Technical and environmental efficiencies and best management practices in agriculture

Abstract

An Input Distance Function (IDF) is estimated to empirically evaluate and analyse the technical and environmental efficiencies of 210 farms located in the Chaudière watershed (Quebec), where water quality problems are particularly acute because of the production of undesirable outputs that are jointly produced with agricultural products. The true IDF is approximated by a flexible translog functional form estimated using a full information maximum likelihood method. Technical and environmental efficiencies are disaggregated across farms and account for spatial variations. Our results show that there is a significant correlation between the two efficiencies. The IDF is used to compute the cumulative Malmquist productivity index and the Fisher index. The two indices are used to measure changes in technology, profitability, efficiency and productivity in response to the adoption of two selected Best Management Practices (BMPs) whose objective is to reduce water pollution. We found significant differences across BMPs regarding the direction and the magnitude of their effect.

Keywords:

• environmental efficiency
• distance function
• phosphorus runoff
• productivity
• profitability
• technical efficiency

JEL Classifications:

• Q25
• Q52

Acknowledgements

We wish to thank Mathieu Gourdes-Vachon from the Club de Fertilisation de la Beauce for his insights about farm practices, Alain Rousseau from INRS for his hydrological simulations, Eric Van Bochove for sharing his expertise in water quality issues and Pascal Ghazalian for useful comments. We are also grateful to numerous seminar audiences for their comments and suggestions. The usual caveat about remaining errors applies.

Notes

¹ Färe et al. (1993) treated environmental effects of an undesirable output and an undesirable input using parametric mathematical programming and nonparametric mathematical programming known as Data Envelopment Analysis (DEA). The DEA approach has been used extensively in studies of SO₂ emission in electric utilities and for nitrogen and phosphorus runoff in agriculture.

² Schmidt and Lovell (1979) described how one could estimate a Cobb–Douglas stochastic cost frontier and then use duality to derive the implicit production frontiers. With these two frontiers, one could measure cost efficiency and technical efficiency, and hence allocative efficiency residually.

³ The materials balance condition of the nitrogen cycle ensures that the nitrogen surplus of output-constrained dairy farms is minimized if farm is nitrogen efficient in the inputs.

⁴ The Output Distance Function (ODF) identifies the largest set of outputs possible given a set of inputs while the IDF identifies the smallest set of inputs necessary to produce a set of outputs. The ODF can thus be interpreted as a multi-output production function allowing deviations (distance) from the frontier.

⁵ To get this result, Atkinson and Dorfman (2005) assume that the ‘bads’ can only be decreased and that, following Pittman (1983), with constant ‘goods’ and technology, ‘bads’ can be reduced only by increasing one or more inputs.

⁶ As mentioned by FKS (2002, p. 433), one could construct a single frontier defined as the maximal combinations of good outputs, given quantities of bad outputs and inputs. Under a separability assumption, this approach essentially reduces to treating the two types of outputs differently in the same aggregator and it does not allow for a natural separation of technical and environmental efficiencies because a single frontier is generated. The implication is that a fully technically efficient farm is also fully environmentally efficient.

⁷ We follow Paul and Nehring (2005) with their external or shift factors. Fuentes et al. (2001) introduce the time trend in the same way and interaction effects with the inputs. This approach is also close to the one applied by Rodriguez-Alvarez et al. (2007) who treat some external factors as quasi-fixed inputs in their description of the production process.

⁸ Outputs and inputs may be endogenous. Rodriguez-Alvarez and Lovell (2004), Atkinson et al. (2003) and Atkinson and Dorfman (2005) use instrumental variables techniques to deal with this issue. In their application featuring electricity power plants, Atkinson and Dorfman (2005) examine identification issues using Hansen's (1982) J test in a Generalized Method of Moments (GMM) framework. Because, Coelli and Perelman (2000) and Rodriguez-Alvarez et al. (2007) define the IDF as the radial (proportional) expansion of all inputs (given the output level), the endogeneity problem does not arise if the random disturbance affecting production processes changes all inputs in the same proportion (Roibas and Arias, 2004).

