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.

翻译：精英公务员在其职业生涯中可能在公共部门与私营部门之间流动，这一过程对公众和社会科学家具有特殊的研究价值。然而，记录此类过程的数据往往不完整：我们需要能够处理大量缺失值的推断工具。本文以法国精英公务员的公私部门流动路径为研究对象，引入基于贝叶斯数据增强的二元马尔可夫切换模型。我们的方法依赖两个互补的数据源：(1) 通过LinkedIn获取的部分个体职业轨迹的详细观测数据；(2) 所有个体在行政记录中留下的信息较少的“痕迹”，我们将其建模用于缺失数据填补。此类模型保持了隐马尔可夫模型的性质，并通过定制采样器以逼近后验分布，同时允许参数随个体和时间变化。通过整合两个数据源，我们可以研究全人口而非仅样本，避免仅使用单一数据源可能产生的偏差。我们证明该方法能够有效检验关于各类公共机构中职业路径的实质性假设。特别地，我们发现ENA（法国国家行政学院）毕业生离开公共部门的概率自1990年以来并未上升，但其返回公共部门的概率有所增加。我们识别出具有不同公私部门行为模式的三类机构集群。