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

TL;DR

This study investigates how a 1000 Euro tuition fee in German states affects student enrollment, using robust high-dimensional modeling and design-based inference to reveal a significant negative impact of up to 4.5 percentage points.

Contribution

It introduces a stability post-double selection methodology with resampling for robust causal inference in high-dimensional settings, improving upon previous methods.

Findings

Tuition fees cause substantial migration effects among states.

Fees lead to a significant decrease in enrollment up to 4.5 percentage points.

Previous models underestimated the effects and often found insignificant results.

Abstract

We use official data for all 16 federal German states to study the causal effect of a flat 1000 Euro state-dependent university tuition fee on the enrollment behavior of students during the years 2006-2014. In particular, we show how the variation in the introduction scheme across states and times can be exploited to identify the federal average causal effect of tuition fees by controlling for a large amount of potentially influencing attributes for state heterogeneity. We suggest a stability 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 up to 4.5 percentage points of fees on student enrollment. This is in contrast to plain one-step LASSO or previous empirical studies with full fixed effects linear panel regressions which generally underestimate the size and get an only insignificant effect.