COMPARISON OF METHODS FOR THE VALUATION OF IRRIGATION WATER: CASE STUDY FROM QAZVIN, IRAN

IRRIGATION AND DRAINAGE

Irrig. and Drain. (2012)

Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/ird.683

COMPARISON OF METHODS FOR THE VALUATION OF IRRIGATION WATER: CASESTUDY FROM QAZVIN, IRAN†

TINOUSH JAMALI JAGHDANI1*, BERNHARD BRÜMMER2 AND JAN BARKMANN3

1Department of Agricultural Economics and Rural Development, Centre for Statistics (ZfS), Georg-August-Universität Göttingen, Germany2Agricultural Market Analysis, Department of Agricultural Economics and Rural Development, Georg-August-Universität Göttingen, Germany

3Environmental and Resource Economics Group, Dept. of Agricultural Economics and Rural Development, Georg-August-Universität Göttingen, Germany

ABSTRACT

Physical availability and adequate distribution of irrigation water are two globally pressing resource management issues. In thelong run, the design of irrigation infrastructure should be based on the economic value of irrigation water, taking into account afull analysis of all associated costs and benefits. In the absence of water markets, non-market valuation methods need to beemployed to assess the economic value of irrigation water. A multitude of valuation methods are available, which often differsubstantially in their results. We compare three different methods using primary data collected from the Qazvin irrigation net-work in Iran. We compare economic values based on contingent valuation (197 rial m–3), the value of marginal product (430/476 rial m–3 depending on functional form assumptions), and change in net rent (1080 rial m–3). The hypothetical nature of thecontingent valuation and the presence of strategic responses may have resulted in understatements of the true water values.Thus, a stochastic frontier analysis was used to correct for undervaluation bias, which is estimated at 272 rial m–3. Our resultssuggest that actual water prices fall substantially short of the estimated economic values in the Qazvin irrigation network:higher water prices would hence improve the allocation of water. Copyright © 2012 John Wiley & Sons, Ltd.

key words: water value; non-market valuation method; contingent valuation; value of marginal product; change in net rent; hypothetical bias

Received 16 February 2011; Revised 14 September 2011; Accepted 15 September 2011

RÉSUMÉ

La disponibilité physique et la distribution adéquate de l’eau d’irrigation sont deux enjeux mondiaux pour la gestion d’uneressource par ailleurs fortement contrainte. A long terme, la conception de l’infrastructure d’irrigation devrait être basée sur lavaleur économique de l’eau d’irrigation en considérant tous les coûts et avantages à travers une analyse exhaustive. En l’absencede marché de l’eau, des méthodes d’évaluation de produits non marchands doivent être utilisées pour donner une valeur économi-que à l’eau d’irrigation. Une multitude de méthodes d’évaluation sont disponibles, et elles diffèrent souvent sensiblement dansleurs résultats. Nous comparons dans cette étude trois méthodes différentes, utilisant des données primaires rassemblées au réseaud’irrigation de Qazvin en Iran. Nous comparons des valeurs économiques basées sur l’évaluation contingente (197 rial m–3), lavaleur du produit marginal (430/476 rial m–3,selon les hypothèses de formes fonctionnelles), et le changement du revenu net(1080 rial m–3). La nature hypothétique de l’évaluation contingente et la présence de réponses stratégiques auraient pu avoircomme conséquence des sous-estimations de la valeur véritable de l’eau. Conséquemment, une analyse stochastique de frontièrea été employée pour corriger le biais de la sous-évaluation, qui est estimée à 272 rial m–3. Les résultats démontrent que les prix réelsde l’eau diffèrent de façon substantielle des valeurs estimées économiquement dans le réseau d’irrigation de Qazvin: un prix élevéde l’eau pourrait par conséquent améliorer l’allocation de l’eau. Copyright © 2012 John Wiley & Sons, Ltd.

mots clés: valeur de l’eau; méthode d’évaluation non-marchande; évaluation contingente; valeur du produit marginal; changement dans le revenu net;biais hypothétique

* Correspondence to: Mr. Tinoush Jamali Jaghdani. Department of Agricultural Economics and Rural Development, Centre for Statistics (ZfS), Georg-August-Universität Göttingen, Germany. E-mail: [email protected]†Comparaison des méthodes d'évaluation économique de l'eau d'irrigation. Etude de cas de Qazvin, Iran.

Copyright © 2012 John Wiley & Sons, Ltd.

T. J. JAGHDANI ET AL.

INTRODUCTION

Economic research has devoted substantial effort to identi-fying optimal (efficient) resource allocation under differentsets of restrictions, to assessing alternative resource alloca-tion mechanisms, and to suggesting policies for improvingthe institutional environment of resource management(Boggess et al., 1993). Although water resources are vitalfor the functioning of any economy, they continue to be de-pleted and degraded at an unsustainable rate (Birol et al.,2006). In many parts of the world, more water is used inagriculture than in any other economic sector, and waterconsumption has a relatively low level of efficiency. Thus,growing urban and industrial demands place increasingstress on the traditional need for water in agriculture. Addi-tionally, free distribution and underpricing of irrigation wa-ter is frequently identified as a primary cause of misuse andoveruse of water resources (Cosgrove and Rijsberman,2000; Hellegers and Perry, 2004).

