A branch-and-bound algorithm for instrumental variable quantile regression

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Mathematical Programming Computation, ISSN: 1867-2957, Vol: 9, Issue: 4, Page: 471-497

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Guanglin Xu; Samuel Burer
Springer Nature
Mathematics; Computer Science
article description
This paper studies a statistical problem called instrumental variable quantile regression (IVQR). We model IVQR as a convex quadratic program with complementarity constraints and—although this type of program is generally NP-hard—we develop a branch-and-bound algorithm to solve it globally. We also derive bounds on key variables in the problem, which are valid asymptotically for increasing sample size. We compare our method with two well known global solvers, one of which requires the computed bounds. On random instances, our algorithm performs well in terms of both speed and robustness.