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.
Additive regression, Endogeneity, Generated regressors, Oracle estimation, Structural equation
Econometrics | Economics
Journal of Business and Economic Statistics
Taylor and Francis
OZABACI, Deniz; HENDERSON, Daniel J.; and SU, Liangjun.
Additive nonparametric regression in the presence of endogenous regressors. (2014). Journal of Business and Economic Statistics. 32, (4), 555-575. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/1634
Copyright Owner and License
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.