Perturbations Around the Risky Steady State

44 Pages Posted: 31 Jul 2020

See all articles by Pierlauro Lopez

Pierlauro Lopez

Federal Reserve Banks - Federal Reserve Bank of Cleveland

David Lopez-Salido

Board of Governors of the Federal Reserve System

Francisco Vazquez-Grande

Board of Governors of the Federal Reserve System

Date Written: July 5, 2020

Abstract

We obtain a novel formulation for first-order perturbations around the risky steady of a general class of dynamic equilibrium models with time-varying and non-Gaussian risk. We offer explicit formulas and conditions for their local existence and uniqueness. First-order perturbations around the risky steady state are not nested in perturbations of arbitrary order around the deterministic steady state. We apply this approximation technique to models featuring Campbell-Cochrane habits, recursive preferences, and time-varying disaster risk. In many applications the proposed approximation represents similarly to global solution methods the implications of the model for asset prices and quantities. Finally, we argue that these perturbations can be viewed as a generalized version of the heuristic loglinear-lognormal approximations commonly used in the macro-finance literature. Therefore, we unify existing theories of risk-adjusted linearizations.

Keywords: Perturbation methods, Risky steady state, Macroeconomic uncertainty, Risk modeling, Intertemporal choice under uncertainty

JEL Classification: C63, G12, E32, E44

Suggested Citation

Lopez, Pierlauro and Lopez-Salido, David and Vazquez-Grande, Francisco, Perturbations Around the Risky Steady State (July 5, 2020). Available at SSRN: https://ssrn.com/abstract=3643629 or http://dx.doi.org/10.2139/ssrn.3643629

Pierlauro Lopez (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of Cleveland ( email )

East 6th & Superior
Cleveland, OH 44101-1387
United States

David Lopez-Salido

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Francisco Vazquez-Grande

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States
202-973-7488 (Phone)

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