Three essays concerning agriculture and energy

Transcription

1 Graduate Theses and Dssertatons Graduate College 2009 Three essays concernng agrculture and energy Mndy Lyn Baker Iowa State Unversty Follow ths and addtonal works at: Part of the Economcs Commons Recommended Ctaton Baker, Mndy Lyn, "Three essays concernng agrculture and energy" (2009). Graduate Theses and Dssertatons Ths Dssertaton s brought to you for free and open access by the Graduate College at Iowa State Unversty Dgtal Repostory. It has been accepted for ncluson n Graduate Theses and Dssertatons by an authorzed admnstrator of Iowa State Unversty Dgtal Repostory. For more nformaton, please contact dgrep@astate.edu.

2 Three essays concernng agrculture and energy by Mndy Lyn Baker A dssertaton submtted to the graduate faculty n partal fulfllment of the requrements for the degree of DOCTOR OF PHILOSOPHY Major: Economcs Program of Study Commttee: Dermot Hayes, Major Professor Bruce Babcock Arne Hallam Chad Hart Sergo Lence Iowa State Unversty Ames, Iowa 2009 Copyrght Mndy Lyn Baker, All rghts reserved.

3 TABLE OF CONTENTS ACKNOWLEGEMENTS ABSTRACT v v CHAPTER 1: GENERAL INTRODUCTION 1 Introducton 1 Dssertaton Organzaton 2 CHAPTER 2: CROP-BASED BIOFUEL PRODUCTION WITH ACREAGE CONSTRAINTS AND UNCERTAINTY Introducton 5 Prevous Lterature 6 The Model Economy 8 Commodty Supply 9 Commodty Demand 11 The Investors 11 Returns to Bofuel Producton 12 Long Run Compettve Equlbrum 13 Implementng the Model 14 Algorthm for Smulatng the Model 15 Commodty Supply 15 Commodty Demand 18 Accountng for Cellulosc Ethanol from Corn Stover and Wood chps 19 Calculatng Returns to Bofuel Producton 19 5

4 Results 22 Senstvty of Results to Requred Levels of Swtchgrass Producton 24 Conclusons 26 Appendx 30 CHAPTER 3: WELFARE CHANGES FROM INCREASED BIOFUEL PRODUCTION ON U.S. AGRICULTURE: THE ROLE OF UNCERTAINTY AND INTERLINKED COMMODITY MARKETS Introducton 32 The Model Economy 35 Commodty Supply 36 Specfcaton of Cost Functon and Crop Yeld Dstrbutons 39 Commodty Demand 42 Corn Demand Equatons 42 The Soybean Complex 43 Wheat Demand Equatons 46 Compettve Equlbrum 46 Calculatng Welfare Changes 47 Farmer Surplus 47 Consumer Surplus 47 Taxpayer Cost 48 Results 53 Senstvty Analyss 64 Comparson wth the Exstng Lterature 64 32

5 v Concluson 70 CHAPTER 4: INSIGHT INTO A POSSIBLE EQUILIBRIUM RELATIONSHIP BETWEEN THE PRICE OF CORN AND ETHANOL: ANALYSIS AND A SMALL SAMPLE MONTE CARLO STUDY Introducton 74 A Theory of the Lnk Between the Corn and Ethanol Markets 75 Futures Prces 77 Intertemporal Arbtrage and the Spot-Futures Prce Relatonshp 78 Testng for Contegraton 80 Data 83 Cost of Carry and Futures Prces 86 Pretestng and Lag Length 88 Seasonalty n the Data 88 Prelmnary (Asymptotc) Results 89 Small Sample Issues wth Johansen s Contegraton Tests 90 A Monte Carlo Study 93 Concluson 100 CHAPTER 5: GENERAL CONCLUSIONS

6 v ACKNOWLEGEMENTS I am grateful for the support of many people n my pursut of ths degree and n the completon of ths dssertaton. Dr. Dermot Hayes, my major professor, was an nexhaustble reserve of encouragement, enthusasm, and patence; wthout healthy doses of each of these, I could not have endured. As an economst, I admre hs ntuton about mportant problems; as a frend, I admre hs loyalty, generosty, and humor. I hope to emulate hm n both of these planes. My commttee members: Dr. Bruce Babcock, Dr. Arne Hallam, Dr. Chad Hart, and Dr. Sergo Lence provded nvaluable gudance n the wrtng of ths dssertaton. Ther recommendatons not only enhanced ths document, but my professonal development as well. Frends who are lberal wth encouragement, as well as red nk, are rare gems. I extend my thanks to Subhra Bhattacharjee, Jerome Dumorter, Carola Grebtus, Lhong McPhal, and Ofr Rubn n partcular for readng and commentng on drafts of my work at a moment s notce. My parents, Carol and Lnda Mallory, whose advce I seek more and more, gave me the greatest gfts parents can bestow on a chld: curosty, motvaton, and most of all love that s not condtoned on success or falure. Lastly, I thank my husband Casey Baker. The patence and devoton he dsplayed throughout ths process were nothng short of remarkable. As much as I sacrfced for ths degree, he sacrfced more.

7 v ABSTRACT Ths dssertaton conssts of three papers, each regardng a partcular aspect of the relatonshp between energy and agrculture. The objectve of the frst paper s to create a model that wll enhance nformed polcy decsons regardng the boeconomy. A forwardlookng stochastc model captures the effect of uncertanty n crude ol prces and commodty yelds on bofuel ndustry development. Acreage lmtatons on feedstocks such as corn, soybeans, and swtchgrass are shown to create competton for acreage among the crops. Investors n the model are ratonal n the sense that they engage n bofuel producton only f returns exceed what they expect to earn from alternatve nvestments. The Energy Independence and Securty Act of 2007 mandates the use of 36 bllon gallons of bofuels by 2022 wth sgnfcant requrements for cellulosc bofuel and bodesel producton. In the model, the prce wedge created by mandated bofuel producton at these levels s $2.50 per gallon for bodesel and $1.07 per gallon for cellulosc bofuel. Long-run commodty prces were hgh n our smulaton, wth corn at $7.38 per bushel and soybeans at $19.57 per bushel. Intense competton for planted acreage drves the hgh commodty prces. The second paper develops a model of the corn, soybean, and wheat markets to calculate welfare effects of ncreased bofuel producton n the Unted States. Demand s dsaggregated nto lvestock feed, food, energy. Uncertan crop yelds permt the valuaton of farm defcency payments as optons. Incorporatng soybean and wheat markets capture ndrect welfare effects through equlbrum prce ncreases. Net welfare loss ranges from $200 mllon to $750 mllon dependng on the sze of bofuel ncrease. Consumers make a

