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To foster a deeper understanding of the mechanisms behind inequality in society, it is crucial to work with well-defined concepts associated with such mechanisms. The aim of this paper is to define cumulative (dis) advantage and the Matthew effect. We argue that cumulative (dis) advantage is an intra-individual micro-level phenomenon, that the Matthew effect is an inter-individual macro-level phenomenon and that an appropriate measure of the Matthew effect focuses on the mechanism or dynamic process that generates inequality. The Matthew mechanism is, therefore, a better name for the phenomenon, where we provide a novel measure of the mechanism, including a proof-of-principle analysis using disposable personal income data. Finally, because socio-economic theory should be able to explain cumulative (dis) advantage and the Matthew mechanism when they are detected in data, we discuss the types of models that may explain the phenomena. We argue that interactions-based models in the literature traditions of analytical sociology and statistical mechanics serve this purpose.

The first aim of this paper is to clarify the differences and relationships between cumulative advantage/disadvantage and the Matthew effect. Its second aim, which is also its main contribution, is not only to present a new measure of the Matthew effect, but also to show how to estimate this effect from data and how to make statistical inference. We argue that one should utilize the positivity of the natural logarithm of the largest generalized eigenvalue for a non-linear dynamic process as evidence when claiming that the Matthew effect is present in the dynamic process that generates individuals’ socio-economic life-courses. Thus, our measure of the Matthew effect focuses on the dynamic process that generates socio-economic inequality and not on the outcome of this process.