Agricultural Economic Water Productivity Differences across Counties in the Colorado River Basin

Abstract

This study estimates the relative contribution of different factors to the wide variation in agricultural economic water productivity (EWP) across Colorado River Basin counties. It updates EWP measures for Basin counties using more detailed, localized data for the Colorado River mainstem. Using the Schwarz Bayesian Information Criterion for variable selection, regression analysis and productivity accounting methods identified factors contributing to EWP differences. The EWP was USD 1033 (USD 2023)/acre foot (af) for Lower Basin Counties on the U.S.–Mexico Border, USD 729 (USD 2023)/af for other Lower Basin Counties, and USD 168 (USD 2023)/af for Upper Basin Counties. Adoption rates for improved irrigation technologies showed little inter-county variation and so did not have a statistically significant impact on EWP. Counties with the lowest EWP consumed 25% of the Basin’s agricultural water (>2.3 million af) to generate 3% of the Basin’s crop revenue. Low populations/remoteness and more irrigated acreage per farm were negatively associated with EWP. Warmer winter temperatures and greater July humidity were positively associated with EWP. When controlling for other factors, being on the Border increased a county’s EWP by USD 570 (2023 USD)/af. Border Counties have greater access to labor from Mexico, enabling greater production of high-value, labor-intensive specialty crops.

1. Introduction

The Colorado River Basin faces a long-term imbalance between water demand and water supplies. The U.S. Bureau of Reclamation (USBR) has projected that demands will exceed supplies by 3.95 km³ (3.2 million acre-feet (maf)) by 2060 [1]. The volume of water rights allocated to competing entities exceeds available supplies. Upper Basin States (Wyoming, Colorado, New Mexico, Utah and Wyoming) have been allocated 9.25 km³ (7.5 maf) as have Lower Basin States (Arizona, California and Nevada), while Mexico has been allocated 1.85 km³ (1.5 maf), for a total of 20.35 km³ (16.5 maf) [2]. However, Colorado River streamflows have averaged only 12.3 maf/year in the 21st Century [3,4]. While climate change is projected to limit supplies further [5], population growth is projected to increase water demand. The current population of the Basin is roughly 40 million. A midpoint projection for the 2060 Basin population is 62 million, with ranges between 49 and 77 million [1]. Because of population growth, municipal and industrial (M&I) water demand is projected to rise from roughly 10.6 km³ (8.6 maf) in 2015 to 12.6–18.6 km³ (10.2–15.1 maf) by 2060 [1].

Because agriculture is the largest water user in the Basin, it is the sector expected to conserve the most in the future to bring water supply and demand into balance [1]. Moreover, the costs of agricultural conservation have been estimated to be much lower than supply enhancement policies [5]. In June 2024, USBR Commissioner Camille Touton testified before Congress that cuts of 2.47 to 4.93 km³ (2 to 4 maf) annually in Colorado River use may be needed to prevent Lakes Mead and Powell (the Basin’s two largest reservoirs) from falling below critical levels for hydropower generation and downstream delivery [6]. While Basin states had contemplated and proposed water use cutbacks, the 2–4 maf reduction was far greater than anything under consideration. In October 2022, California offered a proposal to reduce its Colorado River water use by 0.49 km³ (0.4 maf) [7]. In December 2022, the Southern Nevada Water Authority submitted a proposal with reductions for the Lower Basin, which also proposed cutting Upper Basin consumption by 0.617 km³ (0.5 maf) should Lake Powell elevations fall below critical levels [8]. In May 2023, the Lower Colorado River Basin States (Arizona, California and Nevada) submitted a plan to the USBR to conserve 1.85 km³ (1.5 maf) of Colorado River water by the end of 2024 and 3.7 km³ (3 maf) cumulatively by the end of 2026 [9]. The USBR has accepted this plan as their preferred water management alternative for the Basin [10].

Cutbacks in Colorado River deliveries (both proposed and implemented) have raised concerns over their effects on the sustainability of agricultural production in the Basin [11,12,13,14,15]. Previous research developed estimates of the economic water productivity (EWP) of irrigated agriculture among counties in the Basin [5]. These EWP estimates measured the gross value of crop revenues per unit of water consumed for Basin counties. Such estimates can provide basic information about the opportunity cost, in terms of the foregone value of crop production, if water were reallocated from agriculture to conservation in reservoirs or to other uses.

This study updates county-level EWP measurements in the Colorado River Basin, using more detailed and localized data for agricultural water use by counties on the Lower Colorado River mainstem. These five counties on the mainstem account for 46% of the Basin’s agricultural water use. It uses this updated data for two purposes. The first is to assess how the opportunity costs of water reallocations from agriculture increase as volumes reallocated increase. There are large variations in EWP across Basin counties [5]. Therefore, even significant cuts could, in theory, be made with relatively little impact on Basin-wide agricultural production.

Next, the large variation in EWP across the Basin begs the question of what accounts for this variation. Regression analysis is combined with productivity accounting methods to estimate the relative contribution of different factors to cross-county differences in EWP. We consider the role of climate variables and the implications of climate change for future EWP in the region. We consider the contribution of irrigation technologies and geographical features. As Basin water supplies become dearer relative to demands, there is growing policy pressure to get more value out of irrigation water consumed. The U.S. federal government, through various programs, is currently subsidizing the adoption of improved irrigation technologies in the Basin [5,6]. Finally, our results suggest that proximity to the U.S.–Mexico Border has positive effects on water productivity, while being in low-population, remote areas has negative effects. This suggests that policies that one would not immediately associate with water productivity, such as immigration policy or rural infrastructure investment, may have profound implications for economic water productivity.

2. Materials and Methods

2.1. Water Productivity

One method of assessing the efficiency of agricultural water use is water productivity—the amount of crop output produced per unit of water consumed. For example, this might be measured as bushels of crop produced per acre foot of water applied. Water productivity is often referred to as “crop per drop” [16,17]. A drawback of this physical productivity measure is it is difficult to compare productivity across different crops. How does one compare the productivity of producing bushels of wheat for human consumption, bales of cotton to produce clothing, or tons of alfalfa to feed animals?