In the widespread absence of well-functioning water mar-kets, the ‘correct’ price of irrigation water is difficult to ascer-tain (Young, 2005; Birol et al., 2006; Hanemann, 2006).Farmers are often unable or at least unwilling to pay the fullprovision costs of irrigation water (Sampath, 1992; Wilson,1997; Johansson, 2005; Young, 2005; Hanemann, 2006).In such a situation, any plan to adjust irrigation water alloca-tion or pricing regimes must carefully consider how theadjustments may impact on agricultural production. As acentral step, the economic value of irrigation water for farm-ers needs to be quantified (Tardieu and Prefol, 2002). There-fore, applied economic valuation methods play a key role inwater resources management.

Water development projects are usually economically jus-tified by residual imputation and ‘change in net rent’ meth-ods (Young, 2005). Ex-post evaluations of the actualproject performance, however, often reveal that many pro-jects cannot recover the capital costs, or cannot even coveroperation and maintenance costs.

Systematically inaccurate ex-ante determinations of thevalue of irrigation water may be one of the reasons for thepolicy-related performance problems in the implementedirrigation projects: based on overly optimistic valuationdata, inefficient projects may have been implemented. Thishighlights the importance of testing the prognostic capacityof water valuation methods.

This study compares three different non-market valuationmethods to assess the value of irrigation water to farmers inorder to systematically analyse potential biases in the appli-cation of these methods. In particular, we compare thechange in net rent method, a production function approachand the contingent valuation method (CVM). As suggestedby Young (2005), this allows us inter alia to check for pos-sible differences between deductive methods (change in net


rent in this study) and inductive methods (CVM and produc-tion function approach). Moreover, we extend the standardCVM approach by incorporating attitudinal questions inaccordance with protection motivation theory (PMT) (Rogersand Prentice-Dunn, 1997) and correct CVM results for biasusing stochastic frontier models.

The empirical study was conducted in the Qazvin irriga-tion network in northern Iran. Iran is a semi-arid to arid coun-try with a precipitation level of less than 250mm yr–1 onaverage which occurs mostly during the non-agricultural sea-sons (average of 41 years, Iran Water Resources Manage-ment Co., 2010). Therefore, irrigation for agriculturalactivities is inevitable, and the low cost recovery in irrigationnetworks has been identified as a major policy concern(Cabinet of Iran, 2003, article 6).

WATER VALUATION METHODS

Beyond the methods chosen for comparison in this paper, awide range of methods is available for the valuation of non-market goods and services (such as linear programming, he-donic valuation, travel cost, choice experiments, etc.). Themain argument for the selection of the methods in this studyis the empirical viability of the selected methods in the field.The change in net rent approach (CNR) is an extension ofthe residual imputation method for approximating the valueof water. It is used particularly for valuating policies tar-geted at improving the irrigation of agricultural crops(Young, 2005). Another frequently used alternative to esti-mate the economic value of water in agriculture is the valueof the marginal product method (VMP) (Boggess et al.,1993). Finally, contingent valuation is probably the mostpopular method among the existing non-market valuationtechniques (Bateman et al., 2002). We briefly present theseapproaches and review selected main findings from theexisting literature on them below.

Change in net rent (CNR)

This model defines the increment in net producer incomeassociated with adding water to a production process asthe willingness to pay for incremental water (Young andHaveman, 1985). The method is frequently used by consul-tants and applied water economists for valuing irrigationwater benefits. The ‘Principles and Guidelines’ of theUnited States Water Resources Council (1983) favour theapplication of the closely related change in net incomemethod (CINI)1 for the valuation of water- and land-relatedplans (without explicitly labelling the suggested concept asCINI). In addition, the Natural Resources ConservationService uses this method in its 1998 handbook for the eco-nomic analysis of water resources development projects.More recently, Tardieu and Prefol (2002) used the residual


COMPARISON OF METHODS FOR THE VALUATION OF IRRIGATION WATER

value and CNR to analyse irrigation water pricing policiesin France.

Production inputs Zj and products Yi are indexed eitherwith 0 to denote a production scenario without additionalwater and with 1 if additional water is available. If both in-put (PZj) and product prices (PYi) are unaffected by thechange from 0 to 1, the change in net rent (income) Δp,associated with a discrete addition to water supply per unitof time, is (Young and Haveman, 1985)

Copy

Δp ¼ p1 � p0

¼Xmi¼1

Y1i�PYi �Xnj¼1

Z1j�PZj

� �" #

�Xki¼1

Y0i�PYið Þ �Xl

j¼1

Z0j�PZj

� �" #

(1)

wherePm

i¼1 Y1i�PYið Þ andPk

i¼1 Y0i�PYið Þ are the revenuesfrom production in scenarios 1 and 0, and

Pnj¼1 Z1j�PZj

� �and

Plj¼1 Z0j�PZj

� �are the costs of production in scenarios

1 and 0.Commonly, the input and output variables are parame-

trized for a representative observational unit, regularly, asingle typical farm using official normalized crop prices(United States Water Resources Council, 1983; NaturalResources Conservation Service, 1998).

