EXTENSIONS OF A MAXIMUM ENTROPY ESTIMATED MARKOV DECISION PROCESS IN THE UNITED STATES AGRICULTURAL ECONOMY. A Dissertation.

Transcription

1 EXTENSIONS OF A MAXIMUM ENTROPY ESTIMATED MARKOV DECISION PROCESS IN THE UNITED STATES AGRICULTURAL ECONOMY A Dsseraon presened o he Faculy of he Graduae School a he Unversy of Mssour-Columba In Paral Fulfllmen of he Requremens for he Degree Docor of Phlosophy by DUSTIN J. DONAHUE Dr. Wya Thompson Dsseraon Supervsor DECEMBER 2013

2 The undersgned apponed by he dean of he Graduae School have examned he dsseraon enled: EXTENSIONS OF A MAXIMUM ENTROPY ESTIMATED MARKOV DECISION PROCESS IN THE UNITED STATES AGRICULTURAL ECONOMY Presened by Dusn J. Donahue A canddae for he degree of docor of phlosophy And hereby cerfy ha n her opnon s worhy of accepance. Professor Wya Thompson Professor Pa Weshoff Professor Wll Meyers Professor Doug Mller Professor Felx Frsch

3 DEDICATION The auhor dedcaes hs wor To hs parens for her never-endng and unfalng suppor of hs endeavors; To hs broher for showng hm he power of a man commed o duy; To Terry Seve Russ and he Brehren of Chaanooga Lodge #199 F&AM for provdng hm wh gudance and fraernal love above and beyond ha whch he can ever reurn; To he CoMo Derby Dames for exposng hm o a world ha he never new exsed and for provdng hm a large exended famly far from home; To Zad for seng hm on hs pah and belevng he could succeed; To Waffles for beng hs long-me long-dsance confdan and soundng board; To hs frends and relaves for remndng hm from whence he came.

4 ACKNOWLEDGEMENTS I wsh o express my graude o my advsor Dr. Wya Thompson. Long were he dscussons near argumens over pons of my research ha needed o be changed. Hs paence wh my subbornness s a esamen o hs characer. I would also le o han my commee members for her commens and consrucve feedbac ha hey provded. Ther nsghs have helped o mae me a beer economs loong a all angles of an ssue. I am graeful o he Uned Saes Deparmen of Agrculure s Naonal Insue of Food and Agrculure for awardng me he Naonal Needs Fellowshp whch provded me wh he ably o pursue my docoral degree. I am lewse graeful o he Unversy of Mssour Deparmen of Agrculural and Appled Economcs for s suppor. ~ Dusn J. Donahue

5 TABLE OF CONTENTS ACKNOWLEDGEMENTS... LIST OF FIGURES... v LIST OF TABLES...v ABSTRACT... v I. INCORPORATING DYNAMIC LAND USE INTO A PARTIAL EQUILIBRIUM MODEL: TEST CASES IN MISSOURI AND IOWA 1. Inroducon Pror Leraure Marovan Land Use Decson Process Paral Equlbrum Model Daa and Scope of Model Addonal Specfcaons Model Consrans Model Valdaon Smulaon Resuls: Consan Coeffcen vs. MDP Comparson Concluson References Appendx: Fgures and Tables...28 II. AN ECONOMIC EXAMINATION OF MIDWESTERN WARM SEASON GRASS AREA USING SATELLITE IMAGING DATA 1. Inroducon Pror Leraure Marovan Land Use Decson Process Daa: WSG Reurns Daa: Oher Reurns Daa: Acreage Shares Daa: Pror Probables Spaal Correlaon Issues Consraned and Unconsraned Models WSG Reurns Shoc and Area Response Corn Ne Reurns Shocs and Area Response Concluson References Appendx: Fgures and Tables...65

6 III. A DYNAMIC ESTIMATION OF AN ILL-POSED US FEED DEMAND SYSTEM WITH DISTILLER S DRIED GRAINS 1. Inroducon Pror Leraure Marovan Feed Use Decson Process Daa: Feed and Resdual Use Daa: Explanaory Varables In Sample Dynamc Valdaon Model Elasces Proecon Daa Proecon Shocs and Resuls Concluson References Appendx: Fgures and Tables VITA v

7 LIST OF FIGURES Fgure Page 1.1 Illusraon of he MDP-SPE Model Framewor Marov Decson Process Model and Consan Coeffcen Model Corn and Soybean Acres Planed Comparson o Hsorcal Daa Iowa Marov Decson Process Model and Consan Coeffcen Model Corn and Soybean Acres Planed Comparson o Hsorcal Daa Mssour Mdwesern Land Covers Observed by MODIS Indcaon of Presence for Sx Ou of Ten Years Corn Ne Reurns o Corn Area Planed Elasces Couny Level Aggregaon Unconsraned Corn Ne Reurns o Corn Area Planed Elasces CRD Level Aggregaon Unconsraned Pasureland Renal Rae o Whea Area Planed Elasces Couny Level Aggregaon Unconsraned Pasureland Renal Rae o Whea Area Planed Elasces CRD Level Aggregaon Unconsraned Soy Ne Reurns o Corn Acres Planed Elasces CRD Level Unconsraned Pasureland Renal Rae o Warm Season Grass Acres Elasces CRD Level Unconsraned Ne Reurns Elasces CRD Level Consraned Model Hsorcal Warm Season Grass Area by CRD as a Percen of Toal Land Average Change n WSG Area n Response o Doubled WSG Reurns Average Measured n 1000 Acres a Change n WSG Area n Response o Doubled WSG Reurns Average Measured as a Percen of Base Scenaro Acres Change n Whea Area n Response o Doubled WSG Reurns Average Measured n 1000 Acres a Change n Whea Area n Response o Doubled WSG Reurns Average Measured as a Percen of Base Scenaro Acres Change n Soybean Area n Response o Doubled WSG Reurns Average Measured n 1000 Acres a Change n Soybean Area n Response o Doubled WSG Reurns Average Measured as a Percen of Base Scenaro Acres Change n Corn Area n Response o Doubled WSG Reurns Average Measured n 1000 Acres a Change n Corn Area n Response o Doubled WSG Reurns Average Measured as a Percen of Base Scenaro Acres Change n Corn Area n Response o Lower Corn Ne Reurns Average Measured n 1000 Acres...75 v

8 2.14a Change n Corn Area n Response o Lower Corn Ne Reurns Average Measured as a Percen of Base Scenaro Acres Change n Warm Season Grass Area n Response o Lower Corn Ne Reurns Average Measured n 1000 Acres a Change n Warm Season Grass Area n Response o Lower Corn Ne Reurns Average Measured as a Percen of Base Scenaro Acres Change n Soy Area n Response o Lower Corn Ne Reurns Average Measured n 1000 Acres a Change n Soy Area n Response o Lower Corn Ne Reurns Average Measured as a Percen of Base Scenaro Acres Change n Whea Area n Response o Lower Corn Ne Reurns Average Measured n 1000 Acres a Change n Whea Area n Response o Lower Corn Ne Reurns Average Measured as a Percen of Base Scenaro Acres Change n Corn Area n Response o Hgher Corn Ne Reurns Average Measured n 1000 Acres a Change n Corn Area n Response o Hgher Corn Ne Reurns Average Measured as a Percen of Base Scenaro Acres Hsograms of Changes n Area Allocaed o Each Crop as a Percen of Toal Area by Scenaro +/- 21.9% n Corn Ne Reurns Average DDG Producon Corn Feed and Resdual Use as a Percen of Toal Feed and Resdual Use Hsorcal Amouns versus Dynamc Model Esmaes Soy Meal Feed and Resdual Use as a Percen of Toal Feed and Resdual Use Hsorcal Amouns versus Dynamc Model Esmaes DDG Feed and Resdual Use as a Percen of Toal Feed and Resdual Use Hsorcal Amouns versus Dynamc Model Esmaes DDG Prce o Feed and Resdual Use (as a Percen of Toal Feed and Resdual Use) Elasces by Feedsoc DDG Feed and Resdual Use as a Percen of Toal Feed and Resdual Use Proecons Baselne Hgh DDG Prce (125%) and Low DDG Prce (75%) Shocs Corn Feed and Resdual Use as a Percen of Toal Feed and Resdual Use Proecons Baselne Hgh DDG Prce (125%) and Low DDG Prce (75%) Shocs Soy Meal Feed and Resdual Use as a Percen of Toal Feed and Resdual Use Proecons Baselne Hgh DDG Prce (125%) and Low DDG Prce (75%) Shocs a Soy Meal Feed and Resdual Use as a Percen of Toal Feed and Resdual Use Proecons Baselne Hgh DDG Prce (125%) and Low DDG Prce (75%) Shocs Soy Meal Feed and Resdual Use (as a Percen of Toal Feed and Resdual Use) o DDG Prce Elasces Baselne Hgh DDG Prce (125%) and Low DDG Prce (75%) Shocs v

9 LIST OF TABLES Table Page 1.1 Marovan Land Transon Probables n Iowa Demand Equaon Prce Elasces Comparson of Ne Reurns o Acres Planed Elasces wh Measures of F (Mean Absolue Errors) Unconsraned MDP Models versus MDP Model Consraned wh Coeffcen Consrans and/or Non-Unform Pror Probables Iowa Imposed Non-Unform Pror Probables for Consraned Marovan Model Comparson of Hsorcal Ou of Sample Daa wh MDP-PE and CC-PE Model Base Scenaro Esmaes Dfferences beween Esmaed Marovan and Consan Coeffcen Model Base Scenaros Consan Coeffcen Model Shoc Esmaes Subraced from Marov Model Shoc Esmaes Marov Model Scenaro Dfferences 3.0 Bllon Gallon Shoc Mnus Baselne Scenaro Consan Coeffcen Model Scenaro Dfferences 3.0 Bllon Gallon Shoc Mnus Baselne Scenaro Dfference of Dfferences Across he Marov and Consan Coeffcen Models Consan Coeffcen Model Shoc Dfference Esmaes Subraced from Marov Model Shoc Dfference Esmaes Example Marovan Land Transon Probables Shares and Expeced Ne Reurns by Crop Averaged Across Seleced CRDs and All Sample Years Pror Marov Probables Implemened n Model Percen Mean Absolue Error by Crop Model Aggregaon Comparson Model Percen Mean Absolue Errors by Crop Model Consran Comparson Regonal Acreage n Mllon Acres by Crop Across Base and Shoc Scenaros Average / /05 MDP Transon Probables Feedsoc Sample Mean and Sandard Devaon n Mllon Tons Explanaory Varables Uns Means and Sandard Devaons Percen Mean Absolue Errors by Crop T-Sascs of Model Coeffcen Esmaes by Feedsoc Model Esmae Elasces Average Feedsuff Subsuon Elasces FAPRI Baselne Elascy-Analogous Sysem Impac Mulplers for DDG Feed Use Feed Use Elasces by Feedsoc v

10 EXTENSIONS OF A MAXIMUM ENTROPY ESTIMATED MARKOV DECISION PROCESS IN THE UNITED STATES AGRICULTURAL ECONOMY Dusn J. Donahue Dr. Wya Thompson Dsseraon Supervsor ABSTRACT Wh an ncrease n he US focus on borenewable energy more forces are compeng for agrculural land. Ths srucural change n he agrculural economy warrans re-examnaon of he relaonshps beween agrculural producon decsons and he facors whch nfluence hose decsons. However relevan daa may be lmed. To address hs ssue a maxmum enropy esmaed Marov decson process model (MDP) a model osensbly robus wh lmed daa s employed o examne agrculural decsons n hree sudes. Frs he queson of he MDP s applcaon o endogenous prce changes s addressed by ncorporang he MDP no a srucural paral equlbrum model examnng corn and soybean producon n Iowa and Mssour from Ths model s compared o a calbraed consan coeffcen model and shoced o examne performance dfferences. The MDP was found o be more responsve o changes n prce han a radonal model alhough consrans on he model esmaes were requred o cause he model o follow economc response expecaons. Second he MDP was appled o a newly acqured saelle magng daase showng warm season grass (WSG) area a possble cellulosc ehanol feedsoc n he Mdwesern US from comparng he relaonshps beween WSG corn soy and whea. The model proved problemac wh large daases bu showed he possbly v

11 of WSG compeng wh radonal crops for area respondng o shocs n boh s own prce and ha of corn. Thrd he MDP was appled o US feed and resdual usage. Because of he ncrease n ehanol producon dred dsller s grans (DDG) producon has ncreased creang a more avalable alernave lvesoc feed. DDGs corn and soy meal were examned from and fuure use was proeced. DDGs were found o compee wh corn bu her soy meal relaonshp was unclear. DDG use s expeced o level off and decrease slghly over he nex en years. x

12 I. Incorporang Dynamc Land Use no a Paral Equlbrum Model: Tes Cases n Mssour and Iowa I.1 Inroducon In recen years he Uned Saes has ncreased he focus places on bofuel polcy as a par of s overall energy polcy. Specfcally he Energy Independence and Secury Ac (EISA) of 2007 ncludes mandaes for he use of several caegores of bofuel some of whch can be me usng radonal (sarch based) and cellulosc and agrculural wase based bofuels over he nex decade. Ths mandae (whch may or may no be waved a he dscreon of he Envronmenal Proecon Agency) could sgnfcanly change he manner n whch U.S. land s allocaed for crop producon for he nex decade. Even as a dedcaed energy crop s developed o reduce prce volaly ransmed from he ol mare o radonal crop prces he new crop wll compee wh radonal crops for land. Even seng asde he poenal for new crops he mpac of bofuel on he mx of crops grown n he U.S. has been a maer of debae wh ncreased pressure n corn mares apparen n area shfs n recen years. Because of hs mpac here s benef n nowng how dfferen facors wll affec land allocaon: undersandng hese neracons wll allow polcy maers o mae beer decsons. Many pror sudes exs on land use allocaons (LUA). Ofen LUA models ncorporae a se of consan parameers whch wh oher daa allow for he esmaon of land use. For nsance he Food and Agrculural Polcy Research Insue (FAPRI) ulzes a srucural paral equlbrum (PE) model o proec U.S. commody and crop producon. A PE model s bul wh a seres of lnear or non-lnear equaons modelng boh supply and demand for varous commodes a an aggregaed level. However 1

