Forecasting University Funding: A Non-Linear Approach

Are enrollment-based funding formulas really dependent on enrollment? The recent changes in funding for universities in the province of Quebec, Canada, suggests a disconnect between subsidies and enrollment despite the funding being enrollment based. This disconnection is observed when using a linear model to forecast the funding of the different universities in Quebec. The results show that simply considering linear mechanisms in the models consistently underestimates the funding. This paper explores the importance of taking into consideration these non-linear mechanisms in the funding formula. We estimate the funding models with non-linear vector autoregressive and the margins of error with bootstrap methods. This allows us to directly estimate the funding formula, and thus the non-linear components. We find that the non-linearities are important to explain the funding trends. In particular, the smoothing mechanism, the increase in funding per student and other exceptions leads subsidies to increase despite a stagnation or a decline in enrollment. Moreover, the model developed in this article also provides a ready-made recipe for forecasts in other jurisdictions.