Based on preliminary results of the field survey for theyear 2005, three potential crops were considered for calcu-lating CNR: tomato, grain corn (maize) and wheat. As de-tailed in sections 3 and 4, tomato is a mutually exclusivecrop that can be considered for scenario establishment.Grain corn and wheat had official floor prices during thestudy period and were bought heavily by the national agri-cultural administration. In contrast, the tomato price showedextreme seasonal and local price fluctuations. These factorsargue against the inclusion of tomato. Other crops werenot produced in larger quantities. CNR requires the calcula-tion of the impacts of a production scenario change fromwheat to corn. Corn needs 4000m3 ha–1 more water thanwheat. The CNR value of water is then defined as the differ-ence between net income of wheat and corn productionwithout considering water costs. In this case, wheat produc-tion is scenario 0 and corn production scenario 1.

Value of the marginal product (VMP)

The VMP of any input is the additional revenue generatedby a marginal increase in the use of this input. In the absenceof an undistorted market price for water, the VMP of waterreflects the shadow price of water (Young, 2005) because ifwater provision is constrained to an initial level W, then themaximum willingness to pay in order to marginally relax the

right © 2012 John Wiley & Sons, Ltd.

water constraint by ΔW is equal to the additional revenuefrom the increased input use, i.e. the VMP for an infinitesi-mally small increase in W. For discrete input changes, VMPcan be estimated by Py. [Y(W+ΔW)�Y(W)] where Y islevel of output and Py is the price of output. For very smallΔW, this provides a reasonable approximation to the shadowprice of water (Johansson, 2005). The major challenge liesin the estimation of the functional relationship betweeninputs and the final product; direct calculation from real-world data is seldom possible because of simultaneouschanges in the other inputs. This problem can be avoidedif the observational data are used to estimate a productionfunction, which is straightforward once a functional formfor the production function has been agreed upon.

Husseinzadeh and Salami (2004) checked the effects of theselection of different production functional forms on watervaluation. They conducted a two-stage random sampling innorth-west Iran by interviewingwheat farmers about their out-put and inputs (including irrigation water). The results showthat the choice of functional form has a large influence onthe estimated water value. In addition, they show that all esti-mated VMPs are much higher than the official tariff for water.

The household production function for agricultural productwas specified for the period of spring and summer 2005 as

y ¼ f L;W ; Lab;M;Kð Þ (2)

where y is the total revenue of household production of allplanted crops, plus income from household agricultural ma-chinery works for other farmers in Iranian rial; L is the totalland area owned or rented by the household in hectares; Wis the aggregated amount of water used by each farmer fromdifferent resources for different crops in cubic metres; and Mis an index variable for the household stock of agriculturalmachinery. This index is developed by considering localprices. Therefore, an average price of each vehicle is indexedgiven the common brand of the vehicle in the field area;2 Labis the household’s available agricultural labour force in man-days; and K is the total credit which was received by thehousehold just for agricultural activities during 2005 as aproxy for working capital in Iranian rial.

Contingent valuation method (CVM)

CVM is a survey method frequently used in the socialsciences. It can be used to solicit directly stated preferencesfor changes in the provisioning of irrigation water in termsof maximum marginal willingness to pay. In addition toCVM, the related choice modelling techniques can be used(Bateman et al., 2002). These methods are not often usedin water economics (Southgate, 2000). One of the potentialproblems in the application of CVM is related to inaccurateresponses because of the so-called hypothetical bias whichis induced by the hypothetical nature of the WTP questions



(Hofler and List, 2004; Young, 2005). One advantage incomparison to other methods is that CVM can be extendedto estimate the WTP for water contingent on various pricelevels for different crops.

The CVM method has been successfully applied to irriga-tion water valuation. Tiwari (1998) applied CVM to assessfarmers’ willingness to pay (WTP) for increases in watersupply during wet and dry seasons in northern Thailand.The WTP results are found to be much lower than the resultsof other methods (value marginal product and ability to pay),and below the level necessary for capital cost recovery of theproject. Latinopoulos (2005) assessed WTP for irrigationwater in the Chalkidiki region of Greece. He assesses WTPusing CVM for irrigation water if farmers are interested inshaping the collective irrigation network to manage the un-derground and surface water resources of the region. WTPresults of CVM were again much lower than the results im-plied by the value of land with differing water availability(‘hedonic pricing’). Barkmann et al. (2008) estimate WTPfor changes in the availability of irrigation water in Indonesiausing choice modelling data. The authors find that the WTPfor a reduction in water scarcity by one month was 39 000–40 000 Indonesian rupiah per household and year.