8 v szable transfer to farmers. The sgn of the net costs to taxpayers depends on the sze of the bofuel ndustry. In the thrd paper, the nature of the relatonshp between corn and ethanol prces s explored. Economc fundamentals should requre that the prce of corn and ethanol mantan a long run equlbrum relatonshp. The relatonshp s drven by a long run condton that says entry and ext n the ndustry wll occur mantanng no sustaned profts or losses for the ndustry. Both ethanol producers and tradtonal users of corn have a stake n the behavor of these markets, and ther proftablty wll rely on ther ablty to determne accurately ths relatonshp. I test for contegraton of these prce seres and fnd evdence that corn and ethanol prces are ndeed mantan an equlbrum relatonshp. Statstcal contegraton tests are known to have problems n small samples. Ths s a potental ssue n nterpretng the results mentoned above because ethanol producton only recently consttuted a sgnfcant porton of the corn crop. Wth only a few years of the most recent data for whch we suspect that an equlbrum relatonshp exsted the small sample propertes of contegraton tests are mportant partcularly n ths applcaton. A Monte Carlo study talored to mmc our actual data set s conducted. I fnd that the corn and ethanol prce seres are not long enough to rely on the asymptotc propertes of the contegraton statstcs, and therefore one should use small sample crtcal values n ths knd of analyss.

9 1 CHAPTER 1: GENERAL INTRODUCTION Introducton It s clear that agrcultural markets are ncreasngly nterdependent wth energy markets. U.S. agrculture has long been a consumer of energy as an nput, but wth ncreased bofuel producton stmulated by hgh transportaton fuel prces and governmental mandates agrculture s becomng a major producer of energy as well. Ths new facet n the relatonshp between agrculture and energy markets presents challenges and opportuntes for ndvdual producers of agrcultural commodtes and polcy makers. Ths dssertaton wll explore the nature of these new relatonshps, what they mean to wth regard to exstng polces and to tradtonal players n agrcultural markets. The U.S. government s bofuel polcy has been a mx of per unt tax credts and annual usage mandates. Increasng bofuel producton from commodtes grown on a (nearly) fxed amount of land has profound mplcatons for both the tradtonal users of the commodtes and for the cost to the taxpayer to mantan these programs. On one hand, a producton mandate requres a certan quantty of corn, soybeans, or cellulosc feedstock be devoted to bofuel producton. Wth a (nearly) fxed quantty of land n agrcultural producton, a bndng bofuel mandate causes prces of all agrcultural commodtes to rse. Ths means that the cost of producng bofuels ncreases snce the largest cost s n purchasng feedstock, whch causes the level of support requred n the form of tax credts and subsdes to ncrease to keep bofuel producers n producton. It has been argued that ncreased commodty prces caused by bofuel producton have decreased taxpayer s lablty n farm programs n the form of loan defcency payments

10 2 and counter cyclcal payments. The analyss n ths dssertaton fnds that n fact, ncreasng bofuel producton has a nonlnear effect on farm program labltes. A lttle bt of bofuel producton ncreases commodty prces out of the range where they are lkely to trgger farm program payments, but once commodty prces are hgh enough further ncrease makes almost no dfference n the taxpayer s expected payment to the farmer because ths value s already almost zero. Further, prevous research nto the welfare effects of U.S. bofuel polcy has focused prmarly on the welfare effects drven by acton n the energy markets. Ths dssertaton focuses on welfare transfers occurrng n the agrcultural markets, dsaggregatng demands to show the relatve sze of transfer among dfferent commodty usng sectors. Further, n ths dssertaton ndrect welfare effects are consdered n the soybean and wheat markets whereas prevous lterature only dscusses welfare effects n the corn market. Ths dssertaton partally flls a gap left by prevous research concernng the evolvng relatonshp of energy and agrculture. It attempts to provde nsght nto the way bofuel polcy affects commodty markets, exstng farm programs, and the welfare effects felt by economc agents n these markets. Dssertaton Organzaton Ths dssertaton s organzed nto fve chapters. The present chapter contans a general ntroducton nto the subject at hand, ncludng motvaton as to why the jont study of energy and agrculture s needed, and a descrbes the general organzaton of the dssertaton. Chapters two, three, and four are each concerned wth a specfc queston regardng the

11 3 relatonshp of energy and agrculture. Each of these chapters can be read ndependently as they are largely self contaned. In chapter 2 the objectve s to create a model that wll enhance nformed polcy decsons regardng the boeconomy. A forward-lookng stochastc model captures the effect of uncertanty n crude ol prces and commodty yelds on bofuel ndustry development. Acreage lmtatons on feedstocks such as corn, soybeans, and swtchgrass create competton for acreage among the crops, whch has to be taken nto account. Investors n the model are ratonal n the sense that they engage n bofuel producton only f returns exceed what they expect to earn from alternatve nvestments. These two nsghts drve the result that competton for acreage drves up commodty prces as well as ncreases the cost of supportng bofuel ndustres whch rely on land ntensve crops. Chapter 3 develops a model of the corn, soybean, and wheat markets to calculate welfare effects of ncreased bofuel producton n the Unted States. Demand s dsaggregated nto lvestock feed, food, energy. Uncertan crop yelds permt the valuaton of farm defcency payments as optons. Incorporatng soybean and wheat markets capture ndrect welfare effects through equlbrum prce ncreases. Net welfare loss ranges from $200 mllon to $750 mllon dependng on the sze of bofuel ncrease. Consumers make a szable transfer to farmers. The sgn of the net costs to taxpayers depends on the sze of the bofuel ndustry. In chapter 4 the nature of the relatonshp between corn and ethanol prces s explored. Economc fundamentals should requre that the prce of corn and ethanol mantan a long run equlbrum relatonshp. The relatonshp s drven by a long run condton that says entry and ext n the ndustry wll occur mantanng no sustaned profts or losses for the

