SEARCHING FOR A SUITABLE FUNCTIONAL FORM IN WHEAT
Transkript
SEARCHING FOR A SUITABLE FUNCTIONAL FORM IN WHEAT
I aria Bllkilen Merkcz .·/ro,"IrIIICI Ensflliisli Dergl.'1 fJ),l.1995 SEARCHING FOR A SUITABLE FUNCTIONAL FORM IN WHEAT YIELD RESPONSE TO FERTILIZATION Ahmcl BAYANER 1 Vcdal UZUNLU I AhlllCIOZCELiK: 1. Dr. Cenlwl Res. Jl1sl.fiJ,. fielJCr0l's ..·lnkol'Cl, Tllrkel" 2. Assoc. Pro( U/1/1'. o(.·!l1kw{/. 1'<ICIII'.1 of ,Ig. '( ",ke.!'. ()ZET: Dogu Anadolll 'nun dogu gc<;:il bOlgcsindc bugday \'crimi-glibrc ili~kisini dcgcrlcndinnck alllaclyla fa rklI matcmatikscl maddclcr dcgcrlcndirilmi~tir. Sonu<;:lar hi<;:bir lllodclin digcrinc iisliinlUgli oimadlgllll. ancak kuadratik fOrllulIl agronomik gorii~ a<;:lsll1dan \'c ckonomik dcgcrlcndirnlc bakllllludan lIygun oldugll ortaya <;:Ikml~tlr. Bclli girdi-<;:lktI fiyat oranlannda tavsiyc cdilccck miktarlarda fa/fa bir dcgi~lllc ollllaml~tlr. Bolgc agro-ckolojik karaktcrlcri g07-C ahndlglllda <;:if1<;:ilcrc bim/. fa/Ja giibrc kullanlllll oncrilcbilir. Cif1<;:i vcrilcrini dcgcrlcndinncdc digcr dcgi~lllelcri dc i<;:inc alan gcnel bir model ara~ttrlcl \C polilika iircticilcr i<;:in daha falJa bilgi \'crcbilir. sr~IMARY: J nrious/iIl1Clio/1alfrmlls nrc uscd 10 ('mlunle lI"henl vield re,_jJOllse lo/i'rlifi:er npp/icolioll ill1'..aslcr Margill a/Cenlral .Inalolia (EI/Cl) !?eslllis illdicn!l' Ihal {f/IV sing/c /l/odc/ is slIperior, hO\l'cl'cr, quadralic form seems 10 }il Ihe dala beller a/1d has sO/lie agrollomic raliona/ (l/ul econo/l/ic casiness 10 inlcrprel. Given Ihe illplll - Olllplil price ralios, recolI/lI/cnded applicnllOn rales do nol \'{71Y IIl1lCh. Farmcl's cnn be advised 10 lise s/ighl~V /l/OI'C fi'1'1i1i:cl' Ihall Iheir cUl'rell1 practices lakillg illio acco/flll Ihc agl'o ec%gica/ characl£'l'islics of Ihe I'egioll. . 1 morc genera/ model including, ol!Jcr mriah!es 10 el'a/I/ale /ar//lcrs dala It'll/dill'ield //lore injiml/alionjiJr researchers and IJolin'-lI/a/':ers. Crop rcsponsc analYsis IS an importanl arca of rcsearch lor appropriate fcrtilizcr recommendations \\hich ha\'e generally been dc\dopcd using production functions. and input-output rclationships have been estimated by conducting fcrtilizer experiments in thc lield (NELSON ET AL. 1985) "Dircctly or indirectly. dccisions conccrning optimal ratcs of lcrtilization il1\olvc titting somc typc 0" model to yield data collectcd \\hcn sc\'cral ratcs of fcrtilizer arc applied" (CERRATO and BLACKMARE. 1990), Ob\iOllsly. fcrtilizer rccommendation should bc dcrived using thc most appropriatc modcL Agronomist and agricultural cconomists ha\'c spcnt more than a ccntury in scarch of such a model (PARIS, I(92), Data obtaincd from famlCrs havc not bccn usually uscd for fcrtilizer rccommcndations, Modds l1t thc expcrimental data bctter. HO\\'CVCL goodncss of fit to lanncrs' dala is not as good, and rcscarchcrs arc to rccommcnd also optimal fcrtilizer usc based on lamlCrS data, Von Licbig enunciated a conjccture about crop rcsponsc implying a vcl)' particular family of rcsponsc models (PARIS, 19(2). Von Licbig fomlUlated "thc low of minimum" around 1850 (GUZEL 1(85). Sincc thcn scvcral dillcrcnt rcsponsc models havc bccn algcbraically fonnulatcd and uscd INTRODUCTION Although agriculturc has recci\'cd less attcntion in rcccnl ycars. il still is an important scctor in Turkish cconomy. ll1crc is not any dcvelopcd country in the \\orld that is not developcd in agriculture. Turkcy should thcrcforc, put morc emphasis on agricultural sector if it wants to bc a dc\'cloped counlry, In reccnt ycars. agricultural support policics havc changcd and arc less bcnefkial to fanncrs, Transfcrs to agriculturc h3\'e declined, and thc costs of inputs hm'c increascd t\VO to thrcc fold. Espccially fertilizer, \\'hich itself may increasc yield 10 % to 50 %. (ACIL 1980), became a \cry cxpcnsivc input. 