In CVM studies, the analyst can build a bid function as aresult of a utility difference problem which has been solvedby respondents. A ‘Constant Only Bid Function Model’(Bateman et al., 2002) can be parameterized as follows:

Copy

ln WTPð Þi ¼ b ln Xi þ ei i ¼ 1; 2; . . . ; n (3)

where WTP is the stated willingness to pay for person i, X isa row vector of specific bid determining characteristics forperson i, and e is the error term. Typically, the variablesare transformed in natural logarithms.

During the CVM valuation interviews, some questionswere first asked about the periods of water shortages andlevel of crop losses in 2005. With regard to the culture of bar-gaining and negotiation over the price of goods in many tradetransactions in Iran, the bidding game (Bateman et al., 2002)was chosen after testing other methods in the pilot study. Forour study, one of the lowest levels of unofficially claimedmoney for extra water assignments (quota), which was ob-served during the pilot survey, was selected as the startingpoint of the bidding game (500 000 Iranian rial). Thus, weasked if the respondent would pay 500 000 Iranian rial for24 h of 50 l s–1 extra water allotment in the summer.3 If theanswer was positive, higher bids were given, and if the an-swer was negative, lower bids were given. Once the respon-dents’ maximum stated WTP appeared to be established, wefollowed with additional questions as to why he would notpay more, and the WTP was recorded.

The vector of explanatory variables consists of a list of fac-tors from the questionnaires, and was preselected accordingto economic theory. They cover respondent characteristics


such as agricultural and water use information, water trade in-formation, socio-economic data and water-related attitudes.The attitudinal questions use a Likert scale answer formatand are added to test the influence of protection motivationtheory (PMT). Variables showing explanatory potential inpreliminary tests are selected for the final model. Amongthe promising PMT items tested is ‘expected crop yield in-crease by using more water’, which was included as an inde-pendent variable in the bid function. The other explanatoryvariables included in the final bid model include Rage(respondent age), Population (population of the village),Edu (education level of respondent [1 to 4]), Rland (ratio ofland possession from second land reform to the total landeither possessed or rented), Wquota (weekly assigned waterallotment during spring from canals and wells per hectareof planted area), and RplantedL (ratio of second plantationarea to the total planted area).

Results of different studies show that differences may existbetween the hypothetical bids in CVM surveys and true bidsin real-world settings. According to Hofler and List (2004),if the analyst assumes that the proposed commodity is well de-fined but unfamiliar to the respondent, the WTP is likely to besystematically overestimated (Crocker and Shogren, 1991). Incontrast, the endowment effect can explain the understatementof WTP in certain hypothetical situations. The endowmenteffect means that people are willing to pay less for an objectwhich they do not own compared to the amount they demandin order to sell the same object if they own it (Tversky andKahneman, 1991). Stochastic frontier (SF) models (Aigneret al., 1977) can be applied to overcome the hypothetical biasof contingent valuation studies (Hofler and List, 2004). For SFanalysis, the bid function in Equation (3) is expanded asfollows:

lnWTPHi ¼ b ln Xi þ vi � ui i ¼ 1; 2; . . . ; n (4)

where WTPH is now the observed bid (possibly affected byhypothetical bias) for person i, and X and b are defined above.The error term vi is assumed to be an independently and iden-tically distributed (iid) random variable with E(ni) = 0 andVAR nið Þ ¼ s2n , and it captures random noise. The error termui is assumed to be (iid) non-negative and captures systematicdeviations from the frontier WTP function. ui can have an ex-ponential or half normal distribution which is independent ofvi. The structure of the stochastic frontier model is explainedin detail by, for example, Coelli et al. (1998).

Using an SF approach, b ln Xi þ vi ¼ WTPTi is considered

a set of true or frontier bids (frontier valuations). They areunobserved because of the presence of the vi but potentiallyestimable. vi reflects those factors affecting the frontierWTP value that cannot be recognized by an analyst. The vican be positive or negative (Hofler and List, 2004). Theone-sided error ui is a measure of the gap between true and



hypothetical bids (values) for the ith individual. As uiapproaches zero, the gap decreases, and the hypotheticalvalues become ‘real’ values (Hofler and List, 2004).

Preliminary analyses based on the skewness of the resid-uals confirm that the CVM bias works in the direction ofan underestimation of the true WTP. Therefore, the SFmodel in Equation (3) with a negative one-sided error (� υi)is a suitable basis for the estimation of the hypothetical bias.Maximum likelihood estimation of the parameters of the SFmodel (Equation (4)) can then be used to calibrate the WTPvalues in order to take the bias into account. The calibrationis based on the ratio between stated WTP and the estimatedtrue WTP:

Copy

WTPHi

WTPTi

¼ WTPHi

exp b ln Xi þ vi� �

¼exp b ln Xi þ vi � ui

� �exp b ln Xi þ vi

� � ¼ exp �uið Þ

(5)

With estimates of exp(� ui) based on the conditional ex-pectation of exp(� ui) given the estimated residual vi� ui,we are able to calibrate each person’s stated WTP as follows:

WTPTi ¼ WTPi

exp �uið Þ (6)

where WTPTi is the calibrated WTP bid of the contingent

valuation survey and may now be interpreted as the bias-corrected true WTP (Hofler and List, 2004).

