similar in characteristics to irrigated plots. Their findings indicate that irrigated agriculture had a large potential to improve technical efficiency which could be supported by, for example, farmer training in irrigation agronomy and on-farm water management. Rainfed agriculture seemed to produce close to its production frontier, and improving soil moisture would be a measure for shifting the production frontier upward.

We also found two earlier studies not included in the meta-analysis of Bravo-Ureta _et al_ . (2007) that applied stochastic frontier modeling to irrigated farms: McGuckin _et al_ . (1992) and Karagiannis _et al._ (2003). These two studies are of particular interest for our purpose because they emphasize the importance of distinguishing between irrigation efficiency (as used in the irrigation engineering literature) and economic efficiency involving technical and allocative efficiency [with Karagiannis _et al_ . (2003) referring to Mc Guckin _et al_ . (1992) as well as Farrell (1957)].<sup>21</sup> Irrigation efficiency is only one dimension of input use; it is a physical measure of the irrigation technology assuming a level of management—while technical and allocative efficiency are measures of management capability.<sup>22</sup> Both studies also include irrigation water as a continuous variable (in terms of water applied), and are concerned with farmers’ irrigation water savings. However, the “water savings” discussed are in the form of reduced water applications, not consumption—and therefore potential externalities beyond the farm level in terms of return flows were not explicitly considered.

McGuckin _et al_ . (1992) used farm observations for corn producers in a homogeneous crop region of Nebraska, United States, who applied groundwater by gravity or sprinkler systems as supplemental irrigation. The frontier was estimated as a Cobb-Douglas model of irrigation (in terms of water applied)—with soil conditions, rainfall and irrigation technology included as exogenous variables that shift the frontier, and all other inputs excluded. The authors hypothesize that technical inefficiency of irrigation depends on available field information (e.g., soil moisture monitoring, commercial scheduling and/or weather reports). Their findings indicate that information on field conditions from moisture sensors is a particularly important factor for improving technical efficiency of irrigation practices.

Karagiannis _et al._ (2003) specified a stochastic production frontier model to measure irrigation water efficiency (in terms of water applied) on farms with out-of-season (greenhouse) vegetable cultivation in Crete, Greece. To start out, they proposed to define irrigation water efficiency not along the

> 21 As noted in section 2, Seckler (1996) also started out with a critique on the usefulness of the term irrigation efficiency for guiding water management decisions (especially at the basin level) but—unlike McGuckin _et al_ . (1992), and citing them, Karagiannis _et al._ (2003)—did not elaborate on the relationship between irrigation efficiency and economic efficiency.

> 22 As McGuckin _et al._ (1992) put it: “Compared to a furrow system, a sprinkler irrigation system could reduce water use and increase irrigation efficiency but at the expense of an increase in capital.  With very low cost water, the sprinkler would be allocatively inefficient.  More subtly, a sprinkler could also be technically inefficient.  With improved management, a sprinkler system might use as much water as the furrow system and thus be technically inefficient compared to the well-managed furrow system” (pp. 306-307).

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