A new mobility index for transition matrices
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In this work we construct a mobility index able to grasp the prevailing direction in the evolution of a given set of statistical units. We consider the case of dynamics ruled by a transition matrix, whose states are based on an ordered economic variable (firm size or income, among others) such that the future position of an individual can be better or worse than the current one. The existing indices measure only the absolute value of mobility, without providing information about the main direction in the dynamics. We propose here a whole family of directional indices defined as functions of the transition matrix, so that their absolute value measures the intensity of mobility, and their sign (\(+/-\)) represents the prevailing direction towards improvement/worsening in the dynamics under study.
KeywordsMobility index Prevailing direction Transition matrix Ordered variable
The authors are grateful to Provincia di Prato for the ASIA-ISTAT dataset, and to CRISP (Milano) for the C.OBB. dataset. They also wish to thank E. Fabrizi and the anonymous referees for their constructive comments and suggestions.
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