Effect of crop choce on splt fertlzer applcaton Mra Nurmakhanova Department of Economcs Iowa State Unversty Ames, Iowa (515) 294-5051 mra@astate.edu Selected Paper prepared for presentaton at the Amercan Agrcultural Economcs Assocaton Annual Meetng, Long Beach, Calforna, July 23-26, 2006 Copyrght 2006 by author. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copyrght notce appears on all such copes.
Effect of crop choce on splt fertlzer applcaton Agrculture provdes a wde varety of envronmental amentes and dsamentes. On the postve sde, farms provde open space and scenery. On the negatve sde, agrculture s a major contrbutor to numerous envronmental problems. Ntrogen s an essental plant nutrent requred to produce food and fber. Whle the ncrease n the use of ntrogen fertlzer n agrcultural producton has contrbuted to the ncrease n food and fber producton n the Unted States n recent years, t has also been dentfed as a major contrbutor to the elevated concentraton levels of ntrates n groundwater and surface water. Hgh concentraton levels of ntrates n drnkng water suppled from groundwater and surface water have become a publc concern because of ther rsks to human health. The Pew Oceans Commsson on June 5, 2003 called for the federal government to force farmers to cut polluton runnng nto waterways or rsk losng federal ad (http://www.pewoceans.org/). The commsson s report says problems such as ocean dead zones wll not mprove unless farmers try to lve up to the Clean Water Act. Some of the statstcs show that Iowa and Illnos are two of the bggest sources of ntrogen runnng down the Msssspp Rver to the Gulf of Mexco (US Geologcal Survey). They account for up to 35 percent of the ntrogen washng down the Msssspp Rver watershed, whch covers 41 percent of the lower 48 states. The amount of ntrogen fertlzer appled n excess of the amount taken up by the plant fertlzed s a major source of ntrogen leachng nto ground water. As a consequence, understandng the determnants of fertlzer and pestcde use, ncludng the
Introducton tmng of applcaton as well as the quantty appled s an mportant element n beng able to solve these problems. Targetng vulnerable areas to reduce ntrate leachng and runoff assocated wth ntrogen fertlzer use nto groundwater and surface water s plausble natonal envronmental polcy. The targetng approach recognzes the dfferences n the vulnerablty of varous types of sols and crops to leachng and runoff and, correspondngly, prescrbes dfferent polces to mnmze (or at least mtgate) ntrate leachng or runoff. In order to reduce the ntrogen fertlzer use that s threat to the groundwater under the targeted cropland and surface water adjacent to the targeted cropland, a varety of methods s avalable. One approach s to adopt a fertlzer reducng farmng practce, such as a crop rotaton n whch a legume crop (soybeans) s rotated wth a non-legume crop (corn). The legume crop s used to provde fxed-ntrogen as a substtute for fertlzerntrogen. Adopton of ths sort of crop rotaton can reduce the resdual ntrogen n the sol through a reducton n the frequency and amount of ntrogen fertlzer appled on a feld. Another approach s related to choosng tmng of fertlzer applcaton. Feld experments show that for certan types of sol, applcaton of ntrogen fertlzer after plantng can be more effectve than before plantng n reducng ntrogen losses, thereby reducng the aggregate amount of ntrogen fertlzer that must be appled and, therefore, reducng producton cost. Tme of ntrogen fertlzer applcaton studes have been reported extensvely n the lterature. The general concluson has been that ntrogen fertlzer should be appled nearest to the tme t s needed by the crop,.e., sde-dressed several weeks after corn emergence (Huang et al. 1999).
Introducton Ths study focuses on understandng determnants of farmers decson makng related to crop choce and tmng of fertlzer applcaton when farmers decde on both. One common approach to capturng the nfluence of land allocaton on adoptng alternatve farmng practces related to tmng of fertlzer applcaton s to treat crop choce as an exogenous varable n cross-secton estmaton of the farmng practce choce problem. A typcal approach s to estmate a sngle-equaton, dscrete choce model of technology adopton such as multnomal logt wth crop choce as a rght handsde varable. Alternatvely, some studes estmate the technology choce model condtonal on crop choce. In contrast to prevous work, ths paper estmates the parameters of a nested logt model of the jont probablty of fertlzer applcaton tmng and land allocaton. Relatve to a standard multnomal logt, the nested logt approach relaxes the assumpton of Independence of Irrelevant Alternatves and allows capturng the smlartes among dfferent crop-farmng practce choces. For example, adopton of a partcular cropfarmng practce par may depend on crop specfc ntrogen fertlzer requrement so one would expect that substtuton among fall and sprng fertlzer applcatons for corn would dffer from substtuton patterns among fall and sprng fertlzer applcatons for soybeans. The nested logt framework generalzes the multnomal logt model to allow for correlaton among dfferent groups of crops and farmng practces. Understandng the factors that nfluence adopton of a crop-farmng practce par s mportant for polcy desgn. Through more accurate modelng of crop-farmng practce adopton t s possble to desgn more approprate and effectve nterventons that can mprove envronmental qualty at lower economc cost.