111at has had a ncgati\'c impact on fanncr incomcs. and thc continuity of food supply is thm:ltened. O\\ing to increases in input priccs, f.:lnncrs hm'c to pay morc attention to optimize input usc. ll1C aim of this rcsearch is. thcrcfore. to rccommcnd to fanners optimum fcrtilizer application rate to achicv maximum cconomic yield \\ithin thc contc:\t of currcnt practices. Productivity 111 whcat fanning dcpcnds on a varicty of factors such as soil. climatc, seed quality and type, irrigation. fcrtilizer usc. Thc objccti\'c of this stlldy is to comparc and cvaluatc somc functional fonns to idcntify thc economic optimum ratcs of fertilizcr. 1 Harem",.. l'z/lnl/llmd ()z(:~llk to idcntify cconomlc optimum ratc of fcrtilization. Numcrous rcsearchcrs hm'c compared rcsponsc ['unctions and notcd that thcse models ollcn disagree "hcn indentifying thcse rates of fCltiliZc:'ltion. Among those "'ho hm'c used diffcrcnt response models arc Abraham and Rao, Anderson and Nelson, Barreto and Wcstcrman, Nelson ct ai, Blackmer and Meisinger (CERRATO and BLACKMER. 1990, JAURAGUI and SAIN, 1992) Some rcsponse studics arc summarized hcrc. ABRAHAM and RAO (1966) comparcd se\'cral functional fonns and concludcd, bascd on thc results as well as thc goodness of (it. tcst ofhypothcsis about model paramctcrs fm'or thc quadratic polinomial function. SANCHEZ ct al (J 981) compared altcmati\'c cquations dcrived from field cxpcrimcnts. and suggcsted. that thc rcsponsc model docs not really makc much diOcrcncc. TRONSTAD and TAYLOR (1989) c\'aluatcd 15 functional fonns. cxamining thc crror stmcture and could not assert that any singlc functional fonn was supcrior. Most \\ idcl\" uscd functional lomls arc quadratic squarc root. Cobb-Douglas, transcendcntal. translog, semilog and cxponantial functional fon1lS (HEADY. 1981. HEADY and DILLON, 19G L HEADY et al, 196 L JAURAGUI and SAIN. 1992. PARIS. 1992, CARRETO and BLACKMER. 1990. JOHNSON. JR. ct al 1987. BEAlTIEandTAYLOR 1987). Thc quadratic runction is prcrcrred bccause it is casily gcncralized to models with more thcn on nutJicnt and it allows for casy interpration or linear. cunilineer, and intcraction cffccts (JOHNSON. JR. ct al 1987. JAURAGUI and SAIN, 1992). Quadratic functional fonn has been used in numcrous studics to examine the yield response to rertilizcr use (SEF A. 1981. DIGDIGOGLU. 1982. BABUR., 983. ALEMDAR. 1988. AVCl et al 1988. CARRETO and BLACKMER. 1990, BAnONA ct al. 1991, GRIFFIN and HESTERMAN. 1991. MUKHOPADHYAY et aI, 1991, OZEL and BlCER 1992, ICARDA. 1992. DARA et al. 1992, PARIS, 1992, OZKAYA and OZDEMIR 1992, AGARWAL et al. 1993, JERALD et ai, 1993, REEVES et al, 1993, CAMPBELL et al. 1993, AYISI et al, 1993, EKER 1992, BAYANER and UZUNLY, 1993, AVCI ct al. 1993, AVCIN et al. 1993). lnput-output relations havc also been examined in a number or studies using Cobb Douglas production function (ULUG, 1973, ZORAL. 1973, TONGISI, 1977. ACIL and REHBER. 1978, REHBER 1978, SARIMESELl, 198 I, ARIKAN, 987, OZCELIK. 1989. VURAL et aI, 1993). MATERIALS AND METHODS Virtually all pre\ious studies of this type ha\'c relied on field cxpcrimcntal data. These data fit the model well. Howcver, fanners conditions are not the same as cxperimcntal conditions \\·hich could be controlled by thc rcsearchcrs and cxcept for thc c1imatc cxcluding irrigation, rcsourccs arc not limited. Rcsults obtaincd in such condition arc diffcrcnt than that of farmers conditions. Thcrcrorc it is worth to c\uluate data obtained from thc ramlcrs. 111C data used was obtained rrom thc famlers through a fomlal intcnic\V. Famlcrs "'ere asked the wheat production tcchniquc in Eastcm Margin of Central Anatolia (EMCA). A total of 207 famcrs wcrc intenie\\' of thcsc, 94 Ianners used phosphorus and nitrogcn. Pre\iOllS studies havc gcncrally used quadratic functional form to c\aluatc )1eld rcsponse to fcrtilizer application. This functional foml in most cases fits thc data bcst. Howcver )1c1d data obtaincd from the ranncrs do not exhibit a sl1100th response to lcrtilizcr. Thcreforc, it is il11portantto test diffcrcnt functional foms. An ideal runctional fom is flexible enough to capturc all thc infomation convcyed by thc data set. However, the quality of thc data must also be considered. As COLWELL (1978) obscn'ed, poor data should not deter researchers from using "the best computing procedurcs available," but poor data cannot support strong arguments about whether one or another functional from is best (JAUREGUI and SAIN, 1992). Thcrc are altcmati\cs to the more or less arbitra!y' choice of a pol)nomial function to reprcscnt thc response to fcrtilization, including thc \'ery flexible Box-Cox transfoffi1ation. 