Production Flexibility and the Value of Water Supply Reliability

Transcription

1 Production Flexibility and the Value of Water Supply Reliability Georgina Moreno, Daniel Osgood, David Sunding and David Zilberman July 19, 2006 This project was financed by a grant from the California Department of Water Resources and the U.S. Environmental Protection Agency. The opinions expressed in this paper do not necessarily reflect those of the funding agencies. Assistant Professor, Department of Economics, Scripps College, 1030 Columbia Ave., Claremont, California. (909) , gmoreno@scrippscollege.edu. Corresponding Author. Associate Research Scientist, The Earth Institute, Columbia University. Professor, Department of Agricultural and Resource Economics, UC Berkeley, and Member, Giannini Foundation of Agricultural Economics. Professor, Department of Agricultural and Resource Economics, UC Berkeley, and Member, Giannini Foundation of Agricultural Economics.

2 Abstract The article explores the value of water supply reliability, determined by property rights, on the incentive to invest in agricultural land improvements and other longterm production commitments. We develop a model in which stochastic water supplies are the limiting factor of production and in which farmers make long-term decisions about the share of land to devote to activities that are difficult to curtail in the shortrun. When conditions permit, farmers can also produce crops whose acreage is highly flexible. In such an environment, the effect of improving reliability on production of permanent crops is shown to be ambiguous. Using data from California agriculture, we explore the investment effect of water supply reliability. In the case considered we find that reliability has a statistically and economically significant positive effect on investment incentives. The findings have important policy implications as they suggest how to measure the value of changes in reliability. Keywords: water resources, valuation, reliability, investment 1

3 The reliability of water supply can have important impacts on production and investment decisions in agriculture. In the western U.S., available water supplies are frequently allocated through a system of appropriative water rights. Under this system, water is apportioned by queuing users according to the seniority of their property rights, which are typically correlated with the date of first use. Although this system of water rights has provided incentives for development of water supply infrastructure, it raises concerns about water-use efficiency (Burness & Quirk 1979). Senior water right holders enjoy more reliable water supplies and lower water supply uncertainty than junior right holders. Without the ability to trade, a queuing system may reduce the incentive for farmers to invest in land improvements and other measures requiring commitments that can increase water-use productivity. Our article considers a sequential model of decision making under input uncertainty. Unlike models that build on Sandmo (1970) and use expected utility to capture the impact of uncertainty, we distinguish between short-term and long-term decisions, which allows us to capture the impact of variance and other measures of input supply reliability without assuming risk aversion. Rather, it is the nature of the agricultural production decision itself that makes risk paramount here. The analysis in this article captures several features that are relevant to decisions about water use in agriculture. First, the analysis allows for the possibility that subsidized surface water can be supplemented by other water supplies. Examples are groundwater and water purchased on a water market. These supplies may be more expensive than the basic surface water entitlement, but can have a large impact on overall water use and, by extension, on the value of water supply reliability. Second, our article considers how the reliability of water supply influences farm-level production and investment decisions. In particular, we consider how changes in the reliability of surface water supplies change a farmers willingness to commit to a level of production such as entering into a long-term contract for delivery of farm output, or dedicating a certain share of land to production of permanent crops. In doing so, the farmer 2

4 can enter a new market and earn higher returns but must commit to a given level of production on the improved land for the life of the investment. This commitment fixes the farmer s water demand, thus limiting future production choices and the farmer s ability to respond to changes in water supply conditions. Although water is a variable input, lack of trading and scarcity affects the way the fixed input is utilized. At a general level, our research concerns the link between the reliability of entitlement to property and the incentives to undertake productivity-enhancing capital investments. This theme has been explored in the development economics literature since the evolution of property rights and their effects on aggregate investment are central issues in economic growth. For example, Besley (1995) examines the link between the security of land tenure and the inclination of farmers to make land-value augmenting investments such as planting trees. Taking the example of Ghana, which is in a process of transition from communal to individual land rights, he finds that property rights do indeed matter in that more secure individual land rights facilitate investment. The value of water supply reliability has been addressed in several ways in the economics literature. Several papers have measured the value of reliability in urban water systems. For example, Howe et al. (1994) use contingent valuation methods to value urban customers demand for supply reliability. They define water supply reliability as a water supply short-fall that results in temporary restrictions on lawn watering. More recently, Griffin & Mjelde (2000) use contingent valuation to value urban water supply reliability, defining reliability as a condition of excess demand given aridity level. Both studies focus on optimal management of water supply shortages from the water utilities perspective. However, Griffin & Mjelde (2000) find that the consumer s water-use activities and willingness to pay to avoid a short-fall in water supply is influenced by their accumulated durables. Michelsen & Young (1993) consider how interruptible water markets can mitigate against losses from drought at lower cost than permanent trading of water rights. The 3

5 presence of alternative sources of supply can mitigate the risk of water shortages. This theme is echoed in our article as well, since we allow for the possibility that farmers can supplement their base allocations of unreliable project water with supplemental water procured via water markets or some other mechanism. A feature of our analysis is that the marginal price of supplemental water is negatively correlated with the random supply of project water. The value of reliability has also been addressed in a somewhat different fashion in the literature on groundwater. Tsur & Graham-Tomasi (1991) demonstrate that groundwater serves two roles: (1) to increase the quantity of water supply, and (2) to mitigate against fluctuations in surface water availability. Their analysis focuses on the stabilization value of groundwater that follows from the assumed concavity of the yield response function. Under the assumption of concavity, Jensens inequality implies that the value of reliability is positive. Our article is consistent with Tsur & Graham-Tomasi (1991) in that we conclude reliability has value, but is more detailed in its representation of farm-level decisions. More recently, Marques, Lund & Howitt (2005) develop a quadratic programming model of water reliability and crop choice. Their simulations provide additional evidence that an important relationship between water reliability and agricultural investments exist. Their work further motivates the need for research that derives and explains this relationship. 1 Conceptual Model This section develops a model that captures the trade-off between flexibility and production commitments and considers how that trade-off is influenced by reliability of water supply. The primary source of water for the farmer is surface water from a public irrigation project, provided at subsidized rates, assumed to be free, but delivered in random quantities. The project allocation is given by A. 4

6 We assume that the farmer knows the distribution of project water supplies, which is based on his/her water right. Conditional on the reliability of the underlying water right, the farmer maximizes profits by allocating land between permanent production that requires a long-term commitment, and variable production that can be curtailed following annual realizations of water supply. Permanent production is any land-specific production that is costly to abandon in the short-run, yields relatively high returns or allows the farmer to enter new markets. For example the farmer may invest in land-specific capital, long-term contracts with processors, or plant permanent crops. We assume that permanent production never shuts down, but allow variable production to shut-down. 1 We denote land allocated to permanent production as L p and land allocated to variable production as L v. We assume that water is the limiting resource and land is not a constraint. 2 By allocating land to permanent production, the farmer fixes water demand to that land in the short-run. In contrast, allocating land to variable production allows the farmer to adjust water demand because he/she can abandon this activity at minimal cost. Therefore, when surface water supplies are realized, water is first allocated to permanent production and remaining supplies are allocated to variable production. In addition, the farmer may procure supplemental water supplies, S, from a more expensive alternative water source such as groundwater pumping. Supplemental water is procured at a cost of C(S) after current-year project supplies are realized and allocated to permanent production. We explore land and water allocation outcomes by considering the farmer s problem in two stages: In the short run, the farmer maximizes current-year profits by allocating land to variable production, given prior land allocation to permanent production. In the long-run, the farmer adjusts land allocated to permanent production and maximize profits by allocating land between both types of activities. In the following subsections, we formalize the short-run and long-run land allocation decisions. 5

7 1.1 Short-Run Behavior In the short-run the farmer chooses L v given the permanent production, L p, to maximize short-run profits, Π SR. The water requirement per acre is given by a v for land in variable production and a p for land in permanent production. In order to make the influence of water supply reliability explicit in the farmer s land allocation problem, we express the farmer s short-run optimization problem in terms of the water requirement and land allocation, that is, max L v Π SR = π p ( L p )a p Lp + π v (L v )a v L v C(S) (1) subject to S = a p Lp + a v L v A, (2) where L v = π p = π v = L p = a p = a v = A = land allocated to variable production net returns per unit of applied water for land allocated to permanent production net returns per unit of applied water for land allocated to variable production land allocated to permanent production, fixed in the short-run crop water requirement for land allocated to permanent production crop water requirement for land allocated to variable production allocation of project water Applied water is given by a p Lp for land allocated to permanent production and a v L v for variable production. The function C(S) is the cost of procuring supplemental water, which we assume is twice differentiable and increasing in L v. Returns to each type of land allocation, π p and π v are functions of land allocation and are net of all costs excluding supplemental water costs. This specification reflects both market demand considerations as well as variations in land quality that affect yields and costs per 6

