Analysis of the adoption of irrigation technologies under uncertain water availability. María Jesús Escribano 1 Javier Calatrava-Leyva 2

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1 Analyss of the adopton of rrgaton technologes under uncertan water avalablty María Jesús Escrbano 1 Javer Calatrava-Leyva 2 1 Departamento de Economía y Socología Agrara, IFAPA, Grana (Span). E-mal: maraj.escrbano.ext@juntadeanluca.es 2 Departamento de Economía de la Empresa, Unversd Poltécnca de Cartagena, Cartagena (Span). E-mal: j.calatrava@upct.es Paper prepared for presentaton at the XI Internatonal Congress of the EAAE (European Assocaton of Agrcultural Economsts), The Future of Rural Europe n the Global Agr- Food System, Copenhagen, Denmark, August 24-27, 2005 Copyrght 2005 by María Jesús Escrbano and Javer Calatrava-Leyva. 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. 1

2 ANALYSIS OF THE ADOPTION OF IRRIGATION TECHNOLOGIES UNDER UNCERTAIN WATER AVAILABILITY Abstract Ths paper analyses the adopton process of water-conservng rrgaton technologes by a rsk averse farmer n a context of uncertan water avalablty. Frstly, t s analytcally shown that the ncrease n water effcency that the new technology allows results n a decrease n the cost of the effectve rrgaton water appled, as well as n an ncrease n both effectve water appled and crop producton. It s also concluded that the optmal amount of rrgaton water appled depends on ndvdual rsk preferences of the producer, on the varance and asymmetry of the cost of water appled, and on the elastcty of the margnal productvty of the effectve water appled. Lastly, t s theoretcally shown that an ncrease n the level of uncertanty regardng water avalablty ncentves the adopton of modern rrgaton technologes only f ths allows for a reducton n the amount of water appled. Keywords: rrgaton technology, adopton, rsk, water avalablty JEL Classfcaton: Q25, Q12, D81 1. Introducton The mportant role that more effcent rrgaton technologes play n envronmental resources conservaton explans the ncreasng attenton that the dentfcaton and analyss of the factors that determne ther adopton have receved n the feld of Agrcultural Economcs. Durng the last two decades, numerous studes have tred to analyse whch farmer, agro-clmatc, nsttutonal and socoeconomc varables determne the adopton of these rrgaton technologes. Many authors argue that the dffuson and adopton process of new rrgaton technologes wll be relatvely slow n absence of approprate reforms n water polces. Ths argument s based on the general belef that farmers apply water n excess of crop requrements because they do not perceve restrctons n water supply. The reasons are the large water allotments allocated to farmers that use surface water and the excessve nsttutonal protecton over agrcultural water use rghts, both legally (through the preference gven to agrcultural uses over other uses except domestc ones) and economcally (through subsdsed water prces). Authors such as Caswell et al. (1990), Dnar y Letey (1991), Varela-Ortega et al. (1998) and Moreno and Sundng (2001) have theoretcally studed dfferent polcy optons as an nstrument to encourage the adopton of water-conservng rrgaton technologes. However, the lterature of rrgaton technology adopton has pad lttle attenton to the fact that the use n excess of rrgaton water s not only explaned by the fact that farmers do not perceve water scarcty, but also because water s a rsk-reducng nput (Boggess et al., 199) and because farmers are usually rsk-averse (Anderson et al., 1977). In general, a rsk-averse producer wll use a greater amount of a rsk-reducng nput than a rsk-neutral or rsk-lovng producer. Therefore, rskaverse farmers can be expected to develop crop schedules and farm plans that nvolve water applcatons that exceed the net water requrements of crops, amng to prevent plants from water stress and to reduce the varablty of yelds. In the case of uncertanty n water avalablty, a rsk-averse producer wll allocate water less ntensvely, as analytcally shown by Howtt and Taylor (199). A farmers can rely on several strateges to cope wth water supply uncertanty: usng alternatve supply sources such as groundwater (when avalable); ncreasng rrgaton water effcency through mprovements n the management of 2

