Contemporary Relevance and Ongoing Controversies Related to the CES Production Function

The CES specification has been an important watershed in the development of the production function and its applications over the past fifty years. While the original formulation and estimation were rooted in sound economic theory many issues have been unresolved. In particular, the economic sources of the elasticity of substitution and the meaning of the ``returns to scale'' parameter remained ambiguous. Similarly, the efficient method of estimating the elasticity of substitution is as yet not clear. The primary reason is that several proposed methods of estimating the non-linear CES function did not pay attention to the economic decision processes underlying the observed choices from which estimation begins. Despite these shortcomings substitution and its applications have been so important that a whole lot of applications have been conceptualized. Several important insights have been recorded from the empirical work. However, it was found that the elasticity of substitution concept must be supplemented, or supplanted altogether, by several other explanations, equally rooted in economic theory and well documented empirical regularities, to provide a complete understanding of empirical phenomena. We may need many more years to finally decide which of the developments are worthwhile and which ones deserve discarding. It may take another genius of the stature of Minhas to steer the research out its current turbulence.