University Funding Formulas: An Analysis of the Québec Reforms and Incentives

This paper analyzes the incentives induced by a formula to fund universities based primarily on enrolment. Using a simple game theoretical framework, we argue that the strategic behaviour induced by those formulas is to favour enrollment. We further argue that if the funding value differs by enrolment type, it introduces incentives to substitute enrolment where most profitable. If the public appropriations do not follow the outcomes induced by the formula, the incentives introduce a dynamic "inconsistency," and funding per student can decline. We use these results to discuss the 2018 funding formula changes in Québec. We argue that Québec's latest reform should reduce substitution effects and increase graduate enrolment. We provide simulations of the reform's redistributive effects and show that some universities gain structural advantages over others. Whilst the reform, on a short-term basis, deploys a mechanism to mitigate these advantages, on a long-term basis the effect introduces a larger gap between Québec higher-education institutions.