12 4 ndustry. Both ethanol producers and tradtonal users of corn have a stake n the behavor of these markets, and ther proftablty wll rely on ther ablty to determne accurately ths relatonshp. I test for contegraton of these prce seres and fnd evdence that corn and ethanol prces are ndeed mantan an equlbrum relatonshp. Statstcal contegraton tests are known to have problems n small samples. Ths s a potental ssue n nterpretng the results mentoned above because ethanol producton only recently consttuted a sgnfcant porton of the corn crop. Wth only a few years of the most recent data for whch we suspect that an equlbrum relatonshp exsted the small sample propertes of contegraton tests are mportant partcularly n ths applcaton. A Monte Carlo study talored to mmc our actual data set s conducted. I fnd that the corn and ethanol prce seres are not lkely long enough to rely on the asymptotc propertes of the contegraton statstcs, and therefore one should use small sample crtcal values n ths knd of analyss. The fnal chapter contans general conclusons of the dssertaton, and summarzes the most nterestng fndngs.

13 5 CHAPTER 2: CROP-BASED BIOFUEL PRODUCTION WITH ACREAGE CONSTRAINTS AND UNCERTAINTY Introducton Congress sgned nto law the Energy Independence and Securty Act (EISA) n December The Renewable Fuel Standard, or RFS, n the EISA mandated the use of 36 bllon gallons of bofuels by 2022, of whch 15 bllon gallons can come from corn-based ethanol and 21 bllon must come from advanced bofuels ncludng 16 bllon of cellulosc bofuels and 1 bllon from bomass based desel. The text of the act provdes specfc yearby-year ramp up targets, even though growth n the producton of corn-based ethanol already was strong. In the year 2000, corn-based ethanol producton was 1.63 bllon gallons, and by the end of 2007 producton reached 6.50 bllon gallons. 2 The ncrease n corn-based ethanol producton led to record hgh nomnal corn prces n 2008, and competton for acreage transferred the demand pressure n corn markets to other crops soybeans and hay, for example causng the prces of these to ncrease as well. Ths paper examnes the ncentves requred to encourage producton of the mandated quanttes of bofuels and explore the mpact of these on U.S. agrculture. We present a model based on the assumpton that one can predct bofuel producton levels f one understands the factors nfluencng the decsons made by agents n the economy. Farmers make plantng decsons based on expected market prces. Further, 1 HR 6, The Energy Independence and Securty Act of 2007, avalable at 2 Industry reported levels found at

14 6 farmers recognze that land devoted to bofuel feedstock producton has an opportunty cost, they wll only grow bofuel feedstock such as swtchgrass for cellulosc ethanol producton f t s proftable to do so. Investors who buld bofuel plants do so only f they expect a rskadjusted return on par wth or superor to nvestments made elsewhere n the economy. Exstng plants operate only f the margnal cost of producton s less than the value of output. Those who blend and use bofuels do so only f the market prce of ethanol s less than the prces of alternatves. Takng each decson just descrbed, as well as parameters and data from the lterature, we model the decsons of relevant agents n the economy and the market forces gudng them. We combne the resultng sub-models wthn a stochastc smulaton model of U.S. crop and bofuel markets and calbrate t to reflect actual market condtons as of the sprng of We evaluate the response of market partcpants to changes n ncentves usng ths model. The expanson of bofuel producton happened quckly, and over a short number of growng seasons. The short amount of tme for whch data s avalable creates challenges n estmatng an econometrc model, but polcymakers stll need a tool wth whch to look forward. In order to help fll ths gap we develop a model that smulates the decsons of mportant players n the economy; provdng nsght about the mplcatons of many polcy choces. Prevous Lterature Elobed et al. (2007) provded the frst comprehensve model of the boeconomy. Later, Tokgoz et al. (2007) expand ths work, strengthenng some of ts elements. They nclude

15 7 equlbrum relatonshps for prces of bofuel co-products, most notably dstllers grans. Both use the world agrcultural model from the Food and Agrcultural Polcy Research Insttute (FAPRI) to determne the potental sze of the corn-based ethanol sector and to descrbe how t affects crop and lvestock markets. Frst, they assume bofuel nvestments wll contnue untl expected proft s zero, and they calculate the break-even corn prce that drves margns on new corn-based ethanol plants to zero. Second, they assume ths corn prce clears the market, and they calculate the sze of the bofuel sector requred to brng about ths prce. Fnally, once they determne the break even corn prce, they evaluate ts mpact on U.S. and world agrculture. They gnore bofuels from cellulose and bodesel because ther results suggest these are not economcally vable. They also gnore rsks assocated wth nvestments n bofuel plants. Our model enhances ths work by ncorporatng awareness of rsk nto the decson problem of the bofuel nvestor. Returns to bofuel producton prmarly are a functon of energy and feedstock prces, whch are uncertan. Crude ol prces are the man determnant of the prces of transportaton fuels such as gasolne, ethanol, and desel, and crop yelds affect feedstock costs through ts effects on equlbrum commodty prces. Incorporatng uncertanty n crude ol prces and crop yelds allows us to compare the rsk-adjusted return n the producton of each type of bofuel, determnng whch types are attractve to nvestors. Basng the nvestor s decson on rsk-adjusted returns s more realstc than usng a zero proft condton, whch mples a rsk-neutral nvestor. A stochastc model that delvers probablty dstrbutons over commodty prces and returns n the bofuel ndustry allows us to buld a model n whch the nvestor cares not only about the mean of returns but also about the varance.

