Bounding High Dimensional Comparative Statics

Abstract:

Comparative statics in high dimensional models are empirically demanding and analytically complicated. Computing them exactly requires complete knowledge of the correspondingly many model parameters, which is often infeasible given data availability. Under diagonal dominance, I derive novel bounds on high dimensional comparative statics that are sharp conditional on a set of low dimensional sufficient statistics. Knowledge of these statistics is often more feasible, and the resulting bounds have a simpler analytical form than the exact relationship. I illustrate the method in canonical models across economics and offer new results in the research on peer effects, gains from trade, and competitive equilibrium under gross substitutes.