Nonparametric, Semiparametric, and Bootstrap Methods in Econometrics

该项目包括三个主题的研究与广泛的潜在的实证应用：测试参数模型对非参数的替代品，半参数估计的比例风险模型与未观察到的异质性，和自助方法估计的计量经济模型从时间序列。所有这些都建立在调查员先前的工作基础上。第一个主题是测试一个参数模型（可能是向量值）的条件矩或四分位数函数对非参数的替代品。该研究将开发在平滑的非参数替代模型上一致一致的测试，随着样本量的增加，这些模型与参数模型的距离以最快的速度收敛到零。 还将开发不需要关于替代模型的平滑度的先验知识的测试。这些特性在功效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。 第二个主题是关于估计具有不可观测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分布均不属于已知的有限维参数函数族。它们将被非参数化处理。该研究将特别关注面板数据的固定效应模型，具有随时间变化的协变量的模型，以及未观察到的异质性是异方差性的未知形式的横截面模型。 所有这些模型都与应用研究有关。 第三个主题是关于有限维参数的假设检验，该参数由广义矩量法（GMM）使用相关数据估计。 由于一阶近似对于应用中发现的样本量可能非常不准确，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标称概率可能非常不同。类似地，基于一阶近似的置信区间的真实和标称覆盖概率可能非常不同。块引导提供了一种方法来获得改进的近似依赖数据，但最近的研究表明，改善的量并不大。这项新研究将研究使用筛选引导，其中数据生成过程由有限维参数模型的扩展序列近似，并且引导样本通过筛选近似的模拟生成。在比GMM估计和测试简单得多的设置中，已经发现，筛分引导提供了比块引导大得多的一阶近似的改进。新的研究将调查筛分自助法的改进性能是否扩展到GMM通常用于经济学的测试和模型。此外，本研究还将探讨迭代版本的筛选自助法是否可以用来提供渐近细化，而不需要异方差和自相关一致（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.