Generalized Monotonicity Analysis

Abstract

Complex economic problems often lack the structure for the application of standard comparative statics techniques. Generalized Monotonicity Analysis (GMA) extends usual methods in several directions. First, it provides a new way of endogenously generating parameter moves that yield monotonicity. Second, it allows one to easily study the monotonicity of functions of the initial variables. Third, GMA may be used to derive conditions under which monotonicity obtains with respect to imposed moves of parameters, for example corresponding to parameter aggregates. Fourth, GMA naturally provides lower and/or upper bounds on the sensitivity of variables (or functions thereof) to parameters. Fifth, GMA contributes insights into the theory of comparative statics, for example as far as dealing with with constraints or exploiting additional information about the problem structure are concerned. Several applications are discussed, including constrained optimization, non-supermodular games, aggregation, robust inference, and monotone comparative dynamics.

Keywords: Aggregation, Comparative Statics, Comparative Dynamics, Monotone Comparative Statics, Parameterized Equation, Parameter Transformation, Quantitative Monotonicity Analysis, Robust Inference, Supermodular Games

JEL Classification: C61, C43, C72, D11