Necessity of the continuity assumption for the fixed-effects factor in identification

Determine whether identification in dynamic panel models with interactive effects that include individual fixed effects (treated as a special factor with loadings γ_i and factor values equal to 1 across time) requires the assumption that the coefficient f_γ in the first row of the factor column is drawn from a continuous distribution, or whether identification can be established without imposing continuity on f_γ.

Background

In the extension to models with individual fixed effects, the factor matrix includes a column of ones, and the authors impose an assumption that f_γ (the first row entry in that column) is drawn from a continuous distribution to simplify exposition.

The authors conjecture this continuity is not strictly necessary for identification, suggesting a potential relaxation of assumptions that would broaden applicability and reduce reliance on distributional conditions for fixed-effects components.