Panel Estimation of an Agricultural Water Demand Function

Transcription

1 Panel Estimation of an Agricultural Water Demand 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 Dora Haynes Foundation for financial support of this project. Michael Hanemann, Jeff LaFrance, and David Zilberman have all provided useful advice and comments. Tim Long and Steve Lewis of Arvin Edison Water and Storage District were instrumental in making the data available and answering many questions. Of course, we take complete responsibility for all remaining errors. Ph.D. Candidate and corresponding author; University of California, Berkeley. Professor, University of California, Berkeley and member of the Giannini Foundation of Agricultural Economics. Assistant Professor, Scripps College. 1

2 Abstract Using panel data and a natural experiment in rate reform, this paper estimates the price elasticity of irrigation water demand and decomposes the total elasticity into its direct and indirect components. Our empirical strategy uses an instrumental variables analysis to account for the endogeneity of land allocation in the water demand equation. From the empirical analysis, we find that including the indirect effects of water price changes on output and technology choices, as well as the direct effect of improved water management leads to a significantly more elastic estimate of water demand than found in previous work. 1 Introduction Agricultural producers use the majority of water in the western United States and in many arid regions of the world. As a result of rapid population growth and increasing concern about the environmental effects of surface water diversions, agricultural interests are under increasing pressure to conserve water. Financial incentives, whether embodied in water trading opportunities or increased water rates, are widely touted by economists as an effective means of reducing water consumption in agriculture. On the other hand, it is sometimes postulated that the price of water delivered to farmers is so highly subsidized that there is no significant demand response to modest price changes (Garrido 2003, Jones 2003). Missing from this important policy debate are sound estimates of the price elasticity of farm water demand. Using a unique data set along with an estimation methodology that reflects the role of water in the production function, we are able to answer this and several other important questions about farm water use and land allocation. We first use a novel estimation approach to estimate land allocation between different crops and irrigation technologies. We find that there is evidence of increased levels of fallow land with higher water prices. We also find evidence that precision irrigation technologies are adopted with higher water prices. We do however find evidence of a large cost of adjustment in changing land allocation, as land allocation choices in the previous year are strong predictors of current land allocation, in addition to land quality characteristics such as soil permeability and slope. These results show that expectations of a farmer s response to higher water prices must be conditioned on current land allocation, as well as land quality characteristics. 2

3 The empirical methods we use allow us to distinguish between direct and indirect elasticities of farm water demand. In addition, these results illustrate how water use is conditioned by capital investments, crop choice, and other factors. Choices of outputs and production technologies are assumed to adjust over time, and thus a water price shock will have long-run effects through its influence on output and technology choice that will be distinct from the short-run effects that incorporate mainly management changes. Many previous studies of agricultural water demand rely on simulated data and linear programming techniques (Bontemps & Couture 2002, Hooker & Alexander 1998). In general, these studies consider what the optimal response of an individual is to changes in the price of water under varying parameters. However, these types of studies assume that an individual responds rationally to changes in relative prices, while actual data shows that this is not always the case. Previous econometric studies which have estimated water demand have found varying results. Nieswiadomy (1988) found a 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 uses an econometric analysis to decompose water use by both crop and irrigation technology, something not done in previous econometric studies of water demand (Moore, Gollehon & Carey 1994, Ogg & Gollehon 1989). Much of the previous work on agricultural water demand discusses the importance of land quality characteristics in determining total applied water, however this paper is one of the first to actually estimate the effect of these characteristics using econometric methods. We find evidence that these characteristics (soil permeability, slope, and temperature levels) are significant in determining water demand. Programming models are frequently used to study urban water demand as well (Lund 1995, Jenkins, Lund & Howitt 2003), although due to better data availability, most previous econometric studies of water demand have analyzed urban water demand, using either residential or industrial water use data. One general result from these studies is that water demand is price inelastic, with the absolute value of the estimated price elasticities generally below 0.5 (Hanemann 1998). In a meta-analysis of residential water demand, Dalhuisen, Florax, de Groot & Nijkamp (2003) find a mean price elasticity of demand of -0.41, while Espey, Espey, & Shaw (1997) find a median short-run price elasticity of -0.38, and a median long-run price elasticity of Many of the recent papers in the study of urban water demand have focused on estimation under block rate pricing, and the implications of appropriately 3

