This book has been largely motivated by pedagogical interests. Nonparametric and semiparametric regression models are widely studied by theoretical econometricians but are much underused by applied economists. In comparison with the linear regression model y = zβ + ε, semiparametric techniques are theoretically sophisticated and often require substantial programming experience.

Two natural extensions to the linear model that allowgreater flexibility are the partial linear model y = zβ + f (x) + ε, which adds a nonparametric function, and the index model y = f (zβ) + ε, which applies a nonparametric function to the linear index zβ. Together, these models and their variants comprise the most commonly used semiparametric specifications in the applied econometrics literature. A particularly appealing feature for economists is that these models permit the inclusion of multiple explanatory variables without succumbing to the “curse of dimensionality.”

We begin by describing the idea of differencing, which provides a simple way to analyze the partial linear model because it allows one to remove the nonparametric effect f(x) and to analyze the parametric portion of the model zβ as if the nonparametric portion were not there to begin with. Thus, one can draw not only on the reservoir of parametric human capital but one can also make use of existing software. By the end of the first chapter, the reader will be able to estimate the partial linear model and apply it to a real data set (the empirical example analyzes scale economies in electricity distribution using a semiparametric Cobb-Douglas specification).