Econ Papers Daily / 期刊论文
高维面板数据模型的稳健估计与推断
Robust estimation and inference for high-dimensional panel data models
摘要
This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for non-Gaussian, serially and cross-sectionally correlated and heteroskedastic error processes, (2) we develop an estimation method for high-dimensional long-run covariance matrix using a thresholded estimator, (3) we also allow for the number of regressors to grow faster than the sample size. Methodologically and technically, we develop two Nagaev--types of concentration inequalities: one for a partial sum and the other for a quadratic form, subject to a set of easily verifiable conditions. Leveraging these two inequalities, we derive a non-asymptotic bound for the LASSO estimator, achieve asymptotic normality via the node-wise LASSO regression, and establish a sharp convergence rate for the thresholded heteroskedasticity and autocorrelation consistent (HAC) estimator. We demonstrate the practical relevance of these theoretical results by investigating a high-dimensional panel data model with interactive effects. Moreover, we conduct extensive numerical studies using simulated and real data examples.
中文摘要
本文为相关文献提供了一套完整的工具包，用于在高维面板数据框架下对感兴趣的参数进行稳健估计与推断。具体而言：(1) 我们允许非高斯、序列相关与截面相关以及异方差的误差过程；(2) 我们利用阈值估计量为高维长期协方差矩阵开发了一种估计方法；(3) 我们还允许回归变量数量以快于样本量的速度增长。在方法论与技术层面，我们发展了两类Nagaev型集中不等式：一类针对部分和，另一类针对二次型，且均在一组易于验证的条件下成立。借助这两个不等式，我们推导了LASSO估计量的非渐近界，通过逐节点LASSO回归实现了渐近正态性，并为阈值化异方差与自相关一致（HAC）估计量建立了精确的收敛速率。我们通过研究一个具有交互效应的高维面板数据模型，展示了这些理论结果的实际相关性。此外，我们利用模拟数据和真实数据实例进行了广泛的数值研究。