4 accounting for both the discrete choice of which block to choose, and the continuous choice of how much water to use (Hewitt & Hanemann 1995, Dalhuisen, Florax, de Groot & Nijkamp 2003). This work has found that estimating urban water demand using the discrete-continuous approach finds a much more elastic price elasticity of demand than studies which do not explicitly model both choices. While this type of pricing is common in urban water rates, it is extremely rare in irrigation water rates, and therefore has not been studied in an agricultural context. Another area of research in the urban water demand literature is on the effects of non-price conservation programs, such as educational campaigns. Renwick & Green (2000) find that these type of programs have a significant effect on residential water demand. The rest of this paper is organized as follows: Section 2 develops the conceptual motivation, while section 3 describes the data and provides some summary statistics. Section 4 explains the procedure used to estimate land allocation 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 management decisions into water input demand, and we allow water and management to be substitutes in the agricultural production function. Despite the fact that it is typically assumed there is no substitution between water and other inputs in agricultural production, evidence that the elasticity of substitution between water and labor is non-zero has been shown on occasion (Nieswiadomy 1988). In addition, Wichelns (1991) shows that an increase in the marginal price of water to farmers decreases both the mean and the variance of applied water, even in cases where crop and irrigation technology remain constant. Improved water management can reduce the demand for applied water, as water can be applied at the times which are most beneficial for the crop. For example, a farmer could adjust the timing of water applications so that water is applied for 6-hour intervals each week instead of for 15-hour intervals every two weeks. Improved maintenance of water furrows or drip systems increases the 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 moved into a new use, and out of an existing one. The level of these costs will depend 4

5 on the crop and technology employed, but with perennial crops such as citrus trees, both of these costs are considerable. Due to these costs of adjustment, a producer will only alter their acreage allocation if the change in expected profit is greater than the cost of that change. Therefore, we expect that small changes 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 allocation adjustment. From this logic, we determine that there are at least three possible outcomes after an increase in the marginal price of water. The first possibility is that a producer alters their relative use of management and applied water, substituting increased management inputs for applied water in the production process. Another possibility is that the profitability of water-intensive crops will decrease, and producers will either switch to a less water-intensive crop, adopt precision irrigation technology, or both. Similar types of responses were considered in an analysis of household water demand by Lund (1995), where a household s adaptations to shortages in water supply are decomposed into long-run changes in capital stock and short-run changes in management, such as installing a low-flush toilet and taking shorter showers, respectively. Previous studies have shown that an increase in water price leads to the adoption of precision (water-conserving) irrigation systems by farmers (Caswell & Zilberman 1985, Caswell & Zilberman 1986, Kanazawa 1992). This research also shows that the relative profitability of different types of irrigation technologies is conditional on land quality characteristics. However, with the exception of Kanazawa, these papers assume that crop choice is exogenous in the irrigation technology decisions. Other work has shown that these two choices are highly correlated, and should be modeled simultaneously (Lichtenberg 1989, Green, Sunding, Zilberman & Parker 1996, Moreno & Sunding forthcoming). Lastly, it is possible that when the price of water is very high, producers will choose to take land out of 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 Storage District (AEWSD), a utility serving over 130,000 acres and roughly 150 farming operations located 90 miles north of Los Angeles. In 1994, AEWSD began collection of data on technology and output choice at the field level. 5

6 AEWSD also provided the water price and water delivery data. A water year runs from March until the following February, a time period that parallels the growing season in the district. The district sets the water price at the beginning of each water year, and measures monthly water deliveries at each turnout. 1 We aggregate the water delivery data by year and turnout to obtain total water deliveries by section. Combining these data with the land allocation data, it is possible to piece together a fairly complete picture of water 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 that in 1995, the District enacted a major water rate reform that facilitates identification of the demand function. Like many water authorities, AEWSD prices water according to a two-part tariff. Agricultural producers pay a fixed per-acre fee for access to water, and this fee is paid if the land is left fallow or in production. There is an additional variable fee which is paid per acre-foot of water. 3 In 1995, AEWSD decreased the fixed component and increased the variable one; a change intended to encourage water conservation by increasing its marginal price. By comparing water use before and after the rate reform, we can capture the effects of the price change controlling for factors such as environmental conditions and changes in output prices. Table 1 gives historical water prices to surface water users during the study 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 increased the variable fee by over 40 percent to $65.3. In 1999, the variable charge decreased because AEWSD found it was over collecting revenue after the 1995 price change, as water districts in California are run on a revenueneutral basis. The environmental variables used are chosen to reflect soil and topography characteristics 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. 1 A turnout is the endpoint of water deliveries. As a turnout can provide water to multiple fields, and it is difficult to accurately calculate the water use per field. 2 The panel covers the period from 1994 until Agricultural 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 is close to 326,000 gallons, or enough to serve 1-2 average households for a year. 6