13 consan coeffcen (CC) models necessarly assume ha relaonshps beween daa and land use reman a a sngle level hroughou me. The queson arses wheher or no consan parameers are approprae for LUA models as opposed o a dynamc coeffcen model n whch he relaonshp beween facors deermnng land allocaon and he allocaon decson change over me. One mehod o nroduce dynamc coeffcens s o assume ha land use follows a frs order Marov decson process (MDP). I s a dynamc process n whch he curren land allocaon s a funcon of he las perod s allocaon and a se of non-saonary ranson probables. These probables are esmaed based on daa whch affec he decson process. Ths allows a greaer freedom of movemen n a model whch may allow o reflec realy more accuraely. However radonal PE models have he ably o deermne prce endogenously and solve recursvely for changng mare condons. Pror Marov models have no ncorporaed such prce endogeney. Combnng hese wo capables may provde a more robus model hereby servng as a beer ool for analyss. The quesons hs research nends o answer are 1) Can a land use model ncorporang an MDP endogenously deermne prce and 2) If so how does compare wh a radonal purely consan coeffcen model? To answer hese quesons hs research ncorporaes a MDP no a PE model. I.2 Pror Leraure One of he possble exensons of hs research s examnng he mpacs of bofuel polcy on land use. Wh he ncreasng mporance of bofuels n he Amercan agrculural economy leraure concernng such mpacs on land use and oher areas has ncreased n frequency. Devadoss and Bayham (2010) examne he effecs of reducng 2

14 crop subsdes on bofuel producon. Dcs e al. (2009) examne he amouns of varous feedsocs necessary o sasfy he EISA mandae. Mller and Coble (2011) sudy dfferen possble polcy opons avalable o lawmaers and he mpac of hose proposals on he Souheasern U.S. Km Schable and Daberow (2010) focus on he mpacs of U.S. bofuel polcy on nernaonal energy mares. Whle hs ls of bofuels relaed economc leraure s far from exhausve maes clear ha here are a grea many quesons o answer abou he changng boenergy economy. Ths research focuses on developng a new model o beer address some of hem. Srucural models have been used o solve for land use and agrculural producon for several decades. An early use of he srucural model comes from Womac (1976). He models U.S. agrculural producon a a naonal level ncorporang boh crop and cale producon and consumpon. Shumway (1983) sudes Texas feld crop producon bu hs analyss focuses manly on he supply sde of he equaon and he cos of npus. Adams (1994) follows Womac and ncludes a regonal breadown of he naonal model. A promnen curren use of hs ype of model can be found n he FAPRI Baselne as menoned earler (Weshoff and Brown 2009). The earles use of a MDP o esmae changes n land use s found n Burnham (1973). The auhor assumes ha land use changes n he Souhern Msssspp Alluval Valley can be esmaed by a saonary frs order Marov chan. However he saes n he foonoes ha assumng saonary ranson probables may be oo resrcve for a land use change model. Burnham s concluson s suppored by Hallberg (1969) who sudes frozen dary producs n Pennsylvana usng a non-saonary MDP. Hallberg uses mulple regresson echnques o es he hypohess ha non-saonary Marov 3

15 ranson probables have beer predcve capably han saonary probables. MDPs are used n far more han land use however. Agan Hallberg s sudy s on frm sze n he dary ndusry no land use. Oher sudes usng MDPs for economerc analyss nclude Adelman s analyss of he dsrbuon of frm szes n he ron and seel ndusry (1958); Paap and Van D s analyss of ncome and consumpon n he U.S. (2003); Kelley and Wess sudy of populaon mgraon based on wage dfferenaon (1969); Mller and Plannga s paper analyzng land use changes n Iowa (1999); and Lubows Plannga and Savns use of a nesed log model o analyze naonal nonfederal land use (2008). As saed earler oher models are ulzed n economcs o deermne land use allocaon. One such mehod s an erave lnear program (LP). In an LP a lnear producon funcon s opmzed subec o consrans such as labor coss crop ne reurns and oal acreage consrans. Heady (1954) provdes a dscusson of he logc and advanages of usng lnear programs n agrculural economercs. Tompn (1958) uses lnear programmng o deermne he opmal combnaon of producon acves on a lvesoc farm. A dfferen ype of LP model s used by De La Torre Ugare e al. (2003) and Ray e al. (1998) n he mplemenaon of he POLYSYS agrculural polcy model. However LP models may resul n corner soluons so ranson consrans may be necessary. Anoher model used o esmae land use shares and ranson probables s he mulnomal log model (MNL) (Thel 1969). The MNL s used by McRae (1977) among ohers. The probables assocaed wh a change n sae are esmaed usng a logscal form. Ths funcons smlarly o a Marov chan bu dsregards he pror sae 4

16 esmang changes n land use solely as a funcon of exogenous daa. Such use can be seen n Wu and Segerson (1995); Harde and Pars (1997); and Ahn Plannga and Alg (2000) for nsance. In addon Lubows Plannga and Savns ( ) noe ha he Independence from Irrelevan Alernaves (IIA) propery of MNLs may preclude oherwse opmal choce behavors. They n addon o Lubows (2002) use a model nown as a nesed log model (NLM) o address hs shorcomng of he MNL. The NLM separaes decson saes no subgroups or ness of smlar quales dfferenang hem based on degree of subsuably. The ness Lubows Plannga and Savns use nclude urban non-farm (comprsed of fores and range land) and farm (comprsed of cropland Conservaon Reserve Program land and pasure land). The advanage of he NLM s ha mposes IIA whn ness bu no across ness relaxng he choce resrcons. However because he ness of a NLM are based on subsuably may be less effcen a explanng land use change beween crops. The mxed log model (MLM) s anoher mehod of relaxng he IIA resrcon. The MLM s gven by McFadden and Tran (2000) and aes he choce specfc varables of condonal log and he choce-ndependen varables from he MNL o creae a mxed model n whch addonal choces change he relave probables of he exsng saes. However he MLM sll requres a problem ha s well posed:.e. he observaons avalable exceed he number of unnowns. In he case of he nroducon of a new crop for cellulosc bofuel feedsocs he nown daa are very lmed and he problem may be ll-posed. Golan Judge and Mller (1996) dscuss he use of general maxmum enropy o address he ssue of an ll-posed problem. From hs dscusson and oher exsng land use leraure a model ha esmaes a se of coeffcens drecly 5

17 lnng explanaory sae varables (boh sae dependen and ndependen o avod IIA) wh decson varables as well as ncorporang daa from he sae of he land n he pror perod may be derved o provde a beer f. I s also desrable o ulze an economerc model ha mnmzes choce resrcons on he par of he decson maer. One such model ha fs hose crera s he MDP model. I.3 Marovan Land Use Decson Process Ths research examnes he dynamcs of land use changes by explanng he planng decsons of farmers n he area of sudy. Followng Ahn Plannga and Alg (2000) each farmer n regon ( = 1 I) s assumed o plan a sequence of crops on land ha he manages ha maxmzes he presen dscouned value of expeced ne reurns (1.1) max E[ NR( Xh ) ( )] 0 where s a consan dscoun facor represens a decson o allocae land currenly used for crop (dscree sae varable) n me -1 o crop n me X represens a T h x H marx of observable daa ncludng expeced crop ne reurns and a rend varable and ε represens unobserved varables. Beyond he lm of a farmer mang decsons only for he land he owns or conrols hs maxmzaon s unconsraned. Because of he relave dffculy nvolved wh obanng ndvdual farmer planng decsons a model whch ulzes aggregaed daa s desrable. Therefore n hs paper acres planed aggregaed a he sae level are used o represen he sum of all planng decsons (Golan Judge and Mller 1996). However hs research recognzes ha here exs dosyncrac or agen-specfc componens of a farmer s planng decson whch are unobservable o he economercan. These componens are represened by he 6

18 unobservable sae varable. Over me a farmer s planng decsons are assumed o follow a frs order MDP. The acreage planed o a gven crop s a funcon of he crop planed n he pror perod and a non-saonary ranson probably noed. Tha s here s a non-observable J x K (where J=K) marx of probables for each sae and me perod ransonng from crop o crop from perod -1 o perod. To llusrae Table 1.1 shows he probables for land use ranson n Iowa from esmaed from he model explaned below. If an acre of land was planed wh corn n 1996 has approxmaely a 57% chance of sayng n corn n 1997 a 37% chance of beng planed wh soybeans and a less han 6% chance of beng used n anoher caegory. Here hese numbers provde a vsual example of he naure of Marovan ranson probables; as resuls hey wll be dscussed laer. Marovan ranson probables row-sum o one and are hypoheszed o be affeced by explanaory varables ncludng crop prces. Through hs neracon he varables are explanaory of changes n crop land planng paerns. The model s derved usng maxmum enropy (ME) followng Golan and Vogel (2000); Golan Judge and Mller (1996); and Mller and Plannga (1999). The ME mehod for esmang he model of Marov ranson probables s se forh by Jaynes (1957). The obecve of he ME mehod s o selec he probables ha use he leas nformaon (fewes assumpons) o esmae he probables whle sll sasfyng he consrans. Ths n urn assumes he farmer has he greaes amoun of choce possble. Shannon s (1948) enropy measure s used o measure he amoun of nformaon needed o esmae he coeffcens (Mller and Plannga 1999 Golan and Vogel 2000). The prmal obecve funcon deermnng he opmal ranson probables s 7

19 8 (1.2) 0 ) ln( max T J T J K y y s.. S X where 0 s an H sze vecor of zeroes and y s he share of acreage planed o crop n area durng me. When appled o he esmang equaons (he se of consrans) he soluon o he problem aes he form (1.3) K H h h h H h h h x y q x y q ˆ exp ˆ exp ˆ where h ˆ s he opmal Lagrangan mulpler assocaed wh explanaory varable h and crop and q s a condonal probably whch may be adused by he analys o represen nformaon from before he planng decson ha may bas he farmer s decson. By focusng on he dual of he prmal problem an unconsraned equaon o deermne he opmal mulplers aes he form of (1.4) T K K H h h h T H h K h h x y q x y M exp ln ) ( max. One caegory s ep as a resdual wh s mulplers assumed o be zero. Ths mples ha he resdual land s unaffeced by he explanaory daa. Because of he addve naure of he land caegores he resdual soluon s mplc when all oher caegores are esmaed. Afer he mulplers are esmaed hey are used wh he oher varables o deermne he ranson probables n (1.3). The ranson probables are hen appled o he pror year s crop planngs o deermne curren planngs:

20 9 (1.5) J y y 1 1 ˆ. Wh he acreage shares esmaed elasces can be calculaed o show he effec of a one percen change n he explanaory varables on he ranson probables. (Mller and Plannga 1999) (1.6) ] ˆ ˆ [ 1 1 K h h h h y x. Usng hs elascy one can derve he acreage ranson elasces measurng he change n he acreage allocaon from a one percen change n he explanaory varables as (1.7) J h h y y ˆ. Usng he appendx n Mller and Plannga (1999) as a gude he covarance marx of he coeffcens ( h ˆ ) condonal on he explanaory varables can be esmaed by (1.8) 1 1) ( 1) ( ) ( )' ( 2 2 K K I X Σ I X such ha I s he deny marx and s a T(K-1) 2 x T(K-1) 2 marx where he dagonal elemens are ) 1 ( and he off dagonal elemens are ) (. Wh he MDP defned he focus shfs o defnng he PE model whch wll endogenously deermne prce. I.4 Paral Equlbrum Model The PE model used here s a se of lnear demand and prce equaons desgned o ae he land allocaon decson from he MDP and allow o nerac wh he mare endogenously deermnng prce and allowng ha prce o feed bac recursvely no he

21 varables affecng he farmer s planng decson. The followng equaons specfy he relaonshps beween smulaed varables and he MDP. (1.9) PlanedAcr es y ToalLand To reach acual acres planed o each crop he shares are mulpled by he exogenous oal amoun of land avalable. Shares are used n esmaon because of he MDP s probablsc naure prevenng proecons from beng ed o he las year of esmaon. (1.10) HarvesAcr es PlanedAcr es HHR Acres harvesed for each crop n a gven year are calculaed by mulplyng he acres planed by he average hsorcal harves rae for ha crop. Ths accouns for area harvesed for slage as opposed o gran whch s suded here and may nclude facors le crop falure or area no harvesed for oher uses. (1.11) Producon AcualYel d HarvesAcr es Acual yeld s exogenous so producon s he produc of he area harvesed and he realzed yeld. (1.12) Supply Producon I 1 Toal supply for he regon s he aggregaed producon amouns of each sae. (1.13) Demand 01 11Income 21Prce 31Prce l Demand s a funcon of naonal ncome and prces. Here l ndcaes all dscree saes (crops) n such ha l. Thus boh own and cross prces are ncluded. (1.14) Supply Demand Ths equaon clears he mare and vares prce o sasfy he consran. (1.15) Prce f ( Prce ) 10

22 The mare-clearng regonal prces are lned bac o he sae-specfc prces. By nserng he MDP supply response no he above equaons he model becomes a MDP- PE. The model for hs paper s furher defned by he scope and daa. I.5 Daa and Scope of Model The obecve of hs research s o compare a MDP-PE model wh a CC-PE model. Fgure 1.1 provdes an llusraon of he overall framewor of he model and he relaonshps beween he varables. Area for wo crops ha are already produced commercally s esmaed over a hsorcal perod and combned wh a srucural paral equlbrum model; hen an ou of sample smulaon s run wh and whou an exernal shoc o compare he wo models. Here corn and soybeans are esmaed n Iowa and Mssour for he years wh an ou of sample smulaon n The resdual caegory consss of all oher land avalable n boh saes afer corn and soybean acres are removed. Whle he resdual caegory s ncluded for esmaon purposes s no a focus of hs research: he resdual caegory has no reurns calculaed for. As such one lmaon of hs sudy s ha he focus on corn and soybeans s narrowly defned wh land assocaed wh all oher acves lef as an oher. However as noed below he reamen s conssen among he land use equaons ha are compared n he models presened here. Wh hs framewor n mnd he area varable for he MDP-PE = [Iowa Mssour] he crop caegory varables = [corn soybeans resdual] me varable = [ ] and he explanaory varable h = [corn ne reurns soybean ne reurns nercep]. Sae level daa for corn and soybeans on acres planed acres harvesed yelds ferlzer applcaon raes and farmgae prces for each mareng year 11

