Estimation and Inference in High-Dimensional Panel Data Models

对许多现代经济面板数据集的分析需要考虑未观察到的异质性和高维数据结构。然而，只有少数计量经济学方法被开发来分析具有未观察到异质性的高维面板数据模型。该项目的主要目的是为这些模型设计新的估计和推理技术。我们将重点关注具有交互固定效应的模型，这是一个非常灵活和流行的框架，可以考虑到未观察到的异质性。在具有交互固定效应的低维面板模型中估计未知参数的一种非常常用的方法是Pesaran在2006年引入的所谓的共同相关效应（CCE）估计器。然而，这个非常流行的估计器在高维情况下会失效，并且对高维情况的朴素扩展会显著失败。在这个项目中，我们将开发一种新的cce型估算器，它可以在高维环境下工作。该项目的理论部分将涉及推导所提出的估计量的渐近性质。在第一步中，我们将专注于估计理论并推导估计器的收敛率。在第二步中，我们将转向分布理论并分析基于它的推理过程。该项目的方法和理论分析将辅以模拟研究和实证应用。

The analysis of many modern economic panel data sets requires to account for both unobserved heterogeneity and high-dimensional data structures. Nevertheless, only few econometric methods have been developed to analyze high-dimensional panel data models with unobserved heterogeneity. The main purpose of the project is to devise novel estimation and inference techniques for such models. We will focus attention on models with interactive fixed effects, which are a very flexible and popular framework to take into account unobserved heterogeneity. A very common way to estimate the unknown parameters in a low-dimensional panel model with interactive fixed effects is the so-called common correlated effects (CCE) estimator introduced by Pesaran in 2006. However, this very popular estimator breaks down in high dimensions, and naive extensions to the high-dimensional case fail dramatically. In the project, we will develop a novel CCE-type estimator which does work in high dimensions. The theoretical part of the project will be concerned with deriving the asymptotic properties of the proposed estimator. In a first step, we will concentrate on estimation theory and derive the convergence rate of the estimator. In a second step, we will turn to distribution theory and analyze inferential procedures based on it. The methodological and theoretical analysis of the project will be complemented by simulation studies and empirical applications.