Measuring the causal impact of state behavior on outcomes is one of the biggest methodological challenges in the field of political science, for two reasons: behavior is generally endogenous, and the threat of unobserved variables that confound the relationship between behavior and outcomes is pervasive. Matching methods, widely considered to be the state of the art in causal inference in political science, are generally ill-suited to inference in the presence of unobserved confounders. Heckman-style multiple-equation models offer a solution to this problem; however, they rely on functional-form assumptions that can produce substantial bias in estimates of average treatment effects. We describe a category of models, flexible joint likelihood models, that account for both features of the data while avoiding reliance on rigid functional-form assumptions. We then assess these models’ performance in a series of neutral simulations, in which they produce substantial (55% to 90%) reduction in bias relative to competing models. Finally, we demonstrate their utility in a reanalysis of Simmons’ (2000) classic study of the impact of Article VIII commitment on compliance with the IMF’s currency-restriction regime.