3 the rrgaton system or through the adopton of more effcent new rrgaton technologes; changng to less water demandng crops; and reducng the rrgated area. Ths paper adds to the exstng lterature on the adopton of rrgaton technologes by theoretcally analysng the decson process of the adopton of new rrgaton technologes for a rskaverse farmer under uncertan water avalablty. The most drect precedent s the paper by Moreno and Sundng (2001) that analyse the mpact of uncertanty n water prce on the adopton of rrgaton technologes. Frst, a model of the decson process of a rsk-averse producer regardng the adopton of water conservng rrgaton technologes n a context of uncertan water avalablty has been formulated. Once the decson model s specfed, t s used to analyse the nfluence of water supply uncertanty on the choce of rrgaton technologes. 2. Methodology Feder and Umal (199), that revse the lterature on the adopton of agrcultural nnovatons, classfy the exstng models of farmer decson makng under uncertanty n four categores: - Models based on the expected utlty theory; - Safety-frst algorthms; - Bayesan models that allow to ncorporate farmer s experence and the process of learnng to use the new technology; - Farm programmng models that ncorporate constrants n the varablty of some decson varables, such as land avalablty, land qualty or fnancal credt. However, these methods do not allow to ncorporate the problem of nvestment under rreversblty and uncertanty. Purvs et al. (1995) are the frst to ncorporate t n the modellng of decsons regardng the adopton of agrcultural technologes. The above methods for decson analyss allow to evaluate the optmal decson for a ratonal decson-maker n a context of uncertanty. The most adequate method depends on the nature of uncertanty affectng the decson process, the number of optons avalable for the decson-maker, and hs preferences regardng rsk (Harker et al., 1997). We have opted here to use the Expected Utlty Theory (EUT) that s an adequate methodologcal framework for the ntended theoretcal analyss. The ndvdual decson process regardng the adopton of rrgaton technologcal nnovatons s modelled usng a mcroeconomc decson model smlar to the one proposed by Caswell et al. (1990). Such model s a statc one, n whch the plannng decsons regardng producton actvtes are taken for the on-gong agrcultural season (that s, n the short run) and for a sngle annual crop. We extend the determnstc model by Caswell et al. (1990) by ncorporatng uncertanty. The model proposed here maxmses the expected utlty of proft, expressed as a functon of the three frst moments of the probablty dstrbuton of proft as a Taylor seres polynomal expanson. It s assumed that the producer maxmses hs expected utlty n a two-step procedure. On a frst stage, the farmer decdes the optmal amount of water to be appled to the crop for each rrgaton technology. Once the farmer has decded the optmal amount of water appled for each technology, the choce of the optmal rrgaton technology wll depend on the relatve proftablty of each technology. The producer wll choose that technology that generates a greater level of the expected utlty of proft. Once the decson model has been specfed, and the frst-order condtons for expected utlty maxmsaton have been obtaned, a comparatve statc analyss over such condtons s used to study the nfluence of water supply uncertanty on the adopton of rrgaton technologes.

