An equicorrelation Moulton factor in the presence of arbitrary intra-cluster correlation

- Assuming equicorrelation leads in general to misleadingly small standard errors.
- Define equicorrelation Moulton factor for random-effects models.
- Key role is given by the within-correlation of the covariates.
- For intra-cluster constant covariates the equicorrelation model is correct.

This note highlights the potential pitfalls of using an equicorrelation model to estimate standard errors when the true model has arbitrary intra-cluster correlation. It derives a generalized equicorrelation Moulton factor that quantifies the potential biases in standard errors for OLS estimators. As with the famous Moulton factor, the key role is not played by the correlation of the error terms but rather by the intra-correlation of the covariates themselves.