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.
