidence from eatern Corn Belt tate, uch a Ohio, Indiana, and Illinoi, ugget that farmer typically ue conervation tillage with oybean but not with corn (CTIC, 22). Thu, many typical rotation ued in eatern Corn Belt tate would lead to cycle of carbon accumulation followed by intantaneou emiion when the land i plowed. When deigning policie for carbon equetration, it i thu important to account for crop rotation and potential cycle in equetered carbon that could occur. Further, given the potentially important link between carbon payment, conervation tillage, and crop rotation, payment could alter the proportion of land in different type of crop, and ultimately price. Several exiting tudie ignore thee price effect, potentially leading to biaed etimate of the cot of carbon equetration. Third, given the untable property of carbon in oil and the poibility of cyclical pattern in oil carbon accumulation, it i important to reflect the oil carbon equetration pattern likely to occur in the baeline carbon torage path in agriculture oil before etimating potential gain. The key iue that arie under the Kyoto Protocol i the baeline-how much carbon are we likely to get from oil management in the abence of carbon policy. However, none of the tudie o far take account of cyclical oil carbon equetration pattern in their baeline. In addition, given the fact that carbon potential could be affected by baeline cenario, none of the tudie examine how the total carbon equetration would be enitive with repect to different aumption on the baeline cenario. Several tudie account for baeline equetration, but they do not account for the dynamic of oil torage. Moreover, a addreed in previou tudie (McCarl & 4

17 Schneider, 2; Marland et al., 21; Feng et al., 22), it i critical to deign carbon policy which could ecure the equetered carbon in the oil. Therefore, proper baeline etimate could provide more accurate carbon policy evaluation. Latly, none of tudie o far ha invetigated oil carbon potential in the eatern Midwet Corn Belt region which i the highly productive area. Previou tudie have invetigated different cale uch a regional and U.S. level. Depending on the cope of tudy, there could be different achievement from each tudy. National cale tudy uch a McCarl & Schneider (2) could examine the entire agricultural ector and undertand the overall market impact and feedback of price for the entire U.S. However, given the highly heterogeneou property in oil, there could be aggregation bia and incorrect reult (Antle & Mooney, 1999; Eaterling, 1997; Swallow et al., 1994). Regional tudie (Antle et al., 23; Pautch et al., 21) could utilize more detailed information and derive more efficient policy implication but thee tudie have not provided important price impact. Thi tudy examine the regional cope that could provide more detailed reult uch a county level and derive the price impact. The regional analyi a in thi tudy i alo appropriate to the Climate Change Action Plan (EPA, 1998) that ugget tate identify, develop, and eventually implement mitigation plan for effective policy. 5

18 1.2 Objective In order to tackle the iue dicued previou ection, thi tudy will be broken into three major objective. The firt objective of thi tudy i to develop an empirical dynamic imulation model that examine optimal olution for crop choice and reidue management intenity in row crop agriculture production activitie. To accomplih thi objective, I develop a theoretical model of crop choice and reidue management intenity over corn and oybean. The theoretical model i a dynamic optimization problem that maximize the net preent value of market welfare from thee crop. The model invetigate the optimal olution for the rotation between corn and oybean, reidue management intenity. Thi tudy focue on three Midwetern U.S. tate, Ohio, Indiana, and Illinoi. Thee tate are located in the Corn Belt. The entire Corn Belt produce more than 75 % of total corn and oybean in the U.S., and thee three tate product approximately 43% (USDA, 24). Thee tate have high productive agriculture land and contribute heavily to the U.S. agriculture. However, ome part in thi region, uch a outhern Ohio and Indiana, corn and oybean production i limited by a number of geographical conideration that reduce the value of land for agricultural production. In order to develop the empirical model, a number of etimation are undertaken to develop parameter for the model. The function or parameter etimated include crop yield function, oil carbon equetration function, reidue management impact on crop yield, and land ue change. Particular emphai i placed upon the model that etimate the influence of reidue management on corn and oybean crop yield. While reidue 6

19 management reduce yield for ome crop, like corn, and potentially raie yield for other, like oybean, it reduce cot for both. The imulation model decribed above account for the reduction in cot when converting to conervation tillage, o it i important to have good etimate of the influence of conervation tillage on crop yield. A regreion model i therefore developed to explore how reidue management affect yield for different type of crop, and how thee impact vary acro land of different quality, a uggeted by Porter et al. (1997). The reult indicate that crop yield are highly enitive to reidue management, and that thi influence the optimal patial trategy for equetering carbon. The econd objective of thi tudy i to apply the theoretical model to imulate the et of different baeline cenario and to compare the crop rotation and carbon torage in the region in the abence of carbon incentive. The model i determinitic, o to account for potential uncertainty in the evolution of important parameter in the model, uch a demand, technology, etc., I develop a enitivity analyi that how how crop choice and carbon equetration may be influenced by alternative baeline aumption. The model i developed with empirical data for the three tate region of interet. The model i olved for a 4 year time period for 16 ub-region, and 3 land productivity type in each ubregion uing GAMS oftware and the MINOS olver. The third objective of thi tudy i to apply carbon policie to the empirical crop choice model in order to examine the cot and potential for carbon equetration in the agriculture oil for the tudy region. I apply two different carbon policie to the model. Carbon policy intrument include carbon rental cenario (Sohngen & Mendelohn, 7

20 23) and fixed per hectare payment cenario with different minimum reidue management requirement (35 % minimum reidue intenity & 75 % minimum reidue intenity). The carbon policy analyi how how crop choice, reidue management intenity, crop price, and total carbon gain may be affected by different carbon policie. The patial pattern of carbon gain along thee carbon program will be examined a well. With the preence of different yield potential over the tudy region, it could provide ueful inight where the carbon gain could occur. Note that there could be everal additional benefit from enhancing oil carbon equetration with conervation tillage, uch a reducing oil eroion, improving water quality by reducing run off from field, improving oil fertility, minimizing nutrient loe, improving nutrient cycling (Lal et al., 1998), and increaing wildlife by providing helter and food (CTIC, 24). While thee benefit are certainly important, they are beyond the focu of thi reearch, and therefore not conidered in thi tudy. 1.3 Literature review Long before the iue of the carbon equetration in oil emerged, oil conervation iue trace back to the era of European colonization, and initial field experiment on oil eroion tarted during 192 (Moldenhauer et al., 1994). Organized comprehenive aement of oil conervation began when Soil Conervation Service, currently Natural Reource Conervation Service (NRCS), wa etablihed in

21 Since the Food Security Act of 1985, there ha been ubtantial progre on the improving conervation proce (Weber & Margheim, 2). A the oil conervation iue drew public attention, there have been numerou tudie examine oil conervation problem (for example, McConnell, 1983; Clarke, 1992; LaFrance, 1992; Goetz, 1997; Hopkin et al, 21). For a brief and non-exhautive review, early tudy by McConnell (1983) invetigate optimal private path of oil eroion with maintaining oil depth in agricultural production. The author ugget that ocial and private eroion rate would be the ame. Clarke (1992) and LaFrance (1992) examine the impact of input and output price on the oil eroion problem. Clarke (1992) argue that crop price or input price change could provide incentive to reduce the oil degradation with increaing oil aving input. LaFrance(1992) how that ubidy on the output price could degrade the oil quality. Alo ubidy on the conervation activitie and taxe on cultivation intenity may reduce the oil tock. Unlike the above tudie with ingle crop analyi, Goetz (1997) explore the optimal oil eroion with multiple crop cae. The author argue that diverification and rotation crop are the teady tate reult when oil lo affect the productivity. Myopic farmer have monoculture and it i not teady tate equilibrium. Recent empirical tudy by Hopkin et al (21) invetigate farmer optimal deciion practice with two different oil degradation characteritic, oil depth profile and oil nutrient. The author ugget that optimal reidue management vary with repect 9

22 to oil type and nutrient depletion i more important factor for the optimal deciion than the oil depth depletion. Factor that affect the conervation adoption behavior have been analyzed by many tudie (Griliche, 1957: Antle & McGuckin, 1993: Wu & Babcock, 1998; Uri, 1999; Fuglie & Kacak, 21). The implementation of conervation tillage depend on ite-pecific factor uch a oil type, topoil depth, and local climatic condition and alo geographic and demographic factor are important for adoption (Uri, 1999). Thee tudie have invetigated many factor uch a relative profit from practice alternative, rik, financial contraint, ize of farm, education of farmer, and ite-pecific oil characteritic. Among other, mot thee tudie confirmed that oil characteritic and profit ignificantly affect the conervation tillage adoption behavior. In economic within recent year, everal tudie invetigate cot of carbon equetration and policy implication in agricultural oil management (Antle et al., 23; Pautch et al., 21; McCarl & Schneider, 21; Feng et al, 22). Pautch et al. (21) invetigate the expected cot of carbon equetration in Iowa. The author firt etimate the probability of adopting conervation tillage practice uing large ample point from NRI data with logit etimation. From the probability of adoption of conervation tillage, it i integrated with other imulation approach uch a EPIC. The author compared two different carbon policy cenario, ingle fixed payment per acre v. dicriminative payment per acre cheme, and with two different type of farmer, newly adopting farmer v. all adopting farmer. From their empirical etimate of average cot of carbon equetration in Iowa, the cenario of dicriminative payment to newly adopting farmer 1

23 reult in le cot than the fixed ubidy cheme. Although carbon payment per ton give the mot efficient policy outcome, there i technical difficulty in meauring carbon in oil or the cot of meauring carbon i extremely high. However, the better undertanding carbon potential would enable to deign more efficient policy from lower bound etimate from per ton payment analyi. For a different regional tudy in the North Plain U.S. (Antle et al., 23), the author compare the cot of carbon equetration for different contract method, per hectare payment and per ton of carbon payment. They alo examine the meaurement cot to implement the per ton payment contract. Econometric etimation wa applied to obtain the production and profit and it i applied to get the dicrete land ue choice by imulation model. The author ugget that contract baed on per hectare payment i five time more cotly than the contract baed on per ton of carbon payment. The meaurement cot of per ton carbon payment i etimated to be at leat maller than the efficiency loe of per hectare payment contract. In general, thee tudie compare two different type of carbon incentive program uch a fixed payment cheme (per hectare) and flexible payment cheme (per ton of carbon). The author argued that previou environmental policy uch a Conervation Reerve Program (CRP) i believed to be inefficient for the carbon policy becaue it doe not conider heterogeneou oil characteritic and cot under the fixed per acre payment ytem. Both tudie utilize detailed ample from the tudy region and they provide tatitically repreentative reult. However, the carbon policy imulation 11

24 are baed on the tatic analyi and it i not clear how the carbon policy would change the production and price of crop. Combining two carbon trategie for carbon program wa conidered in the tudy by McCarl and Schneider (21). In their ectoral analyi for the U.S., everal mitigation trategie uch a afforetation, oil equetration, bio-fuel offet, and livetock management were invetigated at the ame time. The author conidered emiion taxe and equetration ubidie for policy intrument. Although detailed decription of the model i not available from their tudy, they argued that total mitigation potential i enitive to the carbon price and adopting mitigation trategie decreae the total agricultural output and increae the price. It i important to invetigate the potential and cot of carbon equetration when both alternative are included in the carbon program. A theoretical tudy by Feng et al (22) develop a dynamic optimization model to invetigate optimal path of carbon emiion, carbon equetration, and carbon tock. In their tudy, the author ugget that carbon equetration in ink hould be implemented a early a poible to reduce the preure on the emiion abatement. They alo argue that any cyclical pattern of carbon equetration and carbon releae i not optimal. In their tudy, there are three different carbon policy ytem are introduced and derived efficient condition theoretically but the author argue that actual implementation depend on the cot of implementation and other political feaibility. In the field of phyical cience, enormou amount of tudie have invetigated oil carbon repone to change in tillage and crop rotation. The tudy by Wet and Pot 12

25 (22) provide the lengthy ummary and tabulation of 67 long term agricultural experimental tudie, coniting 276 paired treatment from the global databae and yntheize thoe previou etimate of carbon equetration rate. The author ugget, on average, that converting conventional tillage to no till could equeter 57 ± 14 g Cm -2 yr -1. Alo, enhancing rotation complexity could equeter about 2±12g Cm -2 yr -1, excluding continuou corn to corn-oybean rotation. Carbon equetration rate reach to peak in 5 to 1 year after converting to no-till. 1.4 Organization The organization of thi tudy i a following. In the next chapter, the theoretical dynamic optimization model i introduced. The baeline model analyi i firt developed and two different carbon policy cenario, carbon rental and fixed payment per hectare, follow. In chapter 3, data and parameter for the dynamic model are provided. It begin with the decription of the tudy region. In the econd ection, the etimation of reidue management impact on yield and it reult are introduced. In the third ection, carbon information in agriculture oil i preented. In the fourth ection, area bae model i introduced and it etimation reult are provided. From the etimation reult, land ue projection i preented. In chapter 4, the empirical dynamic model reult for the baeline i preented. It include the optimal path of crop price, crop choice, tillage intenity, and crop yield 13

26 level over time. After adopting different aumption on the crop demand, input price, and crop yield growth, the optimal olution for enitivity analyi are provided. In chapter 5, model imulation reult are provided for the two different carbon cenario, carbon rental payment and fixed hectare payment with two different minimum reidue management intenity. The reult of carbon rental policy applied to the land ue change aumption i provided. The lat chapter i the concluion of thi tudy. It ummarize the finding from thi tudy and provide the implication. The limit and future development from thi tudy are dicued. 14

