Closed form solutions for the generalized extreme value distribution

This manuscript derives closed form solutions for conditional expectations of order statistics in models that are based on the extreme value and generalized extreme value distributions. Such conditional expectations are of interest in empirical anal-yses when the (identity of the) maximal statistic is observed, but the econometric model also relies on lower-rank order statistics which are unobserved. This is the case, for example, in some (sequential) bargaining models (e.g. Beckert, Smith and Takahashi (2015), for which this manuscript is a companion piece), or in empirical auctions models. The manuscript also provides an algorithm to derive the density of the GEV cumulative distribution function. This density is required to simulate nested logit models following the MCMC approach proposed by McFadden (1999)