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High-productivity firms dominate trade and foreign direct investment, and as globalization advances they gain market share and crowd out domestic firms as lobbyists. In the process, they become increasingly influential in politics at home and abroad. Studying this process poses both theoretical and empirical challenges. Theoretically, acquiring new foreign investments gives firms new reasons to lobby, while some investments are made only because the firm anticipates exercising enough influence over US foreign policy to make them profitable. We address this simultaneity problem by using dynamic structural estimation to study a series of lobbying and investment decisions by individual firms over time. Empirically, an important data limitation is that while we observe investment decisions at the host-country level, we can only observe firms’ aggregate lobbying effort. Structural estimation allows us to overcome this problem by estimating each firm’s unobserved probability to lobby about policy towards each country and regressing the aggregate count of lobbying reports on the predicted value. In the model, firms have agents that make lobbying and investment decisions with respect to every country in every year. There are two state variables: the firm’s investment portfolio (which is discrete) and the relationship between the United States and each host country (which is continuous). The history of investment decisions deterministically sets the firm’s investment portfolio, and the lobbying decision stochastically affects the US-host relationship, which represents firms’ direct influence over US policy and indirect influence over domestic policy in the host country.