Applied Mechanics and Maerials Vols. 275-277 (2013 pp 2718-2722 (2013 Trans Tech Publicaions, Swzerland doi:10.4028/www.scienific.ne/amm.275-277.2718 A orldwide Comparison of aer Use Efficiency of Crop Producion Zhaodan u 1, a, Upmanu all 2,b and Min Zhao 3,c 1 School of Business, Hohai Universy, Nanjing, China 2 Deparmen of Earh and Environmenal Engineering, Columbia Universy, New ork Cy, USA 3 School of Business, Hohai Universy, Nanjing, China a zhaodanwu@gmail.com, b ula2@columbia.edu, c zhaomin3451@sina.com 3 eywords: Cobb-Douglas producion funcion; Sochasic fronier analysis; Variance decomposion; aer use efficiency of crop producion Absrac. orldwide food secury and waer safey issues necessae counries wh low waer use efficiency of crop producion (CUE o increase and reduce regional CUE variaions. CUE funcion was esimaed wh sochasic fronier analysis, and CUE variaion was decomposed on iner-coninenal, inra-coninenal and inernaional level wh variance decomposion mehod. I is proposed ha in order o efficienly improve he CUE and reduce regional CUE variaion, counries wh low CUE should focus more on he facors lised from he decomposion. Scenario analysis proved he effec of improving he mos imporan facor of CUE variaion, and showed some new key facors in he fuure afer we realize he improvemen as menioned in he scenarios. asly we pu forward some specific suggesions on he way o improve he CUE. Inroducion Food shorage and waer safey have been becoming crical concerns relaed o susainable crop producion [1]. Accordingly, waer use efficiency of crop producion (CUE becomes one of he prime arges for any waer conservaion effor. The CUE is always defined as he raio of producivy o waer used [2], or he raio of yield o irrigaion waer requiremen. Here is discussed on he annual level and defined as (1, where CUE, and denoe respecively annual waer use efficiency of crop producion, annual producion of crops, and annual waer invesmen of crop producion. CUE=. (1 e ve found ha exising CUE comparisons mainly involve waer use in differen condions of he same region, or only focus on some specific ems, or address usage efficiency of oher resources combined wh waer use efficiency [3]. e haven found any research ha zooms in on he comparison of CUE for crops worldwide, gives a more complee represenaion of CUE disparies in he world, and provides recommendaions for crop-producion improvemen in counries wh lower CUE, as well as he regional coordinaed developmen. And we will ry o address hem. Mehods and Daa Mehods. The CUE variaion model is buil based on he Cobb Douglas producion funcion, and he SFA and variance decomposion are also adoped here. Difference Model. The model would be formed as (2. The - crop producion, A - oal facor producivy, - capal invesmen for crop producion, mainly relevan o he land developmen [2], machinery & equipmen and planaion crops in he agriculure, - labor invesmen, - waer invesmen, and β 1, β 2, β 3 - producive elasicy of he facors above. All hose indicaors are relevan o he region i in he year. Then boh sides of he equaion are divided by ij, and shows (3 All righs reserved. No par of conens of his paper may be reproduced or ransmed in any form or by any means whou he wren permission of TTP, www.p.ne. (ID: 58.240.39.29-14/12/12,04:08:23
Applied Mechanics and Maerials Vols. 275-277 2719 β1 β2 β3 = A. (2 (( = β 3 1 β2 j 1 ( ( = j A β 1. (3 The is he CUE, reflecing he oupu suppored by a un of waer in he region; he and are he capal-waer efficiency and labor-waer efficiency, which reflec amouns of respecive facors suppored by a un waer. This formula implies ha CUE of a region is deermined by oal facor producivy, capal-waer efficiency, labor-waer efficiency, and waer invesmen. Formula (4 shows he CUE comparison in region i and j. The CUE difference is he weighed produc of four differences, wh weighs represened by a corresponding producive elasicy. j j β 3 j β (( j β j = (A Aj ( 1 ( 2 ( j 1 1 j j j =. (4 Then aking logarhm and variance decomposion [4], we can obain he following