16 8 The Model Economy The agrcultural economy has three goods: corn, soybeans, and swtchgrass. 3 Swtchgrass s a perennal grass natve to the U.S. tall-grass prare, and scentsts consder t a good canddate feedstock for cellulosc ethanol producton (Schmer, et al., 2008). The three major players n the economy are farmers, consumers (who are processors of cereal grans, olseeds, and lvestock), and nvestors. The consumers buy agrcultural commodtes and use them as nput n producng ether food or energy; nvestors can choose to buld a corn ethanol plant, a bodesel plant, or a swtchgrass ethanol plant. Alternatvely, they can smply choose to nvest n an alternatve we call the market portfolo. We ntroduce uncertanty through agrcultural commodty yelds and crude ol prces and assume the two random varables are ndependent wth jont probablty dstrbuton ζ, ζ f g h where ζ s a vector of yeld realzatons and s the realzaton of crude ol prces. By specfyng commodty yelds and crude ol prces as ndependent, we mplctly assume that shocks to domestc bofuel producton do not nfluence world crude ol prce shocks. Agents form expectatons about crude ol prces and future crop yelds. Farmers allocate acreage among corn, soybeans, and swtchgrass, and nvestors plan long-run capacty n the bofuel sectors. Acreage allocaton s carred out mplctly through tme, and we 3 We consder only corn, soybeans, and swtchgrass because we focus on the decson of a farmer who must allocate crop ground. Other cellulosc feedstocks such as woodchps are not well suted to crop ground (Lewandowsk et al., 2003).

17 9 assume that farmers choose the proporton of land n annual crops (an equlbrum cornsoybean rotaton) and land n the perennal, swtchgrass. Wth ths we avod dealng wth the dfference n the tmng of cost and payoff between the annual and perennal crops; what we lose n specfcty n the farmer s yearly decson s not pertnent to the results and permts us to work wth a cleaner model where we can focus on the long run results. Supply s determned by acreage allocatons and by crop yeld realzatons. Demand for the commodtes comes from the lvestock feed, human food and export sectors but s represented n the model by an aggregate demand functon. Demand from the bofuel sectors s determned by producton capacty, whch s determned by a long run equlbrum condton. We descrbe these components of the model n more detal below. Commodty Supply There exsts a sngle representatve and compettve farmer wth an endowment of land, who takes both output prces and hs cost functon as gven. The farmer allocates hs land to three dfferent crops: corn, soybeans, and swtchgrass. The crops are ndexed as follows: corn, = 1; soybeans, = 2; and swtchgrass, = 3. The endowed land s representatve of total U.S. cropland devoted to these commodtes. The farmer s per acre proft s gven by 3 (1) w p c ; 1 where p s crop s output prce, s the realzed per acre yeld of crop, and s the proporton of crop land allocated to crop. The cost functon for crop s ; c, where s a vector of parameters defnng each crop s cost functon. The set of parameters of the

18 10 cost functons of each crop are defned by Θ,, Aggregate (natonal) proft s then calculated by multplyng the per acre proft tmes the amount of acres n producton. The farmer s rsk neutral n proft; he wshes to maxmze expected proft subject to land constrants. To ths end, he chooses a land allocaton vector,, to solve the problem: (2) max Ew 1, 2, 30 s.t If we denote for crop the expected prce by p, the expected yeld for crop by, and the shadow value of land by, the Kuhn-Tucker condtons for ths problem are: ; c ; c p 0, 0, p 0 for = 1, 2, 3 and , 0, Assumng an nteror soluton, the frst order condtons are: c (3) p 0 for = 1, 2, 3 The farmer s prce expectatons are assumed to be such that, when combned wth demand, cause the ex-ante (but post plantng) prce dstrbuton to have a mean of p p p p The optmal acreage decsons combned wth yeld realzatons, ζ, gve the supply functon for each crop: s (4) Q p; μ, Θ, p; μ, Θ

19 11 Notce that both the expected output prce and producton cost of the other crops, enter each crop s supply functon. Commodty Demand d Demand for commodty s denoted by Q p, n ; commodty prces, p p p p The demands are a functon of, and the number of bofuel plants n operaton, n. The set of parameters defnng the demand functon s denoted by demand parameters s defned by Ω,, specfy functonal forms for the demand equatons., and the set of all three. Later, we mplement the model and The Investors In each perod, nvestors can choose among four dfferent optons: a corn-based ethanol plant, a bodesel plant, a swtchgrass ethanol plant, or an alternatve nvestment we call the market portfolo as n the captal asset prcng model (CAPM) of Sharpe (1964). The market portfolo functons as an opton f none of the bofuel nvestments are attractve. We assume nvestors seek the largest rsk-adjusted return on nvestment possble and we assume that there exsts a rskless asset n the economy returnng the rsk-free rate, RFR. Investors use the CAPM to evaluate nvestment alternatves; they calculate the securty market lne to measure the requred rate of return for an asset, a. (5) Requred Return RFR R RFR a a M R M where M s the market portfolo and s the expected return of the market portfolo. a s

20 12 defned by (6) Cov R, R a a 2 M M 2 where the varance of returns on the market portfolo s and R s the return of asset a. The nvestors calculate the dfference n the expected return and requred return of asset a as calculated wth the CAPM. The nvestors choose the project wth the hghest excess returns over the requred return. However, f the dfference s negatve for each of the bofuel plants, an nvestor wll choose to nvest n the market portfolo. As long as the bofuel ndustry earns excess returns over the requred return, t wll contnue to attract nvestment, and thus contnue to expand. M a Returns to Bofuel Producton Input costs n each sector are determned by feedstock, producton, and other captal costs. We do not consder technologcal advancement n the producton of bofuels; non-feedstock producton costs and captal costs are exogenous n the model. Feedstock costs are the most mportant nput cost to bofuel producton, and these are determned by market equlbrum. The annualzed per gallon rate of return to producng bofuel of type a s R a a qa. k p pergal The effectve prce receved by the plant for ts product s qa ; that s, the market prce of the bofuel plus any ncentve offered by the government such as the blenders tax credt. (7) q p tax credt a a a The market prce of bofuel, pa, s a functon of the crude ol prce realzaton,. The

21 13 pergal per gallon cost of producng bofuel of type a s a k p p NFcost pergal (8) pergal a a k p, where the per gallon feedstock cost s denoted by pergal p. That s, n the case of corn-based pergal ethanol producton, p 1 s the equlbrum prce of corn transformed nto a cost per gallon pergal of ethanol, n the case of bodesel producton, p 2 s the equlbrum prce of soybeans pergal transformed nto a cost per gallon of bodesel, and n the case of cellulosc ethanol, p 3 s the equlbrum prce of swtchgrass transformed nto a per cost per gallon of ethanol. The non-feedstock cost of producng bofuel of type a s whch s expressed per gallon and on an annual bass. NFcost a ; ths ncludes captal cost Ths relatonshp essentally measures the annual return on captal nvested over nput costs of the plant. Notce that the producton cost depends on the realzaton of the commodty prces. For example, n a year when crop yelds are relatvely poor producton costs wll be hgher than expected due to hgh equlbrum commodty (feedstock) prces. Lkewse, hgh energy prces mply hgh returns n the bofuel sectors because the output prce of bofuel wll be hgh. Long Run Compettve Equlbrum In our agrcultural economy, a long-run compettve equlbrum s defned by prcng functons p,,,, ζ n Ω Θ for 1, 2, 3 d crop demand functons Q p; n, Ω for 1, 2, 3 s crop supply functons Q ;, p Θζ for 1, 2, 3

