Unbalanced design for random effects. Suppose that the random effects model of Section 11.5 is to be estimated with a panel in which the groups have different numbers of observations. Let T_i be the number of observations in group i.

a. Show that the pooled least squares estimator is unbiased and consistent despite this complication.

b. Show that the estimator in (11-40) 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.