Country Portfolios in Open Economy Macro-Models

This paper develops a simple, general approximation method for computing equilibrium country portfolios – the composition of gross foreign asset and liability holdings – in dynamic stochastic general equilibrium (DSGE) open-economy macro models. The problem it solves is a genuine gap in standard solution technique: the usual approach of taking a first-order approximation around the non-stochastic steady state cannot pin down portfolio holdings at all, because in both the non-stochastic steady state and a first-order approximation all assets earn (expected) returns that make them perfect substitutes, so any portfolio is consistent with equilibrium. The authors’ solution is to combine a second-order approximation of just the portfolio first-order conditions – which captures the covariance between asset excess returns and the marginal utility of consumption, and hence each asset’s value as a hedge against consumption risk – with an ordinary first-order approximation of the rest of the model, yielding a simple closed-form formula for the constant (“zero-order”) component of the equilibrium portfolio. The method applies to any number of assets, to complete or incomplete asset markets, and to any DSGE model otherwise solvable by standard perturbation methods; the paper illustrates it first in a tractable two-country, two-asset endowment economy, where it shows analytically that home investors’ equity home bias is governed by the covariance between domestic capital income and domestic labor income, and then generalizes the method to an n-asset, general-structure open-economy model, including an extension with traded nominal bonds in which monetary shocks affect the optimal hedging portfolio. A final section sketches, without full derivation, how the same logic extends (via a third-order approximation of the portfolio conditions) to solving for the time-varying, first-order-accurate dynamics of portfolios themselves, with the full derivation left to a companion paper (Devereux and Sutherland, 2007).

Alan Sutherland | Macro Paper Warehouse

Country Portfolios in Open Economy Macro-Models