Panel Estimation of an Agricultural WaterDemand Function ∗

Karina Schoengold†, David L. Sunding‡, and Georgina Moreno§

March 7, 2005

∗The authors would like to thank the Giannini Foundation and the Randolph and DoraHaynes Foundation for financial support of this project. Michael Hanemann, Jeff LaFrance,and David Zilberman have all provided useful advice and comments. Tim Long and SteveLewis of Arvin Edison Water and Storage District were instrumental in making the dataavailable and answering many questions. Of course, we take complete responsibility forall remaining errors.

†Ph.D. Candidate and corresponding author; schoeng@are.berkeley.edu, University ofCalifornia, Berkeley.

‡Professor, University of California, Berkeley and member of the Giannini Foundationof Agricultural Economics.

§Assistant Professor, Scripps College.

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AbstractUsing panel data and a natural experiment in rate reform, this

paper estimates the price elasticity of irrigation water demand anddecomposes the total elasticity into its direct and indirect compo-nents. Our empirical strategy uses an instrumental variables analysisto account for the endogeneity of land allocation in the water demandequation. From the empirical analysis, we find that including the indi-rect effects of water price changes on output and technology choices,as well as the direct effect of improved water management leads toa significantly more elastic estimate of water demand than found inprevious work.

1 Introduction

Agricultural producers use the majority of water in the western United Statesand in many arid regions of the world. As a result of rapid population growthand increasing concern about the environmental effects of surface water di-versions, agricultural interests are under increasing pressure to conserve wa-ter. Financial incentives, whether embodied in water trading opportunitiesor increased water rates, are widely touted by economists as an effectivemeans of reducing water consumption in agriculture. On the other hand,it is sometimes postulated that the price of water delivered to farmers isso highly subsidized that there is no significant demand response to modestprice changes (Garrido 2003, Jones 2003). Missing from this important policydebate are sound estimates of the price elasticity of farm water demand.

Using a unique data set along with an estimation methodology that re-flects the role of water in the production function, we are able to answer thisand several other important questions about farm water use and land allo-cation. We first use a novel estimation approach to estimate land allocationbetween different crops and irrigation technologies. We find that there is evi-dence of increased levels of fallow land with higher water prices. We also findevidence that precision irrigation technologies are adopted with higher waterprices. We do however find evidence of a large cost of adjustment in changingland allocation, as land allocation choices in the previous year are strong pre-dictors of current land allocation, in addition to land quality characteristicssuch as soil permeability and slope. These results show that expectations ofa farmer’s response to higher water prices must be conditioned on currentland allocation, as well as land quality characteristics.

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The empirical methods we use allow us to distinguish between direct andindirect elasticities of farm water demand. In addition, these results illus-trate how water use is conditioned by capital investments, crop choice, andother factors. Choices of outputs and production technologies are assumedto adjust over time, and thus a water price shock will have long-run effectsthrough its influence on output and technology choice that will be distinctfrom the short-run effects that incorporate mainly management changes.

Many previous studies of agricultural water demand rely on simulateddata and linear programming techniques (Bontemps & Couture 2002, Hooker& Alexander 1998). In general, these studies consider what the optimal re-sponse of an individual is to changes in the price of water under varyingparameters. However, these types of studies assume that an individual re-sponds rationally to changes in relative prices, while actual data shows thatthis is not always the case. Previous econometric studies which have esti-mated water demand have found varying results. Nieswiadomy (1988) founda price elasticity of water demand of -0.25, while Moore, Gollehon, and Carey(1994) found no response of farmers to increased water rates. Our study usesan econometric analysis to decompose water use by both crop and irrigationtechnology, something not done in previous econometric studies of water de-mand (Moore, Gollehon & Carey 1994, Ogg & Gollehon 1989). Much ofthe previous work on agricultural water demand discusses the importance ofland quality characteristics in determining total applied water, however thispaper is one of the first to actually estimate the effect of these characteristicsusing econometric methods. We find evidence that these characteristics (soilpermeability, slope, and temperature levels) are significant in determiningwater demand.

Programming models are frequently used to study urban water demandas well (Lund 1995, Jenkins, Lund & Howitt 2003), although due to betterdata availability, most previous econometric studies of water demand haveanalyzed urban water demand, using either residential or industrial wateruse data. One general result from these studies is that water demand is priceinelastic, with the absolute value of the estimated price elasticities generallybelow 0.5 (Hanemann 1998). In a meta-analysis of residential water demand,Dalhuisen, Florax, de Groot & Nijkamp (2003) find a mean price elasticity ofdemand of -0.41, while Espey, Espey, & Shaw (1997) find a median short-runprice elasticity of -0.38, and a median long-run price elasticity of -0.64. Manyof the recent papers in the study of urban water demand have focused onestimation under block rate pricing, and the implications of appropriately

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accounting for both the discrete choice of which block to choose, and thecontinuous choice of how much water to use (Hewitt & Hanemann 1995,Dalhuisen, Florax, de Groot & Nijkamp 2003). This work has found thatestimating urban water demand using the discrete-continuous approach findsa much more elastic price elasticity of demand than studies which do notexplicitly model both choices. While this type of pricing is common in urbanwater rates, it is extremely rare in irrigation water rates, and therefore hasnot been studied in an agricultural context. Another area of research inthe urban water demand literature is on the effects of non-price conservationprograms, such as educational campaigns. Renwick & Green (2000) find thatthese type of programs have a significant effect on residential water demand.

