Negative variance estimates in panel data models

Negative values for estimated variances can arise in a panel data context. Empirical and theoretical literature dismisses the problem as not serious and a practical solution is to replace negative variances by its boundary value, i.e. zero. While this is not a concern when the individual variance components is "small" with respect to idiosyncratic variance component (making it indistinguishable from zero in practice), we claim that a negative estimated variance can also arise with a "large" individual variance component, when the orthogonality condition between the individual effects and regressors fails. Estimation problems are considered in the (feasible) generalized least squares and maximum likelihood frameworks.