The sustainability of ecosystems and its relationship to economic growth is intertwined with water management in both developing and developed nations. Water management issues in the agricultural sector often take a central role in controversies over how to allocate this resource that is becoming increasingly scarce in many arid and semi-arid areas around the world. With the agricultural sector being the largest user of freshwater, its use in this sector commands particular attention when it comes to discussions about conservation and sustainability of water in terms of both quantity and quality (Molden, 2007). While country-level estimates are available, estimates for freshwater withdrawals from irrigated agriculture and their impact are difficult to present on a worldwide basis. With an estimated 20 per cent of cultivated land being irrigated, this acreage accounts for 40 per cent of total agricultural production (Rosegrant et al., 2013).
At the same time, there can be significant interregional competition for water use in agriculture (e.g., Middle East or Sub-Saharan African countries) as well as intersectoral competition for water between agriculture, urban and environmental uses (e.g., tourist areas in Southern Europe and North Africa). The value of water used in agriculture must be balanced against these competing uses (Rosegrant et al., 2013). Improved irrigation technologies have contributed to rapid yield increases and to more effective irrigation practices in the two decades. But pumping groundwater for agricultural purposes can be unsustainable in areas where withdrawals exceed recharge. In addition to rapidly depleted groundwater reserves, excessive groundwater extraction can lead to both water scarcity and water quality concerns. Quality concerns arise from human-induced impacts such as salinization, excess nutrients, acidification, toxic waste, saltwater contamination, and eutrophication that are not irrelevant to agricultural water uses (Abdulai and Huffman, 2014).
The recent projections for food and agricultural production by 2050 have brought the agriculturally related water needs front and center (United Nations, 2015). Once climate change scenarios are factored into the discussions, water-need forecasts for agricultural, urban and environmental sectors have elevated the attention to calls for global water security. Productivity is the measure of economic performance which is defined broadly as output per unit of input. The emergence of the Blue Revolution (Calder, 1999) and the Kofi Annan Foundation brought attention to the issue of water use in agriculture by promoting the tag line of more crop per drop (Annan, 2000); that is, focusing attention on water as a specific factor of production, and the practices and technological innovations that can increase agricultural output per unit of water applied (Mendelsohn and Dinar, 2003).
The reality of modelling and measuring agricultural productivity as farm output per unit of input must first acknowledge that any reasonable farm production situation involves multiple variable or quasi-fixed inputs producing a variety of crops. Agricultural water productivity (or crop per drop) is a partial productivity measure that focuses on a single input (irrigation water) similar to labor or land productivity that are often raised in farm production policy discussions. However, in a family-farming rural setting, both land and labor (usually family labor) are considered as quasi-fixed factors of production. Measuring their partial productivity growth rates or quasi-rents can provide useful insights about the use of farming technology and variable inputs utilization. However, irrigation water is a variable input in farm production impacted by the farmer's managerial capability, environmental conditions, the state of irrigation technology and more importantly by other variable inputs use (e.g., fertilization practices). Therefore, proper measurement of agricultural water productivity should be focused on a total factor productivity setting accommodating farm's adjustments beyond the short run.
In doing so, the definition of farm technology must address two important issues related to irrigation water use. First, the quantity of irrigation water applied deviates from the amount of water that is actually consumed by the crop. Second, the irrigation technology choice is not instantaneously mobilized by individual farmers, and its impact on individual productivity rates is ambiguous. The water engineering literature provides an extensive discussion of why applied irrigation water differs from effective water actually utilized by the crop (e.g., Merriam and Keller, 1978; Clemmens, 1991). The farm technology should reflect this deviation to properly measure agricultural water productivity rates. Otherwise, measured farm productivity will misstate the true contribution of irrigation water use, leading to wrong decisions concerning the sustainability of water resources (e.g., Dinar and Yaron 1992; Khanna et al., 2002).
The transition between the alternative irrigation technologies, like any other technological decisions made by individual farmers, does not take place in a single time period. Farmers continuously revise their own perceptions about the effectiveness of each irrigation practice and when they are certain about the potential productivity improvements they move to the new technological regime. The development of new, more effective technologies is the result of innovations in irrigation practices combined with policy schemes to advance the diffusion process (e.g., Dridi and Khanna, 2005; Genius et al., 2014). However, policies intending to advance diffusion rates do not necessarily improve effectiveness; for example, risk averse farmers adopt technologies to hedge against the risk of adverse climatic conditions (Tsur et al., 1990) or soil characteristics and climatic conditions favoring a traditional irrigation system may perform equally well in terms of irrigation water effectiveness (Caswell and Zilberman, 1986).
Taking this line of argument we assume that non-linearities may exist in the adoption of new irrigation technologies. Contrary to previous studies that assume only a single technological regime, we adopt the production function able to identify the different technological regimes that may exist (if any) among farmers. This transition-production function allows for a smooth transition between traditional and innovative irrigation technologies. In this approach the transition from one technological regime to the other depends on the conditional probability of farmers' gains from the adoption of new technologies. The case study addresses a farm-level panel of greenhouse vegetable producers in Crete, Greece. The decomposition of total factor productivity (TFP) growth is undertaken which separates the different technical change, irrigation effectiveness and scale effects. The next section presents the theoretical framework outlining the irrigation water effectiveness from an engineering perspective, the farmer's irrigation technology choice and how this technological framework incorporating the irrigation effectiveness measure and irrigation technology choice are embodied in the TFP growth decomposition. This is followed by the econometric framework, specified to implement this framework followed by the section describing the case study, its data and farmer choices. The next section presents the empirical results and their implications. The final section offers a set of concluding remarks and suggestions for future directions to investigate.