Estimating misspecified moment inequality models

Abstract

This chapter studies partially identified structures defined by a finite number of moment inequalities. When the moment function is misspecified, it becomes difficult to interpret the conventional identified set. Even more seriously, this can be an empty set. We define a pseudo-true identified set whose elements can be interpreted as the least-squares projections of the moment functions that are observationally equivalent to the true moment function. We then construct a set estimator for the pseudo-true identified set and establish its OP (n-1/2) rate of convergence.