Water Use and Agricultural Production

Water Use and Agricultural Production A County Level Analysis of the Continental United States Prepared for EPA Contract Number EP-W-10-002 The Value of Water to the U.S. Economy By: Andrew L. Zaeske, PhD (andrew.zaeske@slu.se) Centre for Environmental and Resource Economics

1. Introduction Agricultural water use is a primary driver of overall patterns of water use in the United States, accounting for 34% of all offstream use and roughly 80% of consumptive use. 1 Use is highly geographically concentrated as well; on average, California alone accounted for 20% and the western states at least 60% of agricultural withdrawals between 1985 and 2005. To fully understand water s use as a productive input in the United States, it is essential to closely examine its use in agriculture. To assess water s use and value in agricultural production, this paper adopts the two error stochastic frontier analysis model of Battese and Coelli (1995) to estimate a translog production frontier for agriculture at the county level. In addition to a standard random production error, this framework includes a non-negative technical inefficiency effect, which takes heterogeneity in producer characteristics into account and estimates production inefficiency simultaneously with the estimation of the production frontier. This provides an estimate of each production unit's distance from the frontier, an improvement over the standard assumption that all deviations from the frontier are due to inefficiency. Our production function uses four inputs: cropland; labor; expenditures on intermediate inputs; and water withdrawals. Factors such as precipitation, potential evapotranspiration, acreage used for specific crops and other farm and climatic factors are accounted for directly in the inefficiency effect regression with dummies for ecological regions, or ecoregions, which are included to capture the effect of common factors that could not be directly measured. 1 Kenny, et al. (2000). 1

Specification tests validate a number of features of the chosen model, including the choice of the two error structure over a basic ordinary least squares (OLS) model and separate functional specifications for the three different county types: rural; micropolitan; and metropolitan. They also provide strong evidence for the chosen inefficiency effect structure compared to various alternatives. The adjusted R² for the OLS regression indicates that over 87% of the variance in the agricultural output data is explained by the translog model, while the inefficiency effects explain 92.3% of the variance in the stochastic frontier model. Water is found to act as a complement in production with employment and cropland, and as a substitute with intermediate inputs. Deriving the marginal products of each factor for each county type, we find that on the margin water detracts from agricultural output in micropolitan and metropolitan counties, while still having a positive effect in rural counties. Changing these into marginal effects and running bootstrap simulations to determine 95% confidence intervals, we find that an additional gallon of water adds between 6 and 7 cents to production in rural counties, while it reduces production in micropolitan and metropolitan counties by 17.5 to 21.4 and 8 to 9 cents, respectively. The inefficiency effect regression finds a number of expected results, with government subsidies and maximum temperature all increasing inefficiency. Dummies for the water rights regimes find significant efficiency differences between them, but again the magnitude of such effects is relatively small. Potential evapotranspiration, a measure of the natural environment s water demand, increases inefficiency in rural counties, but has the opposite effect in the other county types. It seems likely this may be a spillover effect, due to a combination of farm size, crop choice and efficiency of water usage across the different county types. 2

Most crops themselves have negative effects on inefficiency, and therefore positive effects on output, but the magnitude of the coefficients is small relative to all but the largest acreages of any given crop. Paradoxically, water intensive crops are found to be the most efficient, with the highest yield counties having the most acreage of nearly every crop. However, dividing marginal products by crops grown reveals that soybean growing counties have the lowest marginal effect of water, and thus are using water least efficiently. Additionally, these water intensive crops are among the most exported by the United States, representing a significant amount of virtual water exports. The remainder of this paper proceeds as follows. Section 2 outlines the modeling framework and setup. Section 3 describes the sources and some characteristics of the data used for the analysis. Section 4 discusses the output of the stochastic frontier model and provides some policy suggestions, and section 5 concludes. 2. Model Stochastic frontier analysis, independently developed by Aigner, et al. (1977) and Meeusen and van den Broeck (1977), is a procedure for production function estimation which determines the production frontier, or maximum level of output for each combination of inputs. One particular characteristic of stochastic frontier models is the use of two types of uncorrelated errors rather than just a single random error as in many regression models. One is standard normal random error, while the other is a non-negative technical inefficiency effect, which can be viewed as a negative productivity shock. Crucially for this analysis, the technical inefficiency effects are allowed to depend on characteristics of the 3

