Introduction

Nonparametric estimation of regression models has gained wide attention in econometrics in the past few years. Nonparametric models are characterized by very large numbers of parameters. Often they may be difficult to interpret, and their usefulness in applied research has been demonstrated in a limited number of cases. We apply nonparametric regression models to estimation of demand curves of the type most often used in applied research. After estimation of the demand curves, we then derive estimates of exact consumer surplus and deadweight loss, which are the most widely used welfare and economic-efficiency measures in areas of economics such as public finance. We also work out asymptotic normal sampling theory for the nonparametric case, as well as the parametric case (where, except in certain analytic cases, the results are not known).

This study includes an application to gasoline demand. Empirical questions of interest here are the shape of the demand curve and the average magnitude of welfare loss from a tax on gasoline. In this application we compare parametric and nonparametric estimates of the demand curve, calculate exact measures of consumer surplus and deadweight loss, and give estimates of standard errors. We also analyze the sensitivity of the welfare measures to components of nonparametric regression estimators such as window width and number of terms in a series approximation.