This chapter reviews recent advances in nonparametric and semiparametric estimation,
with an emphasis on applicability to empirical research and on resolving issues that arise
in implementation. It considers techniques for estimating densities, conditional mean
functions, derivatives of functions and conditional quantiles in a flexible way that
imposes minimal functional form assumptions.
The chapter begins by illustrating how flexible modeling methods have been applied in
empirical research, drawing on recent examples of applications from labor economics,
consumer demand estimation and treatment effects models. Then, key concepts in
semiparametric and nonparametric modeling are introduced that do not have counterparts
in parametric modeling, such as the so-called curse of dimensionality, the notion of
models with an infinite number of parameters, the criteria used to define optimal
convergence rates, and "dimension-free" estimators. After defining these new concepts,
a large literature on nonparametric estimation is reviewed and a unifying framework
presented for thinking about how different approaches relate to one another. Local
polynomial estimators are discussed in detail and their distribution theory is developed.
The chapter then shows how nonparametric estimators form the building blocks for many
semiparametric estimators, such as estimators for average derivatives, index models,
partially linear models, and additively separable models. Semiparametric methods offer
a middle ground between fully nonparametric and parametric approaches. Their main
advantage is that they typically achieve faster rates of convergence than fully
nonparametric approaches. In many cases, they converge at the parametric rate.
The second part of the chapter considers in detail two issues that are central with regard
to implementing flexible modeling methods: how to select the values of smoothing
parameters in an optimal way and how to implement "trimming" procedures. It also
reviews newly developed techniques for deriving the distribution theory of
semiparametric estimators. The chapter concludes with an overview of approximation
methods that speed up the computation of nonparametric estimates and make flexible
estimation feasible even in very large size samples.
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