Semiparametric estimators are used intensively in applied work as a way of avoiding detailed assumptions on model specifications and as a way of avoiding difficult computational problems. The contribution of this project comes from developing a general asymptotic theory for semiparametric estimators, investigating methods for nonparametric estimation of structural equation models, and using nonparametric estimators of consumer surplus for an empirical analysis of gasoline demand. Knowledge of the asymptotic variance of an estimator is important for large sample inference, efficiency, and as a guide to the specification of regularity conditions. This research develops a general formula with a relatively simple set of regularity conditions for the asymptotic variance of semiparametric estimators. This is an important contribution because at present asymptotic variance calculations for semiparametric estimators are model specific and usually involve a great deal of tedious detail. This project will make semiparametric estimators much easier to use. Nonparametric estimators have gained wide attention in the past few years in econometrics because they impose even fewer restrictions than semiparametric estimators. But nonparametric models are difficult to interpret and their usefulness in applied research has been demonstrated in a limited number of cases. This project applies nonparametric regression models to estimation of demand curves of the types most often used in applied research. Estimators of exact consumer surplus and deadweight loss will be derived from the demand curve estimators. The research includes an application to gasoline demand. This represents an important contribution because estimators of consumer surplus and deadweight loss are the most widely used welfare measures in applied areas of economics such as public finance. The results from the empirical research will provide new insights into the magnitude of welfare loss from carbon taxes that are currently being considered as one of the policy tools for reducing emissions of greenhouse gases.