Figure 1. Qazvin irri


STUDY AREA

The Qazvin irrigation and drainage network is located at theagriculturally advantageous northern edge of the Qazvinplain (Figure 1, Montazar and Rahimikob (2008)). The net-work area extends to the east and west of Qazvin City. Thenetwork irrigates almost 60 000 ha either fully or partially.The network area covers 88 villages and 30 000 farmers.The main canal is 94 km long, but secondary and tertiarycanals are as long as 1100 km (Ghasemi, 2004).

The canal system was designed to deliver water volumet-rically at a constant flow rate of 50 l s–1. Secondary canalsare labelled L1 to L20. Until 2006, a part of the water re-quired for this irrigation system was provided through theZiaran diversion dam with 225 000m3 capacity. It used toprovide 0.14–0.2 km3 of irrigation water to the network areaannually subject to the water flow regime of the TalaganRiver. Construction work on a new dam across the TalaganRiver was finished in September 2006. The aim is that thenew dam will improve water availability to Tehran (capitalcity) without reduction to the Qazvin network. Dependingon the water flow of the Talagan River, most water is pro-vided by the canal in the spring. Talagan water is not avail-able during the summer. Canal water is provided to farmersin allotments of 4320m3 (i.e. 24 h of 50 l s–1) via a conjunc-tive-use irrigation system.

In addition to water from the Talagan canal, farmers havethree additional sources of irrigation water: (i) an officialwell under the control of the central network administration,(ii) community wells belonging to the villages,4 and (iii) afew private wells. The official well provides water mostlyduring the summer months. The community wells operate

gation network



seven to nine months of the year. The agricultural adminis-tration of the county assigns a specific allotment to eachhectare of land. The size of the allotment depends on the wa-ter flow rate of the community wells, the size of arable landsand the cropping pattern in the village. Depending on farmerdecisions and size of individual water allotments, a share ofthe land is left fallow annually and a furrow irrigation sys-tem is used.

Winter wheat is the main crop of the region and is harvestedby the middle of June. The rival crops to wheat are grain cornand tomatoes. As their harvest time is later than wheat, andthey use water allotments which usually come from wells dur-ing the summer, and farmers who are planting grain corn ortomato as well as wheat have lower possibility to engage inmulticropping; the second crop is usually fodder corn.

The region underwent land reforms in 1962 and 1980.Plots from the first land reform are connected to communitywells and are scattered. Plots from the second reform havelimited access to underground water resources but are lessscattered than the first group. Farmers usually belong toone of these categories, but they own or rent some plots ofland belonging to the other category.

The price of water is assessed annually in accordancewith the ‘Fair Distribution of Water Act’ (Majlis of Iran,1983). The water price was 185 000 rial per 4320m3 forthe study period (2005).5 If an extra amount of water isavailable and the farmers have already exhausted theirquota, they may receive an extra allotment. The officialprice of this extra water was 280 000 rial per 4320m3. Theseprices could not cover even the O&M cost of the Qazvinirrigation network (Asadi et al., 2007).

The dependency on the canal water varies throughout thenetwork. Villages near the main canal and diversion dam en-joy the canal water to a larger extent than villages far awayfrom the main canals, who depend to a larger extent ongroundwater. The administration, operation and mainte-nance of the community wells are undertaken by the farmersthemselves.

Field study and sample selection

The field study was conducted from December 2005 toFebruary 2006 in the Qazvin network area. For pragmaticreasons, it was deemed important that respondents have asufficiently clear idea of the quantity of irrigation water theyuse. Pre-studies had shown, however, that many farmerslacked an understanding even of the standard allotment of4320m3 as they could not relate this number to the standardflow of 50 l s–1 for 24 h. It turned out that a good grasp ofthis quantity was related to the actual availability of canalwater in the respective parts of the irrigation network. Ineffect, this meant that only farmers from villages suppliedby the secondary canals L1 to L3 were included in the study.


From the 10 eligible villages willing to cooperate, 4 wererandomly selected. The target respondents were randomlyselected from farmers living in the villages but not settlersand non-farmers. The household questionnaire was designedand tested to ensure that it covered the household socio-economic information of the sample respondents. Moreover,a farm budget questionnaire was also designed to gather thecost–benefit elements of the main crops. This questionnairewas only given to farmers with high expertise.

