Theoretical and Methodological Issues

6.2.1. Theoretical Issues

This thesis employs the neo classical production theory as the basis for the empirical models. The primal approach based on the distance function is used in Chapters 2, 3, 4 and 5 of the thesis. In the context where there is no particular orientation and the profit maximization problem must be solved by choosing inputs and outputs simultaneously, the directional distance function introduced by Chambers et al. (1996 and 1998) is shown to have its dual representation in the profit function. The directional distance function treats outputs and inputs as endogenous and so, is consistent with the economic objective of profit maximization. The dual relation between the directional distance function and the profit function was the basis of Chapter 2. The primal approach using the input distance function, where one is interested in reducing input usage while keeping outputs fixed, is employed in Chapters 4 and 5. In these chapters, we exploit the duality between the input distance function and the cost function to examine economies of scope and the efficiency and interdependency of specific inputs, respectively.

94

A producer has three non-exclusive ways to increase competitiveness: decrease production costs; increase market share; and adjust the prices to the state of the market (Dolgui and Proth, 2010). Whereas decreasing production costs is achieved by the improvement of technical, scale and allocative efficiency, maximising output prices (i.e. a pricing strategy) is achieved by improving marketing efficiency. Additionally, from the farm management perspective, producers are involved in three basic activities: production, marketing and investment (i.e. financial activities) (Kay et al. 2008, p. 42). However, in developing countries, including Benin, the investment activities in the agricultural sector (mainly for small scale farmers) are problematic due to the lack of a financial market. In this thesis, as we do not have data on farms’ investment activities, the analysis related to investment activities is ignored. The outcome is that producers need not only decide how much to produce and how much inputs to use, but also at what price to sell the output. In other words, producers must optimize both their productive and marketing performance. Thus, an integrated microeconomic framework was developed in Chapter 3 to assess the efficiency with which vegetable producers allocate their resources to production and marketing activities. Therefore, output prices are no longer exogenous, but the outcome of producers’ marketing efforts and skills.

Chapter 4 extended the analysis to horizontal crop diversification (mainly for small- scale producers). By diversifying, farmers can benefit from economies of scope (or cost complementarities) that are associated with the use of inputs common to a number of production processes. Besides this, diversification requires giving up the benefits of specializing in one enterprise, like scale economies. Hence, the direction in which diversification affects producer performance is not clear. The stochastic production frontier forms the basis for analyzing the direct and indirect impact of vegetable crops diversification on producer performance. The objective in this chapter, from a theoretical perspective, is to develop a model for measuring economies of scope and technical efficiency from the primal perspective.

Another issue is the role of some inputs in the production process from an agronomic point of view. Most importantly, pesticides are a damage control input rather than a productive input (labor, fertilizers, capital and other materials). In fact, pesticides are used to reduce damage rather than increasing output directly. This agronomic fact is the core of Chapter 5 that examines the efficient use of pesticides in vegetable production, both technically and allocativelly.

95 6.2.2. Methodological Issues

This section discusses the methodological issues in the empirical applications of Chapters 2-5. The first issue is the level of aggregation of outputs. By incorrectly treating vegetable production as a homogenous product, estimation of efficiency may be biased and policy conclusions likely in error. One approach to allow flexibility in the assumptions is the use of a multiproduct technology. In this thesis, we do allow for the multi-output technology, but there are several limitations for adding more outputs (see Chapters 3, 4 and 5). Increasing the number of outputs may lead to the occurrence of zero values, as the likelihood of a farm not producing a particular output increases. That is problematic in non-parametric applications. It also results in a situation where many farms will be located at the frontier.

The second issue is the choice between parametric econometric techniques and non- parametric mathematical programming techniques for measuring efficiency. Developments in comparing both techniques concluded that the overall results drawn by the two approaches are similar (Greene, 2008, p. 114). Consequently, the objective of the study and the data available are the main criteria one can use to make a choice. In Chapters 2, 3 and 5 of this thesis, we use the non-parametric data envelopment analysis (DEA) technique since the primary objective in these chapters was to estimate different efficiency measures (technical, allocative, scale, output, input and marketing) in the case of a multiple output technology. In Chapter 4, the parametric stochastic frontier approach is used because the objective of this chapter was to estimate not only technical efficiency and scale economies but also to assess the presence or absence of economies of scope. Therefore, in Chapter 4, the characteristics of the production function is of particular interest.

When dealing with the non-parametric DEA, one has a choice between radial and non- radial measures of efficiency. The non-radial models are useful in situations where both inputs and outputs are controllable and we seek their improvement. For instance, they reflect the potential for improvement in desired input and output directions. In Chapters 2 and 3, the directional distance function and its dual profit function (Chambers et al. 1996 and 1998) form the basis for the analysis of technical, scale and allocative efficiency. Specifically, in Chapter 2 the directional distance function allows for measuring output and input technical inefficiency of lowland farming. In the context where the same resources are used in the production of outputs and in marketing outputs, a Russell-type efficiency measure is appropriate. The Russell efficiency measure allows for non-proportional increases in output quantity and output price, allowing for different scores of technical and marketing efficiency.

96

In Chapter 3, the Russell-type measure is used to derive technical and marketing inefficiency of vegetable producers. Also, in Chapter 5, the Russell-type measure is employed to measure different technical efficiency scores of productive inputs and damage abatement inputs.

Although the non-parametric efficiency analysis is appealing in many ways, the fundamental practical problem is that any measurement error and any other outcome of stochastic variation is embedded in the inefficiency estimates. In any sample, a single extreme observation can have profound effects on the estimates. Hence, it is important to find an appropriate method to deal with the stochastic nature of production and sampling process. In Chapter 5, the homogenous smooth bootstrap technique developed by Simar and Wilson (1998 and 2000) was used to provide statistical inference for the technical efficiency scores. For the directional distance function, the implementation of the bootstrap technique is very complex and not yet well developed. In Chapter 3, therefore, we rely on outlier detection techniques to examine the sensitivity of the technical and marketing inefficiency estimates.

In Chapter 4, we analyzed scale economies, economies of scope and the direct effect of vegetable crop specialization on technical efficiency. In a multiple-output production technology, the effects of specialization on technical efficiency may be related to input use, indicating that the effect of crop composition on technical efficiency is non-neutral. The non- neutral frontier assumes that the method of application of inputs and the level of inputs (i.e. scale of operation) determine the potential output level. The model developed in this chapter allows for computing a primal measure of economies of scope and for determining the impact of specialization on technical efficiency.

Moreover, in all efficiency analysis frameworks, it is attractive to separate factors that can be controlled by producers and those that producers cannot control, i.e. exogenous variables. To that end, appropriate models for incorporating exogenous variables are needed. In the case of the stochastic frontier analysis (SFA), the one-step method that estimates the frontier and the relationship of technical inefficiency to exogenous variables is shown by Schmidt (2011) to be consistent. Chapter 4 dealt with this issue and used a flexible production functional form and a modified non-neutral method to investigate the impact of specialization on vegetable producers’ performance. The two-stage approach is shown to be valid in the case of the non-parametric DEA approach. The potentially serious problem that DEA efficiency estimates are serially correlated is addressed by using a truncated bootstrap technique (see Chapters 2 & 3).

97