We revisit the much-investigated relationship between schooling and health, focusing on cognitive abilities at older ages using the Harmonized Cognition Assessment Protocol in the Health & Retirement Study. To address endogeneity concerns, we employ a nonparametric partial identification approach that provides bounds on the population average treatment effect using a monotone instrumental variable together with relatively weak monotonicity assumptions on treatment selection and response. The bounds indicate potentially large effects of increasing schooling from primary to secondary but are also consistent with small and null effects. We find evidence for a causal effect of increasing schooling from secondary to tertiary on cognition. We also replicate findings from the Health & Retirement Study using another sample of older adults from the Midlife in United States Development Study Cognition Project.