 # Semiparametric Regression for the Applied Econometrician

## Synopsis

This book provides an accessible collection of techniques for analyzing nonparametric and semiparametric regression models. Worked examples include estimation of Engel curves and equivalence scales, scale economies, semiparametric Cobb-Douglas, translog and CES cost functions, household gasoline consumption, hedonic housing prices, option prices and state price density estimation. The book should be of interest to a broad range of economists including those working in industrial organization, labor, development, urban, energy and financial economics. A variety of testing procedures are covered including simple goodness of fit tests and residual regression tests. These procedures can be used to test hypotheses such as parametric and semiparametric specifications, significance, monotonicity and additive separability. Other topics include endogeneity of parametric and nonparametric effects, as well as heteroskedasticity and autocorrelation in the residuals. Bootstrap procedures are provided.

## Excerpt

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 allow greater 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 . 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 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).

Chapter 2 describes the broad contours of nonparametric and semiparametric regression modeling, the categorization of models, the “curse of dimensionality,” and basic theoretical results.

Chapters 3 and 4 are devoted to smoothing and differencing, respectively. the techniques are reinforced by empirical examples on Engel curves, gasoline demand, the effect of weather on electricity demand, and semiparametric translog and ces cost function models. Methods that incorporate heteroskedasticity, autocorrelation, and endogeneity of right-hand-side variables are included.

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