Testing for Cross-sectional Dependence in Fixed E¤ects Panel Data Models

This paper proposes a new test for cross-sectional dependence in …xed e¤ects panel data models. It is well known that ignoring cross-sectional dependence leads to incorrect statistical inference. In the panel data literature, attempts to account for cross-sectional dependence include factor models and spatial correlation. In most cases, strong assumptions on the covariance matrix are imposed. Attempts at avoiding ad hoc speci…cations rely on the sample covariance matrix. Unfortunately, when the dimension of this variance-covariance matrix is large, the sample covariance matrix turns out to be an inconsistent estimator of the population covariance matrix. This is especially relevant for micro panels with a large number of cross-sectional units observed over a short time series span. This fact undermines existing tests based on the sample covariance matrix directly. This paper uses the Random Matrix Theory based approach of Ledoit and Wolf (2002) to test for cross-sectional dependence of the error terms in linear large panel models with comparable number of cross-sectional units and time series observations. Since the errors are unobservable, the residuals from the …xed e¤ects regression are used. As shown in the paper, the di¤erence can not be ignored asymptotically, and the limiting distribution of the proposed test statistic is derived. Additionally, its …nite sample properties are examined and compared to the traditional tests for cross-sectional dependence using Monte Carlo simulations. Keywords: Cross-sectional Dependence; Panel Data; Fixed E¤ects; John Test. JEL Classi…cation: C13; C33. Email Addresses: Badi H. Baltagi, [email protected]; Qu Feng, [email protected]; Chihwa Kao, [email protected].