The between-groups estimator is a panel-data estimator that runs a regression on group means, so it explains differences across entities rather than changes within each entity over time.
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How it works
Suppose panel data are indexed by entity (i) and time (t). The between estimator first averages the data over time for each entity:
$$
\bar{y}_i = \alpha + \beta \bar{x}_i + \bar{u}_i
$$
It then applies ordinary least squares to those averaged observations.
This means the estimator uses between-unit variation only. If a country has a higher average tax rate and lower average growth than another country, that cross-country difference contributes to the estimate. Year-to-year variation inside each country does not.
Why it matters
The between estimator is useful when the researcher wants to study long-run differences across groups, but it cannot control away time-invariant omitted characteristics the way a fixed-effects estimator can.
So the main trade-off is:
- easier interpretation of cross-group differences,
- but more vulnerability to omitted-variable bias from unobserved group traits.
Knowledge Check
### What source of variation does the between-groups estimator use?
- [x] Differences in time averages across entities
- [ ] Only year-to-year variation within each entity
- [ ] Only random sampling variation with no panel structure
- [ ] Only variation in the error term
> **Explanation:** The estimator collapses each entity to its average values and estimates the relationship across those averages.
### What is a main limitation of the between estimator?
- [x] Unobserved time-invariant differences across groups can still bias the estimate
- [ ] It cannot be used with panel data
- [ ] It ignores cross-sectional variation completely
- [ ] It always has lower variance than fixed effects
> **Explanation:** Because it compares groups rather than differencing them out, omitted group traits can remain in the error term.
### Which estimator is the natural contrast to the between estimator in panel-data analysis?
- [x] Within-groups estimator
- [ ] Treasury-bill estimator
- [ ] Beveridge estimator
- [ ] Bid-ask estimator
> **Explanation:** The within estimator focuses on changes inside each entity over time, which is the opposite source of variation.