Real-Time, Adaptive Learning via Parameterized Expectations

We explore real time, adaptive nonlinear learning dynamics in stochastic macroeconomic systems. Rather than linearizing nonlinear Euler equations where expectations play a role around a steady state, we instead approximate the nonlinear expected values using the method of parameterized expectations. Further we suppose that these approximated expectations are updated in real time as new data become available. We explore whether this method of real-time parameterized expectations learning provides a plausible alternative to real-time adaptive learning dynamics under linearized versions of the same nonlinear system.