7 Yearly temperature averages for the area were obtained from the Western Regional Climate Center. The use of the two temperature variables addresses two sources of variation in temperatures - cross-sectional variation among microclimates within the District and variation across years. Table 2 shows the total acreage in each land allocation choice during the study period. In our empirical analysis, we consider only certain crop and irrigation technology combinations, as some combinations are note observed in our data. For example, truck crops grown under drip irrigation, while technically feasible, are not observed in our sample. The pairs we consider are citrus crops with drip or gravity, grape crops with drip or gravity, deciduous crops 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 include cotton 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 Agricultural Commissioner s Crop Report, with the exception of the price of carrots, which was from the U.S. Department of Agriculture. During the study period crop prices exhibit the volatility commonly observed in agricultural output markets. 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 demand, explaining water use at a particular location as a function of output and technology choices, relative prices, and other factors such as environmental characteristics. Our estimation strategy assumes that each land allocation choice has a fixed input/output ratio in the short run, and this ratio is a function of environmental conditions and management inputs. This approach assumes that the durability of physical capital fixes the input/output ratio in the short run, but that the choice of technology will adjust over time to changes in the relative prices of inputs and outputs. Irrigation systems can be modeled using this framework, since they are comprised of pipes, valves, heads, and other types of equipment. The choice of crop can also be viewed as a particular type of capital investment, as all crops require a significant 7

8 investment in specialized farm equipment and human capital, while perennial crops 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 land quality 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 demand equation. 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 of factors including the quality of the land, the existing allocation of land, as well as relative input and output prices. We use these results to inform our estimation equations and the variables employed in those equations. Previous work has often used a discrete choice model to estimate the crop or technology on a particular field, where a field is defined as a contiguous area planted with the same crop and irrigation technology (Green et al. 1996, Moreno & Sunding forthcoming). However, we do not observe water use at the field level, only the total quantity delivered to each section. In addition, for certain years the land allocation data is only available aggregated by section. This requires the development and use of a non-traditional estimation strategy Estimation of Acreage Totals In our estimation strategy, we make use of the fact that the entire region is never entirely in agriculture and that there is always some land which is fallowed or used for other purposes. We use this land as an outside option available to farmers. We denote the average acreage in non-agricultural uses as A non,t, the section by i and the time period by t. We also use a ijt to denote the acreage in land allocation choice j at section i in time t. We then calculate the ratio of acreage to non-agricultural land, which we use as the dependent variable in our estimations. y ijt = a ijt A non,t (1) The denominator of this equation is the average acreage of land in non- 8

9 agricultural uses. 4 This ratio is defined over the [0, ) range as long as there is some land in non-agricultural uses. Although this outcome is the result of corner solutions (as opposed to censored values), this type of model can be consistently estimated using a Tobit estimation strategy (Wooldrige 2002). The estimation strategy also imposes an upper bound on the estimated values, requiring that the predicted acreage values are in the range of feasible values. 4.2 Land Allocation Estimation Strategy In the following formulation, we let y ijt be the underlying latent variable, y ijt denote the observed (censored) ratio, y it 1 as the Jx1 vector of all the lagged values, α i the vector of section specific variables, p mt, p wt, and p t the management cost, marginal water price, and vector of output prices respectively. Letting j denote the crop/technology pair, we estimate J equations of the following form: y ijt = β 0j + β 1jα i + β 2j p mt + β 3j p wt + β 4jp t + β 5jy it 1 + ɛ ijt (2) Where ɛ ijt η(0, σ 2 j ) The above regression equation includes time specific variables (output prices, marginal water prices, and the minimum wage), land quality variables (slope, soil permeability, average section temperature, and frost-free days), as well as the lagged acreage values. Interestingly, a change in water price will affect both the numerator and denominator of our dependent variable, as both the acreage allocation and the number of acres left fallow are dependant on the price of water. As the price of water increases, we expect a greater amount of land to be left fallow, which will reduce the dependant variable ratio. However, as seen in the summary statistics, acreage totals in precision irrigation increase over the study period. The question of whether the fallowing effect or the adoption effect is greater needs to be examined empirically. 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 well as the relative profitability of each crop and irrigation system. For example, 4 During the study period, this ranges from 10 % to 25 % of the land. (3) 9