27 CHAPTER 2 DYNAMIC CROP CHOICE MODEL The purpoe of thi chapter i to preent a theoretic dynamic crop choice model. Firt, I develop the model to obtain optimal rule for the crop choice between corn and oybean, reidue intenity under the baeline cenario. Then I expand the model with carbon policy cenario and examine how the optimal olution would be affected by the carbon policy implementation. 2.1 Baeline The dynamic model in thi tudy i imilar to the previou tudie in the economic literature (for example, Goetz, 1997; Alig et al., 1997; Park, 1995; Sohngen et al., 1999). The dynamic imulation model in thi tudy maximize the um of conumer and producer urplu, which i the area difference between demand curve and total cot for the production (Alig et al., 1997). The choice variable for the problem are the land allocation of row crop in corn veru oybean, land allocation between conervation and conventional tillage, fertilizer input, and reidue management intenity for each crop. 15

28 The model account for land tranfer between the two crop and conervation choice. The baeline model invetigate the landowner' problem when there i no carbon policy involved. The cot function involve fertilizer input, reidue management intenity, and cot for the conervation veru conventional land choice for each crop. The objective function and contraint for the baeline are hown in equation (2-1) to (2-2). Max fc, f, Rc, R ST, CT, SV, CV, CH, CB, SH, SB.t. X X X X t ρ { T Q C T Q c c c c D ( Q ( Rc, Y ( a, fc ), X )) S D ( Q ( R, Y ( a, f ), X )) c C( R, R, f, f, X, X )} (2-1) c c ct, i, j, t = X ct, i, j, t 1 STi, j, t 1 + CTi, j, t 1 CH i, j, t 1 + CBi, j, t 1 c c cv, i, j, t = X cv, i, j, t 1 SVi, j, t 1 + CVi, j, t 1 + CH i, j, t 1 CBi, j, t 1 ct, i, j, t = X ct, i, j, t 1 + STi, j, t 1 CTi, j, t 1 SH i, j, t 1 + SBi, j, t 1 cv, i, j, t = X cv, i, j, t 1 + SVi, j, t 1 CVi, j, t 1 + SH i, j, t 1 SBi, j, t 1 c c ST + CH X ct, SV + CB X cv, CT + SH X ct, CV + SB X cv f, f, R, R, ST, CH, SV, CB, CT, SH, CV, SB c c.35 R & R 1 (2-2) c c c The notation t, i, and j denote time, region, and land cla repectively. For the empirical etimate in thi tudy, there are 4 year (t), 3 different region (i), and 3 land clae (j). The equation of motion in the equation (2-2) are for the tock of 16

29 conervation corn land (X c ct), conventional corn land (X c cv), conervation oybean land (X ct), and conventional oybean land (X cv). Each land tock change a hift occur among land uage. The land ue hift involve the converion between corn and oybean on the conervation ue (ST & CT), between conventional corn and oybean (SV & CV), between conervation and conventional corn (CH & CB), and between oybean conervation and conventional (SH & SB). The decription of the function and variable for in model i lited in table 2.1. The firt two term in the objective function (2.1) are the um of area under the demand curve for corn and oybean. The function Q C (. ) and Q S (. ) i the total quantity production of the corn and oybean that depend on the yield function (Y c & Y ), fertilizer input (f C & f), total year continuouly in corn and oybean (a), total land of corn (X C ) and oybean (X S ), and the reidue management intenity (R C &R S ). The lat term C(. ) i the cot function for corn and oybean which i the function of fertilizer input, reidue management intenity, and fixed cot for the land in each crop. Let the notation i and j be uppreed and the equation (2.1) and (2-2) could be expreed a current value Hamiltonian, H = V C + λ 1( ST + CT CH + CB) + λ2( SV + CV + CH CB) + λ 3( ST CT SH + SB) + λ4 ( SV CV + SH SB) V T Q C S T Q ( D ( Q ( R, Y ( a, f ), X )) (2-4) 1 c c c c = D Q ( Rc, Y ( a, fc ), X ))

30 Notation Q C (. ),Q S (. ) Y C (. ),Y S (. ) D C (. ),D S (. ) X C ct,x S ct X C cv,x S cv f * * c,f R * * C, R S ST * CT * SV * CV * CH * CB * SH * SB * C Definition Dicount factor Total quantity of corn and oybean Yield function of corn and oybean Demand function of corn and oybean Total conervation land area of corn and oybean ( ha) Total conventional land area of corn and oybean ( ha) Fertilizer input for corn and oybean Reidue management intenity for corn & oybean Converion from conervation corn to conervation oybean Converion from conervation oybean to conervation corn Converion from conventional corn to conventional oybean Converion from conventional oybean to conventional corn Converion from conervation corn to conventional corn Converion from conventional corn to conervation corn Converion from conervation oybean to conventional oybean Converion from conventional oybean to conervation oybean Cot function t Time (total 4) i Study region (total 3) j Land cla (total 3) a Year counting in continuou corn and oybean Table 2.1 Definition of model variable and function *; Control variable in the model 18

31 V i the value function of the firt two bracket in equation (2-1), which i the um of integral of demand function for corn and oybean. C i the cot function conit of input cot uch a fertilizer, fixed cot for corn and oybean, and reidue management. The variable 1 through 4 are cotate variable. To maximize the problem, following condition hould be atified. Equation in 2-5 indicate the firt order condition for the fertilizer input and reidue management intenity. They are jut the imple marginal rule for the input. V f C = c f c, V f C = f V R C = c R c, V R C = R (2-5) Let the demand and total quantity of each crop a following, D Q c c = P = Y c c ct 1 = a bq 2 X c ct + Y c cv X c c cv ; D ; Q = P = Y c ct 1 = c 2 X ct + Y dq cv X cv Combining crop demand and yield function with the optimal rule in (2-5), the optimal fertilizer and reidue management are: P P c c c Yct fc c Yct Rc C =, P fc C =, P Rc Yct f C = f Yct C = R R (2-6) 19

32 2 The firt two equation indicate the firt order condition for the fertilizer input for crop. Marginal value of additional fertilizer input hould be equated to the marginal cot of fertilizer input. The next two condition how the marginal rule for the reidue intenity. Marginal change of value with repect to reidue input hould be equated to the marginal cot of reidue management. The control variable for land hift are all linear in the equation (2-4), o it will lead to the boundary olution for thee variable. The condition are lited in the equation (2-7) below. < = > < < = < < = < = > < < = < < = < = > < < = < < = < = > < < = < < = & ) & ) & ) & ) λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ λ if Max Max SB SB Max SH Max SH iv if Max Max CV CV Max SV Max SV iii if Max Max CB CB Max CH Max CH ii if Max Max CT CT Max ST Max ST i (2-7) Each control variable for the land ue hift are dependent on the combination of cotate variable. The condition in equation (2-7) indicate that there are pair wie pattern which caue land hift. For an example, the deciion on hifting land between

33 conervation corn and conervation oybean (ST v. CT in 2-7 i) take place with oppoite pattern a the relative value between 1 and 3 change. The crop yield function (decribed in chapter 3) indicate that crop yield decreae the longer land remain in a given crop, i.e. Y/a <, where a i the year that land parcel tay in the ame crop. Thu, the co-tate variable are decreaing over time a the land parcel tay in the ame crop over time. Combining with demand and yield function above, the equation of motion for each cotate variable are expreed a: V i) λ1 rλ1 = X c ct V ii) λ2 rλ2 = c X cv V iii) λ3 rλ3 = X ct V iv) λ4 rλ4 = X C + X cv c ct C + X c cv C + X ct C + X = C cv 1 = C = C 2 3 = C P 4 c P P Y c P c ct e Y Y ( αt ) c cv ct Y e ct e ( αt ) ( βt) e ( βt) (2-8) From the equation (2-8), the path of cotate variable over time decreae a time change. The equation in (2-8) how the cotate variable for the conervation land in corn (i), conventional land in corn (ii), conervation in oybean (iii), and conventional oybean (iv). In conjunction with the relation in equation (2-7), the land hift among crop and conervation practice occur a the cotate variable change, in turn, yield level change. For example, from the equation (2-7, i), the choice on the converion from conervation corn to conervation oybean (ST) and converion from conervation oybean to conervation corn (CT) could be affected by the relation between the cotate 21

34 variable 1 and 3. A can be een from the equation (2-8), the cotate variable for each cropland change by yield impact on the continuou crop year for corn () and oybean (). Depending on the different continuou crop year for each crop and conervation ue, the land ue hift would occur in different manner. The value of cotate variable for the conervation corn ( 1 ) i alo related with the conventional corn ( 2 ) (2-7, ii). It would affect the deciion on the converion from conervation corn to conventional corn (CH) and converion from conventional corn to conervation corn (CB). Other relation for oybean land for both conervation and conventional ue could be compared a the ame manner. 2.2 Carbon cenario Carbon rental payment Thi ection preent a dynamic model that include a carbon policy that pay carbon rental on each ton equetered each year, following Sohngen and Mendelohn (23),. The objective function when augmented with carbon rental payment i hown in equation (2-9): Max fc, f, Rc, R ST, CT, SV, CV, CH, CB, SH, SB t ρ { T Q C T Q c c c c D ( Q ( Rc, Y ( a, f c ), X )) S D ( Q c c ( c ct ct c c ( R, Y ( a, f + R K R, R, X, X ) C( f, f, X, X, R, R )} (2-9) ), X )) K K + g( R t = t 1 c, R ) 22

35 R in the objective function i the carbon rental rate and K i the total carbon tock tored in agriculture oil. There i an additional equation of motion for the total carbon tock which i the function of reidue management intenity and conervation land area in corn and oybean. Applying the demand and yield function from the lat ection to thi problem, the optimal reidue management could be found a following rule, P P c Y c ct Rc Yct R C K K + R + λ5 = Rc Rc Rc C K K + R + λ5 = R R R (2-1) Compare (2-1) with the baeline cae in (2-6), there are two additional term for the carbon rental payment. Invoking the negative impact of the reidue intenity on the crop yield level and the variable cot, the optimal reidue input in (2-1) would be greater than the reidue level in (2-6) if other thing are all equal. Moreover, it indicate that a the carbon rental payment R increae, to make the equality in (2-1), reidue management increae. The optimal rule for the land ue hift a in (2-7) are identical in thi problem. However, the cotate variable with carbon policy would be altered. 23

36 24 R K RK r v e Y P C X C X V r iv X K R e Y P C X C X V r iii e Y P C X C X V r ii X K R e Y P C X C X V r i t ct cv cv ct t ct ct ct t c cv c c cv c cv c ct t c ct c c ct c ct = = = + = = + = = + = = + = 5 5 ) ( ) ( ) ( ) ( ) ) ) ) ) λ λ λ λ λ λ λ λ λ λ β β α α (2-11) Now the cotate variable for the conervation land ue in corn and oybean are different from (2-8) o the relative value between thee variable would occur differently and therefore the rule in (2-7) are affected Per hectare payment with minimum tillage In thi ection, the model include a carbon policy that pay fixed payment per hectare bai if any parcel of land i entered into the conervation uage. The model aume that once the land parcel i enrolled, the enrolled land parcel cannot be revered back to the conventional uage. For the conervation land, there i minimum required reidue intenity level. The model i hown in equation (2-12) below;

37 Max fc, f, Rc, R ST, CT, SV, CV, CH, CB, SH, SB.t. X X X X t ρ { T Q C T Q c c c c D ( Q ( Rc, Y ( a, f c ), X )) + 1 c 1 S D ( Q ( R, Y + CP( X ct + X ct ) C( fc, f, X, X, Rc, R )} c c ct, i, j, t = X ct, i, j, t 1 STi, j, t 1 + CTi, j, t 1 + CBi, j, t 1 c c cv, i, j, t = X cv, i, j, t 1 SVi, j, t 1 + CVi, j, t 1 CBi, j, t 1 ct, i, j, t = X ct, i, j, t 1 + STi, j, t 1 CTi, j, t 1 + SBi, j, t 1 cv, i, j, t = X cv, i, j, t 1 + SVi, j, t 1 CVi, j, t 1 SBi, j, t 1 K K + g( R t = t 1 c, R c ct ) c cv ST X, SV + CB X, CT X, CV + SB X f c ct, f, R, R, ST, SV, CB, CT, CV, SB c c cv ( a, f ), X R R c, R 1 (2-12) )) Now the model ha the term for the fixed payment (CP) on the conervation corn and oybean land parcel (X c ct & X c cv). Note that the equation of motion for the conervation corn and oybean are different from previou model. There are not land hift from conervation to conventional land for both crop. However, the other land ue hift uch a tranfer between corn and oybean are identical a before. Uing the ame demand and yield function from (2-5), the optimal rule for the reidue management intenity could be obtained a following. 25

38 = + = + R K R C R Y P Rc K Rc C Rc Y P ct c ct c λ λ (2-13) Note that the carbon policy pay for the conervation land hectare. Compare the equation in (2-13) with the baeline reult (2-6) and the carbon rental cenario (2-1), the optimal rule for the reidue management intenity with per hectare payment policy give the level between the baeline and carbon rental cenario. ) ) ) ) ) 5 5 ) ( ) ( ) ( ) ( = = + = = + = = + = = + = λ λ λ λ λ λ λ λ λ λ β β α α r v e Y P C X C X V r iv CP e Y P C X C X V r iii e Y P C X C X V r ii CP e Y P C X C X V r i t ct cv cv t ct ct ct t c cv c c cv c cv t c ct c c ct c ct To apply the model for the empirical tudy, variou parameter and data are required. In the next chapter, data for the crop yield, reidue management impact on the yield, and carbon information are preented. Baed on the model in thi ection, the empirical dynamic model will be olved in chapter 4. Carbon policy will be analyzed in chapter 5.

