Resolving International Macro Puzzles with Imperfect Risk Sharing and Global Solution Methods

Do gross international asset positions matter for macroeconomic outcomes? In this paper, we argue that they do. In particular, we demonstrate that asset market incompleteness which features a meaningful portfolio choice can resolve the Backus-Smith puzzle: that relative consumptions and real exchange rates are negatively correlated. Because income and nominal exchange rates are positively correlated, countries choose a portfolio that features home bias in bond holdings, which is common in the data. We compare our findings to the predictions of alternative asset market structures frequently used in the literature - such as complete markets or restricting assets to a single bond - and show that they cannot solve the Backus-Smith puzzle without further frictions. We also show that local perturbation methods that use endogenous discount factors to stabilize the model are inaccurate, even when they correctly characterize the average portfolio holdings. Instead, we use a novel global solution method to accurately solve the portfolio problem when asset markets are incomplete, using an approach that generalizes Maliar and Maliar (2015) to solve a wide class of models.