I studied the standard econometrics textbooks about panel data, but most textbooks only mention the difference between balanced and unbalanced panels. The advantage of having balanced panel data is not usually explained. I would like to know: What is the advantage of having a balanced panel? I believe unbalanced panels are much more common in real research.
Econometrics – Advantage of Balanced Panel Data Vs. Unbalanced
econometricspanel data
Best Answer
I believe these are largely historical reasons. In the 1940s, one had to conduct analysis of variance with paper and pencil, so having balanced designs led to simple sums for both means and variances. Any imbalance would require inverting matrices 4x4 or larger (I've done it a couple of times on regression exams, and nearly always screwed up). It is likely that in the 1960s when panel/longitudinal data first came to researchers' attention (probably with PSID), one could reasonably easily run a regression with no structure on errors already, but running GLS required heroic efforts, let alone unbalanced GLS. These days, there aren't any issues, as Dimitriy said, as all estimators are computed in the general form with the most general matrix inversion operations in the background, anyway.
Also, with balanced data sets, you can easily run models with panel autoregressions. With unbalanced panels, these will likely get trickier. I don't think that these models are actually that popular.