This paper studies the problem of specification testing in partially indentified models defined by a finite number of moment equalities and inequalities (i.e., (in)equalities). Under the null hypothesis, there is at least one parameter value that simultaneously satisfies all of the moment...

In parametric models a sufficient condition for local idenfication is that the vector of moment is differentiable at the true parameter with full rank derivative matrix. This paper shows that additional conditions are often needed in nonlinear, nonparametric models to avoid nonlinearities...