Non-Parametric Estimation of Environmental Efficiency Using Data Envelopment Analysis and Free Disposable Hull

Non-Parametric Estimation of Environmental Efficiency Using Data Envelopment Analysis and Free Disposable Hull

Richard Mulwa (University of Nairobi, Kenya)
DOI: 10.4018/978-1-4666-4474-8.ch013
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Nitrogen, phosphate, and herbicide use are three main environmental problems caused by agriculture. Modelling these undesirable outputs and other detrimental side effects of production activities has attracted considerable attention and debate among production economists. A common approach is to treat detrimental variables as inputs mainly using Data Envelopment Analysis (DEA), which has enjoyed a lot of success over the years. On the other hand, Free Disposable Hull (FDH) has not enjoyed as much success as its counterpart, DEA. This chapter demonstrates how environmental efficiency can be modelled using both DEA and FDH under strong and weak disposability assumptions. Results show that weak disposability assumption is more superior in achieving relatively high emission reductions and that FDH tends to allocate efficiency to more DMUs compared to DEA.
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1. Introduction: Farming And The Environment

Nitrogen, phosphate and herbicide use are three main environmental problems caused by agriculture. Nitrogen and phosphate surpluses are induced by excessive application of manure and chemical. Part of these nutrients is taken up by plants, but a part is emitted to the environment. The overuse of fertilizers on crops is typical of farming in general. In addition, increased soil acidity affects plant health and crop yield (WWF, 1986). Acidification is also more prevalent largely due to the use of inorganic nitrogenous fertilizers such as urea and ammonium sulphate. Under high rainfall conditions nitrate leaching occurs, which also promotes acidification (ibid).

Nutrient runoff from cultivation has led to nutrient loading and eutrophication of freshwater and marine systems. This constitutes diffuse (non-point source) pollution in nature. For example, lots of Nitrogen (N) and Phosphorus (P) are used to increase yields in Nyando catchment, a sugarcane growing region, in Kenya. These together with livestock, urban sewage discharges and industrial effluents are the main causes of water pollution in the Nyando river (Njogu, 2000). In situ determination of oxygen levels shows a range of 0.2-0.74 mg/l (Calamari et al., 1992) indicating the river experiences anoxic conditions at certain periods since the effluent loads discharged to the surface water systems have led to is remarkably lower oxygen levels than the recommended WHO standard of 20mg/l.

Phosphate pollution causes eutrophication of surface water which endangers plant and fish life (Clay, 2004). Controlling agricultural phosphorus losses from catchment areas depends on understanding and managing phosphorus use, its fate and transport within the catchment. Phosphorus (P) from agriculture is a highly variable input, from the point of view of spatial and temporal variability, reflecting differences in land use, soil type, management and short and long-term climate variation. In reviewing measured P loss rates, Sonzogoni et al. (1980) highlighted the variability of P loss rates not only between differing land-use categories, but also within a particular land use. Loss rates tended to be greatest from arable cropping and least for low-intensity grassland but, for a given land use, loss rates decreased from coarser (sandy) to finer (clay) textured soils.

Stream flow is required to transport P from a catchment, and hydrological processes strongly influence P loss dynamics. Ryden et al. (1973) proposed that P losses be considered for three types of runoff: surface, storm and base-flow runoff. Although rainfall has a low P content, the highest P concentration is observed in surface runoff, reflecting both the high P content of surface soils and the occurrence of soil erosion. The latter can be especially important in determining P losses under arable conditions, particularly when there is little cover crop and low soil infiltration rates. In comparison with base flow, storm runoff represents precipitation that moves quite rapidly across or through the upper soil horizons, which has highest P contents, before reaching a drainage channel.

Key Terms in this Chapter

Free Disposability: This means that given inputs x , it is possible to decrease the production of any output by any desired amount (i.e. get rid of any output free of charge), or conversely, it is possible to produce any given output y with more input resources than is absolutely necessary ( Kuosmanen and Kortelainen, 2004 ).

Convexity: Implies that if two combinations of output levels can be produced with a given input vector x , then the average of these two output vectors can also be produced with x . This assumption implicitly requires the commodities to be continuously divisible ( Coelli et al., 1998 ).

Materials Balance Condition: This is based on the First Law of Thermodynamics which states that energy/matter can be transformed from one form to another, but cannot be created or destroyed.

Weak Disposability: This allows for radial contractions of observed output bundles in a given output set, i.e., it assumes reductions of all outputs by the same proportion are always feasible given that available inputs are held constant ( Färe and Grosskopf, 2004 ).

Directional Distance Function: This is associated with an explicit direction in which efficiency is gauged. It requires specification of a direction vector .e.g. expanding outputs in direction ( ) and contracting inputs in direction ( ).

Debreu-Farrell Input Efficiency: This measure defines inefficiency as the maximum equi-proportionate reduction of inputs that is attainable without reducing any of the outputs (Kuosmanen and Post, 2001 AU90: The in-text citation "Kuosmanen and Post, 2001" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. ).

Null Jointness: Given a desirable output vector y and undesirable outputs z , if output vector ( y,z ) is feasible and there are no bad outputs produced, then under null-jointness only zero good output can be produced. Equivalently, if some positive amount of good output is produced, then some bad output must also be produced.

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