In the stochastic frontier model we extend the multivariate probability statements of Horrace (2005) to calculate the conditional probability that a firm is any particular efficiency rank in the sample. From this we construct the conditional expected efficiency rank for each firm. Compared to...

We use order statistics to analytically derive demand functions when consumers choose from among the varieties of two brands—such as Coke and Pepsi—and an outside good. Soft-drinks have no price variability across varieties within a brand, so traditional demand systems (e.g., mixed logit)...