The international risk sharing puzzle is at business cycle and lower frequency

We decompose the correlation between relative consumption and the real exchange rate in its dynamic components at different frequencies. Using multivariate spectral analysis techniques, we show that, at odds with a high degree of risk sharing, in most OECD countries the dynamic correlation tends to be quite negative, and significantly so, at frequencies lower than two years - the appropriate frequencies for assessing the performance of international business cycle models. Theoretically, we show that the dynamic correlation over different frequencies predicted by standard open economy models is the sum of two terms: a term constant across frequencies, which can be negative when uninsurable risk is large; a term variable across frequencies, which in bond economies is necessarily positive, reflecting the insurance intertemporal trade provides against forecastable contingencies. Numerical analysis suggests that leading mechanisms proposed by the literature to account for the puzzle are consistent with the evidence across the spectrum.