Decision-making units (DMUs) face considerable variations in their production possibilities as well as the characteristics of the production environments under which they operate. Consequently, DMUs are likely to experience substantial differences in productivity and efficiency levels. In contrast, the received literature assumes that DMUs share similar technological possibilities and only differ with respect to their level of inefficiency. This study develops an analytical framework using random parameters, which accommodates heterogeneity in production possibilities and in characteristics of the production environment. We use this framework to analyze variations in the output elasticity of irrigation across DMUs, and how these differences influence: 1) irrigation water use efficiency (IWUE), using a non-radial input-oriented approach that isolates and measures the efficient use of the irrigation input; 2) technical efficiency, which radially measures the efficient utilization of all inputs; and 3) shadow prices of irrigation withdrawals. We find that IWUE and technical efficiency averaged 72.6% and 83.6%, respectively, and shadow prices averaged $77.5 per million gallons of irrigation water, albeit with significant regional variations.

决策部门（DMU）在其生产可能性以及其运营所处的生产环境的特征方面面临着巨大的变化。因此，DMU可能会在生产率和效率水平上遇到实质性差异。相比之下，现有文献假设DMU具有相似的技术可能性，只是效率低下有所不同。这项研究使用随机参数开发了一个分析框架，该框架适应了生产可能性和生产环境特征的异质性。我们使用此框架来分析不同DMU的灌溉输出弹性的变化，以及这些差异如何影响：1）灌溉用水效率（IWUE），采用非辐射输入法，隔离并衡量灌溉输入的有效利用；2）技术效率，从径向上衡量所有投入的有效利用；3）灌溉取水的影子价格。我们发现IWUE和技术效率分别平均为72.6％和83.6％，影子价格平均为每百万加仑灌溉水77.5美元，尽管地区差异很大。