39 CHAPTER 3 DATA AND PARAMETERS Before developing the numerical imulation model, it i ueful to decribe the data neceary to carry out the imulation. Thi chapter begin by decribing the tudy region uing NRI data. Second, an empirical etimation i conducted to etimate the effect of reidue management on crop yield in the tudy region.. Third, functional form for crop yield that incorporate thee reult are decribed, and additional parameter influencing crop yield are provided. Fourth, carbon dynamic with repect to the reidue management are decribed, and an empirical equation built upon everal tudie in the literature are provided. In addition to variou tudie from agronomy, crop cience, and oil cience that are ued to etimate initial carbon level, carbon dynamic, and teady tate of carbon, I develop empirical etimate of the effect of reidue management and oil quality on corn and oybean yield. Latly, an area bae model i etimated to project the future land ue change, in particular, the urbanization and change of cropland. The projection reult will be incorporated into the empirical dynamic model. It i expected that the total available cropland in the future would be different from now and the pattern of urbanization would affect the carbon equetration potential in the tudy region. 27

40 3.1 Land ditribution There are total 282 countie and over 19.5 million hectare of cropland in Ohio, Indiana, and Illinoi. In order to make the model tractable, region with imilar oil type have been accumulated into 16 geographically ditinct region: 5 in Ohio, 5 in Indiana, and 6 in Illinoi (Figure 3.1). The aggregation of countie in the tudy region i baed upon the ditribution of major oil type uing detailed oil information in SOILS5 data that i provided with NRI. In addition to grouping oil type, NRI dataet i ued to further claify oil quality within geographical region. Thu, within each region, cropland i divided into three land clae that have the different potential for crop productivity and carbon equetration. Within the NRI dataet, there are eight (VIII) different land clae. The firt two highet land quality cla (I & II) are aigned to land cla 1 in thi tudy, the next three land clae (III, IV, V) are allocated to the land cla 2, and the remaining land i allocated land cla 3. The land ditribution in each region and oil quality cla are lited in the table 3.1. Thi tudy focue on corn and oybean alone becaue they are the major land ue in the Eatern Corn Belt tudy region in general. Between 2 and 22, the average proportion of total corn and oybean planted land among total planted crop land i 76 % in Ohio, 91 % in Indiana, and 92 % in Illinoi (USDA, 23). 28

41 29 Figure 3.1 Aggregated oil and yield type in the tudy region

42 ( Hectare) Ohio Cla 1 Cla 2 Cla Indiana Cla 1 Cla 2 Cla Illinoi Cla 1 Cla 2 Cla Table 3.1 Land ditribution in the tudy region ( hectare) Cla1; High land quality cla Cla2; Medium land quality cla Cla3; Low land quality cla 3.2 Crop yield and economic data 3

43 The effect of reidue management on crop yield have been invetigated in numerou tudie (for example, Uri, 2; Dick et al., 1997; Stecker et al, 1995; Dick & Van Doren, Jr., 1985; Bone et al, 1977). Thee author ugget a wide range of impact of reidue management on crop yield, depending on crop, location, oil type, and experimental deign. Depite the numerou tudie, the effect of reidue management on the crop yield level differ among the tudie. There are many potential reaon for the wide difference. Firt, many of thee tudie are baed on pecific ite with pecific type of oil. Acro the landcape, however, there are numerou different type of oil, and likely numerou different impact of adoption of conervation tillage. Further, ite pecific tudie often aume pecific type of management, wherea in reality farmer have adopted a wide range of crop management regime. Thu, the finding in many ite pecific tudie uually do not capture the relation between yield and actual land owner behavior, and they are not tatitically repreentative (Antle et al, 21; Segeron & Dixon, 1999). In order to develop tatitically reliable etimate of the effect of conervation tillage on crop yield for the entire region under tudy, I intead develop crop yield etimate baed on everal different data ource, a noted in the next ection. 31

44 3.2.1 Etimation of yield impact of reidue management Following Segeron and Dixon (1999), yield impact of reidue management for corn and oybean are etimated uing annual county level data for the tudy region from 1988 to The etimation in thi ection pecifically explore the impact of reidue management on corn and oybean yield by regreing buhel per acre on the independent variable uch a precipitation, oil phyical characteritic, and tillage adoption rate (See table 3.2 for variable). Lagged dependent variable for corn and oybean yield are alo included (CLAG for corn and SLAG for oybean) to capture poible autocorrelation. Yield data for each crop were obtained from USDA National Agricultural Statitic Service (NASS, 24) data bae for each year. Total precipitation for January, April, July, and October in each year are ued to capture climatic impact on yield. Climatic data i obtained from 1 different climatic diviion in Ohio and it i etimated for each county (MRCC, 22). The K-factor meaure how erodible the oil i. The higher the number for the k-factor, the le productive the land. For the analyi, the average k-factor for each county i ued (NRI, 21). Reidue management i captured by the variable CTIX, STIX, INTC, and INTS variable. Extenive information on reidue management and crop type for each county were available from CTIC (22). The data contain different tillage adoption acre uch a no-till, ridge- till, mulch-till, reduced-till, and conventional till for corn and oybean ince 1988 to The level of reidue that remain on the field varie by tillage practice. Conventional tillage i the practice that leave le than 15 % of reidue, 32

45 reduced tillage i the type that leave between % of reidue, mulch till and ridge till leave between 35 % to 7 % reidue, and no-till i the type that reidue level i more than 7 %. CTIX and STIX variable are calculated a the proportion of weighted average of reidue remain to total harveted land for corn and oybean repectively. The next variable INTC and INTS are interaction variable between k-factor and tillage intenity index which i multiplication of two variable. I further tet out hypothei of reidue manage impact on yield level uing thee interaction variable. It i aumed that reidue management intenity could affect differently on different quality land. Thi interaction variable could provide additional relation of reidue management on yield through different land quality clae. So the coefficient of interaction variable could capture the effect of reidue management under given quality of land, k-factor. The lat variable T i a time trend variable tarting from 1 in 1998 that could capture technical progre and any fundamental change within 1 year. Dependent variable: Corn(Bu/ac) Dependent variable: Soybean(Bu/ac) Variable definition Variable Definition Cont contant Cont Contant CLAG lag of corn yield SLAG lag of oybean yield JANP precipitation in January JANP precipitation in January APRP precipitation in April APRP precipitation in April JULP precipitation in July JULP precipitation in July OCTP precipitation in October OCTP precipitation in October KFACT k-factor KFACT k-factor CTIX Index of reidue management intenity STIX index of reidue management intenity INTC Interaction variable of k-factor and conervation INTC Interaction variable of K-factor and conervation T time trend T time trend Table 3.2 Variable in crop yield etimation 33

46 The etimation reult in Table 3.3 how expected reult overall. Lagged dependent variable on both equation have poitive relation but inignificant reult for oybean equation. Weather variable how reaonable reult that precipitation on growing eaon uch a July ha poitive impact on yield but precipitation on harvet eaon in October ha negative impact. January precipitation in corn equation how ignificant negative impact on yield level that could poibly capture the effect of moiture on eeding eaon in pring. Soil quality variable k-factor how expected relation on both crop yield becaue higher number of k-factor i le productive land. Corn equation(bu/ac) Soybean equation Variable Coefficient t Variable Coefficient t Cont Cont CLAG SLAG JANP JANP APRP APRP JULP JULP OCTP OCTP KFACT KFACT CTIX STIX INTC INTS T T Table 3.3 Etimation reult of crop yield function 34

47 Reidue management variable CTIX and STIX how negative impact on yield level which ha been uggeted by everal tudie (for example, Bone et al, 1977; Dick & Doren, 1985;Stecker et al, 1995). Although thee variable how negative impact of reidue management on yield level, note that the conervation tillage intenity variable are interacted with the oil quality variable KFACT. The marginal effect of a 1 % change in reidue management i therefore etimated a: i expreed a follow dyield dctix = β + γkfact (3-1) where i the coefficient of CTIX and i the coefficient of INTC. To how how crop yield i affected in region with different oil type, the data i ordered from lowet to highet k-factor, and the marginal effect calculated for each obervation uing equation (3-1). Table 3.4 how four different land qualitie by k-factor percentile packet, and the number are average of marginal yield change on both crop. The reult ugget that with different land qualitie reidue management ha different effect on yield. Corn yield i more heavily influenced by additional reidue management in higher land quality. Reidue management doe not heavily affect corn yield on lower quality land. Soybean yield, however, i not affected by reidue management overall. Thee finding are ued in the dynamic model. 35

48 k-factor Corn(Bu/ac) Soybean(Bu/ac) Upper 25% percentile(highet quality) Between 5% and upper 25% Between 5% and lower 25% Lower 25% percentile (Lowet quality) Table 3.4 Marginal impact of reidue management on yield by land quality Cot and reidue management Although higher reidue management input reduce crop yield, farm profitability may till rie becaue no-till management i oberved to reduce input cot for fertilizer, fuel for machine, machinery repair cot, and labor cot. Numerou tudie invetigate how thee input cot change with tillage choice (for example, Line et al., 199; Clement et al., 1995; Sijtma et al., 1998;Yiridoe et al., 2; Katvairo & Cox, 2; Uri, 2). The etimate of input cot with repect to tillage intenity vary depending on the tudy region and crop type. Experimental tudy in Canada (Sijtma et al., 1998) propoe that there are 44-6 % of annual cot aving with minimum tillage in potato-barley-forage rotation and 1-4 % cot aving in barley-oybean rotation compare to conventional tillage. However, another Canadian experimental tudy (Yiridoe et al., 2) of farm level profitability analyi in Ontario region ugget that the average annual variable machinery cot with no-till practice i the highet. 36

49 For the tudy in the Midwet U.S., Line et al (199) provide the budget analyi on the repreentative farm of 15 acre with corn, oybean, and wheat rotation in Ohio. It ugget that the total annual machinery, labor, and herbicide cot on the conventional tillage i about $47 per acre and $33 per acre with no-till practice. For thi tudy, the cot information on corn and oybean i adopted from the recent enterprie budget analyi (Moore, 23). Total variable cot for conventional corn i about $168 per acre and $173 per acre for no-till corn. Baed on thee reult, for thi tudy I aume that total fixed cot for conventional corn i about $177 and $115 per acre for no-till corn. For oybean, however, total variable cot for both conventional and no-till are about $14 per acre. Total fixed cot for conventional oybean i about $16 and $13 for no-till practice Yield function and parameter For the carbon tudy, it i important to examine crop rotation a well a tillage intenity becaue carbon dynamic for different rotation are different along tillage choice (Lal et al, 1998). Crop rotation are recommended for numerou reaon uch a higher yield, preventing pathogen build up, weed and inect control, and for overall lower cot (Beuerlein, 21). Apparently, farmer alo believe in crop rotation, a NRI data ugget that farmer frequently hift their land uage between corn and oybean in thi region. Experimental tudie how that continuou corn yield level are lower than corn yield level when corn i rotated with and oybean (Porter et al., 1997; Stecker et al., 37

50 1995). In Ohio, for example, corn yield are generally higher by 5-15 % when corn i rotated with oybean, rather than planted continuouly (Beuerlein, 21). For the dynamic crop choice model, it i aumed that yield level decline the longer an individual maintain land in a ingle crop type, and that the magnitude of thi reduction in yield depend on the land quality. Thi aumption follow Porter et al (1997), who howed that corn and oybean rotation yield are up to 25 % higher than continuou corn in poor production region and up to 15 % higher in high production region. Incorporating the above aumption, quadratic function of yield repone by fertilizer for corn and oybean were etimated from agronomy and crop cience tudie (Vitoh et al., 22; Munn et al., 1998). The functional form are in equation (3-2). Y C = [( α + α f 1 2 C α 2 3 fc ) e ( α 5a) ] Y S = [( β + β f 1 2 S β 2 3 fs ) e ( β5a) ] C C (α 4Rc) c ct Q = Y e X + Y S S C X c cv (β 4R) S X ct Y X cv (3-2) Q = Y e + The parameter and were etimated uing the 1 year average crop yield (USDA data bae, 22). The contant term 1 and 1 were etimated to reflect different yield potential in different region and land cla. The etimate of parameter 1 and 1 are hown in table 3.5. The yield function curvature i aumed to be the ame for the entire region o the parameter 2, 2, 3, and 3 are the ame. The lat two term capture 38

51 yield effect by reidue management and continuou corn and oybean effect. The magnitude of each effect i different with land cla (table 3.5). The negative ign in 4, 4, 5, and 5 indicate that yield level decline a reidue management (R C & R S ) increae and a a parcel of land continue in corn or oybean production without converion to the other crop type (a). The impact of yield lo by reidue management ( 4, 4 ) are obtained from the etimation reult from the previou ection in Note that the magnitude of yield lo by reidue management for corn i greater than oybean. Moreover, for the middle oil cla (cla 2) i not affected by reidue management and there i poitive impact on the yield in the low oil cla (cla 3). The yield impact by continuou cropping i negative for both crop ( 5 & 5 ). The magnitude i greater in corn than oybean Crop price and elaticitie A introduced in the previou chapter, the model in thi tudy incorporate crop demand o that the price of corn and oybean vary over time a the total output of each crop change. The etimate of own-price elaticity of corn and oybean (Lin et al, 2; Huang & Lin, 2) are applied to treat the demand curve a the total output change. The author provide many ueful etimate of elaticitie uch a own price and cro price elaticitie, but to make the tudy traightforward, the average etimate of own 39

