Rights, Water Use and Technical Efficiency in U.S. Agricultural Production

Abstract

Use of water in agriculture has a major driving force behind general water use patterns in the United States. To assess water's usage and value to 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 with four inputs: capital; labor; intermediate inputs; and water withdrawals. We include environmental variables to account for climate effects and pay particular attention to pair-wise differences between the riparian and modified riparian, and the prior appropriation and hybrid water regimes, to place an aggregate value on additional restrictions on water use.All of the primary input coefficients are significant, except for the cross-effect between intermediates and water, with intermediates and cropland having similar marginal products across all regions. The two riparian-based regimes have comparable marginal products of water, while the hybrid average is larger than the prior appropriation value by a factor of ten. Similar patterns appear when looking at measures of efficiency, with riparian and modified riparian regimes having nearly equal efficiency and climate losses when taken in dollar terms, while prior appropriation counties display the largest efficiency losses for each measure.We combine the marginal product and the marginal effect of water-based variables on efficiency to construct a more accurate shadow price of water. The efficiency component displays a consistent premium to regulation, with an average value of $0.71 per acre-foot and a maximum of $1.47, but this does not carry through to the shadow prices. Prior appropriation rights counties have the lowest average shadow price of $15.66 and hybrid rights counties the highest at $162.26, compared to the overall average of $51.79. These differences do seem to be primarily due to the efficiency of water use in production and not due to crop choices.