The rest of this paper is organized as follows: Section 2 develops theconceptual motivation, while section 3 describes the data and provides somesummary statistics. Section 4 explains the procedure used to estimate landallocation and water demand as well as the results of these estimations.Section 5 concludes.

2 Conceptual Motivation

In our empirical analysis, we account for the importance of managementdecisions into water input demand, and we allow water and management to besubstitutes in the agricultural production function. Despite the fact that it istypically assumed there is no substitution between water and other inputs inagricultural production, evidence that the elasticity of substitution betweenwater and labor is non-zero has been shown on occasion (Nieswiadomy 1988).In addition, Wichelns (1991) shows that an increase in the marginal priceof water to farmers decreases both the mean and the variance of appliedwater, even in cases where crop and irrigation technology remain constant.Improved water management can reduce the demand for applied water, aswater can be applied at the times which are most beneficial for the crop. Forexample, a farmer could adjust the timing of water applications so that wateris applied for 6-hour intervals each week instead of for 15-hour intervals everytwo weeks. Improved maintenance of water furrows or drip systems increasesthe efficiency with which applied water reaches the root zone of the crop.

In addition, we account for the importance of previous land allocation.There are costs of adjustment, which are incurred both when land is movedinto a new use, and out of an existing one. The level of these costs will depend

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on the crop and technology employed, but with perennial crops such as citrustrees, both of these costs are considerable. Due to these costs of adjustment,a producer will only alter their acreage allocation if the change in expectedprofit is greater than the cost of that change. Therefore, we expect that smallchanges in the marginal price of water may not affect land allocation choices,but that with a significant jump in the price we will observe land allocationadjustment.

From this logic, we determine that there are at least three possible out-comes after an increase in the marginal price of water. The first possibilityis that a producer alters their relative use of management and applied water,substituting increased management inputs for applied water in the produc-tion process. Another possibility is that the profitability of water-intensivecrops will decrease, and producers will either switch to a less water-intensivecrop, adopt precision irrigation technology, or both. Similar types of re-sponses were considered in an analysis of household water demand by Lund(1995), where a household’s adaptations to shortages in water supply aredecomposed into long-run changes in capital stock and short-run changes inmanagement, such as installing a low-flush toilet and taking shorter show-ers, respectively. Previous studies have shown that an increase in waterprice leads to the adoption of precision (water-conserving) irrigation sys-tems by farmers (Caswell & Zilberman 1985, Caswell & Zilberman 1986,Kanazawa 1992). This research also shows that the relative profitability ofdifferent types of irrigation technologies is conditional on land quality char-acteristics. However, with the exception of Kanazawa, these papers assumethat crop choice is exogenous in the irrigation technology decisions. Otherwork has shown that these two choices are highly correlated, and shouldbe modeled simultaneously (Lichtenberg 1989, Green, Sunding, Zilberman& Parker 1996, Moreno & Sunding forthcoming). Lastly, it is possible thatwhen the price of water is very high, producers will choose to take land outof crop production, either permanently or in a particular year.

3 Data and Summary Statistics

The data used in this analysis come from the Arvin Edison Water Stor-age District (AEWSD), a utility serving over 130,000 acres and roughly 150farming operations located 90 miles north of Los Angeles. In 1994, AEWSDbegan collection of data on technology and output choice at the field level.

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AEWSD also provided the water price and water delivery data. A water yearruns from March until the following February, a time period that parallelsthe growing season in the district. The district sets the water price at thebeginning of each water year, and measures monthly water deliveries at eachturnout.1 We aggregate the water delivery data by year and turnout to ob-tain total water deliveries by section. Combining these data with the landallocation data, it is possible to piece together a fairly complete picture ofwater use decisions at the micro level.

The data set includes an 8-year panel of 117 sections (predetermined,time-invariant blocks of land) in AEWSD.2 Also important is the fact thatin 1995, the District enacted a major water rate reform that facilitates iden-tification of the demand function. Like many water authorities, AEWSDprices water according to a two-part tariff. Agricultural producers pay afixed per-acre fee for access to water, and this fee is paid if the land is leftfallow or in production. There is an additional variable fee which is paid peracre-foot of water.3 In 1995, AEWSD decreased the fixed component and in-creased the variable one; a change intended to encourage water conservationby increasing its marginal price. By comparing water use before and afterthe rate reform, we can capture the effects of the price change controlling forfactors such as environmental conditions and changes in output prices.

Table 1 gives historical water prices to surface water users during thestudy period. Before 1995, AEWSD assessed a fixed per acre fee of $136.3,and a variable charge of $45.3 per acre foot of water delivered. In 1995,the District reduced the fixed fee by over 30 percent to $94, and increasedthe variable fee by over 40 percent to $65.3. In 1999, the variable chargedecreased because AEWSD found it was over collecting revenue after the1995 price change, as water districts in California are run on a revenue-neutral basis.

The environmental variables used are chosen to reflect soil and topographycharacteristics relevant to farming and irrigation. These variables (slope,permeability, number of frost-free days per year, and average temperature)are long run averages and do not change over time, but do vary over section.

1A turnout is the endpoint of water deliveries. As a turnout can provide water tomultiple fields, and it is difficult to accurately calculate the water use per field.

2The panel covers the period from 1994 until 2001.3Agricultural water use is generally measured in acre-feet, where each acre-foot is

enough water to cover an acre of land with water at a depth of one foot. An acre-foot isclose to 326,000 gallons, or enough to serve 1-2 average households for a year.

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Yearly temperature averages for the area were obtained from the WesternRegional Climate Center. The use of the two temperature variables addressestwo sources of variation in temperatures - cross-sectional variation amongmicroclimates within the District and variation across years.

Table 2 shows the total acreage in each land allocation choice during thestudy period. In our empirical analysis, we consider only certain crop andirrigation technology combinations, as some combinations are note observedin our data. For example, truck crops grown under drip irrigation, whiletechnically feasible, are not observed in our sample. The pairs we consider arecitrus crops with drip or gravity, grape crops with drip or gravity, deciduouscrops with drip, gravity, or sprinkler, truck crops with gravity or sprinkler,and field crops with sprinkler. The main citrus crop in the region is oranges;deciduous crops include mostly almonds, along with some peaches and apples.Truck crops include potatoes, carrots, and onions, while field crops includecotton and some hay.

We use output prices as one set of information which identifies crop choice.Most of these data were obtained from the annual Kern County AgriculturalCommissioner’s Crop Report, with the exception of the price of carrots, whichwas from the U.S. Department of Agriculture. During the study periodcrop prices exhibit the volatility commonly observed in agricultural outputmarkets. This volatility makes it difficult for a farmer to predict future prices,and may explain why many farmers diversify land allocation.

4 Empirical Model

In our econometric analysis we estimate a reduced form model of water de-mand, explaining water use at a particular location as a function of outputand technology choices, relative prices, and other factors such as environ-mental characteristics. Our estimation strategy assumes that each land allo-cation choice has a fixed input/output ratio in the short run, and this ratiois a function of environmental conditions and management inputs. This ap-proach assumes that the durability of physical capital fixes the input/outputratio in the short run, but that the choice of technology will adjust over timeto changes in the relative prices of inputs and outputs. Irrigation systems canbe modeled using this framework, since they are comprised of pipes, valves,heads, and other types of equipment. The choice of crop can also be viewedas a particular type of capital investment, as all crops require a significant

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investment in specialized farm equipment and human capital, while perennialcrops also require capital investment in plant stock.

One potential problem is the endogeneity of certain explanatory variables,particularly the land allocation variables, as they are functions of both landquality characteristics and water price. Therefore, we use 2SLS estimation,where we estimate the acreage in each crop/technology pair in the first stage,and then use those fitted values to estimate the second stage water demandequation.

4.1 Land Allocation Estimation

In our estimation of land allocation, we note that the relative profitability,and therefore the optimal allocation of land, are influenced by a number offactors including the quality of the land, the existing allocation of land, aswell as relative input and output prices. We use these results to inform ourestimation equations and the variables employed in those equations. Previouswork has often used a discrete choice model to estimate the crop or technologyon a particular field, where a field is defined as a contiguous area plantedwith the same crop and irrigation technology (Green et al. 1996, Moreno& Sunding forthcoming). However, we do not observe water use at the fieldlevel, only the total quantity delivered to each section. In addition, for certainyears the land allocation data is only available aggregated by section. Thisrequires the development and use of a non-traditional estimation strategy.

4.1.1 Estimation of Acreage Totals

In our estimation strategy, we make use of the fact that the entire regionis never entirely in agriculture and that there is always some land which isfallowed or used for other purposes. We use this land as an outside optionavailable to farmers. We denote the average acreage in non-agricultural usesas Anon,t, the section by i and the time period by t. We also use aijt todenote the acreage in land allocation choice j at section i in time t. We thencalculate the ratio of acreage to non-agricultural land, which we use as thedependent variable in our estimations.

yijt =aijt

Anon,t

(1)

The denominator of this equation is the average acreage of land in non-

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agricultural uses.4 This ratio is defined over the [0,∞) range as long as thereis some land in non-agricultural uses. Although this outcome is the result ofcorner solutions (as opposed to censored values), this type of model can beconsistently estimated using a Tobit estimation strategy (Wooldrige 2002).The estimation strategy also imposes an upper bound on the estimated val-ues, requiring that the predicted acreage values are in the range of feasiblevalues.

