Finally, Wadud and White (2000) compared technical efficiency estimates for rice farmers in Bangladesh employing a stochastic frontier model in combination with DEA, and found that inefficiency estimates are similar for both methods. They further analyzed technical inefficiency effects as a function of farm-specific socio-economic factors, environmental factors, and irrigation infrastructure (i.e. dieseloperated irrigation schemes). Results suggest that the inefficiency effects are positively influenced by the irrigation infrastructure. Electrification in rural areas would also be beneficial in reducing technical inefficiency.

Beyond reviewing the studies included in the meta-analysis of Bravo-Ureta _et al._ (2007), we also searched for further applications of frontier models to issues related to agricultural water management.<sup>20</sup> We found three more recent studies, two of which focused on rice farms in Asia and the third on smallholder plots in Ethiopia. Yao and Shively (2007) used panel data for a sample of rice farms in the Philippines over a period when they transitioned from rainfed to irrigated production. A time-varying stochastic frontier model was applied to examine technical efficiency within the context of technical change (i.e. irrigation development). A dummy variable captured whether a given parcel was irrigated during the dry season. The authors find that irrigation was correlated with gains in efficiency vis-à-vis rainfed production. They also find that efficiency was lowered by the distance to irrigation canals, and by problems with siltation of irrigation canals. Thus, the management of irrigation water appears to play a crucial role in influencing technical efficiency.

Gedara _et al._ (2012) used a stochastic frontier model to investigate the factors affecting technical efficiency of rice farms relying on village reservoir irrigation systems in a district in Sri Lanka. The irrigation networks operate on a rotational delivery system based on allocation decisions made by the village’s farmer organization. Water use was assumed to be proportional to the farm area cropped, and variation in the individual use of water was captured by including irrigating time (i.e. the time the water flowed over the land in minutes). The position in the system (e.g. head, middle or tail-end) was also included. The authors find that rice production could increase by 28 percent without increasing other inputs and using current technologies. Encouraging membership in farmer organizations and collective actions organized by them could contribute to efficiency improvements.

Gebregziabher _et al_ . (2012) compared the technical efficiency of irrigated and rainfed smallholder plots in Tigray, Ethiopia with a stochastic frontier model. Referring to Sherlund _et al._ (2002) who noted that the omission of environmental production variable may lead to an upward bias in the estimated technical inefficiency, they used propensity score matching to select rainfed plots that were

> 20 The search was carried out in the database EconLit using the terms “stochastic frontier”, “deterministic frontier” or “data envelopment analysis”, combined with the terms “irrigation”, “water” or “rain” in the title.

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