22 14 nvestment functons n, p for 1, 2, 3 Gven the prcng functons, bofuel plants n operaton, crop yeld realzatons, and crude ol prces, commodty markets clear. That s, s d (9) Q ;, Q ; n, p Θ ζ p Ω for 1, 2, 3 The long-run equlbrum condton requres that, at the margn, the returns of each project equal the requred rsk-adjusted returns as determned by the CAPM: R p, n RR corn ethanol R p, n RR bodesel R p, n RR swtch ethanol corn ethanol bodesel swtch ethanol where RR s the requred return to bofuel prodcton as determned by the CAPM. The zero excess return condtons ensure we have nvestment n each sector untl the prces of feedstock (corn, soybeans, and swtchgrass) are bd up to the pont at whch an nvestor s ndfferent between any of the bofuel plants and the market portfolo. If the return to bofuel producton s less than the requred return for all ndustry szes, then nvestment equals zero n ths bofuel sector. Implementng the Model Our queston s emprcal n nature. The ncentves present for the bofuel ndustry to expand or contract depend on many factors, some of whch are the prce of crude ol, demand for corn and soybeans for food uses, and weather varablty. Explorng more than the most basc results of ths model requres us to specfy functonal forms and evaluate the results

23 15 numercally va the Monte Carlo method. 4 We calbrated the model to sprng 2008, when producers of corn, soybeans, and swtchgrass (hay) were makng acreage decsons. Algorthm for Smulatng the Model Our strategy for smulatng the economy s to specfy functonal forms for both crop supply and demand and to calbrate the dstrbuton of crude ol prces and crop yelds. A jont draw from these dstrbutons mples an equlbrum prce for corn, soybeans, and swtchgrass and thus mples return levels n each bofuel ndustry. The smulaton algorthm s as follows: 1) Form crop yeld and crude ol prce dstrbutons and make jont draws. Calculate bofuel prces from the crude ol prce draws 2) Solve for the equlbrum crop prces for each draw usng the market clearng condtons on crop supply and demand for a gven level of bofuel capacty 3) Calculate the mpled dstrbuton of returns to bofuel producton usng the bofuel prces from (1) and equlbrum crop (feedstock) prces from (2) 4) Determne the tax credt or subsdy level on each bofuel type requred n order for the long run (zero excess return) condton to be met For example, settng the levels of bofuel producton hgh (as n the EISA RFS) causes crop prces to ncrease, due to the ncrease n demand for these commodtes. Ths ncrease n crop (feedstock) prces causes returns to bofuel producton to shrnk and ordnarly would cause the ndustry to contract. If ths s the case, we calculate the subsdy on the sale of bofuel output requred to keep the plants just ndfferent between operatng and not. The followng subsectons descrbe the detals of mplementng ths algorthm further. Commodty Supply We assume the nomnal cost functons of the crops are quadratc, gven by 4 All smulatons were conducted n Matlab.

24 16 2 1, 2, 3 c a 1, 2, 3. The proporton of land allocated to each crop,, s the farmer s choce varable. Ths specfcaton works well because we can separate out ncreasng and constant margnal producton costs, and use the Economc Research Servce (ERS) commodty cost and return budgets as estmates for corn and soybeans. 5 ERS does not keep data on cost and returns to producng grass hay; nstead, we use a producton budget from Oho State Unversty Extenson n The yeld realzatons, ζ, are drawn from the jont beta dstrbuton of yelds usng the algorthm developed by Magnussen (2004). 5 Avalable at The parameters are calbrated to the most recent estmates avalable (2006 crop year), and nflated by the expected percent ncrease n crude ol prces from 2006 to The prce of crude ol n 2006 was $60 per barrel; we run several dfferent long-run crude ol prce scenaros. From the ERS budgets we use fertlzer cost as a proxy for the ncreasng margnal cost porton,, and all other operatng costs as the constant margnal cost porton, a. 6 Avalable at These costs from 2003 are nflated to 2012 levels n the same manner as for corn and soybeans. As wth corn and soybeans, we assume fertlzer s the only element of the ncreasng margnal cost porton,, and all others contrbute to the constant margnal cost 3 porton, a. 3

25 17 corn 1 ζ ~ soybean,, qmax, qmn swtchgrass , q t max corn soybean 2 corn 2 soybean, 2swtchgrass swtchgrass q t mn corn soybean 3 swtchgrass corn 3 soybean 3 swtchgrass The mean of the beta dstrbuton s μ ', wth corn and soybeans n bushels per acre and swtchgrass n tons per acre. Snce trend yelds are mportant (especally for corn), we need to set the mean at a partcular year s trend level. Recall that the long run, n our model, s the length of tme approxmately necessary for the bofuel sectors to reach maturty gven current technology. We set the trend at year , 8 The matrx 1 s the 7 We assume yelds follow a lnear trend, whch we estmated from hstorcal yeld data for the years 1980 through 2006, mantaned by the Natonal Agrcultural Statstcs Servce ( t t t t, t, t corn soybean swtchgrass

26 18 varance-covarance matrx for the yelds of the three crops, and the are the standard 1 devatons of each crop found n. Commodty Demand We specfy a constant elastcty, reduced-form demand functon for each crop; we use the ntermedate term own- and cross-prce demand elastctes for beef from the ERS/Penn State Trade Model 9 as our estmates. The prce dstrbuton of crude ol nfluences commodty demands ndrectly through the number of bofuel plants of each type (corn ethanol, bodesel, and cellulosc ethanol). In our smulaton, crude ol prces are lognormal and 10, 11 calbrated to match current condtons n the futures market: (10) 3 p Ω d Q ; n, p p p n for 1, 2, 3 One of the equlbrum condtons requres the number of bofuel plants n each ndustry to be such that there are no excess returns over the requred return. The parameter 8 Ths s gven n per harvested acre. We use alfalfa as a proxy for swtchgrass yelds, snce the tonnage per acre s approxmately equvalent to the swtchgrass yelds projected n the lterature. 9 Model documentaton of the ERS/Penn State Trade Model can be found at 10 The prces of other fuels (e.g., gasolne and bodesel) are based on ther relatonshp to crude ol prces. 11 Impled volatlty n crude ol prces s estmated from 2007 opton data. We vary the mean of the crude ol prce dstrbuton n dfferent scenaros: $100, $150, and $200 per barrel.