52 price elaticitie are applied. On average, the own price elaticity for corn i about.35 and.43 for oybean in the U.S. Thee price elaticitie are ued to derive demand curve to et up the initial price of corn and oybean, adjuted with total amount of crop production in the year 23. The regional average corn price wa 2.48 dollar per buhel and oybean price wa 7.25 dollar per buhel in 23. The total quantity produced in the tudy region wa about 3 billion buhel of corn and 74 million buhel of oybean in 23. The empirical derived crop demand function are following. c c C = P = 14.3 Q, D * = = 7.94 D P * Q S Thi tudy examine the regional cope in the Midwetern U.S. and the price elaticity etimate above are from the U.S. national level etimate. To apply the U.S. national elaticity etimate to the tudy region, I aume that the price adjutment by quantity change in the tudy region would occur exactly ame manner in other region a the national etimate. So if there i 1 % corn production reduction in the tudy region by carbon policy, there would be the ame policy impact on the corn production (1 % reduction) elewhere in the U.S. and the price impact would be the ame in other region a well. The regional model with in thi tudy could omit certain important feature. There would be different policy impact on the regional production level o the price impact would be different even with the ame price elaticity aumption. Price elaticitie 4

53 would be different region to region and price impact involve more complexity uch a import and export demand. Although regional model overlook ome important feature, thi tudy focue on the element that cannot be invetigated by full-cale model. Thi tudy could examine more detailed information uch a oil propertie, production potential, and carbon dynamic. Parameter 1 Parameter 1 Region Cla1 Cla2 Cla3 Cla1 Cla2 Cla Parameter 2 Parameter 2 All Parameter 3 Parameter 3 All Parameter 4 Parameter 4 All Parameter 5 Parameter 5 All Table 3.5 Parameter for the crop yield function 41

54 3.3 Soil carbon data Etimate of initial carbon To invetigate the carbon equetration potential for the tudy region, initial carbon level in agricultural oil i required. The initial carbon in the tudy region i etimated uing oil information from NRI (USDA, 21). Following the etimation method by Mitchell et al (1998) and Lal (2), the initial carbon in the top 3cm oil depth wa etimated. The equation (3-3) through (3-5) were applied to get the initial etimate of carbon uing NRI oil information AOM n = ( OMLn + OMH n ) 2 (3-3) BM n = [.5( BDLn + BDH n ).6] (3-4) 3 IC = W ( AOM BM [ DU n DL n ]) (3-5) n The equation (3-3) etimate the average of organic matter percent (AOM) and converion factor % for the percent of organic carbon for each layer. OML and OMH are the low and high percent of organic matter for each oil column. Bulk denity average (BM) i etimated a in the equation (3-4) with dry bulk denity converion factor.6 for each layer. BDL and BDH are the low and high range of bulk denity in each oil column. Initial carbon IC (kg m -2 ) i etimated by uing the equation (3-5). The depth of upper and lower column i DU and DL repectively. It i the um of each oil column up 42

55 to 3cm depth from the oil urface. After etimating the initial carbon for each point in NRI ample point, it i etimated for the whole region uing the weight W which i the expanion factor in the NRI data for each ample point. The etimate of initial carbon in each region are hown in table Carbon Dynamic Carbon dynamic in the agricultural oil i affected by many phyical, biological and chemical procee (Lal, 22). Thi tudy focue on the impact of reidue management on organic carbon in the firt 3cm of the oil column. The dynamic of oil organic carbon with repect to reidue management are obtained from variou tudie (Lal et al., 22 & peronal communication, 23; Wet & Pot, 22; Wet & Marland, 22b; Pautian et al., 1997). Among other, Lal (1998) ugget that the gro rate of oil organic carbon equetration i about 4 to 8 kg per hectare per year in cold and humid region. In addition to the rate of oil carbon equetration, there i a linear relationhip between reidue management and carbon equetration (Duiker & Lal, 1999; Pautian et al., 1997). Although enhanced reidue management accumulate organic carbon in oil, the accumulation low a carbon reache a teady tate level. In general, oil cientit ugget that for intenive reidue management practice, uch a no-till (where >9 % reidue remain on the ite) teady tate carbon level are attained in 12 2 year (Dick et al., 1997; Pierce & Fortin, 1997;Vitoh et al, 1997; Wet & Pot, 22). 43

56 (Ton of C / Ha) Ohio Cla 1 Cla 2 Cla Indiana Cla 1 Cla 2 Cla Illinoi Cla 1 Cla 2 Cla Table 3.6 Initial Carbon tored in the tudy region for upper 3cm oil depth. 44

57 The potential carbon equetration through changing reidue management practice range from 5-1 % (Houghton et al., 1997) to 3-5 % (Donigian et al., 1994; Bowman et al., 1999) from the original carbon level. Acknowledging that there are difference in thee etimate, for thi tudy, it i aumed that the maximum attainable carbon i about 3 % above the initial carbon level. Therefore, once there i 3 % gain above the initial level of carbon, there i not additional carbon gain regardle of enhanced reidue management uch a no till. For the purpoe of numerical imulation model, I adopt the aumption that carbon accumulation i linear to reidue management. Different rate of carbon accumulation, however, are applied to the different region and land qualitie explored in thi tudy. Previou tudie ugget that there are poitive relation between carbon accumulation rate and alo oil clay content (Campbell et al, 1996; Bruce & Langdale, 1997). It i uggeted that finer textured oil type can tore carbon fater than coare textured oil type. Thi relation i alo aumed in the CENTURY C model (Parton et al, 1987). According to Campbell et al (1996), there i, 1.6, and 3.9 ton of carbon per hectare gain in the coare-textured, medium-textured, and fine-textured oil repectively after an 11 year period of continuou no till. The poitive relation between the clay content and oil organic matter, which i in turn the relation between clay content and oil organic carbon, i alo upported by Bruce & Langdale (1997). However, Campbell et al (1996) alo find out that carbon gain wa not ignificant in the low productive region regardle of clay content level acro the oil in the low productive area. So it i 45

58 aumed in thi tudy that low productive oil contain le initial carbon and carbon gain compare to high productive oil but there i not variation in carbon gain acro the different region. To reflect the difference in carbon accumulation rate for the different region and land quality, I adopt the etimate reult of Campbell et al (1996). According to the author, there i a linear relationhip between clay content and carbon gain. The carbon gain difference i about.1 ton per 1g/kg clay content. The average clay content in each region and oil quality cla i etimated from NRI oil information SOILS5 (Table 3.7). Calibrating the average clay content, the carbon accumulation rate wa obtained by following rule. C = C + ( R 12 Clay ) / B (3-6) α The equation (3-6) earche for the appropriate parameter to reflect the carbon accumulation aumption in thi tudy. The left hand ide i the maximum carbon level which i aumed 3 % above the initial carbon level. The firt term on the right hand ide C i the initial carbon level. Then apply the clay content to obtain the parameter and B. The reidue level R wa applied 1 indicating 1 % reidue intenity and 12 i the year that i aumed for the conecutive year when the maximum carbon level obtained. 46

59 Average clay (1g/kg) Ohio Cla 1 Cla 2 Cla Indiana Cla 1 Cla 2 Cla Illinoi Cla 1 Cla 2 Cla Table 3.7 Average clay content in 3cm top depth 47

60 Several author ugget that mot carbon in agricultural oil with enhanced reidue management would be lot into the atmophere immediately when the oil i diturbed by plowing (for example, Reicoky et al, 1995; Reicoky, 1997; Lal, 22). However, there are everal different etimate on the amount of carbon lot by plowing after ome period of carbon torage (Pierce et al, 1994; Gilley & Doran, 1997; Reicoky et al., 1995; Wet & Pot, 22; Smith, 24). Although the tudy by Wet and Pot (22) concentrated on the effect of the converion from conventional tillage to no-till, the extenive ummary in their paper ugget that there are variou etimate of carbon lo after plowing. The amount of carbon lo by intenive tillage uch a moldboard plowing i the mot extenive, at more than 4 ton per hectare after 19 day once plowing applied (Reicoky et al, 1995). It i about 134 percent of the carbon in that year crop reidue. From the tudy of the tillage effect on the Conervation Reerve Program (CRP) ite (Gilley & Doran, 1997), there wa more than 8 ton of carbon lo per hectare after nine month of winter fallow condition following tillage on the CRP ite. In thi tudy, it i aumed that the mot of carbon tored by enhanced reidue management would be lot if there i plowing, o the carbon level i aumed to be the initial carbon level. That i to ay, all the carbon tored by reidue management i lot when the parcel of land converted to back to conventional practice. 48

61 3.3.3 Empirical Carbon Dynamic Thi ection decribe how I have taken the empirical reult in the literature and ued them to develop a dynamic model of carbon equetration in agricultural oil. Thi model i ued in the economic model decribed in chapter X of thi thei. Equation 3-7 how the hypotheized carbon accumulation proce. c cv Ct = Ct 1 + β Rt 1 X t 1 + γ X (3-7) t 1 The carbon level at time t depend on the reidue management level R t-1 and the total hectare on the conervation land X c. The parameter i different by region and land cla. The relation between the reidue management and carbon accumulation i linear. The conventional land X cv ha the initial carbon levelγ. Figure 3.2 repreent example of carbon accumulation dynamic. There are three different carbon path in the figure. Vertical axi i carbon per hectare with 35 ton per hectare initial level. Horizontal axi i year up to 3 year. The olid line (Cae 1) repreent the cae when there i continuou not-till for 3 year. Carbon level i increaing from the initial carbon level at 35 ton per hectare until around the year 12 and tay at the contant level 45 ton per hectare, which i about 3 % above the initial carbon level. The flat line with circle marker (Cae 2) how the path when there i continuou conventional till, which i le than 35 % of reidue management. The dotted line (Cae 3) how the path of carbon when the reidue management intenity i ame a the Cae 1 except there i plowing at year 8. The carbon 49

62 increae until year 8 but decreae to the initial carbon level after plowing and increae at the ame rate a previou year and reach to the maximum level at year 22. For carbon accounting, there could be additional carbon gain from conervation tillage becaue there would be le fuel ue for machinery o there could be le carbon emiion into the atmophere. However, there could be more emiion of GHG from conervation tillage compare to conventional way becaue conervation practice involve more herbicide and peticide input (Wet & Marland, 22a). According to the author, the major portion of carbon accounting i in agricultural oil and regardle of carbon effect by reduced fuel uage and more herbicide ue, thee factor are not conidered in thi tudy. 5

63 C(ton/ha) Carbon dynamic example Cae 1 Cae 2 Cae3 Year Cae 1: Continuou no-till (over 95% reidue management) Cae 2: Continuou convention till (le than 35% reidue management) Cae 3: Continuou no-till, plowing at year 9, and continuou no-till Figure 3.2 Carbon dynamic example (ton/ha) 51

64 3.4 Land ue projection Land ue change in the tudy region i etimated following Hardie and Park (1997) and Plantinga et al. (1999). Given the emergence of the literature on patial econometric (ee Anelin, 1988), I tet for the preence of patial autocorrelation in the etimated model. Spatial autocorrelation could be important if, for intance, there i ome unoberved relationhip between the policie in two nearby countie. If thee unoberved factor are related to the error (i.e. they are correlated), then the tandard error for the parameter etimate could be biaed. I thu develop three alternative pecification for the area-bae model of the Midwet, given different aumption about the form of the patial relationhip between county level obervation. Etimate of future land ue area are then developed and compared acro the alternative model Model and data The model etimate the hare of land uage in foret, agriculture, and urban ue in the tudy region. Each hare of land uage i expreed a multinomial logitic function with explanatory variable uch a foret rent, crop rent, urban rent, ditance to the nearet city, population denity, land quality indice, and dummy variable for pecific year (See Table 3.8). 52

65 Variable Definition CONST Contant term FORENT Foret rent DISTANCE Minimum Ditance from major citie to the center of each county DENS Total population divided by total area in each county LCC The ratio of the firt two highet land cla AVLCC Average land cla in each county D82 Dummy variable for 1982 data D87 Dummy variable for 1987 data D97 Dummy variable for 1997 data Crent Crop rent obtained by budget information D1 Dummy for the countie that population denity i upper 2% D2 Dummy for the countie that population denity i between 4%~ 21% D3 Dummy for the countie that population denity i between 6%~41% D4 Dummy for the countie that population denity i between 61%~8% Rho Coefficient for the weight matrix in Spatial model. Table 3.8 Definition of variable 53

66 The functional form of a multinomial logitic function i following P j β j X e = m 1 β j X 1+ j= 1 e, j = 1,,, m 1 (3-8) The left hand ide i the proportion of land allocated to j uage and X i the vector of independent variable and β i the vector of coefficient to be etimated. To have an etimable functional form, thi model can be expreed by log of proportion in different land ue uch a p j ln = βx + u p i, (3-9) m where u i i aumed to be an independently and identically ditributed, normal error term. Becaue the error could diplay heterokedaticity, I adopt White uggetion to correct the covariance matrix (White, 198). In addition to the heterokedaticity that may occur a a reult of the log tranformation in (3-9) or a a reult of the underlying data, one mut carefully conider other problem that could arie with the error in equation (3-9). One problem may be the preence of patial autocorrelation or omitted variable bia. For intance, the error of 54

