Large Sample Sieve Estimation of Semi-Nonparametric Models∗

Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; semi-nonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method of sieves provides one way to tackle such complexities by optimizing an empirical criterion function over a sequence of approximating parameter spaces, called sieves, which are significantly less complex than the original parameter space. With different choices of criteria and sieves, the method of sieves is very flexible in estimating complicated econometric models. For example, it can simultaneously estimate the parametric and nonparametric components in semi-nonparametric models with or without constraints. It can easily incorporate prior information, often derived from economic theory, such as monotonicity, convexity, additivity, multiplicity, exclusion and non-negativity. This chapter describes estimation of semi-nonparametric econometric models via the method of sieves. We present some general results on the large sample properties of the sieve estimates, including consistency of the sieve extremum estimates, convergence rates of the sieve M-estimates, pointwise normality of series estimates of regression functions, root-n asymptotic normality and efficiency of sieve estimates of smooth functionals of infinite dimensional parameters. Examples are used to illustrate the general results.