Semiparametric and Nonparametric Estimation off Structural Models

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The project will develop new methods for estimating the parameters of nonlinear econometric models using semiparametric or nonparametric approaches. Work on three broad lines of research will be undertaken. First, estimation of parameters of linear models subject to sample selection will be considered under a weak nonparametric restriction on the form of the selection correction. Specifically, the selection effect will be assumed to depend only on the conditional mean of some observable selection variable, which is to be estimated using a nonparametric regression method; this estimate will appear in the second-step estimator for the parameters of interest. Second, nonparametric estimation of structural equations using instrumental variables will be investigated. This will involve nonparametric estimation of solutions of integral equations, as well as nonparametric estimation of additive regression models with preliminary nonparametric estimates of regressors. Third, a bound for the attainable efficiency of estimators for monotonic regression models will be derived when the error distribution satisfies a single conditional quantile restriction. Also, a feasible estimation procedure which attains this bound will be developed. This line of research will continue to push the frontier of semiparametric and nonparametric estimation in econometrics. These methods will be extremely beneficial in the development of economic modelling, as more flexible assumptions are allowed and provide benchmarks for traditional estimation techniques.