0\\1ng to the computer 2 Searchmgfor a Sill/able Fill1c/lOnal hOIll In II hear fIeld Re.\ponse (0 rerllhz(({lOn Transcendcntal programming limitations, this tlexiblc Box Cox transfonnation was not used. In this study, data were analyzed using different functional fomls in three steps ( I), \vheat yield response to nitrogen fertilization, (2) wheat yield response to phosphorus fertilization, and (3) wheat yield response to nitrogen and phosphorus fertilization. Primarv analvsis of the data yielded consistantlv' lower' RC. In order to improve RC, ar~ so\\n to wheal, weed chemical application, sowing data, so\\ing method, and tractor 0\\ nership were all included in the models estimated. RC was improved only when area so\\n to wheat (A) and weed chemical application (WCA) were added to the models. Therefore, follo\\ing functional fonl1S were fOffilUlated to be used in the analysis: y ~ Y Linear . Y a + bN 'cl' ' d NI' ' eA ' WCA Quadratic: Y a bN t c N' . d!" c 1" • fNP , gA + WCA Cubic y. a t- bN . cN' . dN' • cl' ' ll" gil-' t- hA ,WCA Squarcroot: Y = a' bN tcN"~ +dl' +cl'''~ 'l\NP)')'~ + gA I WCA lIipcrbol: Y . a b (IN) , c (11)1 • dA ' WCA j t t Semilng (withnut quadratic tClln): c Y c(<i" e,\ + WC't\} N h pC NPll. Y a' b InN· c Inl' , d InN Inl' . cA 1 In Y a ' hN .c cN' . dl' ' cl" . INI' ' gA . WCA In Y , [na ' b InN' c Inl' ' dN ' cP j Ii' ' WCA Transccndcntal (with interactilln): y ~- a Nil 1)1-' C(dN ~ ell' f!\.'p ~\ ~ weAl. In Y ~ Ina t hlnN I e1nl' • dN I cl' , IN!' f I gA , WCA Translog (without quadratic tmll): Y ~ a N" 1" Cld •1N InP" e,'" WCAI. In Y cWCA Translog : Y = aN h C'A+ eWcA. In Y =. Ina + b InN + cA + dWCA (without quadratic tenn) Y = aN b cl'blN idAteWCAI c Ina' h InN I c Inl' ' d InN Inl' ' cA • WCA Translog (with quadratic tcnn): Y a Nil IY': c(t~ln;-";I ~ cOuP, "1'L~ I"P I 1- ~:\ -- WCA} In Y . Ina .blnN j c1nP ~ dOnN)' c{lnl')' 'I1nNlnl' 'gA • WCA Cohb-Douglas : Y " a Nh 1" cdA ' wc". In Y . Ina' b InN' c Inl' ' dA t- WCA t c(lnN)' ~dA -'-eWCA (with quadratic for phosphorus usc; Linear Quadratic Cubic Squareroot : HipcrbJI t Tran~cndcntal (without interaction): Y a Nil pC ClllN 1eP ~ we.'\). dA + cWCA (\\ith quadratic In Y = a + bN"' cN' + dA + eWCA (with quadratic tcnn) + cp; dNI' ' eA . WCA t In Y a' bN Nt. (N 2 t. i I Exponantial (with quadratic tCl1n): y c(r.4 hI' ~ct'\~.j dP cP~-! 11\1' I ~\-+-WCA). Exponantial ; y .. c'" + hN + ,A t dWCAI. In Y = a'+ bN + cAl dWCA (without quardatic tmn) Y = e(8+bN+fN':+dA+eWCAl. InY ~ Ina + blnN tcnn) WCA Exponantial (without quadratic term): y c(a-' \IN ' ell , d!\l' cA ~ we:\1 SClllllog eY = elf' j 0 .... dWCAI N Y =. a + b InN + cA i dWCA (\\'ithout quadratic tClln) Transcendenlal; y. aNhc"N'dAteWcA/ In Y .c Ina"' b InN + cN T dA + Semilog (with quadratic tem! J: eY . c'·· .lC'· WC\! Nh (N')' 1',1 (P')' (NI')f y. a • blnN • c(lnN)' I din!' 'c( Inl')' I l1nNI' + gA I WCA b• + nph c(c blP ~ tlA -+- eWCAj For IlIlrogcn and phosphorus usc: a ' bN I cA • dWCA Y ~ a + blnN + c (InN)' tCllll ) O' In Y - Ina' binI' ' cOnl')' 'dA . cWCA (with quadratic tClln) Y =. a' bN + cN' + dA i cWCA Y ~ a ~ bN + eN' ~ dN' t cA i tWCA Y = a ~ bN + cNII~., dA. cWCA Y =a + b(lIN) + cA + dWCA c Y .:::. e(B+dA-...eWCAl Y api, cl'I" .I," ,WCAI In y. Ina' binI) 1 cl' ' dA ' cWCA Translog Y ,. api, c'" ',1\\'0. In Y Ina" binI' t cA" dWCA (without quadratic tcnn) For nitrogen usc; Linear Quadratic Cubic Squarcroot : Ilipcrbo[ ~ Y , Whcat Yield (kgda). a ~ Constant. b. c. d. c. ( g. h Estimat<"d cocllicicnts. N = Nitrogen application ratc (kg/dn). P •. Phosphorus