23 are aen from he Naonal Agrculural Sascs Servce (NASS). Toal sae land area s aen from he 2010 U.S. Census held consan over me and used o deermne shares. Ferlzer prce daa for anhydrous ammona (N) d-ammonum phosphae (P) and murae of poash (K) are obaned a he regonal level. The NASS regons used are Hearland and Norh Cenral. Naonal corn and soybean farmgae prces as well as soybean meal prces are obaned from NASS as well. Naonal personal ncome s obaned from he Economc Research Servce (ERS). All prces and ncome are n real erms. Consumer prces and ncome are adused usng he consumer prce ndex from he Bureau of Labor Sascs wh farmgae and polcy prces adused usng he producer prce ndex from he same. I.6 Addonal Specfcaons To smulae he model a number of addonal equaons are necessary apar from he land allocaon problem ha was explaned before. (1.16) Pr ce Mssour 02 12Prce Iowa Prces for boh corn and soybeans n Mssour were found o follow Iowa (he larger producer) almos perfecly. Therefore he model solves for Iowa prces and Mssour prces are aen as a funcon of hem. (1.17) E[ NR ] max( FuuresPrce E[ Yeld Bass ] E[ VarableCos PolcyFloo rprce ] ) Expeced ne reurns are equal o he maxmum of sae-level fuures prce and a polcyse floor prce mes expeced yeld mnus expeced varable coss. The naonal fuures prce s gahered from he Chcago Mercanle Exchange and followng crop nsurance (Hofsrand and Edwards 2003) he average of daly selemen prces n February were 12

24 used o calculae he fuures prce used. Corn and whea prces were based on December conracs whle soybean fuures prces were based on November conracs. The fuures prce s adused by subracng he average dfference beween he fuures prce of he chosen monh and he sae-level average farm prce. Alhough hs gap vares from year o year n ways ha are assumed o be predcable farmers are expeced o ncorporae he average dfference beween he prce on he CME and he prce hey receve ha s susaned over hs perod. The floor prce s derved from he Uned Saes mareng loan program bu s assumed o run hgher han he loan rae se by polcy based on he observaon ha he mareng loan benefs plus mare prce ypcally exceeds he loan rae n hose years where paymens were made durng he sample perod.. The polcy floor prce was esmaed as he loan rae plus he average percenage by whch loan defcency benefs plus sae level mare prces exceeded loan raes over he years where here were benefs durng he esmaon perod of hs sudy. Expeced yeld s a rend yeld. (1.18) FuuresPr ce FuuresPrce SaeFuur esdff The naonal fuures prce s ranslaed o he sae level by subracng he average dfference beween he curren sae mareng year prce and he naonal fuures prce. Dcey-Fuller ess were conduced on he dfferences o deermne saonary. No un roo was found a he 1% level of sgnfcance for corn or soybeans n Iowa. Because Iowa prces drve he model Mssour was no esed. (1.19) FuuresPr ce f Prce ) ( Iowa 1 13

25 Ou of sample he fuures prce s esmaed as a funcon of he lagged mareng year prce n Iowa. Iowa prces drve he model and hs equaon closes he prce expecaon sysem. (1.20) E [ VarableCos Corn Soy) ] FerAppRae ( ( Corn Soy) ( N P K ) * Ferlzers [ N P K ] FerPrce ( N P K ) Aggregae per-acre ferlzer coss are ncluded as he varable coss for each crop. Oher varable coss ncludng fuels chemcals and seeds are no ncluded for wo reasons. Frs ferlzer s assumed o explan an mporan par of he dfferences beween corn and soybean coss. Second ferlzer relaes he ey research queson of hs sudy because of how ferlzer requremens and crop roaon nerac. For soybeans he ferlzer coss are he per-acre applcaon raes mes he prce. (1.21) FerAppRa e Corn N 0.5 y max 0.5 y mn y Corn y Soy 1 Corn y Corn Soy 1 S2CAppRae C2CAppRae For corn he ssue of soybean roaon arses. Farmers o fx nrogen n he sol wll plan soybeans afer corn hereby reducng ferlzer coss. Ths funconal form assumes a 50% roaon of all avalable acres n sae-level daa unless here s a poron of corn acreage ha canno be roaed. Gven he recommended corn-over-corn and corn-oversoy applcaon raes come from he Iowa Sae Unversy Exenson Servce (Blacmer Voss and Mallarno 1997) correspondngly hgher ferlzer coss are bul n f saelevel daa sugges ha some corn mus be planed on area ha was allocaed o corn n he prevous year. Curren ferlzer prces and applcaon raes are used because he farmer has nowledge of he prces he faces when he purchases ferlzer as opposed o facng an expecaon of prce. I should be noed here ha he ssue of sol qualy or 14

26 producvy s recognzed as affecng he farmer s decson process (Orazem and Mranows 1994 Thomas 2002 Mller and Plannga 1999). However because hs model s aggregaed a he sae level land qualy dfferences are dffcul o capure and are assumed o resde n he dosyncrac poron of he opmzaon problem. (1.22) (1.23) ln( Demand Corn ) a0 a2 ln( Demand Soy ) a0 a2 corn soy corn soy a1 corn *ln( USCornPrce ) *ln( USSoyPrce ) a3 a1 soy *ln( USSoyPrce ) a3 soy corn *ln( USCornPrce ) * Trend * Trend Demand for corn s a funcon of s own farmgae prce and he farmgae soy prce as well as nerceps and rends. Lewse demand for soy s a funcon of s own farmgae prce he corn farmgae prce and oher erms. For demand regonal producon s used as he dependen varable bu demand for crops grown n hese wo saes mplcly ncludes all uses and all compeng producers domesc and foregn. Regonal demand elasces are based on he mehod appled for a model ha ncluded corn and soybean producon n Illnos (Khanna e al. 2009) usng wh he same esmaes of demand and supply namely demand elasces of for corn and for soybeans and supply elasces of 0.2 for corn and 0.45 for soybeans bu ang no accoun he share of crop producon n hs wo saes (USDA/NASS 2012). Snce (1.22) and (1.23) use a double log form he demand n shown n (1.13) would be he exponenal of (1.22) or (1.23). Esmaon comparson s resrced o valdang he non-consan represenaon of supply whereas he sandard represenaons of demand and prce-clearng equaons are added o smulae he mpac of an exernal shoc n order o show he poenal for dfferences n resuls f non-consan supply parameers are used n polcy analyss. For 15

27 ou-of-sample smulaons he model s calbraed o he fnal year of hsorcal esmaon. The elasces are lsed n Table 1.2. Own-prce elasces are negave and very elasc as s udged approprae gven ha he demands are for crops produced n only wo saes and cross-prce elasces are posve and nelasc. I.7 Model Consrans As wren he model should run unconsraned o choose he coeffcens whch bes f he daa. Indeed an unconsraned model s desrable because may be consdered more sascally vald as more closely reflecs he relaonshps presen n he daa. However n appled economerc wor consrans are ofen mposed f he resuls do no f economc heory or f he daa may no perfecly reflec he suaon faced by he decson maer as n he case of proxes. To see f such consrans were necessary he model s run over he n-sample perod wh acual lagged acreage and explanaory daa. The acreage elasces (1.7) of he ne reurns varables were examned as well as he srucure of he Marov probably marces (1.3). The nal run of he model produced elasces whch do no follow expeced economc heory: own ne reurn elasces should be posve and cross ne reurn elasces should be negave. Of he egh elasces calculaed only he effec of corn ne reurns on soy acres had he expeced sgn. To address hs ssue wo ses of consrans were mposed: he frs was mposed on he value of he coeffcens calculaed n (1.4) he second on he pror probables q n (1.3). The elasces were ndrecly consraned by way of he coeffcens hemselves because elasces are no explcly represened n hs esmaon mehod bu are calculaed ex pos nsead. These consrans were desgned o drec he model as lle as 16

28 possble whle sll ensurng he correc sgns and relave magnudes on own ne reurns elasces. In Iowa resrcng soy ne reurns o corn acres as negave produced resuls whch f heory. In Mssour corn ne reurns o corn area was consraned o be posve. These consrans are mposed o cause he model o follow he nown compeve naure of corn and soybeans. The elasces from boh models averaged over me are shown n Table 1.3. The second se of consrans were mposed on he probably marx (1.3) by nroducng a non-unform se of pror probables (q). Whle specfc crop roaon daa are dffcul o oban Wallender (2013) shows ha whle some area says n corn connuously mos s roaed o soybeans a leas once n hree years. Followng hs he pror probables assumed a corn-corn-soy roaon of aggregae shares wh a very small possbly of land gong no resdual. Corn over corn probables were ncreased slghly o accoun for he small percen of land ha does no roae. These prors are presened n Table 1.4. Mssour pror probables were more dffcul o deermne because of he much broader array of crops grown here. Also Mssour esmaed probables of resdual land gong no corn and soy were very low whou mposng prors herefore Mssour was lef wh unform prors. I.8 Model Valdaon I should be noed ha forcng he model o reflec heory dd no come whou cos. Whle he economcs are more closely followed he consrans mpac he sascal valdy of he errors of he coeffcens derved from he covarance marx n (1.8). For hs reason confdence nervals and -ess are no provded for he coeffcens. The queson also arses as o how he consrans affec he ably of he model o esmae 17

29 land use changes essenally a queson of goodness of f. Due o he dynamc naure of he MDP radonal measures of f (.e. R 2 ) are no sascally vald. Bu a dfferen measure of f for he MDP may be presened: T 1 abs( yˆ (1.24) MAE T y 1 y ) MAE s he percen mean absolue error: he dfference of he esmaed acreage and he acual acreage for each crop normalzed by he acual acreage planed o ha crop averaged over me. As measures devaon from hsorcal daa a lower number ndcaes a beer f. Because y represens a share as opposed o acual acreage hs esmae s a unless percenage. Agan hs does no have he same sascal applcaon as a normal R 2 bu does provde an dea of how he model performs. The MDP n-sample MAEs are lsed n Table 1.3. The consrans on he model decrease s ably o esmae land use changes wh regards o corn acres as shown by he hgher MAEs n he consraned model. However soy acres perform he same or beer n boh Mssour and Iowa. The consrans have some mpac on he model bu may be easer o graphcally valdae he model and o see how compares agans hsorcal acres planed o corn and soy shown n Fgures 1.2 and 1.3. The vercal double-dash lne ndcaes he change from n-sample o ou-of-sample esmaon. Boh follow farly closely over me bu he model msses he changes n 2007 when corn and soy prces sped. The graphs seem o sugges ha he model caches he urns bu msses he magnudes of he changes. Because caches he urns n producon may be useful o see how he model responds o a shoc n prces. Therefore he focus shfs o comparng he performance of a CC verson of he model o he combned prce endogenous MDP-PE. 18

30 I.9 Smulaon Resuls: Consan Coeffcen vs. MDP Comparson To compare he MDP model o a CC model a CC-PE model s creaed and calbraed n par o he consraned MDP-PE esmaon resuls o ensure smlar orders of magnude. The CC-PE acreage response equals he elasces calculaed from he MDP-PE averaged over he n-sample perod. Inuvely hs approach suggess ha an esmaed CC-PE model over he same perod mgh end up wh he consan supply elasces equal o he average values of he non-consan elasces repored above. Ths calbraon s chosen o eep he magnude of response from he CC-PE model n lne wh ha of he MDP-PE model. To provde a baselne for he dfferences n he wo models Table 1.4 shows he ou-of-sample relevan daa for each model and he acual observaons. In comparng he averages of he base scenaros he nal dfferences seem o follow heory: boh he CC-PE and MDP-PE models allocae fewer acres o hese crops when her own prces are lower wh he lower prces n boh cases possbly a resul of smulaed demand weaer han hsorcal demand durng hs perod. However he CC- PE allocaes fewer acres o crops han he MDP-PE and has slghly hgher prces. The acreage dfferences are relavely small bu hs does provde an ndcaon ha despe calbraon he models wll respond dfferenly. Table 1.6 shows hese dfferences more explcly. The dfference beween he wo begns small n acres planed bu spreads apar as he smulaon progresses n mos caegores. Anoher measure of performance of a srucural model can be generaed by smulang he resuls of an exernal shoc. To es he model furher a shoc was appled n he frs year of he smulaon perod. In eepng wh a sylzed applcably o bofuels an exogenous ncrease n regonal ehanol demand of 3.0 bllon gallons n 2006 wh an addonal 500 mllon 19

31 gallons each year was appled. A converson rae of 2.7 gal/bu s assumed based on he lower end of he range esed by Donner and Kuchar (2008). Dsller s grans are ncluded as a percen reducon n oal corn demand from he shoc based on per-gallon dsller s gran producon numbers from USDA (Harman 2013) under he assumpon ha ncreased dsller s grans wll compee wh corn for feed demand aenuang he ncreased demand for corn. Table 1.5 shows he dfferences beween he wo models across he wo scenaros (he dfference of dfferences).the shoc s assumed o be unancpaed so expecaons of fuure crop prces are no affeced by any probably ha farmers mgh oherwse place on he prce mpacs of seadly ncreasng ehanol producon from corn. Before he models are conrased one should examne he sgns and magnudes of he ndvdual scenaro dfferences o evaluae performance and ensure ha he smulaons follow economc heory. Tables 1.7 and 1.8 show he shoc scenaro dfferences subracng he base scenaro from he shoc scenaro. In 2006 he supply sde parameers (acres planed and producon) do no respond due o lagged response varables. However he ncrease n ehanol demand causes an ncrease n he prce of corn as he new demand s flled a he expense of oher demands. The prce of soybeans also ncreases as lvesoc owners and consumers shf consumpon o soybean producs as he prce of corn rses. The CC-PE model has a hgher ncrease n prces han he MDP-PE from he dencal shoc n quany demanded suggesng ha he MDP-PE has a greaer prce elascy of supply whch s o say an dencal change n prce across boh models would evoe a sronger supply response n he MDP-PE. In 2007 he enre model pcs up he shocs as he lagged ncreases n prce cause ncreases n corn acreage planed o help fll he 20

