Equivalent representations of discrete-time two-state panel data models

There are two common approaches to analyzing discrete-time two-state panel data: one focuses on modeling the determinants of state occupancy, the other on modeling the determinants of transition between states. This note shows that there are one-to-one correspondences between the two representations, between the two probability distributions in an unrestricted context, and between low-order Markov models of state occupancy and semi-Markov models of transition between states with strictly limited duration dependence.