Another approach is to examine economic water productivity, which the UN Food and Agricultural Organization defines as the monetary value generated from each unit of water consumed [18]. Output across crops can be compared on a dollar-to-dollar basis. Economic water productivity also allows for the measurement on a whole-farm basis (where farms produce multiple crops) and on a broader regional basis, such as counties, where different regions have different crop mixes.

2.2. Updating Economic Water Productivity Estimates

Developing EWP measures for crop production in the Colorado River Basin at the aggregate county level requires combining county-level crop sales and water consumptive use. This is more difficult than one might imagine. The U.S. Department of Agriculture (USDA) reports overall crop sales at the county level only in Agricultural Census years, the three most recent being 2012, 2017, and 2022 [19,20,21]. The USDA reports state-level water application volumes (not consumptive use) for 2013 and 2018 but does not report county-level water use [22,23]. The Department of Commerce, Bureau of Economic Analysis (BEA) reports county crop receipts annually [24]. The US Geological Survey (USGS) reports estimates of irrigation water withdrawals for crops and crop consumptive use at five-year intervals. The most recent year of reported data is 2015 [25].

BEA and USGS data have been combined to estimate the EWP for Colorado River Basin counties for 2015 [5]. That study uncovered some data anomalies that caused the authors to drop six counties that accounted for 0.1% (one tenth of one percent) of irrigation water use, while still estimating EWP for 55 counties that accounted for 99.9% of Basin water consumed for crop irrigation.

For this analysis, we update estimates of [5], supplementing USGS data with data from the US Bureau of Reclamation’s (USBR) Lower Colorado Accounting System (LCRAS) [26] and data from the Arizona Department of Water Resources [27,28,29]. LCRAS estimates are made annually, and USGS estimates are made every five years. LCRAS reports disaggregated estimates for irrigation districts, cities, Indian reservations and other entities along the Colorado River mainstem. Furthermore, LCRAS estimates receive significant scrutiny from stakeholders in the region.

There are significant differences between water use estimates from USGS and LCRAS for Mohave, La Paz, and Yuma Counties in Arizona and for Riverside and Imperial Counties in California. For example, estimates of system irrigation efficiencies (consumptive use divided by withdrawals) from LCRAS were 64% for Yuma County, 54% for Mohave County and 51% for La Paz County for Colorado River surface water withdrawals (the bulk of water use in these counties). USGS estimated efficiency for all three counties was a uniform 80% applied to all three counties. Separate data from USGS [27,28,29] support an 80% efficiency assumption for groundwater use in Mohave and La Paz Counties. These efficiencies do not seem accurate, however, for surface water withdrawals along the Colorado mainstem.

While USGS reported 1.85 km³ (1.5 maf) of consumptive use for Imperial County, the LCRAS estimates for the Imperial Irrigation District (IID) were more than 3.08 km³ (2.5 maf). According to the IID website, agriculture accounts for 97% of district water use. Accounting for this would adjust agricultural consumptive use downward, but only to 3.03 km³ (2.46 maf). Indeed, IID’s own reports of its consumptive water use match figures from LCRAS [30]. Similarly, USGS consumptive use estimates for Riverside County were 0.75 km³ (0.61 maf), while LCRAS estimates for the Palo Verde Irrigation District and the Coachella Valley Water District in Riverside County combine for a consumptive use total of 0.91 km³ (0.74 maf).

Because LCRAS estimates are carried out annually instead of every five years, rely more on direct estimates based on both measured and simulated return flows and receive regular scrutiny from local water users, we have used LCRAS data to adjust earlier estimates [5,25] of consumptive use for Mohave, La Paz and Yuma Counties in Arizona and for Riverside and Imperial Counties in California. For Arizona counties, this involved relying on USGS groundwater withdrawal and groundwater use efficiency assumptions but using LCRAS surface water withdrawal and consumptive use estimates to calculate county totals. This reduced estimates of consumptive use for the three Arizona counties by more than 0.49 km³ (0.4 maf). For Californian counties, we used LCRAS consumptive use estimates for Riverside and Imperial Counties, which exceeded USGS estimates by 1.23 km³ (1 maf).

In Yuma County, entities withdrawing water, based on LCRAS data, included Gila Monster Farms, Wellton-Mohawk Irrigation and Drainage District (IDD), the University of Arizona, North Gila Valley Irrigation District, Yuma Irrigation District, Yuma Mesa IDD, Unit “B” IDD, Fort Yuma Indian Reservation, Yuma County Water Users’ Association, Cocopah Indian Reservation, and other small-scale users below Imperial Dam. Total consumptive use was estimated to be (from these sources combined) 0.82 km³ (663,381 af). USGS estimated that Yuma County had 0.148 km³ (120,282 af) of groundwater withdrawals in 2015. LCRAS reports on water pumped from shallow wells adjacent to the Colorado River (and treated as Colorado River water for accounting purposes). This total, 0.0174 km³ (14,106 af), was deducted from the USGS 120,282 af groundwater withdrawals estimate. USGS assumed an irrigation efficiency of 0.80 for all water withdrawals from Yuma County. This 80% was applied to off-river groundwater withdrawals in the county for an estimated groundwater consumptive use of 0.8 × (120,282–14,106) = 84,941 af (0.105 km³). Combined on-river and off-river consumptive use was estimated to be a total of 0.923 km³ (748,322 af) for Yuma County.

For Mohave County, USGS total county withdrawals were estimated to be 0.151 km³ (122,367 af), while LCRAS on-river withdrawals were LCRAS withdrawals of 0.122 km³ (98,714 af). The difference, 0.029 km³ (23,653 af), almost exactly matches groundwater withdrawals from Mohave County’s Hualapai Valley groundwater basin. For Mohave County, LCRAS consumptive use estimates of 0.0653 km³ (52,945 af) were combined with consumptive use estimates for the Hualapai Valley. Here, the USGS-assumed [25] 0.8 efficiency estimate was applied to the 0.029 km³ (23,653 af) for groundwater consumptive use of 0.023 km³ (18,923 af).

For La Paz County, on-river consumptive use was estimated relating to the use of the Colorado River Indian Reservation, Cibola Valley IDD, the Hopi Tribe, GSC Farm, LLC, Rayner Ranch, and some minor users between Parker and Imperial dams. This consumptive use totaled 0.39 km³ (316,842 af). USGS estimates of total county water withdrawals exceeded LCRAS estimates of on-river withdrawals by 0.84 km³ (67,959 af). This closely matches separate estimates of off-river groundwater withdrawals in the county’s Butler Valley and McMullen Valley [27,28]. The USGS estimates of 0.8 irrigation efficiency for these basins match almost identically with ADWR estimates. Applying 0.8 × 67,959 = 54,367 af (0.067 km³). Combined La Paz County consumptive use on-river and in the Butler and McMullen Valleys is estimated to be 0.46 km³ (371,209 af).

For Imperial and Riverside Counties in California, estimates of consumptive use were based on LCRAS data for 2015 [26]. For Riverside County, total estimates were calculated as the sum of consumptive use by the Palo Verde Irrigation District 0.49 km³ (399,031 af) and the Coachella Valley Water District 0.42 km³ (342,068 af), for a total of 0.91 km³ (741,099 af) consumed. For Imperial County, consumptive use estimates for the Imperial Irrigation District were added to consumptive use estimates of Yuma Project Reservation Division (Bard Units and Indian Units) 0.059 km³ (47,621 af) and other Imperial County users below Imperial Dam 0.007 km³ (5812 af). As the Imperial Irrigation District (IID) reports that 3% of its water deliveries are for non-agricultural uses, IID agricultural consumptive use was estimated to be 2,480,933 × 0.97 = 2,406,505 af (2.97 km³). This places total Imperial County agricultural consumptive use at 3.03 km³ (2,459,938 af).

Compared to earlier EWP estimates derived solely from USGS data [5], these adjustments yield higher EWP estimates for La Paz, Mohave, and Yuma Counties and lower EWP estimates for Imperial and Riverside Counties. The recalculations do not change the findings [5] that these five counties have among the highest EWP values in the Colorado Basin. Neither do they alter the findings that EWP is higher among counties on the U.S.–Mexico Border, followed by Lower Basin Counties not adjacent to the Border, with Upper Basin Counties having far lower EWP values. From these new estimates, EWP was USD 1033 (USD 2023) for Lower Basin Counties on the U.S.–Mexico Border, USD 729 (USD 2023) for Other Lower Basin Counties, and USD 168 (USD 2023) for Upper Basin Counties. All EWP are reported as USD 2023 per acre foot of water consumed. The estimated consumptive use of water for irrigated crop production for the entire Colorado Basin was nearly 11.72 km³ (9.5 maf). Making use of the more detailed LCRAS data has no effect on the Upper Basin County EWP estimates. For Other Lower Basin Counties, the updates reduce EWP for Riverside County but increase EWP for La Paz and Mohave Counties, leaving overall EWP among Other Lower Basin Counties virtually unchanged. Updated estimates for EWP for Border Counties using LCRAS data were substantially lower (about 30% lower) than earlier estimates [5]. Yet, EWP for Border Counties remains substantially higher than for the rest of the Basin. The major driver of the new, lower estimates was differences in water consumptive use in Imperial County. USGS estimates were 1.23 km³ (1 maf) lower than LCRAS estimates. The LCRAS estimates, however, closely match what Imperial County irrigators report [30], as well as use estimates from other federal decision documents [9].

2.3. Factors Contributing to Economic Water Productivity Differences across Counties

The fact the EWP for Border Counties is 42% higher than for Other Lower Basin Counties and more than six times higher than Upper Basin Counties begs the question, what accounts for the high EWP along the Border? A second question is, does this “on-the-Border” effect still hold once one controls for other factors, such as climate or differences in irrigation technologies?

There are a host of variables one could consider affecting EWP, and agricultural productivity more generally. As others have noted, EWP is a partial productivity measure (aggregate output divided by a single input, water). As such, any factor that contributes to greater output, such as greater use of complementary inputs or greater total factor productivity, will increase the denominator, output, and hence, EWP [16,31,32,33]. This analysis focuses on variables constructed as county-level aggregates to match the scale of our EWP measure. County-level climate variables were obtained from [34,35,36]. Variables capturing topographical features came from [34], while soil characteristics were obtained from [36]. USGS [25] provided data on the percentage of acres adopting drip, sprinkler, and flood irrigation. Data on the (lagged) scale of farm operations came from the 2012 USDA Census of Agriculture [19]. The development economics literature has often found an inverse relationship between farm size and different measures of productivity in developing countries [37,38]. Research in developed countries, in contrast, has found a positive relationship between farm size, productivity, and productivity growth [38,39,40,41,42]. Several studies from North America have also found a positive association between farm size and the adoption of improved irrigation technologies and methods [43,44,45,46,47].

Some researchers have examined the relationship between agricultural production and proximity and economic linkages to urban centers [48,49,50,51]. In the development economics literature, there has been more attention given to the negative effects of remoteness and isolation on agricultural productivity [52,53]. The USDA has developed rural–urban continuum codes as categorical variables to measure the degree of urbanism and rurality across U.S. counties [54]. Metropolitan counties (coded 1–3) are measured in terms of the population size of their metro area. Nonmetropolitan counties are measured (coded 4–9) by the population size of their urban areas and their adjacency to metro areas. Past research has examined relationships between these continuum code values and crop-specific production patterns [48,55], organic farming [56,57], pesticide use [58], adoption of agricultural conservation practices [59] and manufacturing productivity [60,61].

2.4. Estimation Strategy

For multiple regression analysis to examine which factors explain differences in county-level EWP, we are faced with a wide array of potential explanatory variables, but only 55 observations for the dependent variable, EWP. With so many candidate variables, there is the danger of “data dredging” [62,63]. Selecting variables from a large pool of variables from multiple county-level databases runs the risk that some variables will appear as significant and causally important just by random chance. To guard against such overfitting of the data, we employ two approaches.

First, we make use of the Bayesian Information Criterion (BIC) [64] for variable selection. This is also referred to as the Schwarz Information Criterion or the Schwarz Bayesian Criterion. Models with a sample size of N, k explanatory variables and coefficients to estimate and a maximized likelihood function of L (given k and N) are considered.

BIC = kln(N) − 2ln(L)

(1)

Models with a lower BIC are generally preferred. The choice of explanatory variables to include in the model affects L, but the first term represents a penalty on the BIC value for adding additional variables. There is a tradeoff because adding variables increases L but also increases this penalty. The penalty in BIC is greater than other selection criteria, such as the Akaike Information Criterion (AIC) [65]. As such, it guards more against overfitting. If the variables of the true model are within the database, choosing the model with the lowest BIC value maximizes the probability of choosing that true model. This probability goes to 1 as N → ∞ [66,67]. While this property has been demonstrated in Monte Carlo exercises, many researchers reject the premise of a “true model” in most empirical settings, let alone the possibility that a dataset would include all the variables of such a model [68,69].

That said, BIC still has some desirable properties (in addition to avoiding overfitting). Because it tends to select models with fewer variables, it can lead to choosing simpler models that are easier to interpret. It is straightforward to implement. In small-to-medium sample size settings, the BIC tends to outperform other selection criteria (such as the AIC) [67,70]. When there is a high degree of unobserved heterogeneity in datasets (something likely to occur in many actual empirical settings), the BIC outperforms the AIC and the corrected AIC in terms of prediction [71]. If all the variables of the true model are not in the dataset, then the model with the minimum BIC is the most parsimonious model (i.e., the one with the fewest variables) that is closest to the true model (as measured using Kullback–Leibler information) [67]. If a dataset contains a quasi-true model—one with only some (but not all) of the explanatory variables of the true model—the BIC will tend to select that quasi-true model from the dataset [69,71].

A second precaution against spurious associations is to evaluate the variables chosen by minimizing the BIC value in relationship to economic theory and previous empirical findings. Are there prior reasons or explanations why a given variable would be included in a model explaining differences in EWP? The main purpose of this study is not to test hypotheses or confirm findings. Rather, it is to develop better hypotheses about why there is so much variation in EWP across Basin counties.

2.5. Productivity Accounting

In development economics, there is a long tradition of estimating the relative contribution of different factors to agricultural productivity differences between countries or changes in productivity over time [72,73,74,75,76]. These methods have focused on aggregate agricultural output or labor productivity. However, the same methods could be applied to economic water productivity, EWP. Economic water productivity of county i is R_i/W_i, which is crop revenue, R_i, divided by irrigation water consumed, W_i. Factors affecting economic water productivity can be estimated in a regression equation

$$R_i/W_i=\widehat{\alpha }+{\sum }_{n=1}^N{\widehat{\beta }}_n{X}_{in}+{\widehat{e}}_i$$

(2)

where the $\widehat{\alpha }$ and ${\widehat{\beta }}_n$ terms are regression coefficients to be estimated, X_in are n = 1 to N explanatory variables and ${\widehat{e}}_i$ is a stochastic error term. The relative contribution of any given factor X_n to a county’s economic water productivity is $\widehat{\beta }$_nX_n and so depends on both the size of the explanatory variable and the size of the regression coefficient. Suppose (a) that there were three variables in the regression equation and (b) we wished to compare the contribution of those variables to differences in water productivity between two counties i and j, the effects of each variable on the difference in water productivity can be decomposed as follows:

$$(R_i/W_i-R_j/W_j)=({\widehat{\beta }}_1{X}_{1i}-{\widehat{\beta }}_1{X}_{1j})+({\widehat{\beta }}_2{X}_{2i}-{\widehat{\beta }}_2{X}_{2j}) +({\widehat{\beta }}_3{X}_{3i}-{\widehat{\beta }}_3{X}_{3j})+\left({\widehat{e}}_i-{\widehat{e}}_j\right)$$

(3)

where the first three terms on the right are the absolute contribution of each of the three variables to the difference in water productivity between counties i and j, while the last term is unexplained residual not explained by the variables. The first explanatory variable’s contribution as a percentage of all effects,

$$\%{∆}_1=100\times ({\widehat{\beta }}_1{X}_{1i}-{\widehat{\beta }}_1{X}_{1j})/(R_i/W_i-R_j/W_j)$$

(4)

Suppose now we wish to estimate the relative contribution of different factors to differences across two regions, not just between two counties. One region is indexed by i = 1 to I counties, while the other is indexed by j = 1 to J counties. The difference in regional water productivity is just the weighted average of each county’s productivity where the weights for each region ω_i and ω_j are each county’s share of regional water use.

$$\begin{array}{c}{\displaystyle {\displaystyle \sum }_{i=1}^I}{\omega }_i{R}_i/W_i-{\displaystyle {\displaystyle \sum }_{j=1}^J}{\omega }_j{R}_j/W_j=\\ {\displaystyle {\displaystyle \sum }_{i=1}^I}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\omega }_i{\widehat{\beta }}_n{X}_{in}-{\displaystyle {\displaystyle \sum }_{j=1}^J}{\displaystyle {\displaystyle \sum }_{n=1}^N}{\omega }_j{\widehat{\beta }}_n{X}_{jn}+{\displaystyle {\displaystyle \sum }_{i=1}^I}{\widehat{e}}_i -{\displaystyle {\displaystyle \sum }_{i=j}^J}{\widehat{e}}_j\end{array}$$

(5)

Again, regional differences in economic water productivity can be decomposed into the contribution of each explanatory variable and an unexplained residual. Likewise, the percentage contribution of an individual variable can be computed in a similar (but slightly more complicated) manner as in Equation (4).

3. Results

3.1. Distribution of EWP: Implications for Agricultural Water Reallocation

One may rank counties by EWP to develop a marginal revenue curve for irrigated crop production in the Basin (Figure 1).

Marginal revenues begin quite high, exceeding USD 1500 for 16% of the Basin’s water (about 1.5 maf). All EWP values are USD 2023 per acre foot of water consumed. Marginal revenues exceed USD 895 for 63% of the Basin (4.1 maf). At the other extreme, marginal revenues are below USD 100 for nearly 15% of the Basin (1.3 maf) and below USD 200 for 22% of the Basin (2 maf). Counties with the lowest EWP consumed 25% of the Basin’s agricultural water (>2.3 million af) to generate 3% of Basin crop revenue.

One may also use the results to estimate the average opportunity cost (in terms of foregone crop revenues) of reducing water supplies to agriculture in the Basin (Figure 2). Figure 2 assumes, for example, that water is first removed from the counties with the lowest returns first. Then, cutbacks progress to the counties with increasingly higher EWP values. Some caveats are in order here. First, because the EWP values are county averages, they obscure differences in EWP across cropping systems within counties. Counties with high average EWP will grow some crops with lower EWP, while counties with low average EWP will grow some high-EWP crops. Second, policies are unlikely to be enacted that remove water supplies entirely from a county’s agriculture. Such removals could be extremely disruptive to local rural economies. In USDA programs that encourage fallowing land for conservation purposes, there are upper limits on participating acres as a percentage of total acres in any single county [77,78]. Third, the average opportunity cost measure does not include potential impacts on livestock producers who rely on locally produced feed crops. Figure 2, however, does illustrate that inter-county variation is substantial and that large amounts of water could be reallocated from agriculture at relatively low cost, but that beyond a point, such reallocations become costly.

Figure 3 illustrates the point in finer detail. If water reductions are imposed on the counties with the lowest EWP first, then a 1 maf reduction would reduce Basin crop revenues by less than 1%; a 2 maf reduction would reduce Basin revenues by less than 3%; and a 4 maf reduction would reduce Basin revenues by less than 16% (Figure 3a). Again, working from counties with the lowest EWP to higher EWP values, a 10% reduction in agricultural water use would have average revenue losses of less than USD 50; a 20% reduction would have revenue losses of USD 75; and a 30% reduction would have average losses of USD 175 (Figure 3b).

3.2. Regression Variable Selection

Based on the criteria of selecting a model that minimizes the BIC, a model of just five variables was selected (

Table 1. Descriptive statistics for variables included in economic water productivity regression analysis.

Variable	Mean	Median	Standard Deviation	Minimum	Maximum
Economic water productivity	USD 371.06	USD 176.34	USD 420.35	USD 3.47	USD 1925.46
Border county	0.11			0	1
Minimum winter temperature (long-term average, °C)	−6.98	−8.72	6.37	−16.57	6.67
July relative humidity (long-term average	24	21	8	14	68
Small, rural county (rural–urban continuum code = 7–9)	0.55			0	1
Average irrigated acres per farm	191.5	34.2	253.8	7.5	1307.6

). One was a simple dummy variable that equaled one if the county was on the U.S.–Mexico Border and zero otherwise. Second was the long-term average of December-to-February minimum temperatures. Third was the long-term average of July relative humidity. Fourth was the average number of irrigated acres per farm with irrigation. There was wide variation in average irrigated acres in the Basin. This ranged from 7.5 acres per farm in Navajo County, Arizona, which is dominated by small-scale Tribal producers, to 1307.6 acres in Imperial County, California, which is among the top ten U.S. counties in terms of crop sales. Finally, there was a dummy variable that equaled one if the county had a rural–urban continuum code (RUCC) value of 7 through 9, and zero otherwise. Different monotonic groupings of RUCCs (1 to 9) were included in the original dataset. Combining counties coded 7–9 into a single variable had the lowest BIC among alternatives. Counties coded 7–9 either had an urban population of 5000 or less and were adjacent to a metro area or a population of 20,000 or less and not adjacent to a metro area.

3.3. Regression Results

Table 2. Regression results for factors affecting economic water productivity across Colorado River Basin counties, 2015.

Dependent variable: Economic water productivity (county crop cash receipts/unit of water consumed for irrigation)
Adjusted R Square: 0.778   BIC: 54,056     55 observations
	Coefficient	Standard Error	p-Value
Intercept	326.26	113.41	0.0059
Border county	570.47	100.97	0.0000
Minimum temperatures (Dec.–Feb. avg.)	25.54	5.80	0.0001
July humidity	13.43	3.67	0.0006
Rural/urban continuum code 7–9	−188.09	62.98	0.0044
Average irrigated acres per farm	−0.28	0.11	0.0142
Adjusted R Square: 0.777   BIC: 63,544     55 observations
	Coefficients	Standard Error	p-Value
Intercept	447.44	148.16	0.00408
Border county	582.45	102.47	0.00000
Minimum temperatures (Dec.–Feb. avg.)	24.44	6.52	0.00049
July humidity	9.16	5.55	0.10546
Rural/urban continuum code 7–9	−177.81	63.72	0.00758
Average irrigated acres per farm	−0.35	0.12	0.00684
Sprinkler adoption (% of acres)	−112.69	101.43	0.27221
Drip adoption (% of acres)	649.37	873.51	0.46093
Adjusted R Square: 0.778   BIC: 59,790     55 observations
	Coefficients	Standard Error	p-Value
Intercept	291.96	119.00	0.01784
Border County	569.42	101.06	0.00000
Minimum temperatures (Dec.–Feb. avg.)	26.72	5.94	0.00004
July humidity	12.64	3.77	0.00155
Rural/urban continuum code 7–9	−181.79	63.38	0.00611
Average irrigated acres per farm	−0.31	0.12	0.00944
Flood irrigation adoption (% of acres)	95.03	99.05	0.34214

compares three regression specifications. The first is from the model that minimizes the BIC value. The other two regressions include different measures of irrigation technology adoption. The middle regression includes two variables for improved irrigation technology adoption: the share of irrigated acres using sprinkler irrigation and the share of irrigated acres using drip irrigation. The bottom regression includes the share of irrigated acres using more traditional flood irrigation. In the second specification, higher adoption rates of improved irrigation technologies did not have a statistically significant positive impact on EWP. In the third specification, higher adoption rates for flood irrigation did not have a statistically significant negative impact on EWP. Instrumental variable estimate techniques were also applied to account for the possible endogeneity of the irrigation variables. The results were essentially the same. The irrigation variables were not significant.

The above suggests that adoption rates of more efficient irrigation technology do not explain inter-county differences in EWP. What might account for this? One possibility is that many irrigators have already adopted practices (such as laser-leveling, altering timing of plantings and crop choice) to increase the efficiency of flood irrigation [79]. Such innovations would reduce the efficiency gap between flood, sprinkler and drip systems.

Another possibility is that, in hot arid climates, sprinkler systems can have high evaporation losses, negating their advantage over flood systems [80,81]. Perhaps, a simpler explanation is the lack of variability in adoption rates at the county level. Comparing adoption rates between Border Counties, Other Lower Basin Counties and Upper Basin Counties shows that adoption rates are relatively constant across regions (Figure 4).

There is simply very little inter-county variation in the adoption rates of irrigation technologies. Thus, there is little scope for these adoption rates to explain cross-county differences in EWP. This does not mean that irrigation technology does not contribute to farm-level or intra-county variation in EWP. It is just that at our higher level of aggregation, its effects cannot be discerned.

We asked the question at the outset of whether the higher EWP of Border Counties would persist when control variables were included. The answer here is yes. From the BIC-selected model, controlling for other factors, being on the U.S.–Mexico Border increases a county’s EWP by USD 570/af. Because of our simple linear specification, regression coefficients measure USD/af changes in EWP. Each degree Celsius increase in winter minimum temperatures increases EWP by USD 25.54/af. Every percentage point increase in July relative humidity increases EWP by USD 13.43/af. Rural counties with less urban population (RUCC = 7–9) have an EWP that is USD 188.09/af lower than other counties, controlling for other factors. Every 100-acre increase in average irrigated acre per farm reduces a county’s EWP by USD 28/af.

3.4. Productivity Accounting Results

Table 3. Contribution of explanatory variables to economic water productivity (EWP) in three regions of the Colorado River Basin.

	Border Counties	Other Lower Basin Counties	Upper Basin Counties
Economic Water Productivity	USD 1033	USD 729	USD 168
Relative contribution of
Intercept	USD 326	USD 326	USD 326
Border county	USD 570	USD-	USD-
Minimum temperatures (Dec.–Feb. avg.)	USD 151	USD 84	USD (292)
July humidity	USD 268	USD 422	USD 308
Rural/urban continuum code 7–9	USD (2)	USD (18)	USD (129)
Average irrigated acres per farm	USD (286)	USD (89)	USD (73)
Unexplained residual	USD 5	USD 3	USD 26

illustrates how the explanatory variables contribute to EWP in three parts of the Basin. As shown in Equation (2), each variable’s contribution depends on both the regression coefficient and the size of the variable itself. For Border Counties, being on the Border is the dominant positive effect. One can see the positive effect of warm winters. Climate effects combined (winter temperature plus humidity) contribute USD 151 + USD 268 = USD 419. Though large, climate effects are dominated by Border effects. Larger farm size has a drag on EWP among Border Counties. For Upper Basin Counties, one can see the negative effects of below-freezing (negative °C) temperatures. Cold winters are the largest drag on Upper Basin EWP followed by having a higher share of sparsely populated, remote counties (−USD 129). Other Lower Basin Counties benefit from warmer winters, but less so than Border Counties. Climate variables combined contribute significantly to EWP in Other Lower Basin Counties.

Following Equation (5),

Table 4. Contribution of explanatory variables to differences in economic water productivity (EWP) between regions in the Colorado River Basin.

	Difference between Border and Other Lower Basin Counties		Difference between Border and Upper Basin Counties		Difference between Other Lower Basin and Upper Basin Counties
Variable	Absolute Difference	Percentage of Difference Explained by:	Absolute Difference	Percentage of Difference Explained by:	Absolute Difference	Percentage of Difference Explained by:
Economic water productivity (EWP) difference	USD 305		USD 866		USD 561
Border county	USD 570	187%	USD 570	66%
Minimum temperatures (Dec.–Feb. avg.)	USD 67	22%	USD 443	51%	USD 376	67%
July humidity	USD (154)	−51%	USD (40)	−5%	USD 114	20%
Rural/urban continuum code 7–9	USD 16	5%	USD 127	15%	USD 111	20%
Average irrigated acres per farm	USD (197)	−65%	USD (214)	−25%	USD (17)	−3%
Unexplained residual	USD 2	1%	USD (21)	−2%	USD (23)	−4%

shows the relative contribution of different variables to differences in EWP across the three regions of the Basin. Both absolute and percent contributions are reported. Percentages can be positive or negative depending on effects but sum to 100%. Being on the Border was the single largest contributor to EWP differences between the Border Counties and the other two regions. Having less humid summers and larger irrigated farms on average lowered Border County EWP relative to the other regions. Border effects were not operative for differences between the Other Lower Basin and Upper Basin Counties. Here, 87% of the difference in EWP between these two regions was explained by climate variables (winter temperature, 67% and July humidity 20%).

3.5. Warm Winters

The effects of warmer winters on crop productivity are complex. Warmer winters can be associated with greater pest and disease pressures [82,83]. Yet, warmer winters also mean more frost-free days. This allows for longer growing seasons, multi-cropping, and the production of higher-valued fruit and vegetable crops [84]. Studies in Mexico, which start with a warmer climate overall, found mixed effects of warmer winters on farm returns. Studies in cooler climates have found more positive effects of warmer winters [85,86]. One study of the Colorado River Basin found that higher minimum growing season temperatures contributed significantly to greater economic water productivity, EWP [84].

Ortiz-Bobea [87] notes, “Longer growing seasons allow farmers to grow crops that stay longer on the ground, are able to absorb more sunlight and nutrients to produce more biomass and higher yields”. Alfalfa production in the Colorado Basin demonstrates this effect. Warmer winters have been found to positively affect alfalfa yields in California [88]. Alfalfa is a perennial crop that can have multiple cuttings (harvests) in a crop year. Climate determines the number of cuttings. Eight to ten (or even) more cuttings are possible in low desert agriculture, while in cooler intermountain regions of the United States, farmers usually harvest two to four cuttings [89]. Winter-injured alfalfa plants may survive the winter but then have fewer shoots for first cutting, obtaining lower yields [90]. Median and minimum alfalfa yields in Border Counties are more than double median and minimum yields in the Upper Basin (

Table 5. Irrigated alfalfa yields across the Colorado River Basin.

	Irrigated Alfalfa Yields, 2015 (Tons/Acre)
Colorado River Basin Counties	Minimum	Median	Maximum
Border Counties	5.7	7.7	9.0
Other Lower Basin Counties	2.2	5.4	9.0
Upper Basin Counties	2.2	3.5	5.2

Source: [91].

).

A simple regression of county alfalfa yields on our minimum winter temperature variables illustrates the strong positive association between warmer winters and higher alfalfa yields (Figure 5). This single variable fits alfalfa yield with an R² of 0.8158.

The 2012 and 2017 Censuses of agriculture provide county-level data on irrigated alfalfa, although reporting is incomplete [19,20]. In the two Census years, irrigated alfalfa acres are reported for counties that account for 81–82% of total irrigated alfalfa acres. Among this subset of counties, alfalfa accounts for one-third of all irrigated acreage. If one includes all Basin counties and assumes irrigated alfalfa acres are zero in the unreported counties, one obtains a lower-bound estimate that alfalfa accounts for 26–27% of total basin irrigated acres. By either measure, alfalfa represents a significant share of Basin irrigated acreage and crop production. Thus, any factor (such as winter temperatures) that influences alfalfa yields will have a significant effect county-wide EWP measures.

3.6. July Relative Humidity

Agronomic studies may consider the effects of relative humidity (RH) or the vapor pressure deficit (VPD) [92]. The two are related. Relative humidity (RH) is the amount of water vapor in the air versus the amount it can hold. The amount of water that air can hold increases with temperature. VPD is the difference between the amount of moisture in the air and how much moisture the air could potentially hold when saturated. VPD values are independent of temperature. Holding RH constant, VPD rises with temperature. Holding temperature constant, VPD declines with RH. It is possible for temperature and RH to go up together in a way that keeps VPD constant.

In a comprehensive global review of crop water productivity for wheat, rice, cotton and maize, [93] found that increased VPD pervasively led to lower water productivity. High VPD can cause declines in stomatal conductance [94,95,96]. Beyond certain VPD thresholds, photosynthesis and growth can be reduced and there can be higher risk of carbon starvation and hydraulic failure [94,97]. High VPD can increase water loss rates from moist soils, contributing to plant water stress [98]. Greater humidity can also lessen the damaging effects of extreme heat events on crop yields [99,100,101]. A subsequent comprehensive review including leafy, fruiting, and flowering plants, as well as grains, again found pervasive positive effects of higher relative humidity on crop yields [96].

While it is possible for relative humidity above certain thresholds to have negative effects on crops, these levels tend to be relatively high, about 70% or higher [96]. In our dataset, the relative humidity levels are below this threshold and quite low in some areas. Our dataset included squared terms for continuous variables (to account for non-linear effects). The minimizing BIC procedure only included a linear positive effect of humidity, which is consistent with agronomic studies and humidity levels in the region.

3.7. Low-Population, Remote Counties (RUCC = 7–9)

Past studies have found relationships between rural and urban continuum code values, which increase from 1 to 9 as counties become more rural, and economic behavior and performance. Metropolitan and metropolitan-adjacent areas tend to plant relatively more acreage to have higher-value specialty crops than field crops [48,55]. There is also evidence of greater higher-value organic farming in more urban counties [56,57]. Greater organic production was also associated with higher cash rents [56], which have been found to be positively and significantly correlated with EWP [5]. Being adjacent to a city has been found to be associated with lower rates of crop failure [102]. Studies have found a positive association between the degree of urbanization and labor productivity in manufacturing [60,61]. Gale found evidence of ever lower labor productivity in manufacturing as RUCC values for plants increase (i.e., are in increasingly rural areas) [61].

The original dataset includes every combination of monotonic groupings of counties by RUCC (e.g., 1–2, 1–3, 2–4, 8–9, 6–9, etc.) to allow for the possibility of any range of flexible, non-linear effects. The BIC-minimizing specification suggested threshold effects, where there was no difference among counties with RUCCs of 1–6, but there was a common, negative effect for counties with RUCCs of 7–9. This begs the question of why there are apparent negative effects of low population density and remoteness on EWP. Furthermore, [53] note, “Low population density can make education investments costly, and limited infrastructure (whether roads, electricity, or internet) can enhance the friction of distance”. A future research direction could be to examine the relationship between more direct measures of infrastructure quality and EWP.

3.8. Average Irrigated Farm Size

While an inverse relationship between farm size and various productivity measures has been a “stylize fact” in developing countries, work in the United States and Australia has found evidence of agricultural productivity increasing with farm size [39,40,41]. These studies, however, have confined their analysis to relatively homogenous grain producers. In the Colorado River Basin, there is greater heterogeneity in the types of crops grown. There are clear differences in the average irrigated acres by North American Industrial Classification System (NAICS) codes. (Figure 6). NAICS codes classify farms by the type of output that accounts for a majority of their farm income.

Average farm size is greater for farms specializing in grains/oilseeds farms and other crops than for those specializing vegetables/melons, fruit/nuts and greenhouse/nursery crops in five out of seven states. Average farm size is greater for farms specializing in grain/oilseed farms and other crop farms than for those specializing in fruit/nuts and greenhouse/nursery crops in all seven states. Farms growing “other” crops specialize primarily in cotton, alfalfa, other hay or sugar beet crops. Higher-value crops tend to be more labor-intensive than field crops or irrigated pastures.

3.9. Border Effects: The Role of Labor Availability

Labor costs are relatively higher in the Border Counties and Other Lower Basin Counties compared to the Upper Basin (

Table 6. Labor costs as share of total production expenses, 2012.

Region	Labor Costs as a Share of Production Expenses	Farms Specializing in Vegetables/Melons, Fruits/Nuts, and Nursery/Greenhouse Production as a Share of All Farms
Border Counties
Yuma County	28%	51%
Remaining Border Counties	21%	17%
Other Lower (OL) Basin Counties
Riverside County	21%	60%
Remaining OL Basin Counties	17%	14%
Upper Basin Counties	15%	7%

Source: [19].

). Fruits, vegetables and horticultural commodities are highly labor-intensive, with labor costs comprising 40% of the total production costs [103]. The share of farms producing high-value specialty crops (NAICS codes 1112, 1113, 1114) is especially high in Riverside and Yuma Counties and low in Upper Basin Counties.

A significant share of U.S. farmworkers are “shuttlers”, who travel up to 75 miles from their homes (primarily in northern Mexico) to work at a single U.S. farm [104,105]. While this group accounted for 10% of all farmworkers in the United States in 2013–2014 [106], they comprised a larger share of farmworkers in U.S.–Mexico Border Counties. During the winter vegetable season in Southern California and Arizona, hundreds of busloads of farmworkers cross from Mexico into the United States daily [105]. In 2015, Arizona leafy greens production required more than 16.9 million hours of hired labor [107]. A large share of these workers commute into Yuma County from San Luis Rio Colorado in Mexico. The bulk of labor hours are required during the November-to-March harvesting season. Because shuttlers reside in Mexico, where the cost of living is lower, they accept wages that are lower than they otherwise would. In addition to a favorable climate, relatively abundant low-cost labor makes the production of high-value, labor-intensive crops in Border Counties and adjacent counties in the Lower Basin possible.

4. Conclusions

4.1. Implications of Climate Change

Global warming implies higher winter temperatures in the Colorado River Basin. Our regression model implies that this would extend the growing season and increase EWP in some of the cooler, higher-latitude counties of the Basin. Yet, earlier debates over the potential impacts of climate change are pertinent here. Previous researchers have noted that climate alone does not determine productivity. In particular, they have noted that high-productivity agriculture in the U.S. combines a warm climate with irrigation infrastructure [108,109]. Warming alone without a complementary input, water, may limit the positive implications of warmer temperatures. A similar limitation may be present in the Colorado River Basin in the form of labor availability. Future climate may make higher-value, labor intensive specialty crops more agronomically viable in cooler counties. Yet, these counties are farther from the Border and may face labor availability constraints.

Our model results suggest that EWP increases with July relative humidity. Climate change is projected to lead to lower relative humidity on average [101,110]. Events that combine extreme heat and humidity are projected to increase in some regions [111,112]. High humidity could mitigate the negative effects of heat waves [101]. However, in the U.S. Southwest heat extremes have become drier [113], while weather station data suggest that actual declines in relative humidity have been greater than projected by climate models [114]. There remains great uncertainty about future relative humidity and dry extremes in the Southwest because climate models have large variations in projected soil moisture and rainfall [113]. Recent trends, however, suggest lower relative humidity in the region, with negative implications for future EWP.

4.2. Study Limitations and Implications for Future Research

Measures of economic water productivity (EWP) provide an incomplete picture of water resource management [16,17,31,32,33]. EWP is a partial productivity measure, the monetary return per unit of water consumed. As such, it depends on the use of complementary inputs as well as productivity-enhancing public and private investments. Policy recommendations that ignore such complementary linkages may not have their desired outcomes. Because EWP is a “per-unit” measure, it does not measure the status of water resources in absolute terms, which is critical for understanding whether water use practices are sustainable. When EWP measures rely on prices for private goods in the numerator, they exclude non-market environmental impacts that are not priced in private markets.

Despite these limitations, EWP does provide useful information. EWP measures are especially useful as starting points in discussions of reallocations of water from agriculture to conservation or other uses. They provide first-order estimates of the opportunity costs (foregone agricultural production in monetary terms) of reductions in agricultural water use. Our EWP estimates suggest that large reductions in agricultural water use could be made in the Colorado River Basin that would sacrifice little of the region’s agricultural production. This would be true even under some of the very large 2–4 maf cuts that have been proposed. The results suggest that the burden of such cost-minimizing cuts would fall heavily on the Upper Basin, where EWP is much lower than in the Lower Basin. Currently, Lower Basin agriculture has absorbed most of the recent Colorado River supply reductions.

Our EWP measures are county-level averages that obscure from intra-county differences in EWP. Thus far, Lower Basin irrigators have adjusted to cutbacks in Colorado River deliveries by reducing the production of lower-valued crops. Our results, however, suggest that beyond some point, Lower Basin cuts will begin to impact higher-value specialty crop production, where revenue losses would be among the highest in the entire Colorado River Basin.

The EWP estimates reported here make use of more detailed LCRAS data for the Colorado mainstem counties substituted for some of the USGS data. This had no effect on the EWP estimates for Upper Basin Counties and minimal impact on average EWP for Other Lower Basin Counties (<2%). For Border Counties, the effect was to increase EWP for Yuma County, while significantly lowering EWP for Imperial County. The overall effect was a significantly lower average EWP for Border Counties. Yet, even with these downward adjustments, Border Counties still enjoy a sizable EWP advantage over other counties. The USGS water estimates for Imperial County were significantly lower than LCRAS estimates. Yet the LCRAS estimates for the county are consistent with irrigation district reports [30], federal decision documents [9], and implementation reports to the federal government [115].

As noted, using EWP to consider the economic impacts of water reallocations in the Colorado River Basin is a starting point. EWP is too crude a measure to capture the full economic impacts of such reallocations. That said, EWP does provide some intuition behind more sophisticated economic models of Basin water use. These models have also found that substantial reductions in agricultural water use could be made in the Basin at relatively low costs and that a key to minimizing these costs is avoiding reductions in specialty crop production [116,117]. EWP analysis also provides useful information to federal and state agencies offering payments to farmers to forego water use to conserve water in the region’s large reservoirs. Our results suggest that for large-scale water retirement, focusing on the Upper Basin would require less expenditure overall.

Our empirical analysis of inter-county differences in EWP was more of a hypothesis-generating exercise than one of testing or confirmation. Adoption rates for improved irrigation technologies showed little inter-county variation and so did not have a statistically significant impact on inter-county differences in EWP. Future research might examine differences in irrigation technology adoption over time and space where there would be more variation. However, to date, the USGS has not made county-level water consumption data available from their 2020 survey.

We found evidence that more remote, low-population counties had lower EWP, controlling for other factors. Possible explanations could be higher transaction costs in conducting business, or lower quality infrastructure (e.g., roads, broadband internet connections). Future research could examine the effects of infrastructure quality more directly.

Being on the Border had a large, positive effect on EWP, even controlling for differences in climate and irrigation technologies. We hypothesize this is because Border Counties have access to relatively low-cost and abundant labor from Mexico, which makes labor-intensive specialty crop production possible. Thus, water productivity may hinge more on labor availability and U.S. immigration policy than on irrigation investments and technologies. There has been concern voiced over the effects of water scarcity on the sustainability of agriculture in the Colorado Basin [11,12,13,14,15]. Our results suggest that the region can absorb relatively large reductions to water supplies with relatively modest reductions in revenues. In the future, labor scarcity rather than water scarcity could be a greater threat to regional production.