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• Half of parental transfer crowded out by the means-tested scholarship. • IV estimate using nonlinear schedule slightly higher (0.5) than OLS (0.4). • Larger estimated crowding-out effect under IV is driven by non-intact families. • Predictions of the altruistic model (full eviction) not validated. • Means-testing necessary to prevent a windfall effect for wealthy parents. This paper investigates the extent to which means-tested scholarships received by higher education students crowd out parental financial support at the intensive margin. We estimate a private transfer function using survey data collected in France in 2014 on a sample of students aged 18–24 who receive public scholarships. Introducing the amount of public transfer as an exogenous covariate, we find that one additional euro of scholarship is associated with a decrease in parental transfers of 0.40 euro. Using an instrumental variable strategy that exploits the non-linear schedule of the scholarship amount, we find a larger effect with a decrease of about 0.50. Our results suggest that a substantial part of the scholarship benefits low-income parents by reducing the amount of money they give to their student children. [Display omitted] [ABSTRACT FROM AUTHOR]