rel="nofollow" href="#u1456388e-e00b-53be-874b-a1d4692cd78c">2.Tests for Cross-Sectional Dependence in Fixed Effects Panel Data Models
2.1LM Tests for Cross-Sectional Dependence
2.2LMP Test in the Raw Data Case
2.3A Bias-Corrected LM Test in a Fixed Effects Panel Data Model
3.Factor-Augmented Panel Data Regression Models
3.1Motivation
4.Structural Changes in Panel Data Models
4.1Heterogeneous Panels with a Common Structural Break
4.2Model 1: No Common Correlated Effects
4.3Model 2: Common Correlated Effects
4.4Multiple Common Break Points
4.5Endogenous Regressors and Break in Factors
4.6Monte Carlo Simulations
4.6.1Model 1: No common correlated Effects
4.6.2Model 2: Common correlated Effects
4.6.3Case of endogenous regressors
4.7An Empirical Example
4.8Recent Development
4.9Technical Details
4.10Exercises
5.Latent-Grouped Structure in Panel Data Models
5.1Panel Latent Group Structure Models
Chapter 1
Introduction
This book is motivated by the recent development in high-dimensional panel data models with large amount of individuals/countries (n) and observations over time (T). Specifically, it introduces four important research topics in large panels, including testing for cross-sectional dependence, estimation of factor-augmented panel data models, structural changes and group patterns in panels in the following four chapters. To address these issues, we examine the properties of traditional tests and estimators in large-dimensional setup. In addition, we also take advantage of some techniques in Random Matrix Theory and Machine Learning.
Chapter 2 covers testing for cross-sectional dependence in panel data regression models with large n and large T. Cross-sectional dependence, described as the interaction between cross-sectional units (e.g., households, firms and states, etc.), has been well discussed in the spatial econometrics literature. Intuitively, dependence across “space” can be regarded as the counterpart of serial correlation in time series. It could arise from the behavioral interaction between individuals, e.g., imitation and learning among consumers in a community, or firms in the same industry. This has been widely studied in game theory and industrial organization. It could also be due to unobservable common factors or common shocks popular in macroeconomics.
In recent literature, cross-sectional dependence among individuals is a concern when n is large. As serial correlation in time-series analysis, the cross-sectional of dependence/correlation leads to efficiency loss for least squares and invalidates conventional t-tests and F-tests which use standard variance–covariance estimators. In some cases, it could potentially result in inconsistent estimators (Lee, 2002; Andrews, 2005). Several estimators have been proposed to deal with cross-sectional dependence, including the popular spatial methods (Anselin, 1988; Anselin and Bera, 1998; Kelejian and Prucha, 1999; Kapoor, Kelejian and Prucha, 2007; Lee, 2007; Lee and Yu, 2010), and factor models in panel data (Pesaran, 2006, Kapetanios, Pesaran and Yamagata, 2011; Bai, 2009). However, before imposing any structure on the disturbances of our model, it may be wise to test the existence of cross-sectional dependence.
There has been a lot of work on testing for cross-sectional dependence in the spatial econometrics literature, see Anselin and Bera (1998) for cross-sectional data and Baltagi, Song and Koh (2003) for panel data, to mention a few. The latter derives a joint Lagrange multiplier
