Diagnostic Tests of Cross-section Independence for Limited Dependent Variable Panel Data Models


  • The authors thank Qi Li, the editor (Anindya Banerjee), and two anonymous referees for helpful comments. Most of the research for this article was done while the third author was at the University of Cambridge. He acknowledges financial support from Sinopia, quantitative specialist of HSBC Global Asset Management. The opinions expressed in this article do not necessarily represent those of DNB.


This article considers the problem of testing for cross-section independence in limited dependent variable panel data models. It derives a Lagrangian multiplier (LM) test and shows that in terms of generalized residuals of Gourieroux et al. (1987) it reduces to the LM test of Breusch and Pagan (1980). Because of the tendency of the LM test to over-reject in panels with large N (cross-section dimension), we also consider the application of the cross-section dependence test (CD) proposed by Pesaran (2004). In Monte Carlo experiments it emerges that for most combinations of N and T the CD test is correctly sized, whereas the validity of the LM test requires T (time series dimension) to be quite large relative to N. We illustrate the cross-sectional independence tests with an application to a probit panel data model of roll-call votes in the US Congress and find that the votes display a significant degree of cross-section dependence.