An HJB Estimator for Output-Gap Uncertainty
A Worst-Case Filtration Framework for Central-Bank Decision-Making
Abstract
We formulate output-gap estimation as an optimal-control problem in which a central-bank decision-maker chooses a filter that minimises a worst-case quadratic loss under adversarial measurement noise. The resulting HJB equation admits a closed-form Riccati solution; the optimal filter is a Kalman-like linear combination of observed inflation, output, and term-spread signals with weights that depend explicitly on the noise-ambiguity radius. We characterise the comparative statics of the optimal weights and show that the conventional Kalman estimator is recovered in the zero-ambiguity limit.