First-wave international political economy (IPE) was preoccupied with the “complex interdependencies” within a world system that (it believed) was rapidly devolving following the 1971 collapse of the Bretton Woods system of fixed exchange rates. The original IPE scholars were more dedicated to theorizing about the emergence and evolution of global systems than any strict methodology. As IPE developed, it began to emphasize the possibility that institutions could promote cooperation in an anarchic environment, so IPE scholarship increasingly studied the conditions under which these institutions might emerge. Second-wave IPE scholars began to focus on the domestic “level of analysis” for explanatory power, and in particular analyzed the role of domestic political institutions in promoting global economic cooperation (or conflict). They also employed a “second-image reversed” paradigm in which the international system was treated as an explanatory variable that influenced the domestic policymaking process. In opening up the “black box” of domestic politics, in particular as it pertained to foreign economic policy, the “American school” of IPE thoroughly explored the terrain with regression-based statistical models that assume observational independence. As a result, complex interdependencies in the global system were increasingly ignored. Over time the analytical focus progressively shifted to micro-level units—firms and individuals, whenever possible—using neoclassical economic theory as its logical underpinning (with complications for political factors). This third wave of IPE, “open economy politics,” has been criticized in the post-crisis period for its narrow focus, rigid methodology, and lack of systemic theory. Leading scholars have called modern IPE “boring,” “deplorable,” “myopic,” and “reductionist,” among other epithets. A “fourth-wave” of IPE must retain its strong commitment to empiricism while re-integrating systemic processes into its analysis. A new class of complex statistical models is capable of incorporating interdependencies as well as domestic- and individual-level processes into a common framework. This will allow scholars to model the global political economy as an interdependent system consisting of multiple strata.