The Endogenous Kalman Filter
We relax the assumption of full information that underlies most dynamic general equilibrium models, and instead assume agents optimally form estimates of the states from an incomplete information set. We derive a version of the Kalman filter that is endogenous to agents' optimising decisions, and state conditions for its convergence. We show the (restrictive) conditions under which the endogenous Kalman filter will at least asymptotically reveal the true states. In general we show that incomplete information can have significant implications for the time-series properties of economies. We provide a Matlab toolkit which allows the easy implementation of models with incomplete information.
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