Nonparametric, Semiparametric, and Bootstrap Methods in Econometrics

本项目包括三个具有广泛经验应用潜力的课题的研究：参数模型与非参数备选方案的检验，具有未观测异质性的比例风险模型的半参数估计，以及由时间序列估计的计量经济模型的Bootstrap方法。所有这些都建立在调查员之前的工作基础上。第一个主题涉及测试一个(可能是向量值的)条件矩或四分位函数的参数模型与非参数替代方案的对比。这项研究将开发与光滑、非参数替代模型一致一致的测试，这些替代模型与参数模型的距离随着样本量的增加以尽可能快的速度收敛到零。还将开发不需要对替代模型的平稳性先验知识的测试。这些性质在功率方面提供了重要的实际好处，新的研究将为更一般的参数模型和基于时间序列数据的模型开发测试。第二个主题涉及估计具有未观察到的异质性的比例风险模型。基线风险函数和未观察到的异质性的分布都不会被假定为属于已知的有限维参数函数族。他们将得到非参数治疗。研究将特别集中于面板数据的固定效应模型、具有在咒语中随时间变化的协变量的模型，以及其中未观察到的异质性是异方差的未知形式的横截面模型。所有模型都与应用研究相关。第三个主题是关于使用相依数据通过广义矩方法(GMM)估计的关于有限维参数的假设的检验。由于一阶近似与应用中发现的样本大小可能非常不准确，因此当临界值基于一阶渐近近似时，检验拒绝正确零假设的真实概率和名义概率可能会非常不同。同样，基于一阶近似的置信度区间的真实覆盖概率和名义覆盖概率可以非常不同。块Bootstrap提供了一种获得相关数据的改进近似的方法，但最近的研究表明，改进的量并不大。这项新的研究将探索筛子自举的使用，其中数据生成过程由有限维参数模型的扩展序列来近似，并且自举样本是通过模拟从筛子近似生成的。在比GMM估计和测试简单得多的设置中，已经发现筛子自举比块自举提供了比一阶近似大得多的改进。这项新的研究将调查筛子引导程序的改进性能是否扩展到GMM在经济学中通常用于的测试和模型的类型。此外，研究还将调查筛子自举的迭代版本是否可以用于提供渐近精化，而不需要异方差和自相关相容(MAC)协方差矩阵估计。

This project consists of research on three topics with wide potential empirical application: testing parametric models against nonparametric alternatives, Semiparametric estimation of proportional hazard models with unobserved heterogeneity, and bootstrap methods for econometric models estimated from time series. All build on prior work by the investigator. The first topic is concerned with testing a parametric model of a (possibly vector valued) conditional moment or quartile function against a nonparametric alternative. The research will develop tests that are uniformly consistent over smooth, nonparametric alternative models whose distance from the parametric model converges to zero at the fastest possible rate as the sample size increases. Tests which do not require a priori knowledge of the smoothness of the alternative model will also be developed. These properties provide important practical benefits in terms of power, and the new research will develop tests for more general parametric models and for models based on time-series data. The second topic is concerned with estimating proportional hazard models with unobserved heterogeneity. Neither the baseline hazard function nor the distribution of the unobserved heterogeneity will be assumed to belong to a known, finite-dimensional parametric family of functions. They will be treated nonparametrically. The research will focus particularly on fixed-effects models for panel data, models with covariates that are time varying within spells, and cross-sectional models in which the unobserved heterogeneity is an unknown form of heteroskedasticity. All of the models are relevant to applied research. The third topic is concerned with testing hypotheses about a finite-dimensional parameter that is estimated by the generalized method of moments (GMM) using dependent data. Since first-order approximations can be very inaccurate with the sample sizes found in applications, the true and nominal probabilities that a test rejects a correct null hypothesis can be very different when critical values are based on first-order asymptotic approximations. Similarly, the true and nominal coverage probabilities of confidence intervals based on first-order approximations can be very different. The block bootstrap provides a way to obtain improved approximations with dependent data, but recent research has shown that the amount of improvement is not large. The new research will investigate the use of the sieve bootstrap in which the data generation process is approximated by an expanding sequence of finite-dimensional parametric models, and bootstrap samples are generated by simulation from the sieve approximation. In settings much simpler than those of GMM estimation and testing, it has been found that the sieve bootstrap provides a substantially greater improvement over first-order approximations than does the block bootstrap. The new research will investigate whether the improved performance of the sieve bootstrap extends to the kinds of tests and models to which for which GMM is typically used in economics. In addition, the research will investigate whether iterated versions of the sieve bootstrap can be used to provide asymptotic refinements without the need for heteroskedasticity and autocorrelation consistent (MAC) covariance matrix estimation.