Premium
Bounding endogenous regressor coefficients using moment inequalities and generalized instruments
Author(s) -
Choi Jinyoung,
Lee Myoungjae
Publication year - 2012
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2011.00501.x
Subject(s) - endogeneity , instrumental variable , estimator , bounding overwatch , mathematics , upper and lower bounds , moment (physics) , sign (mathematics) , variable (mathematics) , econometrics , regression , statistics , constant (computer programming) , computer science , mathematical analysis , classical mechanics , artificial intelligence , physics , programming language
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.