8 acre. Equation (2) says that any water requirement above A must be purchased from alternative sources. The farmer s short-run optimization problem solves π v(l v )L v + π v (L v ) = C (a p Lp + a v L v A) (3) which implicitly defines the land allocation to variable production as a function of land allocated to permanent production and the annual water supply from the public water project. The farmer maximizes short-run profits by equating the marginal cost of water and marginal revenue from irrigating land in variable production, given the precommitment of land to permanent production, L p. Figure 1 illustrates the equilibrium condition in equation (3), in terms of water requirements. The horizontal axis in the figure is supplemental water and the vertical axis is cost per unit of supplemental water. In the short-run, land and water allocated to pre-committed production is fixed. S 0 is the point A a p Lp = 0, that is, project water allocation just meets the pre-committed water demand. The points to the left of S 0 measure supplemental water procured to meet pre-committed water demand; points to the right of S 0 is supplemental water procured to meet flexible water demand. Thus, marginal revenue from irrigating land in flexible production is only defined for S in the right quadrant of the figure and is given by MRv a v. As specified in the short-run problem, the marginal cost curves are determined by A a p Lv. Suppose that project water supply is A 1, that the water requirement for land in pre-committed production is a v Lv, and that this water requirement exceeds water allocation, that is, a v Lv > A 1. Therefore, the farmer s supplemental water requirement for pre-committed production is A 1 a v Lv, which we denote as S 1 in the figure. Given the water allocation A 1 and the land allocation L v, the marginal cost of supplemental water is given by MC 1. In this case, the first unit of supplemental water for L v can be purchased at a cost of M 1, and the short-run equilibrium occurs where MC 1 = 7

9 MR v /a v. Now suppose that project water supply is A 1 as before, but land allocated to pre-committed production is L f where, L v > L v. The supplemental water required to irrigate L v is denoted as S 2 and the relevant marginal cost is MC 2 in the figure. In this case, the first unit of supplemental water available to the farmer for land in flexible production is M 2, which is above marginal revenue. Thus, given the land allocation L v, it is not worthwhile for the farmer to allocate land to flexible production. Figure 1 also makes apparent the lower threshold level of project water allocation, Â, that induces the farmer to allocate land to variable production. In the figure,  is determined by the marginal cost curve MC 3 and the quantity of supplemental water S 3. Given a water allocation above Â, land is allocated to variable production, and below this level, the water requirements for permanent production pushes the marginal cost of water to levels where it is uneconomic to allocate land to variable production. We also define an upper threshold for allocating land to variable production. Let L S v be the acreage allocated to variable production above which marginal revenue of this activity is negative. If marginal revenue from allocating land to variable production declines, in general, there exists a saturation land allocation to variable production. Formally, L S v = {π v(l v )L v + π v (L v ) = 0}. (4) Now define  as the project water allocation above which the farmer will not increase L v. Above the point of saturation, that is, above  = {A a p L p + a v L S v = A}, (5) it is uneconomic for the farmer to purchase supplemental water. This point is given by S 4 in figure 1. 8

10 1.2 Long-Run Behavior: Allocating Land and Water to Permanent Production We now turn to the problem of long-run land allocation when project water supplies are uncertain. The water supply delivered by the irrigation project has a continuous density g(a; θ) with support [A, A]. The parameter θ indexes the reliability of the water right; an increase in reliability is represented as in increase in θ. We assume that G(A; θ) = 0 and G(A; θ) = 1, where the function G is the cumulative distribution function of project water allocation. From the production thresholds defined above, we find three possible short-run production scenarios that the farmer must consider when choosing land to allocate to permanent production: (Case 1) When A < A < Â, the farmer has insufficient project water to meet water demand for land in permanent production and variable production is uneconomic. In this case, the farmer allocates land only to permanent production and procures supplemental water to meet permanent demand. (Case 2) When  < A < Â, it is economic to procure water for variable production, thus the farmer allocates land to both activities up to the variable production saturation allocation, L S v. (Case 3) Finally, when  < A < A the farmer has sufficient project water to meet permanent demand and procures supplemental for the saturation level of land allocated to variable production, L S v. 3 Based on the possible production scenarios, the farmer chooses the long-run land allocated to permanent production to maximize expected profits, max L p Π LR = + Â(Lp) A Â(Lp) Â(L p) A + Â(L p) [π p (L p )a p L p C(a p L p A)] g(a; θ)da [π p (L p )a p L p + π v (L v)a v L v C(a p L p + a v L v)] g(a; θ)da [ πp (L p )a p L p + π v (L S v )a v L S v C(a p L p + a v L S v ) ] g(a; θ)da, (6) 9