67 two countie next to each other may be more cloely related than the error of two countie that are further apart. Alternatively, ome unoberved factor that affect the proportion of land ue in different countie could be omitted, but correlated with error u i. The correlation with the error term can bia etimate of the tandard error. With county level data, uch unoberved factor could relate to policy variable that are imilar acro countie, or it could be related to economic growth. For intance, economic growth in one county could raie price in that county, cauing potential new migrant to move to nearby countie where land price are lower (Hieh, 2). Depite the growth of the literature on patial econometric, relatively few tudie have attempted to apply the technique to land-ue change model. For policy purpoe, it would be ueful to know if the technique can help make better prediction of future land ue change. Literature on patial econometric ugget that there could be different pecification for capturing patial proce (Anelin, 1988). The patial correlation could occur on the error term, dependent variable, independent variable, or on both ide. The choice of patial proce in the model relie on the empirical proce and theoretical background (Anelin, 23). The mot commonly ued patial model i autoregreive model that patial correlation occur in the error term. The model in thi tudy in equation (3-8) and (3-9), patial proce could only be tractable in the error a in the equation (3-1) and (3-11). I thu tet patial dependency uing following functional form, Y = Xβ + u (3-1) u = ρ Wu + e (3-11) 55

68 The left hand ide Y in equation (3-1) i the dependent variable a before, X i the et of independent variable, and u i the error term which i patially correlated. In equation (3-11), W i an n-by-n weight matrix (where n i the number of obervation) that define patial dependency among obervation, and e i i.i.d. error term. The coefficient to be etimated are β and ρ. The weight matrix i choen arbitrarily, although there have been many tudie invetigating the optimal choice of weight matrice (Cliff & Ord, 1982; Upton and Fingleton, 1985; Anelin, 1988). After teting a range of alternative, I ue a ditance criteria that allow 8 countie a neighbor. The weight matrix i rowtandardized o that the um of each row in the weight matrix um to 1. An alternative method for capturing patial effect i to utilize a fixed effect etimator, which recognize that certain obervation behave imilarly (Cae, 1992). For example, one might expect that land at the urban rural fringe in the ample would have higher level of opportunity cot than land further from citie. One would then want to treat thee countie differently from rural countie, by uing a fixed effect etimator. With a fixed effect etimator, the error term are pecifically aumed to be correlated with the term in X. I explored a number of alternative fixed effect, but ettled on population denity for thi tudy. Thi make ome ene if countie cloer to citie behave differently from rural countie. I rank each county in the dataet by population denity and then ue dummy variable to repreent the quintile (Table 3.8). Data ued in thi tudy wa obtained from variou ource. County level land-ue hare data i from the NRI databae for 1982, 1987, 1992, and 1997 (total 283 countie). The NRI ample fixed plot on the landcape at five-year interval. Etimate from thee 56

69 ample plot are aggregated to the county level for the model. Land rental value are etimated from other data ource for foret, crop, and urban. Following Plantinga et al. (1999), population denity (DENS) i ued a a proxy for urban land value. It i aumed that higher denity increae development force o in turn increae the opportunity cot of maintaining other land ue. The total area of each county i from NRI data and total population i from the Bureau of Cenu data for the ame period of time (1982, 1987, 1992, and 1997). Foret rent (FORENT) i etimated a the dicounted net preent value of timber revenue per acre. Yield function for each of the major pecie in each county are weighted by the proportion of the pecie in each county, uing USDA Foret Service Foret Inventory and Analyi data. Regional timber price are ued in Ohio and Illinoi (OASS, 1999 and IASS, 1999) although only tate level data i available in Indiana (Hoover, 2). Land rent for foretry are obtained with the Fautmann formula (Johanon and Logfren, 1985), auming interet rate are 5 %. Land i aumed to be naturally regenerated, an aumption I upect i true for mot land that converted from agriculture to foretry in thi region over the time period invetigated. In previou reearch, agricultural rent (CRENT) have been etimated with a number of different approache, uch a farm revenue and cot (Stavin and Jaffe 199, Park and Murray 1994, Hardie and Park 1997), ratio of income from competing land ue (Alig 1986, Alig et al. 1988), price of commoditie from agriculture (Lichtenberg 1989, Wu and Broren 1995), and revenue le cot a calculated from farm budget (Plantinga et al. 1999). In thi tudy, annual revenue above variable cot i ued a the 57

70 etimate of the value of cropland. Crop budget obtained from the Cooperative Extenion Service of the three tate are ued to etimate thee value for four major crop produced in the region: corn, wheat, oybean, and oat. Crop yield for each county i etimated from USDA Agricultural Cenu (USDA 1999). Price information i obtained from USDA data bae ytem (USDA 2). County level etimate of crop rent are then determined by weighting the return for each crop in a county by the number of acre in the crop in the county for each period. I control for land quality with two additional variable LCC and AVLCC. There are eight land capability clae in the NRI data that i aeed by lope, oil texture, oil depth, effect of pat eroion, permeability, water holding capacity, and type of clay mineral. Land in the firt four clae i mot uitable for common field crop, foret tree, and range plant (USDA, 1961). Conequently, LCC i the proportion of land in each county in the firt four clae. AVLCC i average cla (weighted by area) in each county. Note that higher AVLCC implie lower quality land. Ditance form the nearet city (DISTANCE) i alo ued in the model. Similar to the population denity variable, thi variable i expected to capture a component of urban land ue demand, although it i likely to play a different role than population denity. Large citie for Ohio are Columbu, Cleveland, Cincinnati, Dayton, Akron, Toledo, and Pittburgh (ome eatern countie in Ohio are uburb of Pittburgh). For Indiana, citie are Indianapoli, Evanville, Fort Wayne, South Bend, Gary, Chicago, Cincinnati, and Louiville. For Illinoi, citie are Chicago, Springfield, Peoria, Rockford, and St. Loui. I alo include dummy variable for year in mot model etimated below. Thi amount 58

71 to etimating a fixed effect model in the panel of data over 4 period. The fixed effect model account for a number of factor that are unoberved in each county, but which are expected to remain the ame over the time period. Example of thee type of variable might be lake and tream, or large capital invetment like timber mill. A dummy variable i alo ued for the firt, econd and lat year in the analyi (1982 = D82, 1987=D87, and 1997 = D97) Etimation reult The obervation for the four time period are pooled and fixed effect are ued for three of the year. The reult for three alternative model are preented in Table 3.9. The Bae Model doe not correct for patial effect, but it doe correct for the preence of heterokedaticity with White conitent etimator of the variance-covariance matrix (White, 198). The remaining heterokedaticity doe not bia the etimate, but it could underetimate the variance in the model, potentially biaing tet of ignificance (Greene, 1997). The Fixed Effect Model (FE Model) incorporate the fixed effect baed on population denity in each county, and the patial model account for a pecific form of heterokedaticity, namely patial autocorrelation. The etimated coefficient in each of the model generally how expected ign and are ignificant. Higher foret rent reduce the proportion of agricultural land to foretland (A/F equation) and urban land to foretland (U/F equation). Higher crop rent increae the proportion of agriculture to foretland (A/F) and urban to foretland (U/F). A higher 59

72 value for the land quality claification (AVLCC) reduce the proportion of land in agriculture uggeting that lower land quality reduce the proportion of agriculture. Thi follow general expectation. Alternatively, a higher proportion of high quality agricultural land increae the proportion of agricultural to foretry land, and it reduce the proportion of urban to foret land (although it i inignificant in all three model). Ditance to the nearet city reduce the proportion of agricultural and urban land to foretland. The reult for urban land probably reflect the fact that mot population center in thi region are located in agricultural region rather than foreted region. Bae Model Fixed Effect Model Spatial Model Regreion A/F U/F A/F U/F A/F U/F CONST 4.83 ** ** ** 1.52* FORENT -.47 ** ** ** -.9 DISTANCE -.3 ** -.8 ** -.3 ** -.6** -.3* -.8** DENS -.3 **.15 ** -.2*.8** -.3**.15** LCC.918 ** ** -.1 AVLCC ** ** ** -.666** -1.77** -.771** D D ** D97.21 **.174 *.173*.352**.166*.21* CRENT.5 **.3 *.5 **.4*.5**.3* D ** 1.37** - - D ** - - D ** - - D Rho * **: 95% Confidence interval *: 9% Confidence interval Table 3.9 Etimation reult of three model 6

73 Population denity (DENS) how expected ign in the U/F equation, but in the A/F equation, higher population denity reduce the ratio of agricultural land to foretland. Thi ugget that population eem to prefer agricultural land for development purpoe. Similar reult are found in previou tudie (Park & Murray, 1994; Hardie & Park, 1997; Ahn et al., 2). Although thee tudie did not invetigate the iue further in detail, Park and Murray (1994) ugget that the relationhip could be coincidental. One explanation for thi i that foretland i more expenive to develop, o that mot development occur on agricultural land rather than foretland. Another explanation i that mot development in thi region i occurring around citie, which happen to be located in agricultural region. I tet thi hypothei more pecifically below. The dummy variable for population denity in the fixed effect model are ignificant only for the mot populated countie in the A/F equation. Thee reult ugget that the relationhip between agricultural land and foretland i non linear for different level of population denity. Countie with the highet population denity have a ignificantly lower ratio of agricultural to foretland. One explanation i that mot development occur on agricultural land rather than on foretland, perhap due to cot. Alternatively, when population denity grow around citie, it may induce a hift of agricultural land to foretland a farmer move away from the region. Similar explanation wa uggeted by Hardie and Park (1997), but they related the iue with farming life cycle and farmer age. Mot of the dummy variable are ignificant in the U/F equation, 61

74 and they decline toward for lower population denitie. A expected, the ratio of urban to foretland i generally higher for more populated countie. The patial model and the bae model diplay different ignificance level for a number of variable. Thi could reflect correlation between the error term and unoberved or omitted variable in the bae model, or it could jut reflect a nuiance (patial autocorrelation). However, ignificance level change mainly for the two variable reflecting uburbanization. For example, DISTANCE and DENS become inignificant in the A/F equation, uggeting that the reult above howing that population prefer agriculture land relative to foret-land could be over-tated. The remaining reult are remarkably conitent with both the bae model and the fixed effect model. Thee reult provide ome meaure of confidence for hypothei tet about the effect of foret and crop rent on the deciion to hold land in agriculture and foretry. The reult of the patial model upport Park and Murray (1994) who ugget that the relationhip of foretland to uburbanization i coincidental. Suburbanizing trend affect mainly the level of urban to foret and agricultural land, however, the deciion to maintain land to agriculture or foretry depend mainly on land rent (and conequently land quality). To invetigate the urbanization pattern in thi region further, I firt examine the land ue pattern in the tudy area. Figure 3.3 how the relation of denity and ditance to large citie. The data for 1997 i reordered from the nearet countie to the large citie in the origin of x axi to further away countie a move out from the origin. In general, denity decreae a move away from the large citie. However, there are everal peak of 62

75 denity in further away countie. Obviouly, the reaon i that I only conider 14 large citie in thi region and there could be other maller but high denity local citie in thi region. Moreover, thi could be capturing the recent uburbanization pattern. Figure 3.4 how the relation of denity and crop and foretland ratio (A/F). It i reordered by denity o the origin of x axi ha the highet denity. It how that A/F ratio i higher in lower denity countie (a move out from the origin). Thee two relation upport the regreion reult in thi tudy and previou finding in other region that urban area coexit more with foret land than with agricultural land. There could be different aumption for having le agricultural land in high denity area. From the developer point of view, it could be le expenive to build up urban facility on agricultural land becaue of acceibility to build up infratructure or le clean up cot. Rental value of houing after built up alo could affect developer. Where houing would be located could affect the houing value i.e. open pace veru foret area. For the cropland owner, a population increae or urban facility approache to their farmland, it could make harder for their activitie uch a complaint from nearby houing neighbor, urban road, or iolation from other farmland o they tend to decreae or top invetment in their farming proce that could be hypotheized a impermanence yndrome (Berry, 1978). It i alo argued that there tend to be overvaluation of urban uage and undervaluation of farm ue near urban-rural fringe o farmer tend to behave a peculator (Nelon et al, 1995). 63

76 ditance denity Countie Figure 3.3 Denity and ditance to large citie. Reordering data from the nearet ditance to large city. (1997 data) denity A/F ratio Countie Figure 3.4 Denity and crop to foretland ratio. Reordering data from the highet denity. (1997 data) 64

77 3.4.3 Projection of land ue The land ue projection for 4 year from now i imulated uing the etimate of area bae model with patial model (equation 3-1 & 3-11). The projection begin with the year 24 and make 1 year prediction to 244. Although the regreion only cover the period 1982 to 1997, I obtain an expected value for the year 24 uing actual price data from that year, and ue that year a the bae. Two cenario are developed to capture a range of potential future change. Both cenario predict the ame total population growth for the three-tate region; however, the cenario dipere the population differently acro the landcape. State level population growth from 2 to 24 i projected to be 26% in Ohio, 31% in Indiana, and 22% in Illinoi (Department of Commerce, 1995). The firt cenario, uniform population growth, aume that population growth occur uniformly acro the countie in each tate. That i, each county experience the ame percentage growth a predicted for the region a a whole. The econd cenario, uburban population growth, place all the population growth in uburban countie around metropolitan area, while allowing population to decline in rural area. Thu, in addition to net migration into the region a a whole, reident are aumed to migrate from rural area to uburban area. For the uburban population growth aumption, we define uburban area a countie urrounding metropolitan area. Both cenario aume the ame total level of population growth in the entire region, but they allocate the growth differently acro countie. 65