27 19 4 s an elastcty measurng the percentage change n quantty demanded of the crop over the percentage change n bofuel capacty, whch depends only on the converson factor of feedstock to bofuel. Accountng for Cellulosc Ethanol from Corn Stover and Wood Chps Bomass sources that do not compete drectly for acres wth hgh-value crops, such as corn and soybeans, would not have large mplct land costs. Snce corn stover and woody bomass do not compete for crop acreage, t seems reasonable to assume the RFS for cellulosc ethanol of 16 bllon gallons per year wll only be met wth a contrbuton of feedstock from these sources f more land-ntensve bomass lke swtchgrass s proftable, stover and woody bomass wll be proftable also. Because ths producton occurs outsde the framework of our model, we need to make assumptons about how much ethanol wll be produced from these sources. We assume ethanol from both corn stover and woody bomass s produced when the economy produces a nonzero amount of swtchgrass ethanol. It remans unclear exactly how much cellulosc ethanol wll come from the sources not competng for land wth tradtonal crops, so we present several scenaros varyng the amount of cellulosc ethanol that must come from swtchgrass to meet the mandate. Calculatng Returns to Bofuel Producton Returns to bofuel producton are affected most by feedstock costs and governmental polcy, wth feedstock costs determned endogenously n the model. Ethanol and cellulosc ethanol plants use corn and swtchgrass as feedstock, but bodesel uses soy ol (not soybeans drectly) as feedstock. Our model produces equlbrum soybean prces but not soy ol prces.

28 20 We estmate a smple lnear relatonshp between the prce of soybeans and the prce of soy ol usng recent data: 12 Soy Ol Prce = Soybean Prce R Each bofuel producton process generates a co-product, whch creates value and offsets some feedstock cost. Corn ethanol produces dred dstllers grans, dred dstllers grans wth solubles (DDGS), or wet dstllers grans, whch are used n beef, pork, and poultry ratons. Dstllers grans have approxmately the same dgestble energy content as corn, so we gve credt to corn ethanol plants for DDGS consstent wth ts ablty to substtute for corn (Shurson et al., 2003). The bodesel producton process yelds glycern, fatty acds, and flter cakes. We credt 8 per gallon to the bodesel producer based on recent market value for these co-products (Paulson and Gnder, 2007). Producton of ethanol from swtchgrass produces lgnn, whch s combustble and used to generate electrcty wthn the faclty, or sold back to the electrcal grd (Aden et al., 2002). We credt swtchgrass ethanol wth 10 per gallon as suggested n Aden et al. The per gallon non-feedstock costs of producng corn-based ethanol and cellulosc ethanol are 76 per gallon and 97 per gallon, respectvely, whle the non-feedstock cost of producng bodesel s 55 per gallon (Paulson and Gnder, 2007; Tokgoz et al., 2007). A bofuel plant s revenue relates drectly to crude ol prces through the relatonshp between crude ol, ethanol, and desel. We estmate the prce of ethanol and desel as determnstc lnear functons of the prce of crude ol, usng monthly spot prces from 12 We estmated the relatonshp from the daly nearest cash prces on the CBOT from October 17, 2005, to September 14, 2007.

29 21 January 1994 through August 2007 of the Cushng Oklahoma crude ol, New York Harbor conventonal gasolne, and U.S. No. 2 wholesale/resale markets: 13 Wholesale Gasolne Prce = Crude Ol Prce Wholesale Desel Prce CrudeOl Prce 2 R R 0.98 E10 (10% ethanol, 90% gasolne) s used for ts ablty to oxygenate gasolne, whch enhances combuston and reduces emssons (NSTC, 1997). Followng Tokgoz et al. (2007), we assume, based on the demand-sde model, that when annual producton s greater than 15 bllon gallons per year, the E10 market becomes saturated, causng ethanol to be prced at the margn accordng to ts energy value (about two-thrds) compared to gasolne (Shapour et al., 1995). When producton s below ths threshold, we assume ethanol s prced at a premum to gasolne and valued for ts propertes as an addtve (Hurt et al., 2006). We nterpolate between the addtve and energy value to preserve a contnuous prcng rule as follows: 1.05* Pgasolne f ethanol producton 14 bl gal Pethanol * Pgasolne f 14 bl gal ethanol producton 16 bl gal.667* Pgasolne f ethanol producton 16 bl gal ethnaol producton 14 where Hstorcal data mantaned at

30 22 Results We mpose bofuel producton at levels set n the RFS of the EISA of 2007 and consder the boeconomy s equlbrum outcomes for three dfferent long-run crude ol prce scenaros. After mposng the bofuel producton levels, our model allows us to solve for the level of subsdy (tax credt) requred to mantan the zero-excess-return condton, n addton to delverng long-run equlbrum crop prce dstrbutons and acreage allocatons. For a crude ol prce of $150 per barrel corn has a mean long-run equlbrum prce of $7.38 per bushel; soybeans, $19.57 per bushel; and swtchgrass, $ per ton. Long-run equlbrum acreage allocatons are 48% of acres n corn, 27% n soybeans, and 22% n swtchgrass or hay. Ths s equvalent to 105 mllon acres of corn, 59 mllon acres of soybeans, and 48 mllon acres of swtchgrass or hay. 14 We compare the level of tax credt requred to mantan the no-excess-return condtons across dfferent crude ol prce scenaros. Table 2 dsplays the results. We could not say, a pror, whether hgh crude ol prces mply hgher or lower tax credt levels requred to acheve long-run equlbrum at the mandated bofuel quanttes. Crude ol prces act on bofuel returns n two ways: hgh crude prces mply hgh bofuel prces, postvely affectng returns, but n addton, hgh crude prces have a negatve effect on returns through upward pressure on commodty prces. Wthout smulatng the model, we cannot determne f the postve or negatve effect s stronger; table 1 llustrates, however, that as crude ol prces 14 Compare ths wth 93 mllon acres, 63.6 mllon acres, and 61.5 mllon acres n corn, soybeans, and hay, respectvely, n 2007.