Prevous research Prevous research Applcaton of dscrete choce models n emprcal studes of the adopton pattern of farmers s qute extensve. Most are behavoral studes that examne the nfluence of factors such as farmer characterstcs (human captal, atttude toward rsk, preferences for envronmental qualty), natural features of the farm (sol structure, slope) and attrbutes of the farm operaton (farm sze, off-farm labor). Some examples of dscrete choce varables are: adopton of conservaton tllage, adopton of rrgaton technologes, adopton of conservaton practces, etc. The emprcal lterature on farmng practce choce has dentfed the avalablty of a feld for workng n sprng as an mportant ncentve for farmng practce adopton (see Fletcher and Featherstone 1987; Fenerman, Cho, and Johnson 1990; Kramer, McSweeney, and Stavros 1983; Huang, Hefner, Taylor, and Ur 2000). Splt applcaton of ntrogen mght provde nsurance aganst the rsk that a late sprng applcaton wll be nfeasble. Factors affectng avalablty of feld n sprng nclude weather condtons, sol characterstcs, and tllage system choce. One consstent fndng n the farmng practce adopton lterature s the mportant role of envronmental condtons. Some studes, such as conducted by Wu and Babcock, Wu and Segerson, and Soule fnd that feld and sol characterstcs such as clay percentage, organc matter content, avalable water capacty, slope, and land capablty class are mportant factors nfluencng the adopton of alternatve farmng practce. Importance of weather condtons on choce of crop and farmng practce has been examned n emprcal lterature by many researchers. It has been found that some clmatc factors such as mean values of maxmum and mnmum temperature durng the
Prevous research crop growng season and mean values of maxmum and mnmum precptaton durng the crop growng season along wth ther standard devatons play an mportant role n choosng crop (Wu et al. 2003). Another consstent fndng n the farmng practce adopton lterature s the mportant role of these clmatc factors on farmng practce adopton (Kurkalova, Clng, and Zhao 2003). Another nterestng outcome of many econometrc studes on farmng practce adopton s the mportance of sol ntrogen testng (see Wu and Babcock; Cooper and Kem 1996; Cooper 1997). Some studes have looked at the nfluence of soco-economc characterstcs of farmers, farm characterstcs, and farm attrbutes on the adopton of farmng practces. They found that some farmers characterstcs such as college educaton and years of experence play an mportant role n farmers decson makng regardng adopton of farmng practces (Cooper and Kem1996; Soule 2001; Wu and Babcock 1998). Another consstent result n econometrc studes on farmng practce adopton s mportance of farm sze (Lchtenberg 2001; Soule 2001). It s not surprsng snce the bgger s the farm sze the more tme t requres to fnsh plantng and the hgher the farmers perceved probablty of not beng able to apply ntrogen after plantng, farmers n ths case wll allocate more ntrogen before plantng. One of the mportant results n farmers practce adopton lterature s that the type of crop grown s mportant n determnng the practce selected (see Wu et al. 2003; Lchtenberg 2001; Huang, Ur, and Hansen 1999). Fertlzer requrements vary by crop. Consequently, farmers decson makng on adoptng farmng practce depends on the choce of crop.
Prevous research The model used n work of Wu et al. on the desgn of sol conservaton polces consders the land allocaton and farmng practce adopton decsons as jont and the authors decompose the jont probablty nto the product of a condtonal (farmng practce crop) and a margnal (crop) probablty. However, they estmate these probabltes ndependently, makng the assumpton that the margnal and condtonal probabltes are uncorrelated. Ths approach to measure the crop choce on farmng practce adopton decson s not satsfyng for the reason that the factors affectng farmng practce also affect crop choce, wth the result that farmng practce adopton s treated as a jont decson wth crop choce. For example, land characterstcs such as feld slope and organc matter content can have a strong nfluence on the choce of crop as well as farmng practce. Ths suggests that crop choce and farmng practce adopton should be modeled as a smultaneous system. Thus, assumpton that the condtonal (farmng practce crop) and margnal (crop) probabltes are uncorrelated gnores more complcated pattern of correlatons among alternatves and as a result, coeffcent estmates of that model are based. As an alternatve, the nested logt framework allows for correlaton among dfferent groups of technology and crops, effectvely capturng the realstc constrants faced by farmers when selectng nputs and outputs. Although specfcaton of the nested logt model mposes an ex ante structure on substtuton patterns, often the relevant structure s qute apparent, especally when the researcher s consderng adopton of well-known farmng practces n a partcular settng. In case of fertlzer applcaton tmng decson studed here, the nestng structure s based on real physcal constrants faced by farmers.
