  Political scientists and sociologists study how individuals switch back and
forth between public and private organizations, for example between regulator
and lobbyist positions, a phenomenon called "revolving doors". However, they
face an important issue of data missingness, as not all data relevant to this
question is freely available. For example, the nomination of an individual in a
given public-sector position of power might be publically disclosed, but not
their subsequent positions in the private sector. In this article, we adopt a
Bayesian data augmentation strategy for discrete time series and propose
measures of public-private mobility across the French state at large,
mobilizing administrative and digital data. We relax homogeneity hypotheses of
traditional hidden Markov models and implement a version of a Markov switching
model, which allows for varying parameters across individuals and time and
auto-correlated behaviors. We describe how the revolving doors phenomenon
varies across the French state and how it has evolved between 1990 and 2022.
