distinguished between irrigated and non-irrigated cropland. In an analysis of China’s agricultural productivity, Jin _et al._ (2010) included irrigation costs among the material input costs. When examining the shifting patterns of agricultural productivity in the United States, Alston _et al._ (2010b) distinguished between irrigated and non-irrigated cropland, and added a miscellaneous input category to account for irrigation fees. Fuglie (2010b), in a study of TFP in the global agricultural economy using FAO data, divided cropland into rainfed cropland and cropland equipped for irrigation, and included irrigation fees in the cost share of agricultural land. Finally, Zhao _et al_ . (2012), in an examination of annual TFP indices for Australia’s broadacre agriculture<sup>17</sup> stated that an important reason for their significant fluctuations were variable climatic conditions, including the amount of moisture retained in the soil. These examples show that water aspects tend to be ignored in studies at national or higher levels. In some cases, irrigation water is indirectly considered through the area of land irrigated. Efforts are made to incorporate irrigation fees, but they may not approximate the price or opportunity cost of water. Not surprisingly, these studies do not provide any conclusions related to the effect of water on agricultural productivity patterns.

A few studies of TFP measurement at the subnational level, such as the provincial and district levels, do incorporate water aspects in more detail. For example, Murgai (1999) provided district-level TFP estimates for the Green and post-Green Revolution period in the Indian Punjab. By distinguishing between availability of canal irrigation and investments in private tubewells (and incorporating the former as an average monthly cost associated with the quantity of canal-irrigated area, and the latter as a cost item in the index of capital accumulation), she was able to identify the water source as an additional factor for the sharp differences in productivity growth across districts and cropping systems over time. Conradie _et al_ . (2009) focused on South Africa’s Western Cape Province and further disaggregated TFP indices for its regions and districts. They found that water availability (included as a dummy variable to indicate whether a district had a major river running through it) was an important explanatory variable. Districts with rapid TFP growth were those that not only showed water availability, but also the adoption of drip irrigation and a switch to export fruit production (which was made possible by a number of other factors, such as the introduction of an improved marketing system and cold storage facilities at the coast).

Besides TFP indices, frontier models are also frequently used in the agricultural production economics literature. The original frontier model was introduced by Farrell (1957) in a seminal paper that lays out a framework to measure economic efficiency, including technical efficiency which represents a firm’s ability to reach the maximum potential output, given a given set of inputs and for a given technology; and allocative efficiency which captures the firm’s ability to adapt optimally to market

> 17  Broadacre agriculture includes non-irrigated grains, beef and sheep production.

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