Panelvaries

Panelvaries is a term used in panel data analysis to describe the degree of variation in a variable across time within each cross-sectional unit (panel) and, when summarized, the overall heterogeneity of trajectories across panels. It is not a standard statistic with a fixed definition in mainstream econometrics, but it appears in methodological notes and practical discussions as a way to discuss dynamic heterogeneity in panel data.

Common definitions of panelvaries emphasize within-panel dispersion over time. A typical approach defines panelvaries as the average, across panels, of the time-series variance of the variable within each panel: panelvaries = (1/N) sum_i var_t(y_it). Alternative definitions focus on between variation, such as the variance of panel means, or on composite measures that combine within- and between-panel dispersion. The chosen definition affects interpretation and is sensitive to the length of the time dimension and to missing data.

Interpretation and use of panelvaries center on understanding heterogeneity in dynamics. Higher panelvaries suggests greater diversity in how panels evolve over time, which can inform model specification decisions, such as whether fixed-effects or random-effects assumptions are appropriate, or whether heterogeneous slopes and error structures should be accommodated. Researchers may use panelvaries to identify groups of panels with similar trajectories or to assess the potential need for more flexible dynamic models.

Limitations include the lack of a universally accepted formula, which requires explicit definition in any analysis. Panelvaries conceptually aligns with within-panel dispersion and dynamic heterogeneity and can complement established approaches in panel data modeling.