producers, allowing for a more in depth analysis of production behavior and the effects of policy and environmental factors. This parametric method is preferable to non-parametric methods such as data envelopment analysis, because it allows for the use of standard hypothesis testing procedures and because it does not restrict producer observations to lie within the frontier estimated. The latter property is particularly desirable because it allows for the presence of measurement errors or other forms of statistical noise in the model, while with nonparametric approaches all deviations from the frontier are assumed to be due to inefficiency. 2 This paper adopts the particular stochastic frontier model of Battese and Coelli (1995), which jointly estimates the production frontier and the technical inefficiency. This model has the following form for panel data, y it = x it β + ν it u it, (1) where the random errors, ν it, are assumed to be independent and both normally and identically distributed with variance σ v, while the inefficiency effects, u it, are assumed to be independently distributed as positive truncations of a normal distribution with mean z it α and standard deviation σ u. In order to determine the effects of additional characteristics on technical inefficiency, it might seem natural to compute a stochastic frontier assuming that the u it s are independent and identically distributed (iid) across producers, then run a second stage regression of any observables of interest on the resulting inefficiency values. Such a two-stage procedure is widely used in such analyses; however, this procedure directly violates the assumption that the 2 Charnes, et al. (1978). 4

inefficiency effects are identically distributed unless all of the αs are simultaneously equal to zero. 3 To avoid this inconsistency, we simultaneously estimate the production function and the mean of the inefficiency effects (z it α). To simplify our understanding of this procedure, it may be more intuitive to view the inefficiency effects as, u it = z it α + ω it, (2) where ω it is a positive truncation of a standard normal with standard deviation σ u such that ω it > z it α. This is mathematically equivalent to the distributional assumption for u it made in equation (1). It is worth noting that by assumption the ω it s must be independently distributed but they are not necessarily identically distributed, nor do they have to be positive. To assist with the solution of the model, it is convenient to reparameterize it in terms of the total variance (σ 2 = σ ν 2 + σ u 2 ) and the share of the variance due to the idiosyncratic inefficiency effects (γ = σ u 2 /σ 2 ). If the inefficiency effects are stochastic, that is γ 0, then β, α, σ, and γ can be estimated simultaneously using the method of maximum likelihood. 4 3. Data Our empirical analysis uses a balanced panel of aggregated farm data at the county level for the continental United States. Use of aggregated data allows for analysis without the need for detailed farm data that would be difficult to find for such large area. Because of this setup, the terms producer and county (-year) will be used interchangeably throughout this discussion. 3 Coelli, et al. (2005). 4 If γ = 0 then the correct specification is an ordinary least squares regression. The full likelihood function and first order conditions are presented in Battese and Coelli (1993). 5

It is important to note that this paper is looking at overall agricultural production, which includes two categories of related economic activity, the growing of crops and the sale of livestock and animal products. This somewhat alters the interpretation of the coefficients of both the production function and inefficiency effect regressions. The main data of interest are levels of inputs used for agricultural production. The Bureau of Economic Analysis' Regional Data Series on Farm Income and Personal Expenses provides values for receipts for agricultural sales and expenditures on intermediate inputs, both total and subdivided into further categories. Adjusting these by the appropriate series tracking inventory changes gives measures of agricultural production and intermediate input use in nominal dollar terms. Finally, use of tailored price series from the United States Department of Agriculture allows us to adjust these into real values. Water use data comes from the U.S. Geological Survey's Water Use Information program, available every five years, which tracks water withdrawals by source and use. Employment data is from the Bureau of Economic Analysis and data for cropland comes from the U.S. Department of Agriculture. Data for the inefficiency effects comes from a number of sources. All climate data is from Coulson and Joyce (2010), which aggregates PRISM data on temperature and precipitation to the county level, providing values for elevation, maximum and minimum temperature, rainfall and potential evapotranspiration (PET). The BEA data sets also include government receipts, net farm income, net corporate farm income, and population, while the USGS data provides amounts of water used for specific types of irrigation. Unfortunately the U.S. Census of Agriculture, which is also collected every five years, is collected on a different schedule from other available data (1982, 1987, etc. versus 1985, 1990, 6

