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There is a widely held general belief that competition, a driving force behind numerous important policy changes, exerts downward pressure on costs, reduces slacks, provides incentives for the efficient organization of production, and even drives innovation forward. To analyze the performance of firms, the concept of productivity growth has been widely used in the literature, and the sources of this growth are largely due to contributions from either scale economies (returns to scale)1 or technical change or both2.
The returns to scale (RTS) property of a production function is regularly used to describe the relationship between scale and efficiency. As for terminology: Constant RTS are said to prevail at a point on the production frontier if an increase of all inputs by 1% leads to an increase of all outputs by 1%. Decreasing RTS are present if outputs increase by less than 1%, while increasing RTS exist if they increase by more than 1%.
An appropriate estimation strategy for the underlying production (technology) structure is essential in understanding RTS characteristics of firms. We find in the literature (Färe et al., 1988) that there are two approaches to the estimation of RTS: the neoclassical approach and the axiomatic approach. The former (usually estimated with some parametric econometric technique) gives one a quantitative measure of RTS, whereas the latter approach (to be estimated in a nonparametric fashion via data envelopment analysis (DEA))3 yields both qualitative and quantitative information about RTS. The latter is been researched in many studies (Førsund, 1996; Banker et al., 1996; Sueyoshi, 1997; Fukuyama, 2000, 2001, 2003; Førsund & Hjalmarsson, 2004; Tone & Sahoo, 2004, 2005, 2006; Hadjicostas & Soteriou, 2006; Førsund et al., 2007; Sueyoshi & Sekitani, 2007a, 2007b; Podinovski et al., 2008)4. However, both methods have become important analytical tools in the empirical evaluation of RTS.
Note that all standard methods of determining RTS proceed by examining tangential planes to the frontier that can be drawn through a given point. This is done either by looking at the constant term (the variable originally introduced in the literature by Banker et al., 1984) that represents the intercept of that plane with the plane in which all inputs are set to zero or, by observing the weights of the corner points of the facet of the frontier associated with that plane. This determination, however, may be difficult because the plane need not be unique. In this study we will, therefore, deal with both the lower and upper bounds of RTS.