Water Demand Management in Arid Area: A DEA Input Distance Function Approach to Analyze Technical and Scale Efficiencies and Irrigation of Farms in Tunisia

Technical and scale efficiencies have been widely studied in agricultural production literature, but many of the inputs used can impact the environment. Environmental impacts can take the form of undesirable output, a non-discretionary production input or, as has been the case in many studies, a conventional input. In this paper, we develop a DEA (Data Envelopment Analysis) model with water salinity as a non-discretionary input and estimate a model of irrigation water demand function based on the role of water in the farm production function. We model production technology by distinguishing six inputs (water, labor, phosphate, farmyard manure, farm size and water salinity) and four outputs (date production, vegetable production, cereal production, and fruit production). The adjusted-DEA model is applied on a transversal data of 138 water users associations farms. On average, the technical efficiency for our sample observations is 0.63, which means that, on average, the farms can produce the same level of outputs with only sixty three per cent of the inputs if they are operating at the input frontier. Moreover, we also observe that there is wide variation in the measure of technical efficiency across farms. Spearman coefficient of rank correlation is used to test whether the farms’ performance rankings, before and after accounting for water salinity, are significantly different. We find that accounting for variations in water salinity does not significantly bias the relative performance of the farms. The mean of scale efficiency levels is about 0.89. The results also show that 70% of farms are operating at below the optimal scale of production and 50% of oases farmers could improve SE (first mention, no full term) if they increased scale in terms of farm size. The shadow prices of irrigation water derived from the adjusted-DEA model are positive, reflecting that water is a normal input in the production process. The estimation of a model of irrigation water demand function enables us to derive the shadow price elasticities of the inputs. It should be noted that the price elasticity of water is significant and quite high. Thus, the high responsiveness of water demand to price suggests that pricing policies can be a potential instrument for water conservation.