Bounding endogenous regressor coefficients using moment inequalities and generalized instruments

Jin Young Choi, Myoung Jae Lee

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The main approach to deal with regressor endogeneity is instrumental variable estimator (IVE), where an instrumental variable (IV) m is required to be uncorrelated to the regression model error term u (COR(m,u)=0) and correlated to the endogenous regressor. If COR(m,u)≠0 is likely, then m gets discarded. But even when COR(m,u)≠0, often one has a good idea on the sign of COR(m,u). This article shows how to make use of the sign information on COR(m,u) to obtain an one-sided bound on the endogenous regressor coefficient, calling m a 'generalized instrument' or 'generalized instrumental variable (GIV)'. If there are two GIV's m 1 and m 2, then a two-sided bound or an improved one-sided bound can be obtained. Our approach is simple, needing only IVE; no non-parametrics, nor any 'tuning constants'. Specifically, the usual IVE is carried out, and the only necessary modification is that the estimate for the endogenous regressor coefficient is interpreted as a lower/upper bound depending on the prior notion on the sign of COR(m,u) and some estimable moment. A real data application is done to Korean household data with two or more children to illustrate our approach for the issue of child quantity-quality trade-off.

Original languageEnglish
Pages (from-to)161-182
Number of pages22
JournalStatistica Neerlandica
Issue number2
Publication statusPublished - 2012 May


  • Bounding parameters
  • Generalized instrument
  • Moment inequalities

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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