Theories about neighbours' influence on children based on social capital, cohesion and disorganisation stress the importance of neighbourhood stability. However, amongst the vast number of studies on the effect of neighbours on a child's education, none has tested whether neighbourhood stability matters. We fill this gap by estimating the causal effect of residential turnover on student test score gains. We show that high neighbourhood turnover reduces value added for students who stay in their neighbourhood, and this effect is more pronounced in more deprived neighbourhoods. Estimation is based on administrative data on four cohorts of secondary school children in England, allowing us to control for unobserved confounding individual effects, neighbourhood fixed effects and trends, plus school-by-cohort shocks. These main results, coupled with auxiliary findings based on survey data, suggest that neighbourhood turnover damages education through the disruption of local ties and social capital, highlighting a so-far undiscovered externality of mobility.