We introduce a nonlinear infinite moving average as an alternative to the standard state-space policy function for solving nonlinear DSGE models. Perturbation of the nonlinear moving average policy function provides a direct mapping from a history of innovations to endogenous variables, decomposes the contributions from individual orders of uncertainty and nonlinearity, and enables familiar impulse response analysis in nonlinear settings. When the linear approximation is saddle stable and free of unit roots, higher order terms are likewise saddle stable and first order corrections for uncertainty are zero. We derive the third order approximation explicitly and examine the accuracy of the method using Euler equation tests.JEL classification: C61, C63, E17
I entertain a generalization of the standard Bolzmann-Gibbs-Shannon measure of entropy in multiplier preferences of model uncertainty. Using this measure, I derive a generalized exponential certainty equivalent, which nests the exponential certainty equivalent of the standard Hansen-Sargent model uncertainty formulation and the power certainty equivalent of the popular Epstein-Zin-Weil recursive preferences as special cases. Besides providing a model uncertainty rationale to these risk-sensitive preferences, the generalized exponential equivalent provides additional flexibility in modeling uncertainty through its introduction of pessimism into agents, causing them to overweight events made more likely in the worst case model when forming expectations. In a standard neoclassical growth model, I close the gap to the Hansen-Jagannathan bounds with plausible detection error probabilities using the generalized exponential equivalent and show that Hansen-Sargent and Epstein-Zin-Weil preferences yield comparable market prices of risk for given detection error probabilities.
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