32 exogenous demand shoc. There are fewer acres planed o soy n Iowa n 2007 despe a hgher soy prce. Ths suggess a bleedover effec from he demand shoc of he prevous year. Acreage s aen ou of soybeans despe he fac ha soybean prces have ncreased. Ths can be explaned by he fac ha he corn prce has rsen hgher han he ncrease n he prce of beans n percen erms; so acreage s aen away from soybeans. The neresng par of he sory occurs n comparng he dfferences n he wo models over me. Table 1.7 shows he dfferences beween he wo models across he wo scenaros (he dfference of dfferences) whch are farly small for all years. Ths s lely due o he fac ha he demands are very elasc n hs model so even large shocs wll cause a small mpac on crop prces n hese wo saes. Small prce dfferences correspond o small dfferences n land allocaon and crop supply. Moreover he calbraed naure of he CC-PE model ensures ha he wo are reasonably close ogeher. Whle hs ensures ha he resuls are comparable may undersae he real dfferences beween he wo approaches. A modes prce ncrease s suffcen o reallocae corn from oher uses o ehanol use based on hs represenaon. Whle Table 1.9 shows he gross changes beween he wo a closer loo a he prces shows a sgnfcan dfference n he models. In he boh models corn prces ncrease n accordance wh he addonal demands of he model. However he MDP-PE conssenly esmaes lower prces han he CC-PE model. And wh he excepon of 2007 spes here s a dsnc posve rend n he dfferences beween he wo models wh regard o prce. Tha s he prces n he CC-PE model rse a a relavely fas rae whle he MDP-PE prces are slower o respond o he ncreased demands from he shoc. Ths suggess ha he MDP-PE s a more responsve model reacng more srongly o he ssues arsng from ncreased 21

33 compeon for corn ehanol. Tha s a modes change n prce wll have a greaer effec on supply n he MDP-PE model. Loong a acreage n 2008 and 2009 suppors hs concluson: he MDP-PE esmaed a lower change n prces han he CC-PE bu has more acres planed o each crop n hose years. I.10 Concluson The purpose of hs research s wofold: can a non-consan land use decson process be ncorporaed no a srucural model wh prce endogeney and f so how wll perform agans a consan coeffcen model? The frs queson s answered n he affrmave n hs case alhough here s a need for more refnemens n he specfcaon of he srucural model. The demand gven here s a placeholder ha could be mproved even o he pon of nroducng a dynamc elemen o demand. There s also room for mprovemen as regards he land represenaon no leas by relaxng he narrow focus on corn and soybean land o ncorporae oher agrculural land use and oher land use caegores. More mporanly was shown ha he model may requre consrans on he coeffcen esmaon o ensure ha economc heory s followed. Polcy has a lmed mpac hrough he ncluson of a prce floor esmaed from mareng loan program mpacs. Bu s an advanage of hs approach ha perms esmaon over small sample szes ha mgh be more germane o forward-loong decson mang as compared o esmaes over daa exendng bac o polcy and mare envronmens ha are no longer relevan. Neverheless a possbly que useful exenson would be o exend he model o nclude more polcy effecs explcly also seng he sage for appled polcy analyss. 22

34 The second queson s answered by comparng a combned MDP-PE wh a CC- PE model ulzng a me-averaged se of acreage ranson elasces from he MDP esmaed from The wo models are hen shoced wh an exogenous demand ncreasng ne demand o corn by requrng he producon of 3.0 bllon gallons of ehanol n 2006 and an addonal 500 mllon gallons each year hereafer. The responses of several mercs ncludng crop prces and area allocaed o each crop were analyzed over As he wo models are calbraed o have smlar elasces a he nal values a ey resul s ha he MDP-PE shows more prce response n he case wh he shoc. The MDP-PE s shown o allow for ncreasng responsveness o changes n prces hrough esmang conssenly lower prces han he CC-PE whle he CC-PE responsveness ends o be lower pah despe changng condons n hs case. Ths resul suggess ha he MDP approach mgh be a means of ang no accoun dynamc effecs such as roaon or crop-specfc human or physcal capal ha could affec crop supply elasces. 23

35 I.11 References Adams G Impac Mulplers of he U.S. Crops Secor: A Focus on he Effecs of Commody Ineracon. PhD dsseraon Unversy of Mssour. Adelman I.G A Sochasc Analyss of he Sze Dsrbuon of Frms. Journal of he Amercan Sascal Assocaon 53: pp Ahn S. A.J. Plannga and R.J. Alg Predcng Fuure Foresland Area: A Comparson of Economerc Approaches. Fores Scence 46(3): pp Blacmer A.M. R.D. Voss and A. P. Mallarno Nrogen Ferlzer Recommendaons for Corn n Iowa. Iowa Sae Unversy Agr. Ex. Serv. Pm May. Burnham B.O Marov Ineremporal Land Use Smulaon Model. Souhern Journal of Agrculural Economcs 5(1): pp De La Torre Ugare D.G. M.E. Walsh H. Shapour and S.P. Slnsy The Economc Impacs of Boenergy Crop Producon on U.S. Agrculure. Washngon DC: U.S. Deparmen of Agrculure OEPNU Ag. Econ. Rep. 816 February. Devadoss S. and J. Bayham Conrbuons of U.S. Crop Subsdes o Bofuel and Relaed Mares. Journal of Agrculural and Appled Economcs 42 (4): pp Dcs M.R. J. Campche D. De La Torre Ugare C. Hellwncel H.L. Bryan and J.W. Rchardson Land Use Implcaons of Expandng Bofuel Demand. Journal of Agrculural and Appled Economcs 41 (2): pp Donner S.D. and C.J. Kuchar Corn-Based Ehanol Producon Compromses Goal of Reducng Nrogen Expor by he Msssspp Rver. Proceedngs of he Naonal Academy of Scences of he USA 105(11): pp Golan A. G. Judge and D. Mller Maxmum Enropy Economercs: Robus Esmaon wh Lmed Daa. New Yor NY: John Wley and Sons. Golan A. and S. Vogel Esmaon of Non-Saonary Socal Accounng Marx Coeffcens wh Supply Sde Informaon. Economc Sysems Research 12(4): pp Hallberg M Proecng he Sze Dsrbuon of Agrculural Frms: An Applcaon of a Marov Process wh Non-Saonary Transon Probables. Amercan Journal of Agrculural Economcs 51: pp Harde I.W. and P.J. Pars Land Use wh Heerogeneous Land Qualy: An Applcaon of an Area Base Model. Amercan Journal of Agrculural Economcs 79(2): pp

36 Harman K Iowa Ehanol Corn and Co-Producs Processng Values. USDA-MO Dep. of Ag. Mare News repor NW-GR November. Heady E. O Smplfed Presenaon and Logcal Aspecs of Lnear Programmng Technque. Journal of Farm Economcs 36(5): pp Hofsrand D. and W. Edwards Crop Revenue Insurance. Dep. Econ. FM-1853 Iowa Sae Unversy. Jaynes E.T Informaon Theory and Sascal Mechancs. Physcal Revew 106(4): pp Kelley A.C. and L.W. Wess Marov Processes and Economc Analyss: The Case of Mgraon. Economerca 37(2): pp Khanna M. H. Önal X. Chen and H. Huang Meeng Bofuels Targes: Implcaons for Land Use Greenhouse Gas Emssons and Nrogen Use n Illnos Emssons and Nrogen Use n Illnos n Transon o a Boeconomy: Envronmenal and Rural Developmen Impacs ed. Madhu Khanna. Farm Foundaon Conference Proceedngs. Km C.S. G. Schable and S. Daberow The Relave Impacs of U.S. Bo-Fuel Polces on Fuel-Energy Mares: A Comparave Sac Analyss. Journal of Agrculural and Appled Economcs 42 (1): pp Lubows R.N Deermnans of Land-Use Transons n he Uned Saes: Economerc Analyss of Changes Among he Maor Land-Use Caegores. PhD Dsseraon Harvard Unversy. Lubows R.N. A.J. Plannga and R.N. Savns Deermnans of Land Use Change n he Uned Saes Dscusson Paper Washngon DC: Resources for he Fuure Augus Wha Drves Land-Use Change n he Uned Saes? A Naonal Analyss of Landowner Decsons. Land Economcs 84 (4): pp McFadden D. and K. Tran Mxed MNL Models for Dscree Response. Journal of Appled Economercs 15: pp McRae E Esmaon of Tme-Varyng Marov Processes wh Aggregae Daa. Economerca 45: pp Mller D.J. and A.J. Plannga Modelng Land Use Decsons wh Aggregae Daa. Amercan Journal of Agrculural Economcs 81(1): pp Mller J.C. and K.H. Coble Incenves Maer: Assessng Bofuel Polces n he Souh. Journal of Agrculural and Appled Economcs 43 (3): pp

37 Orazem P. and J. Mranows A Dynamc Model of Acreage Allocaon wh General and Crop-Specfc Sol Capal. Amercan Journal of Agrculural Economcs 76: pp Paap R. and H.K. van D Bayes Esmaes of Marov Trends n Possbly Conegraed Seres: An Applcaon o U.S. Consumpon and Income. Journal of Busness & Economc Sascs 21: pp Publc Law (PL) Energy Independence and Secury Ac of frwebgae.access.gpo.gov/ cg-bn/gedoc.cg? dbname=110_cong_publc_laws& docd=f:publ pdf. March Ray D.E. D.G. De La Torre Ugare M.R. Dcs and K.H. Tller The POLYSYS Modelng Framewor: A Documenaon. Saff Paper Agrculural Polcy Analyss Cener Dep. of Agrculural Economcs and Rural Socology Unversy of Tennessee. Shannon C.E A Mahemacal Theory of Communcaon. Bell Sysem Techncal Journal 27: pp Shumway C.R Supply Demand and Technology n a Mulproduc Indusry: Texas Feld Crops Amercan Journal of Agrculural Economcs 65 (4): pp Thel H A Mulnomal Exenson of he Lnear Log Model. Inernaonal Economc Revew 10: pp Thomas A A Dynamc Model of On-Farm Inegraed Nrogen Managemen. European Revew of Agrculural Economcs 30: pp Tompn J.R Response of he Farm Producon Un as a Whole o Prces Response of he Farm Producon Un as a Whole o Prces. Journal of Farm Economcs 40(5): pp US Deparmen of Agrculure Naonal Agrculural Sascs Servce (USDA/NASS) Crop Producon 2011 Summary. Avalable a usda.mannlb.cornell.edu/mannusda/vewdocumeninfo.do?documenid=1047. Wallender S Whle Crop Roaons Are Common Cover Crops Reman Rare. Amber Waves. 4 March. Weshoff P. and S. Brown US Baselne Brefng Boo: Proecons for agrculural and bofuel mares. MU-FAPRI Repor #01-09 Unversy of Mssour. Womac A "The U.S. Demand for Corn Sorghum Oas and Barley: An Economerc Analyss." Economc Repor 7615 Deparmen of Agrculure and Appled Economcs Unversy of Mnnesoa S. Paul. 26

38 Wu J. and K. Segerson The Impac of Polces and Land Characerscs on Poenal Groundwaer Polluon n Wsconsn. Amercan Journal of Agrculural Economcs 77(4): pp

39 I.12 Appendx: Fgures and Tables Table 1.1: Marovan Land Transon Probables n Iowa Source: Auhor s Esmaon Corn Soy Resdual Sum Corn Soy Resdual Table 1.2: Demand Equaon Prce Elasces Source: Adapaon of Khanna e al Soybean Demand Corn Demand Varable Elascy Varable Elascy U.S. Corn Prce U.S. Soy Prce U.S. Soy Prce U.S. Corn Prce Table 1.3: Comparson of Ne Reurns o Acres Planed Elasces wh Measures of F (Mean Absolue Errors) Unconsraned MDP Models versus MDP Model Consraned wh Coeffcen Consrans and/or Non-Unform Pror Probables Source: Auhor s Esmaon Unconsraned Consraned Corn Ac Soy Ac Corn Ac Soy Ac Corn NR Iowa Soy NR MAE Corn NR Mssour Soy NR MAE Table 1.4: Iowa Imposed Non-Unform Pror Probables for Consraned Marovan Model Source: Adapaon Based on Wallender Corn Soy Resdual Sum Corn Soy Resdual

40 Table 1.5: Comparson of Hsorcal Ou of Sample Daa wh MDP-PE and CC-PE Model Base Scenaro Esmaes Source: Auhor s Esmaon and NASS Ou of Sample Daa and Esmae Comparsons by Crop and Sae Hsorcal Area Varable Uns Average Iowa Corn Acres Planed Ml ac Iowa Corn Farmgae Prce $/bu Iowa Soy Acres Planed Ml ac Iowa Soy Farmgae Prce $/bu Mssour Corn Acres Planed Ml ac Mssour Corn Farmgae Prce $/bu Mssour Soy Acres Planed Ml ac Mssour Soy Farmgae Prce $/bu Naonal Corn Farmgae Prce $/bu Naonal Soy Farmgae Prce $/bu Marov Decson Process Area Varable Uns Average Iowa Corn Acres Planed Ml ac Iowa Corn Farmgae Prce $/bu Iowa Soy Acres Planed Ml ac Iowa Soy Farmgae Prce $/bu Mssour Corn Acres Planed Ml ac Mssour Corn Farmgae Prce $/bu Mssour Soy Acres Planed Ml ac Mssour Soy Farmgae Prce $/bu Naonal Corn Farmgae Prce $/bu Naonal Soy Farmgae Prce $/bu Consan Coeffcen Area Varable Uns Average Iowa Corn Acres Planed Ml ac Iowa Corn Farmgae Prce $/bu Iowa Soy Acres Planed Ml ac Iowa Soy Farmgae Prce $/bu Mssour Corn Acres Planed Ml ac Mssour Corn Farmgae Prce $/bu Mssour Soy Acres Planed Ml ac Mssour Soy Farmgae Prce $/bu Naonal Corn Farmgae Prce $/bu Naonal Soy Farmgae Prce $/bu

