Understanding the Backus-Smith Puzzle: It’s the (Nominal) Exchange Rate, Stupid

Backus, Kehoe and Kydland (BKK 1992) showed that if international capital markets are complete, consumption growth correlations across countries should be higher than their corresponding output growth correlations. In stark contrast to the theory, however, in actual data the consumption growth correlation is lower than the output growth correlation. By assuming trade imperfections due to non-traded goods, Backus and Smith (1993) showed that there is an additional impediment that works to lower the consumption growth correlation. While Backus and Smith’s argument was successful in partially explaining the low growth correlation puzzle, it contributed to generating another puzzle because the data forcefully showed that consumption growth is negatively correlated with the real exchange rate, which is a violation of the theory. In this paper, by decomposing the real exchange rate growth of the OECD countries into the nominal exchange rate growth and the inflation differential, we find that nominal exchange rate movements are the main source for the Backus-Smith puzzle. We find that the nominal exchange rate moves counter-cyclically with consumption movements, which is a violation of the risk sharing theory with non-traded goods. We also find that the violations are more pronounced when nominal exchange rate changes are larger in absolute value . In contrast, the negative of bilateral inflation differentials is positively correlated with bilateral consumption movements. The latter finding is in accordance with the theory. Furthermore, using intranational data for the United States where the nominal exchange rate is constant, the Backus-Smith puzzle disappears, although complete risk sharing is rejected.