Between Variation
Also known as · between-unit variation · cross-sectional variation
Between variation is the part of a variable's variance that lives in the averages across units — differences between unit-'s mean and unit-'s mean. In a panel, total variation decomposes into between (across units) plus within (within a unit, across time). Pooled OLS uses both; Fixed Effects purges between variation and uses only within.
When to use
Be wary of between variation whenever cross-unit differences could be driven by unobserved fixed traits. PS_4's −18% pooled OLS estimate is built largely on between variation — and that variation is contaminated by states' unobserved fixed safety levels (road quality, terrain). The FE estimate of −7% uses only within-state variation and is therefore much more credible. The "between estimator" exists (run OLS on the unit means) but is rarely used in modern applied work for this reason.