The mover-stayer model, a generalization of the Markov chain model, assumes that there are two types of individuals in the population under consideration: (a) the “stayer,” who with probability one remains in the same category during the entire period of study; (b) the “mover,” whose changes in category over time can be described by a Markov chain with constant transition probability matrix. The transition probability matrix for movers, and the proportion of stayers among the individuals in each category at, say, the initial point in time, are unknown parameters. Various estimators of these parameters are presented herein, and the accuracy of these estimators is compared. We show, for example, that the estimators of these parameters used by Blumen, Kogan, and McCarthy [3] are not consistent estimators, while the estimators recommended herein are. In addition, tests of several hypotheses concerning the mover-stayer model are presented herein. The methods developed in this paper can be applied to the study of various phenomena where panel data are available.