31 23 rse, the tax credt requred to mantan the producton targets decreases. Table 1: Long-run results under dfferent tax credts, RFS mandate, and crude ol prce scenaros E p crude E p corn E p sb E p sg New RFS Low Crude New RFS Md Crude New RFS Hgh Crude ($/barrel) $100 $150 $200 ($/bu) $7.40 $7.38 $7.33 ($/bu) $19.64 $19.57 $19.38 ($/ton) $ $ Land Allocatons ( ) ( ) ( ) Producton Corn (ml bu) 16,760 16,760 16,760 Soybeans (ml bu) 2,908 2,908 2,908 Swtchgrass (ml tons) Usage Bofuel Non-bofuel Bofuel Non-bofuel Bofuel Non-bofuel Corn (ml bu) 5,357 11,402 5,357 11,402 5,357 11,402 Soybeans (ml bu) Swtchgrass (ml tons) Corn ethanol producton (mllon gallons) Bodesel producton a (mllon gallons) Swtchgrass ethanol producton (mllon gallons) Tax credt Corn ethanol ($/gal) Tax credt bodesel ($/gal) Tax credt cellulosc ethanol ($/gal) 15,000 15,000 15,000 1,000 1,000 1, $0.80 $0 $0 $4.10 $2.50 $0.88 $2.04 $1.07 $0.10

32 24 Land allocatons, under the EISA RFS, shft toward crops whose assocated fuels are mandated at a hgh level. Incentves provded to the greener fuels dffuse through the economy and cause a shft n land use patterns, and the ncreased usage of all the crops for bofuels cause hgher commodty prces than n the baselne. If the cellulosc mandates are desgned to avod the feed-versus-fuel trade-off, our results suggest t wll actually exacerbate the problem by nducng hgher feedstuff costs than under the polcy n whch only corn ethanol s produced. Wth a fxed amount of land, t s mpossble to ncrease the amount of each crop devoted to energy and mantan the same level of consumpton of each commodty for food. Wth mandates reducng the prce senstvty of bofuel producers, the other users of the crops, namely food producers, adjust most. Senstvty of Results to Requred Levels of Swtchgrass Producton The amount of cellulosc ethanol than can be feasbly produced from corn stover and woody bomass s uncertan. Ths amount wll be a sgnfcant factor n determnng long-run commodty prces and land use patterns because the amount of cellulosc ethanol not covered by corn stover and woody bomass must be made up wth land-ntensve bomass crops such as swtchgrass. The more land-ntensve bomass needed to meet the cellulosc ethanol requrements, the greater the ntensty of competton for acreage. Table 2 presents the results of several scenaros ncreasng the amount of swtchgrass ethanol needed to meet the new RFS. In the frst scenaro, we consder the case n whch the new standard for cellulosc ethanol s met exclusvely wth corn stover and woody resdue wth no land ntensve bomass needed. Note that we calculate that the subsdy gven to cellulosc ethanol (ncludng corn stover and wood chp ethanol) can be as hgh as $1.07 per

33 25 gallon before the swtchgrass ethanol sector begns to expand. The fnal scenaro requrng 750 mllon gallons of swtchgrass ethanol per year requred tax credts of $0.46, $5.26, and $2.69 for corn ethanol, bodesel and swtchgrass ethanol, respectvely. Wth ncreasng requrements on land-ntensve swtchgrass ethanol, we see hgher commodty prces and hgher subsdy levels needed to mantan the mandated bofuel quanttes.

34 26 Table 2: Senstvty of crop prces and requred subsdy levels to ncreasng swtchgrass ethanol levels Land Allocatons E p crude E p corn E p sb E p sg Producton New RFS Md Crude New RFS Md Crude New RFS Md Crude New RFS Md Crude ($/barrel) $150 $150 $150 $150 ($/bu) $7.38 $9.12 $9.57 $9.66 ($/bu) $19.57 $25.53 $27.09 $27.42 ($/ton) $ $ $ $ ( ) ( ) ( ) ( ) Corn (ml bu) 16,760 15,846 15,723 15,648 Soybeans (ml bu) 2,908 2,656 2,633 2,613 Usage Swtchgrass (ml tons) Bofuel Bofuel Bofuel Bofuel Nonbofuel Nonbofuel Nonbofuel Nonbofuel Corn (ml bu) 5,357 11,402 5,357 10,489 5,357 10,366 5,357 10,291 Soybeans (ml bu) , , ,931 Swtchgrass (ml tons) Corn ethanol producton (mllon gallons) Bodesel producton a (mllon gallons) Swtchgrass ethanol producton (mllon gallons) Tax credt corn ethanol ($/gal) Tax credt bodesel ($/gal) Tax credt cellulosc ethanol ($/gal) ,000 15,000 15,000 15,000 1,000 1,000 1,000 1, $0 $0.30 $0.41 $0.46 $2.50 $4.57 $5.10 $5.26 $1.07 $2.29 $2.59 $2.69

35 27 Conclusons Competton for land ensures that polcy provdng an ncentve to even one type of bofuel and ndrectly to the crop t uses as feedstock wll ncrease the equlbrum prces of all crops. Ths means n order for swtchgrass ethanol to be commercally vable, t must receve a dfferental subsdy over that awarded to corn-based ethanol. Homogeneous subsdy levels for both types of ethanol cannot entce expanson of swtchgrass ethanol. Snce swtchgrass competes for the same acres as corn, and corn-based ethanol s less expensve to produce, corn-based ethanol wll always have a comparatve advantage over swtchgrass ethanol n the absence of a dfferental subsdy. Corn and soybeans also compete for the same acreage, so when energy prces are such that corn-based ethanol expands, the prce of soybeans also ncreases, ensurng that a farmer allocates some land to soybeans. Ths ncrease n soybean prces reduces the proftablty of bodesel even n scenaros n whch energy prces are hgh; and under pre- EISA subsdy levels, the soy ol bodesel sector s not vable under any energy prce consdered. If the EISA mandates are to be met n a voluntary fashon, the bodesel sector requres a hgher subsdy, relatve to corn-based ethanol, than t has today. We calculate the subsdes requred to stmulate bofuel producton to levels mandated n the EISA RFS and fnd that subsdy levels need to be n the range of $0 to $0.80 per gallon for corn ethanol, and $0.88 to $4.10 per gallon for bodesel, even assumng the cellulosc ethanol standard can be met solely wth corn stover and woody bomass. Future crude ol prces largely determne the subsdy levels requred to mantan ndustry szes requred by the EISA RFS.

