Adaptive Estimation, the Block-Block Bootstrap, Optimal Tests with Weak Instruments, and Inference with Common Shocks

自适应估计、块-块引导、弱仪器的最佳测试以及常见冲击的推理

• 批准号: 0417911
• 负责人: Donald Andrews
• 金额: --
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2008-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0417911&HistoricalAwards=false
• 关键词: Adaptive; Estimation; Block; Bootstrap; Optimal

This research covers four difficult areas of applied econometrics. The first project is adaptive estimation of semiparametric and nonparametric models. In many econometric models, such as the smoothed maximum score estimator, the optimal rate of convergence of an estimator depends on an unknown smoothness, say s, of some function(s). This project will specify a general method that takes existing estimators designed for given values of s and use them to construct an estimator that does not depend on s but obtains the optimal rate of convergence for the case of known s up to a logarithmic factor. This method is a generalized variant of Lepskii (1990) method. The second project considers the block-block bootstrap, a method that is useful in time series GMM contexts. The block-block bootstrap, proposed by the PI, yields larger asymptotic refinements than the block bootstrap. This research will develop the block-block bootstrap to cover cases in which an HAC variance matrix estimator is required. The third project deals with optimal tests in an instrumental variable regression model with weak instruments. For models with normal reduced-form errors and known covariance matrix, this project will develop a class of similar invariant tests that have maximum weighted average power in finite samples and develop analogous asymptotic tests for models with non-normal errors and unknown covariance matrices. The research will also develop heteroskedasticity-robust and heteroskedasticity and autocorrelation-robust versions of these tests. The fourth project is on inference in cross-section and panel models with common shocks, such as macroeconomic and political shocks. This research explores the implications of a new asymptotic framework that the PI has developed for cross-section models that allows for general forms of cross-section dependence but yields simple asymptotics. It investigates the properties of GMM estimators and tests in nonlinear cross-section models with common shocks and various procedures in panel models with large numbers of cross-section and time series observations and common shocks. This research contributes original ideas to solve many difficult problems in econometrics. The results will be extremely helpful to applied econometricians, and in the process, improve economic policy-making.

这项研究涵盖了应用计量经济学的四个困难领域。第一个项目是半参数和非参数模型的自适应估计。在许多计量经济学模型中，例如平滑最大得分估计器，估计器的最佳收敛速率取决于某些函数的未知平滑度（例如 s）。 该项目将指定一种通用方法，该方法采用为给定 s 值设计的现有估计器，并使用它们构建一个不依赖于 s 的估计器，但在已知 s 达到对数因子的情况下获得最佳收敛率。该方法是 Lepskii (1990) 方法的广义变体。 第二个项目考虑块块引导，这是一种在时间序列 GMM 环境中有用的方法。 PI 提出的块-块引导程序比块引导程序产生更大的渐近细化。这项研究将开发块块引导程序来涵盖需要 HAC 方差矩阵估计器的情况。 第三个项目涉及使用弱工具的工具变量回归模型中的最优测试。对于具有正态约化误差和已知协方差矩阵的模型，该项目将开发一类在有限样本中具有最大加权平均功效的类似不变检验，并针对具有非正态误差和未知协方差矩阵的模型开发类似的渐近检验。该研究还将开发这些检验的异方差稳健性以及异方差和自相关稳健版本。 第四个项目是关于常见冲击（例如宏观经济和政治冲击）的横截面模型和面板模型的推理。 这项研究探讨了 PI 为横截面模型开发的新渐近框架的含义，该框架允许一般形式的横截面依赖性，但产生简单的渐近。 它研究了 GMM 估计量的特性，并在具有常见冲击的非线性横截面模型中进行测试，以及具有大量横截面和时间序列观测值以及常见冲击的面板模型中的各种程序。 这项研究为解决计量经济学中的许多难题提供了独到的想法。 研究结果将对应用计量经济学家非常有帮助，并在此过程中改进经济政策制定。