  We establish the convergence rates and asymptotic distributions of the common
break change-point estimators, obtained by least squares and maximum likelihood
in panel data models and compare their asymptotic variances. Our model
assumptions accommodate a variety of commonly encountered probability
distributions and, in particular, models of particular interest in econometrics
beyond the commonly analyzed Gaussian model, including the zero-inflated
Poisson model for count data, and the probit and tobit models. We also provide
novel results for time dependent data in the signal-plus-noise model, with
emphasis on a wide array of noise processes, including Gaussian process,
MA$(\infty)$ and $m$-dependent processes. The obtained results show that
maximum likelihood estimation requires a stronger signal-to-noise model
identifiability condition compared to its least squares counterpart. Finally,
since there are three different asymptotic regimes that depend on the behavior
of the norm difference of the model parameters before and after the change
point, which cannot be realistically assumed to be known, we develop a novel
data driven adaptive procedure that provides valid confidence intervals for the
common break, without requiring a priori knowledge of the asymptotic regime the
problem falls in.