noaion (5: Var( + Cov((( = Cov( 3 j = 1 A β j 1 + Cov(β 1 + Cov(β 2. (5 Toal Facor Producivy Model. The facors relaed o oal facor producivy can be grouped ino four ypes: naural facors, crop managemen, agronomy managemen, human capal and sysems [5,6]. The fronier echnology analysis divides oal facor producivy ino fronier echnology and echnical efficiency componens [7]. Considering he similary of he condions in counries of he same coninen, such as naural facors, economic policy(e.g. European Union, and he poenial more frequen communicaion of echnology and managemen, would be assumed ha he fronier echnology varies by coninen, bu is more or less uniform in counries hroughou he same coninen. The oal facor producivy funcion hen should be re-wren as (6: A 5 = exp( A + = 1 ( τ d + V U. (6 0 i i i The A 0 is he inial oal facor producivy, and is he ime rend. The τ i represens he fronier echnological progress rae, and di indicaes if he counry belongs o a coninen in quesion. I is equal o 1 if a counry belongs o he coninen, and 0 if doesn. i=1,2,3,4,5 respecively indicaes he coninens of Africa, he Americas, Asia, Europe and Oceania. U = Ui exp( η ( 18, where U i is he echnical efficiency, a se of non-negaive random variables assumed o accoun for echnical inefficiency in producion, having a half-normal disribuion. η is he parameer o be esimaed. e assume V i.i.d.~n(0, σ 2 v as being independen of he U, o accoun for random variables effec (e.g. weaher. Combining he formulas (6 wh (2 and aking he logarhm of he resul, we arrive a relaionship (7- he sochasic fronier producion funcion. Then we evaluae he sochasic fronier producion funcion (7 in R using maximum likelihood esimaion, replacing σ 2 v and σ 2 u wh σ 2 2 = σ v 2 2 + σ u and γ= σ u / ( σ 2 v + σ 2 2 u (where he σ u is he variance of U i. 5 A 0 + i 1 ( di + β 1 + β2 + β3 = = τ + V U. (7
2720 Applied Mechanics and Maerials I Daa. This research uilizes relevan daa in he years 1990-2007 for 87 counries. Daa come from he FAO STAT or UN. e ve chosen (8 o esimae he annual waer invesmen of crop producion. CA = * + ( P R A. (8 TA The P is he average precipaion in volume; R - oal inernal renewable waer resources; CA - culivaed area; TA - oal area; A - annual agriculure waer whdrawal. Resuls Esimaion Resul. Producion funcion has been esimaed wh he resul summarized in he TABE I. Comparing he τ i value for five coninens, we encouner wildly varying fronier echnological progress raes. Oceania scores highes, s fronier echnological progress rae being 1.81 imes as high as ha in Africa and 1.47 imes as high as ha in he Americas. This dispary reflecs oal facor producivy differences beween coninens. TABE I RESUT OF PRODUCTION FUNCTION ESTIMATION Parameers A 0 β 1 β 2 β 3 τ 1 τ 2 Esimaion 3.6522351*** 0.1545310*** 0.1807067*** 0.4645632*** 0.0232657*** 0.0287475*** (13.5353 (4.1032 (10.0091 (13.0345 (5.6181 (8.2416 Parameers τ 3 τ 4 τ 5 σ 2 γ η Esimaion 0.0262455*** 0.0241949*** 0.0421519*** 3.1542154*** 0.9777525*** -0.0057014*** (7.3311 (8.0337 (4.4013 (7.2663 (292.9211 (-3.8099 Variaion Analysis. Our resuls show CUE varies grealy among coninens. e analyze CUE variaion on iner-coninenal, inra-coninenal and inernaional level. All he analysis includes wo aspecs, which is changes of boh he CUE variaion and each conribuing variaion facor, and specific facor conribuions and heir respecive variaions. Those wh relaively lower CUE should focus on some key facors of he CUE variaion, including hose grealy or increasingly flucuaing facors, or facors of which he conribuion rae is large or increases or flucuaes a lo. Iner-coninenal Disparies. As he dispary beween he fronier echnological progress raes in Africa and Oceania can be found o be he greaes, he variaion of he CUE in Africa and Oceania is decomposed in he curren chaper, o assess he impac of each conribuing facor. e can find changes of boh he CUE variaion and each conribuing variaion facor are differen from each oher. And he main reason of he lower CUE in Oceania is ha he labor-waer efficiency