Nonparametric estimates of price efficiency for the Greek infant milk market: Curing the curse of dimensionality with shannon entropy

Despite the continuous promotion of breastfeeding by the World Health Organization and national health systems, the consumption of breast milk substitutes (BMS) is increasing. Several BMS brands in the market have varying prices and attributes (i.e., energy, protein, vitamins, minerals, etc.). Using data from Greece, we examine which of these are “value for money” choices and which are overpriced relative to their number of attributes. For this purpose, we estimate their price efficiency using data envelopment analysis, where the discrimination power hinges on the curse of dimensionality. To cope with this, we propose a novel use of Shannon's entropy for pre-aggregating vitamin and mineral items. Our empirical results indicate that most of the considered brands are overpriced relative to their number of attributes. This result is more severe for the infant formulae brands than the follow-on formulae, the growing-up milk brands, and brands with higher prices.