Data aggregation in stochastic frontier models: the closed skew normal distribution

The effect of aggregation on estimates of stochastic frontier functions is considered. Inefficiency is assumed associated with the individual units being aggregated. In this case, the aggregated data have a closed skew normal distribution. Estimating the parameters of a closed skew normal distribution is difficult and so we focus mostly on the biases created by ignoring the fact that the data are aggregated. The conclusions are based on both analytical and Monte Carlo results. When data for firms are aggregates over smaller units and the inefficiency is associated with the units and not the firm, empirical work that does not consider the effect of aggregation will attribute the inefficiency of large firms to diseconomies of scale.