I develop a general equilibrium model of trade and horizontal multinational firms with firm heterogeneity and parent-to-affiliate technology transfer to evaluate how multinationals affect international business cycles. When calibrated to match micro and macro features of the United States, the impact of multinational firms crucially depends on the labor supply elasticity and the technology transfer parameter. Surprisingly, with standard (elastic) labor supply, multinationals lead to lower international correlations and higher macroeconomic volatility. A novel mechanism – procyclical exit of multinational firms – drives these results. The results are overturned only when inelastic labor supply and a high level of technology transfer are implemented together. Using novel bilateral data on the number and sales of multinational affiliates, I find evidence that the key model mechanism, i.e., entry and exit by multinationals, increases international output correlation.