Estimating elasticities of input substitution using data envelopment analysis

Abstract

The use of elasticities of substitution between inputs has become the standard method for addressing the effect of a change in the mix of input used for production from a technological or cost standpoint. (Chambers 1988) A researcher that wants to estimate this elasticity, or some other comparative static, typically would do so using parametric production or cost function (e.g. translog or normalized quadratic) with panel data. For a study with only cross-sectional data, the construction of such a function may be problematic. Using a dual approach, a nonparametric alternative in such a situation may be the use of Data Envelopment Analysis (DEA). Cooper et al. (2000) provided a methodology for estimating elasticities of substitution for the technical production problem using DEA. To our knowledge, this has not been extended to the cost efficiency problem, which would be equivalent to estimating Allen partial or Morishima elasticities of substitution between inputs using a cost function (or cost minimization framework). The purpose of this thesis is to show how elasticities of substitution can be derived and estimated for the technical production and cost (overall economic) efficiency DEA under variable returns to scale. In addition, an empirical example using Kansas Farm Management Association (KFMA) data is presented to illustrate the estimation of these elasticities. The results showed that input substitutability is relatively limited at the enterprise level