Some are observed, all leave traces: whole-population modeling of French elite civil servants' career paths
Elite civil servants may come and go between the public and private sectors throughout their career, a process of particular interest for the public and social scientists. However, data to document such processes are rarely completely available: we need inference tools that can account for many missing values. We consider public-private paths of elite French civil servants and introduce binary Markov switching models with Bayesian data augmentation. Our procedure relies on two complementary data sources: (1) detailed observations of some individual trajectories obtained from LinkedIn; (2) less informative ``traces'' left by all individuals in the administrative record, which we model for missing data imputation. This model class maintains the properties of hidden Markov models and enables a tailored sampler to target the posterior, yet allows for varying parameters across individuals and time. By integrating the two sources, we can consider the whole population rather than just a sample, and avoid the biases that would stem from using only a single source. We demonstrate this allows to properly test substantive hypotheses on career paths across a variety of public organizations. We notably show that the probability for ENA graduates to exit the public sector has not increased since 1990, but that the probability they return has increased. We identify three clusters of organizations, with distinct patterns of public-private behaviors.