Pooled Ordinary Least Squares for Panel Data

Pooled OLS is consistent when the composite error term — including any unobserved individual-specific component — is uncorrelated with all regressors in every time period. This strict exogeneity condition is strong; it fails whenever omitted individual characteristics that influence the outcome also correlate with the included regressors. In practice, a Hausman test comparing pooled OLS or random-effects estimates with fixed-effects estimates is used to assess whether this assumption is violated.

Repeated observations on the same individual share an unobserved individual effect, inducing within-cluster serial correlation. Conventional OLS standard errors treat all NT observations as independent, which overstates precision and inflates t-statistics. Clustering standard errors at the individual level corrects for this dependence by using a sandwich variance estimator that allows arbitrary correlation within each cluster, yielding valid inference without requiring a fully specified model for the error structure.

Both assume the unobserved individual effect is uncorrelated with regressors, but the random-effects estimator explicitly models the within-individual error structure and applies generalized least squares, achieving efficiency gains over Pooled OLS. Pooled OLS ignores the panel structure in estimation and is only as efficient as random-effects when errors are homoskedastic and serially uncorrelated within individuals, a condition rarely met in practice.