application rate (kg/daJ. A ~ Area sown to wheat (da). Y ~ a + bP T cA -+ dWCA Y = a t bP • cP' + dA + eWCA Y - a + bP I cP' j dP' -'- eA -'- lWCA Y = a -+ bP + cp'J~ + dA i eWCA Y = a + b (I IP) + cA + dWCA c WCA . Weed chcmical application. WCA 1. if weed chcmical applied. WCA = O. othcrwise. Semilog eY = e,a t 'A" dWCAI ph. Y ~ a + b InP + cA " dWCA (without quadratic tcnn) eY ~elatdAt'WCAI ph (P'l'. Y = a + binI' + c (nl')'" dA I eWCA (wit quadratic tcnn) 0 Agricultural economists and agronomists have generally judged their empirical models onlv on the basis of coefficient of deteffilin~tion (R\ Generallv Exponantial ; Y ~ c,a~ hPtCAtdWCA'. In Y = a + bP + cA + dWCA (without quadratic term) y -= e(a;-bP+cP:!~dA-t cWCAI. In Y= a + bP + cP' .j dA t eWCA (with quadratic tenn) 3 accepted that the higher the lit the better the model. This criterion was cxplicitly followed by numerous researchers. But what happens when all the models exhibit about the same RC (PAR[S, 1992). Consequently, the coefficient of detcrnlination is not a relevant statistics for selecting a model (CERRATO and BLACKMER.. 1(90). These discussions were also supported by JAUREGUI and SAIN (1992), that models used in fertilizer response studies display positive and ncgative features and R" commonly used docs not by itself prO'ide su ffieient support for selecting anyone model O\er others. and therefore other criteria should be used for choosing the appropriate specifkation. 11lis study im"Olvcs fitting cach functional fonllS to data obtained from the fanners and comparing coelllcient of detennination. Sum of Squarcs Errors (SSE). Log of the Likehood Functional (LLF). and correlation coelllcients between actual and predictcd wheat yields (rn) (KMENTA, 1986. WHITE and BUt 1988. OlCELlK. 1(94). RESUL TS AND DISCUSSION "nlC importance of fertilizer use is \\e11 knO\\TI by the majority of thc fanncrs in the rcgion, but thcy are unclcar on appropriate ratcs and mcans of application (SAYANER ct aL 199~) Fertilizer usc dltTers from fanncrs to lanners. depending on their linancial situation and fanning ability. Thc most commomly used fcrtilizer typcs wcre Diamllloniulll Phosphatc (DAP) and Amonium Nitratc (AN) TI1C a\'crage nitrogcn usc \vas 6.~9 kg/da (== AN * 0.26 + DAP * O. [8), and phosphonls use 7. D kg/da (== DAP * 0.46) in EMCA The estimates of the models gi\'en in mcthodolo,b'Y for \\hcat yield rcsponse to nitrogcn (N). phosphorus (P) and nitrogen + phosphorus (N-P) \\cre obtained by Ordinary Least Squarc (OLS) technique. The selection criteria for thcse models are gi\"CI1 in Table l. 2 and 3 for N, P and N-P models respcctively. Criteria taken into acccount arc RC• F-\alue. Log of the Likelyhood Function (LLF) and the correlation coellicient between obser,ed and predicted yield va[ues (rn). \ The coefficients of detennination for models including nitrogen varied bet\\een O. [98 and 0.230 including phosphorus 0.189 and 0.209 and for the full models 0.119 and 2 0.246 All the R valucs for the models are statistically significant at the level of 0.01. The data consistanly exhibited a lower R2 because the data were obtained from the fanners with a low variation. Most of the fanners use about the same amount of fcrtilizer. This typc of data generally exibite the second stage of the classical production function. SSE \alues are higher for transfonned data for the models including nitrogen and phosphorus, indicating that models are not better. and LLF values are some\\hat highcr howcvcr. the ditTerences are not important. rH . on the other hand, does not \'aI} in a grcat detail. TIle models including nitrogen phosphonls are statisticallly proven to be somcwhat bcttcr or superior to those only including nitrogcn or phosphorus in ternlS of SSE, LLF. and rYY criteria. Users are suggested to include both fertilizer types in their analysis for fanner recommendations. Results rcported here indicate that no singlc model can be rccommcnded over others for all situations, rcgardless of the selection