A Tractable Approach to Pass-Through Patterns

For tractability, researchers often use equilibrium models that can be solved in closed-form. In practice, this means imposing unintended substantive restrictions on incidence properties that are central to many policy questions. To overcome this limitation, we characterize a set of joint supply and demand systems yielding closed-form solutions. This class is broad enough to allow substantial flexibility and thus realism, and it nests virtually all other tractable systems in the literature. We apply these more realistic structures to a range of international trade models typically solved in closed-form, thereby deriving several applied insights about, e.g., the cyclicality of wage bargaining and the organization of supply chains. Beyond parametric examples, the Laplace Transform, a standard tool used in applied mathematics and physics in analogous settings that we exploit, provides a general approach to characterizing and approximating incidence at any degree of desired tractability.