10 crops with a low frost tolerance are less likely to be planted in areas with a low number of frost-free days. Precision irrigation systems are relatively more likely to be adopted on land with a high slope, as the gains in inputuse efficiency are greater than on flat land. Therefore, these variables affect both the initial land allocation choices, as well as the decision to adjust that allocation. The lagged acreage variables are included to measure the effect of adjustment costs and the durable nature of technology and output choices. Obviously, perennial crops are durable since they require an established stand of trees or vines. Other sources of adjustment costs in the cropping decision are that growing a crop takes specific human capital (i.e. knowing how to grow grapes does not imply that one knows how to grow lettuce), and also that the long-term relationship between a farmer and a distributor of a crop influences the price farmers receive for their output (Hueth & Ligon 1999). In addition, we expect to observe some element of crop rotation in the annual crops included in the estimations Land Allocation Results The results of the Tobit estimations are presented in Tables 3 and 4. We find that the coefficient on lagged acreage in the same crop and technology is always positive and significant. This shows that there is some cost of adjusting land allocation each period. We also find that this coefficient is larger in magnitude with permanent crops, reflecting the greater cost of moving land out of these crops, and the fact that the decision to invest in these crops should be seen as long-term investment instead of an annual choice. 6 Another interesting result comes from the coefficient on the water price variable. This coefficient is negative and significant with all of the estimated equations. 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 coefficients are all negative. This result tells us that despite the fact that water price 5 For certain crops grown in the region (such as cotton and carrots), it is beneficial to the soil to have rotation between years. 6 We also look at the effect of changes in land allocation between years, which only includes changes in acreage instead of the level of acreage. We find negative coefficients in the lagged acreage of annual crops using this measure, evidence which supports the observations of crop rotation between field and truck crops between years. 10

11 is a positive determinant of acreage in precision irrigation, the magnitude of the effect at the extensive margin due to increased fallowing is greater than the effect at the intensive margin of precision irrigation technology adoption. This result supports the fact that land allocation is altered at both the intensive and extensive margins Calculation of Predicted Land Allocation We note that due to censoring, the predicted value of the observed ratio is not the linear prediction using the estimated parameters. Using Φ to denote the normal CDF, φ the normal pdf, β j as the estimated coefficients in the jth equation, and σ j as the estimated standard error, we use the following formula to calculate the expected value of the observed dependent variable: β ŷ ijt = E[y ijt X ijt ] = Φ( β j jx ijt φ( X ijt )(β σ σ jx ijt + σ j ) j ) (4) j Φ( β j X ijt σ j ) Using this notation, we further define β 3 as the Jx1 vector of estimated coefficients, [β 31 β 32...β 3J ]. These results are easily translated into the predicted acreage totals using the product of the estimated values and the acreage in non-agricultural uses. Â ijt = ŷ ijtânon,t (5) These predicted land allocation variables provide the instruments for the actual land allocation in the water demand estimation. 4.4 Water Demand Estimation The main equation to be estimated is the water demand equation, where water demand is a function of water price, section specific variables, and time specific variables as shown below. The equation we estimate is of total water use in a section with the explanatory variables including acreage in each type of crop and irrigation technology. An alternative option is to estimate the water use per acre with acreage shares included as explanatory variables. We estimated water demand using this specification and found that the water price coefficient is still negative and significant, with a price elasticity close to

