Comparison of Educational Subsidy Schemes in an Endogenous Growth Model

This study considers a three-period overlapping generations model with an endogenous growth setting in which an agent borrows a loan in the first period and repays it in the second period in a perfect credit market. Two educational subsidy schemes are considered: one is provided when an agent borrows (policy y), and the other is provided when the agent repays their loan (policy m). Thus, policy y is an inter-generational educational subsidy, and policy m is an intra-generational educational subsidy. This study characterizes an equilibrium balanced growth path under each policy and compares two policies from the point of growth and social welfare along an equilibrium balanced growth path. The first finding of this study is that under policy y, the growth rate along an equilibrium balanced growth path always forms an inverted U-shape with respect to the tax rate; under policy m, the growth rate does not always form an inverted U-shape, and under a certain condition, educational subsidy lowers the growth rate along an equilibrium balanced growth path. The second finding is that under policy y, as long as social discount factor is sufficiently high, an introduction of educational subsidy improves the social welfare, whereas under policy m, in some cases, social welfare is worse off by an introduction of educational subsidy, even if the social discount factor is sufficiently high. The third finding is that policy y is likely to lead an economy to higher growth and higher social welfare than policy m, as analyzed via numerical simulation.