Nonlinear Filtering and Learning Dynamics
We develop and apply two refinements of particle filtering methods to be used in characterizing the learning behavior of individual agents within an economic model. One refinement extends the use of sufficient statistics conditioned on hidden states and a subset of parameters as a device to induce randomization in the parameters within the algorithm. This allows us to replenish particles and extend the number of time periods to which the numerical results remain reliable. The other refinement focuses the accuracy of the particle filtering algorithm on the portions of the filtered distribution that are more germane to decision problems of the individual agents. We illustrate these methods in an equilibrium model with investors that make robust decisions implemented through the use of exponential tilting.