Prevous research Ths study consders the queston of land allocaton and farmng practce adopton wth reference to the problem of splt fertlzer applcaton. Understandng the factors that nfluence adopton of runoff-reducng practce s mportant for polcy desgn. The nested logt model of jont choce of crop and tmng of fertlzer applcaton s employed to address ths ssue. Data and Model Specfcaton Emprcal Model Ths paper presents an economc model that analyzes the adopton decson of a farmer who s assumed to make a crop choce and fertlzer applcaton tmng decsons by choosng the combnaton that yelds the maxmum expected utlty. Farmer can choose among three crops (corn, soybeans, and hay) and whether to apply fertlzer n sprng only (so) or to use splt applcaton n fall and sprng (fs). Therefore, farmng practce adopton (decson on tmng of fertlzer applcaton) s taken to be a choce over two alternatves: (1) fall and sprng (splt) fertlzer applcaton vs. (2) only sprng fertlzer applcaton. The farmer chooses the crop and farmng practce par that maxmzes hs expected utlty. The crop-farmng practce choces are represented on Fgure 1 as a twolevel nested choce where the farmer chooses crop and tmng of fertlzer applcaton jontly, but for each crop the tmng of fertlzer applcaton mght dffer. Let U nj represent the n -th farmer s utlty from growng crop wth farmng practce j. The farmer wll choose the j -th alternatve f Unj > Unkl k and j l. The farmer s preferences are unknown to the researcher so hs utlty functon s consdered as a random from the perspectve of the analyst (McFadden) and s wrtten as
Data and model specfcaton: Emprcal model (1) Unj = Vnj + εnj, where V nj -s the observed component; ε nj -s an unobserved component (random error term) Suppose that the farmer chooses among = 1,..., T crops and j = fs, so farmng practces and assume that the vectors ( ) n ε of ε nj s for a gven farmer are ndependently and dentcally dstrbuted wth the Generalzed Extreme Values (GEV) dstrbuton, and ε nj are uncorrelated across nests but not wthn nests. Then the probablty that farmer chooses crop and tmng of fertlzer applcaton j s the jont probablty: (2) P j Vj V l exp exp l so, fs θ = θ = Prob( crop, tmng j) = V l T V kl exp exp l= so, fs k= 1 l= so, fs θ θ k θ that can be reduced to: (3) Vj exp θ V l Pj = Prob( crop, tmng j) = exp l= so, fs T V θ kl exp k= 1 l= so, fs θ k θ 1 where = 1,..., T and j = fs, so.
Data and model specfcaton: Emprcal model In (2) frst term P j = Vj exp θ V l exp θ l= so, fs represents the probablty that alternatve j s chosen condtonal on nest beng selected. Second term denotes the probablty that nest s chosen. Specfyng V nj as P = l= so, fs T k= 1 l= so, fs θ V l exp θ V kl exp θ k (4) Vnj = αj Z + β Xj + ηw + γ Y where Z -s a vector of observed ndvdual characterstcs that affect the crop- farmng practce choce; X j s a vector of observed attrbutes of the crop- farmng practce j ; W Y s a vector of ndvdual characterstcs affectng crop choce; s a vector of attrbutes affectng crop choce; α j s a vector of parameters for observed ndvdual characterstcs that affect the crop- farmng practce choce; β s a vector of parameters of observed attrbutes of the crop- farmng practce j ; η s a vector of parameters of ndvdual characterstcs affectng crop choce; γ s a vector of parameters of attrbutes affectng crop choce; Thus, ths model estmates farmng practce and crop choces by ncorporatng both ndvdual characterstcs and choce attrbutes, therefore, the coeffcents of
Data and model specfcaton: Emprcal model ndvdual feld characterstcs vary by choce, but the coeffcents for choce attrbutes do not. Defnng an nclusve value for each crop as l (5) ( ) Z Xl I ln = e α + β l= so, fs The second term n equaton (2) can be expressed as (6) P = T e k= 1 W+ Y+ I η γ θ e k W+ Y+ I η γ θ, where T s the choce of three crops: corn, soybeans, and hay. The nclusve value I explctly lnks crop choce to the technology choce. The coeffcent θ s a measure of ndependence among the choces n the nest gven the -th crop and the statstc 1 s a measure of correlaton (Tran, 2003). When θ = 1 there s complete ndependence among choces n the -th nest, therefore, the model collapses to multnomal logt. Therefore, a test of restrcton that θ = 1 tests whether the IIA assumpton s approprate. θ Data The mplementaton of the framework descrbed requres data, that must be ntegrated from multple sources. The data used n ths paper comes from the 1992 Area Study survey conducted by the Economc Research Servce (ERS) and the Natonal Agrcultural Statstcs Servce (NASS) of the U.S. Department of Agrculture (USDA). A total of 12 Area Study stes were sampled. Areas were selected to correspond to water systems under study by the U.S. Geologcal Survey (USGS) for water qualty.