78 In both cenario, each countie in thi region i aumed to be a price taker on international market for agricultural and foretry product. Thu, the ame change in foret and agricultural price and rent are aumed for each county. Both cenario aume that foretland rental rate rie at.6% per year, while cropland rental rate are aumed to rie at 2% per year. Two ource of information were ued to develop the crop rent prediction for major crop in thi region, FAPRI (2) and USDA (2). Thee tudie predict increae in crop rent of 2% to 4% per year. I ue thi lower value a the baeline aumption for crop rent. Other variable uch a ditance and oil quality are expected to be ame over the year. The reulting land ue projection are hown in Table 3.1. Both foret and agricultural land are projected to decreae over thi time period while urban area i expected to increae. The uburban population growth cenario predict generally larger hift toward urban ue than the uniform population growth cenario. Recall that total population growth in the region i the ame for both cenario, and the only difference i in where the population growth i predicted to occur. Following the empirical etimate above, new reident in uburban area are predicted to ue more land per peron than new reident in rural area. Although there are difference in projection between the different aumption for where population growth occur, projection of total urbanization are imilar acro the three et of empirical etimate. The main difference among the empirical model appear to be in how much land i derived from agricultural land veru foret land. All 66

79 three model ugget more lo of foretland and Suburban population growth cenario give more lo of both cropland and foretry and more urbanization rate than Uniform population growth cenario Change Bae model Uniform Foret Crop Urban Suburban Foret Crop Urban FE model Uniform Foret Crop Urban Suburban Foret Crop Urban Spatial model Uniform Foret Crop Urban Suburban Foret Crop Urban Table 3.1 Land ue projection ( ha) 67

80 CHAPTER 4 BASELINE AND SENSITIVITY ANALYSIS In thi chapter, I preent the reult of the numerical imulation model for a baeline cenario, and for a et of different aumption on important economic parameter, uch a crop demand, input cot, crop yield level, and interet rate. The different aumption are ued to examine how enitive the model i to alternative aumption, and how the optimal choice are affected by different aumption. In particular, the focu i on total land choice for each crop, crop price, tillage intenity, total conervation land for each crop, and total carbon equetration path. For the baeline, it i aumed that demand for each crop rie at 2 % per year, input cot rie at 3 % per year, and dicount rate i 3 % per year. The crop yield could rie over time, for example, by technology progre and it i aumed that it rie 2 % per year. For each aumption, there are two alternative, high and low. The alternative are % and 5 % annual growth of demand, % and 4 % of crop yield growth, % and 5 % of input cot change, and 5 % interet rate. The empirical model in thi tudy examine the 4 year imulation. A common problem for the dynamic tudy, the terminal condition hould be provided o a to 68

81 prevent the model jut hift all the land into corn or oybean and alo conervation or conventional ue. Similar a other previou tudie (Sohngen & Mendelohn. 23; Adam et al, 1996), aume that demand and land ue hift do not occur after the final period and tay for infinite time. 4.1 Total crop choice Combining all the empirical etimate from the chapter 2 and the different aumption, the reulting crop choice under different aumption are diplayed in the figure 4-1 (A-H). Figure 4.1(A) how the reult of baeline for the total land choice between corn and oybean over time. The total crop choice hift between corn and oybean. One of major force for making hift between the two crop i that continuou land uage in one crop reduce the yield level. In general, the total land in corn i lightly greater than the total oybean land. Thi make ene becaue the return to a hectare of corn are typically higher than the return to a hectare of oybean. In figure 4.1(B), the reult of total crop choice under % yield growth aumption i repreented. Crop choice i gradually moving to oybean and all the land hift to oybean after 25 year. Thi occur becaue input cot continue to rie, and without gain in corn yield in particular, oybean are cheaper to produce and therefore are more heavily adopted. Thee reult can be contrated with the higher yield growth aumption, where more land i ued in corn (Figure 4.1, C). With higher yield growth, 69

82 the return to corn outpace the return to oybean and landowner convert to corn. Few acre, however, hift into continuou corn, but landowner do more rotation of corn per oybean rotation to increae return. For the demand growth aumption, the lower demand growth aumption (%) give reult in a larger proportion of oybean (Figure 4.1, D), wherea higher demand growth (5 %) ugget more corn (Figure 4.1,E). With higher price, landowner can increae overall return by planting corn more widely, and vice-vera for lower price. The lower input cot ( %) aumption allocate more land on corn (Figure 4.1, F) and the higher cot (5 %) cenario give increaing land ue trend on corn (Figure 4.1, G). One of poible explanation for thi i that corn production involve more input cot than oybean o corn production i more enitive to the input cot. By impoing high input cot, it hift more land to oybean than the baeline cenario. High dicount rate cenario give imilar crop choice trend over time but the magnitude between the crop i lightly maller than the baeline. There are ome unrealitic reult uch a all of the cropland hift into oybean (Figure 4.1 B & G). Although it would not likely happen in the real world under uch aumption, it repreent the model boundary for the aumption and enitivity of the model. 7

83 ()ha Total Crop Corn Soybean Year ()ha Total Crop Corn Soybean Year A) Total crop choice (Baeline) B) Total crop choice (% yield) ()ha Total Crop Corn Soybean Year ()ha Total Crop Corn Soybean Year C) Total crop choice (4% yield) D) Total crop choice (% demand) Figure 4.1 Total crop choice (continued) 71

84 Figure 4.1 Continued ()ha Total Crop Corn Soybean Year ()ha Total Crop Corn Soybean Year E) Total crop choice (5% demand) F) Total crop choice (% input cot) ()ha Total Crop Corn Soybean Year ()ha Total Crop Corn Soybean Year G) Total crop choice (5% input cot) H) Total crop choice (5% dicount rate) Figure 4.1 Total crop choice 72

85 4.2 Total conervation land ue The choice on the conervation land ue acro corn and oybean under different aumption are now examined. For the baeline cenario (Figure 4.2, A), conervation land uage in oybean i greater than corn. It repreent the pattern in the tudy region that the adoption rate of conervation tillage in oybean i bigger than corn. The total land in conervation hift between corn and oybean a the total crop land. Compare to the total land ue in the figure 4.1(A), in general, the total oybean hectare on conervation practice move around at 3 million hectare, which i about a third of total oybean and 2 million hectare for conervation corn, which i about 11 % out of total corn. In figure 4.2 (A & B), conervation land ue with different yield aumption are preented. With low yield growth ( %), the conervation oybean dominate the other land ue choice over time. Compare to the total crop choice with low demand (Figure 4.1, B), all of the land i devoted to oybean with conervation practice. High yield growth aumption (5 %) give decreaing trend of conervation land ue for both corn and oybean and it reache to zero after 21 year. It i aumed in the model that conervation practice reduce input cot and negative yield impact on oybean i the leat. With riing input cot aumption, low yield growth aumption make conervation practice more profitable. Higher yield make input cot negligible and conventional practice more profitable and more choice on corn. For the demand aumption, low demand give more land ue in conervation practice for both corn and oybean than the baeline and the magnitude i bigger in 73

86 oybean (Figure 4.2, D). High demand aumption make conervation practice for both corn and oybean reduce rapidly and reach to zero after 1-11 year (Figure 4.2, E). The explanation for thi i imilar a the aumption with yield growth. Low demand make conervation oybean more favorable becaue it could ave input cot under increaing input cot and tagnated demand level. For the high demand cenario, conventional practice i more favorable becaue of the high riing demand, i.e. crop price o the input cot are getting le important. However, the cale of change i maller under the demand aumption than the yield growth aumption. The reult with different input cot aumption are hown in figure 4.2 (F & G). Low input cot tranfer all the land ue into the conventional ue for both corn and oybean. However, high input cot aumption gradually move land into the conervation practice for oybean over time. The pattern of conervation practice i imilar acro aumption. The aumption on high yield, high demand, and low input cot make le land ue on the conervation practice for both crop. The oppoite cenario allocate more land on oybean with conervation practice with different cale. For the high dicount rate (Figure 4.2, H), the pattern of conervation land ue for both corn and oybean i imilar a the baeline cenario over time but a it approache to later year the land on conervation practice lightly decreae for both crop. It could be explained that the higher dicount rate at the later period would affect much le preent time compare to the baeline cenario, in particular, input cot aving by conervation practice. Therefore, total hectare in conervation practice could be decreaed. 74

87 ()ha Total conervation crop Corn Soybean Year ()ha Total conervation crop Corn Soybean Year A) Total conervation crop (Baeline) B) Total conervation crop (% yield) ()ha Total conervation crop Corn Soybean Year ()ha Total conervation crop Corn Soybean Year C) Total conervation crop (4% yield) D) Total conervation crop (% demand) Figure 4.2 Total conervation crop (continued) 75

88 Figure 4.2 Continued ()ha Total conervation crop Corn Soybean Year ()ha Total conervation crop Corn Soybean Year E) Total conervation crop (5% demand) F) Total conervation crop (% input cot) ()ha Total conervation crop Corn Soybean Year ()ha Total conervation crop Corn Soybean Year G) Total conervation crop (5% input cot) H) Total conervation crop(5% dicount rate) Figure 4.2 Total conervation crop 76

89 4.3 Crop price In thi ection, the crop price under different aumption are diplayed in Figure 4.3 (A through H). For the baeline, the price are table over time. Soybean price move around at $6 per buhel and corn price ettle around at $3.5 per buhel. The light movement of crop price i mainly for the reaon that the total land ue, in turn, the total output of each crop rie and fall over time. When the yield growth i aumed at % per year, the price of corn and oybean rie over time (Figure 4.3, B). It reflect riing demand of each crop while the contant yield growth of crop by the aumption. Likewie, when the yield level i aumed at 4 % per year (Figure 4.3, C) the overall price of both crop teadily go down over time. For the % demand aumption, crop price are teadily going down over time (Figure 4.3, D) It make ene becaue it reflect that the crop yield rie over time while crop demand i contant over time. For the high demand aumption (5 %), both price of corn and oybean rie rapidly over time (Figure 4.3, E). Figure 4.3 (F & G) how the price path with different input cot aumption, For the low input cot cae, the price path for both corn and oybean i table and imilar a in the baeline cenario. However, with the high input cot aumption, oybean price gradually reduce but corn price rie over time. From the total crop land in figure 4.1 (G), the total crop choice for oybean teadily rie and oppoite for corn make uch price pattern. High dicount rate aumption reult in little effect on crop price over time a the total crop choice. 77

90 ($/bu) Crop price Corn Soybean Year ($/bu) Crop price Corn Soybean Year A) Crop price (Baeline) B) Crop price (% yield) ($/bu) Crop price Corn Soybean Year ($/bu) Crop price Corn Soybean Year B) Crop price (4% yield) D) Crop price (% demand) Figure 4.3 Crop price (continued) 78

91 Figure 4.3 Continued ($/bu) Crop price Corn Soybean Year ($/bu) Crop price Corn Soybean Year E) Crop price (5% demand) F) Crop price (% input cot) ($/bu) Crop price Corn Soybean Year ($/bu) Crop price Corn Soybean Year G) Crop price (5% input cot) H) Crop price (5% dicount rate) Figure 4.3 Crop price 79

92 4.4 Reidue management intenity To grap overall pattern of reidue management intenity acro cenario, it i worthwhile to examine average intenity over time. In table 4.1, the 4 year average reidue management intenity i ummarized acro the different aumption. Note that there are three different land clae in each crop. Cla 1 i the bet quality oil that ha the greatet yield potential and the Cla 3 i the wort quality oil with the leat yield potential. In general, average reidue management intenity i higher in the wort quality oil cla (Cla 3) than in the middle and bet oil clae for both oybean and corn. For both crop, the bet oil quality cla (Cla 1) ha the minimum reidue level which i about 35 % acro the cenario, except % yield and 5 % input cot cae for oybean. The reult reflect the aumption about the yield impact by reidue intenity that the high quality oil cla loe more yield by reidue intenity. Comparing the average reidue intenity acro the cenario, 5 % input cot aumption reult in the highet average reidue management intenity in both crop acro overall oil clae. For the bet quality oil in oybean, average reidue intenity i about 52 %, middle quality oil i about 84 %, and the wort quality oil cla i about 97 %. The major reaon for thi i that the higher input cot make the more choice on cot aving activity uch a increaing reidue input intenity. By the ame token, average reidue management intenity i higher than the baeline when crop yield i aumed low ( %), demand on crop i low ( % demand), and higher dicount rate (5 %). 8

93 On the other hand, when there i high crop yield (4 %), high crop demand (5 %), and low input cot ( %) cenario, the average reidue management intenity for both crop i lower than the baeline cenario. Thee aumption make oppoite force that input cot are getting inignificant compare to thee changing force. Corn Soybean Scenario cla1 cla2 cla3 cla1 cla2 cla3 Baeline 35% 35% 82% 35% 58% 96% % yield 35% 35% 85% 47% 81% 97% 4% yield 35% 35% 35% 35% 37% 78% % demand 35% 35% 79% 36% 7% 97% 5% demand 35% 35% 35% 35% 36% 68% % cot 35% 35% 35% 35% 36% 71% 5% cot 35% 36% 87% 52% 84% 97% 5% dicount 35% 35% 83% 35% 59% 96% Cla 1: The bet quality oil Cla 2: The middle quality oil Cla 3: The wort quality oil Table.1Table 4.1 Average reidue management intenity under different cenario 4.5 Total carbon equetration The total carbon equetration pattern over time i hown in Figure 4.4. It how that it rie lightly over time. The reaon for the increaing trend of total carbon equetration i that there i conervation practice involved even without any carbon 81