12 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 crop production function informs the decision of the appropriate functional form. Other research has shown that a quadratic production function provides a good fit for observed yields and water input levels in agriculture. A quadratic production function implies that we estimate a linear input-demand function. In addition, in contrast to a Cobb-Douglas production function, which assumes a constant price elasticity of demand, a quadratic production function allows the elasticity to differ depending on the price observed. Using these results, we estimate the following model: W D it = γ 0 + γ 1 X t + γ 2α i + γ 3Âit + γ 4 p wt + γ 5 p mt + ɛ it (6) The variables included in the analysis are time dependent variables (average yearly temperature, marginal water price, and the minimum wage), land quality variables (slope, soil permeability, and average section temperature), and the fitted land allocation variables. The marginal water price is perhaps the variable of most interest in this study. We expect the coefficient on water price to be negative since farmers will be more careful with water application at a higher water price. While we do not have data and observations on the marginal price paid to labor, we do use the minimum wage as a proxy for the price of labor. We do not include prices of other non-water and non-labor farm inputs such as fertilizers and pesticides. While labor in the form of better management can be a substitute for applied water, previous results in both economics and agronomy show that there are very few substitutes for 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 comparison, we present the results of the OLS estimation and the IV estimation with robust standard errors. The results are very similar across econometric specifications. We find that the coefficient on water price is negative and significant. This finding demonstrates that marginal price can influence farm water demand - even controlling for other factors such as output choice and capital investments in production technology. The significance of water price in this equation suggests that better management alone can result in a significant amount of conservation, and can do so in the short run. 12

13 4.5 Direct and Indirect Water Price Elasticity One benefit of the estimation strategy we use is that the microeconomic response to changes in water price can be decomposed into direct and indirect effects, where the latter include changes in capital investment and land allocation. Using the notation from equations 2 and 6, we calculate the following formula for the change in water use with respect to the price of water. To calculate these effects, we use the marginal effects from the Tobit estimations. As the Tobit estimations are non-linear by design, the marginal effects differ from the coefficients in the acreage estimations. W D it = γ 4 p wt }{{} direct effect of management + A non,t γ 3β 3 Φ( β X ijt ) (7) σ j }{{} indirect effect of land use changes Converting this to an elasticity measure at mean values gives the following: ɛ p = W D p w p w p w W D = γ 4 W D + A non,t γ 3β 3 Φ( β X ijt σ j }{{} direct price elasticity ) p w W D }{{} indirect price elasticity (8) Table 6 presents the estimated demand elasticities from each econometric specification. The direct elasticities are all negative and significantly different from zero for the average section in our sample, providing evidence of improved water management and conservation at higher water prices. The indirect elasticity is negative, although not as significant as the direct elasticity, implying that a change in the price of water induces water-conserving changes in crop and technology choices. It should also be noted that the indirect effects or water price are greater than the direct effects. Much of this result is due to the fallowing of land, and the estimated indirect elasticity holding acreage constant (but allowing changes in land allocation) is approximately 50% of the value found including fallowing. 7 This pattern is explained by the fact that, while the price of water has been shown to be a significant determinant of adoption of conservation technology in agriculture, it is by no means the only determinant (Green et al. 1996). Other factors 7 This indirect elasticity, which is calculated holding land acreage constant but allowing substitution between crops and irrigation systems is approximately

14 such as weed control, a desire to save on labor costs, or a need to apply fertilizers precisely through the irrigation system can all spur investment in precision irrigation systems. Similarly, the price of water has been shown to have only a relatively small influence on crop choice since the price of water is 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 [ , ]. This finding implies that agricultural water demand is somewhat more elastic with respect to the price of water than indicated by previous studies. Accordingly, one implication of our research is that water rate changes 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 the major rate change. Given the durability of capital investments in irrigation systems, 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 expect that the indirect effects may be larger when measured over a longer time period. 5 Conclusions Freshwater resources are increasingly limited in many arid regions, and understanding the patterns of how individuals use those water resources is crucial for a better understanding of water demand, with the goal of improvements in water management. One available mechanism to change those patterns of use is the price of water, and the measurement of the price elasticity of water demand has been the subject of many previous studies. The majority of these studies have focused on urban water demand, despite the fact that agricultural producers use the majority of water resources in many areas of the world. 8 This paper develops and estimates a model of agricultural water demand based on the role of water in the farm production function. It then presents estimates of the parameters of the model using a unique panel data set from California s San Joaquin Valley. The data we have collected for this analysis is of a level of quality and completeness which is rare in the literature on agricultural water demand. One objective of our analysis is to measure the price elasticity of farm water use, as it provides important information about 8 In many arid regions such as the Western United States, agricultural producers use over 80% of total freshwater consumption. 14

15 the effectiveness of using price reforms to manage water demand. Our results support the hypotheses that farmers respond in two ways to an increase in the marginal price of water, both by reducing their water applications and altering their land allocation. We also find that agricultural water demand is more elastic than shown in previous work on urban water demand, a result which has important implications for differences in the optimal design of policies directed at agricultural users of water as compared to urban users. These predicted values of land allocation and irrigation technology choice are used as instruments in the water demand estimation. The direct ownprice elasticity, or the component due to better management of water resources, is in the range of to -0.38, while the estimated indirect component of the total price elasticity (due to land reallocation and increased levels of fallow land) is Of this total elasticity, the indirect effects of water price on output and technology choices account for roughly 60 percent of the total, while direct effects make up the balance. This finding suggests that more active management has a large influence on water use, although the indirect effects of land use change are also significant, and that in the long run these indirect effects are larger. 15

16 References Bontemps, C. & Couture, S. (2002), Irrigation water demand for the decision maker, Environment and Development Economics 7, Caswell, M. & Zilberman, D. (1985), The choices of irrigation technologies in california, American Journal of Agricultural Economics 67(2), Caswell, M. & Zilberman, D. (1986), The effect of well depth and land quality on the choice of irrigation technology, American Journal of Agricultural Economics 68(4), Dalhuisen, J. M., Florax, R. J. G. M., de Groot, H. L. F. & Nijkamp, P. (2003), Price and income elasticities of residential water demand:a meta-analysis, Land Economics 79(2), Espey, M., Espey, J. & Shaw, W. D. (1997), Price elasticity of residential demand for water: a meta-analysis, Water Resources Research 33(6), Garrido, A. (2003), Transition to full-cost pricing of irrigation water for agriculture in oecd countries, Agencia Catalania del Agua / World Bank Institute, Barcelona, Spain. Green, G., Sunding, D., Zilberman, D. & Parker, D. (1996), Explaining irrigation technology choices: A microparameter approach, American Journal of Agricultural Economics 78(4), Hanemann, W. M. (1998), Urban water demand management and planning: Determinants of urban water use, McGraw Hill Book Co, chapter 2. Hanks, R. J., Gardner, H. R. & Florian, R. L. (1969), Plant growthevapotranspiration relationships for several crops in the central great plains, Agronomy Journal 61, Hewitt, J. A. & Hanemann, W. M. (1995), A discrete/continuous choice approach to residential water demand under block rate pricing, Land Economics 71(2), Hooker, M. A. & Alexander, W. E. (1998), Estimating the demand for irrigation water in the central valley of california, Journal of the American Water Resources Association 34(3),

17 Hueth, B. & Ligon, E. (1999), Agricultural supply response under contract, American Journal of Agricultural Economics 81(3), Jenkins, M. W., Lund, J. R. & Howitt, R. E. (2003), Economic losses from urban water scarcity in california, Journal of the American Water Works Association. Jones, T. (2003), Pricing water, OECD Observer. Kanazawa, M. T. (1992), Econometric estimation of groundwater pumping costs: A simultaneous equations approach, Water Resource Research 28(6), Lichtenberg, E. (1989), Land quality, irrigation development and cropping patterns in the northern high plains, American Journal of Agricultural Economics 71(1), Lund, J. R. (1995), Derived estimation of willingness-to-pay to avoid probabilistic shortage, Water Resources Research 31(5), Moore, M., Gollehon, N. & Carey, M. (1994), Multicrop production decisions in western irrigated agriculture: The role of water price, American Journal of Agricultural Economics 76, Moreno, G. & Sunding, D. L. (forthcoming), Joint estimation of technology adoption and land allocation with implications for the design of conservation policy, American Journal of Agricultural Economics. Nieswiadomy, M. (1988), Input substitution in irrigated agriculture in the high plains of texas, , Western Journal of Agricultural Economics 13(1), Ogg, Clayton, W. & Gollehon, N. R. (1989), Western irrigation response to pumping costs: A water demand analysis using climatic regions, Water Resources Research 25(5), Power, J., Bond, J., Sellner, W. & Olson, H. (1973), The effect of supplemental water on barley and corn production in a subhumid region, Agronomy Journal 65,

