# A differential-equation model shows the proximate cause of the glass ceiling in European academia

## TL;DR

This paper presents a differential-equation model to analyze gender imbalance in European academia, identifying the proximate causes of the glass ceiling through a deterministic mathematical framework.

## Contribution

It introduces a novel ODE-based model to quantify career progression disparities and defines a glass-ceiling index to summarize asymmetries in academic hierarchies.

## Key findings

- The model can pinpoint factors contributing to the glass ceiling.
- Progression rates and success probabilities differ between groups.
- The framework is applicable to other hierarchical contexts.

## Abstract

We introduce a model based on Ordinary Differential Equations to describe how two mutually exclusive groups progress through a career hierarchy, whether in a single organization, or in an entire economic sector. The intended application is to gender imbalance at the top of the academic hierarchy in European Universities, however, the model is entirely generic and may be applied in other contexts also. Previous research on gender imbalance in European universities has focused on large-scale statistical studies. Our model represents a point of departure, as it is deterministic (i.e. based on Ordinary Differential Equations). The model requires a precise definition of the progression rates for the different groups through the hierarchy; these are key parameters governing the dynamics of career progression. The progression rate for each group can be decomposed into a product: the proportion of group members at a low level in the hierarchy who compete for promotion to the next level a given year, multiplied by the in-competition success rate for the group in question. Either of these two parameters can differ across the groups under consideration; this introduces a group asymmetry into the organization's composition. We introduce a glass-ceiling index to summarize this asymmetry succinctly. Using case studies from the literature, we demonstrate how the mathematical framework can pinpoint the proximate cause of the glass ceiling in European academia.