4.2 Land Allocation Estimation Strategy

In the following formulation, we let y∗ijt be the underlying latent variable, yijt

denote the observed (censored) ratio, yit−1 as the Jx1 vector of all the laggedvalues, αi the vector of section specific variables, pmt, pwt, and pt the man-agement cost, marginal water price, and vector of output prices respectively.Letting j denote the crop/technology pair, we estimate J equations of thefollowing form:

y∗ijt = β0j + β′1jαi + β2jpmt + β3jpwt + β′4jpt + β′5jyit−1 + εijt (2)

Where εijt ∼ η(0, σ2j )

(3)

The above regression equation includes time specific variables (outputprices, marginal water prices, and the minimum wage), land quality vari-ables (slope, soil permeability, average section temperature, and frost-freedays), as well as the lagged acreage values. Interestingly, a change in waterprice will affect both the numerator and denominator of our dependent vari-able, as both the acreage allocation and the number of acres left fallow aredependant on the price of water. As the price of water increases, we expecta greater amount of land to be left fallow, which will reduce the dependantvariable ratio. However, as seen in the summary statistics, acreage totals inprecision irrigation increase over the study period. The question of whetherthe fallowing effect or the adoption effect is greater needs to be examinedempirically.

Each of the land quality variables affects what type of crop can be grown,and which irrigation systems can be used at a particular location, as wellas the relative profitability of each crop and irrigation system. For example,

4During the study period, this ranges from 10 % to 25 % of the land.

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crops with a low frost tolerance are less likely to be planted in areas witha low number of frost-free days. Precision irrigation systems are relativelymore likely to be adopted on land with a high slope, as the gains in input-use efficiency are greater than on flat land. Therefore, these variables affectboth the initial land allocation choices, as well as the decision to adjust thatallocation.

The lagged acreage variables are included to measure the effect of adjust-ment costs and the durable nature of technology and output choices. Ob-viously, perennial crops are durable since they require an established standof trees or vines. Other sources of adjustment costs in the cropping decisionare that growing a crop takes specific human capital (i.e. knowing how togrow grapes does not imply that one knows how to grow lettuce), and alsothat the long-term relationship between a farmer and a distributor of a cropinfluences the price farmers receive for their output (Hueth & Ligon 1999).In addition, we expect to observe some element of crop rotation in the annualcrops included in the estimations.5

4.3 Land Allocation Results

The results of the Tobit estimations are presented in Tables 3 and 4. Wefind that the coefficient on lagged acreage in the same crop and technology isalways positive and significant. This shows that there is some cost of adjust-ing land allocation each period. We also find that this coefficient is larger inmagnitude with permanent crops, reflecting the greater cost of moving landout of these crops, and the fact that the decision to invest in these cropsshould be seen as long-term investment instead of an annual choice.6

Another interesting result comes from the coefficient on the water pricevariable. This coefficient is negative and significant with all of the estimatedequations. When we hold total planted acreage constant in the analysis,the coefficient on this variable is positive with precision irrigation. However,when we estimate these results using the modified shares, these coefficientsare all negative. This result tells us that despite the fact that water price

5For certain crops grown in the region (such as cotton and carrots), it is beneficial tothe soil to have rotation between years.

6We also look at the effect of changes in land allocation between years, which onlyincludes changes in acreage instead of the level of acreage. We find negative coefficientsin the lagged acreage of annual crops using this measure, evidence which supports theobservations of crop rotation between field and truck crops between years.

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is a positive determinant of acreage in precision irrigation, the magnitudeof the effect at the extensive margin due to increased fallowing is greaterthan the effect at the intensive margin of precision irrigation technologyadoption. This result supports the fact that land allocation is altered atboth the intensive and extensive margins.

4.3.1 Calculation of Predicted Land Allocation

We note that due to censoring, the predicted value of the observed ratio isnot the linear prediction using the estimated parameters. Using Φ to denotethe normal CDF, φ the normal pdf, βj as the estimated coefficients in thejth equation, and σj as the estimated standard error, we use the followingformula to calculate the expected value of the observed dependent variable:

yijt = E[yijt|Xijt] = Φ(β′jXijt

σj

)(β′jXijt + σj

φ(β′jXijt

σj)

Φ(β′jXijt

σj)) (4)

Using this notation, we further define β3 as the Jx1 vector of estimatedcoefficients, [β31β32...β3J ]′.

