We compare global (fixed-point iteration) and local (first-order, higher-order, risky-steady-state, and quasi-linear) solutions of open-economy incomplete-markets models. Cyclical moments of a workhorse endowment model are broadly in line with the data and similar across solutions calibrated to the same data targets, but impulse responses and spectral densities differ. Alternative local solutions yield nearly identical results. Calibrating them requires nontrivial interest-rate elasticities that make net foreign assets (NFA) “sticky,” causing them to differ sharply from global solutions in experiments altering precautionary savings (e.g., increasing income volatility, adding capital controls). Analytic and numerical results show that our findings are due to the near-unit-root nature of NFA under incomplete markets and imprecise solutions of their autocorrelation. These findings extend to a Sudden Stops model with an occasionally binding collateral constraint. In addition, quasi-linear methods yield smaller financial premia and macroeconomic responses when the constraint binds.