This paper re-defines Esteban and Ray's (Econometrica, 1994) income polarization index to incorporate a role for time. Income polarization captures the extent to which an income distribution concentrates around two or more income levels. Polarization measurement is rationalized as measuring potential conflict in a society where people feel alienated from one another when distant in income but identified with others of similar income levels. We introduce time in this model because the two key ingredients of polarization—alienation and identification—have fewer implications for potential conflict if individual incomes vary over time and feelings of alienation or identification have limited time to form and consolidate. Accordingly, we propose an inter-temporal income polarization measure using panel data in which memory parameters allow past income differences to determine the degree of alienation and identification in a society's income distribution. This leads to measures of income polarization that are sensitive to the history of interpersonal income proximity and distances in past income trajectories.
We illustrate the empirical relevance of this longitudinal perspective with an application to Italian data.