Unbalanced design for random effects, suppose that the random effects model of Section 13.4 is to be estimated with a panel in which the groups have different numbers of observations. Let Ti be the number of observations in group i.

a. Show that the pooled least squares estimator in (13-11) is unbiased and consistent despite this complication.

b. Show that the estimator in (13-29) based on the pooled least squares estimator of β (or, for that matter, any consistent estimator of β) is a consistent estimator of σ²_ε.