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大量弱工具变量下的第一阶段 F 检验AI 解读

A widely adopted approach for detecting weak instruments is to use the first-stage $F$ statistic. While this method was developed with a fixed number of instruments, its performance with many instruments remains insufficiently explored. We show that the first-stage $F$ test exhibits distorted sizes for detecting many weak instruments, regardless of the choice of pretested estimators or Wald tests. These distortions occur due to the inadequate approximation using classical…

工具变量强度的设定检验AI 解读

This paper develops a new specification test for the instrument weakness when the number of instruments $K_n$ is large with a magnitude comparable to the sample size $n$. The test relies on the fact that the difference between the two-stage least squares (2SLS) estimator and the ordinary least squares (OLS) estimator asymptotically disappears when there are many weak instruments, but otherwise converges to a non-zero limit. We establish the limiting distribution of the…

大面板截面独立性的统一稳健拉格朗日乘数型检验AI 解读

This paper revisits the Lagrange multiplier type test for the null hypothesis of no cross-sectional dependence in large panel data models. We propose a unified test procedure and its power enhancement version, which show robustness for a wide class of panel model contexts. Specifically, the two procedures are applicable to both heterogeneous and fixed effects panel data models with the presence of weakly exogenous as well as lagged dependent regressors, allowing for a…

具有一般独立列的数据矩阵的奇异值AI 解读

In this paper, we analyse singular values of a large $p\times n$ data matrix $\mathbf{X}_n= (\mathbf{x}_{n1},\ldots,\mathbf{x}_{nn})$ where the column $\mathbf{x}_{nj}$'s are independent $p$-dimensional vectors, possibly with different distributions. Such data matrices are common in high-dimensional statistics. Under a key assumption that the covariance matrices $\mathbfΣ_{nj}=\text{Cov}(\mathbf{x}_{nj})$ can be asymptotically simultaneously diagonalizable, and appropriate…

非正态误差大面板的截面独立性拉格朗日乘子检验扩展AI 解读

This paper reexamines the seminal Lagrange multiplier test for cross-section independence in a large panel model where both the number of cross-sectional units n and the number of time series observations T can be large. The first contribution of the paper is an enlargement of the test with two extensions: firstly the new asymptotic normality is derived in a simultaneous limiting scheme where the two dimensions (n, T) tend to infinity with comparable magnitudes; second, the…