Stable matchings may fail to exist in the roommate matching problem, both when utility is transferable and when it is not. We show that when utility is transferable, the existence of a stable matching is restored when there is an even number of individuals of indistinguishable characteristics...

Many modern estimation methods in econometrics approximate an objective function, for instance, through simulation or discretization. These approximations typically affect both bias and variance of the resulting estimator. We provide a higher-order expansion of such 'approximate' estimators that...