etc.). This restricts the series that can be plausibly used for the present analysis, as using interpolated data would raise many interpretation issues. However, there are some series we can still utilize, as long as caution is taken to view these variables as a sort of capital stock rather than literal values for the year in question. For example, the farm size distribution for 1982 can be used as a proxy for the farm size distribution in 1985 and thus could be expected to have some explanatory value for 1985 farm production. Variables from the Census of Agriculture that are used in this way include the distribution of farms by size, which is divided into seven categories by acreage, cropland harvested and cropland irrigated. One final issue that arises with the input data is that some counties have zeroobservations for inputs. Rather than exclude these observations from our sample, we adopt a strategy outlined by Battese (2008). For each variable X i that has some observations that take a value of zero, we define D Xi = 1 if X i = 0 and D Xi = 0 if X i > 0. So D X is an indicator variable that tracks when input X is zero for any observation i. We then define X i = max (X i, D Xi ), and use this variable in our estimation in lieu of the original variable X i, including D Xi as a regressor as well. This procedure should avoid bias in the production function parameters that may be caused by dropping the zero-observation producers from the sample. 4. Results Maximum likelihood estimates are obtained using the frontier package for the R statistical computing environment. 5 This package uses the Fortran code of FRONTIER 4.1 as a base, and computes the maximum likelihood estimates using the OLS estimates as an initial 5 Coelli and Henningsen (2011). 7

guess. Model specification tests and final results presented are all output from routines contained in this package. Table 1: Specification Tests Null Hypothesis Log-likelihood χ² Statistic Critical Value Decision Baseline Model -8417.3 (1) γ=0-15714.5 14594 Mixed χ²₁₀₉=85.44 Reject H₀ (2) Uniform Production Function -8552.7 270.81 χ²₂₈=41.34 Reject H₀ (3) Uniform Inefficiency Effects -8558.3 281.95 χ²₇₀=90.53 Reject H₀ (4) Drop 1982 Variables -8540.9 247.33 χ²₂₄=36.42 Reject H₀ (5) No Water Rights Effects -8660.1 485.7 χ²₁₂=22.36 Reject H₀ (6) No Irrigation Effects -8444.7 54.76 χ²₉=16.92 Reject H₀ (7) No Crop Effects -8599.7 364.86 χ²₂₇=40.11 Reject H₀ Mixed χ² critical value computed according to formula from Kodde and Palm (1986). Table 1 presents the results of a series of model specification tests, run using likelihood ratio (LR) statistics. Each presents the result of a standard LR test, except for specification (1) when the generalized likelihood ratio statistic asymptotically has a mixed chi-square distribution. Specification (1) tests the null hypothesis that the share of variance explained by the inefficiency effects, γ, is equal to zero. This hypothesis, which implies that our baseline specification is not an improvement over OLS, is rejected. This provides strong evidence that the inefficiency effects model as specified is the preferred specification. 6 Tests (2) and (3) check the null hypotheses that there is a uniform production function and that there are uniform inefficiency effects, versus the individual alternatives that there are separate production functions and inefficiency effects, a set each for counties classified as rural, micropolitan and metropolitan by the U.S. Census Bureau in 2005. 7 A micropolitan county is 6 Omitted from the table is a test which rejected the null hypothesis that the inefficiency effects are distributed half-normally. This confirms the author s belief that the effects are not random but rather depend on producer characteristics, further validating the chosen model specification. 7 Methodology outlined at http://www.census.gov/population/metro/. It would be ideal to track any county changes over time, but the Census Bureau only began classifying micropolitan areas in 2003. 8

defined to be connected to a core urban area with between 10,000 and 50,000 residents, while a metropolitan county is connected to a core urban area with a population of 50,000 or greater. About 22% of the sample is micropolitan and 34% metropolitan, with the remaining counties classified as rural. Both of these null hypotheses are clearly rejected, indicating that the specification with production function and inefficiency effect parameter dummies for microand metropolitan counties is preferred to one with a single set of parameter estimates for all counties. Finally, specifications (4)-(7) test further restrictions of the inefficiency effects included in the regression. Specification (4) tests whether the Census of Agriculture variables, which we might be suspicious of because they are from earlier years than the rest of the data, are jointly significant. This null hypothesis is rejected, providing some statistical evidence for the inclusion of these values in spite of the possible data mismatch. Specification (5) tests the water rights regime dummies, which will be discussed in more detail in the regression results sections, while specification (6) looks at the inclusion of quantities of irrigation by type. Finally, specification (7) rejects the null hypothesis that the crop acreage variables are jointly equal to zero. The inclusion of each of these sets of inefficiency effects is found to be statistically significant, confirming that our baseline model is the preferred specification. Table 2 presents the primary results of the stochastic frontier analysis, the translog parameter values from the baseline specification, which includes a constant, dummies for 84 ecoregions, micro- and metropolitan counties and D Xi dummies for intermediates, cropland and 9