41 Table 1.6: Dfferences beween Esmaed Marovan and Consan Coeffcen Model Base Scenaros Consan Coeffcen Model Shoc Esmaes Subraced from Marov Model Shoc Esmaes Source: Auhor's Esmaon Base Scenaro Dfference MDP-PE - CC-PE Area Varable Uns Average Iowa Corn Acres Planed Ml ac Iowa Corn Farmgae Prce $/bu Iowa Soy Acres Planed Ml ac Iowa Soy Farmgae Prce $/bu Mssour Corn Acres Planed Ml ac Mssour Corn Farmgae Prce $/bu Mssour Soy Acres Planed Ml ac Mssour Soy Farmgae Prce $/bu Naonal Corn Farmgae Prce $/bu Naonal Soy Farmgae Prce $/bu Table 1.7: Marov Model Scenaro Dfferences 3.0 Bllon Gallon Shoc Mnus Baselne Scenaro Source: Auhor s Esmaon MDP-PE Shoc Scenaro Dfference Area Varable Uns Average Iowa Corn Acres Planed Ml ac Iowa Corn Farmgae Prce $/bu Iowa Soy Acres Planed Ml ac Iowa Soy Farmgae Prce $/bu Mssour Corn Acres Planed Ml ac Mssour Corn Farmgae Prce $/bu Mssour Soy Acres Planed Ml ac Mssour Soy Farmgae Prce $/bu Naonal Corn Farmgae Prce $/bu Naonal Soy Farmgae Prce $/bu Naonal Ehanol Corn Ne Demand Ml bu Regonal Non-Ehanol Corn Demand Ml bu Regonal Corn Producon Ml bu

42 Table 1.8: Consan Coeffcen Model Scenaro Dfferences 3.0 Bllon Gallon Shoc Mnus Baselne Scenaro Source: Auhor s Esmaon CC-PE Shoc Scenaro Dfference Area Varable Uns Average Iowa Corn Acres Planed Ml ac Iowa Corn Farmgae Prce $/bu Iowa Soy Acres Planed Ml ac Iowa Soy Farmgae Prce $/bu Mssour Corn Acres Planed Ml ac Mssour Corn Farmgae Prce $/bu Mssour Soy Acres Planed Ml ac Mssour Soy Farmgae Prce $/bu Naonal Corn Farmgae Prce $/bu Naonal Soy Farmgae Prce $/bu Ehanol Corn Ne Naonal Demand Ml bu Non-Ehanol Corn Regonal Demand Ml bu Regonal Corn Producon Ml bu Table 1.9: Dfference of Dfferences Across he Marov and Consan Coeffcen Models Consan Coeffcen Model Shoc Dfference Esmaes Subraced from Marov Model Shoc Dfference Esmaes Source: Auhor s Esmaon Dfference of Marov and Consan Coeffcen Scenaro Dfferences Area Varable Uns Average Iowa Corn Acres Planed Ml ac Iowa Corn Farmgae Prce $/bu Iowa Soy Acres Planed Ml ac Iowa Soy Farmgae Prce $/bu Mssour Corn Acres Planed Ml ac Mssour Corn Farmgae Prce $/bu Mssour Soy Acres Planed Ml ac Mssour Soy Farmgae Prce $/bu Naonal Corn Farmgae Prce $/bu Naonal Soy Farmgae Prce $/bu Regonal Corn Producon ml bu

43 Fgure 1.1: Illusraon of he MDP-SPE Model Framewor Source: Auhor s Represenaon Fgure 1.2: Marov Decson Process Model and Consan Coeffcen Model Corn and Soybean Acres Planed Comparson o Hsorcal Daa Iowa Source: Auhor s Esmaes and NASS Mllon acres Iowa Corn and Soybean Planed Acres: Acual vs. Esmaed Year MDP Es Corn Ac MDP Es Soy Ac Ac Corn Ac Ac Soy Ac 32

44 Fgure 1.3: Marov Decson Process Model and Consan Coeffcen Model Corn and Soybean Acres Planed Comparson o Hsorcal Daa Mssour Source: Auhor s Esmaes and NASS Mllon acres Mssour Corn and Soybean Planed Acres: Acual vs. Esmaed Year MDP Es Corn Ac MDP Es Soy Ac Ac Corn Ac Ac Soy Ac 33

45 II. An Economc Examnaon of Mdwesern Warm Season Grass Area Usng Saelle Imagng Daa II.1 Inroducon In recen years he Uned Saes has ncreased he focus places on bofuel polcy as a par of s overall energy polcy. Specfcally he Energy Independence and Secury Ac (EISA) of 2007 ncludes mandaes for he use of several caegores of bofuel par of whch can be me usng convenonal (corn sarch based) and cellulosc ehanols over he nex decade. These mandaes (whch may or may no be waved a he dscreon of he Envronmenal Proecon Agency) could sgnfcanly change he manner n whch U.S. land s allocaed for crop producon for he nex decade. One source of cellulosc bofuels s from warm-season grasses (WSG). WSG are perennal grasses normally planed n he sprng and harvesed mulple mes over he course of he year. Noable WSG nclude swchgrass (Pancum vrgaum L.) mscanhus (Mscanhus gganeus) Indan grass (Sorghasrum nuans) and bg bluesem (Andropogon gerard). These grasses grow naurally n he Mdwesern Uned Saes and have been consdered as a means of supplemenng and o some degree possbly replacng corn as an fuel ehanol feedsoc. As a commody WSG may compee wh radonal crops for land and capal. Undersandng hs compeon would be useful o polcymaers n crafng legslaon. However he naure of hs compeon s no nally clear. WSG daa are somewha lmed. Whle sudes have been done o asceran yelds and budges hese sudes are relavely few and focused on small areas chefly owng o a lac of daa. The Naonal Agrculural Sascs Servce (NASS) does no rac WSG 34

46 producon as does oher crops. Normally land use sudes have he amoun of land dedcaed o a parcular crop explaned by varables such as own and cross prces yelds ferlzer coss governmen polces and oher varables ha nfluence a farmer s planng decson. Whou he daa o be explaned however such sudes canno be conduced on a large scale. However some such daa have recenly become avalable. Usng he Naonal Aeronaucs and Space Admnsraon s (NASA) Moderae Resoluon Imagng Specroradomeer (MODIS) saelles land cover mages were obaned dealng acres where WSG were presen n he Mdwesern U.S. These daa colleced a he couny level from (see Wang e. al 2011) can serve as he lef-hand-sde varable n an economerc analyss o esmae he relaonshp beween WSG and oher crops based on he aforemenoned explanaory varables. Ths research performs such an analyss examnng he hsorcal growh of WSG n response o own and cross prce yeld and cos effecs. However he daa are sll lmed and he srucure of he mare mgh no reflec wha would happen f cellulosc bofuel aes off gven he relavely new naure of WSG beng used as a feedsoc. So a more frequenly used mehod of economerc analyss such as Ordnary Leas Squares (OLS) may no be approprae. A mehod whch s robus wh lmed daa or s able o handle ll-posed problems may provde a beer undersandng of he relaonshp beween WSG and radonal crops. To w hs research wll assume land use paerns follow a frs-order Marov Decson Process (MDP). I s a dynamc process n whch he curren land allocaon s a funcon of he las perod s allocaon and a se of non- 35

47 saonary ranson probables. These probables are esmaed based on daa whch affec he decson process. Thus he queson hs research nends o answer s Wha relaonshps f any exs beween warm season grasses and maor radonal crops n he Mdwesern US? To answer hs queson hs research esmaes WSG corn soy and whea area usng an MDP. II.2 Pror Leraure Wh he ncreasng mporance of bofuels n he Amercan agrculural economy leraure concernng such mpacs on land use and oher areas has ncreased n frequency. Devadoss and Bayham (2010) examne he effecs of reducng crop subsdes on bofuel producon. Dcs e al. (2009) examne he amouns of varous feedsocs necessary o sasfy he EISA mandae. Mller and Coble (2011) sudy dfferen possble polcy opons avalable o lawmaers and he mpac of hose proposals on he Souheasern U.S. Km Schable and Daberow (2010) focus on he mpacs of U.S. bofuel polcy on nernaonal energy mares. Whle hs ls of bofuels relaed economc leraure s far from exhausve maes clear ha here are a grea many quesons o answer abou he changng boenergy economy. Ths research aemps o answer a couple of hose quesons. Earler he avalably of local or regonal sudes for WSGs s menoned. These budges whle unable o encompass he enre area of sudy are mporan because hey show dfferen echnques and coss a a local level. These budges ofen compare hay wh swchgrass because he producon processes are so smlar. Such budges have been prepared by Smh (2009) Unversy of Tennessee Exenson (2009) Carpener and 36

48 Brees (2010) Holman e al. (2013) Duffy and Nanhou (2001) Helsel and Alvarez (2012) and Brechbll Tyner and Ilele (2011). However wo papers n parcular have very wde sudy areas and herefore become of parcular neres: Perrn e al. (2008) covers felds n Norh Daoa Souh Daoa and Nebrasa. Also Khanna Jan and Olver (2011) cover Mnnesoa Wsconsn Mchgan Iowa Mssour Illnos Indana and Oho. These wo sudes cover he bul of avalable area and are used as he prmary sources of cos daa for hs sudy. The earles use of a MDP o esmae changes n land use s found n Burnham (1973). The auhor assumes ha land use changes n he Souhern Msssspp Alluval Valley can be esmaed by a saonary frs order Marov chan. However he saes n he foonoes ha assumng saonary ranson probables may be oo resrcve for a land use change model. Burnham s concluson s suppored by Hallberg (1969) who sudes frozen dary producs n Pennsylvana usng a non-saonary MDP. Hallberg uses mulple regresson echnques o es he hypohess ha non-saonary Marov ranson probables have beer predcve capably han saonary probables. MDPs are used n far more han land use however. Agan Hallberg s sudy s on frm sze n he dary ndusry no land use. Oher sudes usng MDPs for economerc analyss nclude Adelman s analyss of he dsrbuon of frm szes n he ron and seel ndusry (1958); Paap and Van D s analyss of ncome and consumpon n he U.S. (2003); Kelley and Wess sudy of populaon mgraon based on wage dfferenaon (1969); Mller and Plannga s paper analyzng land use changes n Iowa (1999); and Lubows Plannga and Savns use of a nesed log model o analyze naonal nonfederal land use (2008). 37

49 As saed earler oher models are ulzed n economcs o deermne land use allocaon. One such mehod s an erave lnear program (LP). In an LP a lnear producon funcon s opmzed subec o consrans such as oal acreage avalably. Heady (1954) provdes a dscusson of he logc and advanages of usng lnear programs n agrculural economercs. Tompn (1958) uses lnear programmng o deermne he opmal combnaon of producon acves on a lvesoc farm. A dfferen ype of LP model s used by De La Torre Ugare e al. (2003) and Ray e al. (1998) n he mplemenaon of he POLYSYS agrculural polcy model. However LP models may resul n corner soluons so ranson consrans may be mposed by he modeler o preven such scenaros. Anoher model used o esmae land use shares and ranson probables s he mulnomal log model (MNL) (Thel 1969). The MNL s used by McRae (1977) among ohers. The probables assocaed wh a change n sae are esmaed usng a logscal form. Ths funcons smlarly o a Marov chan bu dsregards he pror sae esmang changes n land use solely as a funcon of exogenous daa. Such use can be seen n Wu and Segerson (1995); Harde and Pars (1997); and Ahn Plannga and Alg (2000) for nsance. In addon Lubows Plannga and Savns ( ) noe ha he Independence from Irrelevan Alernaves (IIA) propery of MNLs may preclude oherwse opmal choce behavors. They n addon o Lubows (2002) use a model nown as a nesed log model (NLM) o address hs shorcomng of he MNL. The NLM separaes decson saes no subgroups or ness of smlar quales dfferenang hem based on degree of subsuably. The ness Lubows Plannga and Savns use nclude urban non-farm (comprsed of fores and range land) and farm 38

50 (comprsed of cropland Conservaon Reserve Program land and pasure land). The advanage of he NLM s ha mposes IIA whn ness bu no across ness relaxng he choce resrcons. However because he ness of a NLM are based on subsuably may be less effcen a explanng land use change beween crops. The mxed log model (MLM) s anoher mehod of relaxng he IIA resrcon. The MLM s gven by McFadden and Tran (2000) and aes he choce specfc varables of condonal log and he choce-ndependen varables from he MNL o creae a mxed model n whch addonal choces change he relave probables of he exsng saes. However he MLM sll requres a problem ha s well posed:.e. he observaons avalable exceed he number of unnowns. In he case of he nroducon of a new crop for cellulosc bofuel feedsocs he nown daa are very lmed and he problem may be ll-posed. Golan Judge and Mller (1996) dscuss he use of general maxmum enropy o address he ssue of an ll-posed problem. From hs dscusson and oher exsng land use leraure a model ha esmaes a se of coeffcens drecly lnng explanaory sae varables (boh sae dependen and ndependen o avod IIA) wh decson varables as well as ncorporang daa from he sae of he land n he pror perod may be derved o provde a more robus analyss. One such model ha fs hose crera s he MDP model. II.3 Marovan Land Use Decson Process Ths research examnes he dynamcs of land use changes by explanng he planng decsons of farmers n he area of sudy. Followng Ahn Plannga and Alg (2000) each farmer n regon ( = 1 I) s assumed o plan a sequence of crops on land ha he manages ha maxmzes he presen dscouned value of expeced ne reurns 39

