Asymptotic Approximations in Semiparametric and Separable Nonparametric Models

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9730282 Linton One of the areas in which econometrics has made great advances during the last fifteen years is semi-parametric estimation. These new classes of estimators are able to efficiently estimate the parameters of a wide array of non-linear models, such as tobit and probit models, with only very minimal information about such things as the error generation process or the function form of any regression functions. This grant renews support for research on a major problem with semi-parametric estimators. The problem is that the first-order approximations to the asymptotic distributions of these estimators provide poor approximations to their sampling behavior for the sample sizes that are typical in applied economic research. The previous grant developed more accurate formulas for the asymptotic distribution of a wide class of parametric and semi-parametric estimators and test statistics. This project continues this work on: (1)semi-parametric instrumental variable estimators and test statistics; (2) semi-parametric binary choice models; (3) adaptive estimation of linear regression; and (4) specification tests of parametric null against non-parametric alternatives. Computing these estimators typically requires selection of a smoothing parameter called the bandwidth. The new expansions developed provide bandwidth selection methods that are second order optimal. This grant also provides non-parametric methods that circumvent the curse of dimensionality and hence provide flexible but reliable methods. The basic model is additive non-parametric regression for which a number of new methods have recently been proposed. This grant develops a new method which seems to resolve most of the problems with previous methods. In particular, it only involves one-dimensional smoothing operations and so is completely free from the curse of dimensionality. At the same time it is efficient and computationally tractable. Asymptotic normality has been established. The practical performanc e of this method will be addressed. The method will be extended to more general models that allow for some parametric components and to more general types of separability. The project also investigators separability tests. ??