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Using a consistent estimator of the covariance matrix of the asymptotic distribution of the quantile regression estimator with intra-cluster correlation of the error terms, the paper investigates whether and to what extent inter-industry wage differentials derive from worker heterogeneity in the form of unobserved quality. To conduct this study, we pioneer in utilizing a unique data set, the European Union Structure of Earnings Survey for Greece, which follows a two-stage random sampling approach of employees clustered within firms. Data refer to 2010 when the first elements of the economic adjustment programme to deal with the chronic deficiencies of the Greek economy and restore sustainable public finances, competitiveness and set the foundation for long-term growth, gained visibility. Results point to high wage dispersion across industries at the mean of the conditional wage distribution, even after controlling for personal and workplace characteristics. However, evidence for the unobserved heterogeneity hypothesis is rather scant. Therefore, there is room for efficiency wage or rent-sharing theories in accounting for a large part of inter-industry wage differentials tentatively implying that firm heterogeneity in the ability to pay matters more than employee unobservable attributes in the wage determination process.