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Accounting for Risk in a Linearized Solution: How to Approximate the Risky Steady State and Around It
We propose a novel approximation of the risky steady state and construct first-order perturbations around it for a general class of dynamic equilibrium models with time-varying and non-Gaussian risk. We offer analytical formulas and conditions for their local existence and uniqueness. We apply this approximation technique to models featuring Campbell-Cochrane habits, recursive preferences, and time-varying disaster risk, and show how the proposed approximation represents the implications of the model similarly to global solution methods. We show that our approximation of the risky steady ...