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 images. We'll denote by images 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 (images and images). Denoting by images and images two matrices of individual and time dummies, matrices of the type images, 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, ...

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