Fluctuations in GDP are more synchronized internationally than fluctuations in Consumption, and they remain so even between financially integrated economies, where the ranking should in theory be the reverse. This paper shows this happens because correlations in GDP fluctuations rise with financial integration. Finance serves to increase international correlations in both consumption and GDP fluctuations, which explains the persistent gap between the two in the data. The positive association between financial integration and GDP correlation constitutes a puzzle, as theory suggests a negative relation if anything. Nevertheless, it prevails in the data even after the effects of finance on trade and specialization are accounted for.