Data and model specfcaton: Data The Area Studes data ncludes detaled nformaton on both producton actvtes and envronmental characterstcs for 1,799 sample ponts n Iowa and Illnos. Personal ntervews wth farm operators were conducted to collect nformaton on agrcultural practces n the felds and socoeconomc characterstcs of the farms where the sample ponts fell. The sample ponts were chosen to correspond wth Natonal Resource Inventory (NRI) sample ponts, whch nsures that nformaton on sol propertes s avalable, and also provdes a statstcal aggregaton. The expected profts and the varances of the profts from growng corn and soybeans are estmated usng the followng formulas (Ban and Engelhardt): E( π ) = E( p) E( y) + ρ( p, y) sd( p) sd( y) C 2 2 V( π) E( y) V( p) + E( p) V( y) + 2 E( p) E( y) ρ( p, y) sd( p) sd( y), where p s the output prce, y s the crop yeld, C s the non-random producton cost, and E(), V(), sd(), ρ(,) are mean, varance, standard devaton, and correlaton coeffcent operators, respectvely. Because the producton of hay s less senstve to weather condtons, proft from growng hay s assumed to be non-stochastc and estmated by subtractng the ste-specfc producton costs from the expected revenue. Several approaches have been used to estmate farmers expected prces. Future prces, lagged market prces, support prces, and target prces were used to model farmers expected prces. Based on prevous studes, the expected prce for corn was specfed as the hgher of the weghted target prce and the average futures prce n the corn plantng season (Wu et al., 2003). Followng procedure used by Wu and others, the weghted target prce s calculated by multplyng the corn target prce by the porton of corn base
Data and model specfcaton: Data permtted for corn plantng (1-Acreage Reducton Program [ARP] rate for corn). Data on ARP rate and target prce were taken from USDA publcatons. The average futures prce for corn n ts plantng season was estmated as average of closng prces n March on the Chcago Board of Trade (CBOT) for December corn. Soybeans s a non-program crop, and expected prce for soybeans was specfed as the average futures prces n ts plantng season, whch were estmated as the average of closng prces n March on the CBOT for November soybeans. Hay s a mult-year, non-program crop. As expected prces for hay the market prces lagged one year were used. Data on actual county level yelds and annual prces for dfferent crops were gathered from Natonal Agrcultural Statstcs Servce (NASS) webste http://www.nass.usda.gov:81/pedb/. County-level, tme-seres crop data from NASS were used to estmate expected yelds and yeld varance n each county. A trend model y = α + βt + ε was estmated usng OLS n each county for NASS data from 1970 to 1990. The resultng predctons were taken as expected yelds. The estmated resduals were then used to generate the varances of yelds, whch are assumed constant over tme. The nontruncated correlaton between prce and yeld was estmated to be (-0.381) for corn and (-0.192) for soybeans. Chavas and Holt: The perceved varances of corn and soybeans prces were estmated followng 3 t = ω j t j t j 1 t j j= 1 V( p ) p E ( p ) 2
Data and model specfcaton: Data where the weghts are 0.5, 0.33, and 0.17; pt j s the annual average of market prce for corn or soybeans n year t j and Et j 1 s the expectaton, at plantng tme of year t j, of the prce for the crop at harvestng n year t j. Ste-specfc producton costs were developed through the use of USDA s Croppng Practces Survey (CPS) data to generate statstcally representatve costs by state, crop, prevous year crop, and tllage type. Data on weather characterstcs were gathered from the Natonal Clmatc Data Center (NCDC) webste http://cdo.ncdc.noaa.gov/plclmprod/plsql/poeman.poe. Varables defntons The varables used to descrbe the choce of crop are 1) expected proft from growng ths crop, 2) varablty of expected proft, 3) choce of crop n prevous plantng season, 4) clmatc condtons, and 5) sol characterstcs. The varables are assumed to affect the choce of crop n the followng way: 1. Increase n expected proft should ncrease the lkelhood of choosng that crop. 2. Varablty n expected profts should decrease (or at least not ncrease) the lkelhood of choosng that crop (Wu et al. 2003; Kurkalova, Clng, and Zhao 2003). 3. Selecton of ths year s crop mght be affected by the prevous year s crop choce, a reflecton of rotatonal practces n the study regon (Wu et al. 2003, Wu and Babcock 1998). 4. Dfferent clmatc condtons mght favor choce of some crops and prevent choce of other crops. For example, Wu et al. found that crop choce s affected by temperature and precptaton levels durng corn growng season.
