Monotone Comparative Statics for Models of Politics

We elucidate a powerful yet simple method for deriving comparative statics conclusions for a wide variety of models: Monotone Comparative Statics (Milgrom and Shannon 1994). Monotone comparative static methods allow researchers to extract robust, substantive empirical implications from formal models that can be tested using ordinal data and simple nonparametric tests. When these methods apply, they can replace a diverse range of more technically difficult mathematics (facilitating richer, more realistic models), assumptions that are hard to understand or justify substantively (highlighting the political intuitions underlying a model's results), and a complicated set of methods for extracting implications from models. We present an accessible introduction to the central monotone comparative statics results and a series of practical tools for using these techniques in applied models (with reference to original sources, when relevant). Throughout we demonstrate the techniques with examples drawn from political science.