Teacher burnout can directly shape students' learning environments and outcomes, as burnt-out teachers may provide less emotional support and less positive behaviour management to students. Yet studies of the effects of burnout on student outcomes -- particularly non-academic outcomes -- are scarce, even more so in low-income countries. This study attempts to establish a rigorous estimate of burnout on students' social-emotional, executive function, and social competence skills in Ghanaian primary schools. We use a generalised propensity score model, which aims to eliminate bias from unobserved characteristics, to examine how two elements of teacher burnout -- emotional exhaustion and lack of personal accomplishment -- predict student outcomes. We find small negative associations between teachers' emotional exhaustion and students' executive function, and marginally statistically significant negative associations between teachers' emotional exhaustion and lack of personal accomplishment with students' social competence. Implications for educational practice and future research are discussed.