These results are easily translated into the predicted acreage totals usingthe product of the estimated values and the acreage in non-agricultural uses.

Aijt = yijtAnon,t (5)

These predicted land allocation variables provide the instruments for theactual land allocation in the water demand estimation.

4.4 Water Demand Estimation

The main equation to be estimated is the water demand equation, wherewater demand is a function of water price, section specific variables, and timespecific variables as shown below. The equation we estimate is of total wateruse in a section with the explanatory variables including acreage in each typeof crop and irrigation technology. An alternative option is to estimate thewater use per acre with acreage shares included as explanatory variables. Weestimated water demand using this specification and found that the waterprice coefficient is still negative and significant, with a price elasticity closeto -0.4.

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The choice of a functional form for the estimation equation is important.Previous work on residential water demand has generally used linear, log-log,or log-linear functional forms (Hanemann 1998). Information on the cropproduction function informs the decision of the appropriate functional form.Other research has shown that a quadratic production function provides agood fit for observed yields and water input levels in agriculture. A quadraticproduction function implies that we estimate a linear input-demand function.In addition, in contrast to a Cobb-Douglas production function, which as-sumes a constant price elasticity of demand, a quadratic production functionallows the elasticity to differ depending on the price observed.

Using these results, we estimate the following model:

WDit = γ0 + γ1Xt + γ′2αi + γ′3Ait + γ4pwt + γ5pmt + εit (6)

The variables included in the analysis are time dependent variables (aver-age yearly temperature, marginal water price, and the minimum wage), landquality variables (slope, soil permeability, and average section temperature),and the fitted land allocation variables. The marginal water price is perhapsthe variable of most interest in this study. We expect the coefficient on waterprice to be negative since farmers will be more careful with water applicationat a higher water price. While we do not have data and observations on themarginal price paid to labor, we do use the minimum wage as a proxy for theprice of labor. We do not include prices of other non-water and non-laborfarm inputs such as fertilizers and pesticides. While labor in the form ofbetter management can be a substitute for applied water, previous resultsin both economics and agronomy show that there are very few substitutesfor effective water in crop production (see, for example, Hanks, Gardner &Florian (1969) and Power, Bond, Sellner & Olson (1973)).

The results of the water demand estimation are in table 6. For compar-ison, we present the results of the OLS estimation and the IV estimationwith robust standard errors. The results are very similar across economet-ric specifications. We find that the coefficient on water price is negativeand significant. This finding demonstrates that marginal price can influencefarm water demand - even controlling for other factors such as output choiceand capital investments in production technology. The significance of waterprice in this equation suggests that better management alone can result in asignificant amount of conservation, and can do so in the short run.

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4.5 Direct and Indirect Water Price Elasticity

One benefit of the estimation strategy we use is that the microeconomic re-sponse to changes in water price can be decomposed into direct and indirecteffects, where the latter include changes in capital investment and land allo-cation. Using the notation from equations 2 and 6, we calculate the followingformula for the change in water use with respect to the price of water. Tocalculate these effects, we use the marginal effects from the Tobit estima-tions. As the Tobit estimations are non-linear by design, the marginal effectsdiffer from the coefficients in the acreage estimations.

∂WDit

∂pwt

= γ4︸︷︷︸direct effect of management

+ Anon,tγ′3β3Φ(

β′Xijt

σj

)

︸ ︷︷ ︸indirect effect of land use changes

(7)

Converting this to an elasticity measure at mean values gives the follow-ing:

εp =∂W

D

∂pw

pw

WD = γ4

pw

WD

︸ ︷︷ ︸direct price elasticity

+ Anon,tγ′3β3Φ(

β′Xijt

σj

)pw

WD

︸ ︷︷ ︸indirect price elasticity

(8)

Table 6 presents the estimated demand elasticities from each econometricspecification. The direct elasticities are all negative and significantly differ-ent from zero for the average section in our sample, providing evidence ofimproved water management and conservation at higher water prices. Theindirect elasticity is negative, although not as significant as the direct elas-ticity, implying that a change in the price of water induces water-conservingchanges in crop and technology choices. It should also be noted that theindirect effects or water price are greater than the direct effects. Much ofthis result is due to the fallowing of land, and the estimated indirect elas-ticity holding acreage constant (but allowing changes in land allocation) isapproximately 50% of the value found including fallowing.7 This pattern isexplained by the fact that, while the price of water has been shown to be asignificant determinant of adoption of conservation technology in agriculture,it is by no means the only determinant (Green et al. 1996). Other factors

7This indirect elasticity, which is calculated holding land acreage constant but allowingsubstitution between crops and irrigation systems is approximately -0.25.

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such as weed control, a desire to save on labor costs, or a need to applyfertilizers precisely through the irrigation system can all spur investment inprecision irrigation systems. Similarly, the price of water has been shown tohave only a relatively small influence on crop choice since the price of wateris often a small share of the cost of production (Moore et al. 1994).

