The Backus-Smith Puzzle: The Role of Expectations

Efficient risk-sharing dictates a positive relationship between the real exchange rate and relative consumption across countries: consumption should be relatively high where consumption is relatively cheap. However, contrary to the positive relationship predicted by most models, the empirical correlation between bilateral real exchange rates and relative consumptions is typically negative (see Backus and Smith, 1993). In this paper I extend a standard two-country, two-good international business cycle model with internationally incomplete financial markets to incorporate public signals about future innovations to total factor productivity. In this environment, a positive signal increases the relative present value of domestic lifetime income, implying that current consumption can increase by more than current output. This increase in demand in turn generates an appreciation in the real exchange rate, suggesting a potential resolution to the Backus-Smith puzzle. When the economy is calibrated to the United States versus the rest of the industrialized world, numerical simulations deliver a correlation between the exchange rate and relative consumption that is similar to that observed empirically.