Household heterogeneity and real exchange rates

Typical incomplete markets models in international economics make two assumptions. First, households are not able to fully insure themselves against country-specific shocks. Second, there is a representative household within each country, so that households are fully insured against idiosyncratic shocks. We assume instead that cross-household risk-sharing is limited within countries, but cross-country risk-sharing is complete. We consider two types of limited risk-sharing: domestically incomplete markets (DI) and private information-Pareto optimal (PIPO) risk-sharing. We show that the models imply distinct restrictions between the cross-sectional distributions of consumption and real exchange rates. We evaluate these restrictions using household-level consumption data from the United States and the United Kingdom. We show that the PIPO restriction fits the data well when households have a coefficient of relative risk aversion of around 5. The analogous restrictions implied by the representative agent model and the DI model are rejected at conventional levels of significance.