This paper provides a structural analysis of the role of job vacancy referrals (VRs) by public employment agencies in the job search behavior of unemployed individuals, incorporating institutional features of the monitoring of search behavior by the agencies. Notably, rejections of VRs may lead to sanctions (temporary benefits reductions) while workers may report sick to avoid those. We estimate models using German administrative data from social security records linked with caseworker recorded data on VRs, sick reporting and sanctions. The analysis highlights the influence of aspects of the health care system on unemployment durations. We estimate that for around 25% of unemployed workers, removing the channel that enables strategic sick reporting reduces the mean unemployment duration by 4 days.