11 where L v = L(L p, A) is the short-run optimal level of land allocated to variable production, derived above. The first integral in (6) is expected profit when Case 1 occurs, the second integral is expected profit when Case 2 occurs, and the last integral is expected profit when Case 3 occurs. The first-order condition for this problem is MR p EMC = 0, (7) where MR p = π pl p + π p and EMC = Â(Lp) A C (a p L p A) g(a; θ)da + Â(Lp) Â(L p) C (a p L p + a v L v A) g(a; θ)da, (8) the expected marginal cost of water. The equilibrium condition in equation (7) shows that land will be allocated to permanent production until the net returns equal the expected marginal cost of supplemental water. Because water will be used for land in permanent production first and given that the marginal cost of water is increasing, the expected supplemental water costs for land in permanent production must be higher with both permanent and variable production. The second-order condition for this problem is MR p EMC L p < 0. (9) We assume this expression is negative to ensure an interior solution. 1.3 Marginal Impact of Changes in Reliability It is now possible to explore how changes in reliability of water supply affects land allocation. First consider how land allocated to permanent production (L p ) changes in 10

12 response to perturbations of the distribution of project water supplies. We represent a change in the distribution of project supplies as a change in the policy parameter, θ. Totally differentiating (7), the marginal impact of altering θ is dl p dθ = EMC/ θ SOC (10) where SOC is the second-order condition in equation (9), making the denominator in (10) negative. The investment effect of reliability thus depends on the curvature of the cost function for supplemental water supply. This point is explained by the following argument. The expression for a change in expected marginal cost with respect to a change in reliability is EMC θ = Â(Lp) A C g(a; θ) (a p L p A) da θ + A Â(L p) C (a p L p + a v L v A) g(a; θ) da. (11) θ Integrating equation (11) by parts, we can rewrite the derivative as follows EMC θ = Â(Lp) A C G(A; θ) (a p L p A) da θ A ( ) L v a v Â(L p) A 1 C G(A; θ) (a p L p + a v L v A) da. (12) θ Defining reliability synonymously with first-order stochastic dominance, it must be the case that G(A; θ)/ θ 0 (Burness & Quirk 1979). 4 Using this result, we can sign the investment effect of reliability, conditional on the cost of supplemental water. The comparative statics results are summarized in table 1. When the cost function is concave, land allocated to permanent production decreases with increasing reliability. A concave cost function implies that the cost of supplemental water is increasing at a decreasing rate. When the cost function is con- 11

13 vex, an increase in reliability may increase or decrease land allocated to permanent production, depending on the impact of water allocation on land in variable production. A convex cost function implies that each additional unit of supplemental water is becoming increasingly expensive, for example if the supplemental supplies are pumped from a groundwater source. If a change in the annual water allocation, A, has a less than proportional impact on land allocated to variable production, then land allocated to permanent production increases with reliability. If the impact of a change in A on L v is more than proportional then the impact of reliability on land allocated to permanent production is ambiguous. This possibility is overlooked in the work of Marques et al. (2005) which is primarily empirical and utilizes a quadratic programming framework with strong assumptions about convexity. It is also of interest to assess how the land allocated to variable production is influenced by the distribution of project water supplies. Taking a long-run perspective, the expected land allocated to variable production is E[L v (L p, A)] = A Â(L p) L v (L p, A)g(A; θ)da. (13) Integrating (13) by parts, it follows that A Â(L p) L v (L p, A)g(A; θ)da = L v (L p, A)G(A; θ) A Â A Â(L p) L v (L p, A) G(A; θ)da. (14) A Using the short-run optimality condition, we obtain L v (L p, A) A = C (a p L p + a v L v A) π L v + 2π L v C (a p L p + a v L v A). (15) 12