criteria used, "TIle researchcrs can only hope that thc bcst model has some agronomic rational, and produces estimates of economics optimum that are rcasonably frcc of bias (PARIS, 19(2) For the purpose of calculating economcis application rates of fertilizer for recommondation in Eastern Margin of Central Anatolia. among the models estimated, quadratic model was selccted. The results of thc estimatcs are gi\'cn in Tablcs 4, ). and 6. TIlere are three major reasons for using the quadratic. The first. and perhaps most prominent reason is to capture turning points Turning points occur when the elTcct of an additional unit of X causes a change in thc direction of the etTcct of X on Y, i.e., Marginal Product (MP) of X is zero. The qiadratic fonn can easily be generalized to models with more than one nutrients, and it allO\\'s for casy interpretation of linear, cunilinear. and interaction effects. Optimum fertilizer rates for the models were calculated. given the input output pricc ratios (rip) (Table 7) Maxinlllm Searching/or a Sllita"'e Fimcl/onal hOI/lin 1I71C0I fld" ResliOnse ro FerrilIzaTion Models of this sort should include not only fertilizer but also other variables such as. pre\ious crops. soi I nutrient content, available moisture. rainfall received and temperaturc during the gro\\ing period, irrigation if applied. so\\ing equipment, weed and pest chemicals etc. Sush a general model would capture the changcs in whcat yield that is of intercst to both rcscarchers and policy makers. Results obtained arc in famr of quadratic rOml. becausc it has some agronomic rational and economic easiness to intcrpret and secms to l1t the data better. Recommcndcd application rates did not change much. gi\Cll the price ratios. As input prices increase. or output prices decline. input usc reduces or \icc ,'crsa. Dcpcnding on a numbcr of factors. ho\\'c\er. operating arca is bounded \\ith thc sccond stagc of the production function. Fanncrs in EMeA can be recommcnded to use more fertilizer than thcir currcnt application rates \\ith cautious. becausc the region is dry recci\ing around 300 mm rainfall a year. yield is optained by only applying 7. TTl kg/d nitrogcn or 10.041 kg/da phosphorus. Whcn both fertilizers arc applied. maximum yield is reached at 7.830 kg/da nitrogen and 9.190 kg/da phoshorus. Optimum ratcs of nitrogen \aried from 7.200 to 7.625 kg/da, and phosphorus from 8. IO 1 to 9.653 kg/da when only using nitrogcn or phosphorus. For the model including nitrogcn + phosphorus, optimum nitrogcn rates wcre bct\V'ccn 7.72 and 7.8 I kg/da, and phosphorus rates between 9. I I and 9.18 kg/da. SUMMARY AND CONCLUSIONS The objectives of this study \\ere to investigate a suitable functional fonn in '\heat yield response to fertilizer application and to rccommend to fanners optimum fertilizer application rate \\ithin the conte:-.1 of currcnt practices. Because of the nature of the data used, strong econometric e\idence is unlikely that any of the functional forms il)Vestigated can be rccommended O\'cr others. In addition, this type of data docs not fit the models well. comparing \\ith experimelltal data. Nevcrthcless, fanners' data should also be used to recommend fertilizer application rate. 5 BayuniJl'. UZlln!1i and (jz<;xhk Table -t; Wheat yield response to Nitrogen fertili/.ation Variables Intercept N NC A WCA Statistics R: F N Parameters 9.ol567 36.320 - 2.3ol87 0.2 J 573 IS.SolS Standard Error 89.378 28.lIol 2.1536 O.06ol212·· 13.S57 1>.221 6.32 90l ** Significilnt allhe 0.01 Ic\d Table 5. Wheal yield response to phosphonJs fertili7;ltion Variables Intercept P pc A WCA Parameters 83.69ol 12.9ol1 - 0.6olHO 0.2 JOO2 17.7H Stilndard Error 68.olS7 18.997 1.2737 0.06ol973 lol.3ol3 .. Statistics RC F N 0.205 5.7ol 90l ** Significant at the 0.0 I Ic\d Table 6. Wheal yield response to nilrogen and phosphonJs fertiliz;llion Variables Intercepl N N: P pc NP A WCA Paramelers 29.6S3 28.706 ol.1716 0.26332 ol.369ol -10.229 0.20885 16.553 Slanrulrd Error 93.5ol3 57A18 8.3olol7 38. 