94 policie. Motly it come from the wort oil cla becaue it ha the highet tillage intenity. It make ene becaue there would not be much of lo in yield with conervation practice on low quality of land while there could be cot aving by high reidue management. In the figure 4.4, the pattern of total carbon equetration acro the aumption are demontrated. The broad line without a marker i the total carbon path under the baeline cenario. The three dotted carbon path below the baeline are the total carbon with the aumption of 4 % yield, 5 % demand, and % input cot. It i becaue total conervation land uage for both crop with thee aumption approach zero (Figure 4.2 C, E, & G), o the carbon level tay at the initial carbon level. The total carbon i higher than the baeline with the other aumption. Under the low yield aumption ( %), the total carbon equetration level i the highet. Thi i becaue the land in conervation practice with thi aumption i the highet (Figure 4.2, B) and the average tillage intenity i higher than the baeline. The high input cot (5 %) aumption reult in the next highet total carbon equetration pattern. It alo propel the land ue hift to conervation practice in oybean and the highet average tillage intenity. The low demand aumption ( %) alo reult in higher total carbon path and identical reaon could be applied. It ha the higher total conervation land in oybean and corn and higher average tillage intenity. For the higher dicount rate aumption alo expect light higher total carbon than the baeline. 82

95 MMTC Baeline % yield 4% yield %demand 5% demand % input cot 5% input cot 5% dicount rate Total carbon Year Figure 4.4 Total carbon equetration (million ton of carbon) 83

96 CHAPTER 5 CARBON POLICY RESULTS In thi chapter, I provide the reult of carbon policy cenario on et of different aumption. The carbon policie conidered in thi tudy are carbon renting and fixed per hectare payment with two different minimum required tillage intenity level, 35 % and 75 %. Carbon renting policy pay rental baed on the ton of carbon equetered (Sohngen & Mendelohn, 23). The policy of per hectare payment require that once land parcel i involved in the conervation practice, then it i not permitted to tranfer back to conventional tillage. In the firt ection, thee two carbon policie are applied to the baeline cenario in chapter 4. Total crop choice, conervation cropland, average tillage intenity, crop price, amount of carbon gain, and cot of carbon equetration are compared along the different carbon policie. So far, the total available cropland i fixed over time. In the econd ection, carbon renting policy i applied to the baeline cenario while the total available cropland change. The projection of total cropland i utilized by the area bae model etimate in chapter 3. 84

97 5.1 Carbon policie with the baeline Carbon renting policy Carbon renting policy i applied to the empirical dynamic model following (Sohngen & Mendelohn, 23). Several carbon price are applied in thi tudy, $2, $1, $4, $1, and $15 per ton of carbon. Auming the dicount rate 3 % per year, the annual carbon rental i being paid to the landowner are $.6, $.3, $1.2, $3, and $4.5 per ton of carbon a long a the tored carbon i reiding in the oil. Once the carbon i emitted into the atmophere by plowing, thee rental payment are not paid any more. Note that the total crop land i contant over time. The total model run are applied to 45 year and reult are hown only up to 4 th year period to reduce impact by terminal condition In the Figure 5.1 (A through E), the crop choice reult of carbon renting policy are lited. In general, the pattern of crop choice are imilar a the crop choice under the baeline. Total crop choice hift between corn and oybean over time. The rotation between the two crop till exit under the carbon policy, which i caued by the yield lo impact of the continuou crop. Same a the baeline reult, the total hectare in corn are greater than the total oybean hectare. A the carbon price rie (move from figure A to E), the gap between the two crop lightly decreae. In particular, the total oybean hectare with $15 per ton of carbon price are the highet compare to any other cenario. So it indicate that oybean i relatively getting more attractive than corn a the carbon rental increae but the magnitude i mall. 85

98 (ha) 14 Total Crop choice ($2/ton) (ha) 14 Total Crop choice ($1/ton) Corn Soybean 6 4 Corn Soybean 2 Year 2 Year A) Total crop choice ($2/ton) B) Total crop choice ($1/ton) (ha) 14 Total Crop choice ($4/ton) (ha) 14 Total Crop choice ($1/ton) Corn Soybean 6 4 Corn Soybean 2 Year 2 Year C) Total crop choice ($4/ton) D) Total crop choice ($1/ton) (ha) Total Crop choice ($15/ton) Corn Soybean Year E) Total crop choice ($15/ton) Figure 5.1 Total crop choice with carbon renting policy 86

99 The reult of conervation practice for each crop under carbon renting policy are hown in figure 5.2 (A to E). The overall model outcome how expected reult. A carbon price goe up (move from figure A to E), total conervation practice hectare for both crop increae. With low carbon price ($2 per ton), average oybean conervation practice hift around at 2.5 million hectare and corn tay around at 1.5 million hectare. It increae to 2.9 million hectare in oybean and 2.2 million hectare in corn with $4 per ton of carbon price. The highet carbon price ($15 per ton) give about 8 million hectare in oybean and corn for the conervation practice. A in the baeline in chapter 4, total hectare on the conervation practice hift between the two crop. The total hectare for the conervation practice in oybean are greater than corn. Acro the different carbon price, there i not ignificant difference in the crop choice pattern except that the gap between the two crop are lightly reduced (5-2, A v. 5-2, E). Reult of crop price with carbon renting policy are provided in figure 5.3 (A & B). The overall path of crop price are table with mall fluctuation over time a in the baeline cenario. A the carbon price increae, the corn price lightly hift up (figure 5.3, A). The price path with $15 per ton of carbon price i the highet over time. That i becaue the total corn choice i the leat with $15 per ton. For the oybean price path, however, the highet carbon price ($15 per ton) give the lowet price path. A hown in figure 5.1, the total crop choice i the highet with thi carbon price. A carbon price rie, oybean attract more land and it hift up the corn price and down the oybean price to ome extent. In general, the impact on price i bigger on oybean and there i not dramatic change on the crop price by the carbon policy. 87

100 ( ha) Total conervation crop ($2/ton) Corn Soybean Year ( ha) Total conervation crop ($1/ton) Corn Soybean Year A) Total conervation crop ($2/ton) B) Total conervation crop ($1/ton) ( ha) Total conervation crop ($4/ton) Corn Soybean Year ( ha) Total conervation crop ($1/ton) Corn Soybean Year C) Total conervation crop ($4/ton) D) Total conervation crop ($1/ton) 1 ( ha) Total conervation crop ($15/ton) Corn Soybean Year E) Total conervation crop ($15/ton) Figure 5.2 Total conervation crop with carbon renting policy 88

101 $/bu Corn price A) Corn price with carbon renting policy $2/ton $4/ton $15/ton Year $/bu Soybean price $2/ton $4/ton $15/ton Year B) Soybean price Figure 5.3 Crop price with carbon renting policy 89

102 The average reidue management intenity for each crop over different carbon price are preented in table 5.1. A in the baeline cenario, reidue management intenity i higher in the low quality oil cla for both crop. Alo it i higher in oybean than the corn for the middle and low quality oil clae over the carbon price range. A expected, the average reidue intenity i increaing a the carbon price increae except the bet oil cla for corn. For the bet oil quality cla, regardle of carbon price, reidue intenity i at the minimum level (35%) for corn. For oybean, it i required at leat $1 per ton of carbon price to pur more reidue intenity than the baeline in the bet quality oil. For the middle quality oil clae, there i light increae of reidue intenity for corn with $1 per ton of carbon price. There i teady increment of reidue intenity along the carbon price for oybean middle quality oil cla. For the low quality oil cla, there i additional reidue intenity in corn a the carbon price goe up but there i not much of gain in oybean becaue there i high reidue intenity in the baeline for oybean. The total carbon equetration over different carbon price are hown in figure 5.4. The graph how the total cumulative carbon gain over the baeline for 4 year. It i expected that the higher carbon price could timulate more carbon and the figure how the reult a expected. There i not much of gain with lower carbon price at $2 and $1 per ton of carbon price. The ubtantial total carbon gain could be found from $4 per ton of carbon price. With $15 per ton of carbon price, the total carbon gain i the greatet but the increment of carbon gain above the baeline decreae, which reflect the maximum attainable carbon limit a introduced in Figure 3.2. The carbon gain come 9

103 not only from the higher tillage intenity (Table 5.1) but alo form the additional conervation practice hectare (Figure 5.2). Corn Soybean Scenario Cla1 Cla2 Cla3 Cla1 Cla2 Cla3 Baeline 35% 35% 82% 35% 58% 96% $2/ton 35% 35% 83% 35% 59% 96% $1/ton 35% 35% 89% 35% 6% 97% $4/ton 35% 35% 93% 35% 68% 98% $1/ton 35% 36% 97% 39% 82% 98% $15/ton 35% 56% 98% 51% 89% 98% Cla1: The bet quality oil Cla2: The middle quality oil Cla3: The wort quality oil Table.1Table 5.1 Average reidue management intenity with carbon renting policy MMTC Cumulative carbon gain (carbon renting cenario) $2/ton $1/ton $4/ton $1/ton $15/ton Year Figure 5.4 Total cumulative carbon gain above the baeline with carbon renting policy Fixed payment per hectare 91

104 For the carbon policy in thi ection, the payment to land owner are baed on the hectare on which the conervation tillage i practiced. There are two cenario with different minimum requirement for the reidue intenity, 35% and 75%. It i aumed that once the land i ued on the conervation practice, it i not permitted to move back to the conventional uage. The price for thi ection are $2, $1, $2, and $5 per hectare. The reult of per hectare payment are hown in Figure 5.5 (A to D) for 35% minimum reidue management requirement and in Figure 5.6 (A to D) for 75% minimum reidue management requirement. The pattern of crop choice are imilar a before in the baeline and carbon renting cenario. The total crop choice are hifting between the two crop and it tay table acro the different payment. The pattern tay imilar until $2 per hectare for both minimum requirement. However, when the payment i the highet with $5 per hectare, total choice for oybean in the firt 1-12 year i the greatet and corn i the mallet for both requirement cenario. The magnitude i greater in 75 % cenario. 92

105 (ha) Total crop choice ($2/ha) Corn Soybean Year (ha) Total crop choice ($1/ha) Corn Soybean Year A) Total crop choice ($2/ha, 35%) B) Total crop choice ($1/ha, 35%) (ha) Total crop choice ($2/ha) Corn Soybean Year (ha) Total crop choice ($5/ha) Corn Soybean Year C) Total crop choice ($2/ha, 35%) D) Total crop choice ($15/ha 35%) Figure 5.5 Total crop choice with per hectare payment (35% minimum reidue intenity) 93

106 (ha) 14 Total crop choice ($2/ha) (ha) 14 Total crop choice ($1/ha) Corn Soybean 6 4 Corn Soybean 2 Year 2 Year A) Total crop choice ($2/ha, 75%) B) Total crop choice ($1/ha, 75%) (ha) Total crop choice ($2/ha) Corn Soybean Year (ha) Total crop choice ($5/ha) Corn Soybean Year C) Total crop choice ($2/ha, 75%) D) Total crop choice ($15/ha 75%) Figure 5.6 Total crop choice with per hectare payment (75% minimum reidue intenity) 94

107 It i of interet how much of hectare would be involved in the conervation practice with different minimum reidue management requirement when the conervation land parcel are being paid. The reult how the expected outcome in which the conervation land increae a the price goe up (Figure 5.7 & 5-8). On average, there are 1.9 million hectare in conervation corn and 2.9 million hectare in conervation oybean with $2 per hectare payment under 35% minimum reidue management requirement (Figure 5.7, A). For the high reidue intenity requirement (75%), there are 1.8 million hectare in conervation corn and 2.1 million hectare in conervation oybean with $2 per hectare price. Compare to the total cropland (Figure 5.5), the portion of conervation land i about 18% of total corn and 3% oybean with 35% minimum requirement and 17% of total corn and 23% of total oybean i tranferred into the conervation practice with high reidue management requirement (75%) cenario. There i rapid tranition into the conervation practice when conervation land i paid at $1 per hectare with 35 % minimum reidue input requirement (Figure 5.7, B). On average, 81 % of total corn and 85% of total oybean i under the conervation practice with 35 % reidue intenity. For the high reidue management requirement (Figure 5.8, B), there i not many tranfer into conervation tillage compare to $2 per hectare payment. It i about 22% and 24% of total corn and oybean i hifted to the conervation practice. A the price goe up to $2 per hectare on the conervation uage, after 15 year, all of the land i under the conervation practice when 35 % reidue management 95

108 intenity i minimally required (Figure 5.7, C). However, with the high reidue input requirement (75 %), 25 % of corn and 28 % of oybean are hifted to the conervation land. For the $5 per hectare cenario, all of the cropland i under the conervation practice with 35 % reidue management requirement after 5 year. However, with the high reidue input requirement, 1 % of cropland till remain in the conervation tillage, which i the highet productive region. The total cumulative carbon gain above the baeline for 35 % minimum reidue management requirement cenario i diplayed in Figure 5.9. A expected, the total carbon gain increae a the payment price grow. The carbon gain path with $2 per hectare payment gradually increae in the firt 1 year and tay at 6.5 million ton over time. There i jump on the carbon gain path with $1 per hectare payment in the firt 1 year and hift around at 37 million ton over time. However, there i not ubtantial carbon gain with the higher payment uch a $2 or $5 per hectare payment cenario. For 75 % minimum reidue requirement cenario (Figure 5.1), a in the 35 % minimum reidue cae, there i low carbon gain in firt 12 year and tay at about 1 million ton. Unlike the low reidue requirement, there i not ubtantial carbon gain up to $2 per hectare payment. Carbon gain tay at about 15-2 million ton per year over time for both $1 and $2 per hectare cenario. However, with $5 per hectare payment, there i a rapid gain in the firt 12 year and annual gain i about 8 million ton of carbon. 96

