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，例如平滑最大得分估计，估计的最优收敛速度取决于某些函数的未知平滑度，例如s。 这个项目将指定一个通用的方法，现有的估计设计为给定值的s和使用它们来构建一个估计，不依赖于s，但获得最佳的收敛速度的情况下，已知的s的对数因子。该方法是Lepskii（1990）方法的一个推广变体。 第二个项目认为块块引导，一种方法，是有用的时间序列GMM上下文。 PI提出的块-块引导比块引导产生更大的渐近细化。本研究将开发块-块自助法，以涵盖需要HAC方差矩阵估计的情况。 第三个项目是关于弱工具下工具变量回归模型的最优检验。对于具有正态简化形式误差和协方差矩阵已知的模型，本项目将开发一类在有限样本中具有最大加权平均功效的相似不变检验，并开发具有非正态误差和协方差矩阵未知的模型的类似渐近检验。该研究还将开发这些测试的异方差稳健版本和异方差和自相关稳健版本。 第四个项目是关于具有共同冲击（如宏观经济和政治冲击）的横截面和面板模型的推断。 本研究探讨了一个新的渐近框架，PI已经开发的横截面模型，允许一般形式的横截面依赖，但产生简单的渐近的影响。 它研究了GMM估计的性质，并在非线性横截面模型与共同冲击和面板模型与大量的横截面和时间序列观测和共同冲击的各种程序的测试。 该研究为解决计量经济学中的许多难题提供了新的思路。 研究结果将对应用计量经济学家非常有帮助，并在此过程中改善经济政策制定。

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.