14 Thus, A E[L v (L p, A)] = L v (L p, A) + Â(L p) [ C (a p L p + a v L v A) SOC SR ] G(A; θ)da, (16) where SOC SR is the second order condition for the short-run problem, which is negative for a maximum. Differentiating (16) with respect to the policy parameter, θ, we have E[L v (L p, A)] θ = A Â(L p) C G(A; θ) da. (17) SOC SR θ The sign of this derivative depends on the curvature of the cost function. The first term is positive if C < 0 and negative if C > 0, and the second term is negative by first-order stochastic dominance. Thus increasing reliability increases land allocated to variable production when marginal cost of supplemental water is increasing. However, increasing reliability decreases land allocated to variable production when the marginal cost of supplemental water is decreasing. An important implication of the analysis is presented graphically as in figure 2. Consider the case where the water supply distribution takes two values and an increase in reliability, represented as a mean-preserving spread. 5 In the baseline case, the expected profit is given by E[Π 0 (µ, σ)]. An increase in reliability alters the ex-post value of water, which is reflected in a shift in the profit function from Π 0 to Π 1, and the increase in expected profit is E[Π 1 (µ, σ )] E[Π 0 (µ, σ)]. Ignoring the impact of changes in the supply distribution on investment in land improvements, would underestimate the expected profit gain from the increase in reliability as E[Π 0 (µ, σ )] E[Π 0 (µ, σ)]. 2 Empirical Analysis As shown in the previous section and summarized in table 1, the investment effect of reliability on land allocated to permanent production is ambiguous and depends on the characteristics of the cost of supplemental water. However, we determine the 13

15 effect of reliability in a particular case using data from a group of water districts in California s San Joaquin Valley, the San Luis & Delta Mendota Water Authority (Authority). The Authority is an ideal location to test the extent of the investment effect of reliability as it is comprised of two types of water districts that differ according to seniority of entitlement to Central Valley Project water. We test for differences in land allocation in districts with senior rights and districts with junior rights, controlling for agronomic conditions that determine land for the cost of supplemental water. The Authority consists of 32 water agencies and is primarily responsible for operation and maintenance of some of the Central Valley Project facilities in the western San Joaquin Valley, San Benito County and Santa Clara County in California. 2.1 Data We obtained field-level data on land allocation from the California Department of Water Resources (DWR). The data were collected county-by-county from 1994 through 1996 and includes information for approximately one million acres in five counties (Merced, Kern, Madera, Kings, and Fresno) within the Authority. This data set includes approximately 25,000 observations. Since each field represents a single crop, the variable for land allocated to permanent production is binary, indicating whether a field is in permanent production, that is, in production that requires several years to establish, requires land-specific capital, or is typically grown under long term contract. In our data set, permanent production includes permanent crops such as citrus, deciduous fruits and nuts, nursery crops, and vineyards and crops typically produced under contract such as tomatoes and lettuce. Variable production includes cotton, wheat, grain, hay, irrigated pasture, and rice. The water rights, and thus water supply distribution, for each district in the Authority service area are determined by the type of water delivery contract each district has with the US Bureau of Reclamation the primary water supply source in the Authority 14

16 service area. There are two types of contractors in the area: exchange contractors and delivery contractors. The exchange contractors have senior water rights and therefore highly reliable water; delivery contractors have junior rights and less reliable surface water supply. The water right allocated to each field in our data set is determined by the type of district in which the field is located. The variable reliable takes the value of 1 if the field is in an exchange contractor district and 0 otherwise. 6 The difference in the supply distributions is evident in historical deliveries to individual water districts. In the period 1981 to 1997, the standard deviation of annual surface water delivered per-acre was 0.36 (mean of 3.11 acre-feet per acre) for the exchange contractors, and 0.60 (mean of 1.82 acre-feet per acre) for the delivery contractors. Approximately 28% of the acres in the Authority s service area are in exchange contracting districts. The agronomic factors that have been shown to be important determinants of land allocation include soil drainage, slope, and climate (Moreno & Sunding 2005). We construct a measure of soil drainage using data from the Natural Resources Conservation Service s State Soil Geographic Database (STATSGO). For each sample point in the STATSGO data, the soil drainage is classified from fastest drainage (type A) through slowest drainage (type D). For the fields in the study area, Type A was not represented, 17% of the land was classified as type B, 55% as type C, and 28% as type D. Following Ragan (1991), we convert these categories into drainage rates. 7 In the San Joaquin Valley, slope increases with elevation. Elevation also influences weather conditions, especially the number of fog-frost-free days. Cold air tends to concentrate on the valley floor, while the locations higher up the western slope are warmer and drier. Elevation is therefore a natural proxy to control for climate, slope, and other factors that systematically change for farms higher in the valley. Elevation data were obtained from the United States Geological Survey (USGS). Because groundwater is the primary supply of non-project water in the study region and pumping expenses drive groundwater costs, we use depth to groundwater to 15

