(The Evolution of) Post-Secondary Education: A Computational Model and Experiments

We propose a computational model to study (the evolution of) post-secondary education. “Consumers” who differ in quality shop around for desirable colleges or universities. “Firms” that differ in quality signal the availability of their services to desirable students. As long as they have capacity, colleges and universities make offers to students, who apply and qualify. Our model generalizes an earlier literature (namely, Vriend 1995) in an important dimension: quality, the model confirms key predictions of an analytical model that we also supply, and the model allows us to systematically explore the emergence of macro regularities and the consequences of various strategies that sellers might try. We supply three such exercises. In our baseline treatment we establish the dynamics and asymptotics of our generalized matching model. In the second treatment we study the consequences of opportunistic behavior of firms and thus demonstrate the usefulness of our computational laboratory for the analysis of this or similar questions (e.g., the problem of early admission). In the third treatment we equip some firms with economies of scale. This variant of our matching model is motivated by the entry of for-profit providers into low-quality segments of post-secondary education in the USA and by empirical evidence that, while traditional nonprofit or state-supported providers of higher education do not have significant economies of scale, the new breed of for-profit providers seems to capture economies in core functions such as curricular design, advertising, informational infrastructure, and regulatory compliance. Our computational results suggest that this new breed of providers is likely to continue to move up the quality ladder, albeit not necessarily all the way up to the top.