Much empirical research in the social sciences is concerned with estimating conditional mean functions. The most frequently used estimation methods assume that the conditional mean function is known up to a set of constant parameters that can be estimated from data. Such methods are called parametric. Their use greatly simplifies estimation and inference but is rarely justified by theoretical or other a priori considerations. Estimation and inference based on convenient but incorrect assumptions about the form of the conditional mean function can be highly misleading. Semiparametric methods reduce the strength of the assumptions required for estimation and inference, thereby reducing the opportunities for obtaining misleading results. In addition, semiparametric methods mitigate certain disadvantages of fully nonparametric methods that make no assumptions about the shape of the conditional mean function. This article describes three important semiparametric models for conditional mean functions. These are single index, partially additive, and additive models. These models are compared with parametric and fully nonparametric models. An example based on real data illustrates the pitfalls of parametric models and the advantages of semiparametric ones.
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