Secondary data

Annual per hectare expenditure and revenue for typicalmain crops were obtained from the local agricultural office.These data are usually gathered by agricultural centres basedon the sample selection from the county, regional informationon prices, and local expert knowledge on the input quantities,such as the average observed level of labour, fertilizer,manure, pesticide, etc. In addition, official industrial watertariffs for Alvand Industrial City were obtained from the localauthority for further comparison between different tariff ratesin the area.

Software

Econometric analysis was performed using the ‘R’ and‘FRONTIER 4.1’ software packages.

RESULTS

Change in net rent (CNR)

As mentioned above, corn and winter wheat are consideredmutually exclusive crops in order to calculate the CNRvalue for water. Initial estimates of the costs and revenuesfor these crops were obtained from the agricultural centreof the county. Based on the interviews with the farmers ineach village, these data have been adjusted for the studyarea. This adjustment mainly involved corrections on familylabour which does not seem to be adequately reflected in theofficial data. Furthermore, the input prices, which were ini-tially based on county averages, were adjusted to the spe-cific local market conditions. It is obvious that even withthese adjustments individual farms might substantially differfrom the assumed cost and revenue structure (e.g. differ-ences in quality of family labour or in the farmers’ manage-ment capabilities). However, using the detailed farm budgetallows a comprehensive assessment of all inputs used in theproduction process. Both wheat and corn had official floorprices and were bought by the government annually. There-fore, in the study period, the fixed floor prices were effec-tive, and consumer market price fluctuations will not affectfarm revenues.6 Table I shows the main results of theCNR calculation. Net income can increase by 4.3 million


Table I. Change in net rent value of water

Corn Wheat Estimation

Water consumption (m3) 12 000 8 000 –Net income without watercosts (1000 rial)

8 330 4 025 –

Change in water (m3) – – 4 000CNR (1000 rial) – – 4 300CNR per cubic metre (rial) – – 1 080


rial by using an additional 4000m3 of water, after subtract-ing the two residual values of water for wheat and corn.

Production function/VMP

Different functional forms were checked for productionfunction analysis, including Cobb–Douglas, Translog, Nor-malized quadratic and Generalized Leontief. The two latterfunctional forms led to problems with heteroscedasticity, rela-tively high Akaike information criteria, and a large proportionof statistically insignificant parameter estimates. The Cobb–Douglas function was also found to be heteroscedastic, butthree coefficients were significant. The Translog productionfunction was free from heteroscedasticity, but again only threefactors were significant. Therefore, the Cobb–Douglas andTranslog forms are discussed. Table II reports OLS parameterestimates for the Cobb–Douglas production function. Thet-statistics are based on heteroscedasticity-robust standarderrors. The coefficients for land, water and machinery are sta-tistically significant, while those for credit and householdlabour are insignificant.

The VMP of water from the Cobb–Douglas function is430 rial m–3. The value is slightly higher for the Translog7

functional form (476 rial m–3). The significance of allparameters was also checked by the restricted model andANOVA test.8 The coefficients of the restricted modelsand the marginal values were almost the same as those of

Table II. OLS estimates of Cobb–Douglas function

Factors (logarithmic) Estimate

(Intercept) 13.92lgW (water) 0.3214lgL (land) 0.556lgK (credit) 0.003lgM (machinary) 0.08lgLab (available household labour) �0.076Multiple R-squared: 0.809, adjusted R-squared: 0.799F-statistic: 81.1 on 5 and 96 DF, p-value: < 2.2e-16Studentized Breusch–Pagan test:BP = 17.8, DF = 5, p-value = 0.0032


the unrestricted model. Therefore, the results of the unre-stricted models are presented.

Contingent valuation

The analysis of respondent bids for an extra allotment of4320m3 of water in the summer resulted in a WTP of 851000 rial (Table III). Table III shows the results of the OLSregression of the log WTP bids on a number of explanatoryvariables. In particular, the attitudes toward expected harvestincreases, the respondent age, the population of the village,the respondents’ education, and the share of second planta-tions from all the planted area turned out to be statisticallysignificant. A number of additional variables (landowner-ship, number of plots and household size) turned out to bestatistically insignificant and are thus omitted from the finalmodel specification. As can be seen in Table III, WTP bidsincrease as respondents become older. It shows that olderrespondents are more conservative, and they place highervalue on water being delivered to the land. Higher educationalso has positive effects on WTP bids for irrigation water. Itshows that farmers put higher value on water as their levelof education increases. As was expected, the coefficient ofassigned water allotment per planted area (hectare) for eachhousehold has a negative effect on WTP responses. Thismeans that when the allotment per planted area is higher,respondents have less incentive for a greater level of irriga-tion water. Although its coefficient was not significant, itsrestriction was significant in the F-test. The share of land-ownership from the second reform to all the land in thehands of the household (possessed or rented) is another sig-nificant factor in the CVM model that presents watershortages among farms excluded from the second landreform.

