The time-dependent characteristics of relative mobility

Mobility is a significant supplementary piece of information when discussing the inequality of a society based on income distribution. To date, most of its characteristics require disambiguation and specification. In this paper, we will investigate the dependence of relative mobility on sampling time interval both empirically and theoretically. Using the Chinese household income data from the China Health and Nutrition Survey, we find that the relative mobility will initially increase with the sampling time interval and then approach a constant value. To examine this time-dependent characteristic of mobility quantitatively, we employ a money exchange model with uniform saving rate to investigate the relation between the mobility and the sampling time interval. The relation obtained from the model is similar to that of the empirical data. The convergence rate of the mobility can be described in terms of a characteristic time interval found to be solely determined by the saving rate. The higher the saving rate is, the longer the characteristic time interval is. This work can help us better understand the time-dependence of mobility.