196 3.ol1n 9.09H IHl67olol 93.5ol3 .. Statistics RC F N 0.237 3.818 30l 6 SC(lrchlng/or (I SIII/"nl" !';lnclJon(l!l;;-olllln II 71e(l/ rl,,[L! Re.,vms" to F"I'1I[IZ(l11011 Table 7. Optimum fertilizer application rales (kg/da) rip N usc Technical opt. 7.732 7.625 7.520 0.5 1.0 1.5 2.0 2.5 ?A 13 7.306 7.200 N + P use P usc N 1O.0-l1 9.653 9.265 8.877 8A89 8.101 9.190 9.180 9.160 9.1-l0 9.120 9110 P 7.830 7.810 7.790 7.760 7.7-l0 7.720 REFERENCES AVCI. M.. DURUTAN. N.. KARACA, N. and GULER M.. 1988. Agranomic Practiccs U1 Differcnt Cropping Systcms of lllC Central Anatolia. Intcrnational Scminar on thc Farming Systems Rcsearch. ICARDA and the Univ. of Cukurova Facultv of Agriculturc. 3 I September 2 Octobcr. Adana. ABRAHAM. TP .. and RAO. V.Y.. 1966. "An lJ1\'cstigation of Functional Models for Fcrtilizer Rcsponsc Surfaccs". journal oflndian Social and Agricultural Statistics 18:45-61. ACIL. AF.. REHBER E.. 1978. Nc\Whir ilindc Uzi.im Uretiminin Ekonomctrik Analizi, AU.Ziraat Faktiltesi YIIhgl, Ankara. AVCL M.. DURUTAN. N. and PALA, M.. 1993. "Kuzcy Ge~it Balgcsi Baklagil Bugday Sistcminde Farkh Azot Miktarlanl1ln Gerck-79 \'e Bezostaya-I Bugday C:e~itlcrinin Verimlerine Etkileri." Tarla Bitkilcri Merkez Ar~lmla EnstitOsii Dergisi. Cill: 2. SayI: 2. Nisan 1993. Ankara. A(:IL. AF.. 1980. Tanm Ekonomisi. AU. Ziraat Fakliltcsi Yaymlan: 721. Dcrs KitabI: 213. Ankara. AGARWAL. M.A. MOHAN, S.c.. SINGH G \'c KUMAR. N.. 1993. "Economics of Fcrtilizcr Usc (or Barlcy in Sub-Mountane Himalaya Region". Indian journal of Agricultural Research 27(3): 115 125. AvCiN. A. PALA, M. and AVCI, M., 1993. "Orta Anadolu Sartlannda Kunduru-1149 \·c Cakmak-79 Makarnahk Bugday C:e~itIcrinin Awt ihtiyacmm Bclirlenmesi." Tarla Bitkilcri Mcrkez Ar~mna EnstitUsti Dergisi. Cill: 2. Sayi: 3. Ankara. ALEMDAR N.. 1988. Ankara Yarcsinde Kuru Sartlarda Yeti~tirilcn Ban Bugday C:e~itlerinin Azotlu \'c Fosforlu GUbre istegi. Kay Hizmctlcri Genel Mlidlirltigli Toprak \'e GUbrc Ar~mlla EnstituSii MiidUrliigli. Yaym No: 145, Ankara. AYIS\. K.K.. PUTNAM. D.H, VANCE, c.P. and GRAHAM. P.H., 1992. 'Brad\Thizobium Inoculation and Nitrogen Fcrtilizer Effects on Seed Yield and Protein of White Lupin." Agranomy 1. 84: 857 - 861. ARIKAN. R.. 1987. "Tiirkiye'de Scker Pancan Uretimini Etkile\'en Faktarler." Koopcratir~ilik Dergisi. SayI: 76. Nisan-MaYls-Haziran. BABUR Y. 198J Egc Bolgcsi Aluviyal Topraklannda Pengoma 62 Bugdaymm Uretim Fonksiyonu vc Optimizasyonu. Topraksu Ar~lrma 7 BOI'an",., UZI/nll/ and C}rr;x;/ik EnsliWSlL Yaym No: 92, Mcncmcn, DARA. ST. FlXEN. P.E. and GELDERMAN. R. H. 1992. "Sullkicncy Lcvel and Diagnosis and Rccommcndation Intcgrated Systcm Approach for E\'aluating the Nitrogcn Status of Com." Agronomy 1. 84: 1006-1010. izmir. BATIONO, A. CHRISTIANSON, CB. and BAETHGEN. WE, 1990. "Plant Density and Nitrogcn Fcrtilizer EITeet on Pearl Millct Production in Nigcr." Agronomy 1. 82: 290-295. DEM_RC_. R.. 1978. Klr$chir Mcrkcz il~csi Hububat i$lctmcJcrindc Optimal i$lctmc Organizasyonlan \'c Yctcr Gclirli i$lctmc Biiyukluklcrinin Saptanmasl Ozerinc Bir Ar~tInlla (D~entJik Tczi). Ankara Univcrsitesi. Ziraat Fakultcsi. Ankara. S: 22. BAYANER, A, UZUNLU. v.. KEATINGE. 1. D. H., and TUTWILER. R 199). Agriculturat Structurc and Constraints to Increased Production in thc Eastcrn Margin of Ccntral Anatolia. HigWand Rcgional Program. 11le TARM/lCARDA SIVAS - KAYSERI Collaborativc PrQjcct. Ccntral Rcsearch Institutc for Field Crops. Ankara D1GDIGO"LU A 1982 Ol1a Anadolu Bolgcsindc Arpanm Azotlu Gi.ibrc istcgi. Topraksu-Ankara. BAYANER. A, vc UZUNLU. v.. 199). "Orctim Fonksiyonlannm Dencmc Sonu~lannlll Analizindc Kullanu1ll." Tarla Bitkilcri Merkcz Ara$tJnlla Enstiti.isu Dergisi. Cill 2. Sayr I Nis<,n 1993. Ankara. EKER. M.. 1992. Tokat vc Amasya Yareleri Sulu Sartlannda Bugdaym Azotlu Giibrc istegi. Kay Hizmctlcri Gcnel Mlidiirlligli. Yaym No: 119. Tokat. GDZEL H. A 1985. A McthodohogicaJ Approach to Agricultural Yield Functions and Optimization Of FCl1ilizer USA For Whcat in The Acgcan Dcgion. Mastcr 111Cses, ODTO. iktisadi \'C idari Bilimler Fakiiltcsi. Ankara. BEAlTIE B.R and TAYLOR. CR.. 1987. Thc Economics of Production. Ncw York. Jhon Wilcy and Sons Inc. CAMPBELL, CA. ZENTNER. RP.. SELLES, F.. MCCONKEY. B.G. and DYCK, F. 8.. 