17 approximate the marginal price of supplemental water. The California Department of Water Resources provided well-depth data for test wells in the study area. We identified each well s spatial location using the township/range information provided with the well data. In order to assign well-depth to the land allocation data, we calculated the average depth of all of the test wells in each square on the township/range grid. Using the township range information, we mapped the well-depth measures. We computed the variable Depth by kriging over the township/range grid to interpolate depth measures for areas with no test wells. We took advantage the spatial referencing in our three data sources (land allocation, agronomic factors, depth to groundwater) to integrate these data sets into a single GIS database. We used the field as the unit of observation and layered the DWR land allocation data over the other data to spatially link it to the soil drainage, elevation, and groundwater depth that each field enclosed. Although the soil drainage survey areas were much larger than the fields, some fields did bridge drainage areas with two separate soil drainage rates. In this case, we split the field and weighted each sub-field by its share of the area of the entire field. The water district rights type was linked to the field that fell within the district, based on USBR water district boundaries. After dropping fields with incomplete data and those without water delivery information, our study data set had 18,964 observations Estimation Results Table 2 presents the logit estimates of investment choice. 9 All the coefficients in our model are significant. To facilitate interpretation of the coefficients, we also compute the marginal effect and elasticities of each variable on land allocated to a permanent crop. 10 The pseudo-r 2 for this model is and within sample prediction of investment choice was correct for 94 percent of the observations. All of the marginal effects and elasticities are also significant and the signs of the 16

18 control variables are consistent with expectations. Fast draining soils are more beneficial to permanent crops such as trees and vines, therefore, it is not surprising that the sign on drainage is positive. The effect of elevation is similar. A positive sign on elevation indicates that increasing elevation increases the probability of investment in permanent crops production. To the extent that the tree crops in our data are more sensitive to frost, this result is not surprising. The negative sign on the groundwater depth is consistent with the theoretical model since groundwater depth influences the cost of supplemental water that might be consumed in place of unanticipated shocks in surface water deliveries. Our empirical model estimates that water supply reliability has a positive effect on the probability of investing in a permanent crop. Growers in the districts with more reliable water are more likely to invest in permanent crop production, consistent with the theory proposed in this article. The magnitude of the elasticity is also important: growers in districts with senior rights are 40 percent more likely to invest in permanent crop production. This finding indicates that accounting for the land allocation impacts of water supply reliability will have significant implications for welfare analysis of water supply development. 2.3 Water Project Valuation The conceptual and empirical analyses have demonstrated that changing water supply reliability has an important impact on land allocation. In this subsection, we compute a change in profits for a stylized farm in response to increased water supply reliability. We demonstrate how the investment effect of reliability can impact the valuation of new water supply projects. In particular, we show that ignoring the investment effect of reliability, as many analysts do, can significantly underestimate the valuation of a project that alters reliability of water supplies. Consider two stylized crops, a permanent crop such as a tree crop to represent 17

19 permanent production and an annual crop such as a grain to represent variable production. Assuming average conditions in the delivery contracting areas of the western San Joaquin Valley the annual crop generates net returns of $300 per acre, excluding supplemental water costs, and requires 2.5 acre feet of water per acre. The permanent crop generates net returns of $1,850 per acre, again excluding supplemental water costs, and requires 3.75 acre-feet of irrigation water per acre. For the baseline scenario, assume 11 percent of land is allocated to permanent crop production and the remainder to annual crop production. Furthermore, assume that the price of supplemental water is $100 per acre-foot. For consistency with the conceptual model developed in this article, we assume that the farmer allocates project water to permanent production first. Therefore, the farmer procures 2.5 acre-feet per acre on 89 percent of the land and 1.93 acre-feet per acre on 11 percent of the land. Table 3 summarizes the baseline assumptions. Under the baseline assumptions, profits are $ per acre. Suppose that a proposed water project will increases water supply reliability for delivery contractors such that they will face the water supply distribution faced by exchange contractors. After the project is completed, delivery contractors will face an average delivery of 3.75 acre-feet per acre with a standard deviation of If we take the standard approach in valuing this project and assume that reliability of water supply does not affect the land use decision, land allocation will remain the same as before the project. Using this approach, we compute per acre profits as $240.96, given as Model 1 in table 4. An increase in deliveries obviously increases profits. However, our model and empirical estimation suggest that, when faced with a more reliable water supply, the delivery contractors will have an incentive to increase land allocated to the permanent production. Based on the empirical estimates of the marginal effect of reliability (table 2), we predict land allocated to the permanent crop to increase from 11 percent to 15 percent. Allowing for this adjustment in land use we compute profits for our stylized farm as $ per acre (Model 2 in table 4), a 37 percent increase in profits from 18

