Relaxed Optimization: How Close Is a Consumer to Satisfying First-Order Conditions?

We propose relaxing the first-order conditions in optimization to approximate rational consumer choice. We assess the magnitude of departures with a new, axiomatically founded measure that admits multiple interpretations. Standard inequality tests of rationality for any given reference class of preferences can be conveniently repurposed to measure goodness-of-fit with that class. Another advantage of our approach is that it is applicable in any context where the first-order approach is meaningful (e.g., convex budget sets arising from progressive taxation). We apply these ideas to shed new light on existing portfolio-choice data.

Automated summary

We propose a method to approximate rational consumer choice by relaxing the first-order conditions in optimization. We introduce a new measure, derived from axioms, to assess the magnitude of departures with multiple interpretations. Our approach allows for repurposing standard inequality tests to measure goodness-of-fit with a given class of preferences, and it is applicable in any context where the first-order approach is meaningful. We apply these ideas to gain new insights from portfolio-choice data.