Data and model specfcaton: Varables defnton 5. Organc matter contrbutes to plant growth through ts effect on the physcal, chemcal, and bologcal propertes of the sol. It has a 1) nutrtonal functon n that t serves as a source of N, P for plant growth, 2) bologcal functon n that t profoundly affects the actvtes of mcroflora and mcrofaunal organsms, and 3) physcal and physco-chemcal functon n that t promotes good sol structure, thereby mprovng tlth, aeraton and retenton of mosture and ncreasng bufferng and exchange capacty of sols. 6. Feld slope: t s defned as the gradent of the feld, measured as a percentage (Wu and Babcock 1998; Wu et al. 2003). The set of varables that affect farmers decson regardng the adopton of cropfarmng practce par ncludes: clmatc parameters, sol characterstcs, human captal factors, farm characterstcs, and management practce. The decson to adopt a partcular crop-farmng practce par s affected by weather condtons (Fletcher and Featherstone 1987; Fenerman, Cho, and Johnson 1990; Kurkalova, Clng, and Zhao 2003; Wu et al. 2003): - Precptaton n the fall/sprng keeps sols wet longer, thus leavng fewer days for feld work n fall/sprng. - Hgher temperature varablty n fall/sprng leaves less days sutable for the feld work n fall/sprng. To capture the yeld dfferences among NRI stes, physcal varables reflectng land qualty at ndvdual NRI stes are ncluded as ndependent varables nto the model: - Clay content: also affect how much of fertlzer appled n the fall s lost through leachng. The amount and knd of clay greatly affect the fertlty and physcal condton
Data and model specfcaton: Varables defnton of the sol. They determne the ablty of the sol to adsorb catons, retan mosture, and nfluence the shrnk-swell potental, permeablty, plastcty, the ease of sol dsperson, and other sol propertes (Wu and Babcock 1998). To address farmer-level decson makng on each feld, nformaton about farmer for each feld n sample along wth farm s characterstcs nclude: - Educaton of operator: More educated farmers are more aware of negatve envronmental consequences of fall fertlzer applcaton and t mght force operator to apply t n the sprng rather than n the fall. Dscrete varable descrbes farmer s educaton and takes values from 1 tll 6 dependng on formal educaton the operator has (Cooper and Kem 1996; Soule 2001). - Sze of operaton: Total acreage operated by the farmer was ncluded as an ndcator of sze of operaton. The bgger s the farm the more tme t requres to fnsh plantng. Iowa State Unversty Extenson publcatons can be used to estmate the number of acres that can be completed per hour for dfferent types and szes of machnes and total number of feld days requred to complete a seres of machnery operatons, such as tllage and plantng. They also provde wth the dstrbuton of feld days recorded for the Aprl 2 to June 3 perod (Cooper and Kem 1996; Soule 2001). Table 1 presents the lst of explanatory varables used n the nested logt model and ther descrptve statstcs. Educaton of the operator s a dscrete varable that vares from 1, ndcatng that operator s educaton s less than hgh school, to 6 showng that operator fnshed graduate school. Average value of educaton n a study regon s around 3 that corresponds to vocatonal tranng after hgh school.
Data and model specfcaton: Estmaton results Estmaton Results The nested logt was estmated usng full-nformaton maxmum lkelhood (FIML) estmatons. Parameter estmates of factors affectng adopton of crop-farmng practce are presented n Table 2. Table 3 contans the estmates for crop choce determnants. Overall, the model performs well; t correctly predcts the adopton of alternatve crop-farmng practce pars at 71 percent of the sample ponts. The hypothess that the coeffcents of the nclusve values are equal to 1 can be rejected for all specfcatons at least at 1 percent level. Also, all three nclusve values are jontly sgnfcantly dfferent from 1. An nclusve value coeffcent sgnfcantly dfferent from 1 suggests dssmlarty among all avalable alternatves. Ths result supports the choce of a nested logt model, over the more restrctve condtonal logt model that does not allow for correlaton wthn nests. The nclusve value measures the attractveness of choosng fall fertlzer applcaton relatve to only sprng one gven choce of crop. From table 2, whch contans the estmates of factors affectng adopton of crop-farmng practce, we see that the sze of operaton has the expected sgn and s sgnfcantly dfferent from zero. The probablty of fall fertlzer applcaton s ncreasng wth the sze of operaton. The negatve sgn of fall precptaton coeffcent and standard devaton of fall temperature coeffcent suggest that bad weather condtons n the fall wll keep farmers out of feld. The educaton of operator s sgnfcantly dfferent from zero for fall fertlzer applcaton n corn producton suggestng that human captal factors such as knowledge and specalzaton n growng a partcular crop can have a sgnfcant mpact on the crop-farmng practce choce. Sandy sols store less water and are therefore lkely to produce less plant growth than sols wth more clay. The postve effect of clay content
Data and model specfcaton: Estmaton results on the probabltes of choosng fall fertlzer applcaton for soybean and hay reflects ths fact. From table 3, whch contans the estmates for crop choce determnants, we see that for the statstcally sgnfcant varables, the sgns are generally as expected. For example, selecton of ths year s crop s affected by choce of crop n the prevous year, a reflecton of rotaton practces n the regon. If the prevous crop s hay then ts effects on probabltes of choosng corn has postve sgn. Also, f prevous crop s corn then there s hgher chance that farmer chooses corn ths year; however, f prevous crop s soybeans then farmers are more lkely to grow corn and less lkely to grow soybeans. These results reflect the fact that contnuous corn and corn-soybean rotaton are the most popular croppng systems n the study regon. Slope s sgnfcant for crop producton: corn s more lkely to be planted on a sloped land than hay; and the negatve sgn of slope for soybeans, even beng nsgnfcant, ndcates that soybeans are less lkely to be planted on steep land. These results support the fndng of Wu, Adams, Klng, and Tanaka that steeper slopes are more lkely to be allocated to corn and hay than to eroson-prone soybeans. Snce mcrobal actvty s essental for the release of plant nutrents from dead plant materal, a relatvely large amount of organc matter n the sol s often assocated wth elevated crop yelds (Sol Conservaton Servce). Therefore a postve sgn of OM coeffcent s not surprsng n both cases of producng corn or soybeans. The standard devaton of sprng precptaton does not favor choce of corn and soybeans over hay. The negatve sgn of standard devaton of sprng precptaton for corn and postve for soybeans reflect the fact that large ranfall events durng the corn growng season have a negatve effect on the choce of corn and a postve effect on the choce of soybean.
