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The paper investigates the determinants of the Ordinary Least Squares (OLS) bias of the wage return to graduate education for high-school workers in Portugal.

The study uses matched employer-employee data for Portugal, over the 2002–2012 period, to estimate a wage-schooling model that controls not only for individual observed characteristics, firm observed characteristics and year fixed effects, but also for three high-dimensional vectors of fixed effects – one for employees, one for employers and one for job titles.

The main results are the following. First, disregarding individual fixed effects is highly problematic, accounting for 48.5% of the OLS bias. Second, disregarding firm fixed effects is also problematic, accounting for 12.3% of the OLS bias.

The implication for the studies in the labor-supply literature that estimate, by means of instrumental variables, the wage returns to in-school work or to on-the-job schooling is that an instrument dealing with employee’s unobserved ability only may fail to meet the exclusion restriction.

Take the typical instrument based on a policy reform that changes the compulsory schooling level in the population. This instrument may well be argued to be correlated with the education of the employee and uncorrelated with the unobserved ability of the employee, but unfortunately it cannot be seen as orthogonal to the unobserved ability of the employer because of its correlation with the (unobserved) education of the manager. This is a simple corollary of the fact that the employee and the manager belong, in general, to the same population.

Individuals invest a considerable amount of resources in education, which is seen to have positive effects on several dimensions of individual life. Yet, the estimation of these effects is still surrounded by technical difficulties.

To the best of the authors’ knowledge, this is the first study that uses the Gelbach decomposition to investigate the determinants of the OLS bias of the wage return to graduate education for high-school workers.

The aim is to study the impact of schooling on between-groups wage inequality beyond the lens of the standard approach in the literature.

Simple econometric theory is used to make the main point of the paper. Supporting empirical evidence is also presented.

Disregarding the persistence of current earnings implies a bias in the estimation of the wage return to schooling both at labour-market entry and in the rest of the working life.

The use of current earnings as a dependent variable in wage-schooling models may be problematic and requires specific handling.

The impact of schooling on the between-groups dimension of wage inequality may be different than previously thought.

The paper is the first to show that, when current earnings are used as a dependent variable, the identification of a wage-schooling model with the standard (time-invariant external instrument-variable) approach may lead to misleading conclusions.

The aim is to assess how a policy of tertiary education for all affects the shape of the unconditional earnings distribution.

The paper discusses the quantile-regression literature looking at the link between education and wage inequality, also proving new evidence based on unconditional quantile regressions.

The findings support the idea that a policy of tertiary education for all increases the overall level of wage inequality.

The research has implications for public policy and administration. Among the limitations, the paper does not deal with distributional aspects related to other outcomes (e.g. health outcomes) of the policy of interest.

The analysis highlights a series of potential government interventions aimed at reducing the wage-inequality externalities of the policy of interest.

A policy of tertiary education for all, by itself, is not useful to fight wage inequality.

This paper belongs to the small group of studies using unconditional quantile regressions to study the link between education and wage inequality. It is the first study specifically looking at the distributional effects of a policy of tertiary education for all.