Panel Data Econometrics with R

Chapter 3Advanced Error Components Models

3.1 Unbalanced Panels

For unbalanced panels, the number of observations for each individual is now individual specific and denoted by . We'll denote by the total number of observations. Compared to the balanced panel case, three complications appear:

• firstly, the covariance matrix of the errors cannot be written any more as a linear combination of idempotent and mutually orthogonal matrices (for the one‐way error component model, the within and the between matrices), the weights being the variances of the errors ( and ). Denoting by and two matrices of individual and time dummies, matrices of the type , returning either the sum of the values for an individual or for a time series, will explicitly appear, and these matrices are not idempotent;
• secondly, ...