On the Choice of Functional Form in Stochastic Frontiers Models: A Box-Cox Approach

On the Choice of Functional Form in Stochastic Frontiers Models: A Box-Cox Approach

The generalized quadratic Box-Cox transformation is used to test the relative performance of alternative, widely used, functional forms and to examine the effect of prior choice on final efficiency estimates.

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Published in: Empirical Economics

The stochastic production frontier model, which was proposed independently by Aigner, Lovell and Schmidt and Meeusen and van den Broeck in 1977, has dominated the empirical literature of efficiency measurement. Within this framework, several alternative models for estimating productive efficiency have been progressively developed, extending the stochastic production frontier methodology to account for different theoretical issues in frontier modeling. Comparative studies to date have mainly focused on estimates of the degree of inefficiency in the samples under study within different production frontier model specifications (for detailed reviews of the theoretical and empirical work in this area see Coelli, Rao and Battese (1998), Greene (1999), and Kumbhakar and Lovell (2000)).

Apart from the choice of the appropriate production frontier model however, an important issue that arises, which is not unique to efficiency studies, concerns the functional specification of the estimated frontier - the features of the technology employed. Interestingly, empirical applications for the measurement of efficiency have traditionally focused on a single ad hoc imposed functional specification, mostly translog and Cobb-Douglas.

The choice of the appropriate functional form is not a trivial matter however. It is well known that functional forms are both data and model specific, and differ in their convergence properties and their ability to approximate alternative technologies. Simply put, there is no functional form that dominates under all circumstances - the appropriate functional specification is case specific. If the empirical estimates are contaminated with the imposition of an inappropriate functional form, predicted responses arising from the model may be biased and inaccurate, posing serious problems for policy design and/or policy implications. Therefore, when there are no strong theoretical or prior empirical reasons in favor of a specific functional specification, the exploration of the sensitivity of the economic optima, including efficiency, to the choice of functional form becomes crucial.

The objective of this study is to empirically evaluate the performance of different functional specifications in the estimation of technical efficiency for a panel data set of 125 olive-growing farms in Greece. The paper explores the sensitivity of obtained efficiency estimates to the choice of functional specification while maintaining an identical data set and retaining the same assumptions about the underlying technology and the structure of farm efficiencies. The effects of the choice of functional form on the estimates of production structure (such as production elasticities, returns to scale, and technological change) and the determination of the factors influencing farm efficiency are also examined. The latter is particularly important since determining the sources of technical efficiency provides policy makers with insight on the causes of inefficiency and can suggest potential policies that enhance the productivity of the sector under study. 

The estimation of farm-specific technical efficiency is based on the stochastic frontier model of Battese and Coelli (1993; 1995). This stochastic frontier model allows for a more flexible intertemporal variation in efficiency ratings, and identifies the factors influencing the efficiency of sample participants directly from the estimated production frontier. The production frontiers utilized in this comparative study belong primarily to the generalized quadratic family of flexible functional forms. More specifically, technical efficiency measures obtained from the transcendental logarithmic, the generalized Leontief, the normalized quadratic, the squared-root quadratic, the non-homothetic constant elasticity of substitution (CES) and the Cobb-Douglas functional forms are analyzed and compared using the generalized quadratic Box-Cox transformation function that nests all these functional specifications (Appelbaum, 1979; Berndt and Khaled, 1979). In addition to the above functional forms, the comparative analysis includes the minflex Laurent translog and generalized Leontief functional specifications due to their attractive properties in approximating the production technology (Barnett, 1983; 1985). 

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