Applications of Nonparametric Methods in Econometrics

本项目针对持续时间模型开发了随机审查模型的拟合优度检验实用工具，并提出了一种分析非嵌套条件模型的新方法。持续时间分析的文献是计量经济学的大量和不断增长。虽然文献中已经开发了许多灵活的持续时间模型来处理经济数据的重要特征，但绝大多数实证计量经济学研究采用参数持续时间模型。因此，为应用经济学家量身定制方便的规范技术是很重要的。许多研究人员使用依赖于任意样本空间分割的x2检验。此外，残差分析经常用于进行非正式的图形分析。虽然这些技术很有用，但缺乏具有可靠统计基础的通用规范测试。本文研究了参数条件生存函数的Kolmogorov-Smirnov型拟合优度检验。这个测试很容易修改为“集中”研究人员感兴趣的模型特征。研究了基于鞅残差的参数化危险函数的替代规范检验。在应用计量经济学中，通常编写一个以某些变量为条件的模型，而条件变量的概率律不确定。在不同类型的条件模型之间进行选择是一个重要的问题，因为它经常出现在应用计量经济学中。如果这两个模型是嵌套的，则可以使用许多成熟的方法。然而，有许多情况没有被这些传统方法所涵盖。示例包括：(1)条件均值约束模型与条件中位数约束模型的比较，(2)两个不同分位数的条件分位数约束模型的比较，(3)两个非嵌套条件均值约束模型的比较，(4)参数似然模型与条件均值/中位数约束模型的比较。在这些情况下，没有普遍可接受的方法来选择不同的模型。该研究提供了一种基于可能性的模型拟合度量，使研究人员能够以统一的方式比较广泛的条件模型。关键思想是为半参数模型（如条件均值限制模型和条件分位数限制模型）引入“似然”。然后使用该度量来开发模型比较的似然比检验。讨论了实现该方法的一些实际问题。拟议的研究将为来自许多学科的科学家提供软件，以便轻松使用本研究中开发的方法。

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.