Estimation of semiparametric models

A semiparametric model for observational data combines a parametric form for some component of the data generating process (usually the behavioral relation between the dependent and explanatory variables) with weak nonparametric restrictions on the remainder of the model (usually the distribution of the unobservable errors). This chapter surveys some of the recent literature on semiparametric methods, emphasizing microeconometric applications using limited dependent variable models. An introductory section defines semiparametric models more precisely and reviews the techniques used to derive the large-sample properties of the corresponding estimation methods. The next section describes a number of weak restrictions on error distributions -- conditional mean, conditional quantile, conditional symmetry, independence, and index restrictions -- and show how they can be used to derive identifying restrictions on the distributions of observables. This general discussion is followed by a survey of a number of specific estimators proposed for particular econometric models, and the chapter concludes with a brief account of applications of these methods in practice.