Self-Dual Stochastic Production Frontiers and Decomposition of Output Growth: The Case of Olive Growing Farms in Greece

Self-Dual Stochastic Production Frontiers and Decomposition of Output Growth: The Case of Olive Growing Farms in Greece

This paper provides a decomposition of output growth among olive-growing farms in Greece during the period 1987-1993 by integrating Bauer’s (1990) and Bravo-Ureta and Rieger’s (1991) approaches.

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Several recent studies (i.e., Fan, 1991; Ahmad and Bravo-Ureta, 1995; Wu, 1995; Kalirajan et al., 1996; Kalirajan and Shand, 1997) have attempted to explain and to identify the sources of output growth in agriculture.  By using a production function approach, they have attributed output growth into the size effect (input growth), technical change, and improvements in technical efficiency.  In this framework is however assumed implicitly that technical change and changes in technical efficiency consist the only components of total factor productivity (TFP) changes.  Nevertheless, in a purely theoretical ground, returns to scale and allocative efficiency may also be significant sources of TFP growth and consequently, of output expansion.  Bauer (1990) has provided such a decomposition of TFP changes within a cost function framework.

 There are empirical evidence (e.g., Park and Kwon, 1995) that scale economies stimulate output growth even in the absence of technical change and improvements in technical efficiency as long as input use increases.  Analogously, diseconomies of scale could slowdown output growth under similar circumstances, which is more likely to be the case for agriculture.  The scale effect can correctly be omitted in the decomposition of TFP growth only in the case of constant returns to scale (Lovell, 1996).  Since the range of scale economies is not known a priori, it seems appropriate to proceed by statistically testing the hypothesis of constant returns to scale.  If this hypothesis is rejected, the scale effect is present and should be taken into account.  Its relative contribution to output growth depends on both the magnitude of scale economies and the rate of input growth.

On the other hand, output gains may also be obtained by improving allocative efficiency.  As noticed by Bravo-Ureta and Rieger (1991), focusing only on technical efficiency understates the benefits that could be derived by individual producers from improvements in overall performance.  However, in highly protected sector, such as agriculture, allocative inefficiency tends to be an important source of TFP slowdown (Fulginiti and Perrin, 1993; Kalaitzandonakis, 1994).  Nevertheless, in the presence of price support schemes, the improvement of allocative efficiency provides an additional incentive for output increases.  The magnitude of allocative efficiency and the relative contribution of its improvement on output growth remain an open empirical question.

The theoretical framework employed in previously mentioned studies on output growth decomposition analysis cannot incorporate accurately the effects of returns to scale and of allocative inefficiency.  In particular, Lovell (1996) has shown that in a production function framework, the effects of scale economies and of allocative inefficiency on TFP changes cannot be separated from each other even if there are available information on input prices.  Indeed, the effect of returns to scale can only be identified if allocative efficiency is assumed, and this case there is no need for input price data.  Then, output growth may be attributed to input growth, technical change, improvements in technical efficiency, and the effect of scale economies.  In contrast, the effect of allocative inefficiency cannot be identified even if constant returns to scale are assumed.   This seems a serious shortcoming of the production function approach on output growth decomposition analysis.

The aim of this paper is to propose Bravo-Ureta and Rieger’s (1991) approach as an alternative to handle separately the effect of returns to scale and of allocative efficiency (along with input growth, technical change and technical efficiency) in output growth decomposition analysis and still relying on the econometric estimation of a production function frontier. The direct outcome of integrating properly Bauer’s (1990) and Bravo-Ureta and Rieger’s (1991) and approaches would be a complete and accurate analysis of the sources of output growth at the extra cost of information on input price data, which are necessary to identify the effect of allocative efficiency.  As an indirect result, it is shown that the opportunity cost of duality between production and cost frontier functions may be less severe than the maintenance of constant-returns-to-scale assumption suggested by Fare and Primont (1996).  That is, it may be the use of a self-dual production frontier that allows for variable returns to scale, but restricts input substitutability.     

In Bravo-Ureta and Rieger’s (1991) approach, the use of self-dual production frontier functions is important in deriving an analytical (closed form) solution for the corresponding cost frontier and in maintaining the distinction between technical and allocative efficiency.  This may restrict however the functional specification of the underlying frontier production functions.  In the present study, this shortcoming is partially overcame by using a generalized Cobb-Douglas (or quasi translog) frontier production function, proposed by Fan (1991).  This functional specification allows for variable returns to scale, input-biased technical change, and time varying production and substitution elasticities, but it restricts the latter to be unchanged over farms.  Nevertheless, it permits statistical tests for the hypotheses of zero rate of technical change and constant returns to scale.  Thus, this specification represents a reasonably flexible alternative (Fan and Pardey, 1997).

In addition, Bravo-Ureta and Rieger’s (1991) approach has two advantages. First, the resulting inefficiency measures are unbiased from statistical noise as the limiting assumption of the deterministic frontier models (namely, that any deviation from the frontier is attributed to inefficiency), used initially by Kopp and Diewert (1982), is not anymore employed.  Instead, a composed error term is used to account for both statistical noise and efficiency disturbances.  Second, it enables the simultaneous derivation of (input-oriented) technical, allocative, and productive efficiency measures based solely on the econometric estimation of a production frontier function by using a single-equation procedure, under the expected profit maximization hypothesis.  Notice that this was also a maintained hypothesis in previous output growth decomposition studies of Fan (1991), Ahmad and Bravo-Ureta (1995), Wu (1995), Kalirajan et al. (1996), and Kalirajan and Shand (1997).

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