Coordinate free analysis of trends in British social mobility

The paper is intended to make a contribution to the ongoing debate about declining social mobility in Great Britain by analyzing mobility tables based on data from the 1991 British Household Panel Survey and the 2005 General Household Survey. The models proposed here generalize Hauser's levels models and allow for semi-parametric analysis of change in social mobility. The cell frequencies are assumed to be equal to the product of three effects: the effect of the Father's position for the given year, the effect of the Son's position for the given year, and the mobility effect related to the difference between the Father's and Son's positions. A generalization of the iterative proportional fitting procedure is proposed and
applied to computing the maximum likelihood estimates of the cell frequencies. The standard errors of the estimated parameters are computed under the product multinomial sampling assumption. The results indicate opposing trends of mobility between the two timepoints. Fewer steps up or down in the society became less likely, while more steps became somewhat more likely.