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

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，例如平滑最大分数估计器，估计器的最佳收敛速度取决于某个函数的未知平滑度，例如s。本项目将指定一种一般方法，该方法采用为给定s值设计的现有估计量，并使用它们构造一个不依赖于s的估计量，但在已知s的情况下获得最优收敛率，直至对数因子。该方法是Lepskii（1990）方法的广义变体。第二个项目考虑了块引导，这是一种在时间序列GMM上下文中很有用的方法。PI提出的块-块自举法比块自举法产生更大的渐近细化。本研究将发展块-块自举，以涵盖需要HAC方差矩阵估计器的情况。第三个项目处理带有弱仪器的工具变量回归模型中的最优测试。对于具有正态误差和已知协方差矩阵的模型，本项目将开发一类在有限样本中具有最大加权平均幂的类似不变检验，并为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。研究还将开发这些测试的异方差-稳健性和异方差-自相关-稳健性版本。第四个项目是关于具有常见冲击（如宏观经济和政治冲击）的横截面和面板模型的推断。本研究探讨了PI为截面模型开发的一个新的渐近框架的含义，该框架允许一般形式的截面依赖，但产生简单的渐近。它研究了GMM估计器的性质，并在具有常见冲击的非线性横截面模型中进行了测试，并在具有大量横截面和时间序列观测值和常见冲击的面板模型中进行了各种程序。本研究为解决计量经济学中的许多难题提供了独到的思路。这些结果将对应用计量经济学家非常有帮助，并在此过程中改善经济决策。

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.