The calculated total own-price elasticity of water use is in the range [-0.912, -0.221]. This finding implies that agricultural water demand is some-what more elastic with respect to the price of water than indicated by previ-ous studies. Accordingly, one implication of our research is that water ratechanges can have a larger effect on water allocation than previously assumed.It is also worth noting that our panel only includes 7 years of data after themajor rate change. Given the durability of capital investments in irrigationsystems, which can have a useful life of ten years or more, and plant stock,which can last up to forty years for some trees and vines, we would expectthat the indirect effects may be larger when measured over a longer timeperiod.

5 Conclusions

Freshwater resources are increasingly limited in many arid regions, and un-derstanding the patterns of how individuals use those water resources iscrucial for a better understanding of water demand, with the goal of im-provements in water management. One available mechanism to change thosepatterns of use is the price of water, and the measurement of the price elas-ticity of water demand has been the subject of many previous studies. Themajority of these studies have focused on urban water demand, despite thefact that agricultural producers use the majority of water resources in manyareas of the world.8

This paper develops and estimates a model of agricultural water demandbased on the role of water in the farm production function. It then presentsestimates of the parameters of the model using a unique panel data set fromCalifornia’s San Joaquin Valley. The data we have collected for this analysisis of a level of quality and completeness which is rare in the literature onagricultural water demand. One objective of our analysis is to measure theprice elasticity of farm water use, as it provides important information about

8In many arid regions such as the Western United States, agricultural producers useover 80% of total freshwater consumption.

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the effectiveness of using price reforms to manage water demand. Our resultssupport the hypotheses that farmers respond in two ways to an increase inthe marginal price of water, both by reducing their water applications andaltering their land allocation. We also find that agricultural water demand ismore elastic than shown in previous work on urban water demand, a resultwhich has important implications for differences in the optimal design ofpolicies directed at agricultural users of water as compared to urban users.

These predicted values of land allocation and irrigation technology choiceare used as instruments in the water demand estimation. The direct own-price elasticity, or the component due to better management of water re-sources, is in the range of -0.22 to -0.38, while the estimated indirect com-ponent of the total price elasticity (due to land reallocation and increasedlevels of fallow land) is -0.51. Of this total elasticity, the indirect effects ofwater price on output and technology choices account for roughly 60 percentof the total, while direct effects make up the balance. This finding suggeststhat more active management has a large influence on water use, althoughthe indirect effects of land use change are also significant, and that in thelong run these indirect effects are larger.

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Table 1: Summary of Water Prices (in Dollars), 1994 - 2001Year Fixed Variable

Cost Cost1994 136.3 45.31995 94.0 65.31996 94.0 65.31997 94.0 65.31998 80.0 64.81999 80.0 50.82000 80.0 50.82001 58.0 50.8

Fixed costs are paid per acre, while variable costs are paid per acre-foot.

Table 2: Land Allocation Acreage Totals over Time by Crop & Technology

Crop IrrigationType Type 1994 1995 1996 1997 1998 1999 2000 2001Citrus Drip 7,784 7,619 7,837 8,723 8,998 9,399 9,554 9,732

Gravity 871 904 1,046 976 976 369 588 588Grape Drip 4,273 4,249 4,506 5,031 5,245 7,764 6,795 6,894

Gravity 4,670 5,273 5,222 5,248 5,065 3,338 4,186 4,449Deciduous Drip 1,769 1,716 2,147 2,856 3,043 2,200 2,425 2,634

Gravity 1,323 1,191 1,719 1,453 1,556 1,712 1,822 2,020Sprinkler 2,061 2,082 934 1,103 864 1,284 772 813

Truck Gravity 1,827 1,434 1,534 1,438 1,601 1,819 989Sprinkler 12,567 11,271 14,212 5,186 6,793 7,115 6,963 7,255

Field Sprinkler 8,406 8,939 10,197 9,007 6,629 6,815 7,540 7,685All Drip 13,826 13,584 14,490 16,610 17,286 19,363 18,774 19,260Perennial Gravity 6,864 7,368 7,987 7,677 7,597 5,419 6,596 7,057Crops Sprinkler 2,061 2,082 934 1,103 864 1,284 772 813All Annual Gravity 1,827 1,434 1,534 1,438 1,601 1,819 989Crops Sprinkler 20,973 20,210 24,409 14,193 13,422 13,930 14,503 14,940

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Table 3: Tobit Estimation Results - Dependent Variables are the Ratios ofAcreage in Each Crop and Technology Pair to Non-agricultural Land (x 1000)

Citrus Citrus Grape Grape Deciduous Deciduous DeciduousDrip Gravity Drip Gravity Drip Gravity Sprinkler