20 reliability. Allowing changes in land allocation is important in quantifying benefits. Model 1 profits, which do not allow for land use changes are 22 percent lower than the predictions of Model 2, which adjusts for land use change. Relative to the baseline scenario, the value of an increase in reliability is significantly larger for Model 2 than Model 1: $83 per acre in Model 2 compared to $14.19 using Model 1. Thus, the impact of the water supply distribution on land allocation can have a large effect on the valuation of new water supply projects. Although the results presented in table 4 are based on assumptions about a highly stylized farm, they illustrate the bias in valuing reliability when the valuation ignores the land-use response to input uncertainty. Furthermore, we obtain a consistent measure of the value of reliability from a data-driven computation which does not depend on the characteristics of a particular farm. As a robustness check, we use the estimated logit coefficients to compute a change in the value of reliability as the predicted change in the latent variable (Train 2003). 11 This yields an improvement in profits of 43 percent, 12 which is consistent with the more conservative 37 percent improvement predicted by the styled example Discussion This article addresses the impact of a change in the distribution of project water supply on land allocation when the water is allocated in a queuing system. The conceptual model allows for the short-run land-use decisions to depend on long-run commitments that limit the farmer s ability to respond to changing water supply conditions. In doing so, our model captures the economics of land allocation when a stochastic water supply is the limiting factors of production. It also helps explain the commonly observed phenomena of farmers producing relatively low-value crops where production of highvalue crops appears to be otherwise profitable. Using crop production data from California s Central Valley, we test the model. 19

21 Our data set includes an indicator for the type of water right, allowing us to measure reliability consistently with water rights in our study area. The data support the hypothesis that the producer s place in the water supply queue has a significant impact on the farmer s decision to invest in land improvements. The data show that a farmer with a more senior position in the queue is 40 percent more likely to invest in land improvements than a farmer further down in the queue. Given the significant impact of a change in the water supply distribution on economic behavior, it should be factored into cost-benefit analysis of investment in water infrastructure. Ignoring the effects of water supply reliability on land allocation can underestimate the value of secure water rights and lead to inaccurate project evaluation. The framework developed here has implications for a number of important policy problems. For example, by accounting for the investment effect of changes in water supply reliability, the approach presented in this article will produce more realistic evaluations of proposed infrastructure projects and will result in more accurate costbenefit assessment of potential projects. Our framework for understanding the effect of reliability on investment incentives is also important in assessing the potential impacts of reduced reliability due to global climate change (Schlenker, Hanemann & Fisher 2005). 20

22 Notes 1 The results go through if we relax the no shut-down assumption if we have a loss function or disinvestment in permanent water and land use to permanent production. 2 In the western U.S., water resources are frequently the limiting resource (Burhnam 2002). Future research will explore a model with land and water resource constraints. 3 An additional possibility is that the farmer allocates land to permanent production only but does not procure supplemental, however, this scenario occurs when the farmer s project allocation is greater than the water required to for permanent production. This is inconsistent with profit maximizing behavior: As long as the marginal revenue from land in variable production is positive, the profit-maximizing farmer would use the remaining project water for this activity, hence producing both types of goods. Furthermore, the farmer would purchase supplemental water for land in variable production until its marginal revenue equals marginal cost of supplemental water. 4 An extension to this model is to consider alternative definitions of reliability, which would be incorporated in the model by adjusting the assumption that G(A; θ)/ θ 0. 5 This is consistent with the first-order stochastic dominance assumption made earlier. 6 USBR provided water district location and contract type in an ArcInfo data file. 7 The resulting rates of drainage for types A, B, C, and D 3.9, 3.1, 2.4, and 2.1 respectively. Note that regression results are robust to alternate drainage 21

23 quantifications. Parameters recovered for other variables are virtually unchanged when the drainage is simply represented with 3, 2, 1, 0 for A, B, C, and D. 8 The study data set over-samples exchange contractors. 9 Statistical analysis was performed using Limdep 8.0. A battery of alternative diagnostic regressions were estimated, including robust error and probit specifications. Parameters were significant and virtually unchanged across specifications, so the logit results are presented for the sake of simplicity. 10 Marginal effects and elasticities are calculated at the means of the variables. The marginal effects of the discrete reliability variable were calculated as the difference in the probability of permanent crop production with the dummy variable set to one and In the binomial logistic choice regression, the optimizing agent is assumed to be selecting the option that yields the highest profit, where profit is approximated by β x + ɛ. Although profit, the latent variable, is not directly observed, it is possible to reconstruct it using the recovered parameters as ˆβ x. Since this is merely a rough robustness check, we ignore any potential complications due to uncertainty and calculate the value of reliability as the difference between ˆβ x when reliability=1 and ˆβ x when reliability =0. 12 It is possible to to provide a dollar value for the reliability change by assuming a groundwater pumping cost and using the parameter for depth to groundwater. However, to reduce our dependence on assumed quantities, we express the results in terms of percentage change. 13 Stylized farm assumptions were determined before data-based values were calculated. 22

