Asymptotic Approximations in Parametric and Semiparametric Models

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SBR-9423102 Oliver 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 functional form of any regression functions. One problem with these estimators is that 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. This research develops more accurate formulas for the asymptotic distribution of a wide class of parametric and semi-parametric estimators and test statistics. There are three projects. The first project continues the principals investigator's work on second-order approximations of the asymptotic distribution of semi-parametric models. Computing these estimators typically requires the selection of a smoothing parameter, called the bandwidth. The new expansions developed under this grant provide bandwidth selection methods that are second order optimal. The second project develops asymptotic expansions for estimator and test statistics of parametric ARCH time series models. These new expansions are then used to provide bias and size correction procedures and to evaluate the magnitude of small sample effects in these complicated procedures. They also provide more accurate small sample approximations of the sampling distribution. The third project investigates a new class of semiparametric models for duration data and derives their first-order asymptotic theory.