water. 8 The first column presents the ``plain coefficient values, which represent the omitted category, rural. The next two columns present the marginal coefficients for the value of interest interacted with either the micro- or metropolitan dummy. So for example, the true micropolitan direct effect of water will be 0.1629 (0.1202+0.0427) and the metropolitan direct effect of water is 0.0090 (0.1202-0.1112). The ``pooled column presents the results from specification (2) in Table 1, the case where there is a single production function for all counties, and is only presented for the sake of comparison. The ecoregion dummies are chosen to capture any portion of a county being included in a Level III ecoregion as defined by CEC (1997). This should provide better results than assuming that counties that are near each other or grouped by political boundaries necessarily have similar growing conditions, particularly in terms of unmeasured factors such as soil quality and solar intensity. The values in Table 2 inform us about the relative factor intensities of agriculture in the different types of counties. Ignoring cross-factor effects, water and employment have positive effects on output in all county types, but these effects have a concave shape, increasing at a decreasing rate for each additional unit of input. The cross terms for water indicate that it is complementary in production with employment and cropland, and is a substitute with intermediate inputs regardless of county type. Both intermediates and cropland have 8 After removing all counties with no agricultural production, there were no counties with zero employment left. 10

Table 2: Stochastic Frontier Primary Regression Coefficient Rural Micro (Marginal) Metro (Marginal) Pooled log(employment) 0.7110** -0.0911-0.2520* 0.5604** log(intermediates) 0.3527** -0.1492** -0.0498 0.2808** log(cropland) 0.1040** 0.1411* -0.0325 0.0815** log(water) 0.1202** 0.0427-0.1112** 0.1016** Employment² -0.0278-0.0279 0.0970** 0.0132 EI 0.0130** 0.0302** 0.0283** 0.0211** EC -0.0474** -0.0088-0.0547** -0.0630** EW 0.0096** 0.0118* 0.0062 0.0132** Intermediates² 0.0806** -0.0081-0.0325** 0.0725** IC -0.0192** 0.007 0.0211** -0.0085** IW -0.0315** -0.0051* -0.0137** -0.0354** Cropland² 0.0265** -0.0089** -0.0005 0.0246** CW 0.0183** -0.0064* 0.0247** 0.0227** Water² -0.0053** 0.0003-0.0050** -0.0062** σ² 0.9855** 0.9915** γ 0.9230** 0.9213** Omitted from table: Time and county type effects, D indicators and ecoregion dummies Significance Levels: *= 5%, **=1% economies of scale, with their marginal effects increasing as factor use increases. However, the cross terms suggest that cropland and intermediates are substitutes for non-metropolitan counties, which will mute these effects. Finally, the value of γ informs us that over 92% of the variance σ² is explained by inefficiency effects, while the value of σ² has a magnitude of about half of a standard deviation of the empirical distribution of the logarithm of the value of agricultural production. This is equivalent to making the average county about 2.7 times as productive (or unproductive) if certain inherent characteristics and production qualities could be altered. The primary regression coefficients only give a rough idea about average factor intensities, so to get a clearer understanding of the empirical relationships between factor use and output, we calculate the marginal product for each factor and county type, which are given 11

Table 3: Mean Marginal Product (thousand $ per unit change) Pooled Rural Micropolitan Metropolitan Employment 14.17 45.32 2.53-18.87 Intermediates (th $) -0.85-1.15 0.0006-1.01 Cropland (acres) 0.0102 0.0155 0.0178-0.0016 Water (Mgals/yr) -42.46 65.09-194.10-84.84 in Table 3. The marginal product is the shadow price of a factor, with a negative marginal product necessarily implying that a factor is over-used. Labor and cropland have negative marginal products in metropolitan counties, despite on average having positive effects for the overall sample. The overall marginal product of intermediates is negative, with an extra $1,000 of intermediates reducing output by an average of $850. When pooled, it appears that water has on average a negative contribution, but further separation into the three county categories reveals that this is driven by heavy over use in micro- and metropolitan counties. In a rural county, each additional gallon of water adds 6.5 cents to output, while it takes away 8.5 and 19.4 cents respectively in metropolitan and micropolitan counties. Dividing these general results by year reveals that the average marginal product was positive in 1985 and 1990, and negative for the remaining three years. Table 4 provides a closer look at the various marginal effects of water, running a standard bootstrap analysis with 10,000 iterations for each subsample. 9 Here we find that the signs of the marginal effects are robust for each county type, with each marginal effect s confidence interval being either wholly positive or negative. The other interesting finding here is that variability of marginal products is relatively uniform except for micropolitan counties, which exhibit nearly four times as much variability as any other group in the sample. Translating this into dollar terms, an additional gallon of water adds between 6 and 7 cents to 9 Efron and Tibshirani (1986). 12