⁹ The circularity property posits that an index comparing productivity between units k and f, and between l and f, must be able to compare productivity between units k and l via the arbitrary third unit, f. The outcome must be unaffected by the choice of the third unit, f (Førsund, 2002).

¹⁰ One could choose one group as the base, but in this case, the value of the index would depend on the technology chosen. Examples include Berg et al. (1993) and Camanho and Dyson (2006). As mentioned by Førsund (2002), in a time series context, this procedure is similar to the notions of inter temporal and accumulating technologies.

¹¹ This measure suggested by Georgescu-Roegen (1951) is a simplified measure of profitability change because it omits mixed terms (see Althin et al., 1996).

¹² We expect the adoption of a BMP to induce a structural change in the IDF. For example, manure injection implies a modification – or a replacement – of machinery, an increase in the time used to spread the manure and then a possible reallocation of the use of inputs. Using a Chow test (Greene, 2008), we test the hypothesis that the coefficient vectors are the same for the subset of adopters and nonadopters. The size of our data set prevented us from doing estimation on sub-samples of farmers adopting more than one BMP.

¹³ Reinhard et al. (1999) note that the EE measure adds independent information only if the outputs' elasticities are variable, a property of the translog IDF.

¹⁴ ‘Bads’ levels are computed through simulations that estimate the amount of chemical leached from individual Relatively Homogeneous Hydrological Units (RHHUs). RHHUs correspond to small areas whose drainage structures are derived from a relatively high resolution Digital Elevation Model (DEM).

¹⁵ The correlation coefficient between nitrogen runoff and phosphorus runoff was found to be 0.96. The correlation coefficients of the sediment runoff with nitrogen runoff and phosphors runoff were 0.82 and 0.87, respectively.

¹⁶ Because we have imposed linear homogeneity, the input distance function must be quasi-concave.

¹⁷ Just and Pope (1978) contend that the impact of input use on risk may induce a correlation between outputs that would otherwise be independent without risk. The idea is that uncertainty causes variations in the marginal products or contributions of inputs across products.

¹⁸ Without taking into account the ‘bads’ as a technological shifter in the production process, the mean value of the predicted TE is 0.471. The null hypothesis of no significant difference between the means of TE with and without ‘bads’ is rejected at the 5% level.

¹⁹ Coelli et al. (2003) get a predicted mean TE of 0.86 from their sample of Indian dairy processing firms. Paul and Nehring's (2005) predicted mean TE is quite high at 0.93. Their IDF model was applied to US farm level data. FKS (2002) report a median TE of 0.67 for their sample of US dairy farms. The median for our study is 0.49. Finally, Atkinson and Dorfman (2005) report a weighted average TE of 0.55.

²⁰ Estimations results are available from the authors upon request.

²¹ Horbach (2008, p. 172) concludes that ‘… An environmentally oriented research policy has not only to regard traditional instruments like the improvement of technological capabilities of a firm, but also the coordination with soft environmental policy instruments like the introduction of environmental management systems.’

²² Our estimate is higher than Ball et al.'s (2002) 0.09% and 0.08% for leaching and runoff.

²³ Using data covering the 2001–2003 period, Gangbazo and Le Page (2005) find that phosphorus runoff has to decrease by 30.8% in the Chaudière watershed to reach the target of 0.030 mg/l to prevent eutrophication at the water quality stations (Table 4.2, p. 26). These authors also find that 33.8% of the phosphorus runoff is a nonpoint source pollution generated to a large extent by agricultural activities (Table 4.3, p. 28). Clearly, discussing the cost of a 10% reduction is a sensible exercise.

²⁴ Reinhard et al. (1999) have found a positive Spearman rank correlation of 0.87 in their sample of Dutch dairy farms. A similar finding is reported for US dairy farms by FKS (2002) even if the correlation coefficient is noticeably lower than 0.40.