Since the primary role of international financial linkages is to facilitate consumption smoothing in the face of country-specific shocks, the degree of international financial integration should play an important role in the international transmission of business cycles. This paper therefore studies the business cycle implications of restricting international trade in financial assets. The key restriction is that domestic residents must hold all risky claims to domestic output, trading only noncontingent bonds on the international asset markets. We find that restricting asset trade may or may not change the business cycle implications of the model relative to complete markets, depending on the parameterization of the stochastic process for productivity. When there are important differences, these stem largely from differential wealth effects. We also find that restricting asset trade can resolve the chief problem inherent in complete markets models, which is their predictions of too-high consumption correlations and too-low output correlations. When technology follows a random walk process, the restricted asset markets model predicts that cross-country output correlations are positive, and cross-country consumption correlations are smaller than the output correlations, as is typically observed in the data.