rural agriculture, but leads to an output reduction of between 17.5 and 21.4 cents in a micropolitan county and a reduction of 8 to 9 cents in a metropolitan county. The combination of these results suggests micropolitan counties especially are prime for efficiency gains. Table 4: Bootstrap Results for Marginal Product of Water Pooled Rural Micropolitan Metropolitan Mean -42.49 65.05-194.10-84.84 Bias 0.0347 0.0493-0.0033 0.0038 σ 2.73 2.52 9.95 2.69 95% CI Lower Bound -47.97 60.24-214.31-90.22 95% CI Upper Bound -37.29 70.01-175.17-79.73 To begin our policy discussion, it will be useful to take a basic look at the results of the inefficiency effect regression, which are presented in Table 5. For these coefficients a positive sign indicates that a variable increases inefficiency while a negative sign indicates that it decreases inefficiency, with each of these effects being reversed if we consider the effect on agricultural output. The coefficient on year is significant and negative, so inefficiency is generally decreasing over time. Other exogenous factors in this regression include the climatic factors and dummies for water rights regimes. Rainfall s effect is small and not statistically significant, but the other climate factor effects are for each county type. The maximum temperature is positively associated with inefficiency, while the minimum temperature and elevation level are negatively associated with it. Each of these effects gets more extreme as the county type becomes more urban, except for elevation, where the reverse occurs. Interestingly, potential evapotranspiration (PET), a measure of the environment s moisture demand, increases inefficiency in rural counties, but lowers it in both micro- and metropolitan ones. Two likely candidates for this effect are the farm size distribution and crop 13

Table 5: Stochastic Frontier Inefficiency Effects Regression Rural Micro (Marginal) Metro (Marginal) Year -0.0955** Micropolitan 0.3938 Metropolitan 0.3549 Hybrid Rights 193.00** 0.1902 0.34558 Prior Appropriation Rights 193.23** 0.077 0.2189 Riparian Rights 1 193.58** -0.0238-0.17202 Riparian Rights 2 193.46** 0.1504-0.037607 log(government Subsidies) 1.6232e-05** -4.3990e-06-1.1391e-05** Net Farm Income 2.8077e-06 8.2380e-07-8.5260e-06** Net Corporate Farm Income -0.0001** 1.8875e-05 0.0001** Rain 0.0004-0.0003-0.0002 Temporary (Maximum) 0.3701** 0.4724** 0.5754** Temporary (Minimum) -0.4499** -0.4069** -0.4771** PET 0.0529** -0.0635* -0.0867** Elevation -0.1546** 0.1353** 0.1522** Population 3.2570e-07** 1.2065e-07-9.9504e-08 Farms: <10 acres 0.0022** 0.0036** -0.0024** Farms: 10-49 acres 0.0010* -0.0029** -0.0006 Farms: 50-180 acres -0.0012** 0.0006 0.0006 Farms: 180-499 acres 0.0003-0.0012-0.0004 Farms: 500-999 acres 0.0019-0.0034 0.001 Farms: 1000-1999 acres -0.0027* 0.0032-0.0169** Farms: 2000+ acres -0.0044** 0.0004 0.0043* Acres Harvested -6.3456e-06** -2.3368e-06-1.3401e-07 Acres Irrigated 3.5324e-06* -3.1005e-06 3.1255e-06 Operator Owned Farms (#) 0.0011** 7.2746e-04 3.3091e-05 Spray Irrigation (Acres) -0.0012* 0.0020** -0.0009 Flood Irrigation (Acres) -0.0006 0.0022-0.0013 Microirrigation (Acres) -0.0012-0.0001 0.0032** Wheat (Acres) -2.3756E-06** 9.2613e-07-9.6032e-07 Soybeans (Acres) -5.6529e-06** 3.9432e-06 7.1608e-06** Corn (Acres) -3.2623e-06* 2.2210e-06-2.8814e-06 Rice (Acres) -3.6772e-05** -2.0416e-06-3.7487e-05 Tobacco (Acres) -4.7826e-05-1.7000e-05 6.2643e-05 Hay (Acres) 2.1429e-06-4.2314e-07 9.3784e-06** Cotton (Acres) -8.1076e-06** -1.4025e-07-8.8563e-06* Sorghum (Acres) -1.1795e-06 1.8059e-06 1.3793e-05* Barley (Acres) 2.0406e-05** 5.7626e-06 2.1169e-05** 14

choices. The farm size distribution shifts towards smaller farms as the county type moves from rural to micropolitan to urban, so if smaller farms are more efficient in their use of water and thus are less susceptible to this natural constraint, we would expect this type of effect. Additionally, in the data metropolitan farms are on average the most profitable and rural farms the least profitable, which also seems to support this efficiency based argument. The other likely story is the choice of crops. With the limited crop data available, it is not surprising that field crops become more prominent as county populations decrease. More acres of crops such as wheat, sorghum, barley, hay and cotton are planted in rural counties, with crops such as soybeans, corn and rice planted more in micropolitan counties. This follows crop rankings in terms of water intensity from Pimentel, et al. (1997) and Postel (1998), with the most water intensive crops grown most frequently in micropolitan counties and other water intensive crops in rural counties. This does not necessarily fit in with the efficiency due to farm size explanation, unless the micropolitan farms are growing the most water intensive crops efficiently while rural farms are growing moderately water intensive crops inefficiently. Crop yields and the crop coefficients themselves conform to this story. Every crop except hay is grown predominantly in the type of county that has the highest average yield, and a ranking of crops by their marginal effects is nearly the inverse of the aforementioned ranking by water intensity of production. However, a look at the marginal products of subsamples of counties (e.g. micropolitan counties that grow soybeans) seems to refute this argument, with counties that grow water intensive crops having the lowest marginal products of water. 15

Another important set of variables included in the inefficiency effect regression are dummies to measure the effects of legal restrictions on water use, which match the four statelevel water rights regimes in the United States: strict riparian; modified riparian; prior appropriation; and three hybrid states which mix the riparian and prior appropriation traditions. In basic terms riparian systems attach water rights to any property that abuts a body of water and are generally proportional to frontage to the source, while prior appropriation states follow a doctrine generally referred to as first in time, first in right, where the age of claims takes precedence over physical proximity between land and the water source. Importantly, under the prior appropriations doctrine, water rights are severable from land, while under riparian systems they are not. 10 Combining the effects of the micro- and metropolitan dummies with the water rights regime dummies yields the values of the constant for the inefficiency effect regression for each type of county. Rural counties have higher inefficiency, while metropolitan counties are the least inefficient, a result which holds across water rights regimes. Counties with hybrid water rights regimes display the least inefficiency, followed by prior appropriation counties and finally the two-types of riparian counties. This is somewhat surprising, as the use it or lose it nature of most prior appropriation states seems likely to lead to inefficient uses. However, the development of water markets and additional water trading in the Western U.S., where most of these states are located, could explain this difference, especially when recalling the nonseverability of water rights from land ownership that is present in riparian systems. 11 10 Hodgson (2006) provides a general overview of different systems of water rights. 11 Libecap, et al. (2010). 16

Government subsidies have a significant positive effect on inefficiency, with on average $2,400 in subsidies causing a $1,000 loss in agricultural production. This effect is quite diverse across county types, with the amount to cause a thousand dollar loss ranging from an average of $6,200 in metropolitan counties to $1,600 in rural counties. Thus it seems that government farm subsidies are facilitating inefficient production, particularly in metropolitan counties. It is difficult to say anything more specific, because this subsidy data is a generic total of all programs. Adding data on expenditures on specific subsidy programs (crop insurance and commodity subsidies, among others) would be more likely to yield results with clearer policy implications. Next we look at how crops affect inefficiency. Our two general crop variables, acres harvested and acres irrigated, are each significant and have opposite effects, with acres harvested decreasing inefficiency and acres irrigated increasing it. The effect of acres harvested is larger, so increasing each value by one will have a net positive effect on output. When it comes to the crop specific effects, only barley has a significantly positive effect on inefficiency, while five crops - wheat, soybeans, corn, rice and cotton - have negative effects. It should be noted that all of the crop effects are small in magnitude, with the number of acres needed to cause a $1000 change in output generally being larger than the mean of existing acreages, even when only looking at counties that currently grow the crop. As was mentioned earlier in this section, when ranked from lowest to highest by their marginal effect on inefficiency, the crop list closely follows the rankings of crops by water intensity of production in Pimentel, et al. (1997) and Postel (1998), with rice measured as being the least inefficient, followed by cotton, soybeans, corn and wheat. There are few significant differences across county types, with the 17

exceptions all relating to metropolitan counties. Soybeans increase inefficiency in metropolitan counties in spite of their ranking as one of the most efficient crops to grow in rural counties, and hay and barley are each vastly less efficient to grow in a metropolitan setting relative to the other two county types. One major factor that relates to these crop choices is agricultural trade. Soybeans, corn, wheat and cotton are all in the top five agricultural exports for each year since 1989 according to the U.S. Department of Agriculture s Economic Research Service. 12 Exporting these highwater intensity products in large quantities results in a large amount of virtual water trade, i.e., effective trade in water through its use in producing goods. Soybeans in particular seem to be a primary culprit in terms of the inefficiency of water use in agriculture, calling for further exploration of the apparent linkage between high water use and yields across counties. Finally, we present a cautionary note of sorts. The above analysis is fairly cavalier in calling for reallocation of resources, water resources especially. However, there are numerous issues when it comes to implementation, especially the general lack of fully developed markets for trade. Water is often allocated, especially at the state level, 13 and even when purchased, prices are often not closely linked to supply factors such as climate. Key to this semi-market treatment of water, especially in the west, are irrigation districts, political entities that possess primary property rights over water and then distribute it to farmers who own land within the 12 Foreign Agricultral Trade of the United States (FATUS), available: http://www.ers.usda.gov/dataproducts/foreign-agricultural-trade-of-the-united-states-(fatus).aspx [2012, August 31]. 13 e.g. the Colorado River Compact (1922), Arizona v California (latest incarnation, 2000), The Treaty for the Utilization of Waters of the Colorado and Tijuana Rivers and of the Rio Grande (latest official reinterpretation, 1974) for the Colorado River and Wisconsin v. Illinois (latest incarnation, 1980), the Great Lakes Charter (1985) and Great Lakes-St. Lawrence River Basin Water Resources Compact (Signed 2005, Enacted 2009) for the Great Lakes Basin. 18

district. 14 As an example, the Imperial Irrigation District (IID) in Southern California has the rights to nearly two-thirds of California s 13.5 million gallon allocation from the Colorado River. This water is essentially sold at a fixed price, with the current price of $20 per acre-foot (about $61 per million gallons) set in 2009, unless demand is ``likely to exceed supply. 15 Additionally, Libecap et al. (2010) highlight the gains from trade possible from agriculture-to-urban water sales, with a particular sale in 2001 leading to developers buying water from farmers in the IID for roughly 1500 times as much as the farmers themselves had paid the irrigation district. The combination of high value urban uses and low value agricultural uses means that it would likely be more profitable for some farmers to sell their water allocation rather than use it to grow crops. However, there are significant transaction costs present due to existing institutions, especially when state borders are crossed. Increased simplification and uniformity of the treatment of water as an economic good can only facilitate further trades, which this current analysis suggests should be able to increase agricultural efficiency in many counties. 5. Conclusion Use of water in agriculture has a high importance when it comes to overall water use patterns in the United States. Using the two error stochastic frontier analysis model of Battese and Coelli (1995), this paper estimates a production function for agriculture at the county level using four inputs: cropland; labor; expenditures on intermediate inputs; and water withdrawals. The effects of additional factors such as climate variables, acreage for specific 14 Libecap, et al. (2010). 15 Imperial Irrigation District (2009) [1] outlines the Equitable Distribution Plan and Imperial Irrigation District (2009) [2] gives the price schedule. 19

crops and farm characteristics can be determined with the inefficiency effect regression, which is solved simultaneously with the production function estimation. Specification tests strongly validate the choice of model over simpler alternative specifications. Water s marginal contribution to agricultural value is on average negative, with this result being driven by use in micropolitan and metropolitan counties. Water is complementary in production with labor and land, and substitutable with intermediates. An additional gallon of water reduces micropolitan output by an average of 19.4 cents and reduces metropolitan output by an average of 8.5 cents, while it would increase rural output by 6.5 cents. Bootstrap simulations validate these values, implying it is likely that the true marginal products deviate at most 10% from these values. The inefficiency effects regression finds that most climate factors have expected effects, with elevation and minimum temperate being negatively related to inefficiency and maximum temperature positively related. Having smaller farms is found to increase efficiency, as would reductions in government subsidies. In particular, subsidies in metropolitan counties have large negative effects on output, with a $1,000 increase in those subsidies corresponding to a $6,200 drop in output. Potential evapotranspiration increases inefficiency in rural counties, but decreases in it others. This seems to be due to a spillover effect, due to some combination of farm size, crop choice and water use efficiency effects which are heterogeneous across county types. Most crops themselves have negative direct effects on inefficiency, although the magnitudes of these coefficients are all small relative to acreages seen in the data. Water intensive crops are found to be the most efficient, with the highest yield counties having the most acreage of nearly every crop. However, dividing marginal products by crops 20

grown reveals that soybean growing counties have the lowest marginal effect of water, and thus are using water least efficiently. Additionally, these water intensive crops are among the most exported by the United States, representing a significant amount of virtual water exports. This contrast between water use, efficiency and yields provides an interesting result that merits further analysis. Finally, the author cautions that while large scale shifts in water should indeed cause efficiency gains, there are often numerous institutional and legal barriers to such resource shifts. Water trades are often lucrative, and in light of the results of this production analysis, it seems likely that in some cases selling water will provide more value to a rights holder than attempting to use it in production. This highlights the positive economic effects that could come from increased simplification and uniformity of the treatment of water as an economic good. 21

References Aigner, D., Lovell, C., and Schmidt, P. (1977). Formulation and estimation of stochastic frontier production function models. Journal of Econometrics, 6(1):21-37. Battese, George E. (1997). A Note On The Estimation Of Cobb-Douglas Production Functions When Some Explanatory Variables Have Zero Values. Journal of Agricultural Economics, 48(1-3): 250-252. Battese, G. and Coelli, T. (1993). A model for technical inefficiency effects in a stochastic frontier production function for panel data. Working Papers in Econometrics and Applied Statistics 69, Department of Econometrics, University of New England, Armidale. Battese, G. and Coelli, T. (1995). A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Economics, 20: 325-332. Charnes, A., Cooper, W. W., and Rhodes, E. (1978). "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November. Coelli, T. and Henningsen, A. (2011). frontier: Stochastic Frontier Analysis. R package version 0.997-0. Coelli, T. J., Rao, D. P., O'Donnell, C. J., and Battese, G. E. (2005). An Introduction to Efficiency and Productivity Analysis. Springer Science + Business Media, New York, 2nd edition. Commission for Environmental Cooperation (CEC). (1997). Ecological regions of North America - Toward a Common Perspective. CEC, Quebec, Canada. Coulson, David P., and Joyce, Linda A. (2010). Historical Climate data (1940-2006) for the conterminous United States at the county spatial scale based on PRISM climatology. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station. Available: http://www.fs.fed.us/rm/data_archive/dataaccess/us_histclimatescenarios_county_prism.sht ml [2012, August 31]. Efron, B. and Tibshirani, R. (1986). Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statistical Science 1.1: 54-75. Hodgson, S. (2006). Modern water rights: Theory and practice. Food and Agriculture Organization of the United Nations, Rome, Italy. 22

Imperial Irrigation District. (2009) Regulations for Equitable Distribution Plan. Available: http://www.iid.com/modules/showdocument.aspx?documentid=4596 [2012, August 31]. Imperial Irrigation District. (2009). Water Rates. Available: http://www.iid.com/modules/showdocument.aspx?documentid=4325 [2012, August 31]. Kenny, J.F., Barber, N.L., Hutson, S.S., Linsey, K.S., Lovelace, J.K., and Maupin, M.A. (2009). Estimated use of water in the United States in 2005: U.S. Geological Survey Circular 1344, 52 p. Kodde, D. A., and Palm, F. C. (1986). Wald criteria for jointly testing equality and inequality restrictions. Econometrica, 54(5):pp. 1243-1248. Libecap, Gary D., Grafton, R. Quentin, Landry, Clay, O Brien, R.J., and Edwards, E.C., Water Scarcity and Water Markets: A Comparison of Institutions and Practices in the Murray-Darling Basin of Australia and the Western US (December 17, 2010). ICER Working Paper No. 28/2010. Meeusen, W., and van den Broeck, J. (1977). Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error. International Economic Review, 18(2):435-44. National Agricultural Statistical Service (NASS), Agricultural Statistics Board. 1985, 1990, 1995, 2000 and 2005. Agricultural Prices (April issue). U.S. Department of Agriculture. Pimentel, D., Houser, J., Preiss, E., White, O., Fang, H., Mesnick, L., Barsky, T., Tariche, S., Schreck, J., and Alpert, S. (1997). Water Resources: Agriculture, the Environment, and Society. BioScience, 47(2):pp. 97-106. Postel, S. L. (1998). Water for food production: Will there be enough in 2025? BioScience, 48(8):629-637. 23