in Oceania is only 53.32% of ha in Africa. Conribuion changes of variaion facors are also various. Inra-coninenal Disparies. In Africa, he Americas and Asia, CUE variaion flucuaes insignificanly, while decreasing by a margin in Europe, and wh increasing rend in Oceania. Trends of CUE variaion facors vary among differen coninens. In recen years, waer managemen in Asia has been improved a lo, refleced in he decrease of he waer invesmen difference (diff. we observe. In Europe, decrease of oal facor producivy diff. is also consisen wh agronomy and crop managemen in his region. In Oceania, waer invesmen diff. beween counries is especially sark, and exers primary influences on CUE variaion facors (excep for he oal facor producivy diff.. The main facors ha conribue owards CUE variaion always vary among differen coninens. In Oceania is waer invesmen diff. among counries, while for oher coninens, for he mos ime, is he oal facor producivy diff.. Comparing he variaion coefficien for he Annual Agriculural aer hdrawal and aer Invesmen for Crop Producion, we find ha Annual Agriculure aer hdrawal flucuaes greaer. Therefore, improvemens in agriculural waer whdrawal are very imporan for counries wh lower CUE in Oceania. Finally, comparing conribuion rae rends for every CUE variaion facor, subsanial differences beween coninens are noeworhy.
Applied Mechanics and Maerials Vols. 275-277 2721 Inernaional Differences. The CUE variaion among counries in 1990-2007 can be decomposed (Fig.. On average, boh CUE variaion and oal facor producivy disparies beween counries worldwide have decreased from 1990 unil 1992, and have been relaively sable since. Oher CUE variaion facors, like waer invesmen diff., show no significan change, wh he fronier echnology diff. being close o 0 in any given coninen. The key facor urns ou o be he echnical efficiency diff., conribuing up o 80.06%. Overall, conribuion raes for every CUE variaion facor show lle change over he years. Variaion Analysis Conclusions. In he variaion analysis above, we show he CUE variaion on iner-coninenal, inra-coninenal and inernaional level. ey facors of he CUE variaion on each coninen are summarized in he Table II. Scenario Analysis. Based on he assumpion ha he mos imporan facor of he CUE variaion is improved in he six kinds of comparisons in he respecively 5 coninens and he inernaional level, he scenario analysis can be developed. This would help furher undersand he impac of improving he mos imporan facor. The scenarios from 1990 unil 2007 are lised as follows, where he level indicaes he level of waer invesmen in Oceania, and ha of oal facor producivy in oher regions. S 0 : no change of he original level; S 1 : all hose counries wh he level lower han he average, increase o he average level; S 2 : all hose counries wh he level lower han 80% of he average, increase o 80% of he average; S 3 : all hose counries wh he level lower han 60% of he average, increase o 60% of he average. Then we calculae he new CUE variaion and decompose. a. Changes of boh he CUE variaion and each conribuing facor b. Conribuion changes of each variaion facor FIGURE RESUTS OF CUE VARIATION DECOMPOSITION INTERNATIONA Coninen Africa The Americas Asia TABE II E FACTORS OF THE CUE VARIATION ON EACH CONTINENT The Mos Imporan Facor Toal facor producivy diff. Toal facor producivy diff. Toal facor producivy diff. The Second Mos Imporan Facor Facors Flucuaing Grealy or Increasingly Facors h Conribuion Rae Flucuaing Grealy or Increasingly Capal-waer diff. / Toal facor producivy diff. Capal-waer diff. / abor-waer diff. abor-waer diff. abor-waer diff. Toal facor producivy diff.; Capal-waer diff.; abor-waer diff. Europe Toal facor producivy diff. Capal-waer diff. Oceania aer invesmen diff. abor-waer diff. Toal facor producivy diff.; Capal-waer diff.; abor-waer diff. Toal facor producivy diff.; Capal-waer diff.; abor-waer diff.; aer invesmen diff. abor-waer diff. Toal facor producivy diff.; Capal-waer diff. I can be found ha he CUE variaion under S 1, S 2, S 3 would become much smaller han ha under S 0. This can prove ha is effecive o improve he mos imporan facor. So some counries like Zambia, Cosa Rica, Bangladesh should make effors o increase heir oal facor producivy. Also we can conclude wo feaures of he gap beween he CUE variaion under eher S 1, or S 2, or S 3, and ha under S 0. Firsly, varies among comparisons. In Asia or Oceania, CUE variaion under eher S 1, or S 2, or S 3, is always less han 35% of ha under S 0. hile on any oher level, he
