State Space Heterogeneity and Space Determination for Markov Models of Mobility

Abstract

Since the seminal work of Lancaster and Nickell (1979–1980), the consequences of individual heterogeneity on aggregate stochastic processes of mobility are well known. It is possible to briefly characterize these as results of the following phenomenon (Salant, 1977). If we assume that exit rates out of a given state differ between individuals, then the longer the sojourn time the greater the proportion of the population having low exit rates and thus the smaller the mean exit rate. For a comprehensive overview, see Heckman and Singer (1986). There is, however, another source of heterogeneity for stochastic processes of mobility which lies in the definition of the state space of the process. The definition of the state space of a stochastic process has never been considered up to now. Generally, the definition of the state space is a straightforward result of the problem considered; or it is largely constrained by the information given by the data. For example, labour force mobility analysis uses two states (employment, unemployment); geographic mobility uses predefined administrative areas like states, regions, countries, etc.