Measuring Aspects of Mobility, Polarization and Convergence in the Absence of Cardinality: Indices Based Upon Transitional Typology

More unequal yet more alike, the changing patterns of family formation, generational mobility and household income inequality in China: a counter-factual analysis

“…Transition matrices that change the anatomy of the arrival (inheritors) distribution from that of the departure (parents) distribution by moving inheritors into new positions relative to their ancestor's position in the departure distribution are not static matrices. Anderson (2018) characterized such transition matrices as polarizing or converging, when respectively the net transfer of mass is from the center of the departure distribution to the peripheries of the arrival distribution, or from the peripheries of the departure to the center of the arrival distribution. Based upon functions of cell values and initial class sizes, the paper provides indexes on [0,1], measuring the extent to which a given transition matrix exhibits polarizing, converging, upward or downward transitional properties.…”

“…To see if positive assortative marriage matching patterns have intensified over the period, the rank correlations of partners educational and social class status of three marriage cohorts, those that took place, before, during and after the Cultural Revolution, are considered. For an analysis of changing generational transitional patterns household income to child educational achievements and household social class to child educational achievement transitions for the three cohorts are considered following Anderson (2018). This is followed by a counterfactual study of the household income generation process.…”

“…Study of social and educational class transitions to income classes is facilitated by a semi-parametric decomposition of the household income distribution which produces individual household income class membership probabilities in a 5 income class model. 5 Details of various transition matrix typologies, their mobility and polarizing properties and associated indices drawn from Anderson (2018) are outlined and discussed in Electronic Supplemental Material Section C, they are reported in the following. The indices all lay on the unit interval and are asymptotically normally distributed.…”