*7.4. Enhancing Water Use Efficiency*

Farm- and crop-level water use efficiency has been generously reported for different crops under different tillage systems, irrigation levels, and various farm management practices [30,33,39]. By definition, the efficiency is positively correlated with grain yield and negatively correlated with irrigation water application [14]. The effects of the factors on the efficiency can be better understood by comparing their effects on both water applications and crop yield. Water abundance reflected by groundwater use and more wells provide producers easy access and may motivate them to increase the water amount per acre, thus decreasing water use efficiency. In addition, water use efficiency may not have a linear relationship with water application [16,34]. Compared with dryland production or crop growing under drought stresses, a little more water may significantly increase yield, and as a result, the increase in water efficiency can be remarkable [33,34,39], while a higher than usual water use is unlikely to further increase grain yield, and the efficiency change can be reversed [14]. Especially for

water-intensive crops like corn, more water usually means no significant yield increase and a declining water efficiency [31].

The costs of variable inputs were previously found to increase water use while having no effect on the grain yield. As a result, water use efficiency decreased. This is largely because more energy and labor were used to provide more water for the water-consuming crop [51], while the adoption of pressure irrigation systems shows a positive effect. This may be because water is saved for water-intensive corn while the yield is not hurt, and both water conservation and grain yield are maintained for less water-intensive soybeans [6].

The weather-related variables show composite effects on water use efficiency by impacting water use and farm yield [6]. On the one hand, more rainfall reduces the supplemental irrigation amount, which results in a higher irrigation efficiency. In particular, the past experiences of ample precipitation may discourage farmers to use more water for a certain yield level [4,51]. On the other hand, a high temperature may have two types of impacts: (1) a hot growing season in previous years, like the drought events in 2011 and 2012, may promote producers to irrigate more to mitigate potential dry conditions in the current year; (2) in a normal year, like 2013, a slightly higher temperature may not lead to notably more irrigation, while the grain yield may be increased as a result of improved photosynthesis [5,51]. Though more fine-scale explorations are necessary to clarify the effects of climate variability, including the direct effects of rainfall and temperature, the evidence here provides insights on the effects of both experienced and perceived weather changes.

### **8. Conclusions**

Using the 2013 USDA FRIS data, this paper analyzes farmers' production decisions relating to irrigated agriculture in a multi-crop production system. To study the role of water costs, the farm-level water application is decomposed into crop-specific application. For each crop, the total effect can be obtained by summing the intensive and extensive margins of water use. With the aggregate effect at the farm level, we can quantify the effect of a one-unit increase in water price. Furthermore, the effects of exogenous variables are analyzed using a multilevel model approach. Four equations regarding land allocation, water application, crop yield, and economic irrigation water use efficiency are formulated using two-level models.

A fundamental finding from the decomposition of farm-level water application illustrates that the higher costs of surface water are not effective to reduce water use for both corn and soybeans through both intensive and extensive margins, while a proxy of groundwater price has a negative effect on soybean water use. This finding is a surprise, but empirically supported by some evidence. Similar to the mixed effects of water price found by Moore et al. [54], water cost is ineffective in conserving water use once producers have made decisions on crop production. Pfeiffer and Lin [75] found farm-level policies to conserve water use may not be effective. In this case, the surface water price is very low and it may not be effective because the water use is inelastic [80,89]. Comparatively, a much higher groundwater price is effective to conserve water use.

In addition, the results from MLMs allow us to make certain of the relative importance of farmand state-level factors, and the estimation outcomes present the effects of those exogenous variables at both levels. The adoption of pressure irrigation systems reduces the soybean water use and increases the soybean yield. A higher *EIWUE* due to enhanced irrigation methods can also be achieved on both corn and soybean farms.

The findings from MLMs show that the state-level variables on climate variability have consistent effects. A high temperature promotes more efficient water use and higher yield. A high precipitation is correlated with low water application and higher crop yield. Droughts due to less rainfall or high temperature and their perceptions increase farmers' awareness of potential production risks not only during droughts, but in subsequent years [90]. As a result, farmers can be motivated to change land allocation for different crops and irrigate more to mitigate the adverse effects of climate variability. Contrary to Olen et al. [18], we find the irrigation water use is more responsive to precipitation than to

temperature. Given the nonlinear impacts of climatic factors, farmers' responses in adapting to climate risks depend on cropping patterns.

This study also leaves some opportunities for future research. The aggregate effect is estimated for a typical farm growing corn and soybeans taking roughly half of the average farming area. Equations on more crops can be estimated to provide a more complete estimate of the water price effect [80], and regional equations can be estimated to account for structural differences across regions. Ideally, the elasticity with respect to water price can be estimated to quantify the price effect from a different and equally important perspective [60]. Though MLMs are supposed to deal with multiple estimation problems, more empirical and methodological investigations are needed, especially on potential endogeneity problems.

**Supplementary Materials:** The additional Tables S1–S9 are available online at http://www.mdpi.com/2073- 4441/10/11/1637/s1.

**Author Contributions:** Y.F. designed the research, analyzed the data and wrote the paper. Y.F., R.M., and S.C.P. reviewed and commented on the manuscript.

**Funding:** The research was supported by the USDA National Integrated Water Quality Grant Program number 110.C (Award 2012-03652), the USDA Multi-state Grant W-3190 Management and Policy Challenges in a Water-Scarce World, and the USDA Agricultural Research Service Initiative-Ogallala Aquifer Program (FY2016–2017; FY2017–2018).

**Acknowledgments:** We thank Brad Parks for his support when the first author analyzed data at the USDA NASS data lab in St. Louis, Missouri. We also appreciate helpful comments by Laura McCann, Hua Qin, and Corinne Valdivia on an earlier version of the paper. The authors are grateful to participants at the 2017 Agricultural & Applied Economics Association Annual Meetings. This research was conducted while Yubing Fan was a doctoral candidate at the University of Missouri-Columbia.

**Conflicts of Interest:** The authors declare no conflict of interest.
