Inference Based on Continuous Linear Inequalities via Semi-Infinite Programming

Abstract

I develop a consistent, asymptotically normal estimator of bounds on functions of parameters partially identified by the intersection of continuous linear inequalities. The inference strategy uses results from the semi-infinite programming literature to form a convenient estimator. Aside from allowing for continuous constraints, an advantage of the estimator is that it can be used to compute a closed form confidence interval, without numerically inverting a hypothesis test. So it is easy to compute confidence intervals even if the number of parameters is very large, especially when we are interested in a linear function of parameters. I also consider the dual problem of bounding a linear function of a sequence, an infinite dimensional parameter, partially identified by finitely many linear restrictions on the sequence.

Keywords: Bounds estimation, continuous linear inequalities, monotone instrumental variables, inference on semi-infinite linear programs, consistent estimator of the value of semi-infinite programs

JEL Classification: C12