51 (2.1) max 0 E[ NR( Xh ) ( )] where s a consan dscoun facor represens a decson o allocae land currenly used for crop (dscree sae varable) n me -1 o crop n me X h represens a T x H marx of observable daa ncludng expeced crop ne reurns and a rend varable and ε represens unobserved varables. Beyond he lm of a farmer mang decsons only for he land he owns or conrols hs maxmzaon s unconsraned. Because of he relave dffculy nvolved wh obanng ndvdual farmer planng decsons a model whch ulzes aggregaed daa s desrable. Therefore aggregaed acres planed are used o represen he sum of all planng decsons (Golan Judge and Mller 1996). However here exs dosyncrac or agen-specfc componens of a farmer s planng decson whch are unobservable o he economercan. These componens are represened by he unobservable sae varable. Over me a farmer s planng decsons are assumed o follow a frs order MDP. The acreage planed o a gven crop s a funcon of he crop planed n he pror perod and a non-saonary ranson probably noed s here s a non-observable J x K (where J=K) marx of probables for each sae and me perod ransonng from crop o crop from perod -1 o perod. To llusrae Table 2.1 shows a se of probables for land use ranson from as mgh be esmaed from he model explaned below. If an acre of land was planed wh corn n 2001 has approxmaely a 26% chance of sayng n corn n 2002 a 25% chance of beng planed wh soybeans a 3% chance of beng planed wh whea a 6% chance of beng planed wh WSG and a 40% chance of beng used n anoher caegory. These numbers are fconal and only presen o provde a vsual example of he 40. Tha

52 41 naure of Marovan ranson probables; hey are no resuls. Marovan ranson probables row-sum o one and are hypoheszed o be affeced by explanaory varables ncludng crop prces. Through hs neracon he varables are explanaory of changes n crop land planng paerns. The model s derved usng maxmum enropy (ME) followng Golan and Vogel (2000); Golan Judge and Mller (1996); and Mller and Plannga (1999). The ME mehod for esmang he model of Marov ranson probables s se forh by Jaynes (1957). The obecve of he ME mehod s o selec he probables ha use he leas nformaon (fewes assumpons) whle sll sasfyng he consrans. Ths n urn assumes he farmer has he greaes amoun of choce possble. Shannon s (1948) enropy measure s used o measure he amoun of nformaon needed o esmae he coeffcens (Mller and Plannga 1999 Golan and Vogel 2000). The prmal obecve funcon deermnng he opmal ranson probables s (2.2) 0 ) ln( max T J T J K y y s.. S X where 0 s an H sze vecor of zeroes and y s he share of acreage planed o crop n area durng me. When appled o he esmang equaons (he se of consrans) he soluon o he problem aes he form (2.3) K H h h h H h h h x y q x y q ˆ exp ˆ exp ˆ

53 where ˆ h s he opmal Lagrangan mulpler assocaed wh explanaory varable h and crop and q s a condonal probably whch may be adused by he analys o represen nformaon from before he planng decson ha may bas he farmer s decson. Here prors are no unform bu he exac srucure of he prors wll be dscussed laer. By focusng on he dual of he prmal problem an unconsraned equaon o deermne he opmal mulplers aes he form of (2.4) max M ( ) T 1 h1 1 T H K K lnq exp y 1 y K x h h h1 H x h h. One caegory s ep as a resdual wh s mulplers assumed o be zero. Because of he addve naure of he land caegores he resdual soluon s mplc when all oher caegores are esmaed. I should be noed here ha he resdual caegory was shoc esed afer he coeffcens were esmaed and was found o move as expeced wh regard o changes n explanaory daa: ncreases n all ne reurns caegores caused a mared decrease n resdual caegory land whle ncreasng all oher land caegores. Afer he mulplers are esmaed hey are used wh he oher varables o deermne he ranson probables n (2.3). The ranson probables are hen appled o he pror year s crop planngs o deermne curren planngs: (2.5) yˆ y J 1 1. Wh he acreage shares esmaed elasces can be calculaed o show he effec of a one percen change n he explanaory varables on he ranson probables. (Mller and Plannga 1999) 42

54 43 (2.6) ] ˆ ˆ [ 1 1 K h h h h y x Usng hs equaon one can derve he acreage elasces measurng he change n he acreage allocaon from a one percen change n he explanaory varables. (2.7) J h h y y ˆ Usng he appendx n Mller and Plannga (1999) as a gude he covarance marx of he coeffcens ( h ˆ ) condonal on he explanaory varables can be esmaed by (2.8) 1 1) ( 1) ( ) ( )' ( 2 2 K K I X Σ I X such ha I s he deny marx and s a T(K-1) 2 x T(K-1) 2 marx where he dagonal elemens are ) 1 ( and he off dagonal elemens are ) (. Wh he MDP model defned he focus shfs o defnng he daa ha wll be used n he model. Table shows hsorcal averages of he shares and expeced ne reurns by crop. Shares of and ne reurns o WSG are relavely small hsorcally. Corn and soybeans are he mos prevalen crops n he area of sudy and hose wh he hghes ne reurns presumably n par because hey end o be grown on he land wh beer han average growng condons. Changes o ne reurns per acre n WSG may need o be large (such as a 50% or 100% ncrease) o cause a shf n acreage away from corn and soybeans n such areas. Whea also has a relavely small area bu he ne reurns are hgher han hose of WSG. Ths suggess ha WSG may compee more easly wh whea 1 Table 2 does no nclude Indana Mchgan Norheasern Mnnesoa or Oho as explaned n he nex secon.

55 whch s o say ha a more modes change n WSG reurns mgh cause whea acreage o decrease. Whea area may seem oo low o he nformed reader. However he acreage share esmaes for corn soy and whea were aen drecly from NASS; only WSG land cover area s aen from MODIS. Because hs research s dealng wh shares of oal land may sew percepon. To double chec random shares were aen from he daa and mulpled by oal CRD area o oban gross acreage esmaes. The resulng esmaes mached NASS daa o whn one acre whch can be assumed as roundng error. 2 II.4 Daa: WSG Reurns Ths research s chefly concerned wh he ncluson of a new daa source n he esmaon of land allocaed o he producon of WSG: NASA saelle mages. The saelle mage source has been prevously dscussed bu s mporan o dscuss he geographc naure of he daa. As shown n Fgure 2.1 WSG land cover has been prevalen n areas wh large areas of pasureland parcularly areas le Easern Nebrasa and Norh Daoa. Ths s mporan because nforms he dscusson of a proxy prce for WSG. There s no hsorcal prce for WSG so a proxy mus be chosen. Among opons consdered was assumng a bomass prce and converson rae based on pror leraure such as hose found n Brechbll Tyner and Ilele (2011); De La Torre Ugare e al. (2003); or Khanna Shungana and Clfon-Brown (2008) bu hs was seen as problemac because of he lac of varaon and he nably o provde a subsanve movaon for varaon. Anoher dea was o use he prce of hay bu hs daum was dffcul o oban a a couny level. Because of he srong ln beween WSG producon and pasureland he couny-level pasureland renal rae (PRR) colleced by NASS was 2 Table 6 shows he model esmaes for gross acreage whch may be more n lne wh expeced amouns. 44

56 chosen as he proxy for WSG producon ne reurns 3. The PRR whle consdered a good proxy for hsorcal WSG reurns s no colleced by NASS for he easern saes n he area of sudy namely Indana Oho and Mchgan along wh one Crop Reporng Dsrc 4 (CRD) n Mnnesoa. Gven ha area allocaed o WSG n hese regons s relavely low hey were excluded from he area of sudy. Furher NASS only repors PRR a he couny level from bu a sae level for all years n he sudy. To spread he PRR across he mssng years he average absolue dfference beween couny and sae PRR were aen as a measure of bass whch s assumed o be consan over me. Ths dfference was appled o he hsorcal sae raes o ge hsorcal couny raes. Ths provded boh he spaal and emporal varaon desred for hs research and s used o esmae he coeffcens menoned above for WSG reurns. II.5 Daa: Oher Reurns Oher explanaory daa n he model nclude expeced ne reurns for corn soy and whea as well as a rend varable and an nercep. Expeced ne reurns for esablshed crops are esmaed usng couny-level rend yelds varable coss of producon and a proxy for he forward conrac prce a he couny elevaor. Expeced yelds are rend yelds esmaed from couny level daa aen from NASS. Coss of producon are aen from ERS and assgned o counes based on whch Farm Resource Regon hey fall n. To oban couny-level fuures prces prces repored a gran elevaors are nerpolaed a he couny level. 5 These prces are compared o naonal prces repored from NASS and he average dfference over me s calculaed o ac as 3 The pasureland renal rae as well as all prces are n real erms. 4 Also nown as Agrculural Sascal Dsrcs (ASDs). 5 The auhor wshes o han Tm Maszw of he MU Deparmen of Geography for hs wor n nerpolang he gran elevaor prces. 45

57 an esmae of bass. Ths connecs easly obanable naonal level daa o couny level daa. To ln fuures prces o he couny level prces he Chcago Mercanle Exchange (CME) fuures prce was esmaed as a funcon of he lagged naonal mareng year crop prce. Ths creaed an neremporal bass esmae allowng naonal fuures prces o be dsaggregaed down o he couny level. Daly fuures prces were obaned from CME. Followng he procedure used by crop nsurance (Hofsrand and Edwards 2003) he average of daly selemen prces n February were used o calculae he fuures prce used. Corn and whea prces were based on December conracs whle soybean fuures prces were based on November conracs. II.6 Daa: Acreage Shares Esmaes of acreage allocaed o each use s one of he goals of hs sudy. As such acreage daa are necessary. Couny level acreage esmaes are aen from NASS for corn soy and whea. WSG acreage s aen from he NASA MODIS mages menoned before and aggregaed o couny level. All oher land n a couny s aggregaed no a sngle resdual caegory. All oher land as opposed o all agrculural land or all cropland s chosen for wo reasons. 1) The auhor s pror experence wh he MDP has shown ha small resdual caegores can be problemac n esmaon so he larges resdual caegory possble s desrable. 2) WSG can be produced on lands oher han hose radonally allocaed o producon agrculure ncludng CRP land. The possbly of producon n hese oher areas needs o be aen no accoun. Ths provdes an addonal benef n ha eeps oal area consan over me removng he need o esmae and possbly nroducng furher error. Due o he probablsc naure of he MDP shares of oal area are used nsead of gross acreage. 46

58 Usng mxed daases can cause ssues n esmaon. However hs research sees o use as much publcly avalable daa as possble and NASS esmaes are generally acceped. However as Wang e al. (2011) noe here may be an ssue wh he esmaon of WSG area wh regards o sprng whea. The sysem used o classfy he daa could cause sprng whea o be classfed as WSG. Whle he auhor was no able o ndependenly confrm he exsence of msclassfcaon errors s mporan o dscuss he errors possble mplcaons. Frs whea would be double couned n such an nsance whch would bas he share esmaes whch serve as he lef-hand-sde varable for hs research. WSG shares would be oo hgh snce non-wsg area s ncluded n he esmae whch would bas all oher share esmaes downward. Second wh area msclassfed responses o changes n explanaory daa may no follow expecaons. Tha s f area classfed as WSG were acually whea would respond posvely o changes n whea ne reurns as opposed o negavely as would be expeced for compeve WSG. Whle hese ssues are recognzed he area classfed as WSG s assumed o be WSG n he absence of a mehod o ndependenly confrm or correc for such errors. II.7 Daa: Pror Probables As menoned earler q s a se of pror probables whch represens a bas n he decson process (2.1) mposed by he economercan o cause he probables esmaed n he model o reflec he farmer s decson process more accuraely. Table 2.3 shows he pror probables mplemened n he model. These numbers were arrved a by ang a mnmum se of prors (all se a.05) and modfyng hem based on ceran assumpons abou producon agrculure. 1) Corn/soy roaon s srongly followed n he Mdwes ncreasng corn/soy and soy/corn probables. 2) Soy/Whea double croppng 47

59 and soy/whea roaons occur n some areas of sudy ncreasng soy/whea and whea/soy probables. Double croppng does no appear n he daa explcly bu nsead as concurren acres of soybean and whea n a sngle year. The approach here ncreases he poenal for soybean area leadng o more whea area and whea area leadng o more soybean area. These greaer probables would maes sense f n connuous roaon bu overloos he poenal ha soybean and whea ha are double cropped n one year wll be roaed o anoher crop n he nex year. The ncrease n probables o ae soybean and whea roaon no accoun s smaller han he ncrease for corn and soybean roaon correspondng o he expecaon abou whch of hese planng parameers comprses a greaer share of he relevan crop areas. 3) Resdual area because ncludes urban and non-agrculural (margnal) land s lely o reman n ha use once area s allocaed o ncreasng resdual/resdual probables. 4) Because WSG requres an esablshmen perod of hree o fve years and s a perennal area allocaed o WSG s more lely o reman n WSG ncreasng WSG/WSG probables. II.8 Spaal Correlaon Issues A couny level worng wh a daase of hs sze can presen some challenges. For he model o solve n a reasonable amoun of me each couny was coded o solve n auary. However hs presens ssues wh lely correlaon of errors across counes due o facors such as weaher. A hgher level of aggregaon such as naonal daa can address such ssues bu heerogeney across land ypes s los a such a level. One possble medum s solvng wh acreage aggregaed and explanaory daa averaged a CRD level. I should be noed ha n hs manner each CRD solves n auary bu hs s consdered an accepable assumpon because he correlaons across CRDs are lely 48

60 much weaer han he correlaons across counes. There are exernal facors ha can affec wde areas such as weaher paerns n general and parcularly large-scale droughs ha sugges correlaon among CRDs bu hese neracons n error erms are omed here. To compare he wo aggregaon levels corn own ne reurn elasces whea acreage-prr elasces and average error were calculaed afer he esmaon of he coeffcens and compared. A hsogram of couny level and CRD level corn ne reurns o corn area planed elasces can be found n Fgures 2.2 and 2.3. The shapes of he dsrbuons are very smlar hough he couny level has a slghly hgher mean ndcang a greaer level of response. Fgures 2.4 and 2.5 show he reurns of whea acreage o PRR he WSG ne reurn proxy. The shapes of he wo hsograms are lewse smlar bu he couny level has a greaer percenage of counes and years wh a posve elascy whch does no follow expecaons: gven he endency of WSG o grow n poorer qualy sol s expeced o compee wh oher crops ha grow n smlar condons namely whea. I should be noed here ha he magnude of he means repored n he hsograms canno be consdered a rue measure of he effecs because o allow for proper scalng and vsual represenaon of he daa any elasces greaer han hree or less han negave hree were forced o equal o hose values respecvely 6. Bu even ang ha no accoun one can see ha whea area has a very srong reacon o changes n PRR. These wo ses of fgures show ha he CRD level of aggregaon should perform n much he same manner as he couny level n auary. Bu he queson remans as o he relave level of performance beween he wo opons. To address hs 6 Ths change n elasces s purely for cosmec purposes and does no change he values of he coeffcens. 49

