Ghironi, Lee, and Rebucci (2006) and Kollmann (2006) compute
portfolios and changes in net foreign assets using standard first-order approximations around
a deterministic steady state. The second approach makes use of higher-order approximations
to analyze countries’ portfolios and the evolution of external accounts. These methodologies
grew out of Samuelson (1970) and Judd and Guu (2001) and were developed by Engel and
Matsumoto (2006), Evans and Hnatkovska (2007), Devereux and Sutherland (2010a), and
Tille and van Wincoop (2010). A disadvantage shared by these two approaches is that to
this day little is known about the behavior of these economies away from the deterministic
steady state, where the underlying volatilities are not small.