4 . Results An utlty functon expressed as a functon of the frst three moments of the proft probablty dstrbuton can be approxmated by a Taylor Seres polynomal development as (Anderson et al., 1977): 1 1 U 2 6 ( ) = U[ E] + U [ E] V + U [ E] M (1) π where proft depends on the amount of rrgaton water appled, π = π ( a). In our optmsaton problem t s assumed that the farmer can only use the amount of rrgaton water he s enttled to n hs admnstratve concesson. However, n most rrgaton dstrcts, the real water allotment avalable for the farmer, D, s below the volume of water allocated to hm n hs water concesson, as rrgaton dstrcts have dfferent levels of water supply relablty. That s, t s assumed that fnal water avalablty for the farmer, D, s a random varable. Therefore, as the utlty functon of proft can be approxmated as a functon of the frst three moments of the proft probablty dstrbuton, the objectve functon n our optmsaton problem can be expressed as: Max u [ ( a) ] u[ E[ π ( a) ], V [ π ( a) ], M [ π ( a) ] π = (2) Takng frst dervatves wth respect to the decson varable, a, we obtan the frst order condton for expected utlty maxmsaton as: du = E de + V dv + M dm = 0 () Dvdng equaton () by, we obtan equaton (4): E π ( ) de V + E dv M ( ) π + E dm = 0 (4) That can be wrtten as: de dv dm REDQ MSQ = 0 (5) where REDQ V ( π) E( π) = s called the Rsk Evaluaton Dfferental Quotent, and measures the quotent among margnal utlty of the varance of proft and margnal utlty of mean proft. As margnal utlty of proft s postve for a rsk averse producer, whle margnal utlty of the MSQ = M π E π s called the varance of proft s negatve, REDQ wll be postve. ( ) ( ) 4

5 Margnal Skewness Quotent, and measures the quotent between margnal utlty of the thrd-order moment of proft and margnal utlty of expected proft. For a rsk averse producer, the margnal utlty of M (π) wll be postve. The more postve skewness of proft s, the probablty of occurrence of lower levels of proft wll get reduced, ceters parbus. Therefore, f / M (π)>0, then MSQ<0 for a rsk averse producer. Farm proft for a gven technology,, and a gven land qualty,α, can be expressed as: π α ( a) = P q ( h ( α ) a) a C CF, (6) where P s output prce; a s the amount of rrgaton water appled per hectare; ( α ) effcency; q ( h ( ) a) h s rrgaton α s the crop-water response functon; C are varable costs assocated wth rrgaton water appled; CF are fxed costs that do not depend on water applcaton for a gven technology. In order to smplfy the analyss let us consder only two technologes: a tradtonal one for whch the technologcal varable equals 0, and a modern one for whch equals 1. Land qualty, α, h α depends on both can take values between 0 and 1, both nclusve. Water applcaton effcency ( ) rrgaton technology and land qualty. It s also assumed that for land qualty values less that one, α <1, water applcaton effcency for the new technology s greater than for the tradtonal one. Irrgaton effectveness allows to dfferentate between two dfferent concepts, the amount of rrgaton water appled and the effectve rrgaton water (the amount of rrgaton water really taken up by the used by the crops root system). Let us also assume that a sngle crop s produced wth a constant returns to scale technology, and that the producton functon depends only on effectve rrgaton water. In ths case, the Hexem and Heady (1978) quadratc producton functon s used. It has all the propertes of a Neo-Classcal producton functon, that s, concavty and a zero ntercept value ( f ( 0) = 0, f (.) > 0, f (.) < 0 ). To further smplfy, let us assume that both varable and fxed costs do not depend on land qualty. Let us also assume that the varable cost of water concdes wth ts shadow prce or opportunty cost. As we have prevously assumed that water avalablty s a random varable, ts shadow prce wll also be a random varable (Howtt and Taylor, 199). On the other hand, let us assume that fxed costs ncorporate the annual cost of nvestment n rrgaton technology, as well as the costs of labour and other nputs that do not depend on the amount of water appled. It s therefore assumed that, for a gven technology, those nputs other than water are used n a fxed amount that s ndependent of appled rrgaton water, and can be consdered fxed. Fxed costs do not ncorporate land rent. It s also assumed that the nvestment costs assocated wth the adopton of a modern and more effcent rrgaton technology are hgher than the nvestment costs of a more tradtonal rrgaton technology (CF 1 > CF 0 ). From the expresson of farm proft (6), the mathematcal expectaton, the varance and the thrd-order moment of the probablty dstrbuton of proft are calculated. Dfferentatng them wth respect to the decson varable, a, equatons (7), (8) and (9) are respectvely obtaned. [ ( a) ] ( h ( α ) a) h ( ) E de π, α = P q α (7) 5