61 concern he average errors were esmaed for he acreage shares o ac as an ndcaor of f: T I 1 abs( y yˆ ) (2.9) MAE TI y 1 1 MAE s he percen mean absolue error: he absolue dfference of he esmaed acreage and he acual acreage over me for each crop normalzed by he acual acreage planed o ha crop averaged over me. As measures absolue devaon from hsorcal daa a lower number ndcaes a beer f. Because y represens a share as opposed o acual acreage hs esmae s a unless percenage. Ths does no have he same sascal applcaon as a normal R 2 bu does provde an dea of how he model performs specfcally of comparng he relave performance of he wo levels of aggregaon. The measure of f esmaes can be found n Table 2.4. The couny level provdes beer esmaes for soy and whea bu he CRD level provdes beer esmaes for WSG whch provdes a movaon for ulzng he CRD level of aggregaon. II.9 Consraned vs. Unconsraned Models Wh he model aggregaed and runnng a CRD levels analyss urned o he valdy of he resuls. As wren he model should run unconsraned o choose he coeffcens whch bes f he daa. Indeed an unconsraned model s desrable because may be consdered more sascally vald as more closely reflecs he relaonshps presen n he daa. However n appled economerc wor consrans are ofen mposed f he resuls do no f economc heory or f he daa may no perfecly reflec he suaon faced by he decson maer as n he case of proxes. To see f such consrans were necessary he model was run unconsraned and he elasces (as calculaed from (2.7) above) of he ne reurns varables were examned afer mposng a.05% acreage 50

62 share hreshold because areas wh small allocaons o crops could sew resuls by showng very large elasces for relavely small gross effecs. Fgure 2.3 s a hsogram of he elasces for corn ne reurns o corn acres planed. Whle he maory of CRDs and years follow heory wh a low posve mpac here s a no-nsgnfcan poron of areas and years whch have a negave mpac whch does no follow heory. Ths s seen furher n examnng soy ne reurns o corn acres (Fgure 2.6): here s a much wder spread and he maory of elasces are posve. Whle hs may sugges srong soy/corn croppng paerns s dffcul o usfy he asseron ha soy acres wll ncrease when he ne reurns o corn ncrease. WSG elasces are lewse problemac. Whle he relaonshp beween WSG and crops such as corn and soybeans may be argued here should be lle doub ha should have a posve own ne reurn elascy. Fgure 2.7 shows he elasces of pasureland renal raes o WSG area. The spread s exremely broad and over 20% of he elasces are srongly negave. Ths may ndcae a proxy problem bu gven he locaon of WSG pasureland renal raes were deermned o be he bes avalable proxy as suggesed earler. Pasure renal raes represen a poor proxy for WSG reurns n an area f s he case ha pasure and warm season grasses ac as subsues here wh unculvaed WSG replaced by seeded pasure n he even ha pasure reurns rse. These elasces mgh also ndcae oher ssues such as auocorrelaed error erms for example from a mul-year drough. The exac cause s unnown. In lgh of he resuls from Fgures and 2.7 a seres of consrans were mposed on he values of he coeffcens esmaed n (2.4). The elasces were ndrecly consraned by way of he coeffcens hemselves because elasces are no 51

63 explcly represened n hs esmaon mehod bu are calculaed ex pos nsead. These consrans were desgned o drec he model as lle as possble whle sll ensurng he correc sgns and relave magnudes on own ne reurns elasces. Gven he nown compeve naure of corn and soybeans negave cross effecs consrans were mposed on corn and soy ne reurns o soy and corn acres respecvely. Lewse because of nown soy-whea double croppng paerns n a small par of he sudy area cross effec resrcons are no appled beween hose crops. The consrans are no lsed here: her ndrec naure maes analyss unnformave. For he res of hs paper resuls presened wll reflec he consraned model. The consraned ne reurn elasces can be seen n Fgure 2.8. The elasces f heory much more closely wh posve own ne reurn effecs and mosly negave cross effecs. The noable excepon s soy/whea wh mxed cross effecs alludng o doublecroppng. The elasces ndcae a much hgher amoun of double croppng han s nown o exs n he area of sudy. However he amoun by whch one should consran he cross effecs s dffcul o asceran. These elasces are admedly no compleely deal. For nsance he corn ne reurn response o WSG s oo srongly negave greaer han he own reurn response. The greaer magnudes of cross-effec elasces can presen problems wh mulple smulaneous shocs. Tha s f boh reurns o corn and WSG ncrease by he same amoun wll cause a ne decrease n boh corn and WSG area due o he sronger cross effecs. However shocng one prce or reurn a a me should perform followng heory wh decreases n cross purposes and ncreases n own purposes o posve shocs. Wh he correc dreconal mpacs followng a shoc o one expeced ne reurn varable area allocaon wll also move n he correc drecon gven 52

64 exogenous oal area. There reman several poenal drecons for mprovng he consrans mposed here such as by argeng specfc elasces suggesed by prevous leraure on corn soybean and whea area response or else by ensurng more heorecal consrans such as symmery. However he dreconal mpacs are mosly correc and he focus of hs wor on WSGs undermnes somewha he value of basng parameers narrowly on prevous sudes of he man crops. I should be noed ha forcng he model o reflec expecaons dd no come whou cos. Whle he economcs are more closely followed he consrans mpac he sascal valdy of he errors of he coeffcens derved from he covarance marx n (2.8). For hs reason confdence nervals and -ess are no provded for he coeffcens. Furher he ably of he model accuraely o esmae acreage s negavely mpaced. Table 2.5 shows he dfference n gross errors (2.9) beween he consraned and unconsraned models. Whle he consraned model generally does poorer s worse wh he esmaon of WSG: he dfference n WSG errors s more han hree mes greaer han he nex hghes dfference n errors. Whle hs s unforunae he consrans are noneheless mposed o acheve resuls whch when shoced wh prce or polcy changes wll more closely follow economc heory n response f no n acual acreage. Because of he loss of goodness of f he res of he paper wll focus on relave changes n acreages based on shocs o he model. II.10 WSG Reurns Shoc and Area Response Wh he model area and consrans defned he focus of hs paper changes o WSG responses. To provde a frame of reference Fgure 2.9 shows he hsorcal share of 53

65 land allocaed o each CRD averaged over me. To show how WSG responds o changes he model was smulaed dynamcally over he sample perod calculaed eravely usng (2.5). To see how WSG responds o a sgnfcan shoc n prces PRR was doubled for all CRDs and years n he sample perod and he model was run agan. Fgures show he dfferences n area beween he baselne scenaro and he ncreased PRR scenaro averaged over me. Darer WSG areas ndcae greaer ncreases whle corn soy and whea area are darer as more land s los o hose uses. Each fgure has a second fgure wh (e.g. 2.10a) ha shows he dfference n area as a percen of he crop s base acres. Ths shows relave changes as opposed o gross changes. The resuls are surprsng n a couple ways bu before dscussng resuls should be noed ha specfc acreage ransons canno be assumed from hese maps. Because of he probablsc naure of he model shfs n acreage come from mos or all of he oher sources a once and hese maps are represenave purely of he ne effecs. Whle dscusson of such ndvdual ransons s possble would vary based on CRD and over me and such n-deph analyss falls beyond he scope of hs research. Here specfc ransons wll only be dscussed n he broades of erms. Doublng WSG reurns whle holdng all oher crop reurns consan causes WSG o ncrease proporonally mos n areas radonally allocaed o src corn/soybean roaons: namely Iowa souhern Mnnesoa and pars of Illnos as shown n Fgure Ths resul s mporan: shows ha WSG may ndeed compee wh radonal crops for land area f he prces for WSG are hgh enough a leas n hs represenaon of land allocaon. There were small relave ncreases n he wesern par of he sample 54

66 area wh lle o no ncreases n WSG n he upper norhern area coverng upper Mnnesoa and Wsconsn. One odd resul s he sharp border beween norhern Mssour and souhern Iowa. Souhern Iowa shows srong ncreases n WSG growh ncreasng area allocaed o WSG by 20-25% of oal land bu mmedaely across he border he ncreases call o beween 4-7%. The pasureland renal raes are abou $8 hgher on average n ha area of Iowa han hose n norh Mssour resulng n a $16/acre hgher rae under he shoc scenaro whch may explan he dfferences n he wo allocaons. Whea response s shown n Fgure Changes n whea area are sronges n areas where whea s radonally grown: Norh Daoa Souh Daoa and wesern Kansas. Nebrasa s response s no as srong and he mddle and easern pars of he sample area show lle o no land gong leavng whea producon wh he noable excepon beng he area around he booheel of Mssour and souhern Illnos. Bu even here he response s modes. The relave response n Illnos s somewha sronger bu ha owes o he lower amoun of acreage dedcaed o whea producon. Soybean area s shown n Fgure As menoned pror some areas hsorcally allocaed o corn and soybean roaon were planed wh WSG and hose areas are also shown here wh Illnos Iowa and souhern Mnnesoa losng soybean acres. However he loss of soybean land s no resrced o corn/soy areas. The easern Daoas and wesern Mnnesoa also lose soy area. Ths may be ndcave of changes n whea/soy crop roaon paerns gven he modes whea losses here as well. Corn area s shown n Fgure The corn loss area s farly concenraed n he mddle and easern pars of he sample area n gross erms. In relave erms mos areas lose a sgnfcan poron of area allocaed o corn. 55

67 For a broader loo changes n acreage devoed o each crop from he base scenaro and shocs can be seen n Table 2.6. Comparng he frs and second columns of daa show he oal regonal mpac of doublng pasure ne reurns on he allocaon of land. Subsanal land s aen away from corn and soybeans bu a smaller percenage from whea. Ths suggess conrary o pror expecaons ha corn and soy compee more easly han whea for a doublng of pasure reurns. Ths could also be arbuable o he relavely lower pasureland renal raes n he Grea Plans saes. The raes average beween $8 and $20 over me n ND SD NE and KS whle averagng $20 o $35 n IA WI IL and mos of MO. Doublng pasureland renal raes would herefore have a greaer mpac n hose saes where corn and soy are hsorcally grown. Wh hs n mnd he mpac on hose areas are lely much oversaed from he doublng of pasureland renal raes. However hs shoc was no nended o provde hsorcal conex merely o show ha hs model esmaed wh hese daa can generae acreage shfs whch does. Indeed gven he magnude of changes ha dd occur even when areas wh hgher PRR are consdered he model shows ha a much more modes change n PRR may cause land o be allocaed from radonal crops. Furher esng s needed o examne hese effecs more closely and specfcally he mpac of shocs o oher areas of he sysem. Thus hs research ess he model furher by applyng a more hsorcally enable shoc. II.11 Corn Ne Reurns Shocs and Area Response The nal shoc scenaro s nended o show how he model responds n regards o changes n WSG reurns. The magnude of he shoc s admedly srong followng 56

68 he earler hypohess ha a srong change n reurns o WSG would be necessary o shf land away from radonal crops such as corn/soy roaons and s here o provde resuls whch are clearly separable from oher coermnous effecs. I s useful however o see how he model responds o smaller more lely changes n prces. Chen and Khanna (2012) esmae ha by 2022 EISA mandaes wll cause a 23.5% ncrease n he prce of corn gven a conservave esmae on he avalably of sugarcane for ehanol producon. To draw a connecon beween he prce change of ha sudy o he ne reurns used by he model of hs sudy he shoc was mulpled by he average percen dfference beween prces and ne reurns n he hsorcal perod (93%). Ths mehod of assumng a proporonal ln beween prces and ne reurns assumes mplcly ha he prces of npus represened n he corn cos daa are also affeced. Ths represenaon mgh be conssen wh medum- or long-run relaonshps beween corn oupu and npu mares no an mmedae mpac of a prce change on ne reurns. To smulae changes n corn prce he model s run wh a +/- 21.9% dfference n corn ne reurns. Fgures show he changes n area wh respec o he lower corn ne reurns shoc. I s clear ha here are srong smlares beween Fgures 2.13 and There s a dfference n he scale of he wo maps lely a resul of he change n he shoc magnude. Bu he neresng smlary s ha he areas of relavely srong change are he same across separae shocs. Ths remans he case for soy and whea: wh changes n scale he srong areas of change for whea are he Daoas and Kansas and he srong areas of change for soy are he easern Daoas souhern Mnnesoa Iowa Illnos and norhern Mssour. The hgher corn ne reurns shoc follows he same paern. Therefore would be unhelpful o show he same maps agan. WSG are 57

69 somewha of an excepon. The srong areas sll show change bu here s expanson of lands n whch WSG s grown shown n Fgure More acres are allocaed relave o oher areas n Nebrasa and Mssour han n he WSG reurns shoc wh less n cenral and norhwesern Iowa. Fgure 2.18 shows he changes n corn area from he hgher corn ne reurn shoc. The hgher corn ne reurns maps loo he same as he lower (Fgure 2.14) wh a change from gans n area o losses. Ths paern follows for all oher hgher corn ne reurn maps. Therefore hey wll no be presened. The mporan dfference beween he maps are he legends showng he dfference n scales. Snce has been esablshed ha for he mos par he relave srengh of changes by crop shown n Fgures are consan across scenaros may be easer o examne he mpac of he shocs by examnng he daa by oher means. A hsogram of he shoc share dfferences by crop and scenaro averaged over me are gven n Fgure The shocs for he mos par follow economc heory n ha ncreases o corn ne reurns ncrease corn area whle decreasng oher areas. Whea does loo odd wh wha appears o be a no-nsgnfcan poron of he area on he wrong sde of each shoc scenaro. However each of hese are small enough (<.001 n absolue value) ha hey may be consdered effecvely zero. The means of he dfferences bear hs ou. The hsogram shows also ha WSG area does reac o changes elsewhere n he economy. Ths furher suppors he possbly ha WSG could compee wh radonal crops based solely on changes n he oher crops own ne reurns. For a more numercal analyss Table 2.6 also shows he regonal resuls of he wo corn ne reurn shocs. Area moves n he expeced drecon a he regonal level wh hgher corn ne reurns causng ncreases n corn area and decreases o oher crops. 58

