Public–private sectoral wage differentials have been studied extensively using quantile regression techniques. These typically find large public sector premiums at the bottom of the wage distribution. This may imply that low skill workers are ‘overpaid’, prompting concerns over efficiency. We note several other potential explanations for this result and explicitly test whether the premium varies with skill, using Australian data. We use a quasi-differenced Generalized Method of Moments (GMM) panel data model which has not been previously applied to this topic, internationally. Unlike other available methods, this technique identifies sectoral differences in returns to unobserved skill. It also facilitates a decomposition of the wage gap into components explained by differences in returns to all (observed and unobserved) skills and by differences in their stock. We find no evidence to suggest that the premium varies with skill. One interpretation is that the compressed wage profile of the public sector induces the best workers (on unobserved skills) to join the public sector in low wage occupations, vice versa in high wage occupations. We also estimate the average public sector premium to be 6% for women and statistically insignificant (4%) for men.