Applications of Nonparametric Methods in Econometrics

Yale University, New Haven CT

Investigators

Abstract

This project develops practical tools for goodness-of-fit testing of models subject to random censoring models subject to random censoring with specific reference to duration models, and proposes a new method of analyzing non-nested conditional models. The literature of duration analysis is econometrics is large and growing. While many flexible duration models have been developed in the literature to deal with important features of economic data, a large majority of empirical econometric studies employ parametric duration models. It is, therefore important to have convenient specification techniques tailored for applied economists. Many researchers use x2 tests that rely on arbitrary sample space splitting. Also, residual analysis is often employed to conduct informal graphical analysis. While these techniques are useful, general specification tests with sound statistical foundations are lacking. This research develops a Kolmogorov-Smirnov type goodness-of-fit test for parametric conditional survival functions. This test is easily modified to "concentrates" on model features of interest to the researcher. An alternative specification test for parametric hazard functions based on martingale residuals is investigated. It is common in applied econometrics to write a model conditional on some variables, with unspecified probability law of the conditioning variables. Choosing between different types of conditional models is an important issue since it occurs frequently in applied econometrics. If the two models are nested, many well-established methods are available. There are, however, many situations not covered by these conventional methods. Examples include: (1) comparison of a conditional mean restriction model and a conditional median restriction model, (2) comparison of conditional quantile restriction models for two different quantiles, (3) comparison of two non-nested conditional mean restriction models, and (4) comparison of a parametric likelihood model and a conditional mean/median restriction model. There are no generally acceptable methods of choosing between different models in these situations. The research offers a likelihood-based measure of model fit that enables the researcher to compare a broad range of conditional models in a unified manner. The key idea is to introduce "likelihood" for semiparametric models such as conditional mean restriction models and conditional quantile restriction models. The measure is then used to develop a likelihood ratio test for model comparison. Some practical issues for implementing the method are addressed. The proposed research will yield software for scientists from many disciplines to easily use the methods developed in this research.