Elite civil servants may move between the public and private sectors throughout their career, a process of interest for the public and social scientists. However, data on career paths are rarely completely available, calling for inference tools that can handle 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 combines two complementary data sources: (1) detailed observations of some individual trajectories collected from LinkedIn and (2) less informative ‘traces’ left by all individuals in administrative records, which we model for missing data imputation. This framework allows for varying parameters across individuals and time, yet maintains properties of hidden Markov models, enabling posterior exploration with a tailored sampler. By integrating both sources, we can consider the whole population rather than just a sample, and avoid biases that arise when using only a single source. This allows us to properly test substantive hypotheses on career paths across different public organizations. We notably show that the probability ENA graduates exit the public sector has not increased since 1990, but the probability of return has increased. We identify four clusters of organizations, with distinct patterns of public–private behaviours.
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