18 Renwick, M. & Green, R. (2000), Do residential water demand side management policies measure up? an analysis of eight california water agencies, Journal of Environmental Economics and Management 40, Wichelns, D. (1991), Increasing Block-rate Prices for Irrigation Water Motivate Drain Water Reduction, Kluwer Academic Publishers, chapter 14, pp Wooldrige, J. M. (2002), Econometric Analysis of Cross Section and Panel Data, MIT Press, Cambridge. 18

19 Table 1: Summary of Water Prices (in Dollars), Year Fixed Variable Cost Cost 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 Irrigation Type Type Citrus Drip 7,784 7,619 7,837 8,723 8,998 9,399 9,554 9,732 Gravity , Grape 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 4,449 Deciduous 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 2,020 Sprinkler 2,061 2, , , Truck Gravity 1,827 1,434 1,534 1,438 1,601 1, Sprinkler 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 7,685 All Drip 13,826 13,584 14,490 16,610 17,286 19,363 18,774 19,260 Perennial Gravity 6,864 7,368 7,987 7,677 7,597 5,419 6,596 7,057 Crops Sprinkler 2,061 2, , , All Annual Gravity 1,827 1,434 1,534 1,438 1,601 1, Crops Sprinkler 20,973 20,210 24,409 14,193 13,422 13,930 14,503 14,940 19

20 Table 3: Tobit Estimation Results - Dependent Variables are the Ratios of Acreage in Each Crop and Technology Pair to Non-agricultural Land (x 1000) Citrus Citrus Grape Grape Deciduous Deciduous Deciduous Drip Gravity Drip Gravity Drip Gravity Sprinkler Water Price *** *** *** *** *** *** (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 ** (0.46) (1.16) (0.44) (0.56) (0.84) (0.81) (0.79) Slope *** * ** ** (0.044) (0.11) (0.046) (0.096) (0.079) (0.19) (0.12) Soil Permeability ** ** (0.019) (0.095) (0.019) (0.027) (0.037) (0.050) (0.039) Frost-free Days ** * *** * ** (0.006) (0.017) (0.009) (0.016) (0.017) (0.029) (0.023) Section * ** *** Temperature (0.071) (0.18) (0.081) (0.13) (0.15) (0.23) (0.21) Orange Price ** * *** * Index (0.003) (0.009) (0.003) (0.004) (0.005) (0.005) (0.006) Grape Price *** *** *** *** *** *** Index (0.012) (0.029) (0.012) (0.014) (0.022) (0.021) (0.021) Almond Price *** *** *** *** *** *** Index (0.009) (0.023) (0.009) (0.011) (0.016) (0.016) (0.016) Annual Price Index (0.008) (0.022) (0.007) (0.010) (0.013) (0.013) (0.014) Citrus/Drip *** *** *** Lagged Ratio (0.035) (0.13) (0.038) (0.056) (0.066) (0.097) (0.16) Citrus/Gravity *** 2.05 * *** *** Lagged Ratio (0.131) (0.206) (0.155) (0.142) (0.233) (0.234) (0.448) Grape/Drip *** *** Lagged Ratio (0.047) (0.110) (0.045) (0.066) (0.077) (0.12) (0.085) Grape/Gravity ** *** *** 1.29 *** ** *** Lagged Ratio (0.056) (0.299) (0.047) (0.051) (0.080) (0.066) (0.247) Decid./Drip *** 1.45 *** Lagged Ratio (0.073) (0.296) (0.066) (0.081) (0.086) (0.077) (0.106) Decid./Gravity ** ** *** *** 1.58 *** Lagged Ratio (0.139) (0.165) (0.080) (0.088) (0.133) (0.107) (0.137) Decid./Sprinkler * *** *** 1.31 Lagged Ratio (0.132) (0.358) (0.073) (0.206) (0.100) (0.126) (0.100) Truck/Sprinkler * *** ** *** Lagged Ratio (0.038) (0.081) (0.048) (0.049) (0.066) (0.072) (0.067) Truck/Gravity ** *** Lagged Ratio (0.165) (0.876) (0.138) (0.265) (0.245) (0.172) (0.241) Field/Sprinkler *** ** ** Lagged Ratio (0.056) (0.176) (0.044) (0.055) (0.085) (0.085) (0.066) Constant *** *** * ** ** (4.22) (11.4) (4.36) (6.27) (8.00) (12.5) (12.2) Censored Obs Uncensored Obs Pseudo R Log-likelihood Numbers in parentheses are standard errors. denoted by *, **, and ***, respectively. Significance at the 90th, 95th, and 99th percentiles are 20