24 References Besley, T. (1995), Property rights and investment incentives: Theory and evidence from Ghana, The Journal of Political Economy 103(5), Burhnam, T. (2002), Dirt expensive, California Farmer pp Burness, H. S. & Quirk, J. P. (1979), Appropriative water rights and the efficient allocation of resources, American Economic Review 69(1), Griffin, R. C. & Mjelde, J. W. (2000), Valuing water supply reliability, American Journal of Agricultural Economics 82, Howe, C. W., Smith, M. G., Bennett, L., Brendecke, C. M., Flack, J. E., Hamm, R. M., Mann, R., Rozaklis, L. & Wunderlich, K. (1994), The value of water supply reliability in urban water systems, Journal of Environmental Economics and Management 26(1), Marques, G. F., Lund, J. R. & Howitt, R. E. (2005), Modeling irrigated agricultureal production and water use decisions under water supply uncertainty, Water Resources Research 41(8), Michelsen, A. M. & Young, R. A. (1993), Optioning agricultural water rights for urban water supplies during drought, American Journal of Agricultural Economics 75(4), Moreno, G. & Sunding, D. (2005), Simultaneous estimation of technology choice and land allocation with implications for the design of conservation policy, American Journal of Agricultural Economics 87(4), Ragan, R. (1991), Overview of NRCS (SCS) TR-20, Technical report, Maryland Department of Civil and Environmental Engineering (HydroGIS). http : // m anual/old/tr20overview.pdf. Sandmo, A. (1970), The effect of uncertainty on saving decisions, The Review of Economic Studies 37(3),

25 Schlenker, W., Hanemann, W. M. & Fisher, A. C. (2005), Will U.S. agriculture really benefit from global warming? Accounting for irrigation in the hedonic approach, American Economic Review 95(1). Train, K. (2003), Discrete Choice Methods with Simulation, Cambridge University Press. Tsur, Y. & Graham-Tomasi, T. (1991), The buffer value of groundwater with stochastic surface water supplies, Journal of Environmental Economics and Management 21(3),

26 Figure 1: Short-run profit-maximizing land allocation to variable production $/unit of S MC2 MC3 MC1 MC4 M2 M1 S2 S3 S1 S0 S4 Supplemental Water MRv/av

27 Figure 2: Profits with a Mean-Preserving Spread of the Water Rights Distribution Π Π1 E[Π1(µ,σ')] Π0 E[Π0(µ,σ')] E[Π0(µ,σ)] E[A] A

28 Table 1: Comparative statics results for land allocated to permanent production Curvature of C(S) Effect of Project Effect of Reliability on Allocation on Expected Variable Marginal Cost of Permanent Production Supplemental Water Production ( Lv ) ( EMC ) ( ) Lp A θ θ C > 0, C < 0 + C > 0, C > 0 + if a v L v A < 1 + /+ if a v L v A > 1 /+

29 Table 2: Estimation Results for Land Allocated to Permanent Crop Marginal Coefficient Effect Elasticity Mean Drainage (0.0738) (0.0031) Elevation (0.0015) (0.0001) Depth to Groundwater (0.0006) (0.0000) Reliability (0.0893) (0.0044) Constant (0.2396) (0.0106) Standard errors in parentheses. All coefficients significant at least at the 1% level. Number of observations = 18,964 and McFadden R 2 = Marginal effect and elasticity computed as a discrete change from 0 to 1.

30 Table 3: Baseline Scenario Assumptions Annual Permanent Crop Crop Total a (Acre-feet/Acre) Crop Water Requirement Project Allocation Supplemental Water Required ($/Acre) Net Returns 300 1, Cost of Supplemental Water b Baseline Profits a Weighted average over annual and permanent crop production, assuming 11% in the permanent crop. and 89% in annual. b Assumes water is procured at $100 per acre-foot.

31 Table 4: Comparison of Welfare Changes for Stylized Farm Model 1 Model 2 No Investment Effect Investment Effect ($/Acre) Net Returns a Cost of Supplemental Water b Total Profits Increase in Profits c a Excludes cost of supplemental water. b After change, supplemental water requirements are 0.64 acre-feet/acre for permanent crop production and 2.5 acre-feet/acre for the annual crop. c Relative to baseline scenario.