Water Price *** -0.189 *** -0.226 *** -0.146 *** -0.180 *** -0.213 *** -0.182 -0.072(0.026) (0.070) (0.026) (0.032) (0.049) (0.049) (0.045)

Minimum Wage *** 2.08 ** 2.81 *** 1.60 *** 1.90 *** 3.28 ** 2.08 0.37(0.46) (1.16) (0.44) (0.56) (0.84) (0.81) (0.79)

Slope *** 0.180 0.131 * 0.079 ** -0.235 0.059 ** -0.466 -0.068(0.044) (0.11) (0.046) (0.096) (0.079) (0.19) (0.12)

Soil Permeability -0.006 -0.153 0.025 0.012 ** 0.088 -0.048 ** 0.097(0.019) (0.095) (0.019) (0.027) (0.037) (0.050) (0.039)

Frost-free Days ** -0.014 * -0.030 0.015 *** 0.042 * 0.029 ** 0.062 0.011(0.006) (0.017) (0.009) (0.016) (0.017) (0.029) (0.023)

Section 0.092 * 0.346 -0.130 ** -0.308 *** -0.413 -0.043 0.334Temperature (0.071) (0.18) (0.081) (0.13) (0.15) (0.23) (0.21)Orange Price ** -0.008 * -0.015 0.002 *** -0.015 * -0.010 -0.007 0.005Index (0.003) (0.009) (0.003) (0.004) (0.005) (0.005) (0.006)Grape Price *** 0.103 *** 0.100 *** 0.078 *** 0.073 *** 0.099 *** 0.092 0.000Index (0.012) (0.029) (0.012) (0.014) (0.022) (0.021) (0.021)Almond Price *** 0.040 *** 0.063 *** 0.031 *** 0.046 *** 0.047 *** 0.047 0.017Index (0.009) (0.023) (0.009) (0.011) (0.016) (0.016) (0.016)Annual Price 0.003 -0.003 -0.003 0.011 0.002 0.007 -0.002Index (0.008) (0.022) (0.007) (0.010) (0.013) (0.013) (0.014)Citrus/Drip *** 1.18 -0.218 0.041 -0.016 *** 0.226 0.006 *** -0.478Lagged Ratio (0.035) (0.13) (0.038) (0.056) (0.066) (0.097) (0.16)Citrus/Gravity -0.008 *** 2.05 * -0.256 *** 0.446 0.120 *** 0.723 -0.386Lagged Ratio (0.131) (0.206) (0.155) (0.142) (0.233) (0.234) (0.448)Grape/Drip 0.067 0.059 *** 1.39 0.101 *** 0.328 -0.144 0.062Lagged Ratio (0.047) (0.110) (0.045) (0.066) (0.077) (0.12) (0.085)Grape/Gravity 0.027 ** -0.619 *** 0.132 *** 1.29 *** 0.228 ** 0.141 *** -0.746Lagged Ratio (0.056) (0.299) (0.047) (0.051) (0.080) (0.066) (0.247)Decid./Drip 0.066 -0.167 0.029 0.011 *** 1.45 *** 0.256 0.055Lagged Ratio (0.073) (0.296) (0.066) (0.081) (0.086) (0.077) (0.106)Decid./Gravity ** -0.297 ** 0.399 0.048 0.094 *** 0.392 *** 1.58 *** 0.367Lagged Ratio (0.139) (0.165) (0.080) (0.088) (0.133) (0.107) (0.137)Decid./Sprinkler -0.209 -0.302 0.044 * -0.358 *** 0.745 0.047 *** 1.31Lagged Ratio (0.132) (0.358) (0.073) (0.206) (0.100) (0.126) (0.100)Truck/Sprinkler * 0.064 0.001 *** -0.131 ** -0.116 *** 0.244 -0.099 0.012Lagged Ratio (0.038) (0.081) (0.048) (0.049) (0.066) (0.072) (0.067)Truck/Gravity ** -0.334 -0.754 -0.192 *** -0.801 -0.064 -0.082 -0.323Lagged Ratio (0.165) (0.876) (0.138) (0.265) (0.245) (0.172) (0.241)Field/Sprinkler *** -0.151 -0.238 ** 0.110 -0.069 -0.026 -0.102 ** 0.133Lagged Ratio (0.056) (0.176) (0.044) (0.055) (0.085) (0.085) (0.066)Constant *** -16.4 *** -30.2 * -7.64 -2.75 -2.62 ** -28.8 ** -25.7

(4.22) (11.4) (4.36) (6.27) (8.00) (12.5) (12.2)Censored Obs. 598 891 658 698 790 831 838Uncensored Obs. 338 45 278 238 146 105 98Pseudo R2 0.419 0.517 0.397 0.371 0.299 0.370 0.317Log-likelihood -729.6 -120.9 -614.5 -589.5 -438.3 -301.2 -302.9

Numbers in parentheses are standard errors. Significance at the 90th, 95th, and 99th percentiles aredenoted by *, **, and ***, respectively.

