Sampling properties of the directional mobility index and the income of Italian families

We propose statistical inference techniques for testing the directional income mobility. We measure the directional index on income transition matrices about Italian families from 2004 to 2012, and we derive its asymptotic distribution to rigorously determine if mobility has changed. Starting from 2006, results show a prevailing negative mobility, that is the tendency of Italian families to move towards lower income classes. In particular, we observe negative peaks in the mobility values in the period 2010-2012, for middle/high income classes, indicating that Italian families are still suffering the 2008 downturn.