70 The oppose occurs when corn ne reurns decrease. The model esmaes have WSG as very elasc overall: a 20% change n corn ne reurns resuls n 40% changes n WSG area. Ths ndcaes ha furher refnemen of he consrans may be needed or could pon o problems wh he use of pasure renal raes as a proxy for WSG ne reurns a he margn. Also may prove neresng o run hs model a he naonal level as opposed o he CRD level o apply more relevan naonal polcy shocs. II.12 Concluson Ths research sough o examne he relaonshps beween WSG and radonal crops namely corn soybeans and whea. To accomplsh hs WSG daa were obaned from NASA saelle mages and combned wh NASS ERS and gran elevaor daa for corn soybeans and whea. These daa were placed n a dynamc MDP o esmae changes n land use gven a change n reurns o WSG. However ssues arose wh he esmaon of coeffcens and elasces. The daa dd no fully cover he orgnally nended area he compuer could no a solve a model combnng CRD level coeffcens and couny level dummes and nal resuls dd no follow economc heory. To address hese concerns area of sudy was respecfed he level of share and explanaory daa aggregaon was changed o CRD and consrans were mposed on he coeffcens. The respecfed model had a decreased goodness of f bu allowed examnaon of relave changes n acreage n response o a prce shoc. Model performance was esed by changng ey exogenous daa. WSG and corn reurns were changed over he hsorcal perod. WSG ne reurns were doubled o es model performance o a very large shoc n parcular o see f hs specfcaon could perm exploraon of he possbly ha WSG compees wh he man crops n he 59

71 regon. In hs shoc acres allocaed o he dfferen uses moved n he expeced drecon wh area beng appropraely los or ganed from each of he maor crops. Ths resul shows ha f WSG s grown as a dedcaed source for cellulosc bofuel he model approach explored here could represen he degree o whch compees for land wh oher uses. However he MDP whle nally hough o be useful n he esmaon of lmed-daa scenaros proved o be problemac n hs case. In parcular he sze of he mpacs for he very large shoc o he proxy for WSG ne reurns mpled land use changes ha seemed mplausbly large reducng regonal corn soybean and whea area dramacally. The corn ne reurn shocs also provded dreconal effecs ha are correc bu no comparson s made wh oher sudes o confrm ha he magnudes conform o fndngs found n oher sudes and he mpacs of he corn shocs on WSG area sugges ha he model mgh over-sae he subsuon of WSG and oher land uses or a leas corn use. Furher research could ae hs daa sample and apply wh more radonal models o compare resuls. Alernavely refnemens n he esmaon mehod o ae no accoun spaal nerdependence or mpose parameer resrcons ha requre elasces o fall wh ranges ndcaed by oher research where relevan could be underaen. 60

72 II.13 References Adelman I.G A Sochasc Analyss of he Sze Dsrbuon of Frms. Journal of he Amercan Sascal Assocaon 53: pp Ahn S. A.J. Plannga and R.J. Alg Predcng Fuure Foresland Area: A Comparson of Economerc Approaches. Fores Scence 46(3): pp Brechbll S.C. W.E. Tyner and K.E. Ilele The Economcs of Bomass Collecon and Transporaon and Is Supply o Indana Cellulosc and Elecrc Uly Facles. Boenergy Research. 4: pp Burnham B.O Marov Ineremporal Land Use Smulaon Model. Souhern Journal of Agrculural Economcs 5(1): pp Carpener B. and M. Brees Swchgrass for Bofuel Proeced Budges for Crop Esablshed Unversy of Mssour Dep. Agr. App. Econ. Ocober. Chen X. and M. Khanna Food vs. Fuel: he Effec of Bofuel Polces. Amercan Journal of Agrculural Economcs 95(2): pp De La Torre Ugare D.G. M.E. Walsh H. Shapour and S.P. Slnsy The Economc Impacs of Boenergy Crop Producon on U.S. Agrculure. Washngon DC: U.S. Deparmen of Agrculure OEPNU Ag. Econ. Rep. 816 February. Devadoss S. and J. Bayham Conrbuons of U.S. Crop Subsdes o Bofuel and Relaed Mares. Journal of Agrculural and Appled Economcs 42 (4): pp Dcs M.R. J. Campche D. De La Torre Ugare C. Hellwncel H.L. Bryan and J.W. Rchardson Land Use Implcaons of Expandng Bofuel Demand. Journal of Agrculural and Appled Economcs 41 (2): pp Duffy M. and V.Y. Nanhou Coss of Producng Swchgrass for Bomass n Souhern Iowa. Iowa Sae Unversy Ex. PM 1866 Aprl. Golan A. G. Judge and D. Mller Maxmum Enropy Economercs: Robus Esmaon wh Lmed Daa. New Yor NY: John Wley and Sons. Golan A. and S. Vogel Esmaon of Non-Saonary Socal Accounng Marx Coeffcens wh Supply Sde Informaon. Economc Sysems Research 12(4): pp Hallberg M Proecng he Sze Dsrbuon of Agrculural Frms: An Applcaon of a Marov Process wh Non-Saonary Transon Probables. Amercan Journal of Agrculural Economcs 51: pp

73 Harde I.W. and P.J. Pars Land Use wh Heerogeneous Land Qualy: An Applcaon of an Area Base Model. Amercan Journal of Agrculural Economcs 79(2): pp Heady E. O Smplfed Presenaon and Logcal Aspecs of Lnear Programmng Technque. Journal of Farm Economcs 36(5): pp Helsel Z.R. and J. Alvarez Economc Poenal of Swchgrass as a Bofuel Crop n Florda. Dep. Farm Res. Econ. FE900 Unversy of Florda. Hofsrand D. and W. Edwards Crop Revenue Insurance. Dep. Econ. FM-1853 Iowa Sae Unversy. Holman J. R. Gllen J.L. Moyer T. Robers K. Harmoney P. Sloderbec T. Dumler K. Marn S. Saggenborg W. Fc S. Maxwell and C. Thompson Kansas Swchgrass Producon Handboo. Kansas Sae Unversy Agr. Exp. Res. Sa. MF3018 November. Jaynes E.T Informaon Theory and Sascal Mechancs. Physcal Revew 106(4): pp Kelley A.C. and L.W. Wess Marov Processes and Economc Analyss: The Case of Mgraon. Economerca 37(2): pp Khanna M. B. Dhungana and J. Clfon-Brown Coss of Producng Mscanhus and Swchgrass for Boenergy n Illnos. Bomass and Boenergy 32: pp Khanna M. A. Jan and A. Olver Producon of Boenergy Crops n he Mdwes. Unversy of Illnos Urbana-Champagne Dep. Agr. & Cons. Econ. FEFO Aprl. Km C.S. G. Schable and S. Daberow The Relave Impacs of U.S. Bo-Fuel Polces on Fuel-Energy Mares: A Comparave Sac Analyss. Journal of Agrculural and Appled Economcs 42 (1): pp Lubows R.N Deermnans of Land-Use Transons n he Uned Saes: Economerc Analyss of Changes Among he Maor Land-Use Caegores. PhD Dsseraon Harvard Unversy. Lubows R.N. A.J. Plannga and R.N. Savns Deermnans of Land Use Change n he Uned Saes Dscusson Paper Washngon DC: Resources for he Fuure Augus. 62

74 Wha Drves Land-Use Change n he Uned Saes? A Naonal Analyss of Landowner Decsons. Land Economcs 84 (4): pp McFadden D. and K. Tran Mxed MNL Models for Dscree Response. Journal of Appled Economercs 15: pp McRae E Esmaon of Tme-Varyng Marov Processes wh Aggregae Daa. Economerca 45: pp Mller D.J. and A.J. Plannga Modelng Land Use Decsons wh Aggregae Daa. Amercan Journal of Agrculural Economcs 81(1): pp Mller J.C. and K.H. Coble Incenves Maer: Assessng Bofuel Polces n he Souh. Journal of Agrculural and Appled Economcs 43 (3): pp Paap R. and H.K. van D Bayes Esmaes of Marov Trends n Possbly Conegraed Seres: An Applcaon o U.S. Consumpon and Income. Journal of Busness & Economc Sascs 21: pp Perrn R.K. K.P. Vogel M.R. Schmer and R.B. Mchell Farm-Scale Producon Cos of Swchgrass for Bomass. Boenergy Research 1: pp Publc Law (PL) Energy Independence and Secury Ac of frwebgae.access.gpo.gov/ cg-bn/gedoc.cg? dbname=110_cong_publc_laws& docd=f:publ pdf. March Ray D.E. D.G. De La Torre Ugare M.R. Dcs and K.H. Tller The POLYSYS Modelng Framewor: A Documenaon. Saff Paper Agrculural Polcy Analyss Cener Dep. of Agrculural Economcs and Rural Socology Unversy of Tennessee. Shannon C.E A Mahemacal Theory of Communcaon. Bell Sysem Techncal Journal 27: pp Smh R Swchgrass for Bomass. Dep. Agr. Econ. Unversy of Kenucy November. Thel H A Mulnomal Exenson of he Lnear Log Model. Inernaonal Economc Revew 10: pp Tompn J.R Response of he Farm Producon Un as a Whole o Prces Response of he Farm Producon Un as a Whole o Prces. Journal of Farm Economcs 40(5): pp

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76 II. 14 Appendx: Fgures and Tables Fgure 2.1: Mdwesern Land Covers Observed by MODIS Indcaon of Presence for Sx Ou of Ten Years Source: Susan Wang Unversy of Mssour Geography Dep. 65

77 Fgure 2.2: Corn Ne Reurns o Corn Area Planed Elasces Couny Level Aggregaon Unconsraned Source: Auhor s Esmaes Fgure 2.3: Corn Ne Reurns o Corn Area Planed Elasces CRD Level Aggregaon Unconsraned Source: Auhor s Esmaes 66

78 Fgure 2.4: Pasureland Renal Rae o Whea Area Planed Elasces Couny Level Aggregaon Unconsraned Source: Auhor s Esmaes Fgure 2.5: Pasureland Renal Rae o Whea Area Planed Elasces CRD Level Aggregaon Unconsraned Source: Auhor s Esmaes 67

79 Fgure 2.6: Soy Ne Reurns o Corn Acres Planed Elasces CRD Level Unconsraned Source: Auhor s Esmaes Fgure 2.7: Pasureland Renal Rae o Warm Season Grass Acres Elasces CRD Level Unconsraned Source: Auhor s Esmaes 68

80 Fgure 2.8: Ne Reurns Elasces CRD Level Consraned Model Source: Auhor s Esmaes 69

81 Fgure 2.9: Hsorcal Warm Season Grass Area by CRD as a Percen of Toal Land Average Source: NASA MODIS Saelle Imagng Daa 70

82 Fgure 2.10: Change n WSG Area n Response o Doubled WSG Reurns Average Measured n 1000 Acres Source: Auhor s Esmaes Fgure 2.10a: Change n WSG Area n Response o Doubled WSG Reurns Average Measured as a Percen of Base Scenaro Acres Source: Auhor s Esmaes 71

83 Fgure 2.11: Change n Whea Area n Response o Doubled WSG Reurns Average Measured n 1000 Acres Source: Auhor s Esmaes Fgure 2.11a: Change n Whea Area n Response o Doubled WSG Reurns Average Measured as a Percen of Base Scenaro Acres Source: Auhor s Esmaes 72

84 Fgure 2.12: Change n Soybean Area n Response o Doubled WSG Reurns Average Measured n 1000 Acres Source: Auhor s Esmaes Fgure 2.12a: Change n Soybean Area n Response o Doubled WSG Reurns Average Measured as a Percen of Base Scenaro Acres Source: Auhor s Esmaes 73

85 Fgure 2.13: Change n Corn Area n Response o Doubled WSG Reurns Average Measured n 1000 Acres Source: Auhor s Esmaes Fgure 2.13a: Change n Corn Area n Response o Doubled WSG Reurns Average Measured as a Percen of Base Scenaro Acres 74

86 Fgure 2.14: Change n Corn Area n Response o Lower Corn Ne Reurns Average Measured n 1000 Acres Source: Auhor s Esmaes Fgure 2.14a: Change n Corn Area n Response o Lower Corn Ne Reurns Average Measured as a Percen of Base Scenaro Acres Source: Auhor s Esmaes 75

87 Fgure 2.15: Change n Warm Season Grass Area n Response o Lower Corn Ne Reurns Average Measured n 1000 Acres Source: Auhor s Esmaes Fgure 2.15a: Change n Warm Season Grass Area n Response o Lower Corn Ne Reurns Average Measured as a Percen of Base Scenaro Acres Source: Auhor s Esmaes 76

88 Fgure 2.16: Change n Soy Area n Response o Lower Corn Ne Reurns Average Measured n 1000 Acres Source: Auhor s Esmaes Fgure 2.16a: Change n Soy Area n Response o Lower Corn Ne Reurns Average Measured as a Percen of Base Scenaro Acres Source: Auhor s Esmaes 77

89 Fgure 2.17: Change n Whea Area n Response o Lower Corn Ne Reurns Average Measured n 1000 Acres Source: Auhor s Esmaes Fgure 2.17a: Change n Whea Area n Response o Lower Corn Ne Reurns Average Measured as a Percen of Base Scenaro Acres Source: Auhor s Esmaes 78

90 Fgure 2.18: Change n Corn Area n Response o Hgher Corn Ne Reurns Average Measured n 1000 Acres Source: Auhor s Esmaes Fgure 2.18a: Change n Corn Area n Response o Hgher Corn Ne Reurns Average Measured as a Percen of Base Scenaro Acres Source: Auhor s Esmaes 79