36 28 Meetng the RFS causes much hgher commodty prces than n the baselne, suggestng the cellulosc mandate n the EISA whch appear desgned to avod the feedversus-fuel trade-off may actually exacerbate the stuaton relatve to the scenaro wth corn-based ethanol only. Cellulosc ethanol s more expensve to produce, and swtchgrassbased ethanol s more land ntensve than corn-based ethanol. We calculate that the tax credts requred to mantan ndustry szes prescrbed n the 2007 RFS are between $0 to $0.46, $2.56 to $5.26, and $1.07 to $2.69 for corn ethanol, bodesel and swtchgrass ethanol, respectvely. The severty of upward pressure on commodty prces caused by the new RFS wll be determned largely by the ablty to produce cellulosc ethanol from bomass that s not land ntensve: polces that expand cellulosc ethanol beyond levels that can be suppled by corn stover and woody bomass are more expensve n terms of the subsdy requred and the resultng ncrease n food and feed prces. References Aden, A., Ruth, M., Ibsen, K., Jechura, J., Neeves, K., Sheehan, J., Wallace, B., Montague, L., Slayton, A., Lukas, J Lgnocellulosc bomass to ethanol process desgn and economcs utlzng co-current dlute acd prehydrolyss and enzymatc hydrolyss for corn stover. NREL/TP Natonal Renewable Energy Laboratory, Golden, CO. Elobed, A., Tokgoz, S., Hayes, D.J., Babcock, B.A., Hart, C.E The long-run mpact of corn-based ethanol on the gran, olseed, and lvestock sectors: a prelmnary assessment. AgBoForum 10 (1),

37 29 Hurt, C., Tyner, W., Doerng, O Economcs of ethanol. (ID-339). Purdue Unversty Cooperatve Extenson. /ID-339.pdf (accessed Feb. 2008). Lewandowsk, I., Scurlock, J., Lndvall, E., Chrstou, M The development and current status of perennal rhzomatous grasses as energy crops n the US and Europe. Bomass and Boenergy 25, Magnussen, S An algorthm for generatng postvely correlated beta-dstrbuted random varables wth known margnal dstrbutons and a specfed correlaton. Computatonal Statstcs & Data Analyss 46 (2), NSTC. Natonal Scence and Technology Councl, Commttee on Envronment and Natural Resources Interagency assessment of oxygenated fuels. Report to the Offce of the Presdent of the Unted States, Washngton, DC. Paulson, N.D., Gnder, R.G The growth and drecton of the bodesel ndustry n the Unted States. CARD Workng Paper 07-WP 448, Center for Agrcultural and Rural Development, Iowa State Unversty. Schmer, M. R., et al. "Net energy of cellulosc ethanol from swtchgrass." Proceedngs of the Natonal Academy of Scences 105, no. 2(2008): 464. Shapour, H., Duffeld, J.A., Grabosk, M.S Estmatng the net energy balance of corn ethanol. Agrcultural Economc Report No U.S. Department of Agrculture, Economc Research Servce, Offce of Energy and New Uses. Sharpe, W.F Captal asset prces: A theory of market equlbrum under condtons of rsk. Journal of Fnance 19 (3),

38 30 Shurson, J., Spehs, M., Wlson, J., Whtney, M Value and use of new generaton dstller s dred grans wth solubles n swne dets. Alltech s 19th Internatonal Feed Industry Proceedngs, May 12-14, Lexngton, KY. Tokgoz, S., Elobed, A., Fabosa, J.F., Hayes, D.J., Babcock, B.A., Yu, T-H., Dong, F. F., Hart, C.E., Beghn, J.C Emergng bofuels: Outlook of effects on U.S. gran, olseed, and lvestock markets. CARD Staff Report 07-SR 101, Center for Agrcultural and Rural Development, Iowa State Unversty. Appendx: Supplemental Table The followng table contans a summary of the parameter values used to mplement the smulaton. The frst two columns contan supply parameters and the remanng columns contan demand parameters for each commodty under consderaton. Table 3: Parameters used n Monte Carlo smulaton a Corn Soybeans Swtchgrass

39 31 CHAPTER 3: WELFARE CHANGES FROM INCREASED BIOFUEL PRODUCTION ON U.S. AGRICULTURE: THE ROLE OF UNCERTAINTY AND INTERLINKED COMMODITY MARKETS Introducton Ethanol producton ncreased more than fve hundred percent snce the turn of the century 15. Stmulated by a combnaton of tax ncentves, a renewable fuel standard 16, and strong energy prces, the ndustry has experenced seemngly exponental growth (see fgure 1). Ethanol currently s produced almost exclusvely from corn, meanng that each gallon of ethanol produced dverts some corn away from ts alternatve uses, whch are food for humans and feed for lvestock. Increased ethanol producton amounts to a shft outward n the demand for corn, and t s mportant to understand the dstrbutonal mpact of ths shft on other agrcultural sectors. In ths paper we hope to llumnate some pertnent ssues n quantfyng these welfare effects and contrbute to the dscusson that has evolved regardng ther nature and magntude. 15 Accordng the Renewable Fuels Assocaton ndustry statstcs 16 The Amercan Jobs Creaton act of 2004 (H.R. 4520) provded a $0.51 per gallon Volumetrc Ethanol Excse Tax Credt to blender s ethanol whch was reduced to $0.45 per gallon as of January 1, 2009, and the Energy Securty and Independence Act of 2007 (H.R.6) gradually ncreases the Renewable Fuel Standard to 36 bllon gallons per year by 2022.