### Abstract

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 language | English |
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Pages (from-to) | 161-182 |

Number of pages | 22 |

Journal | Statistica Neerlandica |

Volume | 66 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 May 1 |

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### Keywords

- Bounding parameters
- Generalized instrument
- Moment inequalities

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty