A new mobility index for Trandition Matrices

This work treats the construction of a mobility index able to grasp the prevailing\r\ndirection in the dynamics ruled by a given transition matrix. The states of\r\nthe matrix are based on an ordered economic variable, such as firm size, income\r\nor ratings, for which the future state can be better or worse than the current one.\r\nWe propose here a whole family of directional indices, evaluated as a function\r\nof the transition matrix, and defined so that their absolute value measures the intensity\r\nof mobility, and their sign (+/-) represents the prevailing direction towards\r\nimprovement/worsening in the dynamics under study.