Before revision:  We show that a post-double selection strategy combined with stability selection determines a significant negative impact of  fees on student enrollment and identifies relevant variables .
After revision:  We show that a post-double selection methodology to robustly determine the causal effect across types in the transparently modeled unknown response components. The proposed stability resampling scheme in the two LASSO selection steps efficiently mitigates the risk of model underspecification and thus biased effects when the tuition fee policy decision also depends on relevant variables for the state enrollment rates. Correct inference for the full cross-section state population in the sample requires adequate design -- rather than sampling-based standard errors. With the data-driven model selection and explicit control for spatial cross-effects we detect that tuition fees induce substantial migration effects where the mobility occurs both from fee but also from non-fee states suggesting also a general movement for quality. Overall, we find a significant negative impact of fees on student enrollment and identifies relevant variables .