Data and model specfcaton: Estmaton results Varablty of expected profts affects dfferently probablty of choosng corn and soybeans relatve to hay: the postve sgn of varance n expected proft for soybean ndcates that when the varance n expected proft for soybean becomes bgger most probably farmers wll stll prefer plantng soybeans to growng hay. It mght reflect the fact that farmers are not rsk-averse. However, the negatve effect of proft s varance on probablty of choosng corn relatve to hay mght reflect the fact that corn-hay rotaton s very common n the regon of study and farmers can swtch between these crops more quckly. Fnally, ncrease n own proft for any choce of crop ncreases the lkelhood of farmers choosng that crop. Snce nested logt s a nonlnear model, the mpact of any explanatory varable ( x k ) on probablty of choosng any crop-farmng practce par P j s not constant over the range of explanatory varable, therefore, the margnal effects are calculated for mean values of explanatory varables. The margnal effects n table 4 for the varablty n proft from growng certan crop are computed as the dervatve of margnal probablty of adoptng crop wth respect to the varablty of proft. Denote the varablty of proft from growng crop as y and the coeffcent on y as β. The margnal effect of adoptng crop due to a change n the own proftablty of adopton s: P y ( 1 P) = Pβ y wth the cross-proft effect gven by P y j = β PP y j Own-prce elastcty could be calculated as ε P y = = β y (1 P) y P y y wth cross-prce elastcty gven by ε P y = = β y P j y j y j yj P
Data and model specfcaton: Estmaton results In addton, the margnal effect of change n attrbute m n the utlty functon for alternatve J n branch I on the probablty of choce j n branch s gven by: P x j m ( ) 1( ) [ 1( ) ] = β P 1 = I j = J P + j = J P τ P xm j JI J J JI Margnal effects are presented n tables 4 and 5. From a polcy perspectve, margnal effects of proftablty are of the most nterest snce t can be changed by publc nterventon through tax and subsdy programs. Table 4 presents margnal effects of proftablty on a crop choce. Table 5 contans margnal effects of proftablty on choosng the crop-farmng practce par. The proftablty of growng crop has a large effect on crop choces wth own prce elastctes of 0.859 and 1.17 for corn, 1.057 and 1.063 for soybeans, and 0.564 wth 0.645 for hay for fall/sprng and sprng only fertlzer applcaton, respectvely. It ndcates that relatvely modest changes n proftablty can stmulate changes n land allocaton. The on-dagonal elements n tables 4 and 5 are postve, ndcatng that the probablty of choosng crop and crop-farmng practce par ncreases as ts proftablty ncreases. It suggests that farmng practce subsdy programs, perhaps offered by envronmental agences, may meet wth consderable success. Concluson Ths artcle dffers from the prevous lterature on the adopton of farmng practce by estmatng the parameters of a nested logt model. If there s unobserved correlaton among alternatve choces, multnomal and condtonal logt models generate nconsstent parameter estmates because the utlty functon s no statstcally ndependent but s correlated through the error terms across these alternatves. When Independence of Irrelevant Alternatves assumpton fals, then the nested logt s
References approprate method of estmaton. Relatve to a sngle-stage technque lke multnomal logt, the nested logt model relaxes the assumpton of Independence of Irrelevant Alternatves and allows to model dssmlartes n tmng of fertlzer applcaton gven crop choce. The farmng practce adopton s central problem n agrcultural economcs. Some farmng practces can mprove the effcency of farm producton and can provde wth some mportant external benefts such as resource conservaton and envronmental mprovement. Sprng only fertlzer applcaton s an example of such practces. The use of nestng structure confrms the general mportance of envronmental condtons n determnng tmng of fertlzer applcaton. Hgher varablty n weather condtons keeps farmers out of feld therefore forcng them to apply fertlzer n other season. Ths result holds for both fall and sprng. Results also ndcate that fnancal ncentves can have a bg effect on adopton decson of farmers. By controllng for the ndrect effect of crop proftablty on farmng practce and accountng for unobserved correlaton between land allocaton and farmng practce choce, we are able to more precsely estmate the nfluence of these polcy varables on choce of farmng practce.
