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We use official data for all 16 federal German states to study the causaleffect of a flat 1000 Euro state-dependent university tuition fee on theenrollment behavior of students during the years 2006-2014. In particular, weshow how the variation in the introduction scheme across states and times canbe exploited to identify the federal average causal effect of tuition fees bycontrolling for a large amount of potentially influencing attributes for stateheterogeneity. We suggest a stability post-double selection methodology torobustly determine the causal effect across types in the transparently modeledunknown response components. The proposed stability resampling scheme in thetwo LASSO selection steps efficiently mitigates the risk of modelunderspecification and thus biased effects when the tuition fee policy decisionalso depends on relevant variables for the state enrollment rates. Correctinference for the full cross-section state population in the sample requiresadequate design -- rather than sampling-based standard errors. With thedata-driven model selection and explicit control for spatial cross-effects wedetect that tuition fees induce substantial migration effects where themobility occurs both from fee but also from non-fee states suggesting also ageneral movement for quality. Overall, we find a significant negative impact ofup to 4.5 percentage points of fees on student enrollment. This is in contrastto plain one-step LASSO or previous empirical studies with full fixed effectslinear panel regressions which generally underestimate the size and get an onlyinsignificant effect.

How have German University Tuition Fees Affected Enrollment Rates: Robust Model Selection and Design-based Inference in High-Dimensions