1993. "Nitrogcn Management for Spring Wheat Gro\'m Annually on Zcro-Tillagc: Yields and Nitrogen Use Eniciency." Agranomy J. 85: 107 - 114. GRIFFIN, T.S. and HESTERMAN, O.B.. 1991. "Potato Rcsponse to Lcgumc and Fcrtilizer Nitrogen Sources." Agronomy J, 83: 1004-1012. HEADY. EO.. DILLON. IL. 1961. Agricultural Production Functions. Amcs. lo\\'a. CERRATO, M.E. and BLACKMER. AM.. 1990. "Coparison of Models for Dcscribing Com Yield Response to Nitrogen Fertilizer." Agronomy J. 82: 138-143.5. HEADY. E. 0., 1981. Somc Considcrations in thc Design and analysis of fcrtility cxperimcnts for dc\doping-eountl}' usc. In 1.A Sih'a (cd,). Expcrimcntal Dcsigns for Prcdecting Crop Producti\itv \\-jth Emironmcntal and Economic Inputs lor Agrotcclmology Transfcr, Dcpartmental Paper 49. Honolulu. Hawaii: Hawaii Institutc of Tropical Agriculturc and Human Rcsourccs. Uni\'crsity of Hawaii. Pp. 43-54, COLWELL, J.D., AR SUHET. and B. VAN RAil 1988. Statistical Procedures for Developing Gen~ral Soil Fertility Models for Variable Regions CSIRO Di\-jsion of Soils, Divisional Report No. 93. Melbournc. Australia: Commonwcalth Scicntil1c and Industrial Research Organization. 8 Sl!archlngIor a S/IIluh/1! FilnCllOrlal !-i'OIll In lIheul rldcl Response 10 1'''I'I'''Z011011 OZEL. M. ve Bi<;:ER. Y. 1992. Akdcniz Bblgesindc Yeti~tirilen Bugdaym Azotlu Gubre istegi. Kay Hizmetleri Genel MiidurlUgO. Ya)ln No: 180, Tarsus. ICARDA, J992 Collaborativc Rescarch Project on Fertilizer. Use on Barley in Northern Syria. 1984-1988. Part II. Aleppo, Syria. JAUREGUI, MA. and SAIN. E.. 1992. Continous Economic Analysis or Crop Response or Fertilizer in On-Fann Research. ClMMYT Economic Paper. No: 3. Me:-;ico, D.F.. CIMMYT. OZKAYA. T. vc OZDEMiR. S, 1992. "izmir ilinde Pamuk Dretiminde A~m Kimyasal Gubre Kullanll11l Sorunu." Tanm Ekonomisi Dergisi, Cilt: I, Sayt: C Mart 1992. izmir. JERALD, Q. D.. FLETCHER J and LEE. 1.G.. 199~. "Incorporating Stacastics Variables in Crop Response Models: Implications ror Fertilization Decions." Amcr. 1. or Agr. Econ. 75 (May PARIS. Q.. 1992. "1lle Return or von Liebig's "Law or thc Minimum"'" Agronomy J. 84: 1040-1046. REEVES. D.W.. WOOD. e.W. and TOUCHTON. 1.T.. 1993. "Timing Nitrogen Applications ror Com in a Winter Legume Conservation-Tillage System." Agranomy J. 85: 98 - lOG. )993): 377 - 386 JOHNSON. Jr. Ae.. JOHNSON. M.B. ve BUSE. R.e.. 1987. Econometrics. Basic and Applied. MacMillan Publishing Company. Ne\\ York. REHBER E. 1978. Nev~ehir'de Patates Dretcn Tanm i~lctmelerinin Ekonomik Analizi. Doktora Tezi. A D. Ziraat Fakiiltesi. Ankara. KM ENTA, 1.. [986. Elcmcnts or Economctrics. 2nd cd. Macmillan Publishing Company. Ncw York. SANCHEZ. PA. R.K. PERRIN, and S.W. BOLL 1981. C"oncepts or Program Design For Soils Research and Inrol111ation Tranlcnal in Developing Countries." In JA Siha, (cd.), bperimental Designs ror Predicting Crop Productivity \\ith Environmental and Economic Inputs For Agrotechnology Transfcr. Depart mental Paper 49. Honolulu, Hawaii: Hawaii Institute of Tropical Agriculture and Human Resources, University oCHawaii. Pp 55-66. MUKHAPADHYAY. S.K. SEN. H. and lANA. PK. 1991. Economics or Potasium Fertilization in Swced Potato (Lpomoca Potatos L.) Potash Rc\icw. International Potash Institute No: 5-9 Swidzcrland. NELSON. LA. R.D. VOSS. and J. PESEK. 