Evaluating Educational Inequality Within Educational Expansion: A Formal Comparison Between Odds Ratio and the Educational Gini Coefficient

Abstract

Odds ratio (OR) and the educational Gini coefficient (EGINI) defined on a specific social grouping scheme can both be used to gauge educational inequality. In this study, we systematically review the scholarship that underpins the utilities of OR and EGINI and evaluate their properties across four research scenarios of allocating newly created opportunities under educational expansion. Formal analyses suggest that (1) both OR and EGINI monotonically increase (decrease) if the newly created educational positions are entirely delivered to the upper (lower) class. However, the rate of change differs between OR and EGINI. (2) When educational opportunities within expansion are allocated according to the relative populations of social classes, the probabilities of upper and lower classes to receive better education rise by the same extent, suggesting that all social classes benefit from the proliferation of educational credentials. This would drive down the EGINI, but change in OR is not monotonic. (3) EGINI remains unchanged if the newly created educational opportunities are allocated based on the initial class composition of better educated individuals before educational expansion. However, OR is driven to increase by the “Matthew Effect” where the increment in educational probability for the upper class is larger than that for the lower class. The discrepancy of empirical patterns between OR and EGINI is explained, and the practical implications are discussed using a case study of the educational policy evaluation in Britain.