This dissertation is a collection of three essays of empirical investigation in international economics using three distinct econometric methods that allow for nonlinear relationships. The first chapter studies the determinants of illicit financial flows through trade data manipulation based on a threshold regression model. The next two chapters study the effects of institutions on the spillovers present in preferential trade agreement memberships and firm-level productivity growth in Chinese manufacturing, based on a spatial autoregressive model and a model of conditional average treatment effect, respectively.