Long-Run Risk is the Worst-Case Scenario: Ambiguity Aversion and Non-Parametric Estimation of the Endowment Process

Abstract

We study an agent who is unsure of the dynamics of consumption growth. She estimates her consumption process non-parametrically to place minimal restrictions on dynamics. We analytically show that the worst-case model that she uses for pricing, given a penalty on deviations from the point estimate, is a model with long-run risks. This result cannot in general be matched in a fixed model with only parameter uncertainty. With a single parameter determining risk preferences, the model generates high and volatile risk premia and matches Rs from return forecasting regressions, even though risk aversion is equal to 5.3 and the worst-case dynamics are statistically nearly indistinguishable from the true model. ∗Bidder: Federal Reserve Bank of San Francisco. Dew-Becker: Duke University. We appreciate helpful comments from Stefano Giglio and seminar participants at the Federal Reserve Bank of San Francisco and Fuqua. The views expressed in this paper are those of the authors and not necessarily those of the Federal Reserve Bank of San Francisco, the Federal Reserve Board of Governors or the Federal Reserve System.