1985. "Economctric and Statistical Evaluation or Fertilizer Response" In O.P. Engelstad. (cd.), Fertilizer Technolob~' and Usc. 1llird Edition. Madison. Wisconsin: Soil Science Society or America. Pp. 53-90. SARIMEiELi. M., 1981. Seker Pancan Oretim Fonksiyonlannm Ta1unini, MPM Verimlilik Dergisi 1981/2, Ankara. OZ<;: EL_K, A. 1989. Ankara Seker Fabrikasl Ci\'c1.nndaki Seker Pancan Yeti~tiren Tanm i~lctmelcrindc Sckcr Pancan ile Bugday i~in Fiziki Dretim Girdileri \'c Oretimin Fonksiyonel Analizi. AG.Z.F. Yaym No. Ii 13. Ankara. SEFA S. 1981. Batl Ge~it Balgcsi Sularur Ko~ullal1nda Bugdaym Azotlu Giibre istegi ve Olscn Fosfor Analizi Metodunun Kalibrasyonu. Topraksu Eski~ehir. OZ<;:EL_K. A. 1994. Ekonometri. Ankara Oniversitesi Ziraat Fakiiltesi. YavlIl No: 1323. Ankara. TONGISI, B. 1977. Tohe Economics of Resource Use in Northel11 Thailand: 9 VURAL H. FIDAN. H. \·c BAYANER.. A.. 19<)~. "Corum ilinde Bugday Urctiminin Ekonol11ctrik Analizi." Tarla Bitkileri Mcrkez Ara~tmna EnsliWsii Dergisi. Cilt: 2, Say/: 4. Ekim 199~. An Agro - Economic Analysis of Fanning in thc Chiang Mai Vallcy. 1972-197:'. Ph. D. TI1csis. Uni\·crsily of Rcading. TRONSDAT, R. and c.R. TAYLOR. 1989. An Economic and SL:'1tistical Evaluation of Functional Fom1s and Estimation Produccrs For Crop Yield Response To Primary Plant Nutriens. Unpublishicd MS. Thesis. WHITE, K.J. \·c BUI. L.T.M.. 1988. Basic Econometrics: A Computer Handbook Using Shazc'1l1l for Use With Gujarati. McGra\y-HiIL Inc.. New York. ULUG, S.E., 197~. Alpaslan Dcvlct Urctmc Cillligindc Bugday Uretiminin Ekonomik Analizi. Atati.irk Uni. Yay. No. :'1 I. Ankara. ZORAL K.Y.. 1973. Cobb-Douglas Urclim Fonksiyol1ul1 Yukan Pasinlcr Uretiminc O\asmdaki Palales Uygulanmasl. Alali.irk Oni. Yay. No. ~03. 10 s. :'8-:'9. Seoreilmg/or a SlIIr"hle fimetlOnol J"i'olll In IIh"ot }',eld R"sponsc to rCrfJlizollOn Table 1. Selection criteria for the functional relationships betwecn whcat yield and nitrogcn usc Models RC F LLF SSE ryy_ _ Lincar 0.211 8.02 305 :no -513.422 0.459 Quadratic 0.221 6.32 301 340 -5/1.798 0.471 Cubic 0.230 5.25 298070 -5/1.285 0.479 Squarcroot 0.117 6.18 302 900 -513.040 0.466 Hiperbol 0.114 8.16 304170 -513.151 0.461 Transcendental 0.198 5.51 I. 8 l.\: 10() -504.358 0.458 Translog!\\;thout quadratic tcnn 0.198 7.41 1.83:-.:10/' -504.381 0.457 Translog/with quadratic tcnn 0.198 5.50 182" Hi' -504.379 0.457 Semilog!\\'ithoul quadratic tcnl1 0244 8.17 304 150 -5Il233 0.463 Scmilog/\\ith quadratic tenll 0.215 6.09 303840 -51l185 0.463 Exponantial/\\il.hOlil. 0.196 quadratic tenn 7.31 l. 94" I0 -504.500 0.453 Exponantia[/\\;th quadratic tern1 5.62 1.64" lOb -504.161 0.464 0.202 6 11 BilJ'(mar. [Jzllnl" Clnd ()n;:~1ik Table 2. Selection criteria for the functional relationships betwccn wheat yield and phosphorus use Mood R2 Linear ryy_ _ F SSE LLF 0.203 7.64 308490 -513.899 0.450 Quadratic 0.205 5.74 307610 -513.764 0.453 Cubic 0.209 4.66 306060 -513.527 0.457 Squareroot 0.204 5.72 301510 -51:".801 0.452 Hiperbol 0.204 7.70 307980 -513.821 0.452 Transcendental 0.192 5.29 2.18xI0/; -504.735 0.445 Translog/\\ithout quadratic tenn 0.191 7.09 2.23xI0 6 -504.776 0.445 Translog/\vith quadratic tenn O.J92 5.28 2.20x10 6 -504.751 0.445 Semilog/\vithoul quadratic tenn 0.204 7.69 308010 -513.826 0.452 SemilogMith quadratic ternl 0.204 5.72 307920 -513.812 0.452 Exponantial/\\ithout 0.189 quadratic tcnn 7.00 2.8h106 -504.897 0.444 Exponantial/\\ith quadratic tern1 ) -...,.,'.' 2.IOxI0() -504.662 0.446 0.193 J2 Searehmgfor a SI/i/anle 1'llne/lOnal h'alllln II heo/ Yield JI,'sl'0nse to Fer/J117011OrJ Table :i. Selection criteria for the functional relationships bet\\een \vheat yield and nitrogen + phosphonts usc Model R~ F SSE LLF fu_ Lincar 0.222 5.mS ~00910 -512.nO OA72 Quadratic 0.237 3.818 29S240 -51 uns OAX7 Cubic 0.246 3.040 291920 -311.304 0,4% Squareroot 0.2:i5 3.767 2961XO -511.9X6 0,4X4 Hipcrbol 0.21() 6.I~G ~0:n40 -SI~.108 OA(») Transcendental!\\ithout Interaction ten11 0.199 3.594 1.79,,10(> -504.345 0.457 Transccndcntal!\\ith Interaction ten11 0.212 :U04 1.2lx 10" -)O~.557 0,477 4.3()~ 1.29" 10" -50-U44 0,459 :i.2X7 1.24,,10" -50~.G II 0.469 0.217 4.S82 ~02960 -SI3.048 0.4()6 0.233 3.729 2%8XO -512.0% 0.483 E"ponantiall\\;thout quadratic tern) 0.204 4.512 1.52,,10'; -504.025 O.4G~ Exponantial/with 0.209 quadratic tern) 3.254 Uhl({' -503.70S 0.47() Translogl\\ithout quadratic ten11 0.199 Translog/\\ith 0.211 quadratic tern) Scmilogl\\ithout quadratic tern) Semilogl\vith quadratic ten11 13