Bounding comparative statics under diagonal dominance

Abstract

A core purpose of economic modeling is to conduct comparative static analyzes. Often one is interested in its qualitative features, such as if the effect of a shock is positive or above one. Yet, except in highly-stylized models, the theoretically implied relationships are intractable, and empirically demanding, requiring complete identification of the model. We derive new bounds on comparative statics that are more tractable and feasible under partial identification. We require only that the Jacobian is diagonally dominant — intuitively, there is limited feedback in the model. We demonstrate application in two canonical models: a network game and a model of oligopoly competition.