References References Babcock, B.A., N.M. Chaherl, P.G. Lakshmnarayan. Program partcpaton and Farm- Level Adopton of Conservaton Tllage: Estmates from a Multnomal Logt Model. 95-WP 136, CARD. Ban, L. G., M. Engelhardt. Introducton to Probablty and Mathematcal Statstcs. Belmont, CA:Duxbury Press. 1992. Chavas, J.-P., M. T. Holt. Acreage Decsons Under Rsk: The Case of Corn and Soybeans. Amercan Journal of Agrcultural Economcs 72(1990): 529-538. Cooper, J. C. Combnng Actual and Contngent Behavor Data to Model Farmer Adopton of Water Qualty Protecton Practces. Journal of Agrcultural and Resource Economcs 22(1)(1997):30-43. Cooper, J. C., R. W. Kem. Incentve Payments to Encourage Farmer Adopton of Water Qualty Protecton Practces Amercan Journal of Agrcultural Economcs 78(1996):54-64. Fenerman, E., E. K. Cho, S. R. Johnson. Uncertanty and Splt Ntrogen Applcaton n Corn Producton. Amercan Journal of Agrcultural Economcs 72(1990):975-984. Fletcher, J. J., A. M. Featherstone. An Economc Analyss of Tllage and Tmelness Interactons n Corn-Soybean Producton. North Central Journal of Agrcultural Economcs Vol. 9, No.1:207-215. Herrges, J. A., D. Phaneuf. Inducng Patterns Correlaton and Substtuton n Repeated Logt Model of Recreaton Demand. Amercan Journal of Agrcultural Economcs 84(2002):1076-1090. Huang, W., R.G. Hefner, H. Taylor, N.D. Ur. Tmng Ntrogen Fertlzer Applcaton to
References Reduce Ntrogen Losses to the Envronment. Water Resources Management. 14(2000):35-58. Huang, W., N.D. Ur, L. Hansen. Tmng Ntrogen Fertlzer Applcaton to Improve Water Qualty. Resource and Technology Dvson, Economc Research Servce, USDA, Staff Report No. 9407. Kramer, R. A., W. T. McSweeny, R. W. Stavros. Sol Conservaton wth Uncertan Revenues and Input Supples. Amercan Journal of Agrcultural Economcs 65(1983):695-701. Kurkalova, L., C. L. Klng, J. Zhao. Green Subsdes n Agrculture: Estmatng the Adopton Costs of Conservaton Tllage from Observed Behavor. 2003-WP 286, CARD. Lchtenberg, E. Adopton of Sol Conservaton Practces: A Revealed Preference Approach. WP No. 01-12. Department of Agrcultural and Resource Economcs. Unversty of Maryland. College Park. Maddala, G. Lmted Dependent and Qualtatve Varables n Econometrcs. Econometrc Socety Monograph No. 3. Cambrdge: Cambrdge Unversty Press. 1983:67-70. McConnell, K. E. An Economc Model of Sol Conservaton. Amercan Journal of Agrcultural Economcs 65(1983):83-89. Soule, M. J. Sol Management and the Farm Typology: Do Small Famly Farms Manage Sol and Nutrent Resources Dfferently than Large Famly Farms? Agrcultural and Resource Economc Revew 30/2(2001):179-188. Tran, K. Dscrete Choce Methods wth Smulaton. Cambrdge: Cambrdge Unversty Press. 2003: 80-84.
References Wu, J., R.M. Adams, C.L. Klng, K. Tanaka. From Mcrolevel Decsons to Landscape Changes: An Assessment of Agrcultural Conservaton Polces. Amercan Journal of Agrcultural Economcs. 86(1)(2004):26-41. Wu, J., B. A. Babcock. The Choce of Tllage, Rotaton, and Sol Testng Practces: Economc and Envronmental Implcatons. Amercan Journal of Agrcultural Economcs 80(1998):494-511. Wu, J., K. Segerson. The Impact of Polces and Land Characterstcs on Potental Groundwater Polluton n Wsconsn. Amercan Journal of Agrcultural Economcs. 77(1995):1033-1047.