2722 Applied Mechanics and Maerials I former is always more han 48% of he laer. Secondly, he rend of his gap varies in differen comparisons. I is obviously increasing in Europe, while no significan in any oher comparison. These wo feaures are due o wo aspecs. One is he differen conribuion raes of he mos imporan facor in differen regions, and he oher is ha he disribuion of waer invesmen in Oceania and oal facor producivy in oher regions are always various among regions. So he effec of improving he mos imporan facor would vary among differen coninens or on he inernaional level. e also propose ha afer improving he mos imporan facor of he CUE variaion in he scenarios, counries wh lower CUE a ha ime should also pay more aenion o he new key facors of he CUE variaion. From he resuls, hese facors would be he capal-waer efficiency diff. and waer invesmen diff. in Africa, oal facor producivy diff. and waer invesmen diff. in he Americas, Asia, Europe or on he inernaional level, and he oal facor producivy diff. in Oceania. Conclusions This aricle has summarized and decomposed CUE variaions in 87 counries from 1990 unil 2007. I is proposed ha in order o efficienly improve he CUE in he counries and decrease he regional CUE variaion, hose counries wh relaively lower CUE should give priories o waer conservaion and use efficiency improvemen, focusing on he lised key facors. The scenarios analysis can prove he significance of improving he mos imporan facor of he CUE variaion, and give us some new key facors in he fuure afer we realize he improvemen. Addionally, oal facor producivy diff. is he mos imporan facor in he comparisons excep ha in he Oceania, where is also one of he key facors. So here we give some recommendaions for s improvemen, including bio-waer savings echniques [2], reduced soil evaporaion, reasonable srucure allocaion of he knowledge-based and skilled human capal, and good sysems. Those counries wh unscienific facor composions in he crop producion should make effors o opimize he invesmen. aer invesmen can be improved by managing he waer supply according o he demand, especially for hose counries wh low CUE in he Americas and Oceania; counries in Africa and Europe should properly open he finance marke, improve he invesmen and financing mechanism, and opimize he capal srucure in he agriculural economy; is also imporan for counries in Asia o scienifically manage he populaion, enhance he educaion in he rural areas as well as he reasonable flow of he labors, which can benef he improvemen of labor-waer efficiency. Mehods used in his research can also be applied for analyzing mos oher resource efficiencies. Funcions, indexes and daa migh be furher expanded upon, wh every facor checked for applicabily. Facor analysis and variance analysis could be combined ogeher o provide new insighs and predic scenarios wh a differen number and composion of facors. References [1]. Zhang, E. endy, Q. u, e al.: Agriculural aer Managemen, Vol. 64 (2004, p.107 122. [2] Z. Zhang: Crical Reviews in Bioechnology, Vol. 31 (2011 No.3, p.81 293. [3] X. Zhang, S. Chen, H. Sun,. ang and. Shao: Agriculural aer Managemen, Vol. 97 (2010, p.1117 1125. [4] R. Hall and C. Jones: Quarerly Journal of Economics, Vol. 114 (1999 No.1, p.83-116. [5] R. M. Solow: Review of Economics and Saisics, Vol. 39 (1957, p.312-320. [6] J. Farrell: Journal of he Royal Saisical Sociey, Series A (General, Vol. 120 (1957 No.3, p.253-282. [7] Douglas Norh: Insuions, Insuional Change and Economic Performance (Cambridge Universy Press, England 1990.