In order to assess the role of hypothetical bias in the deter-mination of the WTP bids, we proceed with an SF estima-tion of the WTP bids, using the OLS estimates as startingvalues. A likelihood ratio test between the OLS and the SF

Std error T-value Robust t-statistic pr

0.835 16.7 16.39 < 2e-160.082 3.93 3.990 0.00020.0999 5.56 6.206 2.40e-070.004 0.64 0.756 0.5240.023 3.42 2.183 0.00090.075 �1.01 �1.051 0.317

Irrig. and Drain. (2012
)

Table III. OLS estimate of contingent valuation parameters and average stated WTP

Factors (logarithmic) Estimate Std error T-value pr

(Intercept) 2.92 0.905 3.23 0.0017CropIncreaseExpected 0.721 0.275 2.63 0.0102Rage 0.331 0.143 2.31 0.0232Population 0.310 0.106 2.92 0.0044Edu 0.251 0.123 2.04 0.0442RplantedL 0.789 0.365 2.16 0.0336Rland 0.211 0.152 1.39 0.168Wquota �0.181 0.096 �1.88 0.0639Multiple R-squared: 0.255, adjusted R-squared: 0.196,F-statistic: 4.34 on 7 and 89 DFLog likelihood : -34.9, studentized Breusch–Pagan test:BP = 9.57, DF = 7, p-value = 0.214Average of stated WTP for 4320m3 : 851 (1000 rial)Standard deviation of stated WTP for 4320m3: 316 (1000 rial)


model (Table IV) confirms that the latter is statistically pre-ferred over the former. (LR= 6.17, P< 0.01, 1 DF; Koddeand Palm, 1986, Table I). Based on the estimates of exp(� ui)for each observation, we obtain an average for exp(� ui) of0.71, which is used to correct the observedWTP bids accord-ing to the Equation (6). The true WTP (corrected for hypo-thetical bias) is estimated at 272 rial m–3, almost a 40%increase compared to the uncorrected direct WTP from thecontingent valuation. In order to check the independenceof the one-sided random υi, the correlation between υi andother factors has been checked by the Spearman correlationcoefficient. There was no strong correlation between theone-sided error term and the possible explanatory variable.

For better comparison, the results of three different valu-ation methods and prices as well as an official tariff for pres-surized industrial water for Alvand Industrial City9 are

Table IV. ML estimate of contingent valuation parameters andaverage calibrated WTP

Factors (logarithmic) Estimate Std error T-value

(Intercept) 3.951 0.936 4.221CropIncrease 0.871 0.271 3.217Rage 0.237 0.136 1.742Population 0.24 0.098 2.445Edu 0.222 0.110 2.017RplantedL 0.569 0.328 1.734Rland 0.191 0.132 1.448Wquota �0.179 0.084 �2.126sigma-squared 0.272 0.064 4.274gamma 0.874 0.087 10.074Log likelihood: �31.787Average calebrated WTP for4320m3: 1177 (1000 rial)Standard deviation of WTP for4320m3: 262 (1000 rial)

Copyright © 2012 John Wiley & Sons, Ltd. Irrig. and Drain. (2012

reported in Table V. Figure 2 presents visually the differ-ences between the results of the different methods.

DISCUSSION AND CONCLUSION

The results of the valuation methods show notable differ-ences among the three methods tested (Table V, Figure 2).The CNR value of irrigation water is 1080 rial m–3. This es-timate is based on the increase in net income caused by anincrease in the available water volume and the associatedswitch from wheat to corn production. The estimated valuesof the marginal product are relatively close, at 430 rial m–3

for the Cobb–Douglas function, and 476 rial m–3 for theTranslog. These values are statistically different, but conveybasically the same message in economic terms; both areabout 40% of the CNR estimate. The direct result from thecontingent valuation approach yields a WTP at 197 rial m–3,again about 40% of the VMP results. The estimate basedon the correction of WTP for hypothetical bias is 40%higher than the uncorrected WTP but is still substantially be-low the VMP results. Even though there is considerable var-iation among the results from the different approaches, allmodels result in substantially higher values than the officialwater price (42.8 rial m–3). Such a difference betweenshadow prices obtained from valuation methods and officialprices are frequently found in the literature (e.g. Tiwari,1998; Husseinzadeh and Salami, 2004, Latinopoulos,2005). The comparison of the widespread deductive ap-proach (CNR) with the two inductive approaches (VMP,CVM) highlights the tendency of the deductive approachto yield very high water values. This result is in accordancewith Young (2005) who suggested that systematic diver-gences between these two broad categories occur, with de-ductive approaches tending to overestimate water value.One reason for this could be negligence regarding the

)

Table V. Comparison of prices and values (2005)

Origin of value or price Volume (m3)Mean value(1000 rial) Sd (1000 rial)

Unit value(rial m–3)

