In this paper we disentangle transfer pricing patterns by investigating different margins along which profit shifting occurs. We develop a theoretical model in which the price of intra-firm transactions can deviate from the arm's length price to shift profits to affiliates in countries that offer lower corporate tax rates. We find that there is a productivity threshold for firms to engage in transfer pricing (extensive margin), and that more productive firms shift more profits (intensive margin). Moreover, a greater tax differential implies more profit shifting, and there is a trade-off between the tax differential and trade costs. We argue that the specific functional form of the concealment costs that firms face when using transfer pricing is an important determinant of the firm's profit shifting behaviour. The predictions from the theoretical model are confirmed by empirical estimates that are based on Swiss firm level import transactions data along with firm-level information. To perform counterfactual analysis, we use these data to structurally estimate the parameters of the concealment cost function.