Additive nonparametric regression in the presence of endogenous regressors

In this article we consider nonparametric estimation of a structural equation model under full additivity constraint. We propose estimators for both the conditional mean and gradient which are consistent, asymptotically normal, oracle efficient, and free from the curse of dimensionality. Monte Carlo...

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Bibliographic Details
Main Authors: OZABACI, Deniz, HENDERSON, Daniel J., SU, Liangjun
Format: text
Language:English
Published: Institutional Knowledge at Singapore Management University 2014
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Online Access:https://ink.library.smu.edu.sg/soe_research/1634
https://ink.library.smu.edu.sg/context/soe_research/article/2633/viewcontent/AdditiveNonParametricRegressorsEndogenous.pdf
https://ink.library.smu.edu.sg/context/soe_research/article/2633/filename/0/type/additional/viewcontent/UBES_A_917590_Supplement.pdf
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Institution: Singapore Management University
Language: English
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Summary:In this article we consider nonparametric estimation of a structural equation model under full additivity constraint. We propose estimators for both the conditional mean and gradient which are consistent, asymptotically normal, oracle efficient, and free from the curse of dimensionality. Monte Carlo simulations support the asymptotic developments. We employ a partially linear extension of our model to study the relationship between child care and cognitive outcomes. Some of our (average) results are consistent with the literature (e.g., negative returns to child care when mothers have higher levels of education). However, as our estimators allow for heterogeneity both across and within groups, we are able to contradict many findings in the literature (e.g., we do not find any significant differences in returns between boys and girls or for formal versus informal child care). Supplementary materials for this article are available online.