This study investigates the extent of inequitable teacher sorting across educational systems as well as relevant institutional correlates. We use data from the OECD TALIS study from 2018 with a total participating 144,316 teachers, 9063 schools across 46 education systems. We first estimate the relationship between classroom socioeconomic composition and teacher qualifications within each participating educational system. Next, using a three-level hierarchical generalized linear model, we examine whether the relationship between classroom socioeconomic composition and teacher qualifications varies as a function of institutional features via a random slope regressed on school system-level stratification, accountability, autonomy, and competition, controlling for national levels of economic development and teacher shortages. Results show that cross-classroom sorting by specialization is more prominent in more economically developed systems. Between-school tracking, performance-data based school accountability as well as higher levels of school autonomy over staffing and school competition were associated with more pronounced socioeconomic teacher sorting, but the results show that institutional determinants do not generalize easily across different measurements of teacher competence or sorting across schools.