6 dv dm [ π ( a) ],α [ π ( a) ], α = 2 a V = a 2 M (8) (9) Substtutng (7), (8) y (9) n equaton (5) and rearrangng we get the followng equaton (10), that results from the frst order condton for expected utlty maxmsaton. ( h ( α ) a) 2 + 2a REDQ V a MSQ M h ( α ) E P q = (10) Note that equaton (10) mples that, when water avalablty s uncertan, and for a gven land qualty and rrgaton technology, the optmal amount of rrgaton water to be appled s that for whch the margnal value product of the effectve water equals the perceved margnal cost of applyng t. Ths result concdes wth the condton for the optmal resource allocaton n neoclasscal economc theory. However, the stochastc nature of the resource avalablty mples that the optmal decson taken by a rsk averse producer dffer from those that would be taken n a certan envronment. Such decsons depend on the ndvdual rsk preferences of the producer (charactersed by REDQ y MSQ), as well as by the level of uncertanty he s exposed to (represented by the varance and thrd-order moment of the untary cost of rrgaton water). Ths result s smlar to that of Calatrava (2002), that do not consder rrgaton technology n hs analyss, and therefore consders the margnal value product of appled rrgaton water nstead of the margnal value product of the effectve rrgaton water. As REDQ >0 and MSQ < 0 for a rsk averse producer, the numerator n equaton (10), that s, the margnal cost of appled water, wll be greater or smaller than the expected shadow prce of the resource E(C) dependng on the sgn and value of the thrd-order moment of the probablty dstrbuton of the shadow prce of the rrgaton water appled, M (C ), that s, the asymmetry of the cost of water applcatons. If the margnal cost of appled water s greater than the expected shadow prce of water the rsk averse farmer wll use less water than when avalablty s certan. On the contrary, f t s smaller, he wll apply more rrgaton water. When the probablty dstrbuton of the margnal water cost s symmetrc, that s, M (C ) = 0, a rsk averse producer wll apply less water n the optmum than when avalablty s certan. The more varable s the cost, the less water wll be used by the farmer. When the probablty dstrbuton of the cost of water s asymmetrc, ether postve (M (C )>0) or negatve (M (C )<0), and the expresson 2a REDQ V(C ) > a 2 MSQ M (C ) holds, the farmer wll also apply less water. On the other hand, f the water cost s negatvely asymmetrcal (M (C )<0) and the expresson 2a REDQ V(C ) < a 2 MSQ M (C ) holds (ether because MSQ s very negatve due to a hgh level of rsk averson, or because the asymmetry s very negatve 1 ), then the producer wll use more rrgaton water than when ts avalablty s certan. From equaton (10) t can also be concluded that the adopton of a more modern and effcent rrgaton technology allows for a reducton n the cost of the effectve rrgaton water. In the 1 However, the emprcal probablty dstrbutons of water avalablty are usually very negatvely asymmetrcal, what results n probablty dstrbutons of the shadow prce of water that are very postvely asymmetrcal. 6

7 economc range of producton where the allocaton of water s effcent (phase II n the classcal economc theory of producton), margnal productvty of water s decreasng. Wth a decreasng margnal productvty of water, the decreasng cost of effectve water (due to ncreased rrgaton effcency) results n an ncrease n both the output produced and the optmal amount of effectve rrgaton water. However, an ncreased n the effectve water does not mean that rrgaton water appled s ncreased. It may happen that rrgaton water appled, and therefore demanded, be reduced or that t be ncreased. Although the effects of an ncrease n rrgaton effcency over the amount of rrgaton water appled are ambguous, they depend on the specfc characterstcs of the producton technology. Caswell and Zlberman (1986) show that the adopton of a more effcent rrgaton technology results n water savngs dependng on the elastcty of the margnal productvty of the effectve water (EMP), that