We show that imperfect risk-sharing within countries can reconcile the aggregate cyclicality of exchange rates in a two-country setting, i.e. the Backus-Smith puzzle, as long as exchange rates are sufficiently risky with respect to idiosyncratic states. Leveraging theory mapping household heterogeneity into measurable discount-factor wedges, we use household-level data to provide direct empirical support for our mechanism. We then embed this insight in an equilibrium asset-pricing model and show that the observed exchange rate dynamics require that, even when a country experiences higher consumption growth, idiosyncratic risk remains relatively elevated. In a quantitative exercise, we disentangle distinct roles for market incompleteness both within and across countries and match key moments of asset prices and exchange rates.
Suggested citation:
Marin, Emile A. and Sanjay R. Singh. 2026. “Incomplete Markets and Exchange Rates.” Federal Reserve Bank of San Francisco Working Paper 2025-11. https://doi.org/10.24148/wp2025-11