What is it about?
We analyze a decision problem of educational investment under uncertainty about one's innate ability. Mathematically, this requires solving a stochastic optimal control problem with partial observations, which belongs to the class of restless bandit models. We reduce the problem to full observations and show that stopping rules are optimal.
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Why is it important?
Educational choices have far reaching consequences on later life outcomes. Why is it so difficult to get students who stopped investing in their education back on track? We show that the path dependency of educational investment decisions is a natural consequence of the inherent dynamics of skill formation: learning begets learning, and skills beget skills.
Perspectives
Our model explains why incentive schemes designed to boost investment in education may be ineffective if they come to late in time. It does not rely on switching costs, but on the inherent dynamics of human capital formation. We prove a separation theorem, which begs for a generalization to more general state and observation processes. The difficulty compared to existing frameworks is that neither time nor measure changes can be used in the formulation of the control problem with partial observations.
Philipp Harms
Albert-Ludwigs-Universitat Freiburg
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This page is a summary of: Two-Armed Restless Bandits with Imperfect Information: Stochastic Control and Indexability, Mathematics of Operations Research, September 2017, INFORMS,
DOI: 10.1287/moor.2017.0863.
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