109 (ha) Total conervation crop ($2/ha) (ha) Total conervation crop ($1/ha) Corn Soybean Corn Soybean Year 2 Year A) Total conervation crop ($2/ha, 35%) B) Total conervation crop ($1/ha, 35%) (ha) Total conervation crop ($2/ha) (ha) Total conervation crop ($5/ha) Corn Soybean 6 4 Corn Soybean 2 Year 2 Year C) Total conervation crop ($2/ha, 35%) D) Total conervation crop (5/ha, 35%) Figure 5.7 Total conervation crop land with per hectare payment (35% minimum reidue intenity) 97

110 (ha) Total conervation crop ($2/ha) (ha) Total conervation crop ($1/ha) Corn Soybean 12 1 Corn Soybean Year Year A) Total conervation crop ($2/ha, 75%) B) Total conervation crop ($1/ha, 75%) (ha) Total conervation crop ($2/ha) (ha) Total conervation crop ($5/ha) Corn Soybean Year Corn Soybean Year C) Total conervation crop ($2/ha, 75%) D) Total conervation crop ($5/ha, 75%) Figure 5.8 Total conervation crop land with per hectare payment (75% minimum reidue intenity) 98

111 MMTC Total cumulative carbon gain (35% minimum till) $2/ha $1/ha $2/ha $5/ha Year Figure 5.9 Total cumulative carbon gain above the baeline (35% minimum reidue intenity) MMTC Total cumulative carbon gain (75 % minimum till) $2/ha $1/ha $2/ha $5/ha Year Figure 5.1 Total cumulative carbon gain above the baeline (75% minimum reidue intenity) 99

112 5.1.3 Cot of carbon equetration Once the carbon potential i obtained through the different carbon policie and price, it i worthwhile to examine the cot and potential of carbon equetration acro the carbon cenario. Several etimate on the cot and carbon equetration potential are ummarized in table 5.2 through 5-4. In each table, the firt two row how the total carbon tock (ton of carbon) per hectare in the beginning (year 24) and the lat period (year 244) for different carbon payment. Annual carbon gain i the average value of the annual gain by the carbon cenario. Preent value of the carbon gain (million ton of carbon) are the um of all the dicounted carbon gain over the period. Annual equivalent carbon gain i the jut the annual number of the preent value of carbon gain. Total cot (million dollar) i the um of dicounted annual rental payment over the period. Average cot i obtained by dividing the total cot by preent value of carbon gain. For the carbon renting program (table 5.2), there i about 43.4 ton of carbon per hectare in the beginning year and it end up with 44.1 ton of carbon per hectare to 46.2 ton of carbon per hectare depending on the carbon price. Although there are not much of carbon change between the two time period, there i more carbon dynamic a hown in figure 5.4. To analyze the total carbon change more cloely, it i worthwhile to examine annual carbon gain. On average, the carbon renting policy could gain additional annual carbon about 149 thouand ton with $2 per ton of carbon price and 1.2 million ton of average annual carbon gain with $15 per ton of carbon price. Total um of dicounted carbon gain for 4 year would be 2.8 million ton of carbon with $2 per ton of carbon 1

113 price and over 42.8 million ton of carbon with $15 per ton of carbon price. With the dicounted carbon term, the annual equivalent carbon gain would be 121 thouand ton of carbon with $2 per ton of carbon price and 1.8 million ton of carbon gain with $15 per ton of carbon price. The total cot of carbon equetration in preent value term would range from 17, dollar with $2 per ton of carbon price to 193 million dollar with $15 per ton of carbon price. The average cot with $2 carbon price i $.6 per ton. With the highet carbon price at $15 per ton, the average cot of carbon i about $4.5 per ton. In general, the carbon cot etimate i within the range of previou carbon tudie. For the carbon policy with fixed payment per hectare cheme, in general, the program with 75 % minimum reidue management requirement provide more carbon gain than 35 % minimum reidue program acro the payment price (Table 5.3 & 5.4). There i the ame amount of carbon in the initial period, 43.3 ton of carbon per hectare. In 244, there would be 44 ton to 45.8 ton of carbon with 35% minimum reidue program, wherea 44.3 to 47.8 ton of carbon per hectare with 75% minimum reidue cenario. For the annual carbon gain, there i about 264 thouand (413 thouand) carbon gain with $2 per hectare and 1.16 million ton (2.16 million ton) of annual carbon gain with $5 per hectare program when the 35 % minimum reidue (75 % minimum reidue) i required. When the conervation land i paid at $2 per hectare, there could be 5 million ton (1 million ton) of preent value of carbon gain by 35 % minimum (75 % minimum) reidue management requirement. It rie to 36 million ton (71 million ton) with 35 % minimum (75 % minimum) reidue input requirement when $5 per hectare 11

114 i paid. The preent value of total carbon cot climb from 217 million dollar (183 million dollar) up to 22 billion (21 billion) dollar a the payment per hectare rie when 35 % minimum (75 % minimum) reidue i required. With the $2 per hectare payment, the average cot of carbon i $4 per ton of carbon and $18 per ton of carbon when 35 % and 75 % minimum reidue management program. With the highet payment at $5 per hectare cenario, the average cot rie dramatically up to $613 per ton with 35 % minimum reidue and $314 per ton with 75 % minimum reidue requirement. The cenario with fixed payment per hectare with 35 % minimum reidue management reult in the highet total carbon cot and the carbon renting policy cot in the leat manner. The reult confirm the theory and previou tudie that there i efficiency gain in per ton payment than the per hectare payment (Pautch et al., 21 & Antle et al., 23). The patial ditribution of cumulative carbon gain in year 244 are diplayed from figure 5.11 to The total cumulative carbon gain by carbon renting policy with $4 per ton of carbon price in figure 5.11 how that mot of carbon are obtained from overall area in Ohio, except northwetern and outheatern region, and wetern region of Illinoi. Interetingly, region with high quality oil, uch a northwetern Ohio, northern Indiana and northern Illinoi do not provide ubtantial carbon. Within thee region, it i not advantageou for farmer to intenively adopt conervation tillage and maintain their land with that technology permanently. At the other end of the land quality pectrum, uch a outheatern Ohio and outh region of Indiana, carbon gain are 12

115 alo mall becaue conervation tillage ha already been widely adopted and the potential for carbon equetration i low. The two different minimum reidue requirement in the fixed payment program provide intereting patial pattern of carbon gain. Figure 5.12 and 5-13 how the carbon gain when $2 per hectare i paid when the minimum reidue input requirement for the program i 35 % (figure 5.12) and 75 % (figure 5.13). In general, there i oppoite carbon gain pattern between the two requirement. Under the 35 % minimum requirement, northern region in Ohio, Indiana, and Illinoi provide mot of the carbon gain. However, the other region provide more carbon with higher minimum reidue (75 %) requirement cae. For the high quality oil, the yield lo by reidue input i greater than the low quality oil cla and the program require the conervation land be trapped in conervation practice over the 4 year. The higher requirement of reidue intenity make the greater opportunity cot for the high oil quality oil. However, the lower requirement for the program make the le yield lo and the potential of carbon equetration in high quality oil clae i bigger than the low quality oil clae. That could be the reaon for the more carbon gain in the high productive region with 35 % minimum reidue requirement program. 13

116 Total Carbon tored in oil at year t: Baeline = X B t S Scenario = X t Annual carbon flux at year t: B B Baeline = F = X X Scenario = B t S F t = X t+1 S t+1 t X Cumulative carbon gain for cenario by the year t: S B CG = X X S t t Annual carbon gain: S Average of ( CG CG t S t S t+1 t ) Preent value of carbon gain: T 1 t ρ S S ( CG CG ) t+ 1 t, where ρ i the dicount factor Carbon Price Carbon Price ($/ton) $2 $1 $4 $1 $15 Annual carbon rental ($/ton) $.1 $.3 $1.2 $3 $4.5 Carbon per ha in Carbon per ha in Annual carbon gain Preent value of carbon gain Annual equivalent carbon gain Total cot (Preent value) Average cot($/ton) : ton ψ: Million dollar : Million ton Table 5.2 Cot of carbon (Carbon renting policy) 14

117 Payment per hectare $2 $1 $2 $5 Carbon per ha in Carbon per ha in Annual carbon gain Preent value of carbon gain Annual equivalent carbon gain Total cot (Preent value) ψ Average cot($/ton) : ton ψ: Million dollar : Million ton Table 5.3 Cot of carbon (Fixed payment with 35 % minimum reidue intenity) Payment per hectare $2 $1 $2 $5 Carbon per ha in Carbon per ha in Annual carbon gain Preent value of carbon gain Annual equivalent carbon gain Total cot (Preent value) ψ Average cot($/ton) : ton ψ: Million dollar : Million ton Table 5.4 Cot of carbon (Fixed payment with 75 % minimum reidue intenity) 15

118 * All the number are thouand ton Figure 5.11 Cumulative carbon gain in 244 (carbon renting with $4 per ton) * All the number are thouand ton Figure 5.12 Cumulative carbon gain in 244 ($2 per hectare with 35 % minimum reidue intenity) 16

119 * All the number are thouand ton Figure 5.13 Cumulative carbon gain in 244 ($2 per hectare with 75 % minimum reidue intenity) 17

120 5.2 Carbon policy when total cropland change Land ue projection by carbon policy Thi ection explore how potential future land ue change influence the carbon gain uggeted above. In particular, the carbon rental policy i re-examined under alternative cenario that allow total available cropland to change over time. It i obviou that the landcape for next 4 year will be different from now. However, what i not obviou i that how the carbon policy would affect the land ue choice in the future. One of major concern of land ue change i the urbanization pattern that would be influenced trongly by population growth and location factor and it i not clear how it would affect the carbon equetration potential. The future cropland projection i obtained by adopting the etimate reult of area bae model, in particular, the bae model (equation 3-9) reult with uburban growth cenario in chapter 3. To have the proper baeline with land ue change in the future, following tep are applied. Firt, from the dynamic carbon cenario reult in the previou ection, obtain the rental value change for agricultural land. Apply the new agricultural rental value to the area bae model to project land ue change. Second, apply new land ue change to the dynamic model and obtain the econd reult of dynamic model reult and obtain rental value change. Apply again thi rental value to the area bae model and iterate until the land ue change prediction until converge in the agricultural rental value. 18

121 While population and agricultural rent rie at the ame rate a the projection imulation, additional carbon rental value are added to foret and agricultural rent growth and it i re-etimated the land ue. Carbon in tree i calculated uing the etimate of Smith et al. (23) for the above ground carbon only. The data for ditribution and volume of each pecie were obtained from the USDA Foret Service FIA data. Foret group type are Conifer, lowland hardwood (Oak-Gum-Cypre group, Elm-Ah-Cottonwood, and Apen-Birch group), Maple-Beech-Birch group, Oak- Hickory, and Oak-Pine group. The relation between timber volume and age cla for each foret group are etimated uing FIA data. The yield function for thee pecie are adopted from the ATLAS timber model (Mill and Kincaid, 1992). From the FIA data, there are different ite clae depending on the land quality and yield function for thi tudy are etimated uing only medium ite cla that could produce about cubic feet per acre and per year. Yield function capture the growth of each timber over time but it i limited by maximum yield value by the etimated yield function. A carbon rental i added to foret rent in the imulation, foretland increae over time o yield function for each pecie take account timber growth on newly etablihed foretland. Agricultural rental change for the projection are adopted from the reult of the carbon renting policy with baeline cenario in the firt ection of thi chapter. Firt, examine the revenue change in each region for each carbon price. Then etimate the change rate above the baeline for each carbon price. Second, apply thee change rate of agricultural rental to the area bae model to get the new land projection. The reult of land ue projection of cropland are lited in table

122 After applying carbon policy imulation to the area bae model, cropland change along the carbon price cenario are hown in table 5.5. The baeline cenario project that cropland decline 45 thouand hectare within next 4 year. With carbon renting policy, cropland decreae from 446 thouand hectare with $2 per ton of carbon price to 237 thouand hectare with $15 per ton of carbon price cenario. A the carbon price increae, the lo of cropland decreae. Thee etimate are incorporated into the empirical dynamic model for each carbon price and rerun the model. Total cropland change are divided into the annual change rate for each carbon price cenario and total land contraint are added. Although the total cropland of the entire tudy region i projected to loe hectare over time, the total cropland could increae for ome region by uch a deforetation. One of example of the cropland change i hown in figure The map how the projection of cropland with $4 per ton of carbon price cenario. A can be een, there are cropland lo around metropolitan area but alo there are region with increaing cropland. In each region in the dynamic model, there are three different oil clae. To deal with the land ue change, it i aumed that the change occur equally over the oil clae. 11

123 Baeline $2/ton $1/ton $4/ton $1/ton $15/ton Total change Table 5.5 Total Cropland change (ha) * All number are ha Figure 5.14 Cropland change with $4 per ton of carbon price 111