Purpose: The purpose of this study is to analyze the relationship between quality assurance, the traditional "a priori" approach, and a more recently developed empirical classification of universities, as a means of assessing whether the different classification systems fulfill their original purpose. The study analyzes Chilean university classifications because they have been used in setting up higher education public policies. Design/methodology/approach: The existing classifications of Chilean universities were identified in the literature. Researchers determined categories, criteria and/or indicators used, as well as their main purposes as described by the authors of the classifications. All the criteria and indicators identified were directly related to the quality of academic activities and to the results of the university accreditation processes. The institutional accreditation outcomes and variables were studied using univariate and multivariate statistical analysis. Findings: The "a priori" approach proved to be consistent with the results of institutional quality assurance, despite of the variability in individual performances. The empirical systems, however, do not show any contribution to the improvement of public policies in higher education. The results clearly show that classifications based on performance do not necessarily ensure improvements in institutional quality. Originality/value: To the authors' knowledge, this analysis is the first study of the relationship between university classification and quality assurance. The growing number of proposals for different empirical classifications in Chilean universities is evidence of institutional diversity only. However, the classification designs did not respond to purposes such as public policies improvements and other expected results from these instruments.