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

Guanglin Xu, Samuel Burer

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)471-497
Number of pages27
JournalMathematical Programming Computation
Issue number4
StatePublished - Dec 1 2017

Bibliographical note

Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg and The Mathematical Programming Society.


  • Branch-and-bound
  • Complementarity constraints
  • Convex quadratic programming
  • Quantile regression


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