Empirical research documents that an exogenous rise in government purchases in a given country triggers a depreciation of its real exchange rate. This raises an important puzzle, as standard macro-theories predict an appreciation of the real exchange rate. We argue that this prediction might reflect the conventional assumption that government purchases are unproductive. Using a simple frictionless model with efficient international risk sharing, we show that the real exchange can depreciate in response to a rise in government purchases, if these purchases increase domestic private sector productivity, and labor supply is highly elastic. Empirically plausible marginal products of government purchases are sufficient to generate this result.