21 Table 4: Tobit Estimation Results - Dependent Variables are the Ratios of Acreage in Each Crop and Technology Pair to Non-agricultural Land (x 1000) Truck Truck Field Sprinkler Gravity Sprinkler Water Price *** *** *** (0.038) (0.017) (0.033) Minimum Wage *** ** *** (0.347) (0.339) (0.319) Slope *** (0.087) (0.193) (0.099) Soil Permeability *** ** (0.032) (0.085) (0.032) Frost-free Days *** (0.014) (0.994) (0.017) Section *** Temperature (0.138) (0.372) (0.158) Potato Price *** Index (0.012) (0.012) Carrot Price *** ** Index (0.019) (0.017) Onion Price *** *** Index (0.012) (0.011) Cotton Price *** *** Index (0.019) (0.017) Annual Price ** Index (0.015) Permanent Price *** ** Index (0.028) (0.015) (0.026) Citrus/Drip *** *** Lagged Ratio (0.081) (0.095) Citrus/Gravity ** Lagged Ratio (0.199) (0.286) Grape/Drip Lagged Ratio (0.071) (0.073) Grape/Gravity *** *** Lagged Ratio (0.091) (0.086) Decid./Drip * Lagged Ratio (0.095) (0.090) Decid./Sprinkler Lagged Ratio (0.124) (0.108) Decid./Gravity * Lagged Ratio (0.129) (0.123) Truck/Sprinkler *** *** *** Lagged Ratio (0.050) (0.070) (0.048) Truck/Gravity *** *** 1.20 *** Lagged Ratio (0.126) (0.145) (0.125) Field/Sprinkler *** *** *** Lagged Ratio (0.054) (0.067) (0.053) Constant *** Censored Obs Uncensored Obs Pseudo R Log-likelihood Numbers in parentheses are standard errors. Significance at the 90th, 95th, and 99th percentiles are denoted by *, **, and ***, respectively. 21

22 Table 5: Water Demand Estimation Results (Dependent Variable is Total Water Use at Each Section) OLS IV Water Price ** *** (1.89) (2.17) Minimum Wage *** *** (46.7) (55.8) Slope 2.29 * 43.2 (14.7) (24.2) Permeability *** 22.7 *** 25.1 (5.58) (6.67) Section Temperature ** (17.12) (41.9) Annual Temperature *** ** 36.7 (14.03) (16.0) Citrus Drip *** 1.67 *** 1.35 (0.14) (0.26) Citrus Gravity *** (0.45) (9.56) Grape Drip *** 1.29 *** 0.81 (0.17) (0.24) Grape Gravity *** (0.18) (0.98) Deciduous Drip *** (0.23) (1.38) Deciduous Gravity *** 2.83 ** 2.85 (0.30) (1.11) Deciduous Sprinkler *** (0.34) (5.87) Truck Sprinkler *** 1.27 *** 0.74 (0.15) (0.39) Truck Gravity *** (0.36) (4.17) Field Sprinkler *** 1.96 *** 2.06 (0.15) (0.48) Constant (1511.2) (2892.1) Number of obs Adjusted R-sq Numbers in parentheses are standard errors, with the robust IV standard errors are calculated using bootstrapping. Significance at the 90th, 95th, and 99th percentiles are denoted by *, **, and ***, respectively. 22

23 Table 6: Estimated Direct and Indirect Water Demand Elasticities Direct Indirect Total Elasticity Elasticity Elasticity OLS Estimation ** ** (0.09) (0.09) IV *** (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. 23