Crop choce Corn Soybeans Hay Fall Sprng Fall Sprng Fall Sprng Fgure 1. Model of crop and technology choce Table 1. Descrptve Statstcs for Varables n Estmaton Varables Mean Std.Dev. Mnmum Maxmum Indvdual Characterstcs Feld Sze (acres) 63.57 46.84 1.3 380 Educaton of operator 2.97 1.35 1 6 Clay Content 25.93 5.21 3 42 Organc Matter (OM) 4.19 1.6 0.75 8.5 Feld Slope (gradent %) 0.06 0.07 0 0.4 Crop Attrbutes Prevous Crop Corn (=1 f yes) 0.63 0.48 0 1 Prevous Crop Soybeans (=1 f yes) 0.42 0.49 0 1 Prevous Crop Hay (=1 f yes) 0.06 0.24 0 1 Varance of proft ($) 153.1 118.84 0 552 Fall Proft ($) 267.4 43.74 172.32 379.8 Sprng Proft ($) 262.2 39.66 172.32 369.17 Fall Precptaton (n.) 189.8 38.85 130.64 322.14 St. Dev. of Fall Temperature (F o ) 41.72 2.12 33.05 47.52 St. Dev. of Sprng Precptaton (n.) 115.17 19.32 72.02 144.87
Table 2. Nested Logt Estmates for Probablty of Fall Fertlzer Applcaton Gven Crop Choce Corn Soybeans Hay Varables Coeffcent Std.Err. Coeffcent Std.Err. Coeffcent Std.Err. Constant 2.95*** 0.75 1.86*** 0.07 0.72*** 0.02 Educaton -0.149** 0.07 0.32 0.32-0.337 0.512 Acres 0.02*** 0.005 0.057*** 0.014 0.001 0.002 Fall Precptaton -0.02*** 0.004-0.027*** 0.008-0.015 0.021 St. Dev. of Fall Temperature 0.007 0.03-0.110* 0.058-0.718* 0.501 Clay 0.02 0.04 0.19* 0.096 0.125*** 0.042 Total number of observatons used n estmaton 6264 Log of lkelhood functon -3123.4 Percent of correct predctons n sample 71% Note: *, **, and *** ndcate statstcal sgnfcance at 10, 5, and 1% levels. Table 3. Nested Logt Estmates of Crop Choce Corn Relatve to Hay Soybeans Relatve to Hay Varable Coeffcent Std. Err. Coeffcent Std. Err. Constant -8.09** 3.97-8.55*** 1.56 Prevous Crop Corn 0.34*** 0.028-0.12 0.11 Prevous Crop Soybeans 2.06*** 0.59-0.11 0.49 Prevous Crop Hay 0.031* 0.023-0.024*** 0.002 OM 0.48*** 0.012 0.23*** 0.007 Slope 8.06*** 1.83-0.45 0.96 St. Dev. of Sprng Precptaton -0. 23*** 0.004 0.27*** 0.008 Varance of Proft -.0008*** 0.0003.0002* 0.0001 Proft 2.45** 0.97 2.45** 0.97 IV for Corn 0.84*** 0.00 0.84*** 0.00 IV for Soybeans 0.56*** 0.00 0.56*** 0.00 IV for Hay 1.04 0.72 1.04 0.72 Total number of observatons used n estmaton 6264 Log of lkelhood functon -3123.4 Percent of correct predctons n sample 71% Note: *, **, and *** ndcate statstcal sgnfcance at 10, 5, and 1% levels.
Table 4. Margnal Effects and Elastctes on Crop Choce Margnal Effect Elastctes Varables Corn Soybeans Hay Corn Soybeans Hay Increase n proftablty of Corn/Fall Applcaton 0.045-0.031-0.014 0.859-0.755-0.098 Corn/Sprng Applcaton 0.095-0.056-0.039 1.17-0.967-0.125 Soybeans/Fall Applcaton -0.038 0.048-0.01-0.09 1.057-0.079 Soybeans/Sprng Applcaton -0.005 0.022-0.017-1.511 1.063-0.133 Hay/Fall Applcaton -0.007 0.001 0.006-0.278 0.302 0.564 Hay/Sprng Applcaton -0.009-0.006 0.015-0.447-0.489 0.645 Table 5. Margnal Effects on Crop-Farmng Practce Par Margnal Effect Corn/ Soybeans/ Soybeans/ Varables Corn/Fall Sprng Fall Sprng Hay/Fall Hay/Sprng Increase n proftablty of Corn/Fall Applcaton 1.039-0.034-0.132-0.705-0.075-0.093 Corn/Sprng Applcaton -0.034 3.257-0.936-1.917-0.053-0.317 Soybeans/Fall Applcaton -0.132-0.936 2.456-1.365-0.01-0.013 Soybeans/Sprng Applcaton -0.705-1.917-0.365 3.634-0.086-0.561 Hay/Fall Applcaton -0.075-0.053-0.01-0.086 0.225-0.0001 Hay/Sprng Applcaton -0.093-0.317-0.013-0.561-0.0001 0.9849