can be expressed as: ( e) e f ( e) EMP f / (11) For a gven technology and land qualty, the own-prce elastcty of the water demand functon s the nverse of the EMP (Caswell et al., 1990). In the economc range of water allocaton, EMP s postve and ncreasng wth the amount of effectve water. Accordng to Caswell et al (1990), for the adopton of a more effcent rrgaton technology to result n water savngs, the followng condton (12) must hold: EMP u = 1 u a a 0 1 a u0 h0 h h 1 < 1 0 (12) a where u s the cost of water applcaton wth technology. For the adopton of a new technology to reduce water consumpton, two condtons must hold. Frst, condton (12) must hold, what means that EMP should be less than one, that s nelastc, n order to allow for a reducton n water consumpton. Condton (12) mples that water demand should be elastc. Second, the EMP should be greater than EMP, that s, the EMP of water should not be too low, that s the own-prce elastcty of water should not be too hgh. These condtons hold under many crcumstances, except when the margnal productvty of water ncreases wth effectve water. As prevously commented, once the farmers has calculated the optmal amount of water to be appled for each rrgaton technology, then the choce of rrgaton technology depends on the relatve proftablty of each technology. The producer wll choose that technology that allows hm to maxmse hs expected utlty of proft. If a s the optmal amount of water to be appled, then the expected utlty maxmsng proft for the technology and a gven land qualty,α, wll be gven by the followng equaton: ( a ) = P q ( h ( α ) a ) a C [ E; V M ] CF π α (1) ;, It s not possble to analytcally establsh a-pror whether a more effcent technology s also more proftable for a farmer. It may happen that the gans from an ncrease n rrgaton effcency and a reduced consumpton of other non-water nputs be offset by the costs of the nvestment n the new 7

8 technology. It s therefore necessary to emprcally analyse each specfc case and crcumstances to compare the proftablty of the alternatve technologcal optons. Equaton (1) represents the value of proft n the optmum. In that equlbrum pont, the margnal value of appled water equals the margnal costs of applyng water, C, that s gven by the followng equaton: + 2a REDQ V ( a ) MSQ M C E = (14) In the equlbrum, a change n the level of rsk wll result n changes n the expectaton, varance and asymmetry of the cost of appled water, and a new equlbrum and a dfferent level of proft wll be reached. To analyse the effect of changes n the level of uncertanty regardng water avalablty on the choce of rrgaton technology, a comparatve statcs analyss s performed wth equaton (1). Calculatng the partal dervatves of the optmal proft for technology (equaton 1) wth respect to the expectaton, varance and asymmetry of the margnal cost of appled water n the optmum, C, the followng equatons are obtaned: E C = C = a (15) V C = C = 2 2 ( a ) REDQ (16) M C = C = ( a ) MSQ (17) As a s postve, and as REDQ>0 and MSQ<0 for a rsk averse producer, then the followng condtons hold: E C = C < 0 (18) V C = C < 0 (19) M C = C < 0 (20) From equatons (18), (19) and (20), t can be concluded that ncreases n the expectaton, varance or asymmetry of the random cost of appled water wll result on a reducton n the maxmum proft achevable for a gven technology. 8

9 When the adopton of a more effcent rrgaton technology results n a reducton of the amount of water appled, then a 0 > a 1. Then the reducton n the optmal proft as a result of ncreases n the level of uncertanty wll be smaller wth the more effcent technology. The adopton of effcent rrgaton technologes reduces the adverse economc effects of ncreases n water supply rsk. An ncrease n the uncertanty regardng water avalablty wll therefore ncentve the adopton or more effcent rrgaton technologes f such adopton reduces water consumpton. However, f the new technology does not result n water savngs, the adopton wll not be encouraged. 