This paper 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, Monfort, Renault and Trognon (1987) it reduces to the LM test of Breusch and Pagan (1980). Due to 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 U. S. Congress and find that the votes display a significant degree of cross section dependence
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