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Table 4: Tobit Estimation Results - Dependent Variables are the Ratios ofAcreage in Each Crop and Technology Pair to Non-agricultural Land (x 1000)

Truck Truck FieldSprinkler Gravity Sprinkler

Water Price *** -0.484 *** -0.047 *** -0.237(0.038) (0.017) (0.033)

Minimum Wage *** -5.27 ** 0.771 *** -2.72(0.347) (0.339) (0.319)

Slope -0.090 -0.149 *** -0.319(0.087) (0.193) (0.099)

Soil Permeability 0.028 *** -0.276 ** 0.081(0.032) (0.085) (0.032)

Frost-free Days 0.000 1.11 *** 0.057(0.014) (0.994) (0.017)

Section 0.000 -0.535 *** -0.686Temperature (0.138) (0.372) (0.158)Potato Price *** 0.038 0.004Index (0.012) (0.012)Carrot Price *** -0.125 ** -0.043Index (0.019) (0.017)Onion Price *** 0.161 *** 0.079Index (0.012) (0.011)Cotton Price *** 0.217 *** 0.095Index (0.019) (0.017)Annual Price ** -0.030Index (0.015)Permanent Price *** 0.167 -0.023 ** 0.058Index (0.028) (0.015) (0.026)Citrus/Drip *** -0.310 *** -0.406Lagged Ratio (0.081) (0.095)Citrus/Gravity 0.089 ** -0.667Lagged Ratio (0.199) (0.286)Grape/Drip 0.055 0.134Lagged Ratio (0.071) (0.073)Grape/Gravity *** -0.372 *** -0.336Lagged Ratio (0.091) (0.086)Decid./Drip * 0.174 0.046Lagged Ratio (0.095) (0.090)Decid./Sprinkler -0.056 0.023Lagged Ratio (0.124) (0.108)Decid./Gravity 0.174 * 0.219Lagged Ratio (0.129) (0.123)Truck/Sprinkler *** 0.955 *** 0.292 *** 0.324Lagged Ratio (0.050) (0.070) (0.048)Truck/Gravity *** 0.659 *** 1.20 *** 0.455Lagged Ratio (0.126) (0.145) (0.125)Field/Sprinkler *** 0.432 *** 0.205 *** 0.830Lagged Ratio (0.054) (0.067) (0.053)Constant 6.42 -270.4 *** 34.0

7.13 269.2 7.83Censored Obs. 507 843 542Uncensored Obs. 429 93 394Pseudo R2 0.243 0.286 0.230Log-likelihood -1089.5 -300.5 -1023.2

Numbers in parentheses are standard errors. Significance at the 90th, 95th, and 99th percentiles aredenoted by *, **, and ***, respectively. 21

Table 5: Water Demand Estimation Results (Dependent Variable is TotalWater Use at Each Section)

OLS IVWater Price ** -4.07 *** -7.25

(1.89) (2.17)Minimum Wage *** 137.1 *** 271.4

(46.7) (55.8)Slope 2.29 * 43.2

(14.7) (24.2)Permeability *** 22.7 *** 25.1

(5.58) (6.67)Section Temperature ** -37.12 -56.8

(17.12) (41.9)Annual Temperature *** 47.82 ** 36.7

(14.03) (16.0)Citrus Drip *** 1.67 *** 1.35

(0.14) (0.26)Citrus Gravity *** 3.09 1.78

(0.45) (9.56)Grape Drip *** 1.29 *** 0.81

(0.17) (0.24)Grape Gravity *** 1.95 1.02

(0.18) (0.98)Deciduous Drip *** 2.34 1.68

(0.23) (1.38)Deciduous Gravity *** 2.83 ** 2.85

(0.30) (1.11)Deciduous Sprinkler *** 2.50 2.85

(0.34) (5.87)Truck Sprinkler *** 1.27 *** 0.74

(0.15) (0.39)Truck Gravity *** 2.07 1.62

(0.36) (4.17)Field Sprinkler *** 1.96 *** 2.06

(0.15) (0.48)Constant -791.7 743.7

(1511.2) (2892.1)Number of obs. 936 936Adjusted R-sq 0.426 0.372

Numbers in parentheses are standard errors, with the robust IV standard errors are calculated using boot-strapping. Significance at the 90th, 95th, and 99th percentiles are denoted by *, **, and ***, respectively.

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Table 6: Estimated Direct and Indirect Water Demand ElasticitiesDirect Indirect Total

Elasticity Elasticity ElasticityOLS Estimation ** -0.215 0 ** -0.215

(0.09) (0.09)IV *** -0.382 -0.779 -1.170

(0.10) (0.88) (0.90)

Numbers in parentheses are the bootstrapped standard errors of the estimates. Significance at the 90th,95th, and 99th percentiles are denoted by *, **, and ***, respectively.

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