Description ofunit estimation

Change of income by Translog function 4 320 2 300 1 700 476 VMPChange of income by Cobb–Douglas function 4 320 1 960 500 430 VMPWTP by CVM 4 320 850 316 197 Arithmetic (WTP/4320m3)Calibrated WTP by stochastic frontier 4 320 1 177 262 272 Arithmetic (CaWTP/4320m3)Change in net rent 4 000 4 300 – 1 080 Arithmetic (CNR/4000m3)Official price of water quota (Network) 4 320 185 – 42.8 Arithmetic (Tariff/4320m3)Official price of extra quota (Network) 4 320 280 – 64.8 Arithmetic (Tariff/4320m3)Official price of industrial water(Alvand Industrial City)

– – – 994 Original price

Figure 2. Comparison of prices and values per m3 (2005)


stochastic structure of data in deductive reasoning, which isthe average estimate for CNR values in this case. Moreover,the extra contribution of labour or management by house-hold may not be captured in CNR analysis. Therefore,attaching the complete net income gain to the increase inwater can be expected to yield higher CNR values. The dif-ference between VMP and CVM is also of interest. If theVMP is considered the shadow price for irrigation water,lower values from CVM studies are indicative of systematicundervaluation by the respondents. Our calibration exerciseusing a stochastic frontier analysis also showed an underes-timation to a certain extent of the direct WTP bids. A certainamount of underestimation is not surprising since farmerscurrently pay very low water prices, and they may have astrategic incentive to understate their true WTP. Similarly,the current official water prices may have acted as an im-plicit ‘anchor’ that influenced farmers’ responses, meaningthat their stated WTP is not influenced by their actual pro-duction considerations alone (cf. Tversky and Kahneman,1974). Furthermore, farmers may be reluctant to state highWTP bids as they may be uncertain as to what extent they


would actually be able to turn the additional water into addi-tional net benefits. Shortage of family labour or reluctance toinvest in more intensive cropping techniques may legiti-mately reduce WTP for additional water. Technically, thesefactors do not affect WTP for the currently consumed unitsof water. Thus, we would expect a relative undervaluationof additional units as compared to the last consumed unit thatfarmers are regularly entitled to (cf. endowment effect:Tversky and Kahneman, 1991). The stochastic frontier anal-ysis has shown that the effect of any of these reasons on in-dividual WTP bids is not the same for all farmers. Moreover,individual WTP bids are amendable to a calibration exercisethat increases the mean WTP bid estimate. The significanceof the expectation to increase production on WTP bids (thePMT variable in the CVM model) argues against ‘overlyrandom responses’, arguments which are implied by criticiz-ing CVM as a ‘hypothetical’ method.

This research has presented the divergence among threeeconomic valuation methods for the same site and periodin the Qazvin irrigation network in Iran. The gap betweenofficial tariffs and values from all of these methods can be



the main reason for the wasteful use of water as a valuablecommodity. This low price encouraged conservativeapproaches toward any change for a more productive useof water. Along with VMP, CVM can be a measure for cor-recting pricing policies that may lead to a more effective andefficient use of resources. In addition, the divergence be-tween the three methods shows the deficiencies of CNRand suggests that it must be applied with more caution asthe main measure for justifying investment of waterresources development projects in cost–benefit analysis.Furthermore, it can be mentioned that, when applying anyvaluation technique, field conditions must be analysed be-fore the study so that appropriate methods can be implemen-ted later. Fields of further research could include examiningthe effects of social capital on water value in the irrigationnetwork, investigating the flexibility regarding water-savingpractices, comparing the value of groundwater to surfacewater, and imposing correct pricing policies regarding dif-ferent valuation results.

ACKNOWLEDGEMENTS

The authors are grateful to Mrs Tayebeh Aryan andMr AlirezaGhadimi for their help during the fieldwork, and toDr Sebastian Hess and Professor Dr Stephan von Cramon-Taubadel for their comments on an earlier version of thispaper. T. J. Jaghdani gratefully acknowledges financialsupport from the Lichtenberg Foundation during the prepa-ration of this paper.

NOTES

1. The CINI method is essentially the CNR method. If weinvoke the willingness to pay to define the welfarechange measure in the case of discrete changes in aninput, the producers’ willingness to pay for an incrementof an input is the change in net producer income or valueof net rent associated with that increment.

2. During the research it was recognized that motorbikes,tractors and combines were available agricultural ma-chinery which were used by households. The machineindex is defined as 1 for motorbikes, 25 for tractors and100 for combines.

3. Water from the canal is not available during summer andfarmers rely on underground water resources.

4. The number of wells cannot be increased, and exploita-tion of the available wells is controlled by the Ministryof Energy (MoE) in order to stop overexploitation.

5. The average exchange rate was 11 000 rial/euro in 2005.6. By the start of the price reform policy from 19.12.2010,

the floor price policy for wheat and other agriculturalproducts may change.


7. Due to space constraints, the detailed parameter esti-mates for the Translog are omitted from the paper. Theyare available from the authors upon request.

8. Full results available upon request.9. Source: Survey results. Interview with staff in charge of

water charges in the Alborz Industrial Company.

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COMPARISON OF METHODS FOR THE VALUATION OF IRRIGATION WATER: CASE STUDY FROM QAZVIN, IRAN