4. Conclusons Frst, t has been theoretcally shown that, for a gven rrgaton technology and a certan land qualty, the optmal amount of rrgaton water appled under uncertan water supply s that whch equals the value of the margnal productvty of effectve water and the perceved random cost of effectve rrgaton water. Ths result concdes wth the condton for optmal resource allocaton n neoclasscal economc theory. It has also been demonstrated that the ncrease n rrgaton effcency that the adopton of a new technology allows for results n a decrease n the cost of the effectve rrgaton water appled, what causes an ncrease n agrcultural output and n the optmal amount of effectve water appled. However, t can not be asserted whether the technology adopton wll result n an ncrease or a decrease n the amount of rrgaton water appled, that s, n the amount of water demanded by the farmer. On one hand, the stochastc nature of water avalablty mples that the optmal allocaton of rrgaton water by a rsk-averse farmer depends on hs ndvdual rsk preferences, as shown by Calatrava (2002). Such preferences can be charactersed by the Rsk Evaluaton Dfferental Quotent (REDQ) and the Margnal Skewness Quotent (MSQ). The optmal allocaton of water also depends on the varance and asymmetry of the random cost of rrgaton water. On the other hand, as shown by Caswell y Zlberman (1986), the rrgaton technology adopton wll reduce water use only f the elastcty of the margnal productvty of the effectve water appled s less than one, that s, nelastc. Ths mples that water demand should be elastc n order to save rrgaton water through the adopton of more effcent technologes. It has also been shown that f a new rrgaton technology results n a decrease n the amount of water appled, an ncrease n water supply uncertanty wll ncentve the adopton of such technology. On the contrary, f water appled ncreases wth the new technology, an ncrease n uncertanty would dscourage ts adopton. Lastly, t has to be ponted out that t s not possble to theoretcally establsh whether a modern and more effcent rrgaton technology s more proftable for a farmer than a tradtonal one. It may happen that the nvestment costs n the new technology do not compensate gans due to ncreased rrgaton effcency and decreased varable costs. An emprcal analyss should therefore be requred to compare the proftablty of rrgaton technologes under each partcular condton. 5. References Anderson, J.R., Dllon, J.L. and Harker, B. (ed.) (1977). Agrcultural Decson Analyss. Ames E: Iowa State Unversty Press. Boggess, W., Lacewell, R. and Zlberman, D. (199). Economcs of Water Use n Agrculture. In: Carlson, G.A. Zlberman, D. and Mranowsk, J. A. (eds), Agrcultural and Envronmental Resource Economcs. New York: Oxford Unversty Press, Calatrava, J. (2002). Los mercados de agua en la agrcultura y el resgo económco: Una aplcacón en el Valle del Gualquvr. Doctoral Dssertaton. Unversd Poltécnca de Madrd. 9

10 Caswell, M. F. and Zlberman, D. (1986). The Effects of Well Depth and Land Qualty on the Choce of Irrgaton Technology. Amercan Journal of Agrcultural Economcs 68 (4): Caswell, M., Lchtenberg, E. and Zlberman, D. (1990). The Effects of Prcng Polces on Water Conservaton and Dranage, Amercan Journal of Agrcultural Economcs 72 (4): Dnar, A. and Letey, J. (1991). Agrcultural Water Marketng, Allocatve Effcency and Dranage Reducton. Journal of Envronmental Economcs and Management 20: Escrbano Vcente, M. J. (2004). El regadío como nstrumento de la transformacón estructural agrícola: modelos de adopcón de tecnologías de rego en contexto de ncertdumbre. Trabajo del período de nvestgacón del Programa de Doctorado: Economía Agroalmentara y Desarrollo Rural, Unversd de Córdoba. Feder, G. and Umal, D. L. (199). The Adopton of Agrcultural Innovatons. A Revew. Technologcal Forecastng and Socal Change 4: Harker, J.B., Hurne, R.B.M. and Anderson, J.R. (ed.) (1997). Copng wth rsk n agrculture. Wallngford: CAB Internatonal. Hexem, R. W. and Heady, E. O. (ed.) (1978). Water Producton Functon for Irrgated Agrculture. Ames IA: Iowa State Unversty Press. Howtt, R. and Taylor, C. R. (199). Some Mcroeconomcs of Agrcultural Resource Use. In: Carlson, G.A. Zlberman, D. and Mranowsk, J. A. (eds), Agrcultural and Envronmental Resource Economcs. New York : Oxford Unversty Press, Moreno, G. and Sundng, D. (2001). Does Factor Prce Rsk Encourage Conservaton?. 7 th Conference of the Internatonal Water and Resource Economcs Consortum. Grona (Span), -5 June. Purvs, A., Boggess, W. G., Moss, C. B. and Holt, J. (1995). Technology Adopton Decsons Under Irreversblty and Uncertanty: An Ex Ante Approach. Amercan Journal of Agrcultural Economcs 77: Varela-Ortega, C., Sumps, J. M., Garrdo, A., Blanco, M. and Iglesas, E. (1998). Water prcng polces, publc decson makng and farmers response: mplcatons for water polcy. Agrcultural Economcs 19: