Policy Paper Series 1996 Policy Paper No.3 Estimation of Derived Demand for Surface Water on Two Rice Irrigation Districts in the Lower Colorado River Basin~ Texas Martin T. Schultz Lyndon B. Johnson School of Public Affairs The University of Texas at Austin Acknowledgements The author appreciates the many individuals and organizations that provided assistance in the completion of this project. Four individuals served as readers and worked with the author throughout the preparation of this report: David Eaton of the Lyndon 8. Johnson School of Public Affairs (LBJ School), The University of Texas at Austin CUT/A), Peter Wilcoxen of the Department of Economics, UT/A, and Quentin Martin and Jobaid Kabir of the Lower Colorado River Authority (LCRA). Chandler Stolp of the LBJ School introduced the author to data envelopment analysis and discussed its application and interpretation. This project would not have been possible without the support of Bruce Hicks and his staff on the LCRA irrigation districts, Mike Shoppa, Henry Bradford, Thomas Pivonka, Larry Harbers, Kelly Weber, and district water coordinators. These individuals spent many hours with the author over a two­ year period discussing operations and management on the irrigation districts and rice farming. Several other individua Is assisted the author with specific issues at various times during the completion of this report Angie Taylor and Alan Faries of the LCRA Rates Management Division provided infortnation on the development of irrigation water rates. Garry McCauley of Texas Agricultural Experiment Station, Texas A&M University, shared his extensive knowledge of rice farming and provided data from the Less Water-More Rice Research Project. James Engbrock and Rick Jahn of the Texas Agricultural Extension Service offices in Matagorda and Colorado Counties discussed local conditions and provided the author with farm budgets. The author is solely responsible for any errors, interpretations, or omissions. Table of Contents Chapter 1: Summary of Results ................................................ 1 Research Results . ...... 3 How These Results May Be Used by Affected Agencies ......................... 7 Chapter 2: Methods for Determining the Value of Water ............................... 8 The Value of Water in Competitive Markets .................................. 8 Economic Inefficiencies Related to Water Markets in Practice .................. ... 11 Methods of Estimating the Value of Water .................................. .14 Crop Water Production Functions ........................................ 16 Farm Budget Analysis ................................................ 22 Applications of Linear Programming Techniques . 24 Chapter 3: LCRA Rice Irrigation Districts ........................................ 28 The Lower Colorado River Authority . ........... 28 Annual Rice Acreage Requirements . ............ 32 Water Management Practices ........................................... 37 Other Factors Influencing Field-Specific Water Use .............................40 Crop Alternatives and Feasible Crop Areas ...................................42 Farm Budget Residuals ............................................. .. 46 Farmers'Reactions to Changes in the Marginal Cost of Water .....................52 Chapter 4: The Irrigation Efficiency Frontier in First Crop Rice Fields .. .. 60 Data Envelopment Analysis ............................................ 60 DEA-Defmed Technical Efficiency in Rice Irrigation ............................67 Uncontrollable Input Analysis for First Crop Rice Fields ........................ 73 Chapter 5: A Linear Programming Model for Estimating Derived Demand .................. 79 Assumptions of the Linear Programming Model ........................ .......79 The Linear Programming Formulation ................. .................... 82 Chapter 6: Linear Programming Model Results .................................. .. 86 The Linear Programming Solution . ........ 86 The Value of Water on LCRA Irrigation Districts ............................. 96 The Value of the Indirect Subsidy to Farmers ................................ 98 The Potential for Average Cost Pricing ................................... .102 The Price Elasticity of Demand for Irrigation Water ........................... 104 Chapter 7: Conclusions .................................................... 108 The Impact of Water Rights on Farm Water Use .............................. 108 Water Conservation Alternatives ........................................ .109 Institutional Change in Water Rights ..................................... .113 Recommendations for Further Research ....................................114 Bibliography ............................................................ 117 List of Tables Table 1.1 Water COl1S1l1Ilption, Lower Colorado River, Texas, 1980 - 1989 ................. 2 Table 1.2 Short-Rtm Average Value of Water on LCRA Irrigation Districts ................. 6 Table 2.1 Methods of Estimating Derived Demand: Advantages and Disadvantages ............ 15 Table 3.1 Total Water Diversions and Percent of Total Consumptive Uses on the Districts ....... 30 Table 3.2 Interruptible Stored Water Diversions on LCRA Irrigation Districts ................ 30 Table 3.3 1993 Volumetric Irrigation Water Rates .................................. 31 Table 3.4 Rice Acreage Irrigated with Surface Water on LCRA Districts ................... 33 Table 3.5 District Acreage Model Regression Results ............................... .34 Table 3.6 Management Practices and Water Use on Lakeside District in 1993 ............... 39 Table 3.7 Management Practices and Water Use on Gulf Coast District in 1993 .............. 39 Table 3.8 Parameter Estimates and T-Statistics for the Water Management Model ............. 40 Table 3.9 1982 Land Tenure Arrangements in Colorado, Wharton, and Matagorda Cotmties ...... 42 Table 3.10 Estimated Maximum Crop Acreage in Feasible Crop Areas on Lakeside District ...... 44 Table 3.11 Estimated Maximum Crop Acreage in Feasible Crop Areas on Gulf Coast District . .. 46 Table 3.12 Colorado County Rice Budget, 1993 .................................... A8 Table 3.13 Wharton County Rice Budget. 1993 .................................... A9 Table 3.14 Matagorda Cotmty Rice Budget, 1993 ................................... 50 Table 3.15 Long-Rtm Farm Budget Residuals and Farm Profits in Feasible Crop Areas ......... 51 Table 3.16 Short-Rtm Farm Budget Residuals and Farm Profits in Feasible Crop Areas ......... 51 Table 3.17 Parameter Estimates and T-Statistics for the Model of Farmers' Reactions ........... 55 Table 3.18 Summary of Information about the LCRA Irrigation Districts ...................57 Table 4.1 Sample Field Data, First Crop Rice Fields, Texas Gulf Coast ....................64 Table 4.2 Model Parameters and Efficiency Scores (6) for DEA Models 1,2, 3 .............. 70 Table 4.3 Correlation of Factors of Production with Efficiency Measures ...................71 Table 4.4 DEA-Efficient Values for Total Water Use (T') and Inflows (I') in Sample Fields ...... 72 Table 4.5 Model Parameters and Efficiency Scores (6) for Uncontrollable Input Models 4 and 5 .. 74 Table 4.6 Correlation of Factors of Production with Efficiency Measures ................... 75 Table 5.1 Assumptions of the Linear Programming Model .............................80 Table 5.2 Assignment of Model Indices ......................................... 83 Table 6.1 Piecewise Estimates for Derived Demand with Farmer Reaction Curves ............ 87 Table 6.2 Acreage Solutions and Volume of On-Farrn Water Demand without the Farmer Reaction Curve, Lakeside District ...........................90 Table 6.3 Acreage Solutions and Volume of On-Farm Water Demand without the Farmer Reaction Curve, Gulf Coast District .........................91 Table 6.4 Acreage Solutions and Volume of On-Farm Water Demand with the Farmer Reaction Curve, Lakeside District .............................94 Table 6.5 Acreage Solutions and Volume of On-Farm Water Demand with the Farmer Reaction Curve, Gulf Coast District . .... 95 Table 6.6 Short-Run Average Value of Water on LCRA Irrigation Districts ................. 97 Table 6.7 Marginal Value of the Water Delivered to Farmers on LCRA Irrigation Districts ...... 99 Table 6.8 Variable Cost Estimates at Different Pumpage Requirements ................... 103 Table 6.9 Parameter Estimates and T-Statistics for the Linear Farmer Reaction Curve ......... 107 List of Figures Figure 2.1 Hypothetical Marginal Value Product Curves in a Typical River Basin ............. 12 Figure 2.2 Hypothetical Demand Curve for Water in a Typical River Basin ................. 12 Figure 2.3 Value of a Subsidy in an Efficient Water Market ............................13 Figure 2.4 Hypothetical Demand Curve for Irrigation Water on a Public Irrigation District ....... 13 Figure 2.5 The Relationship Between Economic and Teclmical Efficiency on Hypothetical Farms .. 18 Figure 3.1 Actual and Estimated First Crop Acreage on Lakeside District ............. ..... 35 Figure 3.2 Actual and Estimated First Crop Acreage on Gulf Coast District . ......... 36 Figure 3.3 Feasible Crop Areas on Lakeside District . .45 Figure 3.4 Feasible Crop Areas on Gulf Coast District . ....45 Figure 3.5 Projected Water Savings Associated with Increases in the Effective Water Price ...... 56 Figure 4.1 The Relationship Between Field Water Use and Crop Yields, First Crop Fields ....... 63 Figure 6.1 Derived Demand on the Lakeside Irrigation