Computing Moment Inequality Models Using Constrained Optimization

Inference for moment inequality models is computationally demanding and often involves time-consuming grid search. By exploiting the equivalent formulations between unconstrained and constrained optimization, we establish new ways to compute the identified set and its confidence set in moment inequality models which overcome some of these computational hurdles. In simulations, using both linear and nonlinear moment inequality models, we show that our methods significantly improve the solution quality and save considerable computing resources relative to conventional grid search. Our methods are user-friendly and can be implemented using a variety of canned software packages